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BEGIN:VEVENT
SUMMARY:David F. Anderson (University of Wisconsin\, Madison (USA))
DTSTART:20201112T160000Z
DTEND:20201112T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/1
DESCRIPTION:Title: Reaction network implementations of neural networks\nby David F. A
nderson (University of Wisconsin\, Madison (USA)) as part of Seminar on th
e Mathematics of Reaction Networks\n\n\nAbstract\nI will give an overview
of my recent paper with Badal Joshi and Abhishek Deshpande\, which is enti
tled "On reaction network implementations of neural networks." In particu
lar\, I will show how reaction networks can be constructed that "implement
" a given neural network. I will also detail our theoretical results\, wh
ich prove that the ODEs associated with certain reaction network implement
ations of neural networks have desirable properties including (i) existenc
e of unique positive fixed points that are smooth in the parameters of the
model (necessary for gradient descent)\, and (ii) fast convergence to the
fixed point regardless of initial condition (necessary for efficient impl
ementation). I'll start the talk with a brief primer on neural networks\,
but will assume familiarity with reaction networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beatriz Pascual Escudero (Universidad Carlos III (Spain))
DTSTART:20201203T160000Z
DTEND:20201203T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/2
DESCRIPTION:Title: Necessary conditions for ACR in Reaction Networks\nby Beatriz Pasc
ual Escudero (Universidad Carlos III (Spain)) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nA biological system has abso
lute concentration robustness (ACR) for some molecular species if the conc
entration of this species does not vary among the different steady states
that the network admits. In particular\, this concentration is independent
of the initial conditions. This interesting feature confers the system a
highly desirable property in order to adapt to environmental conditions\,
which makes it useful\, for instance\, in synthetic biology. While some cl
asses of networks with ACR have been described (Shinar and Feinberg 2010\;
Karp et al. 2012)\, as well as some techniques to check a network for ACR
(Pérez Millán 2011\; Kuwahara et al. 2017)\, finding networks with this
property is a difficult task in general.\n\nMotivated by this problem\, w
e studied local and global notions of robustness on the set of (real posit
ive) solutions of a system of polynomial equations\, and in particular on
the set of steady states of a reaction network. Algebraic geometry allowed
us to provide a practical test on necessary conditions for ACR. Propertie
s of real and complex algebraic varieties are necessary for the results\,
while the test ends up being a linear algebra computation.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casian Pantea (West Virginia University (USA))
DTSTART:20201203T163000Z
DTEND:20201203T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/3
DESCRIPTION:Title: Inheritance of Hopf bifurcations in reaction networks\nby Casian P
antea (West Virginia University (USA)) as part of Seminar on the Mathemati
cs of Reaction Networks\n\n\nAbstract\nInspired by recent work on multista
tionarity\, we consider the question: "when can we conclude that a network
admits Hopf bifurcations if one of its subnetworks has them?” In partic
ular\, we analyze a number of operations on reaction networks (like adding
certain reactions\, or adding inflows/outflows) that may preserve Hopf b
ifurcations as we build up the network . This is joint work with C.Conradi
\, A. Dickenstein\, and M. Mincheva.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Popovic (Concordia University)
DTSTART:20201112T163000Z
DTEND:20201112T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/4
DESCRIPTION:Title: A spatially heterogeneous stochastic model for chemical reaction netwo
rks\nby Lea Popovic (Concordia University) as part of Seminar on the M
athematics of Reaction Networks\n\n\nAbstract\nI will present a measure-va
lued framework for stochastic modelling of chemical reaction networks with
spatial heterogeneity. Reactions rates at a spatial location are proporti
onal to the mass of different species present locally\, and to a location
specific chemical rate that is allowed to be a function of the local or gl
obal mass of different species. The benefit of the framework is in rigorou
s approximation limits that exploit multi-scale aspects of the system. Whe
n the mass of all species scales the same way\, we get classical determini
stic limit described by PDEs. When the mass of some species in the scaling
limit is discrete while the mass of the others is continuous\, we obtain
a new type of spatial random evolution process in which discrete mass evol
ves stochastically and the continuous mass evolves according to PDEs betwe
en consecutive jump times of the discrete part. Some useful properties of
the limiting process are inherited from the pre-limiting sequence\, and co
uld be used in devising simulation algorithms.\n\nThis is joint work with
Amandine Veber (Paris V\, Polytechnique-Saclay)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nida Obatake (Texas A&M (USA))
DTSTART:20201210T160000Z
DTEND:20201210T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/5
DESCRIPTION:Title: Mixed volume of reaction networks\nby Nida Obatake (Texas A&M (USA
)) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstrac
t\nAn important invariant of a chemical reaction network is its maximum nu
mber of positive steady states. This number\, however\, is in general diff
icult to compute. We introduce an upper bound on this number— namely\, a
network’s mixed volume — that is easy to compute. We show that\, for
certain biological signaling networks\, the mixed volume does not greatly
exceed the maximum number of positive steady states. We investigate this o
vercount and also compute the mixed volumes of small networks (those with
only a few species or reactions). Joint work with Anne Shiu\, Dilruba Sofi
a\, Angelica Torres\, and Xiaoxian Tang.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ankit Gupta (ETHZ (Switzerland))
DTSTART:20201210T163000Z
DTEND:20201210T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/6
DESCRIPTION:Title: Frequency Spectra and the Color of Cellular Noise\nby Ankit Gupta
(ETHZ (Switzerland)) as part of Seminar on the Mathematics of Reaction Net
works\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polly Yu (University of Wisconsin\, Madison)
DTSTART:20210114T160000Z
DTEND:20210114T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/7
DESCRIPTION:Title: Dynamically Equivalent Mass-Action Systems: A Survey of Recent Results
\nby Polly Yu (University of Wisconsin\, Madison) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nUnder mass-action ki
netics\, each reaction network uniquely gives rise to a system of ODEs. Ho
wever\, the converse is not true\; for a given system of ODEs known to com
e from a mass-action systems\, there are many reaction networks that serve
as a candidate. In this talk\, I will introduce the notion of dynamical e
quivalence\, emphasize a convenient way of thinking about it\, and survey
some recent results on dynamical equivalence to complex-balanced or detail
ed-balanced systems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chuang Xu (Technical University of Munich)
DTSTART:20210225T160000Z
DTEND:20210225T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/8
DESCRIPTION:Title: Dynamics of one dimensional stochastic reaction networks\nby Chuan
g Xu (Technical University of Munich) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nIn this talk\, I will present recent
results on criteria for dynamics as well as identity and recursive formul
a of limit distributions of one-dimensional mass-action stochastic reacti
on networks (SRNs). I will also mention applications of these criteria to
weakly reversible SRNs\, and SRNs with transition of dynamics induced by v
olume scales. Finally\, I will list some related topics on bifurcation as
well as tails and approximation of stationary distributions of SRNs . This
talk is based on joint works with Mads Christian Hansen and Carsten Wiuf.
\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinsu Kim (UC Irvine)
DTSTART:20210128T160000Z
DTEND:20210128T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/9
DESCRIPTION:Title: Identifiability of Stochastically Modelled Reaction Networks\nby J
insu Kim (UC Irvine) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nWhen an underlying reaction network is given for a bi
ochemical system\, the system dynamics can be modeled with various mathema
tical frameworks such as continuous-time Markov processes. In this manuscr
ipt\, the identifiability of the underlying network structure with a given
stochastic system dynamics is studied. It is shown that some data types r
elated to the associated stochastic dynamics can uniquely identify the und
erlying network structure as well as the system parameters. The accuracy o
f the presented network inference is investigated when given dynamical dat
a is obtained via stochastic simulations.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Tonello (Freie Universität\, Berlin)
DTSTART:20210211T160000Z
DTEND:20210211T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/11
DESCRIPTION:Title: Boolean interaction networks: some classical results and recent trend
s\nby Elisa Tonello (Freie Universität\, Berlin) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nBoolean interaction
networks are one of the tools in the arsenal of\nmodellers investigating b
iological systems. They aim to capture\nqualitative behaviours\, and can b
e useful especially in absence of\ndetailed kinetic information. I will st
art by giving an overview of the\nmain graph structures associated to Bool
ean networks. I will then\nsummarise some of the results that connect stru
cture to dynamics\, and\ntouch on some current trends and directions of re
search.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelyn Lao (De La Salle University Manila)
DTSTART:20210211T163000Z
DTEND:20210211T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/12
DESCRIPTION:Title: Chemical reaction network decompositions and realizations of S-system
s\nby Angelyn Lao (De La Salle University Manila) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nWe present novel dec
omposition classes of chemical reaction networks (CRNs) derived from S-sys
tem kinetics. Based on the network decomposition theory initiated by Feinb
erg in 1987\, we introduce the concept of incidence independent decomposit
ions and develop the theory of $\\mathscr{C}$- and $\\mathscr{C}^*$- decom
positions which partition the set of complexes and the set of nonzero comp
lexes respectively\, including their structure theorems in terms of linkag
e classes. Analogous to Feinberg's independent decomposition\, we demonstr
ate the important relationship between sets of complex balance equilibria
for an incidence independent decomposition of weakly reversible subnetwork
s for any kinetics. We show that the $\\mathscr{C}^*$-decompositions are
also incidence independent. We also introduce in this paper a new realizat
ion for an S-system that is analyzed using a newly defined class of specie
s coverable CRNs. This led to the extension of the deficiency formula and
characterization of fundamental decompositions of species decomposable rea
ction networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Eilertsen (University of Michigan)
DTSTART:20210114T163000Z
DTEND:20210114T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/13
DESCRIPTION:Title: The current state of quasi-steady-state approximations: manifolds\, t
ime scales\, singularities\, and stochastic fluctuations\nby Justin Ei
lertsen (University of Michigan) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nOver the past decade\, mathematicians hav
e made considerable progress concerning the theory and\napplicability of q
uasi-steady-state (QSS) approximations in chemical kinetics. The applicati
on of Fenichel theory has revealed that QSS reduction in chemical kinetics
is far richer than previously thought\, even in low-dimensional systems t
hat do not exhibit oscillatory behavior. In this talk\, I will discuss rec
ent discoveries that have emerged in the \nfield of mathematical enzyme ki
netics\, including methodologies for obtaining perturbation parameters\, s
ingular points\, dynamic bifurcations and scaling laws. If time permits\,
I will also discuss the applicability of QSS reductions in stochastic envi
ronments\, and comment on some open problems in both deterministic and sto
chastic enzyme kinetics.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Curiel (University of Hawaii at Manoa)
DTSTART:20210128T163000Z
DTEND:20210128T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/14
DESCRIPTION:Title: When do two networks have the same steady-state ideal?\nby Mark C
uriel (University of Hawaii at Manoa) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nUnder the assumption of mass action
kinetics\, the associated dynamical system of a reaction network is polyno
mial. We consider the ideals generated by these polynomials\, which are ca
lled steady-state ideals. Steady-state ideals appear in multiple contexts
within the chemical reaction network literature\, however they have yet to
be systematically studied. To begin such a study\, we ask and partially a
nswer the following question: when do two reaction networks give rise to t
he same steady-state ideal? In particular\, our main results describe thre
e operations on the reaction graph that preserve the steady-state ideal. F
urthermore\, since the motivation for this work is the classification of s
teady-state ideals\, monomials play a primary role. To this end\, combina
torial conditions are given to identify monomials in a steady-state ideal\
, and we give a sufficient condition for a steady-state ideal to be monomi
al.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linard Hoessly (University of Copenhagen)
DTSTART:20210325T160000Z
DTEND:20210325T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/15
DESCRIPTION:Title: On an algebraic approach to product-form stationary distributions of
some reaction networks\nby Linard Hoessly (University of Copenhagen) a
s part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nE
xact results for product-form stationary distributions of Markov chains ar
e of interest in different fields. In stochastic reaction networks (CRNs)\
, stationary distributions are mostly known in special cases where they ar
e of product-form. However\, there is no full characterization of the clas
ses of networks whose stationary distributions have product-form. We devel
op an algebraic approach to product-form stationary distributions in the f
ramework of CRNs. Under certain hypotheses on linearity and decomposition
of the state space for conservative ergodic CRNs\, this gives sufficient a
nd necessary algebraic conditions for product-form stationary distribution
s. Correspondingly we obtain a semialgebraic subset of the parameter space
that captures rates where\, under the corresponding hypotheses\, CRNs hav
e product-form. We employ the developed theory to CRNs and some models of
statistical mechanics\, besides sketching the pertinence in other models f
rom applied probability.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Müller (University of Vienna)
DTSTART:20210311T163000Z
DTEND:20210311T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/16
DESCRIPTION:Title: Detailed balance = complex balance + cycle balance\nby Stefan Mü
ller (University of Vienna) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nWe further clarify the relation between detail
ed-balanced and complex-balanced equilibria\nof reversible chemical reacti
on networks.\nOur results hold for arbitrary kinetics and also for boundar
y equilibria.\n\nDetailed balance\, complex balance\, ''formal balance''\,
and the new notion of ''cycle balance''\nare all defined in terms of the
underlying graph.\nThis fact allows elementary graph-theoretic (non-algebr
aic) proofs of \na previous result (detailed balance = complex balance + f
ormal balance)\, \nour main result (detailed balance = complex balance + c
ycle balance)\,\nand a corresponding result in the setting of continuous-t
ime Markov chains.\n\nJoint work with Badal Joshi.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Boros (University of Vienna)
DTSTART:20210225T163000Z
DTEND:20210225T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/17
DESCRIPTION:Title: Dynamics of planar deficiency-one mass-action systems\nby Balazs
Boros (University of Vienna) as part of Seminar on the Mathematics of Reac
tion Networks\n\n\nAbstract\nFor a deficiency-zero mass-action system with
a single linkage class\, whenever there exists a positive equilibrium\, i
t is globally asymptotically stable. In this talk we discuss what other qu
alitative behaviors could arise when the deficiency is one. We restrict ou
r attention to the planar case. Joint work with Josef Hofbauer.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tung Nguyen (University of Wisconsin-Madison)
DTSTART:20210311T160000Z
DTEND:20210311T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/18
DESCRIPTION:Title: Prevalence of deficiency zero for random reaction networks\nby Tu
ng Nguyen (University of Wisconsin-Madison) as part of Seminar on the Math
ematics of Reaction Networks\n\n\nAbstract\nIn the study of reaction netwo
rks\, there is usually a strong connection between the network structure a
nd the qualitative behavior of the dynamical system. Certain network struc
tures such as deficiency zero ensure many desirable behaviors of the dynam
ical systems including existence and stability of equilibrium.\n\nIn this
talk\, I will attempt to address a natural question: how prevalent these s
tructures (in particular deficiency zero) are among random reaction networ
ks. To answer this question\, it is important to have a framework to gener
ate random reaction networks. I will present two such frameworks: an Erdos
-Renyi framework\, and a stochastic block model framework-which is essenti
ally a more generalized version of Erdos-Renyi. Next\, I will examine the
scaling limit (as the number of species goes to infinity) of the probabili
ty that a random reaction network has deficiency zero.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Rendall (Johannes Gutenberg University Mainz)
DTSTART:20210408T153000Z
DTEND:20210408T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/19
DESCRIPTION:Title: Using Bogdanov-Takens bifurcations to study existence and stability o
f periodic solutions\nby Alan Rendall (Johannes Gutenberg University M
ainz) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbst
ract\nHopf bifurcations are a favourite way to prove the existence of peri
odic\nsolutions of a dynamical system. The aim of this talk is to describe
a variant\nof this procedure using the less familiar concept of a Bogdano
v-Takens\nbifurcation. Surprisingly\, the latter procedure has the advanta
ge that\nalthough the bifurcation itself is more complicated the condition
s which need\nto be checked to determine the stability of the periodic sol
utions produced are\nmore straightforward. I will give a general discussio
n of these matters\,\nillustrating them by the example of a model for the
kinase Lck. This is\nbased on work with Lisa Kreusser\, where we studied t
he occurrence of\ninteresting dynamical features\, such as multistability\
, periodic solutions and\nhomoclinic loops\, in models for enzymes subject
to autophosphorylation. I will\nalso discuss how features of this type ca
n be lifted from smaller to larger\nreaction networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoxian Tang (Beihang University)
DTSTART:20210422T150000Z
DTEND:20210422T150000Z
DTSTAMP:20260404T094508Z
UID:MoRN/20
DESCRIPTION:Title: Multistability of One-Dimensional Reaction Networks\nby Xiaoxian
Tang (Beihang University) as part of Seminar on the Mathematics of Reactio
n Networks\n\n\nAbstract\nWe report our recent progress on multistability
of reaction networks. For the networks with one-dimensional stoichiometric
subspace\, we have the following results.\n (1) If the maximum number of
positive steady states is an even number N\, then the maximum number of st
able positive steady states\n is N/2.\n (2) If the maximum number of posit
ive steady states is an odd number N\, then we provide a condition on the
network such that the maximum number of stable positive steady states is (
N-1)/2 if this condition is satisfied\, and this maximum number is (N+1)/2
otherwise.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyukpyo Hong (KAIST)
DTSTART:20210513T150000Z
DTEND:20210513T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/21
DESCRIPTION:Title: Derivation of stationary distributions of stochastic chemical reactio
n networks via network translation\nby Hyukpyo Hong (KAIST) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nLong-term
behaviors of biochemical reaction networks are described by steady states
in deterministic models and stationary distributions in stochastic models.
Unlike deterministic steady states\, stationary distributions capturing i
nherent fluctuations of reactions are extremely difficult to derive analyt
ically due to the curse of dimensionality. In this talk\, we introduce a n
ew method to derive stationary distributions from deterministic steady sta
tes by transforming reaction networks to have a special dynamic property b
ased on chemical reaction network theory. Specifically\, we merge nodes an
d edges to make a steady state complex balanced\, i.e.\, the in- and out-f
lows of each node are equal\, and then we derive a stationary distribution
from the complex balanced steady state. Furthermore\, we provide a user-f
riendly computational package\, called CASTANET\, that transforms BRNs and
then analytically derives their stationary distributions.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amirhosein Sadeghimanesh (Coventry University)
DTSTART:20210422T153000Z
DTEND:20210422T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/22
DESCRIPTION:Title: Studying dynamical behavior of the three connected populations with A
llee effect using algebraic tools\nby Amirhosein Sadeghimanesh (Covent
ry University) as part of Seminar on the Mathematics of Reaction Networks\
n\n\nAbstract\nWe consider three connected populations with the strong All
ee effect\, and give a complete classification of the steady state structu
re of the system with respect to the Allee threshold and the dispersal rat
e. One may expect that by increasing the dispersal rate between the patche
s\, the system would become more well-mixed hence simpler. However\, we sh
ow that it is not always the case\, and the number of steady states may (t
emporarily) increase by increasing the dispersal rate. Besides sequences o
f pitchfork and saddle-node bifurcations\, we find triple-transcritical bi
furcations and also a sun-ray shaped bifurcation where twelve steady state
s meet at a single point then disappear. The major tool of our investigati
ons is a novel algorithm that decomposes the parameter space with respect
to the number of steady states using cylindrical algebraic decomposition w
ith respect to the discriminant variety of the polynomial system. This is
a joint work with Gergely Röst.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolette Meshkat (Santa Clara University)
DTSTART:20210408T150000Z
DTEND:20210408T150000Z
DTSTAMP:20260404T094508Z
UID:MoRN/23
DESCRIPTION:Title: Absolute concentration robustness in networks with many conservation
laws\nby Nicolette Meshkat (Santa Clara University) as part of Seminar
on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Wiuf (University of Copenhagen)
DTSTART:20210520T150000Z
DTEND:20210520T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/24
DESCRIPTION:Title: On the sum of two reactions\nby Carsten Wiuf (University of Copen
hagen) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbs
tract\nIt is standard in (bio)chemistry to represent a series of reactions
by a single reaction\, often called a complex reaction in contrast to an
elementary reaction. For example\, photosynthesis $6\\ \\text{CO}_2+6\\ \\
text{H}_2\\text{O}\\ \\to \\ \\text{C}_6\\text{H}_{12}\\text{O}_6+6\\ \\te
xt{O}_2$ is such complex reaction. We introduce a mathematical operation t
hat corresponds to summing two chemical reactions. Specifically\, we defin
e an associative and non-communicative operation on the product space $\n_
0^n\\times \n_0^n$ (representing the reactant and the product of a chemica
l reaction\, respectively). The operation models the overall effect of two
reactions happening in succesion\, one after the other. We study the alge
braic properties of the operation and apply the results to stochastic reac
tion networks\, in particular to reachability of states\, and to reduction
of reaction networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mercedes Perez Millan (Universidad de Buenos Aires)
DTSTART:20210520T153000Z
DTEND:20210520T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/25
DESCRIPTION:Title: Circuits of multistationarity in structured enzymatic networks\nb
y Mercedes Perez Millan (Universidad de Buenos Aires) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nIn this work we focu
s on minimal sets of intermediate species\nand their location in the netwo
rk to allow for multistationarity in the\ncorresponding mass-action chemic
al reaction system. This question has also\nbeen studied in Feliu and Wiuf
(2013) and also in Sadeghimanesh and Feliu\n(2019) using degree theory te
chniques. Our results simplify the analysis\nfor chemical reaction systems
with certain structure\, called "linearly\nbinomial networks" [Dickenstei
n\, P.M.\, Shiu\, Tang (2019)]. We apply our\nresults on several signaling
networks. We also refer to the problem of\nlifting of multistationarity\,
and we give easy combinatorial conditions\nfor MESSI networks [P.M.\, Di
ckenstein (2018)] to be linearly binomial.\nThis is joint work with Alicia
Dickenstein\, Magalí Giaroli and Rick\nRischter.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Vassena (FU Berlin)
DTSTART:20210513T153000Z
DTEND:20210513T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/26
DESCRIPTION:Title: Sign-sensitivity of metabolic networks: which structures determine th
e sign of the responses\nby Nicola Vassena (FU Berlin) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nPerturbations a
re ubiquitous in metabolism. A central tool to understand\ntheir effect is
sensitivity analysis\, which investigates how the network\nresponds to ex
ternal perturbations. In this talk we follow a structural\napproach\, only
based on the network stoichiometry and not requiring any\nquantitative kn
owledge of the reaction rates. We consider perturbations of\nreaction rate
s\, at equilibrium\, and we investigate the responses of the\nreaction flu
xes. We focus in particular on the sign of such responses\,\ni.e. whether
a response is positive\, negative or whether its sign depends\non the reac
tion rates parameters. We identify and describe certain kernel\nvectors of
the stoichiometric matrix\, which are the main players in the\nsign descr
iption.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nidhi Kaihnsa (Brown University)
DTSTART:20211028T153000Z
DTEND:20211028T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/27
DESCRIPTION:Title: Cooperativity and Absolute Interaction\nby Nidhi Kaihnsa (Brown U
niversity) as part of Seminar on the Mathematics of Reaction Networks\n\n\
nAbstract\nThis is based on a joint work with Yue Ren\, Mohab Safey El Din
\, and Johannes Martini. We consider a measure of cooperativity based on
the minimal absolute interaction required to generate an observed titratio
n behavior. We describe the corresponding algebraic optimization problem a
nd show how it can be solved using the nonlinear algebra tool \\texttt{SCI
P}.\nMoreover\, we compute the minimal absolute interactions for various b
inding polynomials that describe the oxygen binding of various hemoglobins
under different conditions.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tang Quoc Bao (Karl-Franzens-University of Graz)
DTSTART:20210923T153000Z
DTEND:20210923T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/28
DESCRIPTION:Title: Convergence to equilibrium for chemical reaction-diffusion systems\nby Tang Quoc Bao (Karl-Franzens-University of Graz) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nThis talk presents
the quantitative large time behaviour of reaction-diffusion systems modell
ing complex balanced chemical reaction networks. The convergence to equili
brium is investigated by using the so-called entropy method\, which is rob
ust enough to apply to renormalised solutions. When the system possesses n
o boundary equilibria\, the solution is shown to converge exponentially to
equilibrium with a semi-explicit rate. For certain systems with boundary
equilibria\, we investigate the competition between attraction of the posi
tive equilibrium and hypothetical convergence towards the boundary to show
the dominance of the former.\n\nThis talk is based on joint works with La
urent Desvillettes and Klemens Fellner.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Badal Joshi (California State University San Marcos)
DTSTART:20210916T153000Z
DTEND:20210916T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/29
DESCRIPTION:Title: Dynamic Absolute Concentration Robustness\nby Badal Joshi (Califo
rnia State University San Marcos) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nOutput or functional robustness in bioch
emical systems has been experimentally observed in the IDHKP-IDH glyoxylat
e bypass regulation system and the EnvZ/OmpR system in E. coli. To model o
utput robustness\, we define the notion of dynamic absolute concentration
robustness (dynamic ACR) in systems of ODEs. A species in a biochemical re
action network has dynamic ACR if its concentration converges to the same
positive value irrespective of overall initial conditions. Dynamic ACR bui
lds on the notion of static ACR wherein the concentration of a species has
the same value in any positive steady state. We will define stronger and
weaker forms of both static and dynamic ACR along with various naturally
occurring domains/basins for each. We will give a complete classification
of small networks\, using both algebraic and topological characterization\
, by their static ACR\, strong static ACR\, dynamic ACR\, and weak dynamic
ACR properties.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Shiu (Texas A&M University)
DTSTART:20210916T150000Z
DTEND:20210916T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/30
DESCRIPTION:Title: Absolute concentration robustness and multistationarity\nby Anne
Shiu (Texas A&M University) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nA reaction system exhibits “absolute concent
ration robustness” (ACR) in some species if the positive steady-state va
lue of that species does not depend on initial conditions. We present resu
lts characterizing ACR for small networks\, specifically\, those with only
a few species or reactions - or with low-dimensional stoichiometric subsp
ace. We also investigate the relationship between ACR and multistationari
ty (that is\, the capacity of a network to admit multiple positive steady
states). Finally\, we highlight several open problems on these topics.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hye-Won Kang (University of Maryland)
DTSTART:20210923T150000Z
DTEND:20210923T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/31
DESCRIPTION:Title: Stochastic Modeling of Reaction-Diffusion Processes in Biology\nb
y Hye-Won Kang (University of Maryland) as part of Seminar on the Mathemat
ics of Reaction Networks\n\n\nAbstract\nInherent fluctuations may play an
important role in biochemical and biophysical systems when the system invo
lves some species with low copy numbers. This talk will present the recent
work on the stochastic modeling of reaction-diffusion processes in glucos
e metabolism. In this talk\, I will introduce a compartment-based model fo
r a simple glycolytic pathway using a continuous-time Markov jump process\
, which describes system features at different scales of interest. Then\,
we will see how the multiscale approximate method reduces the model comple
xity. We will briefly discuss how the compartment size in the spatial doma
in can affect the spatial patterns of the system.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Giordano (University of Trento)
DTSTART:20211118T163000Z
DTEND:20211118T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/32
DESCRIPTION:Title: Looking at biochemical reaction networks through the lens of the BDC-
decomposition\nby Giulia Giordano (University of Trento) as part of Se
minar on the Mathematics of Reaction Networks\n\n\nAbstract\nSome properti
es and emerging behaviours of a biochemical reaction network are exclusive
ly due to its structure (i.e.\, its stoichiometry along with qualitative a
ssumptions) and are independent of parameter values\, which are often unce
rtain\, unknown or time-varying. Structural analysis is aimed at assessing
properties that hold for a whole family of systems\, characterised by a g
iven structure\, regardless of parameter values and precise functional exp
ressions. We propose the BDC-decomposition as a tool for both a local and
a global representation of a nonlinear system with an underlying network s
tructure. We show how the BDC-decomposition can help us structurally asses
s important properties\, including stability\, stabilisability and the sig
n of steady-state input-output influences in complex interconnected uncert
ain systems\, with a special focus on biochemical reaction networks.\n\nGi
ulia Giordano is currently an Assistant Professor at the University of Tre
nto\, Italy. She received the B.Sc. and M.Sc. degrees in electrical engine
ering and the Ph.D. degree in systems and control theory from the Universi
ty of Udine\, Italy\, in 2010\, 2012\, and 2016\, respectively. She visite
d the California Institute of Technology\, Pasadena (CA)\, USA\, in 2012\,
and the University of Stuttgart\, Germany\, in 2015. She was a Research F
ellow at Lund University\, Sweden\, from 2016 to 2017\, and an Assistant P
rofessor at the Delft University of Technology\, The Netherlands\, from 20
17 to 2019. She was recognised with the Outstanding Reviewer Letter from t
he IEEE Transactions on Automatic Control in 2016 and from the Annals of I
nternal Medicine in 2020. She received the EECI Ph.D. Award 2016\, the NAH
S Best Paper Prize 2017\, and the SIAM Activity Group on Control and Syste
ms Theory Prize 2021. Her main research interests include the analysis and
the control of dynamical networks\, with applications especially to biolo
gy and epidemiology.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:***
DTSTART:20211014T150000Z
DTEND:20211014T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/33
DESCRIPTION:Title: *** Networking event (closed to registered participants) ***\nby
*** as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstra
ct\nDear colleagues\,\n\nThank you very much for participating in the ‘M
athematics of Reaction Networks’ seminar series! We will resume the seri
es in September\, and information on the exact dates will appear on https:
//researchseminars.org/seminar/MoRN as usual.\n\nWe are very happy that so
many of you attended the talks and engaged in inspiring discussions after
wards! To our surprise\, we also noticed many new names/faces among the at
tendees. We are excited about this\, and we would like to provide an oppor
tunity to get to know each other better.\n\nWe would like to host a ‘net
working event’ in October (tentatively on October 14)\, at the same time
as the regular seminars. The idea is that all interested people may brief
ly introduce themselves or give a short presentation (indicating their bas
e institution\, research interests and background\, and optionally showing
some results or advertising open research positions). The presentations w
ill take place either in one or several rooms\, and interaction will be en
couraged.\n\nAs soon as we know how many people are interested\, we will s
end out further details. So\, please let us know if you would like to part
icipate by sending an email by August 30.\n\nHave a nice Summer!\n\nDaniel
e\, Elisenda\, and Stefan (organizers of MoRN)\n\nThis is a closed event a
nnounced through the mailing list. Only people that registered earlier can
join.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Dickenstein (University of Buenos Aires)
DTSTART:20220519T153000Z
DTEND:20220519T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/35
DESCRIPTION:Title: Beyond Boolean Networks\nby Alicia Dickenstein (University of Bue
nos Aires) as part of Seminar on the Mathematics of Reaction Networks\n\n\
nAbstract\nI will report on work in progress with Juliana García Galofre\
, Mercedes Pérez Millán and Reinhard Laubenbacher\, which is an invitati
on to model biological networks with any (fixed) finite number of states f
or every node\; in particular\, to predict the qualitative behavior of gen
e regulatory networks. To model the dynamics\, we represent each transitio
n function via operations used in multivalued logic\, which are intuitive
and close to biological interpretations. We generalize several good proper
ties of Boolean networks and we give an algorithm for computing the steady
states of the system that in many instances has a complexity that does no
t essentially increase with the number of states.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gheorghe Craciun (University of Wisconsin\, Madison)
DTSTART:20220127T160000Z
DTEND:20220127T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/36
DESCRIPTION:Title: Reaction networks\, global stability\, and toric differential inclusi
ons\nby Gheorghe Craciun (University of Wisconsin\, Madison) as part o
f Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nKey prope
rties of reaction network models (such as polynomial dynamical systems giv
en by mass-action kinetics) are closely related to fundamental results abo
ut global stability in classical thermodynamics. For example\, the Global
Attractor Conjecture can be regarded as a finite dimensional version of Bo
ltzmann’s H-theorem. We will discuss some of these connections\, and we
will focus especially on introducing toric differential inclusions as a to
ol for proving the Global Attractor Conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Germán Enciso (University of California\, Irvine)
DTSTART:20211209T163000Z
DTEND:20211209T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/37
DESCRIPTION:Title: Stochastic Modeling of Nucleosome Dynamics and Gene Expression\nb
y Germán Enciso (University of California\, Irvine) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nDNA is tightly packag
ed around histone proteins in order to increase its density inside cells\,
and a potential mechanism for DNA expression regulation is to control DNA
-histone interactions. In this talk I will present recent models of this b
ehavior\, including a novel ultrasensitive\, noncooperative mechanism for
DNA packaging\, as well as a collaboration to study time-dependent NFkB in
puts in inflammatory signaling.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio del Sole (Università bocconi di Milano)
DTSTART:20211028T150000Z
DTEND:20211028T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/38
DESCRIPTION:Title: Scaling limits of stochastic models with Fast Absorption and Slow Esc
ape\nby Claudio del Sole (Università bocconi di Milano) as part of Se
minar on the Mathematics of Reaction Networks\n\n\nAbstract\nAutocatalytic
reaction systems often exhibit a peculiar switching behaviour\, due to ra
ndom fluctuations and discreteness in the number of molecules\, which prod
uces the phenomenon of discreteness-induced transitions. The 2-dimensional
version of a model proposed by Togashi and Kaneko (2001) is a prominent e
xample of such patten. We analyze this model within a multiscale framework
\, in which fast autocatalytic cascades are triggered by much slower inflo
w and outflow reactions. Under suitable assumptions\, we study the limit b
ehaviour of the rescaled stochastic process\, and prove weak convergence t
o a naturally arising piecewise-deterministic Markov process on the Skoroh
od space equipped with Jakubowsky S-topology. Building upon this model\, w
e discuss extensions of such procedure to a larger family of autocatalytic
reaction systems\, in which a fast subsystem is rapidly absorbed into a s
et of absorbing states\, occasionally giving rise to abrupt state switches
of possibly random size.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Agazzi (Duke University)
DTSTART:20211209T160000Z
DTEND:20211209T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/39
DESCRIPTION:Title: Large Deviations for Degenerate Markov Jump Processes\nby Andrea
Agazzi (Duke University) as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nThe dynamics of a network of chemical reactions u
nder the laws of mass action kinetics are typically modeled as a system of
coupled ordinary differential equations. This macroscopic model can be re
covered\, under the appropriate scaling\, as the functional law of large n
umbers for a family of jump Markov processes capturing the discrete nature
of the underlying\, microscopic dynamical model. The large deviations beh
avior of these models has been recently investigated under relatively stro
ng assumptions on the existence of reactions with rates bounded away from
0\, allowing to guarantee the nondegeneracy of the Markov process being in
vestigated. We show that these assumptions\, which are violated by many mo
dels of interest\, can be significantly relaxed\, establishing large devia
tions principles for a large class of degenerate jump Markov processes.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Ovchinnikov (City University of New York)
DTSTART:20211118T160000Z
DTEND:20211118T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/40
DESCRIPTION:Title: Structural parameter identifiability of ODE models\nby Alexey Ovc
hinnikov (City University of New York) as part of Seminar on the Mathemati
cs of Reaction Networks\n\n\nAbstract\nStructural parameter identifiabilit
y analysis is one of the key steps of the analysis of an ODE system that d
epends on parameters. This problem is to decide whether the parameters of
the system can be determined by a given subset of the variables of the sys
tem. We will discuss recent algorithms addressing this problem as well as
related remaining challenges.\n\nBio: Alexey Ovchinnikov received the Dipl
oma in Mathematics and Applied Mathematics from Moscow State University\,
Russia\, in 2004\, and the M.S. and Ph.D. degrees in Mathematics from Nort
h Carolina State University\, Raleigh\, NC\, USA\, in 2005 and 2007\, resp
ectively\, and a Candidate of Physical and Mathematical Sciences degree fr
om Moscow State University\, Russia\, in 2008. He is a Professor at the De
partment of Mathematics of Queens College\, City University of New York (C
UNY)\, USA\, and a Doctoral Faculty of the Ph.D. Programs in Mathematics a
nd in Computer Science at the CUNY Graduate Center. Prior to joining CUNY\
, he was a Research Assistant Professor at the Department of Mathematics\,
Statistics and Computer Science\, University of Illinois at Chicago\, USA
(2007–2009). His research interests are in symbolic and symbolic-numeri
c computation for differential and difference equations and their applicat
ions to problems in the sciences. He is an editorial board member of Advan
ces in Applied Mathematics and of Journal of Symbolic Computation. He was
the recipient of a 2010 National Science Foundation (NSF) CAREER Award and
of a 2013 Alfred P. Sloan Foundation – CUNY Junior Faculty Research Awa
rd in Science and Engineering.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Walcher (RWTH Aachen)
DTSTART:20220210T163000Z
DTEND:20220210T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/41
DESCRIPTION:Title: Michaelis-Menten - The quest for small parameters\nby Sebastian W
alcher (RWTH Aachen) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nThere is a vast amount of literature on the classical
Michaelis-Menten reaction network for an enzyme-catalyzed reaction\, with
a focus on reduction of dimension. The publications make evident that the
re exist different communities interested in this matter. The difference i
s manifest both in the type of questions asked and in the type of argument
s found acceptable. From a mathematical perspective\, the standard reducti
ons can be traced back to singular perturbation theory\, as first noted in
the seminal paper by Heineken\, Tsuchiya and Aris. Thus one obtains conve
rgence results as some "small parameter" approaches zero. But from a pract
itioner's perspective\, there remains a quest for stronger\, quantitative
results to be used in applications\, and there is a variety of "small para
meters" to be found in the literature. The talk aims at bridging (or at le
ast narrowing) the gap between the communities from the mathematics side.\
n
LOCATION:https://stable.researchseminars.org/talk/MoRN/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Rahkooy (Max Planck Institute for Informatics\, Saarbrücken
)
DTSTART:20220210T160000Z
DTEND:20220210T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/42
DESCRIPTION:Title: Computations On Toricity/Binomiality of Chemical Reaction Networks\nby Hamid Rahkooy (Max Planck Institute for Informatics\, Saarbrücken)
as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\n
Chemical Reaction Networks (CRN) with Toric steady state\nvarities (or bin
omial steady state ideals) are of high interest. In\nthis talk\, we summar
izy several theoretical as well as computational\nresults on toricity/bino
miality of CRNs. We\nintroduce the geometric\nconcept of shifted toricity
(in contrast to algebraic binomiality) and\npresent experimental and theor
etical results for detecting (shifted)\ntoricity. We present a polynomial
time algorithm for detecting\nbinomiality of reversible CRNs. Finally\, if
time allows\, we discuss\nsome experiments on parametric toricity/binomia
lity using quantifier\nelimination and comprehensive Gr\\"obner systems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wasiur Khuda Bukhsh (University of Nottingham)
DTSTART:20220127T163000Z
DTEND:20220127T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/43
DESCRIPTION:Title: Incorporating age and delay into models for biophysical systems\n
by Wasiur Khuda Bukhsh (University of Nottingham) as part of Seminar on th
e Mathematics of Reaction Networks\n\n\nAbstract\nIn many biological syste
ms\, chemical reactions or changes in a physical state are assumed to occu
r instantaneously. For describing the dynamics of those systems\, Markov m
odels that require exponentially distributed inter-event times have been u
sed widely. However\, some biophysical processes such as gene transcriptio
n and translation are known to have a significant gap between the initiati
on and the completion of the processes\, which renders the usual assumptio
n of exponential distribution untenable. In this talk\, we consider relaxi
ng this assumption by incorporating age-dependent random time delays (dist
ributed according to a given probability distribution) into the system dyn
amics. We do so by constructing a measure-valued Markov process on a more
abstract state space\, which allows us to keep track of the 'ages' of mole
cules participating in a chemical reaction. We study the large-volume limi
t of such age-structured systems. We show that\, when appropriately scaled
\, the stochastic system can be approximated by a system of partial differ
ential equations (PDEs) in the large-volume limit\, as opposed to ordinary
differential equations (ODEs) in the classical theory. We show how the li
miting PDE system can be used for the purpose of further model reductions
and for devising efficient simulation algorithms. To describe the ideas\,
we will use a simple transcription process as a running example.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Deshpande (International Institute of Information Technol
ogy\, Hyderabad)
DTSTART:20220224T163000Z
DTEND:20220224T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/44
DESCRIPTION:Title: Autocatalytic recombination networks\nby Abhishek Deshpande (Inte
rnational Institute of Information Technology\, Hyderabad) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nAutocatalytic s
ystems are ubiquitous in the ‘‘origin of life" models. In this talk\,
we will study the dynamics of the relative populations in autocatalytic re
combination networks\, and show that it can be analyzed using autonomous p
olynomial dynamical systems. In addition\, we will use results from reacti
on network theory to prove permanence of several families of autocatalytic
recombination networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Sta (University of Leeds)
DTSTART:20220224T160000Z
DTEND:20220224T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/45
DESCRIPTION:Title: Mathematical modelling of a receptor-ligand system\nby Lea Sta (U
niversity of Leeds) as part of Seminar on the Mathematics of Reaction Netw
orks\n\n\nAbstract\nEffector T cells rely on IL-7 signalling for their sur
vival. The IL-7 receptor (IL-7R)\, composed of the common gamma chain and
the specific alpha chain\, is also associated with the kinase JAK3 which t
riggers its signalling pathway. Recent single-cell analysis showed a seemi
ngly paradoxical observation: increased availability of gamma chains reduc
es the IL-7 response. We describe two IL-7R mathematical models that provi
des an explanation for this inhibitory activity and shows that a balance b
etween the IL-7R subunits is crucial for optimal signaling. Use of the Gro
ebner basis provides analytical expressions for the maximum IL-7 response
(or amplitude) and for the half maximal effective concentration (EC50) of
our models. The results obtained inspired the study of a more general fami
ly of sequential models of receptor with extrinsic kinase.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Gunawardena (Harvard Medical School\, Department of Systems
Biology)
DTSTART:20220519T150000Z
DTEND:20220519T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/46
DESCRIPTION:Title: Parameter geography\nby Jeremy Gunawardena (Harvard Medical Schoo
l\, Department of Systems Biology) as part of Seminar on the Mathematics o
f Reaction Networks\n\n\nAbstract\nI will discuss some puzzling findings f
rom our analysis of parametric regions for bistability in multisite\nmodif
ication systems (Nam et al\, PLoS Comput Biol 16:e1007573 2020)\, which re
main unexplained\nand poorly understood. The findings suggest that paramet
ric regions can have macroscopic shape\nproperties\, such as volume\, that
seem to behave reasonably as conserved quantities are changed but this is
not matched at the level of individual parameter points\, which can exhib
it surprisingly complicated behaviours.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Rempala (Ohio State University)
DTSTART:20220310T160000Z
DTEND:20220310T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/47
DESCRIPTION:Title: Approximating bio-chemical dynamics using survival models\nby Gre
g Rempala (Ohio State University) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nIn a stochastic chemical network one can
often use the notion of a reaction hazard in order to provide a simple st
atistical model for the system evolution. This approach is especially hel
pful if we want to consistently follow the fate of a single molecule of s
ome special species through its different transformations\, as is the cas
e\, for instance\, for a single individual in the classical model of a sto
chastic epidemic network. I will provide a short overview of the survival
approach and give some examples extracted from a much broader recent work
completed jointly with Daniele Cappelletti.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Otero Muras (Institute for Integrative Systems Biology)
DTSTART:20220428T150000Z
DTEND:20220428T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/48
DESCRIPTION:Title: Detection of bistability in biochemical reaction networks: from mass
action to arbitrary kinetics\, and from deterministic to stochastic regime
s\nby Irene Otero Muras (Institute for Integrative Systems Biology) as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn
this talk\, I will describe the mathematical conditions and algorithms th
at we have developed over the last decade (together with Antonio A. Alonso
) for the detection of multistationarity and bistability in biochemical re
action networks: from a condition for multistationarity for biochemical re
action networks with mass action kinetics\, to the most recent development
s in bistability detection for networks of arbitrary kinetics. Our approac
h relies on concepts from Chemical Reaction Network Theory\, Bifurcation T
heory and Nonlinear Optimization. I will explain the relevance of bistabil
ity in the context of cell decision making\, and how cell decisions and bi
stability are affected in the presence of molecular noise.\n\nMoreover\, I
will illustrate the specific biological problems that we have solved in t
he context of systems and synthetic biology using tools for efficient bist
ability detection (like elucidating mechanisms responsible for differentia
l signalling\, or designing programmable genetic biosensors in bacteria).\
n
LOCATION:https://stable.researchseminars.org/talk/MoRN/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Johnston (Lawrence Technological University)
DTSTART:20220310T163000Z
DTEND:20220310T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/49
DESCRIPTION:Title: Analyzing Steady States of Mass Action Systems through Network Splitt
ing\nby Matthew Johnston (Lawrence Technological University) as part o
f Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nThe proce
ss of network translation corresponds a mass action system to a generalize
d mass action system with equivalent dynamics. Recent research has shown t
hat\, when the generalized chemical reaction network underlying the second
network has desirable structure\, such as weak reversibility and low defi
ciency\, then we may use the network to establish properties of the steady
state set and to explicitly construct a steady state parametrization. In
this talk\, I will extend this theory by introducing the method of "splitt
ing" networks. In a split network\, we allow the original network to be pa
rtitioned into subnetworks\, called "slices"\, while imposing that the uni
on of the subnetworks preserves the stoichiometry of the original network.
I show that this process expands the scope of mass action systems whose s
teady states can be characterized by the method of network translation.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimiliano Esposito (University of Luxembourg)
DTSTART:20220324T163000Z
DTEND:20220324T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/50
DESCRIPTION:Title: Free energy transduction in chemical reaction networks from enzymes t
o metabolism\nby Massimiliano Esposito (University of Luxembourg) as p
art of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nI wi
ll rigorously define energy transduction in open chemical reaction network
s (CRNs). The method is based on the stoichiometric matrix and the chemost
atted species to identify the fundamental set of thermodynamic forces and
fluxes contributing to the CRN dissipation at steady state. Transduction a
rises when some fluxes flow against their force thus creating negative con
tributions to the dissipation. This is possible because other fluxes power
transduction by being aligned with their force and ensuring the overall p
ositivity of the dissipation. Transduction is an emergent phenomenon arisi
ng at the network level because fluxes of elementary reactions are always
aligned with their force. I will apply our method to study the efficiency
of metabolic pathways in central metabolism. Our method generalizes to arb
itrary (nonlinear) CRNs the work by Terrell L. Hill on free energy transdu
ction in pseudo first order (linear) CRNs.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Bibbona (Politecnico di Torino)
DTSTART:20220324T160000Z
DTEND:20220324T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/51
DESCRIPTION:Title: Bayesian inference of RNA life-cycle kinetic rates from sequencing da
ta with multiple latent clustering\nby Enrico Bibbona (Politecnico di
Torino) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAb
stract\nWe here propose a hierarchical Bayesian model to infer RNA synthes
is\, processing\, and degradation rates from sequencing data\, based on an
ordinary differential equation system that models the RNA life cycle.\nWe
parametrize the latent kinetic rates\, that rule the system\, with a nove
l functional form\, and estimate their parameters through 6 Dirichlet proc
ess mixture models. Owing to the complexity of this approach\, we are able
to simultaneously perform inference\, clustering and model selection. We
apply our method to investigate transcriptional and post-transcriptional r
esponses of murine fibroblasts to the activation of proto-oncogene Myc. Ou
r approach uncovers simultaneous regulations of the rates\, which had not
previously been observed in this biological system.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugo Dourado (Heinrich-Heine-Universität Düsseldorf)
DTSTART:20220428T153000Z
DTEND:20220428T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/52
DESCRIPTION:Title: Optimality principles of cellular resource allocation: enzyme/substra
te relationship and growth laws\nby Hugo Dourado (Heinrich-Heine-Unive
rsität Düsseldorf) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nMuch recent progress has been made to understand the
impact of proteome allocation on bacterial growth\; much less is known abo
ut the relationship between the abundances of the enzymes and their substr
ates\, which jointly determine metabolic fluxes. Here\, we suggest an opti
mal relationship between the concentrations of enzymes and their substrate
s as a consequence of the optimal biomass allocation: for a cellular reac
tion network composed of effectively irreversible reactions\, maximal reac
tion flux is achieved when the dry mass allocated to each substrate is equ
al to the dry mass of the unsaturated (or “free”) enzymes waiting to c
onsume it. Calculations based on this optimality principle successfully pr
edict the quantitative relationship between the observed enzyme and metabo
lite abundances in E. coli\, parameterized only by dissociation constants
($K_m$). This optimal relationship is also shown to explain the emergence
of linear “growth laws” of proteome allocation under carbon limitation
\; these can be seen as approximations to the optimal enzyme/substrate rel
ationship\, including the existence of aparent protein “offsets” at ze
ro growth. The apparent offsets relate directly to the levels of substrate
saturation of catalytic proteins\, explaining also how the “under-utili
zation” of enzymes results from a trade-off between biomass allocation t
o enzymes and to metabolites.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maya Mincheva (Northern Illinois University)
DTSTART:20221013T150000Z
DTEND:20221013T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/53
DESCRIPTION:Title: Chemical Reaction Networks with Time Delays\nby Maya Mincheva (No
rthern Illinois University) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nDelay mass-action systems provide a model of c
hemical kinetics in which past states influence the current dynamics. In t
his work\, we obtain a graph-theoretic condition for $\\mathit{delay\\\,s
tability}$ which is linear stability independent of rate constants and de
lay parameters. The graph-theoretic condition involves cycles in the $\\ma
thit{directed\\\,species}$-$\\mathit{reaction\\\,graph}$ of the network\,
which encodes how different species in the system interact. \nSeveral inte
resting examples on sequestration networks with delays are presented.\n\nT
his is a joint work with George Craciun\, Casian Pantea and Polly Yu.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shu Wang (Massachusetts Institute of Technology)
DTSTART:20221013T153000Z
DTEND:20221013T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/54
DESCRIPTION:Title: Inferring CRN properties from single-cell 'omics data\nby Shu Wan
g (Massachusetts Institute of Technology) as part of Seminar on the Mathem
atics of Reaction Networks\n\n\nAbstract\nIn recent decades\, single-cell
'omics technology has allowed for measuring the abundance of $10^1$-$10^4$
distinct biochemical species in $10^3$-$10^6$ cells from a single experim
ent. Such large datasets potentially contain rich information about the un
derlying (bio)chemical reaction networks (CRNs) in cells. We design single
-cell 'omics data analysis methods to infer CRN properties\, such as the s
toichiometric subspace of a complex-balanced CRN\, by combining data scien
ce techniques with algebro-geometric results from CRN theory. \n\nEmail
: sw543@cornell.edu\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomislav Plesa (University of Cambridge)
DTSTART:20221027T150000Z
DTEND:20221027T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/55
DESCRIPTION:Title: Integral feedback in synthetic biology: Negative-equilibrium catastro
phe\nby Tomislav Plesa (University of Cambridge) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nA central goal of syn
thetic biology is the design of molecular\ncontrollers that can manipulate
the dynamics of intracellular networks\nin a stable and accurate manner.
To address the fact that detailed knowledge\nabout intracellular networks
is unavailable\, integral-feedback controllers (IFCs)\n have been put forw
ard for controlling molecular abundances.\nThese controllers can maintain
accuracy in spite of the uncertainties in the controlled networks.\nHoweve
r\, this desirable feature is achieved only if stability is also maintaine
d.\nIn this talk\, we show that molecular IFCs can suffer from a hazardous
instability called\nnegative-equilibrium catastrophe (NEC)\, whereby\nall
nonnegative equilibria vanish under the action of the controllers\,\nand
some of the molecular abundances blow up.\nWe analyze the performance of a
family of bimolecular IFCs \nwhen uncertain unimolecular networks are co
ntrolled\,\nand show that it is possible to safeguard against NECs.\nIn co
ntrast\, when IFCs are applied on uncertain bimolecular \n(and hence most
intracellular) networks\,\nwe show that preventing NECs generally becomes
an intractable problem\nas the number of interacting molecular species inc
reases.\nNECs therefore place a fundamental limit to\ndesign and control o
f molecular networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ugur Cetiner (Harvard Medical School)
DTSTART:20221027T153000Z
DTEND:20221027T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/56
DESCRIPTION:Title: Reformulating non-equilibrium steady-states\nby Ugur Cetiner (Har
vard Medical School) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nMarkov processes are widely used to model stochastic
systems in physics and biology. Their steady-state probabilities are given
in terms of their transition rates by the Matrix-Tree theorem (MTT). The
MTT uses spanning trees in a graph-theoretic representation and reveals th
at\, away from thermodynamic equilibrium\, steady-state probabilities beco
me globally dependent on all transition rates and the resulting expression
s grow super-exponentially in the graph size. The overwhelming complexity
and lack of thermodynamic insight have impeded analysis\, despite substant
ial progress in proving exact fluctuation theorems away from equilibrium.
We exploit a graph-theoretic representation of Markov processes to reformu
late non-equilibrium steady state probabilities in a way that makes their
descriptions independent of system size and gives them thermodynamic meani
ng. Our results suggest how we can “follow the energy” to unravel the
functional logic of non-equilibrium systems in physics and biology.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murad Banaji (Middlesex University London)
DTSTART:20221110T160000Z
DTEND:20221110T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/57
DESCRIPTION:Title: Splitting reactions preserves nondegenerate behaviours in chemical re
action networks\nby Murad Banaji (Middlesex University London) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nInherit
ance results attempt to answer the question: which enlargements of a chemi
cal reaction network (CRN) preserve its capacity for interesting behaviour
s such as multistationarity or oscillation? What are the potential effects
on the dynamics of a CRN of adding new reactions and/or species\, or modi
fying reactions? Such results allow us to make claims about large networks
based on their subnetworks. This talk will focus on a particular inherita
nce result: under mild assumptions\, splitting reactions and inserting int
ermediate complexes preserves the capacity of a mass action CRN for nondeg
enerate multistationarity and oscillation. This allows us to claim\, more
generally\, that introducing enzymatic mechanisms into mass action systems
preserves their capacity for these behaviours. The main result is motivat
ed by the fact that intermediates are often omitted from CRN models in bio
logy\, but the effects of leaving out intermediates are not always well un
derstood.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Yvinec (Université de Tours)
DTSTART:20221110T163000Z
DTEND:20221110T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/58
DESCRIPTION:Title: Stochastic Becker-Döring model: large population and large time resu
lts for phase transition phenomena\nby Romain Yvinec (Université de T
ours) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbst
ract\nWe present results on a stochastic version of a well-known kinetic n
ucleation model for phase transition phenomena.\nIn the Becker-Döring mod
el\, aggregates grow or shrink by addition or removal of one-by-one partic
le at a time.\nUnder certain conditions\, very large aggregates emerge and
are interpreted as a phase transition.\nWe study stationary and quasi-sta
tionary properties of the stochastic Becker-Döring model in the limit of
infinite total number of particles\, and compare with results from the det
erministic nucleation theory.\nOur findings are largely inspired from rece
nt results from stochastic chemical reaction network theory.\n\nJoint work
with Erwan HINGANT\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Howells (University of Wisconsin-Madison)
DTSTART:20221201T163000Z
DTEND:20221201T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/59
DESCRIPTION:Title: Stochastic reaction networks within interacting compartments\nby
Aidan Howells (University of Wisconsin-Madison) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nStochastic reaction networ
ks have proven to be a useful tool for the understanding of processes\, ch
emical and otherwise\, in homogeneous environments. There are multiple ave
nues for generalizing away from the assumption that the environment is hom
ogeneous\, with the proper modeling choice dependent upon the context of t
he problem being considered. One such generalization\, introduced by Duso
and Zechner in 2020\, involves a varying number of interacting compartmen
ts\, or cells\, each of which contains an evolving copy of the stochastic
reaction system. The novelty of the model is that these compartments also
interact via the merging of two compartments (including their contents)\,
the splitting of one compartment into two\, and the appearance and destruc
tion of compartments. We will discuss results pertaining to explosivity\,
transience\, recurrence\, and positive recurrence of the model\, and explo
re a number of examples demonstrating some possible non-intuitive behavior
s.\n\nBased on join work with David F. Anderson.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick DeLeenher (Oregon State University)
DTSTART:20221201T160000Z
DTEND:20221201T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/60
DESCRIPTION:Title: The basic reproduction number for linear semigroups in R^n with an in
variant cone\nby Patrick DeLeenher (Oregon State University) as part o
f Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe consid
er linear ODEs dx/dt=Ax on R^n and first characterize the class of operato
rs A that have the property that e^{tA}(K) is contained in K for all non-n
egative t. These turn out to be the so-called cross-positive operators on
K\, or equivalently\, the class of resolvent-positive operators (with resp
ect to K). We then introduce the notion of a basic reproduction number R0
and discuss the trichotomy which says that R0-1 and the spectral abscissa
s(A) of A always have the same sign (positive\, negative or zero). Basic r
eproduction numbers are often easier to calculate than the spectral abscis
sa\, which is why they are so popular in epidemiology and ecology. We shal
l illustrate these concepts and results on a simple model of an infectious
disease\, and if time permits\, show that controlling R0 one way may have
an opposite effect on the spectral abscissa. This suggests that one shoul
d be (more) careful when lowering R0 in order to control an infectious dis
ease.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruth J. Williams (University of California San Diego)
DTSTART:20230126T163000Z
DTEND:20230126T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/62
DESCRIPTION:Title: Comparison Theorems for Stochastic Chemical Reaction Networks\nby
Ruth J. Williams (University of California San Diego) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nContinuous-time Mar
kov chains are frequently used as stochastic models for chemical reaction
networks\, especially in the growing field of systems biology. A fundament
al problem for these Stochastic Chemical Reaction Networks (SCRNs) is to u
nderstand the dependence of the stochastic behavior of these systems on th
e chemical reaction rate parameters. Towards solving this problem\, in thi
s paper we develop theoretical tools called comparison theorems that provi
de stochastic ordering results for SCRNs. These theorems give sufficient c
onditions for monotonic dependence on parameters in these network models\,
which allow us to obtain\, under suitable conditions\, information about
transient and steady state behavior. These theorems exploit structural pro
perties of SCRNs\, beyond those of general continuous-time Markov chains.
Furthermore\, we derive two theorems to compare stationary distributions a
nd mean first passage times for SCRNs with different parameter values\, or
with the same parameters and different initial conditions. These tools ar
e developed for SCRNs taking values in a generic (finite or countably infi
nite) state space and can also be applied for non-mass-action kinetics mod
els. We illustrate our results with applications to models of chromatin re
gulation and enzymatic kinetics.\n\nThis is based on joint work with Felip
e Campos\, Simone Bruno\, Yi Fu and Domitilla Del Vecchio.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisenda Feliu (University of Copenhagen)
DTSTART:20230209T160000Z
DTEND:20230209T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/63
DESCRIPTION:Title: On the generic dimension and nondegeneracy of steady states of reacti
on networks\nby Elisenda Feliu (University of Copenhagen) as part of S
eminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn the conte
xt of (bio)chemical reaction networks\, the dynamics of the concentrations
of the chemical species over time are often modelled by a system of param
eter-dependent ordinary differential equations\, which are typically polyn
omial or described by rational functions. The dynamics of a reaction netwo
rk are also often constrained into invariant linear subspaces called stoic
hiometric compatibility classes. The study of the steady states of the sy
stem translates then into the study of the positive solutions to a paramet
ric polynomial system. The set of positive solutions lives inside a comple
x algebraic variety and hence tools from algebraic geometry naturally find
application in this field. \n\nIn this talk I will discuss recent results
addressing the following questions: What is the expected dimension of the
algebraic variety of steady states? Can the dimension be "wrong" in an op
en set of parameters? Under what conditions is the intersection of the alg
ebraic variety of steady states with the stoichiometric compatibility clas
ses generically finite? \n\nThese are fundamental questions to understand
the algebraic nature of the objects under study\, and have been previously
brought up in the study of reaction networks\, for example in the contex
t of weakly reversible reaction networks. Additionally\, knowing the answe
r to these questions in advance is often necessary to be able to apply the
mathematical machinery coming from complex algebraic geometry. \n\nThis t
alk is based on join work in progress with Oskar Henriksson and Beatriz Pa
scual-Escudero.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarang Sunil Nath (Technical University of Denmark)
DTSTART:20230209T163000Z
DTEND:20230209T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/64
DESCRIPTION:Title: Constructing Equivalent Electrical Circuits for (Bio)chemical Reactio
n Networks\nby Sarang Sunil Nath (Technical University of Denmark) as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn
this work\, we develop and demonstrate a technique to transform reaction n
etworks into modular electrical circuits that embody the same dynamic beha
viour. After mathematically proving the equivalence of both representation
s\, we illustrate the potential of the electrical framework to analyse osc
illatory or chaotic systems. The approach is then applied to solve for eff
ective rate constants in heterogeneous catalysis\, to enumerate flux subcy
cles in the dihydrofolate reductase (DHFR) reaction pathway\, and to simul
ate a simplified model of E. coli glycolysis. In addition to being an eleg
ant analogy that bridges separate fields of research\, we believe that the
devised methodology will be a valuable tool that can be leveraged by (bio
)chemists and (bio)chemical engineers to investigate and quantify the dyna
mics of their specific reaction systems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Randone (IMT School for Advanced Studies Lucca)
DTSTART:20230223T160000Z
DTEND:20230223T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/65
DESCRIPTION:Title: Dynamic Boundary Projection: Refining Deterministic Approximations Of
Stochastic Reaction Networks Through Dynamic Boundary Projection\nby
Francesca Randone (IMT School for Advanced Studies Lucca) as part of Semin
ar on the Mathematics of Reaction Networks\n\n\nAbstract\nTo exactly compu
te the mean dynamics of stochastic reaction networks\, the solution of the
Chemical Master Equation (CME) is rarely feasible. Deterministic rate equ
ations (DRE)\, while proven to converge to the average population dynamics
for infinite individuals\, may exhibit significant discrepancies for fini
te populations\, especially in the presence of intrinsic noise\, unstable
or multi-stable dynamics. Therefore\, it is often necessary to resort to c
omputationally expensive simulations. Dynamic Boundary Projection (DBP) is
a method that couples together a truncated version of the CME\, describin
g the evolution of a subset of states and a set of DREs\, used to shift th
e observed subset across the state space. I will show how we can apply DBP
to SRNs even when they exhibit oscillatory orbits\, multi-scale populatio
ns\, or multiple stable equilibria. Moreover\, I will present an extension
aiming at reducing the computational costs of the method by suitably defi
ning a family of rescaled approximating processes. \n\nThe talk is based o
n joint work with Mirco Tribastone and Luca Bortolussi.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Ali Al-Radhawi (Northeastern University)
DTSTART:20230223T163000Z
DTEND:20230223T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/66
DESCRIPTION:Title: Graphical characterizations of robust stability in biological interac
tion networks\nby Muhammad Ali Al-Radhawi (Northeastern University) as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nPr
evious studies have inferred robust stability of reaction networks by util
izing linear programs or iterative algorithms. Such algorithms become tedi
ous or computationally infeasible for large networks. In addition\, they o
perate like black-boxes without offering intuition for the structures that
are necessary to maintain stability. In this work\, we provide several gr
aphical criteria for constructing robust stability certificates\, checking
robust non-degeneracy\, verifying persistence\, and establishing global
stability. By characterizing a set of stability-preserving graph modifica
tions that includes the enzymatic modification motif\, we show that the st
ability of arbitrarily large nonlinear networks can be examined by simple
visual inspection. We show applications of this technique to ubiquitous m
otifs in systems biology such as Post-Translational Modification (PTM) cy
cles\, the Ribosome Flow Model (RFM)\, T-cell kinetic proofreading and oth
ers.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:János Tóth (Budapest University of Technology and Economics)
DTSTART:20230126T160000Z
DTEND:20230126T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/67
DESCRIPTION:Title: Chaos in kinetic differential equations: Towards a rigorous approach.
\nby János Tóth (Budapest University of Technology and Economics) as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nA
large part of theoretical work with kinetic differential equations focuses
on conditions of exotic behavior like multistationarity and oscillation.
Although experiments and numerical calculations suggest the presence of ch
aos in chemical kinetics\, these works use approximations and heuristics.
In this talk\, we will construct a formal chemical reaction network that c
an rigorously be proved to show chaotic behavior.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaxin Jin (The Ohio State University)
DTSTART:20230309T160000Z
DTEND:20230309T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/68
DESCRIPTION:Title: Algorithm for finding weakly reversible low deficiency realizations o
f polynomial dynamical systems\nby Jiaxin Jin (The Ohio State Universi
ty) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstra
ct\nDifferent networks can generate the same dynamical system under mass-a
ction kinetics. In this talk\, we first show that the problem of identifyi
ng an underlying weakly reversible deficiency zero network is well-posed\,
in the sense that the solution is unique whenever it exists. And we desig
n an efficient algorithm for the identification of these networks. Then we
generalize the idea on identifying a weakly reversible but deficiency one
network along with an efficient algorithm. Further\, we prove the uniquen
ess of such identification under some conditions. These are joint works wi
th Gheorghe Craciun\, Abhishek Deshpande and Polly Yu.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Stefana Sorea (SISSA Scuola Internazionale Superiore di Stu
di Avanzati)
DTSTART:20230309T163000Z
DTEND:20230309T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/69
DESCRIPTION:Title: Disguised toric dynamical systems\nby Miruna-Stefana Sorea (SISSA
Scuola Internazionale Superiore di Studi Avanzati) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nWe study families of p
olynomial dynamical systems inspired by biochemical reaction networks. We
focus on complex balanced mass-action systems\, which have also been calle
d toric. They are known or conjectured to enjoy very strong dynamical prop
erties\, such as existence and uniqueness of positive steady states\, loca
l and global stability\, persistence\, and permanence. We consider the cla
ss of disguised toric dynamical systems\, which contains toric dynamical s
ystems\, and to which all dynamical properties mentioned above extend natu
rally. By means of (real) algebraic geometry we show that some reaction ne
tworks have an empty toric locus or a toric locus of Lebesgue measure zero
in parameter space\, while their disguised toric locus is of positive mea
sure. We also propose some algorithms one can use to detect the disguised
toric locus. This is joint work with Laura Brustenga i Moncusí (Universit
y of Copenhagen) and Gheorghe Craciun (University of Wisconsin-Madison).\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianhua Xing (University of Pittsburgh)
DTSTART:20230323T160000Z
DTEND:20230323T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/70
DESCRIPTION:Title: Reconstructing cellular dynamics from single cell data\nby Jianhu
a Xing (University of Pittsburgh) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nA grand challenge in single cell studies
is to construct a quantitative\, predictive\, and genome-wide mathematica
l model describing cellular dynamics. Single-cell (sc)RNA-seq\, together w
ith RNA velocity and metabolic labeling\, reveals cellular states and tran
sitions at unprecedented resolution. A frontier of research is how to extr
act dynamical information from the snapshot data. In this talk I will firs
t discuss our recently developed dynamo framework (Qiu et al. Cell\, 2022)
\, focusing on the underlying mathematical framework. Then I will discuss
our recent efforts of reconstructing full dynamical equations using discre
te calculus on graphs (Zhang et al. to be submitted). I will conclude with
an example of applying the formalism\, together with transition path anal
yses originally developed in chemical physics\, to study how epithelial-to
-mesenchymal transition couples with cell cycle (Wang et al. Sci Adv 2020\
, eLife 2022\, Hu et al.\, in preparation).\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Hening (Texas A&M University)
DTSTART:20230323T163000Z
DTEND:20230323T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/71
DESCRIPTION:Title: Population dynamics under environmental and demographic stochasticity
\nby Alexandru Hening (Texas A&M University) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nThis work looks at the lo
ng term dynamics of diffusion processes modelling a single species that ex
periences both demographic and environmental stochasticity. In this settin
g\, the long term dynamics of the population in the absence of demographic
stochasticity is determined by the sign of $\\Lambda_0$ \, the external L
yapunov exponent: $\\Lambda_0<$ implies (asymptotic) extinction and $\\Lam
bda_0>$ implies convergence to a unique positive stationary distribution
$\\mu_0$. If the system is of size $\\frac{1}{\\epsilon^2}$ for small $\\e
psilon>0$\, the extinction time is finite almost surely. One must therefor
e analyze the quasi-stationary distribution (QSD) $\\mu_\\epsilon$ of the
system.\n\nWe look at what happens when the population size is sent to inf
inity\, i.e.\, when $\\epsilon\\to 0$. In contrast to models that only tak
e into account demographic stochasticity\, our results demonstrate the sig
nificant effect of environmental stochasticity – it turns an exponential
ly long mean extinction time to a sub-exponential one.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Conradi (HTW Berlin)
DTSTART:20230413T150000Z
DTEND:20230413T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/72
DESCRIPTION:Title: Monomial parameterizations and the dynamics of biochemical reaction n
etworks\nby Carsten Conradi (HTW Berlin) as part of Seminar on the Mat
hematics of Reaction Networks\n\n\nAbstract\nThe dynamics of biochemical r
eaction networks can be described by ODEs with polynomial right hand side.
Due to high measurement uncertainty\, few experimental repetitions and a
limited number of measurable components\, parameters are subject to high u
ncertainty and can vary in large intervals. One therefore effectively has
to study families of parametrized polynomial ODEs. In this presentation ne
tworks are considered where the steady state variety can be parameterized
by monomials. I discuss how one can exploit these parameterizations to der
ive polynomial conditions for the occurrence of multistationarity or Hopf
bifurcations.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Máté Telek (University of Copenhagen)
DTSTART:20230413T153000Z
DTEND:20230413T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/74
DESCRIPTION:Title: New results on the (dis)connectivity of the parameter region of multi
stationarity\nby Máté Telek (University of Copenhagen) as part of Se
minar on the Mathematics of Reaction Networks\n\n\nAbstract\nDespite recen
t developments\, describing the set of parameters that enable multistation
arity in a reaction network is a challenging problem. Under certain assump
tions on the network\, one can associate a critical polynomial to the netw
ork that gives information about multistationarity. Especially\, if the pr
eimage of the negative real line under the critical polynomial is connecte
d then the parameter region of multistationarity is connected. In the firs
t part of the talk\, I will present several new sufficient conditions on t
he critical polynomial that imply connectivity. I will give several exampl
es of reaction networks where our algorithm can be applied. In particular\
, we show that the parameter region of multistationarity of the sequential
and distributive phosphorylation cycle with up to seven binding sites is
connected. In the second part\, I will discuss a reaction network whose pa
rameter region of multistationarity is not connected.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Ortiz-Muñoz (Santa Fe Institute)
DTSTART:20230427T150000Z
DTEND:20230427T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/75
DESCRIPTION:Title: A Mathematical Approach to Modeling Complex Structures and their Dyna
mics\nby Andrés Ortiz-Muñoz (Santa Fe Institute) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nIn this presentatio
n\, we introduce a novel mathematical approach for modeling complex struct
ures and their dynamics using the concept of meronomy. Meronomy allows for
a systematic organization of the various types of parts\, or merons\, fou
nd within a system and their hierarchical relationships. We define complex
structures as collections of interconnected parts originating from a mero
nomy. To connect structural theory to quantitative aspects of dynamics\, w
e propose a notion of cardinality for meronomies. We show that the cardina
lities of classes of complex meronomical structures give rise to the proba
bility and combinatorial generating functions of stochastic chemical react
ion networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radek Erban (University of Oxford)
DTSTART:20230427T153000Z
DTEND:20230427T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/76
DESCRIPTION:Title: Chemical Reaction Networks: Systematic Design\, Noise Control and Lim
it Cycles\nby Radek Erban (University of Oxford) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nChemical reaction net
works describe interactions between biochemical species. Two types of math
ematical models of reaction systems will be considered: (i) deterministic
models which are written in terms of reaction rate equations (i.e. ordinar
y differential equations (ODEs) for concentrations of biochemical species
involved)\; and (ii) stochastic models of reaction networks\, given in ter
ms of the Gillespie stochastic simulation algorithm\, which provides more
detailed information about the simulated system than ODEs. I will discuss
methods for systematic design of relatively simple reaction systems with e
xotic dynamical behaviour\, including applications to synthetic biology an
d DNA computing. Considering deterministic models of reaction networks\, I
will present examples of reaction systems with multiple oscillating solut
ions or systems whose deterministic models (based on reaction rate equatio
ns) undergo specific bifurcations. Since reaction networks in biological a
pplications often involve species at low-copy numbers\, stochastic effects
may become a significant part of the dynamics. In such circumstances\, to
ols for controlling the intrinsic noise in the system are needed for a suc
cessful network design. To this end\, the so-called noise control algorith
m will be presented. The algorithm structurally modifies any given reactio
n network under the mass action kinetics\, in such a way that controllable
state-dependent noise is introduced into the stochastic dynamics\, while
the deterministic dynamics (based on reaction rate equations) are preserve
d. I will present reaction networks with noise-induced oscillations and mu
lti-stability.\n\nReferences:\n[1] Radek Erban and Hye Won Kang\, "Chemica
l Systems with Limit Cycles"\, submitted\, available as https://arxiv.org/
abs/2211.05755 (2022)\n\n[2] Radek Erban and S. Jonathan Chapman\, "Stoch
astic Modelling of Reaction-Diffusion Processes"\, Cambridge Texts in Appl
ied Mathematics\, Cambridge University Press (2020)\n\n[3] Tomislav Plesa\
, Konstantinos Zygalakis\, David Anderson and Radek Erban\, "Noise control
for molecular computing"\, Journal of the Royal Society Interface\, Volum
e 15\, Number 144\, 20180199 (2018)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tian Hong (University of Tennessee\, Knoxville)
DTSTART:20230511T150000Z
DTEND:20230511T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/77
DESCRIPTION:Title: Mass-action models of regulated degradation\nby Tian Hong (Univer
sity of Tennessee\, Knoxville) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nA key goal of systems biology is to use pre
dictive models to understand complex regulatory networks in living cells.
Mathematical modeling and analysis have been successful in uncovering dyna
mics and steady-state properties\, such as multistability and oscillation\
, of biologically important reactions networks including multisite phospho
rylation cycles. However\, it remains unclear how emergent dynamics may ar
ise from other prevalent regulatory networks in nonintuitive ways. In this
study\, we introduce a family of mass-action models for elementary bioche
mical reactions involving only binding\, production\, and degradation. We
show that altered degradation rate constants of macromolecules upon the fo
rmation of high-order complexes can lead to multistability and limit-cycle
oscillation. These models can be used to capture dynamics of RNA transcri
pts for most human genes\, as well as many proteins. Interestingly\, multi
stability and oscillation require the same structurally minimal motif in t
he context of this model family. In addition\, oscillations originating fr
om these models have diverging periods\, and we use stochastic simulations
to show their utility of robustly generating cell clusters with diverse g
ene expression patterns in cell populations.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryan Hernandez (University of the Philippines Diliman)
DTSTART:20230511T153000Z
DTEND:20230511T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/78
DESCRIPTION:Title: Independent decompositions of chemical reaction networks and parametr
ization of positive steady states of chemical reaction systems\nby Bry
an Hernandez (University of the Philippines Diliman) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nA chemical reaction n
etwork (CRN) is composed of reactions that can be seen as interactions amo
ng its units called species. Endowed with kinetics\, the chemical reaction
system (CRN with kinetics) has an associated set of ordinary differential
equations (ODEs) that models the dynamics of the system. In chemical reac
tion network theory\, we are interested in connections between the CRN and
the properties of the associated ODEs. In this talk\, we discuss decompos
itions of CRNs into independent subnetworks and how it can be used for par
ametrization of positive steady states of mass-action systems\, especially
for those with complex underlying networks. To facilitate the discussion\
, we demonstrate examples to show how to efficiently get independent decom
positions and steady state parametrizations using MATLAB. Independent deco
mpositions could also be used to parametrize positive steady states of non
-mass-action systems with considerable independent subnetworks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gábor Szederkényi (Pazmany Peter Catholic University (PPKE))
DTSTART:20231026T150000Z
DTEND:20231026T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/79
DESCRIPTION:Title: Analysis and application of kinetic flow models\nby Gábor Szeder
kényi (Pazmany Peter Catholic University (PPKE)) as part of Seminar on th
e Mathematics of Reaction Networks\n\n\nAbstract\nIn this contribution\, n
onnegative flow models in kinetic and compartmental form will be studied.
The motivation of the research came from the results on ribosome flow mode
ls (RFMs) which are deterministic dynamical systems used to describe ribos
ome movement during mRNA translation. Over the past 15 years or so\, many
of the advantageous properties and applications of these models have been
demonstrated in the literature. In the talk\, an essential generalization
of RFMs will be presented. The class of systems we propose can handle arbi
trary directed network (graph) structures and general nonlinear (even time
-varying) cell transition rates in contrast to the simpler structures and
transition rates studied previously. Under the general assumptions\, impor
tant properties of the models (e.g. stability\, monotonicity\, passivity\,
Hamiltonian structure) can be shown\, which can be well exploited in dyna
mical analysis and control design. The basis of the analysis is the theory
of chemical reaction networks and compartmental systems. Of further inter
est\, a special spatial discretization of flow models used in vehicle flow
modelling can be shown to belong to the generalized RFMs. This opens up a
n exciting opportunity to study the links between biochemical reaction net
works and certain transportation models.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhou Fang (ETH Zürich)
DTSTART:20231026T153000Z
DTEND:20231026T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/80
DESCRIPTION:Title: A divide-and-conquer method for analyzing high-dimensional noisy gene
expression networks\nby Zhou Fang (ETH Zürich) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nIntracellular gene ex
pression systems are inevitably random due to low molecular counts. Conseq
uently\, mechanistic models for gene expression should be stochastic\, and
central to the analysis and inference of such models is solving the Chemi
cal Master Equation (CME)\, which characterizes the probability evolution
of the randomly evolving copy-numbers of the reacting species. While conve
ntional methods such as Monte-Carlo simulations and finite state projectio
ns exist for estimating CME solutions\, they suffer from the curse of dime
nsionality\, significantly decreasing their efficacy for high-dimensional
systems. Here\, we propose a new computational method that resolves this i
ssue through a novel divide-and-conquer approach. Our method divides the s
ystem into a leader system and several conditionally independent follower
subsystems. The solution of the CME is then constructed by combining Monte
Carlo estimation for the leader system with stochastic filtering procedur
es for the follower subsystems. We develop an optimized system decompositi
on\, which ensures the low-dimensionality of the sub-problems\, thereby al
lowing for improved scalability with increasing system dimension. The effi
ciency and accuracy of the method are demonstrated through several biologi
cally relevant examples in high-dimensional estimation and inference probl
ems. We demonstrate that our method can successfully identify a yeast tran
scription system at the single-cell resolution\, leveraging mRNA time-cour
se microscopy data\, allowing us to rigorously examine the heterogeneity i
n rate parameters among isogenic cells cultured under identical conditions
. Furthermore\, we validate this finding using a novel noise decomposition
technique introduced in this study. This technique exploits experimental
time-course data to quantify intrinsic and extrinsic noise components\, wi
thout requiring supplementary components\, such as dual-reporter systems.\
n
LOCATION:https://stable.researchseminars.org/talk/MoRN/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Krishnan (Imperial College London)
DTSTART:20231109T160000Z
DTEND:20231109T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/81
DESCRIPTION:Title: Systems explorations of substrate modification systems\nby J. Kri
shnan (Imperial College London) as part of Seminar on the Mathematics of R
eaction Networks\n\n\nAbstract\nThe post-translational modification of pro
teins is a basic way of establishing protein functionality. There are many
examples of classes of reversible modification (phosphorylation\, ubiquin
ation\, acetylation). Typically proteins are reversibly modified at multip
le site by associated enzymes. In some instances\, the same enzymes can pe
rform multiple modifications or demodifications. In such cases\, different
types of chemical mechanisms are possible: distributive\, wherein each mo
dification is associated with the enzyme binding to the substrate\, and th
en dissociating after the modification\, and processive wherein the enzyme
is bound to the substrate as multiple modifications are effected. Substra
te modifications could also occur in a particular sequence (ordered)\, or
could occur in any order (random).\n\nInterest in substrate modification s
ystems arises from the fact that they are fundamental ingredients of cellu
lar networks on one hand\, while also being complex molecular information
processors in their own right. In this talk\, we discuss various aspects
of the information processing characteristics of substrate modification sy
stems. We first discuss some aspects of the intrinsic behaviour of these s
ubstrate modification systems and connect them to basic ingredients (eg. c
hemical mechanism\, substrate modification ordering\, commonality of enzym
es). Following this\, we discuss how such substrate modification systems
may behave as part of networks. We discuss the relevance of the results an
d insights for both systems and synthetic biology\n\n(Joint work with Vaid
hiswaran Ramesh and Thapanar Suwanmajo).\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucie Laurence (INRIA)
DTSTART:20231109T163000Z
DTEND:20231109T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/82
DESCRIPTION:Title: Scaling methods for stochastic chemical reaction networks\nby Luc
ie Laurence (INRIA) as part of Seminar on the Mathematics of Reaction Netw
orks\n\n\nAbstract\nIn this talk we investigate stochastic chemical reacti
on networks with scaling methods. This approach is used to study the stabi
lity properties of the associated Markov processes\, but also to investiga
te the transient behavior of these networks. It also gives insight on the
impact of complex features of these networks such as their polynomial rate
s\, leading to the coexistence of multiple timescales. These methods will
be illustrated by the study of a particular CRN.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizabeth Gross (University of Hawaiʻi at Mānoa)
DTSTART:20231130T160000Z
DTEND:20231130T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/83
DESCRIPTION:Title: Mixed volumes of networks with binomial steady-states\nby Elizabe
th Gross (University of Hawaiʻi at Mānoa) as part of Seminar on the Math
ematics of Reaction Networks\n\n\nAbstract\nThe steady-state degree of a c
hemical reaction network is the number of complex steady-states for generi
c rate constants and initial conditions. One way to bound the steady-state
degree is through the mixed volume of the steady-state system or an equiv
alent system. In this work\, we show that for partionable binomial network
s computing the mixed volume is equivalent to finding the volume of a sing
le mixed cell that is the translate of a parallelotope. We highlight this
theorem by giving a formula for the mixed volume of species-overlapping ne
tworks. This is joint work with Jane Coons and Mark Curiel.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oskar Henriksson (University of Copenhagen)
DTSTART:20231130T163000Z
DTEND:20231130T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/84
DESCRIPTION:Title: Finding all steady states with tropical geometry\nby Oskar Henrik
sson (University of Copenhagen) as part of Seminar on the Mathematics of R
eaction Networks\n\n\nAbstract\nThe point of departure of this talk is the
following seemingly simple question: Suppose we are given a reaction netw
ork with (generalized) mass action kinetics\, and a choice of rate constan
ts and total amounts – how do we find numerical approximations of *all*
the positive steady states?\n\nOne possible method is to use numerical alg
ebraic geometry to completely solve the steady state equations over the co
mplex numbers\, and then use interval arithmetic methods to filter out the
real positive solutions. This approach has the advantage of finding all p
ositive steady states with probability 1 (including unstable ones that wou
ld be hard to find with traditional ODE methods)\, and additionally makes
it possible to *certify* in the end that all steady states have been found
.\n\nIn this talk\, I will outline the basic ideas behind this type of num
erical algebraic geometry solvers\, and then describe recent joint work in
progress with Feliu\, Helminck\, Ren\, Schröter and Telek\, where we use
tropical geometry and matroid theory to determine the so-called *steady s
tate degree* of a network\, which is needed to ensure efficiency and certi
fiability.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Cappelletti (Politecnico di Torino)
DTSTART:20231214T160000Z
DTEND:20231214T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/85
DESCRIPTION:Title: Stochastic reaction networks in stochastic environment\nby Daniel
e Cappelletti (Politecnico di Torino) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nIn the typical definition of stochas
tic reaction networks\, the rate functions only depend on the current stat
e and do not change over time. However this is not true in many biological
systems\, where the rate functions change over time. In this study we con
sidered the more general case of the rates depending on both the current c
onfiguration and another stochastic process\, which we call "environment"
and is not directly affected by the system of interest. We study the posit
ive recurrence of this more general model under the assumption of "monomol
ecularity"\, and under certain conditions characterize the stationary dist
ribution (when it exists) as a mixture of Poisson distributions\, which is
uniquely identified as the law of a fixed point of a stochastic recurrenc
e equation. This recursion can be utilized for numerical computation of mo
ments and other distributional features.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marty Golubitsky (Ohio State University)
DTSTART:20231214T163000Z
DTEND:20231214T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/86
DESCRIPTION:Title: Homeostasis in Input-Output Networks\nby Marty Golubitsky (Ohio S
tate University) as part of Seminar on the Mathematics of Reaction Network
s\n\n\nAbstract\nA typical example of homeostasis occurs in warm-blooded m
ammals where the animal’s internal body temperature $x_o$ is held approx
imated constant on variation of the external ambient temperature I.\n\nOur
mathematical study of homeostasis focuses on networks of differential equ
ations. First\, we assume that the network has an input node $(x_i)$\, an
output node $(x_o)$ \, and a set of n regulatory nodes $(x_{r_1}\, …\, x
_{r_n})$ where only the input node depends explicitly on an external ambie
nt parameter $I$. Second\, we assume that there exists a stable equilibriu
m that leads to an input-output function $x_o(I)$. Third\, we replace home
ostasis (where the output is held approximately constant on variation of $
I$) by infinitesimal homeostasis (where the derivative $(dx_o/dI)$ vanishe
s).\n\nWe use graph theoretic methods to classify infinitesimal homeostasi
s. First\, we show that there are three kinds of three-node network motif
(feedforward loops\, substrate inhibition\, and negative feedback loops) e
ach of which leads to a different kind of homeostasis. Second\, we show th
at every network leads to a unique set of possible patterns of infinitesim
al homeostasis. Where possible\, we illustrate our results through exampl
e.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Shiu (Texas A&M University)
DTSTART:20240208T160000Z
DTEND:20240208T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/87
DESCRIPTION:Title: Absolute concentration robustness: Algebra and geometry\nby Anne
Shiu (Texas A&M University) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nMotivated by the question of how biological sy
stems maintain homeostasis in changing environments\, Shinar and Feinberg
introduced in 2010 the concept of absolute concentration robustness (ACR).
A biochemical system exhibits ACR in some species if the steady-state val
ue of that species does not depend on initial conditions. Thus\, a system
with ACR can maintain a constant level of one species even as the environm
ent changes. Despite a great deal of interest in ACR in recent years\, the
following basic question remains open: How can we determine quickly wheth
er a given biochemical system has ACR? This talk presents new methods for
deciding ACR\, which harness computational algebra.\n\nThis is joint work
with Luis David García Puente\, Elizabeth Gross\, Heather A Harrington\,
Matthew Johnston\, Nicolette Meshkat\, and Mercedes Pérez Millán.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Rojas La Luz (University of Wisconsin-Madison)
DTSTART:20240208T163000Z
DTEND:20240208T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/88
DESCRIPTION:Title: Unveiling Surprising Connections Between the Classical Theory of Reac
tion Networks and Generalized Lotka-Volterra Systems\nby Diego Rojas L
a Luz (University of Wisconsin-Madison) as part of Seminar on the Mathemat
ics of Reaction Networks\n\n\nAbstract\nWe explore the relationship betwee
n Reaction Networks and Population Dynamics\, with a specific focus on Gen
eralized Lotka-Volterra systems. Surprisingly\, we find strong analogies b
etween classical Mass Action Kinetics results (like the Horn-Jackson theor
em and the deficiency-zero theorem) and new counterparts in Generalized Lo
tka-Volterra systems\, hinting at a deep connection\, where previously non
e was known. Notably\, in the Generalized Lotka-Volterra setting\, we can
prove that “complex-balanced” equilibria (properly defined) are global
ly attractive (which corresponds to the “global attractor conjecture" in
the Reaction Networks setting). As an example\, we show how to apply this
new theory to characterize global stability for a large class of cooperat
ive Generalized Lotka-Volterra systems. We can also extend our results to
analyze the properties of variable-k systems\, an area not fully explored
in the context of Generalized Lotka-Volterra systems. This exploration unl
ocks untapped insights into the mathematical foundations of these systems\
, shedding light on their connections and paving the way for new avenues o
f research and discovery in this field. This is joint work with Gheorghe C
raciun and Polly Yu.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Oyarzun (University of Edinburgh)
DTSTART:20240314T160000Z
DTEND:20240314T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/89
DESCRIPTION:Title: Analysis of genetic-metabolic circuits using piecewise affine dynamic
al systems\nby Diego Oyarzun (University of Edinburgh) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nCell survival d
epends on the interplay of biochemical networks that sense\, transmit and
process environmental cues. In particular\, the interplay between metaboli
sm and gene regulatory networks allows cells to switch on or off specific
pathways in response to changing environmental conditions. This control st
rategy typically appears in the form of feedback loops where key regulator
y metabolites up- or down-regulate enzyme expression. In this talk I will
present some of our work on the analysis and design of coupled genetic-met
abolic networks. I will show how to timescale separation and piecewise con
stant approximations can be jointly employed to predict the long-term dyna
mics nonlinear models with complex combinations of positive and negative f
eedback loops. This work results from a long-term collaboration with Madal
ena Chaves at INRIA Sophia Antipolis\, see e.g Chaves & Oyarzún\, Automat
ica\, 2019.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Loeser (University of California San Diego)
DTSTART:20240222T163000Z
DTEND:20240222T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/90
DESCRIPTION:Title: Fluid Limit for a Stochastic Model of Enzymatic Processing with Gener
al Distributions\nby Eva Loeser (University of California San Diego) a
s part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nI
n this talk\, we consider a stochastic chemical reaction system arising as
a model for enzymatic processing in a cell. This can also be thought of a
s a multi-server multiclass queue with reneging operating under the random
order of service discipline. Stochastic primitives for the model such as
production/interarrival times\, processing/service times\, and lifetimes a
re assumed to be generally distributed. We establish a fluid limit for a m
easure-valued process that keeps track of the remaining lifetime for each
entity in the system. We prove uniqueness for fluid model solutions under
mild conditions and study the asymptotic behavior of fluid model solutions
as time goes to infinity. This talk is based on joint work with Ruth Will
iams.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingjian Wen (University of Houston)
DTSTART:20240222T160000Z
DTEND:20240222T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/91
DESCRIPTION:Title: CRNs Enabling Unbiased Exploration of the Reaction Space in Batteries
\nby Mingjian Wen (University of Houston) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nChemical reaction networks (
CRNs)\, when integrated with machine learning (ML) techniques\, can offer
unprecedented opportunities to interrogate complex chemical systems. Here\
, as an example\, I will delve into the use of graph neural networks and C
RNs to facilitate data-driven exploration of the chemical reaction space i
n Li-ion batteries\, aiming to find the optimal reaction pathways that lea
d to the formation of the solid-electrolyte interphase. Additionally\, I w
ill touch on other CRN problems where ML holds promising solutions.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Doty (University of California\, Davis)
DTSTART:20240509T150000Z
DTEND:20240509T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/92
DESCRIPTION:Title: Execution bounded chemical reaction networks\nby David Doty (Univ
ersity of California\, Davis) as part of Seminar on the Mathematics of Rea
ction Networks\n\n\nAbstract\nChemical reaction networks (CRNs) model syst
ems where molecules or agents interact according to a finite set of reacti
ons such as A + B → C\, representing that if a molecule of A and B colli
de\, they disappear and a molecule of C is produced. Although traditionall
y used to model natural chemical systems\, CRNs are also studied as a prog
ramming language for describing the desired behavior of synthetic chemical
systems. Synthetic CRNs can compute Boolean-valued predicates $\\phi \\co
lon \\mathbb{N}^d \\to \\{0\,1\\}$ and integer-valued functions $f\\colon
\\mathbb{N}^d \\to \\mathbb{N}$\; for instance X1 + X2 → Y can be though
t to compute the function min(x1\,x2).\n\nWe study the computational power
of execution bounded CRNs\, in which only a finite number of reactions ca
n occur from the initial configuration (e.g.\, ruling out reversible react
ions such as A ⇌ B). Our main negative results\, showing limitations on
the computational power of execution bounded CRNs\, are based on character
izing execution bounded CRNs as precisely those that have a "linear potent
ial function": a nonnegative linear function of the network's state\, whic
h every reaction strictly decreases. This equivalence is proved using a va
riant of Farkas' Lemma and may be of independent interest.\n\n(joint work
with Ben Heckmann)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Winfree (California Institute of Technology)
DTSTART:20240509T153000Z
DTEND:20240509T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/93
DESCRIPTION:Title: Chemical reaction networks and stochastic local search: satisfying ho
meostasis and self-organization\nby Erik Winfree (California Institute
of Technology) as part of Seminar on the Mathematics of Reaction Networks
\n\n\nAbstract\nWe discuss stochastic chemical reaction networks that do s
omething when something is wrong\, and do nothing when all is right. Such
networks can solve NP-complete problems such as 3SAT and graph coloring\,
sometimes efficiently. This may be interpreted as a form of homeostasis t
hat aims to preserve a set of combinatorial constraints. Moving from well
-mixed to surface-localized contexts reduces network size from polynomial
in the problem instance to constant size\, and suggests re-interpretation
in terms of self-organization instead of homeostasis.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minjoon Kim (POSTECH)
DTSTART:20240314T163000Z
DTEND:20240314T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/95
DESCRIPTION:Title: A path method for non-exponential ergodicity of Markov chains and its
application for chemical reaction systems\nby Minjoon Kim (POSTECH) a
s part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nW
e present criteria for non-exponential ergodicity of continuous-time Marko
v chains on a countable state space. These criteria can be verified by exa
mining the ratio of transition rates over certain paths. We applied this p
ath method to explore the non-exponential convergence of microscopic bioch
emical interacting systems. Using reaction network descriptions\, we ident
ified special architectures of biochemical systems for non-exponential erg
odicity. In essence\, we found that reactions forming a cycle in the react
ion network can induce non-exponential ergodicity when they significantly
dominate other reactions across infinitely many regions of the state space
. Interestingly\, special architectures allowed us to construct many detai
led balanced and complex balanced biochemical systems that are non-exponen
tially ergodic. Some of these models are low-dimensional bimolecular syste
ms with few reactions. Thus this work suggests the possibility of discover
ing or synthesizing stochastic systems arising in biochemistry that posses
s either detailed balancing or complex balancing and slowly\nconverges to
their stationary distribution.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Nghe (CNRS - ESPCI ParisTech)
DTSTART:20240411T150000Z
DTEND:20240411T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/96
DESCRIPTION:Title: Autocatalysis from stoichiometry toward experiments\nby Philippe
Nghe (CNRS - ESPCI ParisTech) as part of Seminar on the Mathematics of Rea
ction Networks\n\n\nAbstract\nMotivated by devising physical-chemical syst
ems that evolve\, we ended up examining the stoichiometric definition of a
utocatalysis. We then identified minimal necessary stoichiometric motifs.
Then\, I will shortly present our current progress on kinetic criteria. Fi
nally\, I will highlight challenges to find experimental autocatalytic sys
tems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakob Lykke Andersen (University of Southern Denmark)
DTSTART:20240411T153000Z
DTEND:20240411T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/97
DESCRIPTION:Title: Enumeration of Autocatalytic Pathways\nby Jakob Lykke Andersen (U
niversity of Southern Denmark) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nGiven an arbitrary reaction network we are
interested in analysing its capabilities\, and in particular if it contain
s autocatalytic pathways. In this presentaion we see how pathways can be f
ormally modelled as integer hyperflows\, enabling their enumeration throug
h integer linear programming (ILP). We then add necessary constraints for
pathways to be autocatalytic. Finally we look at next steps in refining th
ese constraints.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muruhan Rathinam (University of Maryland\, Baltimore County)
DTSTART:20240523T153000Z
DTEND:20240523T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/98
DESCRIPTION:Title: Stochastic Filtering of Partially Observed Reaction Networks\nby
Muruhan Rathinam (University of Maryland\, Baltimore County) as part of Se
minar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe describe r
ecently developed Sequential Monte Carlo methods for the computation of th
e conditional distribution of the state and/or parameters from the observa
tions of the molecular copy numbers of a subset of the species either in c
ontinuous time or in discrete snapshots in time. In addition to presenting
theoretical justification\, we also provide numerical examples.\n\nThis i
s joint work with Dr. Mingkai Yu (UMBC)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David F. Anderson (University of Wisconsin - Madison)
DTSTART:20240425T153000Z
DTEND:20240425T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/99
DESCRIPTION:Title: Chemical mass-action systems as analog computers: implementing arith
metic computations at specified speed\nby David F. Anderson (Universit
y of Wisconsin - Madison) as part of Seminar on the Mathematics of Reactio
n Networks\n\n\nAbstract\nRecent technological advances allow us to view c
hemical mass-action systems as analog computers. In this context\, the in
puts to a computation are encoded as initial values of certain chemical sp
ecies while the outputs are the limiting values of other chemical species.
The broad goal of this nascent field is to develop systems that can oper
ate in the niche of a (wet) cellular environment\, rather than to directly
compete with modern digital computers.\n\nThere have been numerous works
that design reaction networks that carry out basic arithmetic. However\,
in general\, these constructions have speeds of computation (i.e.\, a rate
s of convergence) that depend intimately upon the inputs to the computatio
n itself\, sometimes making them unusably slow. In this talk\, I will dis
cuss how we designed a full suite of “elementary” chemical systems tha
t carry out arithmetic computations (such as inversion\, addition\, roots
\, multiplication\, rectified subtraction\, absolute difference\, etc.) ov
er the real numbers\, and that have speeds of computation that are indepen
dent of the inputs to the computations. Moreover\, we proved that finite
sequences of such elementary modules\, running in parallel\, can carry out
composite arithmetic over real numbers\, also at a rate that is independe
nt of inputs. I will close with a number of open questions and directions
for future work.\n\nThis is all joint work with Badal Joshi\, and the rele
vant paper can be found here: https://arxiv.org/abs/2404.04396.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Müller (University of Vienna)
DTSTART:20240425T150000Z
DTEND:20240425T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/100
DESCRIPTION:Title: From reaction networks to "positive algebraic geometry" - and back\nby Stefan Müller (University of Vienna) as part of Seminar on the Mat
hematics of Reaction Networks\n\n\nAbstract\nEvery power-law dynamical sys
tem (and hence every polynomial dynamical system) used in chemistry and bi
ology (for example\, in ecology and epidemiology) and even in economics an
d engineering can be written as a reaction network with (generalized) mass
-action kinetics. \n\nOver the last 10 years\, we have focused on positive
equilibria that are determined by the underlying graph (complex-balanced
equilibria). As one highlight\, we have characterized unique existence (in
every invariant set and for all rate constants) using sign vectors of sub
spaces arising from the stoichiometric coefficients and the kinetic orders
.\n\nRecently\, we have turned to general equilibria\, and we study positi
ve solutions to parametrized systems of generalized polynomial equations (
with real exponents) in abstract terms. We identify the relevant geometric
objects of the problem\, namely the coefficient polytope and the monomial
difference and monomial dependency subspaces. As our main result\, we rew
rite polynomial equations in terms of binomial equations (on the coefficie
nt polytope). First applications concern real fewnomial and reaction netwo
rk theory.\n\n(Joint work with Georg Regensburger.)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Robert (INRIA)
DTSTART:20240523T150000Z
DTEND:20240523T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/101
DESCRIPTION:Title: A Stochastic Analysis of Particle Systems with Pairing\nby Phili
ppe Robert (INRIA) as part of Seminar on the Mathematics of Reaction Netwo
rks\n\n\nAbstract\nMotivated by a general principle governing regulation m
echanisms in biological cells\, we investigate a general interaction sche
me between different populations of particles and specific particles\, ref
erred to as agents. Particles and agents may bind and form a pair which m
ay have some specific functional properties. A pair splits after some rand
om amount of time. In a stochastic context\, with a set of J different typ
es of particles\, using a Markovian model for the vector of the number of
paired particles\, we study the asymptotic behavior of the time evolution
of the number of paired particles with the total number of particles used
as a scaling parameter. The analysis of the time evolution of this chemi
cal reaction network is done via the proof of an averaging principle with
three timescales. This is a joint work with Vincent Fromion and Jana Zaher
ddine.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tung D. Nguyen (University of California\, Los Angeles)
DTSTART:20241010T150000Z
DTEND:20241010T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/102
DESCRIPTION:Title: Reaction network operations that double the steady-state capacity\nby Tung D. Nguyen (University of California\, Los Angeles) as part of S
eminar on the Mathematics of Reaction Networks\n\n\nAbstract\nA great deal
of recent research has focused on proving that certain operations on reac
tion networks preserve dynamical properties of interest in applications. O
ne such property is the capability for multistationarity (multiple steady
states). However\, little is known about how high the number of steady sta
tes can increase after such an operation. Here we construct operations tha
t\, under certain conditions\, double a network's steady-state capacity (t
he maximum number of positive steady states). These operations typically i
ntroduce one new species and several new reactions.\n\nMoreover\, we estab
lish sufficient conditions for these operations to increase the number of
stable steady states. This allows for the possibility of turning a monosta
ble (one stable steady state) network into a multistable (multiple stable
steady states) one. The operations can also be tuned to control the locati
ons of the new stable steady states\; in particular it is possible to crea
te new stable steady states near the location of unstable steady states in
the old system.\n\nA joint work with Badal Joshi\, Nidhi Kaihnsa and Anne
Shiu.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ankit Gupta (ETH Zurich)
DTSTART:20241010T153000Z
DTEND:20241010T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/103
DESCRIPTION:Title: Complete characterization of kinetics-independent robust perfect ada
ptation in biochemical reaction networks\nby Ankit Gupta (ETH Zurich)
as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\n
Biological cells must precisely regulate the levels of key biomolecular sp
ecies to survive and perform their functions. A specific form of this regu
lation is Robust Perfect Adaptation (RPA)\, where certain species maintain
certain levels despite external disturbances\, without the need to fine-t
une the system’s parameters. Although RPA has been extensively studied m
athematically\, identifying it in complex\, high-dimensional networks—al
ong with understanding the associated regulatory mechanisms—remains a si
gnificant challenge.\n\nThis talk introduces a novel approach to identifyi
ng all RPA properties that emerge independently of the network’s kinetic
s in general deterministic reaction networks. The approach demonstrates th
at each RPA property corresponds to a subnetwork with specific topological
characteristics. By leveraging this connection\, we show that these struc
tures give rise to all kinetics-independent RPA properties\, enabling the
systematic identification of all these properties by enumerating such subn
etworks. Additionally\, we identify the integral feedback controllers resp
onsible for realizing each RPA property\, framing our findings within the
control-theoretic framework of the Internal Model Principle.\n\nThis is jo
int work with Prof. Yuji Hirono (Osaka University) and Prof. Mustafa Khamm
ash (ETH Zürich)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Tonello (Freie Universität Berlin)
DTSTART:20241024T150000Z
DTEND:20241024T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/104
DESCRIPTION:Title: Discrete interaction networks: attractors and cycles\nby Elisa T
onello (Freie Universität Berlin) as part of Seminar on the Mathematics o
f Reaction Networks\n\n\nAbstract\nIn a discrete interaction network\, spe
cies concentrations are assumed to\ntake on a finite number of values. Int
eraction graphs encode the positive\nand negative influences between speci
es\, and can be explored for insights\ninto the network’s dynamics. It i
s now well-established that in asynchronous dynamics\, multistationarity i
s only possible in the presence of positive interaction cycles\, while neg
ative interaction cycles are linked to cyclic attractors. However\, intera
ction graphs often contain many intertwined cycles\, raising the question:
which specific cycles are\nassociated with the network's long-term behavi
or? How can we identify and locate them? In this talk\, we will provide an
overview of some answers found in the literature\, as well as discuss new
results and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atsushi Mochizuki (Kyoto University)
DTSTART:20241121T160000Z
DTEND:20241121T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/105
DESCRIPTION:Title: Biological functions and functional modules originated in structure
of chemical reaction network\nby Atsushi Mochizuki (Kyoto University)
as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\n
In living cells\, chemical reactions are connected by sharing their produc
ts and substrates\, and form a complex network system. Biological function
s arise from the dynamics of chemical reaction networks\, and are regulate
d by changes in the amount/activity of enzymes that catalyze reactions in
the system. In this talk\, I will introduce our recent theoretical approac
h to determine the behaviors of chemical reaction systems caused by change
s in the amount/activity of enzymes\, based solely on network topology. (1
) We found that the qualitative response of chemical concentrations (and r
eaction fluxes) to changes in enzyme amount/activity can be determined fro
m the network structure alone. (2) Non-zero responses are localized to fin
ite ranges in a network\, and each range is determined by a subnetwork cal
led a “buffering structure”. The buffering structure is defined by the
following equation from local topology of a network 𝜒≔−(# of chemi
cals)+(# of reactions)−(# of cycles)+(# of conserved quantities)=0 where
the index 𝜒 is analogous to the Euler characteristic. We proved that a
ny perturbation of a reaction parameter inside a buffering structure only
affects the concentrations and fluxes inside the buffering structure\, and
does not affect the concentrations and fluxes outside. Finally\, (3) buff
ering structures govern the bifurcation of the steady state of a reaction
network. The bifurcation behaviors are localized to finite regions within
a network\, and these regions are again determined by buffering structures
. These results imply that the buffering structures may be the origin of t
he modularity of biological functions derived from reaction networks. We a
pplied this method to the cell cycle system and demonstrated that the regu
lation of different checkpoints is achieved by buffering structures.\n\nRe
ferences\n\nMochizuki A. & Fiedler B. (2015) J. Theor. Biol. 367\, 189-202
.\n\nOkada T. & Mochizuki A. (2016) Phys. Rev. Lett. 117\, 048101\n\nOkada
T. & Mochizuki A. (2017) Phys. Rev. E 96\, 022322\n\nYamauchi\, Hishida\,
Okada\, Mochizuki (2024) Phys. Rev. Research 6\, 023150\n\nYamauchi\, et
al. (In preparation)\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wasiur Khuda Bukhsh (University of Nottingham\, UK)
DTSTART:20241107T160000Z
DTEND:20241107T173000Z
DTSTAMP:20260404T094508Z
UID:MoRN/106
DESCRIPTION:Title: Enzyme kinetic reactions as interacting particle systems: Stochastic
averaging and parameter inference\nby Wasiur Khuda Bukhsh (University
of Nottingham\, UK) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nIn this talk\, I will consider a stochastic model of
multistage Michaelis--Menten (MM) type enzyme kinetic reactions describing
the conversion of substrate molecules to a product through several interm
ediate species. The high-dimensional\, multiscale nature of these reaction
networks presents significant computational challenges\, especially in st
atistical estimation of reaction rates. This difficulty is amplified when
direct data on system states are unavailable\, and one only has access to
a random sample of product formation times. To address this\, we proceed i
n two stages. First\, under certain technical assumptions akin to those ma
de in the Quasi-steady-state approximation (QSSA) literature\, we prove a
stochastic averaging principle that yields a lower-dimensional model. Next
\, for statistical inference of the parameters of the original MM reaction
network\, we develop a mathematical framework involving an interacting pa
rticle system (IPS) and prove a propagation of chaos result that allows us
to write a product-form likelihood function. The novelty of the IPS-based
inference method is that it does not require information about the state
of the system and works with only a random sample of product formation tim
es. We provide numerical examples to illustrate the efficacy of the theore
tical results. Preprint: https://arxiv.org/abs/2409.06565\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Bibbona (Politecnico di Torino)
DTSTART:20241024T153000Z
DTEND:20241024T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/107
DESCRIPTION:Title: New deterministic scaling limits of models of nanoparticle growth\nby Enrico Bibbona (Politecnico di Torino) as part of Seminar on the Mat
hematics of Reaction Networks\n\n\nAbstract\nWe consider the following nan
oparticle growth model\, where the species $M$\nrepresents monomers\, and
$P_i$ are nanoparticles of size $i$:\n\\[ \n \\left\\{ \n \\begin{arr
ay}{l}\n mM \\xrightarrow{\\nu N^{1-m}} P_m\, \\\\\n M + P
_i \\xrightarrow{\\nu N^\\theta} P_{i+1}\, \\quad i \\in \\{1\,\\ldots\, N
\\}\n \\end{array}\n \\right.\n\\]\n$M(0) = N$\, $P_i(0) = 0$ for all
$i$. We demonstrate that the proportion of particles\, at time $N^αt$\,
with a size within the interval $N^{1−β} [a\, b]$ (for any positive $a$
\,\n$b$)\, approaches a deterministic limit for large $N$. This is subject
to the scaling\nconditions $\\theta + \\alpha + \\beta = 0$ and $1 + \\al
pha = \\beta$. We fully characterize such a scaled size distribution and e
stablish its satisfaction\, in terms of Schwartz distributions\, of the Li
fshitz-Slyozov transport partial differential equation (PDE). We remark\nt
hat the special case $\\beta = 1$ (which implies $\\alpha = −1$ and $\\t
heta = 0$) is the so-called classical scaling. In this case the convergenc
e of the stochastic model to an infinite system of ODEs\, named after Beck
er and Döring\, is a classical result\, see e.g.\n[3]. Moreover\, after a
further coarsening step\, the ODE model was shown to be\nwell approximate
d by the solution of the above mentioned PDE [2\,5]. We show\nin a single
step how this PDE solution limit arise directly from the stochastic\nmodel
\, both under the classical scaling and in a wider range of scalings. To\n
prove the result we use a the framework originally developed for epidemic
models in [1]. Preliminary results based on simulations alone are availabl
e at [4]. This is joint work with Daniele Cappelletti\, Anderson Melchor H
ernandez\, Gabor Lente\, Elena Sabbioni\, Paola Siri\, and Rebeka Szabo.\n
\n[1] D. Cappelletti and G. A. Rempala\, Individual molecules dynamics in
reaction\nnetwork models\, SIAM Journal on Applied Dynamical Systems\, 22
(2023)\, pp.\n1344– 1382.\n\n[2] E. Hingant and R. Yvinec\, Deterministi
c and stochastic Becker-Döring equations: Past and recent mathematical de
velopments\, in Stochastic Processes\,\nMultiscale Modeling\, and Numerica
l Methods for Computational Cellular Biology\, Springer International Publ
ishing\, 2017\, pp. 175–204.\n\n[3] I. Jeon\, Existence of gelling solut
ions for coagulation-fragmentation equations\, Communications in Mathemati
cal Physics\, 194 (1998)\, pp. 541–567.\n\n[4] E. Sabbioni\, R. Szabó\,
P. Siri\, D. Cappelletti\, G. Lente\, and E. Bibbona\,\nFinal nanoparticl
e size distribution under unusual parameter regimes. ChemRxiv. 2024.\n\n[5
] A. Vasseur\, F. Poupaud\, J.-F. Collet\, and T. Goudon\, The Becker-D¨o
ring\nsystem and its Lifshitz–Slyozov limit\, SIAM Journal on Applied Ma
thematics\,\n62 (2002)\, pp. 1488– 1500.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomislav Plesa (University of Cambridge)
DTSTART:20241107T163000Z
DTEND:20241107T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/108
DESCRIPTION:Title: Mapping dynamical systems into chemical reactions\nby Tomislav P
lesa (University of Cambridge) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nPolynomial dynamical systems are used to mo
del a wide range of physical processes. \nA subset of these dynamical syst
ems that can model chemical reactions under mass-action kinetics are calle
d chemical systems. A central problem in synthetic biology is to map gener
al polynomial dynamical systems into dynamically similar chemical ones. I
n this talk\, I will present a novel map\, called the quasi-chemical map\,
that can systematically solve this problem. The quasi-chemical map introd
uces suitable state-dependent perturbations into any\ngiven polynomial dyn
amical system which then becomes chemical under sufficiently large transla
tion of variables. This map preserves robust dynamical features\, such as
generic equilibria and limit cycles\, as well as temporal properties\, suc
h as periods of oscillations. Furthermore\, the resulting chemical systems
are at most one degree higher than the original\ndynamical systems. I wil
l demonstrate the quasi-chemical map by designing relatively simple chemic
al systems with exotic dynamics and predefined bifurcations.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinsu Kim (POSTECH)
DTSTART:20241121T163000Z
DTEND:20241121T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/109
DESCRIPTION:Title: New path methods for addressing the boundary issues in stochasticall
y modeled reaction networks\nby Jinsu Kim (POSTECH) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nFoster-Lyapunov cr
iterion is a popular approach for studying the ergodicity of Markov chains
. To verify this criterion\, we examine the infinitesimal behavior of a Ma
rkov chain\, specifically up to the first jump from the initial state. How
ever\, this approach often faces limitations when the dominant jump (usual
ly at the boundaries of the state space) is not in a preferred direction.
In this talk\, we introduce two new path methods to address this limitatio
n. Specifically\, we use the probability of a Markov chain following certa
in paths to study its (exponential) ergodicity. Using these path methods\,
we demonstrate how we identified a class of chemical reaction networks wh
ose associated Markov chains are (exponentially) ergodic.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polly Yu (University of Illinois Urbana-Champaign)
DTSTART:20241212T163000Z
DTEND:20241212T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/110
DESCRIPTION:Title: Necessary conditions for non-monotonic steady state response\nby
Polly Yu (University of Illinois Urbana-Champaign) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nNon-monotonic (or "bip
hasic") dose responses are often observed in experimental biology\, which
raises the question of which network motifs might underlie such behaviours
. It is well known that the presence of an incoherent feedforward loop (IF
FL) may give rise to a non-monotonic response\, and it has been informally
conjectured that this condition is also necessary. We disprove this conje
cture with an example. Moreover\, we show that a version of the conjecture
does hold. Towards this aim\, we consider several related notions (infini
tesimal homeostasis\, biphasic response\, and stable biphasic response) an
d their underlying network motifs.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Baake (Bielefeld University)
DTSTART:20241212T160000Z
DTEND:20241212T173000Z
DTSTAMP:20260404T094508Z
UID:MoRN/111
DESCRIPTION:Title: Genetic recombination\, stochastic reaction systems\, and moment clo
sure\nby Ellen Baake (Bielefeld University) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nWe consider the dynamics o
f recombination between genetic sequences in a finite population. This no
nlinear system is equivalent to a stochastic reaction network and\, surpri
singly\, it has the property of moment closure. More precisely\, the expec
tations of products of frequencies of subsequences follow a closed system
of differential equations\, as long as the subsequences do not overlap. We
discuss extensions of the model under which moment closure is conserved o
r destroyed\, and would like to discuss these observations in the context
of moment closure in reaction systems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Badal Joshi (California State University San Marcos)
DTSTART:20250213T160000Z
DTEND:20250213T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/112
DESCRIPTION:Title: Bifunctional enzyme action as a source of robustness in biochemical
reaction networks: a novel hypergraph approach\nby Badal Joshi (Califo
rnia State University San Marcos) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nSubstrate modification networks are ubiq
uitous in living\, biochemical systems. We use a directed hypergraph\, a g
eneralization of a directed graph where a directed edge connects a nonempt
y set of nodes to another nonempty set of nodes\, to model the substrate m
odifications. This substrate ''skeleton'' portrays information about chang
es to the substrates while not showing the detailed reaction steps\, the i
dentity of enzymes or that of substrate-enzyme compounds. One skeleton can
underlie multiple different detailed models and reaction mechanisms. We s
how that certain dynamical properties\, such as the existence of positive
steady states or presence of concentration robustness can be inferred dire
ctly from the substrate skeleton. Concentration robustness is the property
where the concentration of one species or a positive-integer linear combi
nation of species is invariant across all positive steady states. We intro
duce the notion of ''current'' on a directed hypergraph\, which is one of
the two crucial ingredients along with bifunctional enzyme action required
to produce concentration robustness. This approach is a departure from pr
evious deficiency based results as it applies to arbitrary substrate modif
ication networks. This is joint work with Tung Nguyen.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grzegorz A. Rempala (The Ohio State University)
DTSTART:20250213T163000Z
DTEND:20250213T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/113
DESCRIPTION:Title: Likelihood Functions for Individual-Level Chemical Reaction Models\nby Grzegorz A. Rempala (The Ohio State University) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nWhen analyzing chem
ical reaction systems\, it is often useful to consider the fate of individ
ual molecules. For such systems\, one can construct an individual-level li
kelihood function—a statistical tool that evaluates how well a specific
parametric reaction model fits empirical data. These likelihood functions
are typically applied in the context of time series data representing real
izations of reaction network trajectories. In this talk\, I will introduce
the concept\, discuss its essential applications\, and explore useful app
roximations\, particularly in the setting of mass-transfer models. A key e
xample will be the stochastic SIR network model\, though similar construct
ions can be applied to enzyme kinetics and other reaction systems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Despande (International Institute of Information Technolo
gy\, Hyderabad)
DTSTART:20250410T153000Z
DTEND:20250410T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/115
DESCRIPTION:Title: Disguised toric locus of a reaction network\nby Abhishek Despand
e (International Institute of Information Technology\, Hyderabad) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nUnder ma
ss-action kinetics\, complex-balanced systems emerge from biochemical reac
tion networks and exhibit stable and predictable dynamics. For a reaction
network G\, the associated dynamical system is called disguised toric if i
t can yield a complex- balanced realization on a possibly different networ
k G1. This concept extends the robust properties of toric systems to those
that are not inherently toric. In this work\, we study the disguised tori
c locus of a reaction network — i.e.\, the set of positive rate constant
s that make the corresponding mass-action system disguised toric. Our prim
ary focus is to compute the exact dimension of this locus. We subsequently
apply our results to Thomas-type and circadian clock models.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takashi Okada (Kyoto University)
DTSTART:20250313T160000Z
DTEND:20250313T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/116
DESCRIPTION:Title: Structural Bifurcation Analysis of Chemical Reaction Networks\nb
y Takashi Okada (Kyoto University) as part of Seminar on the Mathematics o
f Reaction Networks\n\n\nAbstract\nThis talk is part of a series on the st
ructural analysis of chemical reaction networks. In the first talk present
ed by Prof. Mochizuki\, we introduced special subnetworks known as bufferi
ng structures (BSs)\, defined by specific topological conditions. A BS has
the property of confining the effect of a parameter perturbation on stead
y-state concentrations and fluxes within it. In this talk\, we present ano
ther role of BSs\, namely\, confinement of steady-state bifurcation behavi
ors. Specifically\, when a bifurcation occurs\, there must be a particular
subnetwork that destabilizes the system. It can be shown that such a subn
etwork must be either a BS or the complement of a BS. Furthermore\, depend
ing on which part of the network destabilizes\, we can identify which para
meters can trigger the bifurcation and which part of the network exhibits
bifurcating behavior. Our results are based on the network’s structural
properties and suggest that certain biological functions may emerge as a d
irect consequence of network topology.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florin Avram (Universite de Pau)
DTSTART:20250227T160000Z
DTEND:20250227T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/117
DESCRIPTION:Title: On synergies between mathematical epidemiology(ME)/ecology\, and che
mical reaction network theory (CRNT)\, and some open questions\nby Flo
rin Avram (Universite de Pau) as part of Seminar on the Mathematics of Rea
ction Networks\n\n\nAbstract\nMathematical epidemiology (ME) is both a dom
ain of great practical interest\, and a huge collection of open problems\,
which are of potential interest to all the mathematical community. A few
of these have been tackled in the recent papers of Avram\, Adenane\, Halan
ay\, Johnston and Vassena [VAA24\, AAN24\, AAHJ]\, using CRN methods like
the inheritance of bifurcations\, etc\, which were previously unknown in M
E.\n\nIn this paper we further explore the challenging question of finding
Lyapunov functions for quadratic ME models. The question has already been
touched upon\, under models governed by matrices with various structures
in ME (multi-group\, multi-patch\, multi-vector and meta-population models
)\, ecology\, and CRNT\, and it was often found that a Lotka-Volterra type
function may be found\, whose coefficients are the left eigenvector of so
me matrix. Our goal is to unify the previous works\, under a general ”ec
o-epidemiological” SIR-PH model introduced in Avram & al [AAB+23]\, and
in particular to find conditions which guarantee two remarkable phenomena
occurring sometimes in ME/ecology problems:\n\n1. The ”strong (global st
ability) threshold property” (STP)\, which ensures the uniqueness of a f
ixed interior point\, and the fact that it is globally stable whenever it
exist\, seems to have originated in ME and ecology Lajmanovich\, Yorke\, B
eretta\, Capasso\, Li and Shuai [LY76\, BC86\, SvdD13].\n\n2. The competit
ive exclusion principle (CEP) – see for example Iggidr\, Kamgang\, Salle
t\, Tewa\,\nBichara\, Souza [IKST06]\, which may be viewed as an extension
of the STP\, to the case when\nseveral boundary points exist.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Duvall (Northeastern University)
DTSTART:20250227T163000Z
DTEND:20250227T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/118
DESCRIPTION:Title: Interplay between Contractivity and Monotonicity for Reaction Networ
ks\nby Alon Duvall (Northeastern University) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nThis work studies relatio
nships between monotonicity and contractivity\, and applies the results to
establish that many reaction networks are weakly contractive\, and thus\,
under appropriate compactness conditions\, globally convergent to equilib
ria. Verification of these properties is achieved through a novel algorith
m that can be used to generate cones for monotone systems. The results giv
en here allow a unified proof of global convergence for several classes of
networks that had been previously studied in the literature.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Floyd (University of Chicago)
DTSTART:20250313T163000Z
DTEND:20250313T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/119
DESCRIPTION:Title: Limits on the computational expressivity of non-equilibrium biophysi
cal processes\nby Carlos Floyd (University of Chicago) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nMany biological
decision-making processes can be viewed as performing a classification ta
sk over a set of inputs\, using various chemical and physical processes as
"biological hardware." In this context\, it is important to understand th
e inherent limitations on the computational expressivity of classification
functions instantiated in biophysical media. Here\, we model biochemical
networks as Markov jump processes and train them to perform classification
tasks\, allowing us to investigate their computational expressivity. We r
eveal several unanticipated limitations on the input-output functions of t
hese systems\, which we further show can be lifted using biochemical mecha
nisms like promiscuous binding. We analyze the flexibility and sharpness o
f decision boundaries as well as the classification capacity of these netw
orks. Additionally\, we identify distinctive signatures of networks traine
d for classification\, including the emergence of correlated subsets of sp
anning trees and a creased "energy landscape" with multiple basins. Our fi
ndings have implications for understanding and designing physical computin
g systems in both biological and synthetic chemical settings.\n\nThis is j
oint work with Suri Vaikuntanathan\, Arvind Murugan\, and Aaron Dinner (ht
tps://arxiv.org/abs/2409.05827).\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Software Showcases
DTSTART:20250424T150000Z
DTEND:20250424T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/120
DESCRIPTION:Title: Several software packages relevant for reaction networks analyses\nby Software Showcases as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nThis week's seminar will take a different format.
Four different groups will be introducing their software packages that ar
e relevant for reaction networks. This will be followed by breakout rooms
to learn more about these packages.\n\nSpeakers:\n\n$\\color{blue}\\underl
ine{\\textbf{1. Herbert Sauro (University of Washington) -- Tellurium}}$\n
\n$\\textbf{Keywords:}$ Simulation\, SBML\, High Performance\, reusable li
brary\n\n$\\textbf{Website:}$ \nhttps://tellurium.analogmachine.org/\, \n
https://tellurium.readthedocs.io/en/latest/index.html\n\n$\\textbf{Recordi
ng:}$ https://youtu.be/yzVOZlQwM74 \n\n$\\color{blue}\\underline{\\textbf{
2. Torkel Loman (University of Oxford)\; Vincent Du (UNC Chapel Hill) -- C
atalyst}}$\n\n$\\textbf{Keywords:}$ Chemical reaction networks\, ODE Simul
ations\, Stochastic simulations\, Network analysis\n\n$\\textbf{Website:}$
https://github.com/SciML/Catalyst.jl\n\n$\\textbf{Recording:}$ https://yo
utu.be/h9zUQWoyWo0\n\n$\\color{blue}\\underline{\\textbf{3. Marcus Aichmay
r (University of Kassel) -- Sign Vector Conditions}}$\n\n$\\textbf{Keyword
s:}$ chemical-reaction-networks\, generalized mass-action systems\, defici
ency zero theorem\, robustness\, sign vectors\, SageMath\n\n$\\textbf{Webs
ite:}$ \nhttps://github.com/MarcusAichmayr/sign_vector_conditions\n\n$\\te
xtbf{Recording:}$ https://youtu.be/H_bYwr1KEi0\n\n\n$\\color{blue}\\underl
ine{\\textbf{4. Janos Toth (Budapest University of Technology and Economic
s) -- ReactionKinetics.wl}}$\n\n$\\textbf{Keywords:}$ From Exact Stochast
ic Simulation to Qualitative and Structural Analysis of Reactions\, a Wolf
ram Language (Mathematica) package\,\nTÓTH\, J.\; NAGY\, A. L.\; PAPP\, D
.\, Springer\, 2018.\n\n$\\textbf{Recording:}$ https://youtu.be/8j_7G_tJsb
0\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:AmirHosein Sadeghimanesh (Coventry University)
DTSTART:20250410T150000Z
DTEND:20250410T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/121
DESCRIPTION:Title: Designing Machine Learning Tools to Characterize Multistationarity o
f Fully Open Reaction Networks\nby AmirHosein Sadeghimanesh (Coventry
University) as part of Seminar on the Mathematics of Reaction Networks\n\n
\nAbstract\nChemical Reaction Networks (CRNs) are the mathematical formula
tion of how the quantities associated to a set of species (molecules\, pro
teins\, cells\, or animals) vary as time passes with respect to their inte
ractions with each other. Their mathematics does not describe just chemica
l reactions but many other areas of the life sciences such as ecology\, ep
idemiology\, and population dynamics. We say a CRN is at a steady state wh
en the concentration (or number) of species do not vary anymore. Some CRNs
do not attain a steady state while some others may have more than one pos
sible steady state. The CRNs in the later group are called multistationary
. Multistationarity is an important property\, e.g. switch-like behaviour
in cells needs multistationarity to occur. Existing algorithms to detect w
hether a CRN is multistationary or not are either extremely expensive or r
estricted in the type of CRNs they can be used on\, motivating a new machi
ne learning approach. This talk is about a recent attempt to design machin
e learning tools to predict multistationarity of reaction networks.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Grunberg
DTSTART:20250508T150000Z
DTEND:20250508T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/122
DESCRIPTION:Title: Error bounds for the linear noise approximation to stationary distri
butions of chemical reaction networks\nby Theodore Grunberg as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nSpecies in
teracting according to chemical reactions are often modeled by a continuou
s time Markov chain that describes the evolution of counts of the species
over time. Such Markov chains typically have a large or infinite number of
states and are thus computationally difficult to analyze. Therefore\, app
roximations exploiting the fact that the volume and molecular counts are b
oth large are often used. The most common such approximations are the reac
tion rate equations (RREs)\, which are a deterministic model\, and the lin
ear noise approximation (LNA)\, which is a diffusion approximation to fluc
tuations about the solution of the RREs. Limit theorem results\, due to Ku
rtz (1971)\, establish the validity of the RREs and of the LNA for finite
times. However\, such results do not justify approximating the stationary
distribution of a chemical reaction network using the RREs or LNA. The val
idity of these approximations for the stationary distribution has only bee
n investigated for special cases\, such as when the Markov chain’s state
space is bounded in concentration\, or when the chemical reaction network
has a special structure. Here\, we use Stein’s method to derive bounds
on the approximation error for the LNA applied to the stationary distribut
ion of a chemical reaction network. Specifically\, we give a non-asymptoti
c bound on the 1-Wasserstein distance between an appropriately scaled Mark
ov chain and its LNA\, under certain technical conditions\, that decays to
zero with increasing system size. Our results do not require that the Ma
rkov chain’s state space be bounded\, nor do they require that the chemi
cal reaction network have a special structure. We further show how global
stability properties of an equilibrium point of the RREs are sufficient to
obtain such error bounds. Our results can be used to check when the LNA i
s a suitable approximation of the stationary distribution of a chemical re
action network without having to perform computationally costly simulation
s.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakob Ruess (INRIA)
DTSTART:20250508T153000Z
DTEND:20250508T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/123
DESCRIPTION:Title: From single cells to microbial consortia and back: stochastic chemic
al kinetics coupled to population dynamics\nby Jakob Ruess (INRIA) as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nAt
the single-cell level\, biochemical processes are inherently stochastic. S
uch processes are typically studied using models based on stochastic chemi
cal kinetics\, governed by a chemical master equation (CME). The CME descr
ibes the time evolution of the probability distribution over system states
and has been a tremendously helpful tool in shedding light on the functio
ning of cellular processes. However\, single cells are not living in isola
tion but are part of a growing population or community. In such contexts\,
stochasticity at the single-cell scale leads to population heterogeneity
and cells may be subject to population processes\, such as selection\, tha
t drive the population distribution away from the probability distribution
of the single-cell process.\n\nHere\, I will introduce a multi-scale mode
ling framework that allows one to capture coupled stochastic single-cell a
nd population process. I will show that the expected population distributi
on of such multi-scale models can be calculated by solving a modified vers
ion of the CME that is of the same dimensionality as the standard CME. I w
ill then show how such models can be used to explain experimental data on
plasmid copy number fluctuations and population growth in media that selec
ts against cells that have lost the plasmid. Finally\, I will present an o
ptogenetic recombination system that allows one to partition yeast populat
ions into different cell types via external application of blue light to c
ells and show how our modeling framework can be used to predict and contro
l emerging dynamics of the population composition in response to time-vary
ing light stimuli.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Johnston (Lawrence Technological University)
DTSTART:20251009T150000Z
DTEND:20251009T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/124
DESCRIPTION:Title: Extending the Basic Reproduction Number to Biochemical Reaction Netw
orks\nby Matthew Johnston (Lawrence Technological University) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe exten
d the next generation matrix method for computing the basic reproduction n
umber in mathematical epidemiology to computing an analogous number for es
tablishing the stability of boundary faces in biochemistry. In epidemiolog
y\, the basic reproduction number indicates whether a disease can invade a
population\, with values below one leading to disease-free stability and
values above one signaling an outbreak. In biochemistry\, the number deter
mines whether certain chemical species persist or go extinct\, with values
greater than one leading to persistence. The next generation matrix metho
d approach is typically significantly more computationally tractable than
standard Jacobian or Routh-Hurwitz methods for establishing stability\; co
nsequently\, the method could have significant applications for understand
ing metabolic function.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carles Checa Nualart (University of Copenhagen)
DTSTART:20251106T160000Z
DTEND:20251106T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/126
DESCRIPTION:Title: An effective criterion for multiple positive solutions of vertical s
ystems\nby Carles Checa Nualart (University of Copenhagen) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe present
a criterion for determining when a vertically parametrized polynomial syst
em admits multiple positive zeros for some parameter values. Our approach
is based on the higher deficiency algorithms from chemical reaction networ
k theory. Under certain assumptions\, these algorithms reduce the problem
to checking the feasibility of a linear system of equalities and inequalit
ies (polyhedral cones). Our criterion requires that the linear part of the
system (stoichiometric matrix) has a row reduction whose underlying graph
is a forest\, implying a highly structured pattern of zeros\, which is of
ten realized in steady state varieties. Using the same polyhedral cones\,
we also provide sufficient conditions to derive connectivity of the parame
ter region yielding multiple positive solutions and to guarantee the exist
ence of a pair of distinct nondegenerate positive zeros. This is joint wor
k with Elisenda Feliu.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabina J Haque (University of Michigan)
DTSTART:20251120T160000Z
DTEND:20251120T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/127
DESCRIPTION:Title: Graph-theoretic and algebraic geometric approaches to biochemical re
action networks\nby Sabina J Haque (University of Michigan) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nUnder mass
-action kinetics\, systems of biochemical reactions are modeled by chemica
l reaction networks (CRNs)\, a class of graphs that gives rise to polynomi
al dynamical systems. Approaches in this field include chemical reaction n
etwork theory and the more recent linear framework. In this talk\, I will
focus primarily on the linear framework\, a graph-theoretic approach to ti
mescale separation in biochemical systems. I will discuss a graph-theoreti
c construction within the framework that mimics what would happen if a sin
gle parameter in a graph is taken to infinity\, producing what we call an
asymptotic graph. I consider how properties of the asymptotic graph\, such
as its steady states\, serve as an appropriate representation for a linea
r framework graph in this limit. Time permitting\, I also speculate on som
e extensions of this construction beyond the scope of the linear framework
to parameter identifiability and the steady state varieties of CRNs\, sug
gesting areas for future work at the intersection of graph theory\, algebr
aic geometry\, and dynamical systems.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Roussel (University of Lethbridge)
DTSTART:20251204T160000Z
DTEND:20251204T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/128
DESCRIPTION:Title: Every qualitative stability analysis method implies model reduction
procedures\nby Marc Roussel (University of Lethbridge) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nA qualitative s
tability analysis method will typically give us necessary\,\nand sometimes
sufficient\, conditions for a dynamical system to display\nparticular beh
aviors such as oscillations\, multistability or patterning.\nOnce we have
identified how a network satisfies those conditions\, we can\nsimplify a m
odel by eliminating components that do not contribute to the\nbehavior. In
the context of chemical reaction networks\, this might mean\neliminating
chemical species\, often by combining reactions. I will\nillustrate this i
dea using the Ivanova criterion for multistability and a\nmodel for the co
ntrol of Hmp\, an NO detoxifying enzyme\, in Streptomyces\ncoelicolor.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingyi Ma (University of Wisconsin–Madison)
DTSTART:20251023T153000Z
DTEND:20251023T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/129
DESCRIPTION:Title: Mathematical Analysis for a Class of Stochastic Copolymerization Pro
cesses\nby Jingyi Ma (University of Wisconsin–Madison) as part of Se
minar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn this talk\
, I want to present a rigorous mathematical framework for analyzing a clas
s of stochastic copolymerization processes\, where finitely many types of
monomers attach and detach at the tip of a polymer chain. These dynamics a
re modeled as a continuous-time Markov chain on an infinite tree-like stat
e space. The sharp criteria for transience\, null recurrence\, and positi
ve recurrence in terms of the attachment and detachment rates will be esta
blished. In the transient regime\, explicit formulas for the almost sure a
symptotic composition of the polymer and its growth velocity are provided.
We expect that the mathematical methods used and developed will also enab
le the study of even more complex models in the future.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Müller (University of Vienna)
DTSTART:20251023T150000Z
DTEND:20251023T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/130
DESCRIPTION:Title: Existence\, uniqueness\, and stability of equilibria in (generalized
) mass-action systems\nby Stefan Müller (University of Vienna) as par
t of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe rep
ort on several recent results for reaction networks with (generalized) mas
s-action kinetics\, short (G)MAK.\n\n1. In the setting of MAK\, complex-ba
lanced equilibria are asymptotically stable. We further clarify the binomi
al structure of mass-action systems\, and extend the stability result to '
binomial differential inclusions'\, a very general class of dynamical syst
ems.\n\n2. For GMAK\, complex-balanced equilibria need not be stable. We p
rovide sufficient (sign) conditions for linear stability.\n\nFor both resu
lts\, we use a new decomposition of the graph Laplacian and monomial evalu
ation orders (inducing 'banana' regions or 'wedges' in log coordinates).\n
\nFor two more results\, we use our new framework for parametrized systems
of generalized polynomial equations\, which covers equilibria of reaction
networks with (G)MAK.\n\n3. In full generality\, we characterize the uniq
ue existence of solutions for all parameters. As a sufficient condition\,
we provide a 'genuine' multivariate Descartes rule of signs.\n\n4. For MAK
\, we extend the deficiency one theorem (from deficiency one to *dependenc
y* one and from single to multiple terminal linkage classes).\n\nThis is j
oint work with Georg Regensburger and Abhishek Deshpande.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Vassena (Leipzig University)
DTSTART:20251009T153000Z
DTEND:20251009T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/131
DESCRIPTION:Title: Instability and Oscillations in Reaction Networks\nby Nicola Vas
sena (Leipzig University) as part of Seminar on the Mathematics of Reactio
n Networks\n\n\nAbstract\nIn the past two decades\, much mathematical rese
arch on reaction \nnetworks has focused on multistationarity\, both under
mass-action and \nmore general kinetics. Multistationarity typically arise
s in parameter \nspace when a stable steady state loses stability through
a real-zero \neigenvalue crossing. More recently\, attention has turned al
so to \nstability loss via purely imaginary eigenvalues (Hopf bifurcation)
\, \nwhich is associated with periodic oscillations.\n\nIn this talk\, bas
ed on established results from dynamical systems \ntheory developed in lat
e 1970s and 1980s\, I will first clarify that \nfor monostationary network
s\, in essence\, any loss of stability \nnecessarily leads to oscillations
. I will then present sufficient \nconditions for oscillations expressed a
s algebraic criteria (for \nmass-action kinetics) and as minimal network m
otifs (for general \nkinetics). In turn\, excluding Hopf bifurcations in m
onostationary \nnetworks with a stable steady state is equivalent to 'univ
ersal’ \nstability\, meaning that the unique steady state is locally sta
ble for \nall parameter choices. I will conclude with a conjecture \nchara
cterizing universal stability for reaction networks with general \nkinetic
s. This is ongoing joint work with Peter F. Stadler and Alex \nBlokhuis.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balázs Boros (Bolyai Institute\, University of Szeged)
DTSTART:20251106T163000Z
DTEND:20251106T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/132
DESCRIPTION:Title: Bifurcations in small mass-action systems\nby Balázs Boros (Bol
yai Institute\, University of Szeged) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nWe give an overview of the recent de
velopments on the smallest quadratic mass-action reaction networks that ad
mit Andronov-Hopf\, Bautin\, Bogdanov-Takens\, fold\, or cusp bifurcations
. Then\, we discuss the analogous questions in the class of bimolecular ma
ss-action reaction networks. Finally\, we briefly discuss the inheritance
theory of mass-action reaction networks\, which allows us to lift nondegen
erate behaviors from a network to its enlargement.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casian Pantea (West Virginia University)
DTSTART:20251120T163000Z
DTEND:20251120T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/133
DESCRIPTION:Title: Weakly reversible deficiency zero realizations of polynomial ODE sys
tems with parameters\nby Casian Pantea (West Virginia University) as p
art of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWeak
ly reversible deficiency zero (WR0) mass-action systems are known to have
remarkably stable dynamics\, with a unique positive asymptotically stable
steady state in each compatibility class. Suppose we have an ODE polynom
ial system whose coefficients depend affinely on a set of parameters (for
example\, mass-action systems). We present an algorithm which outputs the
region of parameters where our ODE system is identical with that of a weak
ly reversible\, deficiency zero mass-action system\, whose nice dynamical
properties it inherits. The algorithm is based on computations on polyhedr
a\, and was developed in polymake. This is joint work with Neal Buxton (
WVU).\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Popovic (Concordia University)
DTSTART:20251204T163000Z
DTEND:20251204T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/134
DESCRIPTION:Title: Sensitivity of dynamics in Autocatalytic Reaction Networks of Togash
i-Kaneko type\nby Lea Popovic (Concordia University) as part of Semina
r on the Mathematics of Reaction Networks\n\n\nAbstract\nThe Togashi–Kan
eko (TK) model is a prototypical example of an auto- catalytic reaction ne
twork exhibiting dramatic switching behavior that is a result of the stoch
astic dynamics at small volumes. I will present a study of the TK model wi
th additional mutations\, using a stochastic averaging principle to make u
se of the multi-scale feature of its dynamics. I will demonstrate a sensit
ivity of the model to even slight departures from symmetry in the autocata
lytic reactions\, using a detailed analysis of the stationary distribution
of the fast process when the state of the slow process is fixed. This is
joint work with Yi Fu\, HyeWon Kang\, Wasiur Khudabukhsh\, Greg Rempala an
d Ruth Williams.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nidhi Kaihnsa (University of Copenhagen)
DTSTART:20260409T150000Z
DTEND:20260409T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/135
DESCRIPTION:Title: Connectivity in Parameter Regions of Reaction Networks\nby Nidhi
Kaihnsa (University of Copenhagen) as part of Seminar on the Mathematics
of Reaction Networks\n\n\nAbstract\nI will discuss the general problem of
connectivity in the parameter regions of reactions networks. In particular
for different phosphorylation networks. The talk will be based on multipl
e joint works with Feliu\, Telek\, de Wolff\, Yürük\, and Wang. I will c
onclude with some open problems in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyukpyo Hong (University of Wisconsin-Madison)
DTSTART:20260226T163000Z
DTEND:20260226T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/136
DESCRIPTION:Title: Ubiquitous Asymptotic Robustness in Biochemical Systems\nby Hyuk
pyo Hong (University of Wisconsin-Madison) as part of Seminar on the Mathe
matics of Reaction Networks\n\n\nAbstract\nLiving systems maintain stable
internal states despite environmental fluctuations. Absolute concentration
robustness (ACR) is a striking homeostatic phenomenon in which the steady
-state concentration of a species remains invariant despite changes in tot
al supply. In this talk\, we introduce a previously underappreciated phen
omenon\, namely asymptotic ACR (aACR): approximate robustness can emerge s
olely from the network structure\, without requiring exact ACR motifs or n
egligible parameters. We find that aACR is more pervasive than classical A
CR and prove that this ubiquity stems solely from network structure. This
notion of aACR would provide a rigorous and practical tool to analyze robu
st responses in broad biochemical systems. This is joint work with Diego R
ojas La Luz and Gheorge Craciun.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oskar Henriksson (Max Planck Institute of Molecular Cell Biology a
nd Genetics\, Dresden)
DTSTART:20260212T160000Z
DTEND:20260212T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/137
DESCRIPTION:Title: The polyhedral structure of the disguised toric locus\nby Oskar
Henriksson (Max Planck Institute of Molecular Cell Biology and Genetics\,
Dresden) as part of Seminar on the Mathematics of Reaction Networks\n\n\nA
bstract\nThe disguised toric locus of a reaction network is the set of rat
e constants for which the associated mass action system is dynamically ide
ntical to a complex-balanced mass action system. The starting point of thi
s talk is a recent result from joint work with Boros\, Craciun\, Jin\, and
Rojas La Luz (2510.03621)\, showing that the disguised toric locus is hom
eomorphic to a prism over the disguised toric flux locus\, which is a poly
hedral cone with a rich combinatorial structure. This result has both theo
retical and practical consequences: it leads to new results on the geometr
y of the disguised toric locus\, and provides a computational strategy for
explicitly computing the disguised toric locus for networks that were out
of reach with previous methods.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Jin Huang (Kyoto University)
DTSTART:20260312T160000Z
DTEND:20260312T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/138
DESCRIPTION:Title: A Structural Approach to Identifying Indicator Species in Chemical R
eaction Networks\nby Yong-Jin Huang (Kyoto University) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nCellular phenot
ypes display high diversity\, reflecting the complex functional states of
individual cells. While transcriptomics has traditionally been used to det
ermine these states\, recent advances in single-cell technologies are shif
ting interest toward more detailed classification via metabolomic phenotyp
ing\, which directly reflects cellular function. However\, the large numbe
r of metabolites poses challenges for both measurement and computational c
lustering in the task of phenotypic classification. A fundamental question
therefore arises: which subset of species suffices to represent the syste
m's overall state?\n\nThis talk introduces a novel theory that\, based sol
ely on the structural information of chemical reaction networks\, identifi
es indicator species—whose concentrations uniquely determine all others
and thus distinguish multistable equilibria. An implementing algorithm is
applied to biochemical pathway databases. Numerical experiments demonstrat
e that classification based solely on these indicator species matches or s
urpasses full-set accuracy\, with superior robustness under measurement no
ise. These results provide a rigorous\, topology-based foundation for sele
cting indicator species\, advancing metabolic phenotyping and biomarker di
scovery.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucie Laurence (University of Bern)
DTSTART:20260212T163000Z
DTEND:20260212T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/139
DESCRIPTION:Title: Noise induced stabilization in stochastic chemical reaction network<
/a>\nby Lucie Laurence (University of Bern) as part of Seminar on the Math
ematics of Reaction Networks\n\n\nAbstract\nChemical reaction networks (CR
Ns) are commonly analyzed through deterministic or stochastic models that
track molecular populations over time. In regimes with large molecule coun
ts\, stochastic dynamics are typically approximated by deterministic mass-
action kinetics. We present a CRN that defies this expectation: while the
deterministic system is unstable\, exhibiting finite-time blow-up of traje
ctories within the interior of the state space\, its stochastic counterpar
t is positive recurrent.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Cuniberti (Politecnico di Torino)
DTSTART:20260312T163000Z
DTEND:20260312T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/140
DESCRIPTION:Title: Stochastic ordering tools for reaction network models\nby Giulio
Cuniberti (Politecnico di Torino) as part of Seminar on the Mathematics o
f Reaction Networks\n\n\nAbstract\nStochastic reaction networks are mathem
atical models with a wide range of applications in biochemistry\, ecology\
, and epidemiology\, and are often complex to analyze. Except for some spe
cial cases\, it is generally difficult to predict how the abundances of al
l considered species evolve over time. A possible approach to address this
issue is to develop tools to compare the model under study with a similar
one whose behavior is better understood. The main contribution of our wor
k is to provide direct and computable conditions that can be used to ensur
e the existence of an ordered coupling between two stochastic reaction net
works and to identify which parameter changes in a given model lead to an
increase or decrease in the count of certain species. We also make an algo
rithm available that implements our theory and we illustrate it with sever
al applications. This is joint work with Daniele Cappelletti and Paola Sir
i.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaxin Jin (University of Louisiana at Lafayette)
DTSTART:20260326T160000Z
DTEND:20260326T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/141
DESCRIPTION:Title: Homeostasis Patterns and Infinitesimal Homeostasis in Reaction Netwo
rks\nby Jiaxin Jin (University of Louisiana at Lafayette) as part of S
eminar on the Mathematics of Reaction Networks\n\n\nAbstract\nHomeostasis
is a regulatory mechanism that keeps a specific variable close to a prescr
ibed value as other variables fluctuate. This notion can be formulated rig
orously when a system is modeled as an input-output network with distingui
shed input and output nodes\, where the dynamics determine the correspondi
ng input-output function. In this setting\, homeostasis can be defined inf
initesimally\, namely when the derivative of the input-output function van
ishes at an isolated point. Combined with graph-theoretic ideas from combi
natorial matrix theory\, this provides a framework for computing homeostas
is points and classifying homeostasis types. \n\nIn the first part of the
talk\, we introduce the notion of a homeostasis pattern\, a set of nodes t
hat are simultaneously infinitesimally homeostatic\, and show that all suc
h patterns can be described using a combinatorial structure associated wit
h the network\, called the homeostasis pattern network. In the second part
\, we study infinitesimal homeostasis in chemical reaction networks\, wher
e conservation laws complicate the standard analysis. We present criteria
for the existence of infinitesimal homeostasis with and without conservati
on\, and introduce the notion of infinitesimal concentration robustness\,
where the output remains nearly constant under perturbations of conserved
quantities.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Faul (University of Fribourg)
DTSTART:20260226T160000Z
DTEND:20260226T163000Z
DTSTAMP:20260404T094508Z
UID:MoRN/142
DESCRIPTION:Title: On the abelian structure of noncompetitive chemical reaction network
s\nby Louis Faul (University of Fribourg) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nCRNs of interest in biochemi
stry and systems biology are embedded in complex networks so that local CR
Ns have to respond to internal and environmental cues. We describe the net
work’s response to such perturbations using a Markov chain whose state s
pace is the set of CRN’s static states\, from where no reaction is possi
ble. We study noncompetitive CRNs\, a class of networks whose static sta
tes are rate-independent\, and is a special instance of Abelian networks
. One can thus use a unified algebraic and probabilistic framework for ana
lyzing their long-term behavior.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebeka Szabo (University of Pécs)
DTSTART:20260326T163000Z
DTEND:20260326T170000Z
DTSTAMP:20260404T094508Z
UID:MoRN/143
DESCRIPTION:Title: Discrete state deterministic approach\nby Rebeka Szabo (Universi
ty of Pécs) as part of Seminar on the Mathematics of Reaction Networks\n\
n\nAbstract\nChemical reaction networks are typically modeled using two ap
proaches: deterministic models\, which are suitable for large systems\, an
d stochastic descriptions\, which are accurate at smaller scales. However\
, the transition between these two models has been unclear. We introduce a
continuous-time\, discrete-state deterministic (CDD) approach that bridge
s this gap by using a newly introduced concept called reaction extent. A r
eaction is considered complete when its coordinate reaches an integer valu
e. Numerical simulations demonstrate the stepwise changes in concentration
and the underlying dynamics. Additionally\, this method shows potential f
or application to various types of chemical reaction systems. Joint work w
ith Gábor Lente.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hye-Won Kang (University of Maryland Baltimore)
DTSTART:20260409T153000Z
DTEND:20260409T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/144
DESCRIPTION:Title: Multiscale Approximation and Parameter Estimation in Stochastic Mode
ls of the Glycolytic Pathway\nby Hye-Won Kang (University of Maryland
Baltimore) as part of Seminar on the Mathematics of Reaction Networks\n\n\
nAbstract\nIn this talk\, I will introduce a glycolytic pathway that inclu
des multiple enzyme-catalyzed reactions. We assume that some enzymes are
present in low copy numbers and thus adopt a continuous-time Markov chain
framework to capture stochastic effects. To further reduce network complex
ity\, we apply a multiscale approximation method and derive a reduced ODE
model that describes the system's behavior on a slow timescale.\n\nThe red
uced model involves two key species and contains fewer parameters—expres
sed as functions of those in the full model--which facilitates more tracta
ble parameter estimation. Assuming that only the reduced species are obser
vable\, we generate synthetic data from the full model and use it to estim
ate the parameters in the reduced model. This approach demonstrates how ti
me-series data from a subset of species can enable effective estimation of
composite parameters in a reduced system.\n\nThis is joint work with Arna
b Ganguly.\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Wiuf (University of Copenhagen)
DTSTART:20260423T153000Z
DTEND:20260423T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/145
DESCRIPTION:by Carsten Wiuf (University of Copenhagen) as part of Seminar
on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Howells (Politecnico di Torino)
DTSTART:20260507T153000Z
DTEND:20260507T160000Z
DTSTAMP:20260404T094508Z
UID:MoRN/146
DESCRIPTION:by Aidan Howells (Politecnico di Torino) as part of Seminar on
the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gábor Szederkényi (Pazmany Peter Catholic University)
DTSTART:20260423T150000Z
DTEND:20260423T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/147
DESCRIPTION:by Gábor Szederkényi (Pazmany Peter Catholic University) as
part of Seminar on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maya Mincheva (Northern Illinois University)
DTSTART:20260507T150000Z
DTEND:20260507T153000Z
DTSTAMP:20260404T094508Z
UID:MoRN/148
DESCRIPTION:by Maya Mincheva (Northern Illinois University) as part of Sem
inar on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MoRN/148/
END:VEVENT
END:VCALENDAR