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1.
Bull Math Biol ; 84(6): 65, 2022 05 11.
Artigo em Inglês | MEDLINE | ID: mdl-35545688

RESUMO

We consider a natural class of reaction networks which consist of reactions where either two species can inactivate each other (i.e., sequestration), or some species can be transformed into another (i.e., transmutation), in a way that gives rise to a feedback cycle. We completely characterize the capacity of multistationarity of these networks. This is especially interesting because such networks provide simple examples of "atoms of multistationarity", i.e., minimal networks that can give rise to multiple positive steady states.


Assuntos
Redes e Vias Metabólicas , Modelos Biológicos , Cinética , Conceitos Matemáticos
2.
Bull Math Biol ; 81(4): 1143-1172, 2019 04.
Artigo em Inglês | MEDLINE | ID: mdl-30599071

RESUMO

We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (1) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (2) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ-OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness, as we demonstrate for the EnvZ-OmpR pathway.


Assuntos
Redes e Vias Metabólicas , Modelos Biológicos , Proteínas da Membrana Bacteriana Externa/metabolismo , Proteínas de Bactérias/metabolismo , Fenômenos Bioquímicos , Proteínas de Escherichia coli/metabolismo , Histidina Quinase/metabolismo , Cinética , Conceitos Matemáticos , Complexos Multienzimáticos/metabolismo , Transdução de Sinais , Biologia de Sistemas , Transativadores/metabolismo , Via de Sinalização Wnt
3.
J Math Biol ; 72(1-2): 467-98, 2016 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-25986743

RESUMO

We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic is known to lead to persistence and permanence of chemical species under genetic kinetic assumptions, while the same result is conjectured but as yet unproved for general endotactic networks. The algorithms we present are the first capable of verifying endotacticity of chemical reaction networks for systems with greater than two constituent species. We implement the algorithms in the open-source online package CoNtRol and apply them to a large sample of networks from the European Bioinformatics Institute's BioModels Database. We use strong endotacticity to establish for the first time the permanence of a well-studied circadian clock mechanism.


Assuntos
Fenômenos Bioquímicos , Modelos Biológicos , Algoritmos , Animais , Relógios Circadianos , Cinética , Conceitos Matemáticos , Redes e Vias Metabólicas , Fosforilação , Programação Linear , Biologia de Sistemas
4.
Bioinformatics ; 30(11): 1633-4, 2014 Jun 01.
Artigo em Inglês | MEDLINE | ID: mdl-24489373

RESUMO

UNLABELLED: We introduce CoNtRol, a web-based framework for analysis of chemical reaction networks (CRNs). It is designed to be both extensible and simple to use, complementing existing CRN-related tools. CoNtRol currently implements a number of necessary and/or sufficient structural tests for multiple equilibria, stable periodic orbits, convergence to equilibria and persistence, with the potential for incorporation of further tests. AVAILABILITY AND IMPLEMENTATION: Reference implementation: reaction-networks.net/control/. Source code and binaries, released under the GPLv3: reaction-networks.net/control/download/. Documentation: reaction-networks.net/wiki/CoNtRol.


Assuntos
Modelos Químicos , Software , Internet
5.
Math Biosci ; 326: 108387, 2020 08.
Artigo em Inglês | MEDLINE | ID: mdl-32470445

RESUMO

Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the delay parameters. Several interesting examples on sequestration networks with delays are presented.


Assuntos
Modelos Biológicos , Fenômenos Bioquímicos , Retroalimentação Fisiológica , Cinética , Modelos Lineares , Conceitos Matemáticos , Transdução de Sinais , Biologia de Sistemas
6.
Math Biosci Eng ; 16(6): 8243-8267, 2019 09 16.
Artigo em Inglês | MEDLINE | ID: mdl-31698666

RESUMO

Mass-action kinetics and its generalizations appear in mathematical models of (bio)chemical reaction networks, population dynamics, and epidemiology. The dynamical systems arising from directed graphs are generally non-linear and difficult to analyze. One approach to studying them is to find conditions on the network which either imply or preclude certain dynamical properties. For example, a vertex-balanced steady state for a generalized mass-action system is a state where the net flux through every vertex of the graph is zero. In particular, such steady states admit a monomial parametrization. The problem of existence and uniqueness of vertex-balanced steady states can be reformulated in two different ways, one of which is related to Birch's theorem in statistics, and the other one to the bijectivity of generalized polynomial maps, similar to maps appearing in geometric modelling. We present a generalization of Birch's theorem, by providing a sufficient condition for the existence and uniqueness of vertex-balanced steady states.


Assuntos
Simulação por Computador , Modelos Teóricos , Teoria de Sistemas , Algoritmos , Cinética , Conceitos Matemáticos , Modelos Químicos , Fosforilação , Termodinâmica
7.
Commun Stat Simul Comput ; 42(1): 121-137, 2013 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-23125476

RESUMO

We describe a statistical method for predicting most likely reactions in a biochemical reaction network from the longitudinal data on species concentrations. Such data is relatively easily available in biochemical laboratories, for instance, via the popular RT-PCR technology. Under the assumed kinetics of the law of mass action, we also propose the data-based algorithms for estimating the prediction errors and for network dimension reduction. The second algorithm allows in particular for the application of the original algebraic inferential procedure described in [4] without the unnecessary restrictions on the dimension of the network stoichiometric space. Simulated examples of biochemical networks are analyzed, in order to assess the proposed methods' performance.

8.
Comput Biol Chem ; 33(5): 361-7, 2009 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-19709932

RESUMO

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current method, unlike some of the graphical approaches proposed in the literature, uses the values of the experimental measurements only relative to the geometry of the biochemical reactions under the assumption that the underlying reaction network is the same for all the experiments. The proposed approach utilizes algebraic statistical methods in order to parametrize the set of possible reactions so as to identify the most likely network structure, and is easily scalable to very complicated biochemical systems involving a large number of species and reactions. The method is illustrated with a numerical example of a hypothetical network arising from a "mass transfer"-type model.


Assuntos
Biologia Computacional , Simulação por Computador , Modelos Estatísticos , Algoritmos , Funções Verossimilhança
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