On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure

Vlysidis, Michail; Kaznessis, Yiannis N.

doi:10.3390/e20090678

Cited by 8 publications

(5 citation statements)

References 49 publications

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“…The estimation of the higher moments in this way is denoted by the superscript S, that means that the MEP has been used, this closure scheme is known as the zero-information (ZI) closure, and has been recently used by Vlysidis and Kaznessis, using factorial moments for the Slogi chemical reaction network [ 60 ]. It does not matter to use one polynomial basis or the factorial moment basis because both polynomial and factorial basis are related by a transformation matrix.…”

Section: Results Of Applications To Chemical Reactions Networkmentioning

confidence: 99%

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Muñoz-Cobo

Berna

2019

Entropy

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In this paper first, we review the physical root bases of chemical reaction networks as a Markov process in multidimensional vector space. Then we study the chemical reactions from a microscopic point of view, to obtain the expression for the propensities for the different reactions that can happen in the network. These chemical propensities, at a given time, depend on the system state at that time, and do not depend on the state at an earlier time indicating that we are dealing with Markov processes. Then the Chemical Master Equation (CME) is deduced for an arbitrary chemical network from a probability balance and it is expressed in terms of the reaction propensities. This CME governs the dynamics of the chemical system. Due to the difficulty to solve this equation two methods are studied, the first one is the probability generating function method or z-transform, which permits to obtain the evolution of the factorial moment of the system with time in an easiest way or after some manipulation the evolution of the polynomial moments. The second method studied is the expansion of the CME in terms of an order parameter (system volume). In this case we study first the expansion of the CME using the propensities obtained previously and splitting the molecular concentration into a deterministic part and a random part. An expression in terms of multinomial coefficients is obtained for the evolution of the probability of the random part. Then we study how to reconstruct the probability distribution from the moments using the maximum entropy principle. Finally, the previous methods are applied to simple chemical networks and the consistency of these methods is studied.

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Section: Results Of Applications To Chemical Reactions Networkmentioning

confidence: 99%

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Muñoz-Cobo

Berna

2019

Entropy

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“…As a final note on the future extensions of this work, we would like to emphasise that, when dealing with non-equilibrium mesoscopic systems, we need to make a proper distinction between the predictions of the stochastic approach and those of the ODEs based on the traditional law of mass action kinetics. For example, it has been recognised that the size of the system, which does not appear in the ODEs, is an important bifurcation parameter [ 50 , 51 ]. In the context of catalytic surface reactions, a work along these lines was presented in [ 52 ].…”

Section: Discussionmentioning

confidence: 99%

Non-Equilibrium Thermodynamics and Stochastic Dynamics of a Bistable Catalytic Surface Reaction

Pineda

Stamatakis

2018

Entropy

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Catalytic surface reaction networks exhibit nonlinear dissipative phenomena, such as bistability. Macroscopic rate law descriptions predict that the reaction system resides on one of the two steady-state branches of the bistable region for an indefinite period of time. However, the smaller the catalytic surface, the greater the influence of coverage fluctuations, given that their amplitude normally scales as the square root of the system size. Thus, one can observe fluctuation-induced transitions between the steady-states. In this work, a model for the bistable catalytic CO oxidation on small surfaces is studied. After a brief introduction of the average stochastic modelling framework and its corresponding deterministic limit, we discuss the non-equilibrium conditions necessary for bistability. The entropy production rate, an important thermodynamic quantity measuring dissipation in a system, is compared across the two approaches. We conclude that, in our catalytic model, the most favorable non-equilibrium steady state is not necessary the state with the maximum or minimum entropy production rate.

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“…However, several assumptions underlying the original model were purposefully modified what changed the underlying interaction network, such as the dissociation of EGFR dimers when phosphorylated or bound to other molecules. In addition to contrasting rules to reactions, another intensively studied aspect, finalised with positive conclusions, was whether stochastic simulation can reveal new properties of a system previously modelled as deterministic one (Vlysidis and Kaznessis, 2018; Hahl and Kremling, 2016; Bustos et al, 2018). As simplistic as it may sound, none of the comparisons mentioned were intended to painstakingly disassemble reaction using the rules of a relatively medium-sized model and compare simulation results.…”

Section: Introductionmentioning

confidence: 99%

Comparison of rule- and ordinary differential equation-based dynamic model of DARPP-32 signalling network

Wysocka

Simpson

Page³

et al. 2022

Preprint

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Dynamic modelling has considerably improved our understanding of complex molecular mechanisms. Ordinary differential equations (ODEs) are the most detailed and popular approach to modelling the dynamics of molecular systems. However, their application in signalling networks, characterised by multi-state molecular complexes, can be prohibitive. Contemporary modelling methods, such as rule-based (RB) modelling, have addressed these issues. Although the advantages of RB modelling over ODEs have been presented and discussed in numerous reviews, no direct comparison of the time courses of a molecular system encoded in the two frameworks has been made before. To make such a comparison, a set of reactions that underlie an ODE model by Fernandez et al. [1] was manually encoded in the Kappa language, one of the RB frameworks. A comparison of the models was performed at the level of model specification and results were acquired through model simulations. We found that the Kappa model recapitulated the general dynamics of its ODE counterpart with minor differences. These differences occur whenever molecules have multiple sites binding the same interactor. The notation of such rules requires a complete listing of all possible binding configurations. Furthermore, activation of these molecules in the RB model is slower than in the ODE one but can be corrected by revision of the rate constants used in the relevant rules. We conclude that the RB representation offers a more expressive and flexible syntax that eases access to fine-grain details of the model, facilitating model reuse. In parallel with these analyses, this manuscript reports a refactored model of a DARPP-32 interaction network that can serve as a canvas for the development of a more complex interaction network to study this particular molecular system.

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On Differences between Deterministic and Stochastic Models of Chemical Reactions: Schlögl Solved with ZI-Closure

Cited by 8 publications

References 49 publications

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Non-Equilibrium Thermodynamics and Stochastic Dynamics of a Bistable Catalytic Surface Reaction

Comparison of rule- and ordinary differential equation-based dynamic model of DARPP-32 signalling network

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