Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time-averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ～ N(β) with β = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.     

Positions of steady states in two-component chemical systems

The general kinetic equation for two-component chemical systems is analyzed. It is shown that the positions of steady states in concentration spaces can be detected by a qualitative analysis of the chemical mechanism.

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Dynamics of chemical reactions and nonphysical steady states

Data on the position of nonphysical (lying beyond the region of determination) steady states are shown to be of use for understanding the dynamic behavior of chemical reactions, in particular, the reasons for slow relaxations.

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Dynamic properties of a heterogeneous catalytic reaction with several steady states

For the simplest catalytic mechanism (three-stage) permitting several steady states of the surface, a qualitative analysis of the properties of its kinetic model trajectories has been performed. Types of the steady states have been determined. Absence of oscillations (damped and undamped) has been shown.

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Для простейшего каталитического механизма (трехстадийного), допускающего несколько стационарных состояний поверхности, проведен качественный анализ свойств траекторий его кинетической модели. Определены типы стационарных состояний. Показано отсутствие осцилляций (затухающих и незатухающих).

     

Identifiability of chemical reaction networks

We consider the dynamics of chemical reaction networks under the assumption of mass-action kinetics. We show that there exist reaction networks for which the reaction rate constants are not uniquely identifiable, even if we are given complete information on the dynamics of concentrations for all chemical species of . Also, we show that there exist reaction networks such that their dynamics are identical under appropriate choices of reaction rate constants, and present theorems that characterize the properties of , , that make this possible. We use these facts to show how we can determine dynamical properties of some chemical networks by analyzing other chemical networks.     

Reachability,persistence, and constructive chemical reaction networks (part I): reachability approach to the persistence of chemical reaction networks

For a chemical reaction network, persistence is the property that no species tend to extinction if all species are initially present. We investigate the stronger property of vacuous persistence: the same asymptotic feature with a weaker requirement on initial states, namely that all species be implicitly present. By implicitly present, we mean for instance that if only water is present and the reaction network incorporates the information that water is made of hydrogen and oxygen, then hydrogen and oxygen are implicitly present. Persistence is inherently interesting and has implications for the global asymptotic stability of equilibrium states. Our main tools are the work of A. I. Vol’pert on the nullity and positivity of species concentrations, and the enabling notion of reachability. The main result states that a reaction network is vacuously persistent if and only if the set of all species is the only set of species that both is closed with respect to reachability and causes the implicit presence of all species. This paper is the first in a series of three articles. Two sequel papers introduce additional formalisms and use them to describe two large classes of reaction networks that are used as models in biochemistry and are vacuously persistent.     

Analysis of fluctuations in chemical reactions with several steady states

The effect of fluctuations in nonequilibrium systems is treated in terms of the stochastic theory. A solution of the fundamental equation is analyzed using the Monte-Carlo method /1, 2/. The results are compared with the conclusions following from the equations corresponding to a phenomenological model.

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Linear conjugacy of chemical reaction networks

Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant species. It is known that two networks may possess the same governing mass-action dynamics despite disparate network structure. To date, however, there has only been limited work exploiting this phenomenon even for the cases where one network possesses known dynamics while the other does not. In this paper, we bring these known results into a broader unified theory which we call conjugate chemical reaction network theory. We present a theorem which gives conditions under which two networks with different governing mass-action dynamics may exhibit the same qualitative dynamics and use it to extend the scope of the well-known theory of weakly reversible systems.     

Predictive chemical kinetics: Density functional and hartree–fock calculations on free-radial reaction transition states

Density functional theory (DFT ) using gradient-corrected «nonlocal» functionals is used to calculated the thermochemistry and barrier heights for several types of peroxyl radical isomerizations currently being studied by kineticists. The calculations are generally in good agreement with experimental data, where such data are available. An important exception is that the O—H bond strengths in hydroperoxides are all predicted to be too weak by about 7 kcal/mol. The calculated reaction barriers are a few kcal/mol lower than the experimental estimates, but comparable in accuracy to the much more computationally expensive second-order Møller–Plesset (MP 2) predictions. Various theoretical methods converge on a 42 ± 2 kcal/mole barrier for CH₃OO → H₂CO + OH. The DFT calculations can be used to predict reaction barriers in cases where no reliable experimental data are available. The effects of the choice of basis set and correlation functional are explored. Improvements needed to make these calculations most valuable to the chemical kineticist are discussed. © 1994 John Wiley & Sons, Inc.     

A possible construction of chemical reaction networks

The chemical reaction networks and the sequence networks represent the pathways of a complex chemical process. In order to study the pathways separately the systematization of the elementary processes included in the possible mechanism is inevitable.This systematization was realized by a special procedure based on linear algebraic methods and enabled us to select the corresponding processes from the possible mechanism. The efficiency of the procedure has been illustrated by its application to the liquid phase oxidation of ethylbenzene and the elementary processes have been selected using a computer program.     

Reduction of chemical reaction networks using quasi-integrals

We present a numerical method to identify possible candidates for quasi-stationary manifolds in complex reaction networks governed by systems of ordinary differential equations. Inspired by singular perturbation theory, we examine the ratios of certain components of the reaction rate vector. Those ratios that rapidly approach a nearly constant value define a slow manifold for the original flow in terms of quasi-integrals, that is, functions that are nearly constant along the trajectories. The dimensionality of the original system is thus effectively reduced without reliance on a priori knowledge of the different time scales in the system. We also demonstrate the relation of our approach to singular perturbation theory which, in its simplest form, is just the well-known quasi-steady-state approximation. In two case studies, we apply our method to oscillatory chemical systems: the 6-dimensional hemin-hydrogen peroxide-sulfite pH oscillator and a 10-dimensional mechanistic model for the peroxidase-oxidase (PO) reaction system. We conjecture that the presented method is especially suited for a straightforward reduction of higher dimensional dynamical systems where analytical methods fail to identify the different time scales associated with the slow invariant manifolds present in the system.     

Atoms of multistationarity in chemical reaction networks

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this question is ‘yes’ in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace. We also prove an analogous result when a smaller network is obtained from a larger network by ‘removing species.’ Our results provide the mathematical foundation for a technique used by Siegal- Gaskins et al. of establishing bistability by way of ‘network ancestry.’ Additionally, our work provides sufficient conditions for establishing multistationarity by way of atoms and moreover reduces the problem of classifying multistationary CFSTRs to that of cataloging atoms of multistationarity. As an application, we enumerate and classify all 386 bimolecular and reversible two-reaction networks. Of these, exactly 35 admit multiple positive steady states. Moreover, each admits a unique minimal multistationary subnetwork, and these subnetworks form a poset (with respect to the relation of ‘removing species’) which has 11 minimal elements (the atoms of multistationarity).     

Reactant subspaces and kinetics of chemical reaction networks

This paper studies a chemical reaction network’s (CRN) reactant subspace, i.e. the linear subspace generated by its reactant complexes, to elucidate its role in the system’s kinetic behaviour. We introduce concepts such as reactant rank and reactant deficiency and compare them with their analogues currently used in chemical reaction network theory. We construct a classification of CRNs based on the type of intersection between the reactant subspace R and the stoichiometric subspace S and identify the subnetwork of S-complexes, i.e. complexes which, when viewed as vectors, are contained in S, as a tool to study the network classes, which play a key role in the kinetic behaviour. Our main results on new connections between reactant subspaces and kinetic properties are (1) determination of kinetic characteristics of CRNs with zero reactant deficiency by considering the difference between (network) deficiency and reactant deficiency, (2) resolution of the coincidence problem between the reactant and kinetic subspaces for complex factorizable kinetics via an analogue of the generalized Feinberg–Horn theorem, and (3) construction of an appropriate subspace for the parametrization and uniqueness of positive equilibria for complex factorizable power law kinetics, extending the work of Müller and Regensburger.     

Polynomial time algorithms to determine weakly reversible realizations of chemical reaction networks

Weak reversibility is a crucial structural property of chemical reaction networks (CRNs) with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given CRN. They are based on linear programming and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks, too.     

Fluctuation theorem for entropy production in a chemical reaction channel

Fluctuation theorem for entropy production in a mesoscopic chemical reaction network is discussed. When the system size is sufficiently large, it is found that, by defining a kind of coarse-grained dissipation function, the entropy production in a reversible reaction channel can be approximately described by a type of detailed fluctuation theorem. Such a fluctuation relation has been successfully tested by direct simulations in a linear reaction model consisting of two reversible channels and in an oscillat...     

Some consequences of thermodynamic feasibility for chemical reaction networks

Power law dynamics is used to describe the stability behavior in metabolic networks such as chemical reaction networks (CRN’s). These systems allow multiple steady states within a single stoichiometric class. On the other side thermodynamic constraints such as loop-less fluxes represented by the Gorban theorem of alternatives applied to these networks reveal considerable restrictions to their dynamics by eliminating multistability of CRN’s in general. Thermodynamic feasible CRN’s are contained in the class of injective CRN’s. We can give an alternative proof of the detailed balance with Brewer’s Fixed Point Theorem. Furthermore we can derive by the loop-less principle the extended detailed balance. This paper establishes a link between recent research in CRN theory and thermodynamic basics. The result has also consequences for the picture of multiple steady states as assumed for cell differentiation and regulation. CRN’s provide from their perspective not enough means to maintain multistability without regulation or external control.