Reaction network analysis

The screen for each chemical kinetic calculation simultaneously displays a variety of characterizations in multiple windows and allows analysis of time/temperature-dependent species and reaction information including species concentrations, species steady-state analysis, individual reaction rates, net production/destruction rates, reaction equilibrium analysis and the temperature/time history of the system. The interactive user-sorting of the species and reaction information from the numerical simulations is mouse/cursor driven. An additional feature also allows interactive analysis and identification of dependent and independent species and reaction pathways, on-line reaction network analysis and pathway/flowchart construe-... 

Reaction network analysis. The kinetics and mechanism of water-gas-shift reaction on Cu(lll)... 

Now that the basic principles of the reaction network analysis have been enumerated, we proceed to analyze in detail the water-gas shift reaction (WGSR) microkinetic model. Due to its industrial significance, the catalysis and kinetics of the WGSR has been a key example in microkinetic modeling [17-26]. In the meantime, we have shown [13,14] that reliable microkinetic models for the WGSR on Cu(lll) may be developed based on rather rudimentary kinetic considerations. 

The error in the conversion of CO provided by this overall rate equation is virtually zero as compared with the exact microkinetic model, which points to the robustness of the reaction network analysis approach presented here. 

Reaction network analysis as a means to study the hierarchy and interconnectedness of industrial processes to commodity chemicals... 

Sheen, D.A., Manion, J.A. Kinetics of the reactions of H and CH3 radicals with n-butane An experimental design study using reaction network analysis J. Phys. Chem. A, 118,4929-4941 (2014)... 

To recognize the different levels of representation of biochemical reactions To understand metabolic reaction networks To know the principles of retrosynthetic analysis To understand the disconnection approach To become familiar with synthesis design systems... 

One useful trick in solving complex kinetic models is called the steady-state approximation. The differential equations for the chemical reaction networks have to be solved in time to understand the variation of the concentrations of the species with time, which is particularly important if the molecular cloud that you are investigating is beginning to collapse. Multiple, coupled differentials can be solved numerically in a fairly straightforward way limited really only by computer power. However, it is useful to consider a time after the reactions have started at which the concentrations of all of the species have settled down and are no longer changing rapidly. This happy equilibrium state of affairs may never happen during the collapse of the cloud but it is a simple approximation to implement and a place to start the analysis. 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

A kinetics analysis, if not available a priori, leading to a reaction network with specified associated rate laws, together with values of the rate parameters, including their dependence on T. 

It can be straightforwardly verified that indeed NK = 0. Each feasible steady-state flux v° can thus be decomposed into the contributions of two linearly independent column vectors, corresponding to either net ATP production (k ) or a branching flux at the level of triosephosphates (k2). See Fig. 5 for a comparison. An additional analysis of the nullspace in the context of large-scale reaction networks is given in Section V. 

Stoichiometric analysis goes beyond topological arguments and takes the specific physicochemical properties of metabolic networks into account. As noted above, based on the analysis of the nullspace of complex reaction networks, stoichiometric analysis has a long history in the chemical and biochemical sciences [59 62]. At the core of all stoichiometric approaches is the assumption of a stationary and time-invariant state of the metabolite concentrations S°. As already specified in Eq. (6), the steady-state condition... 

Besides the two most well-known cases, the local bifurcations of the saddle-node and Hopf type, biochemical systems may show a variety of transitions between qualitatively different dynamic behavior [13, 17, 293, 294, 297 301]. Transitions between different regimes, induced by variation of kinetic parameters, are usually depicted in a bifurcation diagram. Within the chemical literature, a substantial number of articles seek to identify the possible bifurcation of a chemical system. Two prominent frameworks are Chemical Reaction Network Theory (CRNT), developed mainly by M. Feinberg [79, 80], and Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83]. An analysis of the (local) bifurcations of metabolic networks, as determinants of the dynamic behavior of metabolic states, constitutes the main topic of Section VIII. In addition to the scenarios discussed above, more complicated quasiperiodic or chaotic dynamics is sometimes reported for models of metabolic pathways [302 304]. However, apart from few special cases, the possible relevance of such complicated dynamics is, at best, unclear. Quite on the contrary, at least for central metabolism, we observe a striking absence of complicated dynamic phenomena. To what extent this might be an inherent feature of (bio)chemical systems, or brought about by evolutionary adaption, will be briefly discussed in Section IX. 

An early systematic approach to metabolism, developed in the late 1970s by Kacser and Burns [313], and Heinrich and Rapoport [314], is Metabolic Control Analysis (MCA). Anticipating systems biology, MCA is a quantitative framework to understand the systemic steady-state properties of a biochemical reaction network in terms of the properties of its component reactions. As emphasized by Kacser and Burns in their original work [313],... 

Although the importance of a systemic perspective on metabolism has only recently attained widespread attention, a formal frameworks for systemic analysis has already been developed since the late 1960s. Biochemical Systems Theory (BST), put forward by Savageau and others [142, 144 147], seeks to provide a unified framework for the analysis of cellular reaction networks. Predating Metabolic Control Analysis, BST emphasizes three main aspects in the analysis of metabolism [319] (i) the importance of the interconnections, rather than the components, for cellular function (ii) the nonlinearity of biochemical rate equations (iii) the need for a unified mathematical treatment. Similar to MCA, the achievements associated with BST would warrant a more elaborate treatment, here we will focus on BST solely as a tool for the approximation and numerical simulation of complex biochemical reaction networks. 

Closely related to the approach considered here are the formal frameworks of Feinberg and Clarke, briefly mentioned in Section II. A. Though mainly devised for conventional chemical kinetics, both, Chemical Reaction Network Theory (CRNT), developed by M. Feinberg and co-workers [79,80], as well as Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83], seek to relate aspects of reaction network topology to the possibility of various... 

B. L. Clarke, Stability analysis of a model reaction network using graph theory. J. Chem. Phys. 60(4), 1493 1501 (1974). 

John Ross, Igor Schreiber, Marcel O. Vlad, and Adam Arkin. Determination of Complex Reaction Mechanisms Analysis of Chemical, Biological, and Genetic Networks. Oxford University Press 2005... 

Fig. 9.4 Reaction network for the formation of CVD binder carbon during the synthesis of a C3 material from methane. The supporting data were collected from model experiments with carbon-coated ceramic channels and consecutive gas analysis as described [31,32] in the literature. The colored boxes indicate the main reactive intermediates.

The fast stage of relaxation of a complex reaction network could be described as mass transfer from nodes to correspondent attractors of auxiliary dynamical system and mass distribution in the attractors. After that, a slower process of mass redistribution between attractors should play a more important role. To study the next stage of relaxation, we should glue cycles of the first auxiliary system (each cycle transforms into a point), define constants of the first derivative network on this new set of nodes, construct for this new network an (first) auxiliary discrete dynamical system, etc. The process terminates when we get a discrete dynamical system with one attractor. Then the inverse process of cycle restoration and cutting starts. As a result, we create an explicit description of the relaxation process in the reaction network, find estimates of eigenvalues and eigenvectors for the kinetic equation, and provide full analysis of steady states for systems with well-separated constants. 

In multiscale asymptotic analysis of reaction network we found several very attractive zero-one laws. First of all, components eigenvectors are close to 0 or +1. This law together with two other zero-one laws are discussed in Section 6 "Three zero-one laws and nonequilibrium phase transitions in multiscale systems". 

A multiscale system where every two constants have very different orders of magnitude is, of course, an idealization. In parametric families of multiscale systems there could appear systems with several constants of the same order. Hence, it is necessary to study effects that appear due to a group of constants of the same order in a multiscale network. The system can have modular structure, with different time scales in different modules, but without separation of times inside modules. We discuss systems with modular structure in Section 7. The full theory of such systems is a challenge for future work, and here we study structure of one module. The elementary modules have to be solvable. That means that the kinetic equations could be solved in explicit analytical form. We give the necessary and sufficient conditions for solvability of reaction networks. These conditions are presented constructively, by algorithm of analysis of the reaction graph. 

In this subsection, we summarize results of relaxation analysis and describe the algorithm of approximation of steady state and relaxation process for arbitrary reaction network with well-separated constants. 

The general case of solvable systems is essentially a combination of that two Equations (79) and (80), with some generalization. Here we follow the book by Gorban et al. (1986) and present an algorithm for analysis of reaction network solvability. First, we introduce a relation between reactions "rth reaction directly affects the rate of sth reaction" with notation r s r s if there exists such A, that This means that concentration of A, changes in the rth reaction... 

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