Biochemical reaction network modeling

Biochemical Reaction Network Modeling and Gene-Protein Network Modeling... 

Mayeno AN, Yang RSH, Reisfeld B. 2005. Biochemical reaction network modeling anew tool for predicting metabolism of chemical mixtures. Environ Sci Techol 39 5363-5371. 

For exposure to multiple chemicals, PBPK modeling is further limited as a predictive tool, as all interactions among the various chemicals within the organism must be known and incorporated into the model. Difficulties in multiple-chemical exposure are clearly illustrated in drug-drug and drug-food interactions, where one substance affects the pharmacokinetics or pharmacodynamics of another. To address the need for predictive capability for individual and mixtures of chemicals, new advances and approaches are required. Biochemical reaction network modeling is one nascent approach, as described in Section 3.4. 

Reisfeld B, Mayeno AM, Yang RSH. Predictive metabolomics The use of biochemical reaction network modeling for the analysis of toxicant metabolism. Drug Metab Rev 2004 36(supplement 1) 9. 

This is not the place to expose in detail the problems and the solutions already obtained in studying biochemical reaction networks. However, because of the importance of this problem and the great recent interest in understanding metabolic networks, we hope to throw a little light on this area. Figure 10.3-23 shows a model for the metabolic pathways involved in the central carbon metabolism of Escherichia coli through glycolysis and the pentose phosphate pathway [22]. 

Many methods have been developed for model analysis for instance, bifurcation and stability analysis [88, 89], parameter sensitivity analysis [90], metabolic control analysis [16, 17, 91] and biochemical systems analysis [18]. One highly important method for model analysis and especially for large models, such as many silicon cell models, is model reduction. Model reduction has a long history in the analysis of biochemical reaction networks and in the analysis of nonlinear dynamics (slow and fast manifolds) [92-104]. In all cases, the aim of model reduction is to derive a simplified model from a larger ancestral model that satisfies a number of criteria. In the following sections we describe a relatively new form of model reduction for biochemical reaction networks, such as metabolic, signaling, or genetic networks. 

Yang RSH, Mayeno AN, Lyons M, Reisfeld B. 2010. The application of physiologically-based pharmacokinetics (PBPK), Bayesian population PBPK modeling, and biochemical reaction network (BRN) modeling to chemical mixture toxicology. In Mumtaz M, editor, Principles and practices of mixture toxicology. Hoboken (NJ) John Wiley Sons. 

Bruggeman, F.J., Bakker, B.M., Homberg, J.J. and Westerhoff, H.V. (2005a) Introduction to computational models of biochemical reaction networks. In Computational Systems Biology. A. Kriete and R. Eils, eds. (London, UK Elsevier Academic Press), pp. 127-148. 

As discussed earlier, PBPK modeling has limitations when applied to chemical mixtures in which significant (xenobiotics and endogenous) chemical-chemical interactions are expected. An approach to address this issue is biochemical reaction network (BRN) modeling and integrated models that combine PBPK and BRN models. These approaches are described below. 

Another two key concepts in metabolic engineering are metabolic pathway analysis and metabolic pathway modeling. The former is used for assessing inherent network properties in the complete biochemical reaction networks. It involves identification of the metabolic network structure (or pathway topology), quantification of the fluxes through the branches of the metabolic network, and identification of the control structures within the metabolic network. 

We should identify or classify classes of network structures that, from their structures alone, it is possible to tell whether they have the capacity to exhibit certain behavior. Given a biochemical reaction network, we can ask the following question Under which circumstances would this network exhibit phenomena like periodic oscillations and/or bistability For example, we would want to know the answer to this question when modeling the cell division cycle and circadian rhythm where periodic oscillations are required. For mass-action kinetics models, an extensive theoretical work already exists that answers this type of question for large classes of reaction networks. One such set of results is the deficiency theory.The deficiency 8 of a reaction... 

A particularly challenging problem is the understanding and modeling of biochemical and metabolic reactions, and even more so of metabolic reaction networks. Much work will go into this field in the next few years. 

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

The general theory is now reduced to a toy model , using the following assumption there are simple, arbitrary rules for the probability of a molecular interaction. The complex network of biochemical reaction chains is expressed by one single formula. 

As outlined in the previous section, there is a hierarchy of possible representations of metabolism and no unique definition what constitutes a true model of metabolism exists. Nonetheless, mathematical modeling of metabolism is usually closely associated with changes in compound concentrations that are described in terms of rates of biochemical reactions. In this section, we outline the nomenclature and the essential steps in constructing explicit kinetic models of metabolic networks. 

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. 

The crucial step in model building is model formulation, since the mathematical modeling is intended to represent a large network of multiple biochemical reactions, controlled by complex regulatory processes that... 

Crampin EJ, Schnell S (2004) New approaches to modelling and analysis of biochemical reactions, pathways and networks. Prog Biophys Mol Biol 86(1 ) l-4... 

Part II of this book represents the bulk of the material on the analysis and modeling of biochemical systems. Concepts covered include biochemical reaction kinetics and kinetics of enzyme-mediated reactions simulation and analysis of biochemical systems including non-equilibrium open systems, metabolic networks, and phosphorylation cascades transport processes including membrane transport and electrophysiological systems. Part III covers the specialized topics of spatially distributed transport modeling and blood-tissue solute exchange, constraint-based analysis of large-scale biochemical networks, protein-protein interactions, and stochastic systems. 

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

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