Biochemical reaction networks

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]. 

Reactive systems form the core of chemistry and most biological functions are based on the operation of complex biochemical reaction networks. In dealing... 

Different from conventional chemical kinetics, the rates in biochemical reactions networks are usually saturable hyperbolic functions. For an increasing substrate concentration, the rate increases only up to a maximal rate Vm, determined by the turnover number fccat = k2 and the total amount of enzyme Ej. The turnover number ca( measures the number of catalytic events per seconds per enzyme, which can be more than 1000 substrate molecules per second for a large number of enzymes. The constant Km is a measure of the affinity of the enzyme for the substrate, and corresponds to the concentration of S at which the reaction rate equals half the maximal rate. For S most active sites are not occupied. For S >> Km, there is an excess of substrate, that is, the active sites of the enzymes are saturated with substrate. The ratio kc.AJ Km is a measure for the efficiency of an enzyme. In the extreme case, almost every collision between substrate and enzyme leads to product formation (low Km, high fccat). In this case the enzyme is limited by diffusion only, with an upper limit of cat /Km 108 — 109M. v 1. The ratio kc.MJKm can be used to test the rapid... 

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. 

E. Klipp, W. Liebermeister, and C. Wierling, Inferring dynamic properties of biochemical reaction networks from structural knowledge. Gen. Inform. Ser. 15(1), 125 137 (2004). 

S. L. Bell and B. 0. Palsson, Expa A program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21(8), 1739 1740 (2005). 

A. Arkin and J. Ross, Computational functions in biochemical reaction networks, Biophys. J., 67, 560-578 (1994). 

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. 

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

Prediction of both qualitative and quantitative biochemical reaction networks, for chemicals outside of the training set but within the chemical class, including chemical mixtures, is possible at this stage. The confidence level for such predictions will increase as more and more validations are made. 

Figure 5.12 The principle of tiering in risk assessment simple questions can be answered by simple methods that yield conservative answers, and more complex questions require more sophisticated methods, more data, and more accurate risk predictions. PEC = Predicted Environmental Concentration, PNEC = Predicted No Effect Concentration, HI = Hazard Index, CA = Concentration Addition, RA = Response Addition, TEF = Toxicity Equivalency Factor, RPF = Relative Potency Factor, MOA = Mode of Action, PBPK = Physiologically Based Pharmacokinetic, BRN = Biochemical Reaction Network.

BRN Biochemical reaction network. A system of biochemical reactions that interact with each other. 

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. 

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. 

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