Chemical reactions biochemical reaction networks

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... 

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. 

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. 

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. 

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. 

Hydrogen bond (HB) networks play a relevant role on the dynamics of chemical and biochemical reactions in solution. The structure of HB network is determined by many-body energy cooperativity associated with polarization effects. Electronic density fluctuations induced by thermal effects or photoexcitation, assist and drive energy transfer processes in solution [46]. An interesting aspect related to the formation of HB networks is the role that they may have played in the origin of self-organized structures associated with life [47]. Therefore, the stmcture, dynamics and more recently, the electronic properties of these complex HB networks have been the subject of several fundamental investigations. In this section, we review recent applications of MBE decomposition schemes to the calculation of the electronic absorption spectra of liquid water and HCN. 

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. 

Models for biochemical switches, logic gates, and information-processing devices that are also based on enzymic reactions but do not use the cyclic enzyme system were also introduced [76,115,117-122]. Examples of these models are presented in Table 1.3. It should also be mentioned that in other studies [108,112-114,116], models of chemical neurons and chemical neural networks based on nonenzymic chemical reactions were also introduced. 

Equations 4.42 and 4.43 present a possible explanation for the frequent occurrence in biochemical networks of sequential reactions with many steps n. For an overall reduced (dimensionless) chemical affinity of, let us say, A/RT0 = 5, the dimensionless chemical reaction rate vch/v is, according to Figure 4.3, close to 1, and the dimensionless lost work rate is the product 5 x 1 = 5, as shown in Figure 4.4. In Figure 4.3, this product is represented by the area left of the vertical axis at (A/RT0) = 5. 

The study of chemical reactions covers a variety of phenomena, ranging from the microscopic mechanisms of reaction processes through structural changes involving macromolecules such as proteins, to biochemical networks within cells. One common question concerning these seemingly diverse phenomena is how we can understand the temporal development of the system based on its dynamics. 

In a linear chemical reaction system, there is a unique steady state determined by the chemical constraints that establish the NESS. For nonlinear reactions, however, there can be multiple steady states [6]. A network comprised of many nonlinear reactions can have many steady states consistent with a given set of chemical constraints. This fact leads to the suggestion that a specific stable cellular phenotypic state can result from a specific NESS in which the steady operation of metabolic reactions maintains a balance of cellular components and products with the expenditure of biochemical energy [4]. Similarly, the network of chemical and mechanical signals that regulate the metabolic network must also be in a steady state. Important problems, then, are to determine the variety of steady states available to a system under a given set of chemical constraints and the mechanisms by which cells undergo... 

Elaborate models have been developed to account for the behavior of cellular biochemical networks. Boolean network models use a set of logical rules to illustrate the progress of the network reactions [10]. These models do not take into explicit account the participation of specific biochemical reactions. Models that account for the details of biochemical reactions have been proposed [11,12]. The behavior of these models depends on the rate constants of the chemical reactions and the concentrations of the reactants. Measurements like those described below of reaction fluxes and reactant concentrations will be able to test such network models. In the following sections, we will use simple examples to illustrate the characteristic steady-state behavior and propose an approach to measure fluxes and concentrations. 

For each set of constant input and output concentration constraints a system of linear chemical reactions has a unique steady state. For a network of nonlinear biochemical reactions, however, there could be several steady states compatible with a given set of constraints. The number and character of these steady states are determined by the structure of the network including the extent of nonlinearity, the number and connectivity of the individual chemical reactions and the values of the reaction rate constants and the concentrations of the reactants. The higher the order of a chemical reaction, the more steady states may be compatible with a given set of chemical constraints. The simple trimolecular reaction system of Schlogl [13] illustrates how a third-order chemical reaction can have two stable steady states compatible with a single set of chemical constraints ... 

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