Quantitative biochemical kinetic models

The next step in formulating a kinetic model is to express the stoichiometric and regulatory interactions in quantitative terms. The dynamics of metabolic networks are predominated by the activity of enzymes proteins that have evolved to catalyze specific biochemical transformations. The activity and specificity of all enzymes determine the specific paths in which metabolites are broken down and utilized within a cell or compartment. Note that enzymes do not affect the position of equilibrium between substrates and products, rather they operate by lowering the activation energy that would otherwise prevent the reaction to proceed at a reasonable rate. 

A., et al. BioModels database a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res. 2006, 34 D689-D691. 

Chemical Biophysics Quantitative Analysis of Cellular Systems by Daniel Beard and Hong Qian Alls a significant niche. The text is a concise yet clear exposition of the fundamentals of chemical thermodynamics and kinetics, aimed specifically at practitioners of the new science of systems biology. It is marvelously illustrated with biochemical examples that will aid those who aim to analyze and model the workings of biological cells. 

A critical problem in the application of pharmacokinetic principles to risk extrapolation is the potential change in metabolism or other biochemical reactions as external exposure levels of the toxic agent decrease. Linear pharmacokinetic models are often used. However, there are numerous examples of nonlinear behavior in the dose range studied, and these nonlinear kinetics pose significant problems for quantitative extrapolation from "high" to "low" doses if the kinetic parameters are not measured (27-29). 

SECM images contain information about both local reactivity and the topography of the sample surface. However, it is our opinion that the greatest utility of SECM in biological and biochemical investigations is its ability to map chemical species and reactivity (i.e., processes) rather than topography. Since the theoretical models of SECM are based on established electrochemical principles, the data can often be interpreted in a quantitative manner, and kinetic investigations at fixed lateral tip position are possible with a time resolution of ms or better. 

First consider the mathematical descriptions of cell kinetics which define the drug effects for cancer chemotherapy. Quantitative models to describe mammalian (or other) cell growth and death are still relatively crude. Although the complicated biochemical events leading to DNA and other chemical production, cell mitosis, and population growth have been studied qualitatively in some depth and quantitative aspects of some reactions are known, synthesis of this with a comprehensive description has not yet been completely accomplished. 

While many researchers have focused on the tools of molecular biology and genetics to determine biochemical mechanisms of nutrient action in animal models, a few have focused on mathematical modeling of kinetic data to achieve a quantitative understanding of the dynamics of nutrient metabolism in vivo (for recent symposia, see Abumrad, 1991 Coburn, 1992). Three recent developments stimulated interest in mathematical modeling. First, there is an opportunity to integrate quantitative characteristics of the dynamics of nutrient metabolism with knowledge of nutrient action mechanisms and health status. Second, it appears that some animal models do not mimic nutrient metabolism and health status of humans. Third, stable isotope tracers and reliable methods to measure minute amounts of them in human tissues have become more readily available. 

As stated, a number of PBPK/PD models have been developed for individual nerve agents (sarin, VX, soman, and cyclosarin) in multiple species. Chapter 58 in the current volume discusses tiie development of such models. Standalone PBPK or compartmental models have also been developed that describe the pharmacokinetics of certain countermeasures, such as diazepam (Igari et al., 1983 Gueorguieva et al., 2004) and oximes (Stemler et al., 1990 Sterner et al., 2013). However, to date, few models for specific countermeasures have been harmonized and linked to NA PBPK/PD models to be able to quantitatively describe their pharmacokinetic and pharmacodynamic interactions. This is partly due to the fact that most PBPK/ PD models developed for NAs and other OPs focus on the inhibition of ChEs as the critical endpoint. The lack of a mathematical description of the disruption of other complex biochemical pathways presents a problem for linking these NA models to those of many countermeasures. For example, the conventional NA countermeasures, atropine and diazepam, as well as many novel countermeasures, do not directly impact ChE kinetics because they act at sites distinct from the active site of the esterases, such as muscarinic, GABA, or NMDARs (Figure 69.2). 

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