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Abstract: Zymogen and procofactor concentrations in physiological biochemical systems (PBS) have not yet been explained. The problem in question is to determine optimal plasma clotting factor (factors II, VII, IX, and X and cofactors V and VIII) concentrations for coagulation system (CS) as a whole. Constrained optimization technique is used to solve this problem. The constraint is determined by the ability of the CS to perform its physiological function – thrombin generation (and hence clot formation) – under vessel injury conditions. The constraint statement is based on the CS dynamics equations. In solving the problem the Lagrange multiplier is used. A hypothesis is advanced that this problem can be solved based on principle of minimum protein consumption subject to an above constraint. The results obtained indicate that the optimal clotting factor concentrations are in good agreement with those measured by biochemical techniques. A comparison between the theoretical results and experimental data lends support for our hypothesis that zymogen and procofactor concentrations in the CS (and, probably, for other biochemical systems) are determined by the principle of minimum protein consumption. [Copyright &y& Elsevier]

Abstract: Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem. [Copyright &y& Elsevier]