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Generalized chemical kinetic simulation method
The generalized chemical kinetic simulation method (GCKSM) is oriented to formalized, primarily portrait, description of performance pattern of arbitrary biological systems. Formalization is performed according to a block principle: a system simulated is divided into elementary subsystems to describe each subsystem individually. Elementary subsystems are described in terms of formal blocks. A formal block is uniquely characterized by an ordered list of formal dynamic variables , ordered list of formal parameters , and the law of information transformation (Fig. 1). 5 formal blocks are shown in Fig. 1. The first block describes the formal bimolecular reaction. The list of this block includes three formal variables x1, x2, and x3 that have the meanings of reaction product concentrations. The list includes two formal parameters k1 and k2, constants of the direct and reverse reactions, respectively. The law of transformation of information in this case is specified by a system of common autonomous differential equations determining the instantaneous rates of changes in x1, x2, and x3 concentrations. The laws of information transformation in blocks 2 - 5 are also specified by systems of differential equation obtained from chemical kinetic reasoning under conditions of ideal mixing. In the general case, however, GCKSM imposes no special limitations on the language describing information transformation operators, allowing continuous, discrete, arithmetic, logical, stochastic, and other transformations to be used. A particular selection is determined by the specificity of an elementary process, type of the problem to be solved, analytic methods selected for solving the problem, etc.
Note that the overall list of formal blocks that can be used while simulating actual biosystems is in no way confined (and cannot be confined principally) by the list shown. Moreover, new formal blocks may be added to the current list if necessary, expanding thereby the simulation arsenal. However, if we are limiting the simulation of biological systems to the chemical kinetic approach, these blocks are sufficient for describing the elementary processes, including the models considered below.
Within the frames of GCKSM, the modeling of an object under study is comprised out of description of elementary processes in terms of the formal blocks. In this process, each formal block used is supplied by the formal sense through identifying its formal variables and parameters. One and the same formal block may be used numerously in modeling. For example, the block “bimolecular reaction” may be used in description of any bimolecular reaction. When all elementary processes are completely described, their integrity comprises the model of an object under study. If the model consists of the formal blocks 1 - 5, then it corresponds to the system of autonomous differential equations in which dynamic variables are represented by concentrations of the system’s components (genes, proteins, mRNA, low molecular compounds, complexes, etc.). The differential form of a model is deduced by applying the principle of summing up the rates of elementary processes. The essence of this principle is that the total rate of alterations of concentrations of components in the system equals to the sum of the rates of alterations of concentration of the particular component in all elementary processes.
Calculation algorithms: The current GCKSM uses Gear’s methods for numerical integration of models.