Kinetic theory and mathematical model of cell metabolism

Abstract

1. A differential equation of the kinetics of metabolic systems is formulated $$\frac{{dn_i }}{{dt}} = \mathop \sum \limits_j J_{ji} - \mathop \sum \limits_k J_{ik} $$ whereni is the quantity of a metabolite in a comparment i,Jji the influx from j to i andJik the outflux from i to k. 2. The fluxesJji orJik can be described as the product of throttling factor × intensive factor. The thermodynamical nature of the intensive factor is considered and the idea of quasi-equilibrium introduced. 3. The notion of parametric action is outlined. Rate processes concerned with the flexibility of the throttling factor are considered as transmission of information; this facilitates an investigation of the parametric interaction or informational correlation in chemical reaction systems. 4. The flexibility of the throttling factor reveals that the equation of kinetics is non-linear. Any feedback system has to be represented by such non-linear equations. 5. There are some cases in which non-linear behaviour may be represented approximately by a step-function; therefore, finite theory may be useful in such systems. 6. Since the limit of applicability of the continuous analysis based on differential equations of kinetics is well appreciated, binary functions or parameters are introduced into the equation of kinetics in order to unify the two types of analysis, finite and continuous. A hybrid computing system is used for this purpose. 7. Kinetics of mRNA and repressor formation is especially considered and an appropriate hybrid system suggested. In simplifying this system the switching circuit model proposed previously is obtained. 8. A mathematical model of cell differentiation is proposed. A flip-flop circuit is assumed, composed of reactions at the genetic and other levels under the influence of inducible enzymes. The continuous kinetics in this model cell may function only under the control of such a molecular automaton. 9. A pattern of active (1) or inactive (0) states of DNA (101001 ...) may be superimposed upon the information at the genetic level. Cell differentiation is the most striking and permanently lasting variation of this pattern. In addition, temporal variations (repression and induction; open or closed states) which may be of physiological significance, are considered. 10. Energy for parametric action must be distinguished from energy for the response. The relation between entropy of activation and negative entropy of information, e. g. of DNA, is discussed. 11. In the appendices (I to III) thermodynamics of an open system are discussed; a thermodynamical function, such as a chemical potential in a dynamical system, is logically defined. Finally, the maximum principle and the importance of cybernetics are discussed.