196
G. DETCHEV, and A. MOSKONA t
We look upon the two regulatory mechanisms as co-operating to
attain their ends-an optimal selfregulation of cell metabolism in such a
way as to work with minimum dissipation of free energy. This common
aim was formulated by us at the last symposium on quantitative biology of
metabolism on Helgoland [2].
To elaborate the problem we search for the most natural method of
describing the synthetic evolution of interrelations and the common functional organization of metabolism by means of appropriate mathematics.
Since sufficient kinetic data about metabolic processes are still lacking, we
select a thermodynamic method which adequately treats the liberation and
utilization of energy in the living cell, irrespective of the underlying mechanisms of molecular interactions. The additional application of formal
kinetics in considering the problem offers us, on the other hand, the possibility of a constant source of new biochemical conceptions with reference
to the functional cell organization.
When making use of the thermodynamics of irreversible processes we
encounter difficulties of a fundamental nature:
(1) Almost all chemical reactions which take place in biological systems
run far from their equilibrium.
(2) The linear phenomenologic correlations between the corresponding
rates of the chemical reactions and their affinities, as well as ONSAGER'S
relations of mutuality are invalid because of the existence of feedbacks.
The latter, however, are those which regulate the relations between the
reaction rates.
(3) The theorem of minimum entropy production does not hold for
biological systems.
By making use of the theory for optimal regulation and of PONTRIJAGIN'S maximum principle and by considering cell metabolism as a selfregulated system, we succeeded in overcoming these difficulties.
For this purpose we take into account that the rates of enzymatic reactions are not constant but changing, thus transforming the metabolic network into a subject accessible to regulation. The concentrations of metabolites turn into coordinates of the n-phase space of metabolism and the rate
constants to regulatory parameters. The sum of the latter in the n-phase
space of regulation constitutes the system's control.
However, the control parameters are not independent of one another;
among them certain relations are to be assumed that describe the existing
feedbacks and consequently the functional organization of cell metabolism.
In our previous paper [2] we called these relations 1p-functions. Now we
shall term the relations which reflect regulation by modulating enzyme
activity 1p-functions, and the others, referring to regulation by means of
synthesis of enzymes,
G. DETCHEV, and A. MOSKONA t
We look upon the two regulatory mechanisms as co-operating to
attain their ends-an optimal selfregulation of cell metabolism in such a
way as to work with minimum dissipation of free energy. This common
aim was formulated by us at the last symposium on quantitative biology of
metabolism on Helgoland [2].
To elaborate the problem we search for the most natural method of
describing the synthetic evolution of interrelations and the common functional organization of metabolism by means of appropriate mathematics.
Since sufficient kinetic data about metabolic processes are still lacking, we
select a thermodynamic method which adequately treats the liberation and
utilization of energy in the living cell, irrespective of the underlying mechanisms of molecular interactions. The additional application of formal
kinetics in considering the problem offers us, on the other hand, the possibility of a constant source of new biochemical conceptions with reference
to the functional cell organization.
When making use of the thermodynamics of irreversible processes we
encounter difficulties of a fundamental nature:
(1) Almost all chemical reactions which take place in biological systems
run far from their equilibrium.
(2) The linear phenomenologic correlations between the corresponding
rates of the chemical reactions and their affinities, as well as ONSAGER'S
relations of mutuality are invalid because of the existence of feedbacks.
The latter, however, are those which regulate the relations between the
reaction rates.
(3) The theorem of minimum entropy production does not hold for
biological systems.
By making use of the theory for optimal regulation and of PONTRIJAGIN'S maximum principle and by considering cell metabolism as a selfregulated system, we succeeded in overcoming these difficulties.
For this purpose we take into account that the rates of enzymatic reactions are not constant but changing, thus transforming the metabolic network into a subject accessible to regulation. The concentrations of metabolites turn into coordinates of the n-phase space of metabolism and the rate
constants to regulatory parameters. The sum of the latter in the n-phase
space of regulation constitutes the system's control.
However, the control parameters are not independent of one another;
among them certain relations are to be assumed that describe the existing
feedbacks and consequently the functional organization of cell metabolism.
In our previous paper [2] we called these relations 1p-functions. Now we
shall term the relations which reflect regulation by modulating enzyme
activity 1p-functions, and the others, referring to regulation by means of
synthesis of enzymes,