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G. DETCHEV, and A. MOSKONA t
(c) Equations minimizing the Hamilton function
H [x (t), P (t), k (t), t]
(d) H[x(T),p(T), k(T), T] = 0
Here the first system of n-differential equations reflects the kinetics of
the biochemical reactions. With the second one are introduced n-auxiliary
functions, the so-called impulses, corresponding in our case to the chemical
potentials of the metabolites; equations (c) minimize the auxiliary functions,
called Hamiltonian by analogy with statistical mechanics and corresponding to the momentary dissipation of free energy; condition (d), valid for
open thermodynamic systems, makes it possible to find the time T, which
the system needs to reach the new steady state.
Having found the optimal regulation k (t) of metabolism by means of
this system of equations, we are able to determine the distribution of energy
flows in the cell, as well as the so called synthesis functions
(i = 1, 2, ... , n)
(j = 1, 2, ... , n)
(3)
An illustration of the synthesis functions would be the following: let us
assume that the concentration of a metabolite is changed. By altering the
enzyme activity the regulatory mechanism enters immediately into action
and changes the rates of the respective reactions. If the change in the metabolite concentration exceeds the regulatory capability of the first mechanism,
and consequently a certain concentration of the metabolite penetrates into
the cell nucleus, the regulation by enzyme synthesis is resorted to. This
mechanism operates at the level of crude modelling of enzyme functions,
whereby an approximate adjustment of the synthesis is effected, after which
it switches off. The subsequent fine tuning in is effected again by the first
mechanism and by a combination of the first and second regulatory mechanisms the rates of the reactions or the regulatory mechanisms are changed,
due to the metabolite concentrations. In this way the synthesis functions
are modulated and the optimization of cell metabolism is realized.
The synthesis functions reflect the controlling parameters as a function
of the momentary state of the system and of the momentary concentrations
of the metabolites. In so far as under the influence of the metabolites the
goal of the control is achieved, we may call the biological entities selfregulating systems. In this manner cell metabolism is considered concomitantly
as a thermodynamic and as an optimal system.
Our investigations point to some basic regularities, typical of controllable thermodynamic systems, clearly expressed by the following comparison:
. For a thermodynamic system the 1 st principle of thermodynamics provides us only with the energy balance of the system. It can predict neither
G. DETCHEV, and A. MOSKONA t
(c) Equations minimizing the Hamilton function
H [x (t), P (t), k (t), t]
(d) H[x(T),p(T), k(T), T] = 0
Here the first system of n-differential equations reflects the kinetics of
the biochemical reactions. With the second one are introduced n-auxiliary
functions, the so-called impulses, corresponding in our case to the chemical
potentials of the metabolites; equations (c) minimize the auxiliary functions,
called Hamiltonian by analogy with statistical mechanics and corresponding to the momentary dissipation of free energy; condition (d), valid for
open thermodynamic systems, makes it possible to find the time T, which
the system needs to reach the new steady state.
Having found the optimal regulation k (t) of metabolism by means of
this system of equations, we are able to determine the distribution of energy
flows in the cell, as well as the so called synthesis functions
(i = 1, 2, ... , n)
(j = 1, 2, ... , n)
(3)
An illustration of the synthesis functions would be the following: let us
assume that the concentration of a metabolite is changed. By altering the
enzyme activity the regulatory mechanism enters immediately into action
and changes the rates of the respective reactions. If the change in the metabolite concentration exceeds the regulatory capability of the first mechanism,
and consequently a certain concentration of the metabolite penetrates into
the cell nucleus, the regulation by enzyme synthesis is resorted to. This
mechanism operates at the level of crude modelling of enzyme functions,
whereby an approximate adjustment of the synthesis is effected, after which
it switches off. The subsequent fine tuning in is effected again by the first
mechanism and by a combination of the first and second regulatory mechanisms the rates of the reactions or the regulatory mechanisms are changed,
due to the metabolite concentrations. In this way the synthesis functions
are modulated and the optimization of cell metabolism is realized.
The synthesis functions reflect the controlling parameters as a function
of the momentary state of the system and of the momentary concentrations
of the metabolites. In so far as under the influence of the metabolites the
goal of the control is achieved, we may call the biological entities selfregulating systems. In this manner cell metabolism is considered concomitantly
as a thermodynamic and as an optimal system.
Our investigations point to some basic regularities, typical of controllable thermodynamic systems, clearly expressed by the following comparison:
. For a thermodynamic system the 1 st principle of thermodynamics provides us only with the energy balance of the system. It can predict neither