Optimal autoregulation of the cellular metabolism

Kurzfassung

Der Stoffwechsel wird als harmonisches System von im Raum organisierten und in der Zeit koordinierten Reaktionen betrachtet. Ein solches System besitzt Eigenschaften, die für das System als ganzes charakteristisch sind, für eine einzelne Reaktion aber nicht zutreffen. Die biologischen Objekte sind als geregelte physikalisch-chemische Systeme zu betrachten, bei denen die „Geschwindigkeitskonstanten“ der am Metabolismus teilnehmenden Reaktionen direkt von der Enzymaktivität abhängen. Wenn sich die Enzymaktivität verändert, ändert sich gleichzeitig die „Kontrolle“ des Systems. Es wird das normale Optimum, auf welches sich der Stoffwechsel einer Zelle einstellt, bestimmt; ferner werden die Gleichungen für Reaktionen angegeben, welche die „Kontrolle“ des Systems so durchführen, daß das Optimum erreicht wird. Biologische Systeme sind selbstregelnde Systeme.

Summary

• 1. Metabolism is considered as a harmonious system of reactions rigidly organized in space and coordinated in time possessing properties characteristic of it as a whole but not specific for any single reaction.

• 2. An optimum of energetic flows of metabolic processes has been postulated. The network of metabolic processes is directed to it in such a way that the result provides a minimum dissipation of free energy in the system.

• 3. The treatment of this question is based upon the thermodynamics of irreversible processes in open systems and the mathematics of the dynamic programming afterBellman and ofPontrjagin's maximum principle.

• 4. The thermodynamic expression of the optimum to which the metabolism in a normally developed cell endeavours is derived.

• 5. A system of differential equations is formed, which reflects: (a) the formal kinetics of the biochemical reactions, (b) the energetics of the biochemical reactions, (c) the connection between the kinetics, the energetics and the control respectively of the system.

• 6. From the equations received the controls of the system, i. e. the activities of the enzymes, as well as of the concentrations of the participating metabolites, can be defined as functions of time.

• 7. In the interpretation of the above items, an attempt was made to extend the conventional thermodynamics of the irreversible processes so that it could include a regulatable physico-chemical system.

• 8. By introduction of several regions into the space of metabolism corresponding to different kinds of reactions, such as irritation, stimulation, injury and death, the different behaviour of the metabolic reactions with respect to the acting factor can be clearly demonstrated. Competion represents the motive power of the autoregulation, whereas the system of feedbacks is the apparatus of realization. Thus for given conditions the optimum organization can be reached.