Further Studies on Mathematical Physics of Metabolizing Systems with Reference to Living Cells

摘要

In previous papers we studied the effects of forces, produced by metabolism, on the mechanical stability of the metabolizing system. In this paper various other effects of those forces are discussed. First of all it is shown that, whenever those forces are of such a nature as to make the system unstable and cause its eventual division, their effect is also that of increasing the size of the system. This reminds of the relation between rate of growth and division in living cells. Further the effects of those forces on molecules and colloidal particles, present in the system, but not directly participating in metabolism, are studied. It is shown that those forces produce a nonhomogeneous distribution of those molecules and particles, and thus alter the structure and the physical constants of the system. For single molecules the effect is negligible; but for colloidal particles of a size above 10−5cm it may be very large and may produce a concentration of those particles at the surface of the system, altering thus the permeability of the latter. Those effects are present only as long as the system metabolizes. This may have a bearing on the sudden change of permeability of living cells after death. Since, under the influence of those forces the permeability of a system becomes a function of the intensity of the metabolizing processes, the fundamental equations describing such systems are much more complicated than those studied hitherto. One particularly interesting feature is that those equations now possess in general not one, butseveral stable solutions,so that the specification of all the parameters, which determine the external conditions, does not determine the configuration of the system in a unique way. As shown previously, such a situation leads to various hysteresis phenomena. One type of such a hysteresis, particularly interesting from the point of view of possible biological applications, is illustrated on a numerical example. It consists in an irreversible transition of the system from a state of slower growth and greater stability into a state of more rapid growth and lesser stability, under the influence of certain reversible changes in the environment of the system.