Mechanism of Division of Metabolizing Systems

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Abstract
In an extension of the work of N. Rashevsky, the problem is treated of the determination of the distribution of concentrations and consequent distribution of osmotic forces in a metabolizing liquid sphere subject to a general infinitesimal deformation. The principle of virtual displacements in the form of an inequality is applied as a criterion of the instability (tendency to divide) of the system. This gives an algebraic equation determining the critical radius at which the system becomes unstable, and the equation is analyzed in detail with reference to the influence of the physical parameters of the system. In particular, it is found that, for a certain range of size of the system, this critical value is practically independent of the surface tension. Finally, the diffusion equations are integrated for a system where the rate of reaction is not constant, but a linear function of the concentration, and a procedure similar to the above is outlined.