A New Kinetic Model of a Growing Bacterial Population

Abstract

SUMMARY:A chemical open system of fixed volume in a constant environment tends towards a steady s t a t e in which its mass remains unchanged. Such a system is not a satisfactory kinetic model of a growing bacterial population, which increases its mass and volume, or grows, logarithmically, in a constant environment. However, when the material limiting the volume of an open system is itself one of the dynamic components the system can then grow logarithmically of its own accord. If the surface-area-to-volume ratio of such an 'expanding system' remains unchanged logarithmic growth can continue indefinitely, and in a constant environment the system enters a time-dependent 'exponential state '. Autocatalysis is not involved in the Iogarithmic growth of an expanding system ; but when an autocatalytic stage is included the growth curve can exhibit a typical log-phase during which growth rate is virtually independent of concentrations of source material above a threshold level. The properties of expanding systems are deduced from those of open systems by non-mathematical arguments, and some of the implications of the expanding system concept in practical and theoretical microbiology are discussed. It is suggested that the spontaneous occurrence of expanding systems in a non-living environment might be the first step towards the evolution of living organisms. Throughout the paper all reactions are treated as reversible, since there seems to be no justification for the concept of an irreversible chemical change. The reactions are also assumed to be homogeneous, unimolecular, and of the first order, except where otherwise stated. Those assumptions are made in order to keep the examples in the text as simple as possible; but the * Present address :

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