SUMMARY: A chemical open system of fixed volume in a constant environment tends towards a steady state 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 logarithmic 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.


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