Growth Rate and Generation Time of Bacteria, with Special Reference to Continuous Culture

Abstract

SUMMARY:The relations between growth rate, generation time distribution and age distribution in growing bacterial cultures are derived. The effect of inheritance on generation time is probably negligible. Some applications to experimental data exemplif'y the mathematical results. The validity of the principal assumptions is discussed.It appears to be tacitly assumed by many bacteriologists, in particular by some who are concerned with the study of continuous cultures, that there is a simple relationship between growth rate and generation time. It is sometimes stated that during the phase of steady expohential growth of a batch culture the following equation holds :where N (supposed very large) is the number of organisms in the culture, v is the number growth rate constant, and 7 is the mean generation time (in a sense not clearly defined). Equation (1) is false except in special cases that are apparently never realized in practice. Similarly, in the steady state of a continuous culture running at dilution rate D it is usually false that log 2 D = -. 7The true relationships, though more subtle, differ quantitatively from ('I) and (2) by very little, but so far as (2) is concerned, that little is an expression of the selective power which is so important a feature of continuous culture.In this paper I describe some simple quantitative features of bacterial populations which result from the dispersion of the individual generation times. I assume (i) that the populations under discussion are homogeneous, i.e. that they consist of organisms of only one type, and that the cultures have continued in steady growth long enough for the age distribution to have become constant; fii) that the numbers of organisms present are so large that variations can be regarded as continuous, and statistical fluctuation as negligible. Some of the mathematical results are not new, but they are somewhat inaccessible to bacteriologists, and I have given simple derivations, glossing over many difficulties which the pure mathematician must attend to, but which are resolved by observation for the bacteriologist.To avoid the use of inappropriate or ambiguous phrases, I adopt the following terminology : the ' inception ' and ' termination ' of an organism are t N 8 t d logarithms are used throughout.

Age-dependent stochastic models for understanding population fluctuations in continuously cultured cells

“…Following Powell [12], This equation has a simple physical interpretation. If we consider mitosis as a one-step irreversible transition, the first term is the transition probability per unit of time, while the second term is the survival probability V(a).…”

“…Other theoretical studies have considered stochastic processes in cell division, synchronous growth curves and/or age distributions of exponential cultures within deterministic models [11][12][13][14][15]. For instance, Bremer [14] has reduced the cell cycle variability of E. coli to variability of times between rsif.royalsocietypublishing.org J R Soc Interface 10: 20130325 the end of DNA replication and the next cell division.…”

Sporulation in Bacillus subtilis. Theoretical and Experimental Studies in Continuous Culture Systems

“…(Murrell, 1967;Mandelstam, Microbiologists, particularly those interested in continuous culture, describe cultures in terms of 'organism' as the basic unit; that is, in terms of 'recognizably separate entities' (Powell, 1956). For a sporulating system, however, there is no a priori argument for adopting the organism level as the unit for quantitative representation of initiation to spore formation.…”

In Situ Determination of Bacterial Growth in Mixing Zone of Hydrothermal Vent Field on the Hatoma Knoll, Southern Okinawa Trough

“…The microbial cells were observed using epifluorescence microscopy (BX50, Olympus Corp.) and counted 100 microscopic fields per filter sample. Doubling time and growth rate constant are index for microbial growth rate, and generally calculated from the data during the exponential growth phase having a constant interval of cell dividing (Powell 1956). Our experiment did not provide the time course population growth and we could not determine the exponential growth phase precisely.…”