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THE GROWTH OF BACTERIAL CULTURESBY JACQUESMONOD

Pasteur nstitute, Paris, FranceINTRODUCTIONThe study of the growth of bacterial cultures does not consti-tute a specialized subject or branch of research: it is the basicmethod of Microbiology. It would be a foolish enterprise, anddoomed to failure, to attempt reviewing briefly a "subject"which covers actually our whole discipline. Unless, of course, weconsidered the formal laws of growth for their own sake, an ap-

proach which has repeatedly proved sterile. In the present reviewwe shall consider bacterial growth as a method for the study ofbacterial physiology and biochemistry. More precisely, we shallconcern ourselves with the quantitative aspects of the method,with the interpretation of quantitative data referring to bacterialgrowth. Furthermore, we shall consider z exclusively the positivephases of growth, since the study of bacterial "death," i.e., of thenegative phases of growth, involves distinct problems and meth-ods. The discussion will be limited to populations consideredgenetically homogeneous. The problems of mutation and selectionin growing cultures have been excellently dealt with in recentreview articles by Delbriick (1) and Luria (2).No attempt is made at reviewing the literature on a subjectwhich, as we have just seen, is not really a subject at all. Thepapers and results quoted have been selected as illustrations of thepoints discussed.

DEFINITION OF GROWTH PHASESAND GROWTH CONSTANTSDivision RATE AND GROWTH ATE

In all that follows, we shall define "cell concentration" asthe number of individual cells per unit volume of a culture and"bacterial density" as the dry weight of cells per unit volume of aculture.Consider a unit volume of a growing culture containing at timet, a certain number x, of cells. After a certain time has elapsed,

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372 MONODall the ceils have divided once. The number of ceils per unitvolume (cell concentration) is then

x = xx2;after n divisions it will be

x -- xt.2.If r is the number of divisions per unit time, we have at time t~:

or using logarithms to the base 2.log2x2 - log2xl, ............... [11

where r is the mean division rate in the time interval t~-tx. Indefining it we have considered the increase in cell concentration.When he average size of the cells does not change in the timeinterval considered, the increase in "bacterial density" is propor-tional to the increase in cell concentration. Whether growth isestimated in terms of one or the other variable, the growth rateis the sameLHowever, as established in particular by the classical studiesof Henrici (3), the average size of the cells may vary considerablyfrom one phase to another of a growth cycle. It follows that thetwo variables, cell concentration and bacterial density, are notequivalent. Much confusion has been created because this im-portant distinction has been frequently overlooked. Actually, oneor the other variable may be more significant, depending on thetype of problem considered. In most of the experimental problemsof bacterial chemistry, metabolism, and nutrition, the significantvariable is bacterial density. Cell concentration is essential onlyin problems where division is actually concerned, or where aknowledge of the elementary composition of the populations isimportant (mutation, selection, etc.).

a Theuse of log base 2 in placeof log base 10simplifies all the calculationsconnectedwith growth ates. It is especially convenient or the graphicalrepre-sentation of growth urves. If log2 of the bacterial density (1og2--3.322og~0)plotted against time, an increaseof one unit in ordinatescorrespondso one divi-sion (or doubling). The number f divisions that have occurred during any timeinterval is givenby the difference of the ordinates of the correspondingoints.It is desirable hat this practice shouldbecomeeneralized.

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GROWTHOF BACTERIAL CULTURES 373Although the two variables are not equivalent, it is convenientto express growth rates in the same units (i.e., number of doublings

per hour) in both cases. When cell concentrations have beenestimated, it is equivalent to the true division rate. When acterialdensity is considered, it expresses the number of doublings ofbacterial density per unit time, or the division rate of cells postu-lated to be of constant average size. In all that follows, unlessspecified, we shall consider growth and growth rates in terms ofbacterial density.These definitions involve the implicit assumption that in agrowing culture all the bacteria are viable, i.e., capable of division

or at least that only an insignificant fraction of the cells are notcapable of giving rise to a clone. This appears to be a fairly goodassumption, provided homogeneous populations only are con-~idered. It has been challenged however [Wilson (4)] on the basisof comparisons of total and viable counts. But the cultures ex-amined by Wilson were probably not homogeneous (see p. 378),and the value of the viable count in determining the "absolute"number of cells which should be considered viable under theconditions of the culture is necessarily doubtful (see p. 378).Direct observations by Kelly & Rahn (5) contradict these findingsand justify the assumption. [See also Lemon (42) and TopleyWilson (43).]

GROWTHPHASESIn the growth of a bacterial culture, a succession of phases,characterized by variations of the growth rate, may be conveni-ently distinguished. This is a classical conception, but the differentphases have not always been defined in the same way. The follow-ing definitions illustrated in Fig. 1 will be adopted here:1. lag phase: growth rate null;2. acceleration phase: growth rate increases;3. exponential phase: growth rate constant;4. retardation phase: growth rate decreases;5. stationary phase: growth rate null;6. phase of decline: growth rate negative.This is a generalized and rather composite picture of the growthof a bacterial culture. Actually, any one or several of these phasesmay be absent. Under suitable conditions, the lag and acceleration

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374 MONODphases may often be suppressed (see p. 388). The retardationphase is frequently so short as to be imperceptible. The same issometimes true of the stationary phase. Conversely, more complexgrowth cycles are not infrequently observed (see p. 389).

i

6TIME

FzG.1.--Phases o[ growth. Lower urve: log bacterial density. Upper urve:variations of growthate. Vertical dotted ines mark he limits of phases.Figuresrefer to phases s defined n text (see p. 373).GROWTH CONSTANTS

The growth of a bacterial culture can be largely, if not com-pletely, characterized by three fundamental growth constantswhich we shall define as follows:Total growth: 2 difference between initial (xo) and maximum(x~) bacterial density:G -- Xm~-

Exponential growth rate: growth rate during the exponentialphase (R). It is given by the expressionlog2x2- log2x2R= t2 --xs "Croissaneeotale," Monod941.

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GROWTHOF BACTERIAL CULTURES 375when h-t1 is any time interval within.the exponential phase.Lc~g time and growth lag.--The lag is often defined as the durationof the lag phase proper. This definition is unsatisfactory for tworeasons: (a) it does not take into account the duration of theacceleration phase; (b) due to the shape of the growth curve, itdifficult to determine the end of the lag phase with any precision.As proposed by Lodge & Hinshelwood (6), a convenient lagconstant which we shall call lag time (T0 may be defined as thedifference between the observed time (tr) when the culture reachesa certain density (xr) chosen within the exponential phase, and the"ideal" time at which the same density would have been reached(t0 had the exponential growth rate prevailed from the start, i.e.,had the culture grown without any lag T~ = tr-t~, or

log~, - log~x0

The constant thus defined is significant only when cultureshaving the same exponential growth rate are compared. A moregeneral definition of a lag constant should be based on physiologicalrather than on absolute times. For this purpose, another constantwhich may be called growth lag (L) can be defined

L = TrR.L is the difference in number of divisions between observed andideal growth during the exponential phase. T~