Microbial Growth Rates in Nature · MICROBIAL GROWTHRATES types of growing populations (Fig. if, ig, and lh). An example of growth plus setting (Fig. if) might be the bottom flora

BACTERIOLOGICAL REVIEWS, Mar. 1971, p. 39-58Copyright © 1971 American Society for Microbiology P

Microbial Growth Rates in NatureTHOMAS D. BROCK

Department ofMicrobiology, Indiana University, Bloomington, Indiana 47401

INTRODUCTION ...........................................................Commitment to Nature.....................................................What is Nature? ............................................................

POPULATION PROBLEMS ..............................................ASSESSMENT OF MICROBIAL NUMBERS OR MASS.........................DEFINING BOUNDARIES OF THE HABITAT ...............................ARTIFICIAL SUBSTRATES .............................................USE OF THE MICROSCOPE IN NATURE ................................MEASUREMENT OF GROWTH RATE OF SINGLE ORGANISMS............GROWTH RATES OF DEVELOPING MICROCOLONIES........GROWTH RATES OF FILAMENTOUS ORGANISMS .....................METHODS BASED ON ANALYSIS OF THE CELL-DIVISION CYCLE........

Labeled Thymidine Methods...............................................GROWTH RATES OF PROCARYOTES AS MEASURED BY THYMIDINE

AUTORADIOGRAPHYEcological Approximations for Labeling Experiments..........................Rate of Appearance of Unlabeled Cells.........................................

GENETIC METHODS ....................................................METHODS ESPECIALLY SUITED TO STEADY-STATE POPULATIONS......INOCULUM SIZE: RATE OF EFFECT.....................................CONCLUDING STATEMENT ............................................LITERATURE CITED.....................................................

INTRODUC1 IONThe survival of a species in a natural habitat

depends ultimately on its ability to grow at a

rate sufficient to balance death due to predation,parasitism, or natural causes. Although many

aspects of the ecology of a species may be de-ducible from behavior of the species in culture,it seems evident that at some stage of the studythe investigator must return to nature and studythe behavior of the population in its naturalhabitat. This seems even more important now

than it was several decades ago because we are

now more aware of the tremendous physiologicalversatility of microbes as evidenced by theexistence of biochemical feedback loops, in-ducible and repressible enzymes, etc. What a

species can do in a culture medium is not neces-

sarily what it is doing in its natural habitat.Environmental factors of all kinds may differdrastically in nature from what they are in cul-ture, and they may differ in ways we may not even

perceive. This is especially true when we con-

sider that in nature microbes live in microen-vironments which may differ widely from themacroenvironment which we are capable ofmeasuring with ordinary instruments and chemi-cal procedures. For instance, nutrient qualityand quantity, pH, and osmotic pressure are

among the factors which can differ between micro-

environment and macroenvironment. Hence, itis difficult (if not impossible) to simulate pre-cisely the physicochemical conditions of thenatural environment in the laboratory. Further-more, in nature an organism is always faced withcompetition from other organisms, difficult toduplicate in the laboratory.

It might seem virtually impossible to measuremicrobial growth rates in nature, as a result ofthe small size of microbes and the fact thatmany species live together. It is the purpose ofthis review to show that natural microbial growthrates can be measured by a variety of methodsadaptable to different kinds of habitats or differ-ent kinds of organisms. The review also considerssome of the misconceptions about the measure-ment of growth rates and evaluates some of thepitfalls to successful application of these methods.An attempt is made, when possible, to comparenatural growth rates with those of the samespecies under presumably optimal conditions inthe laboratory.

Commitment to Nature

There is a natural tendency for the microbialecologist to take the easy way out and stay inthe laboratory. All sorts of laboratory deviceshave been constructed which give the illusion ofduplicating natural conditions: chemostats,

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turbidostats, temperature-gradient blocks, soilperfusion columns. Although these devices per-mit interesting experiments, they do not replacestudy of organisms in nature. At some stage,studies in nature must be conducted, preferablybefore the investigator's ideas about what micro-organisms might be doing in nature become toofirmly fixed. Once some idea of what organismsare doing in nature is obtained, ecologicallyrelevant laboratory study of organisms can beconducted in a more meaningful way. Ideally,one should move back and forth from nature tolaboratory rather frequently, always checkingnatural observations with laboratory study andvice versa.

What is Nature?Any microbial habitat which is not completely

controlled can be called a natural habitat. Amicrobial habitat may be quite tiny. The mam-malian intestinal tract, for instance, is not onebut many microbial habitats. A single soil crumbmay be the home of several kinds of organisms,each in its own niche, and one niche may differchemically or physically from other niches onthe crumb. Except in extreme environments inwhich selective conditions are so rigorous thatpopulations of single organisms may attainmacroscopic dimensions, microbial niches aremicroscopic ones, and the microscope is an in-strument indispensable for this exploration.

POPULATION PROBLEMSA microbial population is any group of cells

of one or more types which can be defined interms of its extent in space and time. A popula-tion may be, for instance, a microbial colonywhich has a fixed location in space, a species ofalga which is distributed widely throughout theplankton of a lake but defined in terms of itscharacteristic morphology, or the sum total ofcells in the rumen, which may be regarded as asingle population defined in terms of location.

In terms of growth kinetics, two types ofpopulations can be easily recognized: the steady-state population and the exponentially growingpopulation. The latter, not common in nature,is a closed population of which the members areall growing continuously with no gain from orloss of cells to the environment. The steady-state population may also contain cells whichare growing continuously, but cells are beinglost from the population at the same rate theyare being added. There are, of course, manygradations between exponential and steady state.Thinking about the steady state makes us con-sider the whole problem of cell migration, which

a. PieW ese--,t i -tattlin a. 0*-,-w o d.Closed Static

*. DIV~d1as Tre*.t-Atweowhpis 11tas_ Type K. Closed 0 1.1"Sottmieg (Iup....teI.

FIG. 1. Diagrammatic representation of possiblecell populations. Arrows outside the boxes indicate cellmigration; arrows inside the boxes refer to cell divisionstaking place within the system. Based on Cleaver (15).

can play a significant role in changes in popula-tion number. (In fact, one of the most importantdistinctions between a natural and a laboratorypopulation is that in the former migration canoccur.) Examples of different kinds of popula-tions, based on the ideas of Gilbert and Lajtha(22), are shown in Fig. 1.The upper part of Fig. 1 portrays situations

in which no cell division is occurring, and changeoccurs only due to input and output. An ex-ample of a simple transit population (Fig. la)is the microflora of the air, or the drift phyto-plankton being swept down a river from onelake to another. An example of a settling popu-lation (Fig. lb) is the mud surface of a lake,on which algae may be deposited, or the rectumof a mammal, which is the repository of vastmicrobial populations from the large intestine.An example of a decaying population (Fig. lc)is the population in the mammalian intestinaltract after oral antibiotic therapy, in which wash-out but not growth can occur. Another exampleof a decaying population is the darkened hot-spring algal mats described by Brock and Brock(11). An example of a closed static population(Fig. id) is a dry sample of soil held in the labora-tory.The lower part of Fig. 1 portrays situations in

which cell division occurs as well. An example ofa dividing transit population (Fig. le) is thebacterial flora at a given location in the mam-malian intestine, or an algal component able todivide in a moving stream. Of course, virtuallyany natural dividing population will experiencesome immigration and emigration, and hencecould be assigned formally in this category,although from a practical standpoint it is onlywhen transit is the major component of popula-tion change that it becomes relevant to recognizethe situation. Depending on the relative rates ofimmigration and emigration, the dividing transitpopulation (Fig. le) grades into the other three

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types of growing populations (Fig. if, ig, andlh). An example of growth plus setting (Fig.if) might be the bottom flora of a shallow lake,where an algal species lives both in the waterand on the bottom. A Sphaerotilus bloom is anexample of a stem-type population, to borrow aterm from the mammalian cell biologist. In thiscase (Fig. ig), immigration is unimportant andemigration by sloughing or release of swarmersis common. The closed dividing population(Fig. ih) is the familiar exponentially dividingpopulation of the microbial physiologist, andis found only transiently in nature.

It is important to emphasize that a steady-state population as defined by an ecologist isquite different from that defined by a microbialphysiologist. The physiologist thinks of thesteady state from the viewpoint of the indi-vidual cell and defines it as the situation in which"the distribution of each intensive random var-iable (e.g., cell age or cell protein) does notdepend on the time when the sample is chosen"(45), a situation which exists most commonlywhen the population is in exponential growth.To the ecologist, concerned with the populationrather than the individual, exponential growth isanything but a steady state.

ASSESSMENT OF MICROBIAL NUMBERSOR MASS

In any study of microbial growth rates, it isnecessary to assess population numbers. Thephycologist or protozoologist does this by per-forming direct microscopic counts of the or-ganisms in a sample from the habitat. If theorganisms vary widely in volume, he will notmake a simple count, but rather an estimate ofthe volume of cellular material of a given species.Procedures for such estimates are well established(43, 58). The mycologist may use similar methods(46). Because of the small size of bacteria, thebacteriologist has used direct microscopic countsrather infrequently (16), relying instead on viablecounts. Although such methods are useful forphysiological and genetic studies in the labora-tory on single species with plating efficienciesthat approach 100%, they are usually unsuitedfor ecological investigations. Many studies (e.g.,32, 48) have shown that the viable count is al-ways much lower than the direct microscopiccount. Perfil'ev and Gabe (48) give ratios varyingfrom 13,000:1 to 737,000:1. Although lowratios could be due to faulty plating techniques,even under the best conditions at the mostabout 10% of the bacteria in a natural populationmay be counted. The reason, of course, thatviable counts are done in spite of this serious

limitation is that it is often virtually impossibleto recognize a bacterial species microscopically,and at least when one has a colony on an agarplate one can subculture it and proceed to anidentification. Another reason is that directmicroscopic counts are difficult and tedious.Finally, viable counts permit assessment ofpopulations whose densities are too low formeasurement by more direct methods.

It should be clearly recognized, however, thatviable counts cannot reveal how rapidly orga-nisms are growing in nature. (For an exceptionto this statement, see the discussion below ofMeynell's work.) It is merely necessary to notethat a bacterial spore, which contributes nothingto the function of the ecosystem at the time ofsampling, will produce a colony on an agar plate.Viable counts are useful in studies of microbialdispersal, and it is in this way that they are bestused in ecological studies. The tracing of a sourceof pollution from a viable count of Escherichiacoli in a water supply is an example of this kindof study.

If we cannot assess bacterial numbers in anatural habitat by viable counts, how then arewe to do it? First, direct microscopic counts areoften possible when the bacterium in question islarge or morphologically distinct. Examples ofthis approach are the enumeration of Chromatiumin lakes (35) or of Leucothrix mucor attached toseaweeds (10). Second, identification may bepossible at the microscopic level by the use offluorescent-antibody procedures (26, 52). Third,we may be dealing with habitats in which onlyone or a restricted number of kinds of organismsare present, so that species identification is noproblem (2). Admittedly there are cases in whichnone of these situations obtains, but new methodscan probably be devised.

El-Shazly and Hungate (18) obtained ameasure of the microbial mass in a rumen fer-mentation by measuring the rate of gas produc-tion of samples of rumen contents containing arate-saturating quantity of fermentable substrate,so that gas production was a function only ofpopulation size. The absolute population sizecould not be measured, but relative changes inpopulation density could be. A precisely analo-gous method can be used by those working withphotosynthetic organisms. The rate of photo-synthesis (measured with '4CO2) can be measuredunder conditions of saturating light intensity.Changes in population density will then be re-flected by changes in the rate of 14CO2 uptake.A cell constituent which may be of considerable

value in determining relative population densi-ties of actively metabolizing microbes is adeno-sine triphosphate (ATP) (29). Sensitive techniques

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are available for its measurement, and ATPconcentration should be proportional to bio-mass. Of course, only in natural systems wheremicrobes constitute the majority of the biomasscould ATP determinations be used to estimatethe relative population density of microbes.

Chlorophyll has been used frequently as anindex of algal biomass, but is not a reliable onebecause chlorophyll content per cell may varywidely as a function of light intensity (12). Epply(19) described a method for measuring standingcrop by extrapolating the photosynthesis-ratecurve back to zero time.

Estimating population size of filamentousorganisms is more complex, but at least the temp-tation to use viable counting procedures does notarise. The direct way to measure lengths of fila-ments is to enlarge the field of view either byphotography, projection, or drawing with cameralucida, and then to measure the lengths of fila-ments with a ruler or map reader. This approachhas been used by soil mycologists (46). A simplerway, and one which is probably just as accurate,is to use a stereological technique. A grid isthrown across the field and the number of inter-sections of filaments with lines of the grid iscounted. Olson (43) described five differentstereological procedures, each suitable to a par-ticular system or providing a particular degreeof accuracy. We have used one of his methodsfor assessing aggregate lengths of filamentousbacteria on artificial substrates with considerablesuccess (3), and we can recommend it for con-venience, rapidity, and relative accuracy.

DEFINING BOUNDARIES OF THE HABITAT

Before a study is begun, the boundaries of thehabitat must be defined. Initially one must de-cide on the scale of the investigation. For studyof microbial growth in soil, for instance, a di-mension as large as a field or as small as a soilcrumb could be selected. For a lake, the wholebody of water could be investigated, or anyfraction of this body, such as the planktonicregions, the littoral, the thermocline, or the bot-tom sediments. Even in a habitat as sharplybounded as the rumen, it might in some casesbe useful to consider subsections (e.g., rumenwall, food particles) in which particular speciesor processes might be concentrated.For study of the growth rate of a single species,

it is usually preferable to examine the smallesthabitat encompassing the boundaries or the fieldof influence of the organism. Thus L. mucor livesas an epiphyte of benthic algae on the littoral ofsea coasts (6). It would be unprofitable to studythe whole vast littoral region rather than the

specific seaweeds with which L. mucor is as-sociated.

It is essential to know the type of distributionwhich the organism has throughout the habitat.Animal and plant ecologists (27, 38) use theterms "dispersion" or "pattern" when referringto this aspect. If a population is randomly dis-persed, its distribution will follow a Poissondistribution. Random dispersion is rare in naturalpopulations, the species more frequently beingpatchy or clumped. In such cases, the varianceand the mean are not equal, as in the Poisson,and departures from randomness can be detectedby deviations of the distribution from a Poissonseries. Greig-Smith (27) gives a variety of statisti-cal tests which can be used to detect such dif-ferences and to express them quantitatively. Ingeneral, all these methods use data derived bycounting the number of individuals in a series ofquadrats.A quadrat is a real or imaginary area of known

size which is thrown across the field. Despite itsname, a quadrat need not be square but can haveany convenient shape; for example, the area en-compassed by a microscope field is a quadrat. Itis obvious that the quadrat size must be largeenough so that distributions obtained are notbiased by quadrat size. This point, discussed indetail by Kershaw (34), is illustrated in Fig. 2. Itcan be seen that if the quadrat size is either toosmall or too large, patchiness will be missed. Theideal quadrat size for detecting patchiness wouldhave an area approximately equal to the area ofthe clump, since some quadrats would containlarge numbers of organisms and others would bevirtually devoid of organisms.To assess growth rates over the whole extent of

the habitat, it is important to use quadrat sizeslarge enough to eliminate changes in numbercaused by patchiness. At the same time, very largequadrat sizes make the work of counting un-necessarily tedious.

It is essential to study habitats in which theorganism of interest is actually growing. Manyorganisms are carried by streams or currents farfrom the site where they reproduce. For instance,Staphylococcus aureus grows in the kidney,forming so-called foci of infection. Cells fromthese foci are sloughed into the blood and carriedto distant parts of the body. It is easy to assessstaphylococcal numbers in the blood stream, butit would be incorrect to use changes in thesenumbers as a measure of staphylococcal growthrates in the kidney. In algal blooms, the cellsoften float to the surface and are carried by windand current to quiet backwaters where they ac-cumulate in vast numbers. The factors that con-

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:. A0W CL%~

FIG. 2. Relationship between -.uadrat size and the de-tection of nonrandom distribution. If the populationwere sampled with quadrats A o,' 3, only slight non-randomness would be seen, with C very marked non-randomness; with D and E the distribution would appearprogressively more random. Thus, the most markeddemonstration of nonrandomness would be with aquadrat area about equal to the area of the clump.Based on Kershaw (34).

trol algal blooms can not be ascertained bystudying algae in such backwaters rather than inthe part of the water where the algae are actuallygrowing.

ARTIFICIAL SUBSTRATESThe use of artificial substrates greatly simplifies

many studies in microbial ecology. The substratewhich has been most commonly used in bothaquatic and soil microbiology is the glass micro-scope slide (14, 53). The main advantage is easeof microscopic examination, but an additionaladvantage for rate studies is that one knows pre-cisely the time microbial growth could commence.For studies on colonization and successionartificial substrates are ideal. The substrate maybe both physically and chemically analogous tomany natural substrates such as rocks andminerals. A wide variety of materials (e.g.,plastics) other than glass can be used (53). Ifnecessary, even opaque materials can be used inconjunction with incident fluorescence micros-copy. In fouling studies, the artificial substrate isat th. same time the habitat of interest.

In soil or other heterogeneous systems, micro-scope slides are difficult to use because (i) theycannot be removed and replaced without dis-turbing the environment; (ii) the opacity of theparticulate material makes microscopy difficult;and (iii) it is difficult to make microscopic ob-servations of living organisms, so that subsequentisolation of an organism of interest is usually notpossible. Because of these and other difficulties,Perfil'ev and Gabe (48) devised special flat-glass

microcapillaries which could be inserted into thehabitat for colonization and then removed andexamined periodically (Fig. 3). These flat capil-laries, called by them "pedoscopes" (if used insoil) or "peloscopes" (if used in mud), are farsuperior to round capillaries for microscopy, andhave been used in the Soviet Union for manyyears. Their use will no doubt become more gene-ral as a result of the appearance of English trans-lations of Perfil'ev's two books (47, 48). Throughthe use of these capillaries, Russian workers havediscovered and studied new bacteria that live at themud-water interface: Lieskeella, Dictyobacter,Cyclobacter, Trigonobacter, Metallogenium, andothers. (The taxonomic validity of all of theseentities is not accepted by all bacterial taxon-omists.) In addition, new bacterial genera havebeen described from soil and water. Further, withthe use of microcapillaries, Perfil'ev has beenable to observe the microzonation which developsat the mud-water interface. For instance, in themud of Lake Khepo-Yarvi, eight microzonesdeveloped over a vertical distance of 2 mm. Fromthe surface down, these were photosynthetic zone(diatoms), iron oxidation zone (Ochrobium andGallionella), predatory bacterial zone (Dictyo-bacter), Azotobacter zone, filamentous bacterialzone, Cyclobacter zone, Lieskeella zone, andsulfide oxidation zone (Thiospira). Below theeighth zone, conditions became highly reducing,as shown by the presence of FeS.The value of flat-glass capillaries for many

ecological studies is clear. The book by Perfil'evand Gabe (48) should be consulted for details ofmethods and results, as well as for techniques usedto actually construct the capillaries. In addition,this book has a detailed discussion of how capil-laries can be used in continuous-flow systems andwith micromanipulators.

_=? /

FIG. 3. Capillary peloscope of Perfil'ev and Gabe(48). A. Capillary peloscope inserted at the mud-waterinterface. B. Cross section of typical capillaries. C.Capillaries mounted on a microscope slide for observa-tion. D. Capillary cells in a protective channel with fix-ingfluid.

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USE OF THE MICROSCOPEIN NATURE

Two approaches are possible. One can take themicroscope to the field-in the sense of actuallysubmerging it in the environment-or one canbring the field to the microscope. The first ap-proach is fraught with difficulties and has beenused only rarely. Staley (54) immersed a phasemicroscope in a small pond in Michigan and usedit to study algal growth. This technical tour deforce may serve as an example of the greatdifficulties with which the microbial ecologist isfaced. In the first place, even with a submergedmicroscope a glass slide was necessary and servedas an artificial surface. The slide was immersedin the water near the microscope and was trans-ferred periodically to the microscope stage forobservation and photography. To permit periodicviewing without diving, the microscope wasplaced at the surface of the water, with the eye-pieces emerging from the pond. Staley watchedand periodically photographed algae and bacteriawhich appeared on the slide, and thus determinedthe manner and rate of growth. Although inprinciple the same or a modified technique couldbe used in more rigorous environments such asdeep waters, rivers, the ocean, perhaps even hotsprings, in practice the difficulties arising areprobably too great in terms of the informationgained. A much simpler approach is to bring thesubmerged glass slide from the field to the micro-scope and to observe and photograph it by usinga water-immersion lens. This was the approachused by Bott and Brock (3) to study bacterialgrowth rates in a small greenhouse pond. Micro-scope slides which were marked with a diamondpencil at a number of locations were submergedin the water. At intervals, the slides were broughtto the surface and carried submerged to themicroscope in glass petri dishes. Locations con-taining organisms were photographed and theslides were then returned to the pond. Thetemperature was not altered significantly and theslides were out of the pond for just a few minutes.Since at least 5 mm of water was present over thesurface of the slide, presumably the organisms,0.5 to 1.0 lsm in thickness, did not become dis-turbed. An alternate method would be to use themicrocapillaries of Perfil'ev and Gabe (48),discussed earlier.

In soil, experiments of this type are considerablymore difficult due to the nature of the substrate.A single slide cannot be removed and reinsertedperiodically without disturbance. Microscopy ofundisturbed soil particles is even more difficult.Recently, Casida (13) made a useful advancetowards direct microscopy of undisturbed soil

particles. The procedure involves the use ofincident illumination of the soil particle by lightwhich passes through the objective in reversedfashion. The bacterial cell so illuminated diffractsthe light, and light of some wavelengths returnsthrough the objective to the ocular. Variouscolors are seen, the cell thus being differentiatedfrom the dark background of the soil. However,actively growing bacteria do not exhibit thisdiffraction phenomenon, so that the techniquepermits observation in soil only of those cellswhich are in a dormant state. Microorganismslarger than bacteria cannot easily be seeneither. Casida concludes that the technique willpermit continuous observation of the growth,activities, and interactions of soil microorganisms,although if only dormant cells are observed it isnot clear how one can study growth in situ; nogrowth rates have as yet been presented. Ifnothing else, the report of this technique may per-haps encourage further study and experimentationwith the light microscope, the most powerful toolof the microbial ecologist.

MEASUREMENT OF GROWTH RATEOF SINGLE ORGANISMS

The most direct method of measuring growthrate is to measure the size or mass of a singleorganism at various times. This method, which isrelatively easy to use in plant and animal ecology,is difficult to use in microbial ecology for severalreasons. (i) It is often difficult or impossible toreturn periodically to precisely the same organism.(ii) Only nondestructive measurements can beused, such as measurement of size. Mass, themost important ecological parameter, may notrelate too precisely to size. Interference micros-copy does permit an estimate of cell mass, but isdifficult to apply routinely or to very small cells.(iii) The procedure is tedious, especially with slow-growing organisms, as one must wait for longperiods of time to obtain data on even a singlecell. During the wait, the microscope may be tiedup and cannot be used for other things. (iv) B3e-cause only a single organism is studied at a time.the data obtained may not be representative ofthe population as a whole.

There has been a considerable amount of workinvolving measurements of growth rates of singlecells (usually bacteria or yeasts) in pure culture.This work, most recently reviewed by Painter andMarr (45), provides some clues concerning thegrowth of microbes in nature. Painter and Marrdiscuss some of the difficulties of accuratelymeasuring growth rates of individual cellsmicroscopically from changes in cell size. Forcells the size of bacteria, the error of measurement

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is such that distinction between linear and ex-ponential growth cannot readily be made. Theconsensus seems to be that the individual bac-terial cell may grow exponentially, whereas theindividual eucaryotic cell does not. For mostecological work, the distinction may not be tooimportant. What is needed is merely a measure ofhow long it takes for a young cell to increase insize and to divide.

In his studies with a submerged microscope,Staley (54) observed the growth of Chlorella in asmall Michigan pond. During the day a singlecell increased in size, and at night this enlargedcell divided into four daughter cells. This isidentical with the behavior of Chlorella culturesgrowing in alternating light and dark in thelaboratory (56). Not all of the cells observed byStaley managed to complete division in 24 hr. Incertain cases, if a cell did not complete divisionduring the first night it continued to enlargeduring the second day and then completed divisionthe following night.Measurement of growth rates of filaments in-

volves the same principle as that of unicells, butmicroscopic recognition of the growing element iseasier. No study of direct measurement of filamentgrowth in nature has come to my attention, al-though much work on growth of single fungusfilaments in laboratory culture has been done (50).

GROWTH RATES OF DEVELOPINGMICROCOLONIES

The growth rate of microorganisms that formmicrocolonies in nature can be estimated bycounting the number of cells per microcolony atdifferent time intervals. Counting numbers iseasier than measuring the sizes of single cells;hence, it is more convenient for routine work.When evaluating counts of microcolonies, oneshould keep in mind that immigration or emigra-tion of cells could have occurred during theintervals between counts.

Bott and Brock (3) determined growth rates ofaquatic bacteria developing at marked locationson microscope slides immersed in a small pond.The changes observed during the growth of asingle microcolony are shown in Fig. 4. Consider-able heterogeneity in developing microcolonieswas observed. Some colonies never got beyondthe two- to four-cell stage. Others developed intolarger aggregates, after which most of the cells inthe colony lysed. In others, the cells spread outafter the colonies reached the 16- to 32-cell stage,making identification of the colony difficult. Onlya few colonies developed to really large size(e.g., 128 cells or larger). Presumably, many ofthe organisms which initiated colonies on the

FIG. 4. Development of a single microcolony on aglass slide immersed in a small pool. Time is expressedin hours after immersion. Drawings from photomicro-graphs of Bott and Brock (3).

slide were not well adapted to a sessile existence,and they succumbed after utilizing organic ma-terial adsorbed to the slide in their immediateenvironment. However, even the organisms whichwere well adapted (as shown by their formationof larger colonies) never completely dominatedthe habitat because grazing organisms such asprotozoa eventually moved in and consumedthem. Doubling times obtained by counting onthe photographs the numbers of cells per micro-colony were in the range of 2 to 10 hr.

In this study (3), both immigration and emigra-tion were observed. Not infrequently, a cellwould undergo division and one of the daughtercells would swim away; the remaining cell wouldremain attached to the glass and undergo furtherdivision. This phenomenon is common in stalkedbacteria such as Caulobacter (49), but was alsoseen for bacteria without obvious stalks. Thetechnique of Helmstetter (28) for obtaining

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growth-synchronized populations of bacteriadepends on the fact that the parents remain ad-herent to a support and the just-formed daughtersare washed free.However, in flowing-water habitats the or-

ganisms are usually types in which both productsof division adhere tightly to the substrate, so thatemigration is of little consequence; the evolu-tionary advantage of adhering tightly to the sub-strate in this situation is obvious.

In estimating growth rates, immigration isprobably a lesser source of error than emigration;if microcolonies are widely spaced, the probabilitythat an immigrant will settle within a colony isfairly low. Two biological factors which couldaffect immigration are antibiosis, which couldreduce it, and chemotaxis, which could increaseit. A technique involving ultraviolet radiation forquantifying immigration rates is described below.For routine work, it would be desirable to be

able to quantify growth rates of microcolonies-without the complications involved in removingthe slides, locating and photographing thecolonies, and replacing the slides, especially whenall of these operations must be done quickly andwithout disturbance to the organisms. To obviatethese problems, Bott and Brock (3) immersed aseries of slides at a single location and removedtwo or three at different time periods. On eachslide, the cell count in a large number of micro-colonies was made, and the average number ofcells per microcolony was calculated for thattime period. By plotting numbers of cells permicrocolony at different immersion times, thegrowth rate could be calculated. Assuming thatthe organisms in the developing microcoloniesare sufficiently distinct so that the microcoloniesarising from cells belonging to the same speciescan be recognized microscopically, the lumpingof data from different microcolonies is valid as ameasure of the growth rate of a single organism.If, however, such recognition is not possible, thegrowth rates obtained represent the averagegrowth rate for the aggregate of microbial specieson the slide. For some ecological work, this latterinformation is still useful.

In many aquatic habitats, bacteria do not de-velop on the slides as discrete microcolonies butare scattered more or less randomly. This distribu-tion might arise through growth if daughter cellsmoved away from mothers before settling down.On the other hand, it could arise as a result ofimmigration in the absence of growth. To dis-tinguish growth from immigration, Bott andBrock (2, 3) employed ultraviolet radiation.Slides which were immersed were irradiated witha germicidal ultraviolet source at regular intervalsduring the experiment, the intervals calculated to

be about equal to the generation time of thepopulation. Thus, newly attached immigrantswere killed before they divided. The rate of in-crease of cell numbers on unirradiated slides is afunction of both immigration and growth, whereason the irradiated slides it is a function only ofimmigration.

Several conclusions could be drawn from theseirradiation experiments. Microcolonies neverdeveloped on irradiated slides, showing thatmicrocolonies arose as a result of growth. Inmost habitats, immigration is quantitativelyunimportant. The rate of increase in cell number,even if distribution on the slides is essentiallyrandom, is caused primarily by growth on theslides. Therefore, if the immigration rate is notsubtracted no serious error will be introduced incalculating growth rates. It should be noted thatthe habitats studied were relatively unpollutedand microbial drift through the water was low.In habitats in which drift is high, immigrationmay be more significant.

Modifications of the ultraviolet radiation tech-nique can be envisaged which would make itadaptable to other habitats. In soil, which ultra-violet radiation would not penetrate, gammaradiation might be substituted. In some otherhabitats, germicidal chemicals might be used.The only requirement is that the agent in questionnot cause cells to be liberated from the surface,since if that occurred the immigration rate wouldbe underestimated. Bott and Brock (unpublisheddata) tested a number of chemicals, includingethyl alcohol, formaldehyde, mercuric bichloride,and hydrochloric acid, but these proved un-satisfactory either because they modified thesurface in such a way that attachment was in-hibited or they caused detachment.

GROWTH RATES OF FILAMENTOUSORGANISMS

Various methods (43) are available for quanti-fying filamentous organisms and can be used inconjunction with slide immersion and ultravioletradiation to measure growth rate. Representativedata on the growth rate of Sphaerotilus on glassslides (4) are given in Fig. 5. The glass slides werecolonized initially by unicellular swarmer cells.In the ultraviolet-irradiated slides no Sphaerotilusfilaments appeared, whereas on the unirradiatedslides colonization by swarmers was followed byoutgrowth of Sphaerotilus filaments. Growth ratesfor filamentous bacteria living in hot springs havealso been measured in this way (Bott and Brock,unpublished data). In most of these habitats, bothunicellular and filamentous bacteria developedon the same slides, and the doubling times ofboth kinds of bacteria were fairly similar.

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FIG. 5. Quantitative counts of total Sphaerotiluscells and offilaments on glass slides immersed in a smallstream. On the ultraviolet-irradiated slides, single cellsnever develop into filaments. From Bott and Brock (4).

When expressing the doubling time of thefilaments, the value given is the rate of increasein the aggregate length of filaments per unit area.This could be due either to increase in lengths ofexisting filaments or to the increase in number ofattaching filaments. Again, studies using ultra-violet radiation permit these alternatives to bedistinguished. In all cases studied, growth was dueprimarily to increase in length of filaments. Onirradiated slides only short filaments were ob-served. On unirradiated slides, the lengths offilaments got progressively longer as immersiontime increased. The rate of increase of length offilaments was exponential over two decades,suggesting that growth was occurring along thewhole lengths of the filaments, rather than onlyat the tips as it does in filamentous fungi. If thelatter growth habit occurred, rate of increaseshould have been as the square rather than theexponential.

METHODS BASED ON ANALYSISOF THE CELL-DIVISION CYCLE

The typical division cycle of a eucaryotic cellis given in Fig. 6. In this cycle, mitosis can berecognized morphologically and deoxyribonucleicacid (DNA) synthesis can be recognized auto-

radiographically by the use of radioactivelylabeled thymidine. In many cell types, the time ofmitosis represents a constant fraction of the totalcell-division cycle. If this is true and if the timeoccupied by mitosis is known, the division rate ofa population can be calculated by a formuladerived originally by Crick (cited in 30),time of mitosis/total time of cell-division cycle Xlo& 2 = loge (1 + 2R/1 + R), where R is thefraction of cells in mitosis. If interphase is rela-tively long and R is thus small, this formulareduces to time of mitosis/total time of cell-division cycle = 1.44R. The use of this formulaassumes that the rate of entry of cells into mitosisis uniform.

This approach was used by Warner (57) toestimate division rate of the protozoan Entodiniumin the rumen. The time for mitosis was deter-mined by microscopic observation of entodiniausing a warm stage; a value of about 15 min wasobtained. It was assumed that this value holds forall cells of that species in the population. Thefraction of cells in mitosis (r) was then countedat different times and the time for cell divisionwas thus obtained. The minimum mean doublingtime found was 5.5 hr, which corresponds to amaximum division rate of about four generationsper day. However, dividing forms were muchmore common at night than during the day. Thetrue division time of the population can be calcu-lated by averaging the various division times overthe 24-hr period; it is 15 hr (see 31). The maximalgrowth rate obtained for entodinia in culture wasone division every 2 to 4 days, suggesting thatconditions in culture are far from optimal formultiplication.

Labeled Thymidine MethodsThe duration of the cell cycle can also be esti-

mated by labeling with radioactive (3H or 'IC)

FIG. 6. Cell circle in an eucaryote. Arrow indicatesthe direction in which cells progress in the cycle.

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thymidine. The problem of determining growthrate of mammalian cell population in vivo bythymidine labeling is, in principle, the same asthe problem of determining growth rate of amicrobial population in nature, and the book byCleaver (15) provides a detailed summary of theconcepts involved.

If a population is labeled with a brief pulse oftritiated thymidine, only those cells in S phase(i.e., engaged in DNA synthesis) will be labeled.After continued growth of the population, thelabeled cells will pass through mitosis as a wave,and this fraction can be estimated by preparingautoradiograms at different times and countingthe fraction of labeled cells which are in mitosis.At least in mammalian cells, mitotic figures canbe easily recognized. The results to be expectedfrom the ideal case and the results obtained in anactual example are given in Fig. 7. Initially, thereare no labeled mitoses until a time equal to G2has passed, after which the fraction of labeledmitoses rises to 1.0 in a period equal to the dura-tion of mitosis (M). The labeled fraction remainsat 1.0 for a period equal to the duration of the Sphase minus the duration of mitosis (S - M),and subsequently falls to zero. The second waveof labeled mitoses appears after a further timeequal to G1 + G2. It is thus possible to calculatethe duration of the various phases from the timeperiods exhibited by the graph. Although theshape of the experimental curve does not pre-cisely follow the ideal, it is close enough for mostpractical purposes.The limitations of any technique involving the

use of radioactive thymidine should be kept inmind. It must be known that the population inquestion assimilates this compound and in-corporates it only into DNA. If there is a largepool of nonradioactive thymidine, this will affectthe kinetics of labeling; consequently, it is es-sential at the end of the pulse to add an excess ofnonradioactive thymidine, which dilutes anylabeled material remaining in the pool. It isessential to know that the tritiated thymidineitself does not alter the cell cycle (e.g., throughradiation damage). The labeling time must bekept short, but it must be long enough to permitlabeling sufficient for detection on the autoradio-grams. The technique can be applied only to sys-tems in which the number of dividing cells issufficiently high that the fraction of labeledmitoses can be determined accurately.

If pulse labeling, which often requires manipu-lation of the culture, is not possible, continuouslabeling can be used. With this method, theisotope is added once and maintained in excessthroughout the labeling period. To determine the

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FIG. 7. Fraction of labeled mitoses as a function oftime after a pulse of 3H-thymidine. Upper: ideal casewith no intercell variation. Abbreviations: L, durationoflabeling; ti, time for mitosis; t,, duration ofS phase;t1, duration of G, plus one-half of Tm; t2 duration of G2plus one-half of ti; G1 and G2 as on Fig. 6. Bottom:actual data for mouse L cells. G1, 5.7 hr; S, 12.2 hr; G2,4.4 hr; M, 0.9 hr; T (total cell cycle time), 23.2 hr.Taken from Fig. 4.5 of Cleaver (15).

parameters of the cell cycle with this method,three functions must be determined: the fractionof labeled mitoses, the fraction of labeled cells,and the average grain count per cell. A typicalcontinuous-labeling experiment is shown in Fig.8. The upper curve, showing the rate of increasein labeled mitoses, is used to calculate G2, as inthe pulse-labeling technique. The fraction oflabeled cells increases linearly (middle curve) as aresult of the entry of cells into the S period. Withpopulations in exponential growth, there aremore young cells than old; hence the rate of entryof cells into S is greater than the rate of celldivision. For this reason, the rate of increase inlabeled cells is faster than the rate of cell divisionand cannot be used directly as a measure ofdivision rate. The labeled fraction will reach1.0 at a time equal to G1 + G2, and since G2 wasestimated already G1 can now be calculated byusing the data obtained in the middle curve. Themaximum amount of radioactive thymidine whicha cell can incorporate in one cycle (estimated bythe average grain count) corresponds to a singlecomplete round of DNA synthesis. Since thistakes the whole S phase to complete, the time ittakes for the average grain count per cell to reacha constant level corresponds approximately to theS period (lower part of Fig. 8). [In actual fact,this procedure slightly overestimates the dura-tion of the S period; the complications are dis-cussed by Cleaver (15).]

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FIG. 8. Continuous-labeling experiment with 3H-thymidine and human skin epithelium cells. The uppercurve is used to determine t2 (4.5 hr) in the same manneras in Fig. 7. The middle curve is used to estimate t1 +t2 (16.3 hr); thus both t1 and t2 can be calculated. S

(5.4 hr) is estimated from the lower curve. The otherparameters can then be calculated. Taken from Figure4.6 of Cleaver (15).

An alternative method of measuring the rate ofentry of cells into the S phase involves a doublelabeling technique, a pulse of tritiated thymidinebeing used for the first labeling followed after adefined time interval by a pulse of "4C-thymidine.Autoradiograms can be prepared by using adouble-emulsion technique which permits count-ing separately radioactivity due to tritium orcarbon-14. The interval between exposures to thetwo labels should be less than G2 + M to ensurethat labeled cells do not divide during the periodof labeling (36).

If it is possible to determine the DNA contentper cell by microspectrophotometry of Feulgen-stained autoradiograms, the relative duration ofthe four phases of the cell cycle can be determinedmore directly, since cells in G2 will have twice theDNA content of cells in G1. The population needbe labeled only for a brief period before fixationso as to label the S-phase cells. By microspectro-photometry, the unlabeled cells can be dividedinto G, and G2; the mitotic cells are detectedcytologically, and the S phase cells by autoradiog-

raphy. In this way, the fraction of the cells in eachof the four phases is estimated and the relativedurations of the four phases can be determined(see p. 123 of reference 15 for details). To con-vert these relative values into absolute ones, it isnecessary to determine by other methods theduration of one of the stages of the cell cycle inabsolute terms. The advantage of this method isthat it requires only brief labeling and only asingle sample of the population. The disadvantageis that it requires microspectrophotometry, whichis laborious and can be performed only on fairlylarge cells.Although the methods described above have

been applied extensively to mammalian systems,they have been used only rarely with eucaryoticmicroorganisms, usually with pure cultures [seeCleaver (15) for references]. However, the po-tential value of these methods for microbialecology is clearly so great that their descriptionhere appears justified.

GROWTH RATES OF PROCARYOTESAS MEASURED BY THYMIDINE

AUTORADIOGRAPHYThe measurement of the growth rates of

procaryotes presents some new complicationsbecause procaryotes do not exhibit the typicalmitotic cell-division cycle described above foreucaryotes. In the bacteria which have beenstudied, DNA synthesis in exponential popula-tions occurs throughout virtually the whole of thecell cycle, being interrupted only briefly at thetime of cell division (37). Consequently, if apulse of tritiated thymidine is given to a growingbacterial population, virtually all cells becomelabeled to some extent, in contrast to the situa-tion in eucaryotes in which only cells in S phaseget labeled at all, and these heavily. A secondproblem is that since procaryotes do not divideby mitosis, it is impossible to evaluate micro-scopically the fraction of cells in division. Last,because of the small size of most procaryotes andthe low DNA content per cell, grain counting onautoradiograms is difficult; even heavily labeledcells have only a few silver grains over them.

If grain counting is possible, growth rate canbe estimated by a continuous-labeling method.Referring to Fig. 8, it can be seen that the timerequired for the mean grain count per cell to reachsaturation is approximately equal to the length ofthe S phase, and if the S phase occupies 90 to 97%of the cell cycle (the situation in E. coli), thelength of the cell cycle (virtually the same as thedoubling time) can be estimated.

It would be desirable to have methods whichdid not require grain counting. An approach I

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used (10) was to measure the rate of accumulationof labeled cells in the population during con-tinuous labeling. The marine bacterium L. mucorwas used in this study. This is a large, filamentousepiphyte of seaweeds which is readily recognizedin natural material. Since the filaments projectperpendicularly from the surface of algal fronds,microscopy and preparation of autoradiograms isrelatively easy. In growing laboratory cultures,the rate of accumulation of radioactive cells islinear with time at least until 80% of the cells areradioactive. (Some cells never become radioactiveeven after long time periods, so that if incubationwith tritiated thymidine is continued indefinitelythe rate of accumulation of radioactive cells fallsoff.) The rate of accumulation of radioactive cellsis proportional to the doubling time of the culture,and about 1% of the cells get labeled in 0.002generation. This relationship, determined for apure culture, could then be used to estimatedoubling time in nature (10). With this technique,one assumes that the rate of accumulation ofradioactive cells is linear and begins without alag, just as it does in pure cultures, and that non-radioactive thymidine, which might dilute theradioactive material, is absent from seawater. Itis desirable to analyze samples incubated atseveral different times to ensure that the rate ofincorporation is indeed linear in nature.

This technique requires a study with laboratorycultures growing at known rates so that the fielddata can be converted into real doubling times,and it requires the assumption that there isnothing intrinsically different about the waycultures and natural samples incorporate tritiatedthymidine.For determinations of relative rather than abso-

lute growth rates, preliminary studies withlaboratory cultures are not necessary. From thelabeling rates of different natural populations it ispossible to deduce which populations are growingfastest. For some studies, such relative ratessuffice. However, to determine the contribution ofa particular organism to food chains, absoluterates are essential.

Ecological Approximations for LabelingExperiments

The labeling of DNA is a particularly valuabletechnique for the study of growth rates becauseDNA is the only macromolecule in the cell whichdoes not turn over and because synthesis doesnot occur in nongrowing cells. In exponentiallygrowing populations, in which turnover is negli-gible, the rate of synthesis of any macromoleculecould be measured because all materials aresynthesized at the same rate. Since even in steady-

state populations turnover and resting synthesismay be low, the measurement of the rate ofsynthesis of some macromolecule other thanDNAmight be acceptable as a first approximation forecological work.A point which needs to be emphasized is that

in any labeling experiment the time of incubationwith the isotope must be kept short (i) to preventany secondary changes from taking place duringthe time the population is confined to the bottle,(ii) so that the concentration of isotope alwaysremains in excess, and (iii) so that the experimentis terminated before any recycling of the label hasoccurred.

Rate of Appearance of Unlabeled CellsAnother radioautographic method which has

some advantages over those described aboveinvolves measuring the rate at which unlabeledcells appear in a population which is fully labeledand then placed in medium which lacks label.Because of the semiconservative replication ofDNA, after one cell division the specific radio-activity of each of the two offspring will be halved;consequently, one can measure growth rate bymeasuring the time taken for the grain count todecrease by half. The advantage of this method isthat the labeled population can be placed undercompletely natural conditions, eliminating effectsof confinement to bottles or to effects of theisotope itself. The disadvantages are that thepopulation must be removed from its naturalenvironment for labeling and that after severalcell divisions the mean grain count will be reducedto such low levels that an accurate count will notbe possible. Thus, the method seems best adaptedfor studying the behavior of species after intro-duction into foreign environments. This methodapparently has not been used in ecology, althoughit is widely used by mammalian cell biologists(15). The genetic method of Meynell (discussedbelow) is formally equivalent to this isotope-dilution method.

In bacteria or other small organisms in whichgrain counting is difficult, a modification of thismethod might be to measure the rate of appear-ance of unlabeled cells in a fully labeled popula-tion. After the first cell division, all cells will stillbe labeled, but the labeled fraction will decreaseby half after the second and subsequent celldivisions (Fig. 9). By counting the labeled andunlabeled cells after various periods of time, thedoubling time of the population can be calculated.Although for both of these methods a fully

labeled population is desirable, the methods canbe less accurately applied to partially labeledpopulations. This would be of considerable value

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I-

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FIG. 9. Change in specific radioactivity of a popula-tion as a function of time after labeling. "A" is the timethat elapses before labeled cells pass through the non-dividing compartments and begin to decrease in radioac-tivity. "B" is the time for the specific radioactivity todecrease by one-half, which is equivalent to the doublingtime. After Fig. 7.5 ofCleaver (15).

if full labeling required excessively high isotopeconcentrations or long incubation times.

GENETIC METHODSAn interesting method using genetically marked

cells was devised by Meynell (40, 41) to measurethe growth rates of bacteria in the animal body.As Meynell notes, bacterial growth in vivo isusually much slower than it is in laboratorycultures. This could be either because the animalis an unfavorable habitat for bacterial growth orbecause bacteria are being killed in vivo so thatthe division rate is greater than the rate of in-crease of the viable count. These two possibilitiescan be distinguished only if a method is availableto measure bacterial growth when some cells aredying. The technique which Meynell used was tointroduce a nonreplicating genetic marker intothe bacteria before inoculation into the animal.As shown in Fig. 10, at each cell division thefraction of the population which contains thelabel will be halved. One determines the totalpopulation and the population with the geneticlabel at different time periods; from the rate atwhich the marker is lost, the doubling time canthen be calculated. This method is formallyanalogous to the isotope dilution method de-scribed above, but it is simpler because it elimi-nates autoradiography and direct microscopy,the labeled and unlabeled populations being as-sessed by plating procedures.

In his first work, Meynell (40) made use of thefact that when a lysogenic bacterium is superin-fected with an appropriate mutant of its prophage,the mutant enters the bacterium but does notreplicate. Its presence can be assessed after induc-tion by plating on an indicator bacterium which isspecific for the superinfecting phage. Preliminaryexperiments showed that the marked populationdid behave as predicted during cell division upuntil the 10th generation, after which the pro-portion of marked bacteria decreased at a rateless than predicted, probably because about 0.1%of the original bacteria were lysogenized by thesuperinfecting phage so that replication couldoccur. Mice were inoculated intravenously withE. coli K-12 lysogenized with phage lambda band superinfected with lambda hc. Within 30 min,the bacteria had cleared from the blood and werelodged in the liver and spleen. Assessment of totalviable counts showed that the viable countdropped about three decades in the first 8 hr anddid not decrease farther over the next 48 hr. Theproportion of labeled organisms remained con-stant over the duration of the experiment,showing that no replication occurred.

In a second study (42), Meynell applied thistechnique to a study of the replication, killing,and excretion in the feces of Salmonella typhi-murium which had been inoculated into the mouseorally. The genetic label was a histidine geneintroduced in the abortively transduced state.Since the gene in an abortive transductant doesnot replicate, it is passed to only one of thedaughter offspring at division. The proportion ofcells in the population containing the gene isdetermined by plating on medium without histi-dine and scoring for the tiny colonies formed bythe abortive transductants. Since excretion was a

First SecondInital-ly Generatlon GeneratIon

FiG. 10. Distribution ofa nonreplicating genetic ele-ment among dividing bacteria. The closed circle is thenonreplicating element; the open circle and line repre-sent the replicating genome. At each generation, thefraction of cells containing the marker decreases byone-half. Based on Meynell (40).

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major factor in loss of viable cells from the in-testine, the ability to distinguish excretion fromdeath is clearly of value. In most cases, the bac-teria underwent only a few divisions in the in-testine. If the mice had been treated with strepto-mycin to eliminate normal intestinal bacteriabefore inoculation (the infecting strain used beingstreptomycin resistant), cell division was morerapid. The results showed that the normal mouseintestine contained a mechanism which wasbacteriostatic and weakly bactericidal to S.typhimurium.In neither of the two systems described above

did much bacterial division occur. In anotherstudy, Maw and Meynell (39) studied the growthin the mouse of S. typhimurium, a natural patho-gen of this animal. The marker was a superin-fecting mutant of phage P22. After intravenousinoculation the organism became lodged in thespleen. The viable count doubled every 24 hr,whereas the true doubling time as determinedfrom rate of dilution of the genetic marker was8 to 10 hr. This should be compared with theminimum division rate observed in the test tubeof 0.5 hr. The division rate in the spleen was atbest only 5 to 10% of the maximum observed invitro, and the death rate in the spleen was quitelow. These results show that the maximumpotential growth rate is not reached in vivo evenby an organism which is highly pathogenic.

Despite the fact that Meynell's method is re-stricted to organisms for which the relevantgenetic combinations can be constructed, it isclearly an interesting one with considerablepromise. It should be useful in many cases inwhich it is of value to measure the division rate oforganisms newly introduced into a habitat. Itsuse in studies of host-parasite relations may giveus new insights into mechanisms involved in theestablishment of colonizing species.

METHODS ESPECIALLY SUITED TOSTEADY-STATE POPULATIONS

A system in steady state is in a time-independentcondition in which production and consumptionof each element of the system are exactly bal-anced, the concentrations of all elements withinthe system remaining constant even though thereis continual change. Steady-state microbialpopulations are found in a number of naturalhabitats: the rumen (31), the intestinal tract (21),hot springs (11), and perhaps even infected ani-mals (23, 24). In the steady state there is no changein population size, even though cell division istaking place. Because of this, it is impossible tomeasure growth rates from changes in absolutenumbers, and one must seek more ingeniousmethods.

As I have pointed out elsewhere (8), an im-portant item in characterizing a specific steady-state system is its time constant. Althoughfluctuations in growth rate may occur over ashort period of time, on a long view of the systemthese fluctuations can be ignored. Thus, in thesystem of decomposition which occurs on thedeciduous-forest floor, there is a great change innutrient input in the autumn when leaves fall, buton an annual basis the forest floor ecosystem is insteady state because no net accumulation of leavesoccurs (44). In the rumen, great changes occurdaily as a result of feeding, but in the long runthe system is constant (31).The chemostat is an excellent laboratory model

of a steady-state population (5), and it is in-structive to consider how one measures growthrate in a chemostat, the principles developedthere being readily adapted to natural situations.Measurement of growth rate requires a knowl-edge of the volume of the system (v) and its flowrate (f). The turnover time is v/fand the doublingtime is equal to the turnover time.

Let us consider how the principle of the chemo-stat can be applied to a natural system. In a well-mixed system such as the rumen, the problemreduces to one of determining the rate at whichmaterial passes through, that is, the flow rate f.Hungate (31) discussed this problem in detail. Ifa pulse of an inert material (the marker) is givenat zero time and if mixing is completed quickly,the rate of change in concentration of this inertmaterial will give a measure of the turnover time.Because of mixing of the marker with unmarkedcontents and with material entering later, not allthe marker leaves during one turnover time, eventhough during this period the total materialleaving equals the total entering. The half-time,that is, the time at which the concentration ofmarker reduces to one-half the initial, is equal to0.69 of the turnover time. Suitable markers foruse in the rumen include nondigestible materialsfrom the feed such as lignin or silica, or artificialmarkers such as iron oxide, chromic oxide,polyethylene glycol, rubber, etc.

If we know the turnover time (flow rate), andwe know that the microbial population is insteady state, we know the doubling time of thepopulation. To calculate the productivity of thepopulation, that is, the number of new cells pro-duced per day, we must also know the absolutepopulation size, which can be determined bydirect microscopic count. In the sheep rumen,there are about 1010 bacteria per ml and since theaverage volume of the sheep rumen is 5 liters, thetotal population is about 5 x 1013 bacteria. If theturnover time were 24 hr, 5 X 101u bacteria wouldbe produced per day.

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In this discussion it has been assumed thatbacteria disappear from the system only bypassing out of it. If predation or lysis occurswithin the system, the estimate of productivitycould be low. Further, the estimate is for therumen as a whole and assumes that it is a com-pletely mixed system. It is quite possible thatthere are microhabitats within the rumen (e.g.,the surfaces of food particles) where growth israpid and other habitats with reduced ability tosupport microbial growth, so that the techniquedoes not necessarily measure the maximum po-tential growth rate possible for rumen micro-organisms. If for some reason knowledge of thispotential were needed, one of the techniquesdescribed earlier in this paper, such as measure-ment of the rate of development of microcolonies,would be necessary. Although this has not beenspecifically done for the rumen, it could probablybe done relatively easily (R. Hungate, personalcommunication).

If measurement of flow rate is not possible,growth rate in a steady-state system can be de-termined from the rate at which organisms leavethe system, assuming that all organisms producedwithin the system are excreted intact and can becollected and counted. If the total number oforganisms in the system is also known, the growthrate can be calculated. With this technique, neitherthe volume nor the flow rate needs to be measured,but the system must be completely mixed. Thismethod was used by Gibbons and Kapsimalis (21)to measure the growth rate of the total intestinalmicroflora of hamsters, guinea pigs, and mice.The animals were placed in individual cagescontaining coarse-screen bottoms, and the fecalpellets which dropped through were collected.Twice a day for 3 days the pellets were collected,weighed, and homogenized in a diluent, afterwhich direct microscopic counts were performed.Estimates of the total quantity of bacteria ex-creted per day were made by multiplying thenumber of bacteria per gram of feces by the aver-age number of grams of feces excreted per day.After the excretion rate was determined, theanimals were sacrificed and the bacterial count ofthe entire intestinal canal was determined. Theaverage number of generations per day was thencalculated. The doubling times of the intestinalbacteria calculated in this way were fairly low,varying from less than one to about six doublingsper day. The intestinal flora of mice seemed togrow faster than those of hamster and guinea pig,but for all three species of animals the rates weremuch lower than those of typical intestinalbacteria in laboratory culture.One possible limitation of this experiment is

that bacteria might be destroyed within the intes-

tine by predation, parasitism, or lysis. To checkthis, Gibbons and Kapsimalis (21) repeated theirexperiments with gnotobiotic mice inoculatedwith a pure culture of E. coil. Even under thesepresumably ideal conditions, E. coli grew ataverage rate of only 1.2 divisions per day. Oneexplanation for this observation may be that en-vironmental conditions (e.g., nutrient availability,pH, presence of natural inhibitors) may be in-herently unfavorable for more rapid growth.Another possibility is that in certain micro-environments within the intestinal tract thegrowth rate is much higher than for the intestinaltract as a whole. It seems to me that the latterexplanation has considerable merit, since theintestinal tract is highly heterogeneous bothphysically and chemically, and it is well estab-lished (51) that high bacterial populations liveattached to the walls of the intestinal tract. If allthe bacteria are growing in microenvironmentswhich occupy only 10% of the total intestinalvolume and after being sloughed into the lumengrow no further, the growth rate in these micro-environments would be 10 times that of theintestinal tract as a whole. Furthermore, in theseexperiments the assessment of total number ofcells per intestinal tract included both growingand nongrowing cells. If all the cells were pro-duced in 10% of the habitat and after enteringthe rest of the habitat grew no further, theywould still be counted in the assessment of totalnumbers and would enter into the overall calcu-lation. For instance, if the total bacteria excretedwere 1,000 X 109 and if the count for the wholeintestine were 1,000 X 109 but only 10% of thecells were from growing habitats, then the growthrate would be 1,000/100 = 10 generations per dayrather than 1. This serious error could be elimi-nated if only the cells in growing habitats werecounted, although such counts could be doneonly if it were known where growth was takingplace. Autoradiographic methods might providea solution to this last problem.Another approach to the measurement of

steady-state growth was taken by Brock andBrock (11) for use in their studies on thermophilicalgae in hot-spring drainways. It involved meas-urement of the algal wash-out rate after growthwas prevented by darkening the system. Imaginea chemostat operating under steady-state condi-tions but with unknown volume and flow rate. Inprinciple, the generation time could still be de-termined if growth were completely inhibited ina manner which did not otherwise alter the sys-tem. Wash out would still continue and thewash-out rate could be estimated by performingcell counts at various intervals of time. Since

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Ts = 40 HOURS

HKXM

FIG. 11. Rate of loss of algal cells from a darkenedportion of a hot-spring algal mat. From Brock andBrock (11).

growth balances wash out, the growth rate couldthen be determined.

This approach was relatively easy to use in hotsprings because the effluent channels provide flowrate and temperature characteristics that arerelatively constant over extended periods of timeand because the algal population which developsreaches a steady state when the thickness of themat is such that self shading occurs. Waterflowing across the surface of the mat causeserosion of the cells through mechanical action,and the lost cells are replaced by newly grownones. In areas of laminar water flow, a uniformmat develops from which replicate samples canbe taken at different time periods. In studies atMushroom Spring extending over 3 years (7, 11,12), population density at selected stations re-

mained fairly constant. However, if the systemwas darkened the algae disappeared quickly andwere virtually absent within 2 to 3 weeks.The results of a typical darkening experiment

are given in Fig. 11. It can be seen that within 2days after darkening the population density beginsto decrease and that the rate of loss is exponentialover at least two decades. In the example of Fig.11, the half-time of the rate of loss was 40 hr. Ifthe assumptions made above are valid, thedoubling time of the population in the steadystate was 40 hr.During the first day or two after darkening

there is virtually no loss of cells. Perhaps this lagreflects normal adaptation of the algae to alter-nating day and night, wherein during the dayproducts of photosynthesis are stored for use asenergy sources during the night (12). Further,although cell division may occur only during thenight, as in Chlorella (54), this does not affect thecalculation of the doubling time of the popula-tion. Finally, for the technique to work the mech-anism by which the cells are lost from the systemdoes not really matter; erosion, lysis, or predationcould be responsible. (In a system in which cellsdie but do not disappear, viable counting orautoradiography might be used to measure lossrate.)In the hot-spring system it was possible to show

directly that cell loss was due to erosion in thefollowing way (unpublished data). Temperaturesaround 70 C are near the upper limit for blue-green algal growth, so that water flowing over themats comes from alga-free areas. Large volumes ofwater were collected just downstream from sta-tions where darkening experiments had previouslybeen done (the mats being first allowed to returnto the steady state), and these water samples werepassed through membrane filters to remove thealgal cells. The algae were then counted on themembrane filters by using vertical illuminationon a fluorescence microscope, the algae beingrecognized because of the intense red auto-fluorescence imparted by chlorophyll and phyco-cyanin. In this way, the density of algal cells inwater which had flowed over the mat could becalculated. This calculated erosion rate was sim-ilar to the loss rate measured in the darkeningexperiments, thus providing evidence that cell lossin the steady state is due to erosion rather thanto lysis or predation.Another factor to be taken into consideration

is the error which might arise if cells from watersettled under the darkened area. If the mat understudy receives water from an upper algae-con-taining area, since such water contains algae, theloss rate would be underestimated if settlingoccurred. This point was checked (unpublisheddata) by placing glass slides containing depressionwells on top of portions of algal mats under theblack covers. Some algal cells did settle onto the

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slides and, at intervals, slides were removed andalgal densities were quantified. The study showedthat settling rate was two to three decades lowerthan wash-out rate, so that this factor was not amaterial source of error. Apparently, once thecells are taken into the rapidly flowing water theirchances of settling are poor until the water hasreached the foot of the spring, at which flow rateis much slower. In other habitats, settling may bemore significant; thus, controls for settling shouldalways be used.

It should be emphasized that the steady-statedarkening technique measures only the growthrate of the population as a whole. It is possible(in fact, likely) that growth rates of differentsubsets of the population may vary quite markedlyfrom this average value. In these compact algalmats in which self-shading is considerable, cells inthe deeper parts of the mat receive much lesslight than do surface cells. Quantitative graincounts of autoradiographs of mats labeled with'IC from CO2 showed a progressive decrease inlabel from the surface to the bottom of the mats,which were 5 mm thick (12). Thus, although inthe study presented in Fig. 11 the population as awhole was doubling every 40 hr, the cells at thesurface were photosynthesizing faster and wereprobably developing faster than those at thebottom. This is, of course, the same problemwhich we discussed earlier in relation to measure-ment of growth rate in the rumen and intestinaltract. In terms of what the organisms are doingto the ecosystem, it is the growth rate of thewhole population which is of interest. If onewishes to determine the fastest growth rate whichan organism is capable of realizing in nature,another technique will be necessary.The measurement of wash-out rates in growth-

inhibited, steady-state populations can be ap-plied with suitable modifications to other systems,both photosynthetic and heterotrophic. Withphotosynthetic systems, removal of the energysource without disturbing the system is relativelyeasy and could be applied to other algal habitatssuch as rivers, soils, and rocks. (The darkening ofa whole lake would probably be beyond thecapabilities of most research studies.) It is im-portant to know in such studies that the factorsaffecting wash out are not themselves altered bydarkening. For instance, if loss of algae was duenot to erosion but to animal grazing, it would benecessary to ascertain that the animals involvedwere not themselves affected (physiologically orbehaviorally) by darkening.With heterotrophic systems, the inhibition of

growth would probably require the use of anantibiotic which was specific for the organism of

interest but did not affect other activities of thesystem. For studies of bacterial growth in higheranimals, a whole array of suitable antibiotics isalready available. For instance, to study thegrowth rates of intestinal organisms, antibioticssuch as streptomycin and neomycin, which do notpass through the intestinal wall into the bloodstream, could be easily used. It is well known thatadministration of such antibiotics orally resultsin inhibition of growth and elimination of in-testinal bacteria. Although these antibiotics havebeen used both experimentally and clinically tosterilize the intestine, they have not been used inquantitative measurements of the rate of wash outof bacteria from the intestines.One study involving the growth of Mycobac-

teriwn tuberculosis in the lungs of mice is relevantto this discussion. Gray and Cheers (24) showedthat after an initial establishment period whichtook 6 weeks, the M. tuberculosis populationreached a steady-state level in the lung which wasmaintained for at least the next 12 weeks. If in-fected mice were treated with drugs (pyrazinamideplus isoniazid) after the steady state had becomeestablished, there was a prompt exponential dropin numbers with a half-time of less than a week.This interesting experiment was done for anotherpurpose than measuring growth rate, and becauseonly viable counts were made it is not clearwhether loss is due to lethal effects of the drugs orto destruction of cells by the animal after growthhad been inhibited. In the latter event, these datacould be used to calculate the steady-state growthrate.Even if a population is not in steady state,

growth rate might in principle still be measured.In a habitat in which absolute cell numbers areincreasing, losses will still occur through preda-tion, lysis, grazing, or wash out. Under these con-ditions, loss rates could be measured by a growth-inhibition procedure for samples taken at differ-ent times, and the loss rates obtained at each timecould then be added to the observed rate of in-crease at each time, thus making possible a calcu-lation of the actual growth rate. Admittedly, thistechnique is laborious.A stable population size does not necessarily

indicate a steady state in which growth is oc-curring. The organism may be in a habitat inwhich grazing, lysis, and wash-out losses areessentially zero but in which conditions are un-favorable for growth. A situation of this kind wasfound by W. N. Doemel (Ph.D. Thesis, IndianaUniversity, 1970) in his studies on the growth rateof the eucaryotic alga Cyanidium caldarium inacid hot springs. Artificial channels placed in theflowing water provided fresh habitat for coloniza-

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tion and growth by C. caldariwn. After an ex-

tended exponential increase in cell numbers, thepopulation reached a constant level. Darkeningof a portion of the channel at this time did notresult in immediate wash out, although coloniza-tion did not occur on a fresh darkened channel.The constant population level reached by theorganism thus resembles a stationary phaserather than a steady state. The probable explana-tion is that in its niche there are rarely predatoryor grazing organisms, and, because the cells are

quite dense and the flow in the acid streams is notvery turbulent, erosion of cells from the mat bythe mechanical action of the water is minimal.Another method for measuring growth rate in

the steady state is to inhibit wash out, grazing, or

other losses and to measure the rate at which thepopulation whose density was kept in check byone or more of these factors increases after thecheck has been removed. This presupposes thatthe limiting factor can be eliminated withoutaltering the system in other ways. Gambaryan(20) used this method to measure generation timesof bacteria in muds of Lake Sevan (U.S.S.R.).In this habitat, bacterial growth took placeprimarily in the liquid phase, and protozoa or

other animals feeding on the bacteria could beeliminated by passing the muddy water throughfilter paper. Controls showed that these filtratesdid not differ significantly in physiochemicalrespects from the original muddy water. To ob-tain an estimate of the generation time in mud,bottom samples were filtered and the filtrate wasdivided into two samples; one of these was usedto obtain the initial bacterial count and the otherwas placed in a test tube which was sealed andimmersed in the lake at the sampling site. After24 hr, the test tube was removed, samples of theinitial and final samples were passed throughmembrane filters, the organisms were stained on

the filters, and microscopic counts were per-formed. Generation time was calculated from theformula: generation time = (time of incubation)(log 2) divided by (log final count minus loginitial count). In various parts of the lake,generation times of 10 to 281 hr were determined.Unfortunately, controls to show that the popula-tion density was being kept in check by protozoaand other animals which consume bacteria werenot included.

El-Shazly and Hungate (18) used an analogousapproach to measure net growth rate of rumenmicroorganisms. The population densities ofsamples of rumen material were assessed im-mediately after removal and again after incuba-tion in vitro for 1 hr under simulated rumenconditions. The relative population densities were

estimated by making maximal fermentation rate

measurements; thus, rates of change in populationsize could be determined. It must be assumed thatthe only role of the glass bottle is to confine thegrowing population and prevent wash out andthat secondary changes do not take place duringthe 1-hr incubation. To check this, studies werealso carried out on samples incubated in dialysisbags in the rumen of a fistulated animal; the dataobtained were similar to those obtained in vitro.It must also be assumed that losses due to proto-zoal grazing are negligible. In these studies, thenet growth values per hour ranged from -7 to+27% of the population, but even in a singleanimal marked differences were observed over adiurnal feeding cycle. Net growth was smallest(or even negative) justbefore the morning feeding,when bacterial nutrients were probably limiting;the highest growth rate was found several hoursafter feeding. By adding growth rates obtainedover the diurnal cycle, a daily growth rate (turn-over time) of 1.92 was obtained, in good agree-ment with estimates made from calculations ofwash-out rates from use of nonmetabolizabletracers to measure dilution rate.

Experiments of this type could, in principle,be done in any habitat in which losses due tograzing are low or in which grazers could beeliminated. However, since incubation time mustbe kept very short to avoid secondary changes inthe bottle, accurate methods for assessing popu-lation size are necessary to permit detection ofsmall differences. An incubation time less thanone-tenth the doubling time is probably desirable.In phytoplankton studies, population densitiescan be assessed very accurately by use of "CO2,making it possible to use this method fairlyeasily; Eppley (19) has applied it with somemodifications to measurement of growth rates ofphytoplankton living in the sea off La Jolla,Calif. (The study was actually designed to measurethe standing crop of photosynthetically activephytoplankton, but it determines growth rate aswell.) Samples of seawater were filtered through150-,Am netting to remove larger animals andwere then incubated on shipboard under insitu light and temperature conditions with "(C02.Samples were taken at 24 and 48 hr, and theassimilated radioactivity was determined bymembrane filtration. From changes in rate of l<:uptake after 24 and 48 hr, the specific growth rate(k) was calculated from the equation k = 1/daysIn (48 hr-uptake - 24-hr uptake/24-hr uptake).Apparent growth rates of about one to twodoublings per day were obtained. The incubationtimes which Eppley used were long, but were sochosen to avoid problems associated with diurnalperiodicity in algal photosynthesis. Shorter incu-bation times could be used if high specific radio-

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activity "CO2 was used and if periodicity wasobviated by incubating under saturating light toobtain the potential maximum photosynthesisrate. With such modifications, the method be-comes precisely analogous to that of El-Shazlyand Hungate (18).

INOCULUM SIZE: RATE OFEFFECT

An interesting technique quite different fromany of the above has been used to estimate thegrowth rate of the spirochete Treponema palidumin syphilitic lesions in the rabbit (17). An averageincubation time of 17 days is required for ademonstrable lesion after the intradermal injec-tion of 500 organisms; and the time required forthe development of a lesion is reduced by 4 daysfor each 10-fold increase in inoculum size. Sincea 10-fold increase in number is equivalent to 3.3generations, the generation time of the spirochetein vivo can be estimated as 4 days/3.3 generationsor 1.2 days (29 hr) per generation. It is assumedthat each inoculated cell is capable ultimately ofproducing a lesion.With modifications, this technique might be

applicable to various other situations (in, forexample, nodulation rate by rhizobia or the rateof establishment of a component of the intestinalflora).

CONCLUDING STATEMENTA wide variety of methods for measuring

microbial growth rates in nature is available. Atleast one of the methods described should beapplicable to any specific ecological situation.

Is the result obtained worth the effort? This canbe answered only in the context of a particularstudy. In a large ecosystems study, the unavail-ability of information on microbial growth rateswould be a serious lack. In a simple study of thephysiological ecology of a single organism, theknowledge of growth rate may be a useful param-eter for the interpretation of the response of anorganism to environmental variables. In our ownstudies on the ecology of L. mucor (33) andthermophilic blue-green algae (11), a knowledgeof growth rates provided an important insightinto how these organisms succeed in their naturalhabitats. Such information is of considerablevalue in interpretation of evolutionary processes,and it significantly supplements the conclusionsdrawn from studies of the same organisms inlaboratory systems. Indeed, without such studiesin nature, the laboratory studies are not too useful.

ACKNOWLEDGMENTSThis investigation was supported by research grants GB-7815

and GB-19138 from the National Science Foundation and by re-

search contract C00-1804-22 from the Atomic Energy Commis-sion.

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Documents

Microbial Growth Rates in Nature · MICROBIAL GROWTHRATES types of growing populations (Fig. if, ig, and lh). An example of growth plus setting (Fig. if) might be the bottom flora