GROWTH O F PROTOZOA I N PURE CULTURE 11. EFFECT UPON THE GROWTH CURVE OF DIFFERENT CONCENTRA-

TIONS O F NUTRIENT MATERIALS

AUSTIN PHELPS I The Hopbins Marine Station, Paci$c Grove, California

FIVE FIQURES

In a recent paper (Phelps, '35), a method for the study of populations of the ciliate, Glaucoma pyriformis,2 in a con- trolled sterile medium has been described, and an initial in- vestigation of the growth curve has been made. Since, in re- cent years, the problem of the effect of concentration of ex- cretory products, as opposed to the effect of diminution of food supply, as limiting factors of the growth of a population in a closed system, has evoked much attention from investi- gators, and since the results obtained along this line have in most cases been somewhat inconclusive, it seemed profitable to continue the study of the growth of Glaucoma pyriformis in the direction of altering the concentration of food in the culture medium and observing the effect thereof upon the division rate and total yield of the population.

The protozoa, and the bacteria and yeasts, have proven favorite subjects for this type of research, because of the speed with which they multiply, as well as the relative ease with which they are handled. A review of the literature on this subject together with a statement of the present status of the problems of crowding in populations is to be found in

'As pointed out in the previous paper there is some doubt as to the identity of this organism. Dr. Andre Lwoff has identified i t as identical to the one em- ployed by himself and identified by Dr. Edouard Chatton as Ghucoma pyriformis.

479

National Research Fellow in the biological sciences.

THB JOURNAL OF EXPERIMENTAL ZOOWXTY, VOL. 72, NO. 3

480 AUSTIN PHELPS

Allee ( '31, '34). All the investigations on the effect of excre- tory products on the protozoa, both as regards division in iso- lation cultures and the growth of populations in mass cultures have, until very recently employed perforce mixed strains of bacteria of unknown quantity as a source of food. There is every reason to believe that the metabolic activities of these bacteria so complicate the system employed that conclusions in regard to the effect of the protozoan metabolic products on the protozoa themselves are unreliable.

MATERIALS AND METHODS

The animals employed and the technique of culturing them have been described elsewhere (Phelps, '35). A few altera- tions and improvements have, however, been introduced into the present work. Instead of employing yeast extract (Difco) exclusively, a liquid yeast autolysate, which has been prepared regularly at the Hopkins Marine Station and which has been described by Jensen, ('19) was employed for one of the two sets of experiments. Also, it was found expeditious to use Schott glass sintered aeration flasks, as described by Kluyver, Donker and Hooft, '25, in place of 1,000 cc. Erlenmeyer flasks. The volume of culture fluid employed was in most cases 500 cc.

A refinement in the method of counting which proved to be time saving, especially where heavy concentrations of animals are to be counted, was employed to a large extent in the course of the following experiments. Instead of making counts of living animals, the animals were first killed by placing 10 cc. of the culture medium containing the animals to be counted, in a test tube, containing 2 cc. of Noguchi fixing fluid. The latter is made as follows:

100 cc. M ij j KsHPO,

M 3 KH,PO, 25 cc.

The fixed animals were then diluted to an appropriate extent in distilled water, and 0.5 cc. quantities of the mixture were

40 per cent f o r m a h 12.5 cc.

GROWTH OF PROTOZOA IN PURE CULTURE. I1 481

counted under the dissecting microscope. The distilled water causes the fixed animals to swell very considerably, so that the counting may be performed with greater speed and ease than when living animals were counted directly. There is, however, one limitation to this method. The fixed animals, after being placed in distilled water must be shaken immediately and for not more than 45 seconds. Otherwise the shaking will cause them to break up and render the count unreliable. After the shaking is finished, and the animals have been placed in watch glasses or depression dishes for counting, they may be left for as long as an hour without going to pieces. Numerous tests in which both living and killed animals taken from the same culture were counted, have given convincing evidence that the method of counting fixed animals is fully as accurate as the more direct method of counting living ones.

As in former experiments, the temperature was kept con- stant at 25°C. k 0.1"C. by the use of a water bath. The re- action was adjusted to a pH of 6.6, during the preparation of the medium by the addition of small amounts of NaOH or HCl. The pH was tested constantly, and found to remain ihed at about pH 6.6 from the time of inoculation until the end of the logarithmic growth phase had been passed. All cultures were so placed that they had indirect illumination during the day, and very faint electric illumination at night. At the end of each experiment the culture which had been under observation was tested for contamination by the method described in the first paper and cultures which were found to contain any other organism in addition to Glaucoma were not considered in the results.

EXPERIMENT8

$cries I . I n series I the growth of populations was ob- served when different concentrations of Difco yeast extract were employed as a source of food. All concentrations over 0.1 per cent were found to require aeration, and so were kept in 2000 cc. aeration flasks with a continuous flow of air circulating through the cultures, since it has been repeatedly

482 AUSTIN PHELPS

found that in a non-aerated flask, lack of air rather than ex- haustion of the supply of nutrient material or poisoning by excretory products, may be the decisive factor in limiting the growth of the population. An example of this is given in figure 1 showing the growth of Glaucoma in 10 per cent liquid yeast extract. In one of the two experiments performed the culture was aerated, while in the second no aeration was pro- vided. It will be seen that aeration prolonged the logarithmic growth phase from a limit of 80,000 animals per cubic centi- meter to about 330,000 animals per cubic centimeter. When

Fig.l Growth o f Glaucoma in 10 per cent liquid yeast. The upper curve represents an aerated culture and the lower one a non-aerated culture.

employing aeration flasks it was found necessary to add a drop or two of oleic acid, in order to prevent excessive foam- ing of the medium. The inoculum consisted of about 100 animals per cubic centimeter, taken from stock cultures con- taining 0.1 per cent yeast extract. The results of the six ex- periments in this series are shown in table 1, which indicates the concentrations of medium employed, the division rate during the logarithmic growth phase, the number of animals at the end of the logarithmic growth phase in each case, and the maximum yield of the population at each concentration.

GROWTH OF PROTOZOA IN PURE CULTURE. II 483

I n figure 2 the number of animals at the end of the logarithmic growth phase and also the maximum yield are plotted against the concentration of the medium. Figure 3 is a composite graph showing the growth of organisms in each of the six ex-

TABLE 1

UONOENTEATION

per cent 0.1 0.5 1.0 2.0 2.5 3.0

DIVISION BATE

hour8 3.8 3.8 3.8 3.8 3.8 3.8

MAXIMUM AT END OF MGAEITIIMIO PHASE

12,500 44,000 85,000

108,000 110,000 113,000

XAXIMIJM YIELLl

19,000 74,000 138,000 264,000 302,000 310.000

Fig.2 The lower curve represents the number of animals produced at the end of the logarithmic growth phase at different concentrations of Difco yeast ex- tract. The upper curve shows maximum yields at different concentrations.

periments. The experiments have been reduced to a common time denominator in order to make the logarithmic phases of the curves superimposable, and those parts of the growth curve which precede the logarithmic growth phase are not

484 AUSTIN PHELPS

shown. Animals taken from the stock cultures containing 0.1 per cent yeast extract, upon being placed in much higher concentrations suffered a shock, and failed to divide for some- times as much as 30 hours. The question of the effect of concentration of medium on the initial stationary phase and the lag phase will not be considered in the present paper.

Series 11. I n series I1 varying concentrations of liquid yeast autolysate were employed, in the place of Difco yeast

J. 0

Fig.3 Composite figure (see text) showing growth of animals in different concentrations of Difeo yeast extract.

extract. Concentrations over 2 per cent were found to re- quire aeration, and were kept in aeration flasks. All lower concentrations were kept in 1000 cc. Erlenmeyer flasks. Cultures were started with a concentration of about 100 animals per cubic centimeter taken, in the case of the lower concentrations, from stock cultures containing 2 per cent yeast extract. When concentrations of 15 per cent and 20 per cent of yeast extract were employed it was found advisable to place

GROWTH O F PROTOZOA IN PURE CULTURE. I1 485

the animals in 10 per cent yeast extract for a few days before starting the experiment, in order to lessen the shock to the animals of changing the food concentration too suddenly.

In table 2 are shown the concentrations of liquid yeast ex- tract, the division rate during the logarithmic phase, the

Fig. 4 The lower curve represents the number of animals produced at the end of the logarithmic growth phase at different Concentrations of liquid yeast autolysate. The upper curve shows maximum yields at different concentrations.

486 AUSTIN PHELPS

number of animals per cubic centimeter at the end of this phase, and the final maximum yield per cubic centimeter. Figure 4 shows the number of animals per cubic centimeter at the end of the logarithmic growth phase and the maximum number of animals per cubic centimeter, plotted against the concentration of the medium. Figure 5 is a composite graph

J

ti

a

$

Q 4 E a c

J

Fig. 5 Composite figure (see text) showing growth of animals in different con- centrations of liquid yeast autolysate.

showing the results of the nine experiments comprising this series. The explanation and comments which were given in connection with figure 3 also apply to figure 5.

RESULTS

From the above tables and figures it will be seen that the yield in animals per cubic centimeter at the end of the logarith- mic growth phase, as well as the maximum yield in each ex- periment is, within wide limits, directly proportional to the

GROWTH OF PROTOZOA I N P U R E CULTURE. 11 487

amount of food employed. This may not be evident upon first glance, for it is seen that the actual numbers of animals are not strictly proportional to the concentrations of food. Close observation of table 2, however, shows that the straight line relationship between food and yields of animals falls down radically when very weak concentrations of food are em- ployed. The formula which represents the proportionality be- tween the concentration of food and the number of animals

TABLE 2

OONOENTBATION

PET Cent

0.05 0.2 0.4 0.6 2.0 6.0 10.0 15.0 20.0

DIVILIION U T E

how78 6.0 4.2 3.8 3.8 3.8 3.8 3.8 3.8 3.8

MAXIMUM AT END OP MOAEITHMIO PHASE

2,500

16,000 25,000 64,000

338,000 512,000 510,000

10,000

200,000

hcAxI?dw YIELD

7,100 21,500 30,000 44,700 92,000 250,000 415,000 615,000 725,000

produced both at the end of the logarithmic growth phase, and at the maximum growth of the population, is :

where A represents the number of animals produced by a con- centration of medium represented by a, etc. Where Difco yeast is employed the value of K is found to be 4,500 per cubic centimeter, for the yields at the end of the logarithmic growth phase, and 6,000 per cubic centimeter for the maximum yield. I n the case of the liquid yeast autolysate the value of K is 4,000 per cubic centimeter for the yields at the end of the logarithmic growth phase and 12,500 per cubic centimeter for the maximum yields.

As a result of the proportionality between yields of animals and concentrations of medium, the conclusion is unavoidable that under the conditions of the experiment, and within the limits set forth, the sole factor which limits the extent to which

a:b:c: . . ... z = (A-K):(%K):(GK):.. ...( Z-K)

488 AUSTIN PHELPS

the population may grow logarithmically as well as the sole factor limiting the final density of the population, is the quantity of food available. For if other factors, such as ‘physical crowding’ or concentration of excretory products tended to limit the numbers of animals, their effect would become more and more evident as the cultures become denser and denser, and hence a true proportion between the yields of animals and the concentration of food would not be found. It is not until the concentration of 2 per cent of Difco yeast extract or 15 per cent liquid yeast autolysate is employed, giving maximum populations of 300,000 to 750,000 per cubic centimeter respectively, that any factors other than food enter in as limiting factors to the maximum yield obtained. Furthermore, a scrutiny of the data presented shows that, in the presence of sufficient food, the division rate is constant and unvarying until a population of 85,000 per cubic centimeter (in the case where Difco yeast is used as food), to 500,000 per cubic centimeter (when liquid yeast extract is used), has been reached. This shows conclusively that metabolic wastes dis- charged into the medium do not influence the division rate until these high densities of population have been reached. A final significant point which the experiments demonstrate is that the division rate is entirely independent of the concentra- tion of food present in the medium, provided that a certain minimum (0.4 per cent in the case of liquid yeast extract) is present. Concentrations below this minimum may still sup- port growth for a time, but they do not permit the optimum division rate to occur.

DISCUSSION

Jahn (’34), points out that in the present stage of investi- gation there are at least eight important factors which are usually operative, as variables, upon the development of proto- zoan populations. These may be summarized as: 1) the available food, 2) the concentration of metabolic wastes, 3) the hydrogen ion concentration, 4) the oxygen tension, 5 ) the carbon dioxide tension, 6) the temperature, 7 ) light, 8) com- pounds produced by other organisms which accompany the

GROWTH OF PROTOZOA IN PURE CULTURE. Ir 489

protozoa in their environment. He further points out, and it is a point which may not be too strongly emphasized, that if the effect of any one of these factors is to be investigated all of the other factors must be controlled. It has been only quite recently, and then in very few cases, that this has been done.

In discussing the present work, it should be pointed out that of the eight variables mentioned, nos. 1, 3, 6 and 7 have been controlled and no. 8 has been excluded altogether. Nos. 4 and 5 have been controlled by means of heavy aeration in those cultures which supported the heavier concentrations of ani- mals. As regards the lighter populations, in the weaker con- centrations of foods, it is assumed that since the division rate is in all cases the same, and since the number of animals both at the end of the logarithmic growth phase, and at the peak of the population, is within limits, directly proportional to the amount of food employed, the variations in CO, or 0, tensions which occur as a result of the growth of the animals are not sufficient to influence the normal course of the development of the populations. For these reasons it is felt that the con- clusions which have been drawn in regard to the effects of a varying food supply and of excretion products upon the growth of the protozoan population are established on a thor- oughly sound basis.

Since the pioneering work of Woodruff ( '11, '13), there have been many studies on the effects of protozoan excretion products upon the division rate of protozoa and upon the limits to which a population, in a limited environment, can continue to grow. These works have been thoroughly re- viewed by Allee ('31), Beers ('33) and Jahn ('34). Hereto- fore the general conclusion has been that the effect of excre- tory products upon the division rate is observable at very low population densities. Thus, Woodruff ( '11) finds an effect of excretory products when one to four animals have lived in about 0.5 cc. of medium for 24 hours. Likewise Meyers ('27), Calkins ( '26), Greenleaf ( '26), Peterson ( '29) and Beers ('33), have found an effect of excretory products upon proto- zoan division rates using volumes of media, periods of time,

490 AUSTIN PHELPS

and numbers of animals of the same order of magnitude as those employed by Woodruff.

I n view of the above investigations, the present work is re- markable in demonstrating that a population of protozoa can grow to tremendous densities before the effect of excretory products upon the division rate is observed. Thus, concen- trations of animals more than 1,000 times greater than those observed in the investigations cited above were obtained in the present work before the effects of excretory products upon the division rate were observed. The explanation in some cases may lie in the fact that in all but one of the works mentioned above a population of mixed bacteria was growing along with the protozoa, and the excretory products of these bacteria had a depressing effect upon the protozoan division rate. I n the work of Beers, however, this factor does not occur, as the Didinium nasutum and Stylonychia pustulata employed by this author were raised in a non-nutrient salt solution, with washed Paramecium as a source of food. A second explana- tion undoubtedly lies in the fact that different kinds of food cause the protozoa to produce excretory products which are vastly different both quantitatively and qualitatively, so that under one set of conditions a sparse population may produce excretory products which influence the division rate, while under different conditions the same population may grow to a considerably greater density before excretory products show the slightest influence upon the division rate. The present work furnishes evidence for this explanation, since it has been seen that when one type of yeast extract was employed Glaucoma was unable to continue growing at an optimum rate of speed after the population had become more dense than 85,000 per cubic centimeter, whereas when a different type of yeast extract was employed the same animals continued to grow at a maximum rate until a density of 500,000 per cubic centimeter had been reached. In this connection it should be emphasized that in all the experiments described in the present work the animals were raised on an exclusively protein diet, and the experiments are intended to bring out certain potenti-

GROWTH O F PROTOZOA IN PURE CULTURE. I1 491

alities of protozoan populations, rather than to reproduce a process which may take place in nature.

COMPARISON WITH THE GROWTH OF BACTERIA AND YEASTS

The author has pointed out, Phelps ('35), that only recently has a true comparison between the growth of bacteria and yeasts on one hand, and protozoa on the other, being possible. It is only when a protozoan population is raised in absolutely pure culture, so that all of its food is derived from the culture medium, and no extraneous biological processes are present to complicate the system, that its growth can be compared with that of other lower organisms.

The question of the effect of the concentration of medium on the division rate of bacteria and yeasts and on the final yields of these organisms is still in an unsettled condition. Two re- cent reviews of the subject, Henrici ( '28) and Rahn ( '32), draw different conclusions, quoting much the same literature in support of their generalities. Henrici says (p. 40), referring to the question of the effect of excretory products upon the growth of bacteria and yeasts :

The observations of Penf old and Norris, Salter, and Graham- Smith with bacteria, of Brown, Zikes and Montank with yeasts, that the rate of growth and the final yield are proportional to the concentration of tbe nutrient in the medium, seem to offer a serious obstacle to the toxic theory, for it seems more likely that toxic products of growth would accumulate more rapidly and thus inhibit growth sooner with a medium of higher nutrient value, rather than the reverse.

A perusal of the literature cited in this quotation makes it seem a bit difficult to understand how the generalities stated above could have been derived from most of the papers quoted. Thus, Penfold and Norris ('lz), working with B. coli, and testing the effect of peptone between the concentrations of 0.0125 per cent and 1.25 per cent, find that the division rate is affected only in concentrations below 0.4 per cent, i.e., when the concentration is too dilute to support optimum growth. From concentrations of 0.4 per cent up to 1.25 per cent the

492 AUSTIN PHELPS

division rate is the same within the limits of error. These authors made no investigation of the final yield of organisms. Salter ('19), studying the effect of concentrations of peptone on B. communis between the ranges of 0.5 per cent and 5.0 per cent, shows a decrease in generation time with increase in con- centration, but since the cultures were carried only 8 hours and there is no evidence that a maximum was obtained, generalities in regard to this latter point cannot be made. In the work of Graham-Smith ('21), who studied the effect of concentrations of meat extract on Micrococcus pyogenes, counts of the popula- tions were made only once every 24 hours, and as a result none of his curves shows logarithmic growth. Therefore, the state- ment often found in the literature that this work shows that the growth rate is increased by an increase in the concentra- tion of food employed, cannot be accepted. The maximum yields shown by this author increase as the concentration of nutrient is increased, but they are not proportional to the concentrations of food. The work of Brown ('05), cited by Henrici, does not contain experiments in which the concentra- tion of food is varied in order to test the effect upon growth. This author does state, however, with reference to his earlier work : If equal volumes of a solution containing varying quantities of nutritive matter were seeded with a small number of yeast cells, the total number of cells found in each experiment at the termination of reproduction was approximately the same, so long as the amount of the food supply present lay within certain wide limits. Thus it is seen that Brown not only fails to support the generalities mentioned above, but some of his work is in actual opposition to one of them, namely that the maximum yield is proportional to the concentration of nutritive material. The work of Zikes ('19), shows in three out of four experiments that the growth rate of yeast is slightly increased (about 5 per cent) when the concentration of wort is increased eight to twelve times. The maximum yields in this author's cultures increase as the amount of wort is increased, but they are not

GROWTH O F PROTOZOA IN PURE CULTURE. I1 493

proportional to the increase in the concentrations of wort. Finally in the tables of Montank given in Henrici's book there is evidence that yeast cells grow more rapidly in stronger con- centrations of food than in weaker ones. Since mixtures of dextrose and peptone were used in these experiments, and since the relative amounts of dextrose and peptone varied with the different concentrations of food employed, it is difficult to say whether the increase in division rate is due to an increase in concentration of peptone, in concentration of dextrose, or to a closer and closer approach to an optimum balance between dex- trose and peptone. Since the tables of Mcmtank give no indica- tion that a maximum yield was achieved in his experiments, his work cannot be said to indicate that the maximum yield of yeast cells is proportional to the concentration of food em- ployed. To sum up, on19 two of the six works referred to, those of Salter and Zikes, show that the logarithmic growth rate is increased by increase in the concentration of medium employed, and none of these investigations indicates that the maximum yield is proportional to the concentration of food. There are, however, two works, overlooked by recent reviewers of the subject, which indicate that given the proper conditions, the maximum yield in yeasts and certain other fungi may be, within limits, proportional to the concentration of nutrient material. Rubner ( '13) using varying concentrations of wort finds that the total amount of nitrogenous matter formed by yeast cells is proportional to the concentration of food em- ployed. Pringsheim ( '14), employing Saccharomyces, Asper- gillus niger, and Mucor rhizopodiformis, in a very simplified culture medium, shows that over certain ranges, the yields, expressed as dry weights, are proportional to the amount of nutrients employed. This latter author also finds an increase in growth rate with increases in the concentration of food.

The writer feels that on the whole a more accurate state- ment of the present status of the problem is given by Rahn ('32, p. 251) :

With increasing amounts of food, the crop, i.e., the final number of cells in a culture, usually increases.

494 AUSTIN PHELPS

With a liberal supply of building material, increases of energy food will cause no acceleration in growth, but a longer growth period, and, therefore, a larger crop. This is limited by accumulation of fermentation products or of inhibiting cell secretions. With all food components increasing, the crop will still be limited by fermentation products of cell secretions. The law of diminishing returns becomes quite evident.

If we now compare the growth of populations of Glaucoma in different concentrations of medium, with that of bacteria and yeasts under similar conditions, two important features may be considered. First, the division rate of bacteria and yeasts appears, in some cases to be slightly affected by changes in the concentration of food, and in other cases to be unaf- fected thereby; in Glaucoma it is seen that the division rate during the logarithmic growth phase is absolutely constant be- tween very wide ranges of concentration of food. Secondly, the maximum yield of bacteria and yeasts is not proportional to the concentration of nutrient medium, in most cases, but is lower per unit of nutrient material when the concentration of nutrient is high than when it is low. I n the case of Glaucoma, on the other hand, the yield at the end of the logarithmic growth phase, as well as the final yield, is within wide limits, directly proportional to the concentration of food present. Ac- cording to Rahn, this is the situation which one expects to find, when food is the sole limiting factor of the growth of the population, and it is a situation which has not yet been demon- strated in the bacteria nor in most of the work on yeasts. To sum up, the vast majority of evidence indicates, if we accept the very logical interpretation of Rahn, that the growth of bacteria and yeasts is, under most conditions, limited partly by food, partly by excretory products of the cells, and as the nutrient medium is made stronger excretory products be- come more and more dominant as a limiting factor of the growth of the population, and the amount of food available be- comes less and less important in this respect. In contrast the present work shows that the protozoan, Glaucoma, the amount of food available is the sole limiting factor of the growth of the population within very wide limits, and that when excre-

GROWTH O F PROTOZOA IN PURE CULTURE. I1 495

tory products finally enter as a limiting factor to growth, their effect is relatively sudden and almost completely inhibiting.

In conclusion I take great pleasure in expressing my grati- tude to Prof. C. B. van Niel for valuable suggestions in connec- tion with this work, and to my wife for drafting the figures and typing the manuscript.

SUMMARY

Experiments have been performed on the ciliate, Glaucoma pyriformis, to determine the effect of different concentrations of nutrient material upon the growth.

It is found that within wide limits the division rate during the logarithmic growth phase is at a maximum, and is inde- pendent of the concentration of food.

Within wide limits the number of animals at the end of the population is directly proportional to the concentration of nutrient material employed. This is interpreted as indicating that excretory products of the protozoa have no effect either upon the division rate or upon the final yield until relatively enormous concentrations of animals have been reached.

Previous work on the effect of excretory products upon the growth of protozoa, has indicated that growth is effected by excretory products when relatively few animals have lived in a culture medium for a short time. The discrepancy between the present work, and that which has preceded it, in this re- spect, is believed to be due to differences in culture method, and in food.

Most of the studies in regard to the effect of different con- centrations of food upon the growth of bacteria and yeasts, have not shown that the maximum yield is proportional to the concentration of food employed. This is interpreted as in- dicating that under most conditions both the amount of food available, and the concentration of excretory products, com- bine to limit the growth of the population. The growth of populations of Glaucoma differs markedly from that of bac- teria and yeasts in this respect.

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496 AUSTIN PHELPS

LITERATURE CITED ALLEE, W. C. 1931 Animal aggretions. The University of Chicago Press.

BEERS, C. D. 1933 1934 Eecent studies in mass physiology. Biol. Rev., vol. 9, pp. 1-48.

The relation of density of population to rate of reproduction in the ciliates Didiium nasutum and Stylonychia pustulata. Arch. f. Protist., Bd. 80, S. 36-64.

BROWN, A. 1905 Influences regulating the reproductive functions of Sac- charomyces cerevisiae. J. Chem. SOC. Lond., vol. 87, p. 1395.

CALKINS, G. N. 1926 The biology of the protozoa. Lea and Febiger, Philadelphia and New York.

GRAHAM-SMITH, G. 8. 1920 The behavior of bacteria in fluid cultures as indi- cated by daily estimates of the numbers of living organisms. J. Hygiene, vol. 19, pp. 133-204.

GREENLEAF, W. E. 1926 The influence of volume of culture media and cell proximity on the rate of reproduction of Infusoria. J. Exp. Zool.,

HENRICI, A. T. Morphologic variation and the rate of growth of bacteria. Chas. C. Thomas, Springfield and Baltimore.

JAHN, T. L. 1934 Problems of population growth in the protozoa. Collecting Net, Woods Hole, vol. 9, pp. 34-41; pp. 47-48.

JENSEN, 8. 0. 1919 The lactic acid bacteria. Kgl. Danske Vidensk. Selsk. Skrifter, Naturvis. og. rnathernatisk Afd. 8, Raekke 5.

KLUYVER, A. J., H. J. L. DONKER AND F. V. HOOFT 1925 Uber die Bildung von Acetylmethylcarbinol and 2, 3-butyleneglycol im Stoffwechsel der Hefe. Biochem. Zeit., vol. 161, pp. 361-378.

LWOFF, A. 1932 Recherches biochimiques sur la nutrition des protozoaires. Le pourvoir de synth6se. Monographies de 1’Institut Pasteur, Paris, Masson et Cie.

1927 Relation of density of population and certain other factors to survival and reproduction in different biotypes of Paramecium caudatum. J. Exp. Zool., vol. 49, pp. 1-43.

PENFOLD, W. J., AND D. NOR~IS 1912 The relation of the concentration of food supply to the generation-times of bacteria. J. Hygiene, vol. 12, pp.

The relation of density of population to rate of reproduction in Paramecium caudatum. Physiol. Zool., vol. 2,

PHELPS, A. 1935 Growth of protozoa in pure culture. I. Effect upon the growth curve of the age of the inoculum and of the amount of the inoculum. J. Exp. Zool., vol. 70, pp. 109-130.

RARN, 0. 1932 Physiology of bacteria. P. Blakiston’s Son and Co., Philadelphia. RUBNEE, M. 1913 Die Ernahrungsphysiologie der Hefezelle bei alko-

Holischer GLrung. Veit und Comp., Leipsig. SALTER, R. C. 1919 Observations on the rate of growth of B. coli. J. Infec.

Diseases, vol. 24, p. 260. WOODRUFF, L. L. 1911 The effect of excretion products of Paramecium on its

rate of reproduction. J. Exp. Zool., vol. 10, pp. 557-581. The effect of excretion products of Infusoria on the same and

on different species with special reference to the protozoan sequences. in infusions.

ZIKES, H. 1919 Uber den Einfluea der Konzentration der Wurze auf die Biologie der Hefe. Centr. f. Bakt., I1 Abt., Bd. 49, 8. 174.

v01. 46, pp. 143-169. 1928

MEYERS, E. C.

527-531. PETERSEN, WALBUR~A A. 1929

pp. 221-254.

1913

J. Exp. Zool., vol. 14, pp. 575-582.