T H E RATE OF T H E MULTIPLICATION O F YEAST AT DIFFERENT TEMPERATURES* BY OSCAR TV. RICHARDS
Changes in the rate of multiplication of yeast' that accompany changes in the temperature of the culture medium are masked, in the usual test tube culture, by the toxic effect of the products of their metabolism on the yeast cells. These excretions injure the larger buds and the population gradually reaches an equilibrium number2. Consequently, the apparent effect of temperature becomes progressively less as the equilibrium of the population approaches.3 The influence of temperature on the multiplication of yeast, uncomplicated by the inhibitory action of the excretion products, can be measured only during the period during which the rate of growth is constant and the retarding effect of the toxic excretion products is circumvented? Unless the culture medium is changed at sufficiently frequent intervals to maintain it effectively constant, only the first part of the growth cycle is usable, as the growth rate begins to decrease a t about 30 hours after seeding. During this period the numbers of cells present are less and the errors of counting are higher. The technical difficulties involved in properly renewing the culture medium prevented the use of longer growth periods in this investigation. I. The method of culturing the yeast and making the counts has been described elsewhere3. A pure strain of Saccharomyces cerevzsiae Hansen was used. When the logarithm of the number of cells present in a unit sample of the culture medium is plotted against time, the resulting graph is a straight line, within the experimental error, for periods of time extending from I to 2 hours after seeding until about 30 hours. After a lag period of less than 2 hours the rate of growth is constant. A similar lag period is described by S l a t ~ r .The ~ effect of this short latent period is minimized in the experiments, as only the linear part of the curve was used in making the measurements. A lag period would merely shift the position of the growth curve further from the origin on the time axis. A long lag period would delay the time of reaching the equilibrium population, but would not affect the numerical value of the
* From the Department of Biology, Clark University, Worcester, and the Laboratory of General Physiology, Harvard University, Cambridge.' 'These ex eriments will be designated as those made a t Worcester and Cambridge. The yeast is t f e same in both cases except that a single cell of the yeast used at Cambridge was isolated and the yeast used in the Worcester experiments belongs to the pure line started by this cell. Richards: Bot. Gazette (1928). Richards: Ann. Bot., 42, 271 (1928). Richards: J. Gen. physiol., 11, 525 (1928). 6 Biochem. J., 12, 248 (1918).
1866
OSCAR W. RICHARDS
equilibrium level. This relation has been shown by Lotka’ in connection with his treatment of the dynamics of an epidemic of malaria. At a definite stage during an epidemic there is reached an equilibrium between the population of malarial organisms and the infected human population. I n this case Lotka has shown that the incubation period (a lag period) has only a constant effect on the equilibrium because the lag period merely slows down somewhat the progress of the events in the system. The cultures of the experiments a t temperatures below room temperature were made by immersing the tubes in a light-tight box in a constant-temperature thermostat of the type described by Crozier and Stier,2 or in a small beaker of water in a Kelvinator.3 The other cultures were maintained in either a Freas or Thelco incubator. Two measures of the rate of multiplication were used: the slope of the growth curve, and the reciprocal of the time required by the culture to produce a definite number of cells. The latter was obtained by determining the time of intersection of the growth curve and a line corresponding to antilog 0.50 cells. Technical difficulties make it impractical to seed each set of tubes with exactly the same number of cells. The rate of growth of yeast also varies with the age of the seeding. Even with seedings of nearly the same age there is some normal variation in the rate of multiplication. The best method for minimizing these variations seemed to be to grow a control set with each experimental set and to adjust the curves so that all of the controls had Should the same rate of growth. The controls were maintained a t 30%. this experiment be repeated the control temperature should be preferably about z o to 4’ lower in order to obtain more uniform growth a t the “control” temperature (cf. Sec. IV). To minimize the variations, the growth curves for each control and, for the corresponding set of data a t each temperature were plotted on tracing paper and the intercept of the growth curve of the control and the line of antilog 0.50 was marked. Another graph had a line drawn which was the most representative of all of the control growth rates and the line of antilog 0 . 5 0 was drawn on this graph. Then each of the sets on tracing paper was placed on this master graph and the growth line of the control made to coincide with the line of the master graph. The slopes and intercepts for the expenmental sets were then measured on the master graph. 11. The rate of growth is expressed as the tangent of the angle that the growth curve makes with the time axis. These rates may be conveniently plotted as the logarithm of the tangent against the reciprocal of the absolute temperature, as in Fig. I . A straight line then expresses the relation between the Am. J. Hyg., Jan. Supplement (1923). J. Gen. Physiol., 10, 501 (1927). a The Kelvinator was loaned to me for these experiments through the courtesy of the Worcester Electric Light Company. 1
*
1867
RATE OF MULTIPLICATION OF YEAST
rate of multiplication of the yeast and the temperature between about 9 ' and 29'C. with the exception of the observation a t IO'. Another straight line expresses this relation between 9' and 4' The divergence of the measurement at IO' from the others seems to be due to hysteresis. To avoid this effect i t is necessary that the yeast used at
FIR.I Rate of multiplication of yeast measured by the slope of the growth curves.
V A
'521
325
333
344.1
349
Cmbrldae e i p t s ou1tum, *d.& Womentar exptn,
357
36:
10YT.abJ.
FIQ.2 Rate of multiplication of yeast measured by the slope of the growth curva., Same as Fig. I , except that the variation in the dflerent series is not minimlaed by adjust'ing the rates of growth of the controh to be the same (cf. note in text).
the lower temperatures be first well adapted to the particular temperature of the experiment. When the yeast is properly adapted the rates are higher and more self-consistent. I n the experiments in which the cultures were adapted to the temperature the adaptation period was 7 days for the Cambridge experiments and I O days for the Worcester experiments.
1868
OSCAR W. RICHARDS
Above 30' the rates decrease in a n accelerated manner. This is partly due to certain cells being selectively destroyed and partly due to some effect of the nature of a thermal destruction. When these two effects are measured separately it will probably be possible to determine the nature of the thermal destruction by a method similar to that used by Hechtl for asomewhat analogous case. This effect is shown more clearly by the other measure of the rate of cell proliferation discussed in the next section.
FIG. 3 Rate of multiplication of yeaat measaed by the reciprocal of the time required to produce a given crop.
The changes in the trends of the rates are also shown if the slopes of the original growth curves are used without minimizing the variations of averaging the rates of the controls, as is shown by Fig. 2 . The increment in this figure has probably no really exact meaning; it might be suggested as a case where faulty interpretation gives a non-significant p. The rates for the lower temperatures are the same in both figures, m when the yeasts are adapted at a given temperature it is no longer possible to maintain a strictly comparable control at a higher temperature. Thus the regions at 9' and 30' seem to be critical temperatures; they occur a t regions that have been emphasized by Crozier2 as significant in this respect. The scattering of the velocities around 30' seems to indicate a real "break" in the curves of the velocities, rather than an effect of the chemical constituents of the medium varying with the temperature, as suggested by Sherwood and F ~ l m e r . ~ J. Gen. Physiol., 1 , 667 (1918).
J. Gen. Physiol., 9, 525 (1926).
* J. Phys. Chem., 30,738 (1926).
RATE O F MULTIPLICATION O F YEAST
1869
The decrease in the rate of growth at temperatures higher than 30’ suggests that budding would cease a t about 4 4 O , which is in accordance with the observations gathered by Guilliermondl with various yeasts.
111. The measurements from the other criterion of the rate of growth may be exhibited in a similar manner, by plotting the logarithm of the reciprocal of the time to yield a certain crop against the reciprocal of the absolute temperature, Fig. 3. This graph shows the same features as the previous figures. The different slopes of the curves of the velocities in Fig. 3 from those of Fig. I are probably due to the fact that the length of the lag period varies with the temperature. A change in the lag period would change the time of the intercept of the growth curve and the line of antilog 0.50 cells. Consequently these measurements contain the effects of temperature on both the lag period and the rate of growth. This effect, which was obviated by the method used in Section 11, makes the rates of Fig. 3 less reliable than those of Figs. I and 2 and prevents obtaining a good fit or a significant increment. Strumia and McCutcheonZfind variations in the length of the lag period for their measurements of larger amounts of yeast for the first nine hours of growth. Large seedings permit more precise measurements of the lag period, but the greater amount of excretion products shortens the time during which multiplication occurs a t a constant rate. Until the technical difficulties incident to keeping large seedings of yeast growing a t a constant rate are overcome it will not be possible to separate the effect of temperature on the lag period from the effect of temperature on cell proliferation. The numerical values obtained by solving the Arrhenius temperature equation3 for each group of data are given on the figures. I n general these values correspond with the classes of values found for growth proce~ses,~ but the present values are for cell multiplication during the increase of a population and they are not to be compared directly with these for growth of a multicellular organism or the elongation of an unicellular organism. Values of the critical increment of the Arrhenius equation that may be used for analytical purposes can only be obtained when the causes of variation mentioned in this paper are adequately controlled. IV.
It is possible to locate more precisely the upper critical temperature for the multiplication of yeast by studying the changes in the form of the cells. -
“Les L e w e s ” (1912). * From unpublished manuscript communicated personally to the writer. * The Arrhenius equation is
k&
=
EWT,-VT~
Ea
when ki is.the velocity, or proportional measure of it, a t the temperature TI, and kz the corresponding velocity a t the temperature Tr. The temperatures must be expressed in the absolute or Kelvin scale. When on1 approximate values of p are desired, they may be obtained from a nomogram, Richards: j. Phys. Chem., 30, 1219(1926). ‘Crozier: J. Gen. Physiol., 10, 53 (1926);Castle: 11, 407 (1928).
1870
OSCAR W. RICHARDS
Irregular elongate cells are occasionally seen in cultures incubated a t 30'C. at from IO to 3 0 hours after seeding. Later these cells are not found, and as the strain used is pure and the technic known to be adequate to prevent infection, it seemed necessary to see if their occurance was associated with certain temperatures. Cells that occasionally infest a tube accidentally are different from these abnormal forms both in shape and size. The bizarre cells resemble more those cells seen in very old cultures or in cultures maintained at high temperatures.'
FIQ.4 The frequency of the occurrence of the abnormal cells described in the text (cf. Fig. 5, b ) .
Four experiments were made b y growing a series of tubes at temperatures from 28' to 32' and by determining the frequency of these abnormal cells. The incubator containing the controls varied about *0.7', but the water thermostat in which the experimental tubes were grown varied only a few hundredths of a degree. This permitted comparing the cells grown in the usual laboratory incubator having fair temperature control with a group grown a t more adequately controlled temperatures. The results are expressed in Fig. 4. The difference in shape between the usual form of S. cerevisiae and these abnormal forms is shown in Fig. 5 . The drawings are tracings of enlarged photomicrographs made by the method described elsewhere2. Up to and including 30' we find more abnormal ceIls in the group grown in the water thermostat. At 30' the frequencies are approximately equal, and a t 31' the frequencies are exactly reversed. At a temperature maintained between 29.5' and 30.5' more of these unstable, morphologically different cells appear, which suggest that this is a critical temperature which 1 Guilliermond: "Lea L e w e s " (1912). *Richards: Bot. Gazette (1928).
RATE O F MULTIPLICATION OF YEAST
1871
disturbs the budding process. This effect does not change the constancy of the rate of multiplication of the yeast. A temperature of 30 degrees has been shown to be accompanied by critical effects in various kinds of vital activities.'
v. The existence of such a critical temperature for the growth of yeast is of great importance, because the temperature of 30' is customarily used as a normal temperature in the study of the vital activities of yeast. This critical temperature may not be the same for all strains of the same species of yeast, and i t is possibly different for different species. The unusual forms are not of frequent occurance unless the temperature is maintained constant within narrow limits, which is not achieved by the types of laboratory incubators in most general use a t the present time. The better types of temperature control which will come with wider use of adequate thermostats makes a thorough knowledge of FIQ.5 these special temperature zones prerequia, Normal cells. site for the study of the metabolism of b, Abnormal cells. yeast and similar organisms, as well as constant conditions of culture medium. It is possible that this special effect of temperature a t which investigations using yeast are frequently made may be responsible for part of the irregularities apparent in the published accounts of such studies. This is particularly true for the investigations that are primarily concerned with the first 24 hours growth after seeding, because it is during this period that the budding process is most sensitive to effects associated with certain temperatures. During later growth the effect of temperatures is hidden by the greater effect of the waste products secreted by the yeast on the rate of increase of the yeast population. The writer wishes to express his indebtedness to Dr. W. J. Crozier for helpful suggestions and friendly criticism during the progress of these experiments. Summary The rate of the multiplication of t'he yeast Saccharomyces cerevisiae increases regularly with increase of temperature between 4' and 30°, except that the rate of change alters a t go. Above 30' a decrease in the rate of growth is associated with an increase in temperature. At 30°C. abnormal, elongate cells are produced which indicates that this temperature effects the process of bud formation in a critical manner. More of these abnormal cells appear if the temperature is maintained mit,hin narrow limits of variation. The need for precise control of the temperature of yeast cultures is emphasized. Crozier: J. Gen. Physiol., 9,
j2j (1926).
