Kinetics of Spore Germination NEIL G

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JOURNAL OF BACTERIOLOGY, May, 1965 Vol. 89, No. 5 Copyright @ 1965 American Society for Microbiology Printed in U.S.A. Kinetics of Spore Germination NEIL G. McCORMICK Department of Microbiology, School of Medicine, University of Virginia, Charlottesville, Virginia Received for publication 23 November 1964

ABSTRACT MCCORMICK, NEIL G. (University of Virginia, Charlottesville). Kinetics of spore germination. J. Bacteriol. 89:1180-1185. 1965.-An empirically derived equation was developed which accurately describes the time-course of the decrease in optical density during spore germination. A method is described for calculating the final value, the inflection point, and the maximal velocity from knowledge of three experimental values and the initial value at time-zero. A number of germination curves were ana- lyzed by application of the equation, and the effects of various environmental conditions on the parameters of the equation (k, c, and a) are noted. The constant c was found to be dependent upon the temperature and perhaps upon the degree of heat

activation and the L-alanine concentration. The constants k and a appear to be more basic functions of the initial state of the spore suspension. Variation of the concentration of spores changes only the initial optical density, but does not change any of the three constants.

The conversion of a spore to an actively me- decrease in OD during a constant time interval tabolizing vegetative cell occurs in three separate (Rode and Foster, 1962) or as the slope of the stages: (i) activation, (ii) initiation, and (iii) straight line portion of a semilogarithmic plot of outgrowth (Murrell, 1961). Activation is de- the percentage of ungerminated spores versus fined as a treatment which conditions the dor- time (Hachisuka et al., 1955; Woese and mant state to allow rapid germination. Activa- Morowitz, 1958; O'Connor and Halvorson, 1961). tion by treatment with heat or reducing agents Woese, Morowitz, and Hutchinson (1958) pro- is a reversible process (Keynan et al., 1964). posed that, after an initial lag, the fraction of Initiation involves the irreversible degradation of ungerminated spores decreased according to the the rigid spore wall, and outgrowth describes the first-order kinetic equation stages from initiation to subsequent vegetative growth. Since activation and initiation may be ODt- ODf = -kt studied separately from outgrowth, an accurate ODi- ODf (1) kinetic analysis should provide clues as to the mechanism involved in the breaking of dormancy. where ODt is the optical density at time t, ODi is Throughout this paper, the term germination the initial optical density, and ODf is the final will refer to the initiation stage only. limiting value of optical density at the comple- The kinetics of germination were measured by tion of germination. following the loss in heat resistance, the increase Analysis of a large number of germination in stainability, or the decrease in optical density curves obtained by continuously recording the (OD; Powell, 1950, 1951); by observing phase- decrease in OD during germination demonstrated contrast darkening (Pulvertaft and Haynes, that the straight-line portion of the semilog- 1951); and by the release of dipicolinic acid arithmic a (Woese and Morowitz, 1958). Good agreement plot spans relatively short period of exists among thes various methods (Campbell, time, and that, as germination proceeds, each 1957; Woese and Morowitz, 1958). OD measure- curve deviates from linearity. ments provide the most convenient method for It is the purpose of this communication to studying the process of spore germination. The derive an empirical expression describing the inability to fit the time-course curve of the de- entire time-course of events during spore ger- crease in OD to any classically employed kinetic mination and to analyze the effects of various equation has made it difficult to obtain a kinetic experimental conditions on the parameters of the description of the germination process. Germina- equation. Preliminary reports of this work have tion rates have been expressed as the percentage appeared (McCormick, 1964a, b). 1180 VOL. 89, 1965 KINETICS OF SPORE GERMINATION 1181

MATERIALS AND METHODS OD at time t, equation 4 becomes Clean spore suspensions of Bacillus cereus strain T were prepared as described by Church, lnln F Yi-Yf 1- lnln rYi Yf Halvorson, and Halvorson (1954). The germina- LYi-Yt2J LYi-Yt j tion reaction mixture consisted of 100 ,moles of -C = -iln t2/tl tris(hydroxymethyl)aminomethane (Tris) buffer (6) (pH 8.5); sufficient spores to insure an initial OD of 0.800 (approximately 1.5 X 109 spores per milli- lnln Yi Yf -lnlnm rYi Yf liter); and distilled water to a total of 0.9 ml. At = vi - Yt3iiyt2/- zero-time, 0.10 ml of L-alanine solution (concen- ln t3/t2 tration as described in text) was added, and the decrease in OD was measured at 625 m,u in a Gil- Equation 6 may be simplified by selecting yt ford recording spectrophotometer. Spores were values such that t2/t1 = t3/t2. This procedure activated by heating concentrated spore suspen- eliminates the denominators and permits the sions (OD = 1.5) in a water bath (65 C) for varying solution for the final limiting OD, yf. lengths of time as described in the text. [ln(yi- yt1)][ln(yi -Yt3)] RESULTS - [ln(yi - yt2)I[ln(yi -Yt2)] An ln(yi- yf) = (7) Mathematical development of the equation. (yi- - Yt3) empirically derived equation was reported which n Yt)(Yi accurately describes the time-course of spore (yi - Yt2)(Yi - Yt2) germination (McCormick, 1964a). As the OD of Thus, it is possible to predict the limiting (equilib- a germinating spore suspension decreases, it rium) value, Yf, of the reaction (as well as all asymptotically approaches a limiting value as other values) from knowledge of a minimum of germination approaches completion. This limit- three experimental values at selected times if the ing value has usually been determined by allow- initial value at exactly t = 0 is known. ing the reaction to proceed until no further change From equation 3, the basic expression used in OD is detected. Normalization of the data to throughout this is represent the total decrease in OD as unity allows study obtained any part of the reaction to be expressed as a Y = e-kt-c (8) fraction of the total reaction completed. If this fraction is designated as Y, then where k = In 1 /Yo. This equation generates a sigmoid curve from zero to unity as the variable Y = f(t) (2) (t) goes from zero to infinity. Since the function exists only for positive values of time between A plot of lnln 1/Y versus ln t results in a linear zero and infinity, the value of the function and relationship with a negative slope. This linear all of its derivatives can be shown to vanish function takes the form identically at zero by application of the Theorem of Mean Values. This is of some interest, because lnln I/Y = -c In t + lnln l/Yo (3) it implies that a reaction described by the equation does not start at its maximal velocity, but where Yo is the value of Y at t = 1, and -c is the accelerates from an initial velocity of zero to its slope. To calculate Y, it is necessary that the maximal velocity in a finite interval of time. The final limiting value be known precisely. If the importance of this is more apparent when reaction proceeds in accordance with equation 3, considering reactions which conform to the equa- then the following relationship holds: tion but which do not appear to possess any lnln 1/Y2 - nln induction period. 1/Y, The velocity or rate expression given by the In t2/tl first derivative of equation 8 is lnln 1/Y3-lnln 1/Y2 (4) kcY In t3/t2 dY/dt = (9)+(9) Since which generates a skewed distribution function. y Yt-Yi Yi Y(5 Equation 9, when equated to zero, yields two Yf-Yi Yi-Yf solutions for t (t = 0, t = oo), which represent, respectively, the limits of the times at which the where yf is the limiting OD as t approaches xc, reaction approaches zero from the right and y i is the initial OD at t = 0, and Yt is the observed completion (equilibrium) from the left. These 1182 McCORMICK J. BACTERIOL.

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d f I I,,,11 i lll 1 2 6 7 10 I25 67 10 20 . 25ta a5 7 20 TIME (min.) TIME (min.) TIME (min.) FIG. 1. Effect of temperature, heat activation, and L-alanine concentration on L-alanine-induced germination of spores of Bacillus cereus T. (a) Germination was conducted at the temperatures indicated, with the use of spores heat-shocked 4 hr, and at a final L-alanine concentration of 0.10 1t; (b) loglog 1IY versus log t plot of the data in (a). (c) Germination was conducted at 30 C and 0.01 M final L-alanine concentration with the use of spores heat-shocked for the number of hours noted; (d) loglog 11Y versus log t plot of the data in (c). (e) Germination was carried out at 30 C with 4-hr heat-shocked spores at the L-alanine concentrations depicted; (f) loglog 11Y versus log t plot of the data in (e). limiting values for an existing process can, at best, at by application of equation lOb. It thus becomes only be approached but never achieved, for in possible to determine the inflection point, even achieving them the process itself ceases to exist. though the reaction under investigation may not Equating the second derivative to zero (equa- appear to possess any induction period by tion 10) yields the times at which maximal currently accepted extrapolation procedures. The (equation lOb) and minimal (equation lOa and maximal velocity of the reaction may then be lOc) rates are attained. estimated by substituting the solution of equation lOb into equation 9. Application of the equation to spore germination d2Y/dt2 = kcY ( - c- = 0 (10) data. To describe the germination properties of spores by the use of equation 8 and to relate these t = 0 (lOa) properties to the environmental conditions kc initially imposed on the germinating spore t = ) (lOb) population, it is necessary to study the effects of varying conditions on the values of the constants t o=0 (lOc) k and c. The three variables chosen for study were the temperature of germination, the duration of If equation 8 accurately describes the reaction, heat activation, and the concentration of the then the inflection point may be uniquely arrived germination inducer. The effects of changes in VOL. 89, 1965 KINETICS OF SPORE GERMINATION 1183 these variables on the time-course of germina- TABLE 1. Variation in the constants c, k, and ax tion and, more particularly, on the constants are as a function of temperature, L-alanine illustrated in Fig. 1. concentration, and degree of heat Figure la shows the effect of temperature on activation* the shape of the germination curves. A plot of Heat L-alanine these data according to equation 3 is shown in Fig. activation TemTemp concn c k a lb. The value of c (- slope) is seen to increase to a maximum at approximately 25 C, and then to hr C M decline rather sharply as the temperature rises 4 11.2 0.10 1.85 151 .530 above 30 C. It is tempting, at first glance, to 15 2.20 135 .475 20 2.32 64 .450 assume some direct relationship between the 25 2.35 31 .435 slopes in Fig. lb and the apparent maximal rates 30 2.25 14.8 .450 observed in Fig. la. However, this assumption is 33 2.05 9.5 .468 not justified, as will be seen in the following 35 1.75 7.0 .486 discussion. 38 1.34 4.5 .530 The effect on germination of changes in the 40 1.12 3.3 .590 degree of activation is described in Fig. lc and ld. It is apparent that the slopes of the lines are 4 30 0.001 2.15 25.0 .895 approximately equal. The value of k, however, 0.005 2.20 22.2 .620 0.01 2.22 20.5 .560 does not remain constant but is seen to decrease 0.02 2.19 19.5 .470 as the extent of activation is increased. In this 0.04 2.20 18.0 .458 case, the maximal rates of the various curves 0.10 2.20 14.0 .450 observed in Fig. lc have no apparent relationship to the linear plots in Fig. ld. 0 30 0.01 2.22 50.5 .850 The effect of changes in the concentration of 0.5 2.22 35.5 .705 the germination inducer (L-alanine) is shown in 1 2.20 27.3 .646 Fig. le and lf. Changes in this variable, as with 2 2.20 22.6 .597 activation, appear to have little effect on the 4 2.20 19.8 .556 value of c. Whether the value of c is truly in- 8 2.21 14.9 .527 variant with L-alanine concentration can be * The values for c refer to the negative slopes decided only by obtaining germination data at of the linear plots in Fig. 1 according to equation both higher and lower concentrations of L-alanine 3. Since k = In 1/Yo, the values for k are obtained than those employed to date. Table 1 summarizes by multiplying the value of the intercepts at the the data from Fig. 1. From the preceding data, it t = 1 axis by 2.303. can be inferred that the value of c is temperature- dependent but not necessarily dependent upon the degree of activation or the concentration of measured is concerned only with those spores L-alanine. Preliminary results indicate that this participating in the reaction, an additional term apparent invariance exists at all temperatures must be employed to generate the experimental tested. For example, at 40 C the value of c is curve by the use of equation 8. Under maximal approximately 1.1 regardless of the degree of conditions, the final limiting OD is approximately heat activation or L-alanine concentration. 40% of the initial OD. Therefore, under maximal Likewise, at 35 C the value for c remains 1.8 at conditions the difference between ODi and 0.4 all L-alanine concentrations and degrees of heat ODi represents 100% of the reaction being activation tested. The value of k, however, is a measured. This ratio of ODf to ODi will be function of these latter variables. referred to as the constant a, and varies from Inspection of the curves in Fig. la, lc, and le approximately 0.4 under maximal conditions to brings out the fact that the asymptotic values values approaching 1.0 under minimal conditions. approached by the decreasing OD readings are The manner in which a varies as a function of not the same under all conditions in spite of the temperature, heat activation, and L-alanine con- fact that all of the curves started out centration is shown in the last column in Table 1. germination Thus, from a complete knowledge of the initial at the same initial OD value. Under suboptimal conditions, i.e., ODi (a function of the concentra- conditions, the spores in the population were not tion of spores in the suspension), the extent of all germinated at the completion of the reaction. prior activation, the concentration of the inducer, This was verified microscopically by noting the and the temperature of germination, it is possible number of spores which were stainable with to predict the complete kinetic behavior of L-ala- 0.1% crystal violet. Since the reaction being nine-induced germination of spores of B. cereus T. 1184 McCORMICK J. BACTERIOL. All germination experiments reported here were of 0.006 actually represents only 1% of the total carried out in 0.10 M Tris buffer (pH 8.5). Pre- reaction. For example, a plot of the data at small liminary results indicate that the pH of the sys- values of ODi - ODt may give a value of log 2.0 tem and probably the nature of the buffer em- instead of the extrapolated value of log 2.5. Al- ployed also affect the value of the constants. though on the graph this difference may appear It has been suggested by some investigators to be very significant, it actually represents the that the germination rate is dependent upon the difference between 0.006 and 0.002 OD units, concentration of the spore suspension. Analysis which is difficult to ascertain with any degree of of several germination curves obtained with accuracy. different dilutions of the same basic suspension of Vary and Steinberg (1964) carried out a statis- spores through a 10-fold range in initial OD re- tical analysis on the fit of the equation to micro- sulted in the finding that no change was effected germination curves, in which the times that in- in the value of any of the constants. The linear dividual spores begin to germinate, as well as the plots resulting from these data were identical; duration of the process for each spore, were the only difference between the resulting equa- noted under phase-contrast optics. As reported tions for each curve was in the value of OD i. by Vary and Halvorson (1965), the frequency distribution curves obtained in this manner were DISCUSSION found to be in excellent agreement with the curves The process of spore germination can be de- predicted by equation 9. scribed by equation 8. To obtain a general equa- Ultimately, it is hoped that a complete de- tion for any germination curve, the constant a scription of germination may be formulated in must be included. Thus, the complete equation which the initial state and composition of the becomes reaction mixture are incorporated into the constants k, c, and a, and from this description a ODt = ODi(1 - [ -a]e-kti) (11) model for the breaking of the dormant state may Equation 11 now allows us to predict the time- emerge. course of any spore germination curve when the ACKNOWLEDGMENTS constants c, and a are known. of k, Application This investigation was supported in part by the equation 8 permits a more complete description of Fluid Research and Development Fund, Uni- the kinetics of spore germination than has been versity of Virginia, and by Public Health Service possible heretofore. Maximal rates may be de- grant AI 06037-01 from the National Institute of termined with considerable accuracy free from Allergy and Infectious Diseases. arbitrary extrapolation procedures. The finding that, at constant temperature, alteration in the LITERATURE CITED extent of heat activation or in L-alanine concen- CAMPBELL, L. L. 1957. Bacterial spore germination tration has little effect on the value of the con- -definitions and methods of study, p. 33-38. stant c suggests that c for a given system may be In H. G. Halvorson [ed.], Spores. American represented by some function of the absolute Institute of Biological Sciences, Washington, temperature. The constants k and a are functions D.C. of the heterogeneity of the spore suspension with CHURCH, B. D., H. HALVORSON, AND H. G. HAL- respect to the permeability of the spores to L-ala- VORSON. 1954. Studies on spore germination: its nine, the number of sites within independence from alanine racemase activity. combining each J. Bacteriol. 68:393-399. spore (believed to be molecules of L-alanine de- FREESE, E., S. W. PARK, AND M. CASHEL. 1964. hydrogenase; O'Connor and Halvorson, 1961; The developmental significance of alanine de- Freese, Park, and Cashel, 1964), and other unde- hydrogenase in Bacillus subtilis. Proc. Natl. fined differences between individual spores, as Acad. Sci. U.S. 51:1164-1172. well as functions of the L-alanine concentration HACHISUKA, Y., M. ASANO, N. OGAJIMA, M. and the degree of activation. KITAORI, AND T. KUNO. 1955. Studies on spore The fit between the curve predicted by equa- germination. I. Effect of nitrogen sources on tion 8 and the experimental data has been excel- spore germination. J. Bacteriol. 69:399-406. lent with all curves tested. Those deviations KEYNAN, A., Z. EVENCHIK, H. G. HALVORSON, AND J. W. HASTINGS. 1964. Activation of bac- which do occur on a loglog 1/Y versus log t plot terial endospores. J. Bacteriol. 88:313-318. are due to the inability to measure OD accurately MCCORMICK, N. G. 1964a. The time-course of in the range of OD i-ODt < 0.01. Ina germina- spore germination. Biochem. Biophys. Res. tion curve carried out under maximal conditions Commun. 14:443-446. where ODi - ODf = 0.6, an ODi - ODt value MCCORMICK, N. G. 1964b. Application of a new VOL. 89, 1965 KINETICS OF SPORE GERMINATION 1185

equation describing the kinetics of spore germi- Adenosine and spore germination; phase-con- nation. Bacteriol. Proc., p. 36. trast studies. J. Gen. Microbiol. 5:657-663. MURRELL, W. G. 1961. Spore formation and germi- RODE, L. J., AND J. W. FOSTER. 1962. Ionic germination as a microbial reaction to the environ- nation of spores of Bacillus megaterium ment. Symp. Soc. Gen. Microbiol. 11:100-150. QMB1551. Arch. Microbiol. 43:183-200. O'CONNOR, R. J., AND H. 0. HALVORSON. 1961. VARY, J. C., AND H. 0. HALVORSON. 1965. Kinetics L-Alanine dehydrogenase: a mechanism con- of germination of Bacillus spores. J. Bacteriol. trolling the specificity of amino acid-induced 89:1340-1347. germination of Bacillus cereus spores. J. Bac- VARY, J. C., AND W. STEINBERG. 1964. Kinetics of teriol. 82:706-713. germination of aerobic Bacillus spores. Bac- POWELL, J. F. 1950. Factors affecting the germi- teriol. Proc., p. 36. nation of thick suspensions of Bacillus subtilis WOESE, C., AND H. J. MOROWITZ. 1958. Kinetics spores in L-alanine solution. J. Gen. Microbiol. of the release of dipicolinic acid from spores of 4:330-338. Bacillus subtilis. J. Bacteriol. 76:81-83. POWELL, J. F. 1951. The sporulation and germina- WOESE, C. R., H. J. MOROWITZ, AND C. A. tion of a strain of Bacillus megatherium. J. Gen. HUTCHINSON III. 1958. Analysis of action of Microbiol. 5:993-1000. L-alanine analogues in spore germination. J. PULVERTAFT, R. J. V., AND J. A. HAYNES. 1951. Bacteriol. 76:578-588.