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 condi- tions 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 concentra- tion 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 equa- tion 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. z w -j (-) 0. 20 TIME (min.) 2.0[- a.o- 1.0 1.0 ,m .1 .5 0 0.10 I .06 .1 .01 .0o 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 germi- nation 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 concentra- tion 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.