Kinetics of Heat Activation and of Thermal Death of Bacterial Spores JA-MES J. SHU LL,' GERALD T. CARGO,

AND

ROBERT R. ERNST

Syracuse University, Syracuse, New York, and TJTilmot Castle Co., Rochester, New York Received for publicationi 10 June 1963

ABSTRACT SHULL, JAMES J. (Syracuse University, Syracuse, -N.Y.), GERALi) T. CARGO, ANI) ROBERT R. ERNST. Kinetics of heat activation and of thermal death of bacterial spores. Appl. -Microbiol. 11:485-487. 1963. Hypotheses concerning kinetics of heat activation and of thermal death of bacterial spores were formulated, and were employed to derive equations describing nonlogarithmic thermal death curves. The equations permitted evaluationi of the validity of experimental data and provided a means for testing the hypotheses presented.

Thermal death of microorganisms genierally obeys firstorder kinetics (Stanier, Doudoroff, and Adelberg, 1963). This concept has led to the use of D values (the time required to reduce the number of viable microorganisms by 90 %7 under specified treatment conditions) and first-order reactioni-rate constants (k) to describe the resistance of microorganisms to heat; these values, in turn, have been employed to predict extinction of a population of microorganisms under the specified treatmenit conditions. However, several investigators have reported nonlogarithmic thermal death curves for certain strains of bacterial spores (Halvorson, 1958; Stern and Proctor, 1954; Shull and Ernst, 1962). In such cases, D values cannot be applied meaningfully, and a more generally applicable description is desired. These spores may behave as a bimodal population with respect to heat resistance for which the death curve is described by the sum of two exponential functions, or they may exhibit a lag followed by a logarithmic decline in the population of viable spores. The latter case is unexplained and has resisted mathematical treatment. Halvorson (1958) suggested that the initial lag could be attributed partly to heat activation of dormant spores and partly to a "multiple-hit" inactivation process. He reasoned that, if heat activation were completely responsible for the initial lag, the logarithmic portion of the thermal death curve should extrapolate to the population of spores observed by direct count, a phenomenon he did not observe. However, this hypothesis would hold true only if nonactivated spores and activated spores were of equal heat resistance. If heat activation preceded thermal death, or if nonactivated spores were of greater resistance 1 Present address: American Sterilizer Co., Erie, Pa.

than activated spores, a time delay would result before all remainiing viable spores were activated and equally susceptible to heat, and the logarithmic portion of the death curve would extrapolate to a point in excess of the direct counit. The latter situation was observed by lialvorson (1958) and inferred in the report of Shull and Ernst (1962). Shull and Ernst (1962) demonstrated that heat activation can be responsible for a signiificant portion of the initial lag in the thermal death curves of spores of Bacillus stearothermophilus, but it was still niot clear how much of the lag could be attributed to heat activation, and whether the death of the spores obeyed first-order kinetics. We have re-examined this system in an effort to resolve three questions. (i) Does heat activation obey first-order kinetics? (ii) Does theirmal death of B. stearothermophilus obey first-order kinietics? (iii) What, if any, is the relationship between heat activation and thermal death? Let us suppose that a hypothetical population of spores is heated at a conistant temperature. The number of activated spores (those capable of colony formation on a suitable medium) at time t is denoted by A t, and the number of nonactivated spores (those capable of conversion to the activated state upon heating) at time t is denoted by Nt. Then the number Lt of living spores at time t is given by Lt = Nt + At. The initial number of activated spores is Ao, and the initial number of nonactivated spores is No. Furthermore, let us make the following assumptions: first,

485

2Vt

=

Noe-at

where a is the activation-rate constant; second, the number of activated spores remaining at time t from the original activated population is A oe-kt where k is the death-rate constant; third, heat activation must precede thermal death of nonactivated spores. An examination of the behavior of At and Lt over a short interval of time yields the following differential

equations: At' = -kAt + I,t'

-kAt

aVoeat(1)

(1)

(2) When a # k, the solution of equation 1 subject to the initial conditions is =

SHULL, CARGO, AND ER'NST

486) A,

=

Aoeht +

k-a

(e-at - e-kt)

(3)

A slight modificationi is necessairv when a = k. Upon integration, equation 2 becomes Lt,-, = -k ]

At dt tl

(4)

APPL. AIICROBIOL.

equation 3 revealed that, for a given population of spores, a change in the ratio of a to k would result in a change in the shape of the initial portion of the thermal death curve. V'alues a and k are temperature-dependent, and the ratio of a to k may also change with temperature. Therefore, any system in which the temperature changes during a significant portion of the experiment would give rise to distortions in the thermal death curve. Consequently, the curve reported by Shull and Ernst (1962) is probably distorted as the result of a relatively long heating time. Because the data at hand are subject to this procedural error, answers to the questions posed must await acquisition of more exacting experimental data or application of the hypothetical equations to data available in other laboratories.

Equation 3 describes the behavior of the activated spore population in the hypothetical system as the sum of two terms; the first term accounts for the first-order death of the initial activated spore population; the second describes the activation and subsequent death of nonactivated spores. Equation 4 indicates that the total number of deaths occurring between time t1 and time t2 is equal to the product of the death-rate constant and the area under the death curve for the time period in question. ACKNOWLEDGMENTS If the constants Ao, No, k, and a can be determined for a Gerald T. Cargo gratefully acknowledges the support given experimental curve, then, upon substitution of the of the National Science Foundation (grant GP-1086). numerical values of the constants in equation 3, the hypothetical death curve can be plotted for comparison with the experimental curve. Ao, of course, can be determined directly from the experimental data. If k < a, an analysis of equation 3 reveals that the slope of the semilog plot of At approaches - k as t becomes arbitrarily large; in this case, - k is merely the final slope of the semilog plot of the experimental curve. When t1 = 0 and t2 = 0o, equation 4 yields Lo

r0

= k f

At dt

and consequently Lo can be estimated by taking the product of the death-rate constant and the area under the experimental curve of At. The value of No is then given by the equation No = Lo - Ao. Finally, the constant 4-. a can be determined from equation 3 by employing values 4 of t and A t from the experimental curve. Alternatively, one 4 might solve for a and No using simultaneous equations 0 derived from equation 3. Suitable modifications must be -i made when a < k. Upon applying the above procedure to the experimental curve of Shull and Ernst (1962), we found k = 1.75 units-', Lo = 6.0 X 105 spores, Ao = 1.3 X 105 spores, No = 4.7 X 105 spores, and a = 1.86 units-'. We then plotted the curve described by equation 3 on the basis of the calculated values and compared the resulting curve with the experimental curve (Fig. 1). Although the curves are similar in shape, there are some critical differences. If we assume that the experimental curve is valid, it appears that our values for a and No are in error. When corrections were made to satisfy the beginning of the 0 1 2 3 4 5 experimental curve, it appeared that either the delay in Time - arbitrary units the death of the spores was not completely the result of heat activation, or heat activation did not behave accordFIG. 1. Heat activation and thermal death of Bacillus stearoing to first-order kinetics. However, examination of thermophilus. Experimental data fromt Shutll and Ernst (1962).

VOL. 1 l, 1963

ACTIVATION AND THERMAL DEATH OF SPORES LITERATURE CITED

HALVORSON, H. 0. 1958. The physiology of the bacterial spore. Technical University, Trondheim, Norway. SHULL, J. J., AND R. R. ERNST. 1962. Graphical procedure for comparing death of Bacillus stearothermophilus spores in saturated and superheated steam. Appl. Microbiol. 10:452-457.

487

STANIER, R. Y., M. DOUDOROFF, AND E. A. ADELBERG. 1963. The microbial world, 2nd ed. Prentice-Hall, Inc., Englewood Cliffs, N.J. STERN, J. A., AND B. E. PROCTOR. 1954. A micro-method and apparatus for the multiple determination of rates of destruction of bacteria and bacterial spores subjected to heat. Food Technol. 8:139-143.

AND

ROBERT R. ERNST

Syracuse University, Syracuse, New York, and TJTilmot Castle Co., Rochester, New York Received for publicationi 10 June 1963

ABSTRACT SHULL, JAMES J. (Syracuse University, Syracuse, -N.Y.), GERALi) T. CARGO, ANI) ROBERT R. ERNST. Kinetics of heat activation and of thermal death of bacterial spores. Appl. -Microbiol. 11:485-487. 1963. Hypotheses concerning kinetics of heat activation and of thermal death of bacterial spores were formulated, and were employed to derive equations describing nonlogarithmic thermal death curves. The equations permitted evaluationi of the validity of experimental data and provided a means for testing the hypotheses presented.

Thermal death of microorganisms genierally obeys firstorder kinetics (Stanier, Doudoroff, and Adelberg, 1963). This concept has led to the use of D values (the time required to reduce the number of viable microorganisms by 90 %7 under specified treatment conditions) and first-order reactioni-rate constants (k) to describe the resistance of microorganisms to heat; these values, in turn, have been employed to predict extinction of a population of microorganisms under the specified treatmenit conditions. However, several investigators have reported nonlogarithmic thermal death curves for certain strains of bacterial spores (Halvorson, 1958; Stern and Proctor, 1954; Shull and Ernst, 1962). In such cases, D values cannot be applied meaningfully, and a more generally applicable description is desired. These spores may behave as a bimodal population with respect to heat resistance for which the death curve is described by the sum of two exponential functions, or they may exhibit a lag followed by a logarithmic decline in the population of viable spores. The latter case is unexplained and has resisted mathematical treatment. Halvorson (1958) suggested that the initial lag could be attributed partly to heat activation of dormant spores and partly to a "multiple-hit" inactivation process. He reasoned that, if heat activation were completely responsible for the initial lag, the logarithmic portion of the thermal death curve should extrapolate to the population of spores observed by direct count, a phenomenon he did not observe. However, this hypothesis would hold true only if nonactivated spores and activated spores were of equal heat resistance. If heat activation preceded thermal death, or if nonactivated spores were of greater resistance 1 Present address: American Sterilizer Co., Erie, Pa.

than activated spores, a time delay would result before all remainiing viable spores were activated and equally susceptible to heat, and the logarithmic portion of the death curve would extrapolate to a point in excess of the direct counit. The latter situation was observed by lialvorson (1958) and inferred in the report of Shull and Ernst (1962). Shull and Ernst (1962) demonstrated that heat activation can be responsible for a signiificant portion of the initial lag in the thermal death curves of spores of Bacillus stearothermophilus, but it was still niot clear how much of the lag could be attributed to heat activation, and whether the death of the spores obeyed first-order kinetics. We have re-examined this system in an effort to resolve three questions. (i) Does heat activation obey first-order kinetics? (ii) Does theirmal death of B. stearothermophilus obey first-order kinietics? (iii) What, if any, is the relationship between heat activation and thermal death? Let us suppose that a hypothetical population of spores is heated at a conistant temperature. The number of activated spores (those capable of colony formation on a suitable medium) at time t is denoted by A t, and the number of nonactivated spores (those capable of conversion to the activated state upon heating) at time t is denoted by Nt. Then the number Lt of living spores at time t is given by Lt = Nt + At. The initial number of activated spores is Ao, and the initial number of nonactivated spores is No. Furthermore, let us make the following assumptions: first,

485

2Vt

=

Noe-at

where a is the activation-rate constant; second, the number of activated spores remaining at time t from the original activated population is A oe-kt where k is the death-rate constant; third, heat activation must precede thermal death of nonactivated spores. An examination of the behavior of At and Lt over a short interval of time yields the following differential

equations: At' = -kAt + I,t'

-kAt

aVoeat(1)

(1)

(2) When a # k, the solution of equation 1 subject to the initial conditions is =

SHULL, CARGO, AND ER'NST

486) A,

=

Aoeht +

k-a

(e-at - e-kt)

(3)

A slight modificationi is necessairv when a = k. Upon integration, equation 2 becomes Lt,-, = -k ]

At dt tl

(4)

APPL. AIICROBIOL.

equation 3 revealed that, for a given population of spores, a change in the ratio of a to k would result in a change in the shape of the initial portion of the thermal death curve. V'alues a and k are temperature-dependent, and the ratio of a to k may also change with temperature. Therefore, any system in which the temperature changes during a significant portion of the experiment would give rise to distortions in the thermal death curve. Consequently, the curve reported by Shull and Ernst (1962) is probably distorted as the result of a relatively long heating time. Because the data at hand are subject to this procedural error, answers to the questions posed must await acquisition of more exacting experimental data or application of the hypothetical equations to data available in other laboratories.

Equation 3 describes the behavior of the activated spore population in the hypothetical system as the sum of two terms; the first term accounts for the first-order death of the initial activated spore population; the second describes the activation and subsequent death of nonactivated spores. Equation 4 indicates that the total number of deaths occurring between time t1 and time t2 is equal to the product of the death-rate constant and the area under the death curve for the time period in question. ACKNOWLEDGMENTS If the constants Ao, No, k, and a can be determined for a Gerald T. Cargo gratefully acknowledges the support given experimental curve, then, upon substitution of the of the National Science Foundation (grant GP-1086). numerical values of the constants in equation 3, the hypothetical death curve can be plotted for comparison with the experimental curve. Ao, of course, can be determined directly from the experimental data. If k < a, an analysis of equation 3 reveals that the slope of the semilog plot of At approaches - k as t becomes arbitrarily large; in this case, - k is merely the final slope of the semilog plot of the experimental curve. When t1 = 0 and t2 = 0o, equation 4 yields Lo

r0

= k f

At dt

and consequently Lo can be estimated by taking the product of the death-rate constant and the area under the experimental curve of At. The value of No is then given by the equation No = Lo - Ao. Finally, the constant 4-. a can be determined from equation 3 by employing values 4 of t and A t from the experimental curve. Alternatively, one 4 might solve for a and No using simultaneous equations 0 derived from equation 3. Suitable modifications must be -i made when a < k. Upon applying the above procedure to the experimental curve of Shull and Ernst (1962), we found k = 1.75 units-', Lo = 6.0 X 105 spores, Ao = 1.3 X 105 spores, No = 4.7 X 105 spores, and a = 1.86 units-'. We then plotted the curve described by equation 3 on the basis of the calculated values and compared the resulting curve with the experimental curve (Fig. 1). Although the curves are similar in shape, there are some critical differences. If we assume that the experimental curve is valid, it appears that our values for a and No are in error. When corrections were made to satisfy the beginning of the 0 1 2 3 4 5 experimental curve, it appeared that either the delay in Time - arbitrary units the death of the spores was not completely the result of heat activation, or heat activation did not behave accordFIG. 1. Heat activation and thermal death of Bacillus stearoing to first-order kinetics. However, examination of thermophilus. Experimental data fromt Shutll and Ernst (1962).

VOL. 1 l, 1963

ACTIVATION AND THERMAL DEATH OF SPORES LITERATURE CITED

HALVORSON, H. 0. 1958. The physiology of the bacterial spore. Technical University, Trondheim, Norway. SHULL, J. J., AND R. R. ERNST. 1962. Graphical procedure for comparing death of Bacillus stearothermophilus spores in saturated and superheated steam. Appl. Microbiol. 10:452-457.

487

STANIER, R. Y., M. DOUDOROFF, AND E. A. ADELBERG. 1963. The microbial world, 2nd ed. Prentice-Hall, Inc., Englewood Cliffs, N.J. STERN, J. A., AND B. E. PROCTOR. 1954. A micro-method and apparatus for the multiple determination of rates of destruction of bacteria and bacterial spores subjected to heat. Food Technol. 8:139-143.