Microbial population dynamics in bioprocess sterilization

Microbial population dynamics in bioprocess sterilization Arthur A. Teixeira* and Alfredo C. Rodriguez¢ *Agricultural Engineering Department, University o f Florida, Gainesville, F L ?British Columbia Institute o f Technology Burnaby, B C Canada

Introduction The design of thermal sterilization processes has been traditionally based on the assumption that thermal inactivation of bacterial spores can be modeled by a single first-order reaction. This can be described as a straight-line survivor curve when the logarithm of the number of surviving spores is plotted against time of exposure to a lethal temperature. However, actual survivor curves plotted from laboratory data frequently reveal considerable deviation from this single straight line, particularly during early periods of exposure. This is a result of additional competing reactions that take place, such as heat activation and preliminary inactivation (early inactivation of less heat-resistant spore fractions). L2 These deviations from the straightline model often make it difficult to test or validate a thermal process microbiologically. Plate count results from a spore suspension subjected to the variable time-temperature history of a commercial thermal process often do not agree with predicted results from the straight-line model. Also, the increasing use of high temperature-short time sterilization processes requires the use of better kinetic models because these competing reactions may predominate over the inactivation reaction during relatively brief exposures to ultra-high lethal temperatures.

Population dynamics of bacterial spores Several analytical and numerical methods have been developed for predicting the dynamics of bacterial spore populations during commercial sterilization processes. 3-6 Models currently used are based on the observation that inactivation may be approximated by first-order reaction kinetics, as first described by Chick. 7 An integration procedure is required to apply those models to nonisothermal processes in which temperature varies as a function of time. The Fo concept is commonly used for this purpose in the design of food sterilization processes, and has been recently applied to the sterilization of bioreactor media by Boeck

Address reprint requests to Dr. Teixeira at the Agricultural Engineering Department, University of Florida, Gainesville, FL 32611

©

1990 Butterworth Publishers

et al. 8 This concept involves representing the total heat applied during the cycle by an equivalent length of time at a constant reference temperature, usually 250°F (121°C). This equivalent length of time is known as the F value, and can be used to calculate the probability of microbial survivorship. Application of nonlinear regression to data from nonisothermal experiments was proposed as an alternative by Wang et al. 9 Some models based on the idea that activation and inactivation may be considered sequential chemical reactions have been published, ~°,~ but this hypothesis of sequential reaction kinetics was tested and found to be incorrect by Lewis et al. ~2 Attempts to compare predictions from those models with experimental data have shown very important discrepancies that reveal the need for more precise models. 13,t4 As a result of increasing knowledge about microbiological changes (transformations) in spores exposed to high temperature, various transformations have been identified that may occur concurrently with thermal inactivation. Of these, the most significant are activation, t5 injury, ~6,~7 and revival/8 They have important and direct influences on the number of survivors found in sterilized products, but they have not been considered in traditional mathematical models. Consideration of those transformations inspired development of a more comprehensive population model of a suspension of bacterial spores treated at lethal temperature. Activation is a transformation of viable, dormant spores enabling them to germinate and grow in an enumeration medium. Activation occurs in the pH range 2.0 to 8.5. ~5 The usual method of activating spores is exposure to heat. Keynan et al.~5 mentioned that activation was first discovered in mold spores, that it was used as early as 1919, and that the main agents of activation are heat, acidity, thiol compounds, and strong oxidizing agents. Their discussion of possible activation mechanisms supported the idea that the macromolecules responsible for maintenance of the dormant state are-proteins rich in cystine and stabilized by S-S linkages. Lewis et al. 12 published an important paper on dormancy and activation of bacterial spores in which they reported that the kinetics of heat activation and inactivation do not conform to a pattern of two consecutive first-order reactions.

Enzyme Microb. Technol., 1990, vol. 12, June

469

Literature Survey Injury is a transformation of bacterial spores exposed to high but sublethal temperature that modifies their capacity to germinate and grow. Thermally injured spores are unable to develop visible signs of growth with standard growth media and incubation conditions that are optimal for growth of untreated spores, and they have increased susceptibility to inhibitors. 17,19 However, they retain colony-forming capabilities when media or growth conditions, such as incubation temperature, nutrients, and germinants, are modified. Germination is a multistage process, possibly with several pathways for completion of each stage. Complete, irreversible inactivation of one or more stages would trap a spore protoplast within the structures maintaining dormancy, and the spore effectively would be inactive. If such inactivation can be bypassed, a spore is classified as injured. Spores subjected to ultrahigh temperature may be injured but not completely inactivated; consequently, heat injury may be an important factor in evaluating the success of a sterilization process. Sublethal thermal processing may activate an alternative germination mechanism allowing injured spores to grow only at lower than normal incubation temperature.16 A less heat-resistant population consists of germinated spores that have lost their heat resistance, or vegetative cells, or (in the case of multiple genome bacteria), spores that are genetically less heat-resistant. However, a less heat-resistant population can produce colonies in an enumeration medium that are indistinguishable from those originated by mature activated spores.

dependence of rate constants and model validation for nonisothermal cases are reported in Rodriguez et al. 2 This work led to the derivation of equation (1) for an improved kinetic model. It contains the summation of three exponential terms instead of the single exponential term that is traditionally used. Each term requires its own rate constant and activation energy constant. These constants can be obtained from special treatment and manipulation of the laboratory data from traditional thermal death-time (TDT) experiments. The summation of these three terms (preliminary inactivation, activation, and predominant inactivation) will produce the peaks and valleys that are found in actual data during early exposure periods to lethal temperatures. N(t) = N3oexp(-Kd3t) + Nlo[1-exp(-Kat)]

exp(-Kdt) + N 2 o e x p ( - K d t )

(1)

The first term in equation (1) describes rapid decay of any initial, less heat-resistant fraction, N30; it produces any initial steep decline in the number of survivors. The second term describes thermal activation and subsequent inactivation of dormant spores, N~. It is a pulse rising rapidly from an initial value of NI0, peaking, and then decaying slowly. This term gener-

New developments From consideration of the above information, Rodriguez et al. 1 tested the following hypotheses for a population of B. subtilis spores: (1) inactivation activation, and injury are simultaneous and independent first-order reactions; (2) less heat-resistant fractions of a spore population may exist; and (3) a heat-activated, alternative germination system exists allowing B. subtilis spores to grow when the incubation temperature is 32°C instead of the standard 45°C incubation temperature. These hypotheses led to a new conceptual model of a bacterial spore population treated at lethal temperature. The conceptual model was analyzed to derive a mathematical model from which dynamic responses of spore populations to lethal temperature regimes could be determined. The mathematical model was solved for formulae of the responses to a constant lethal temperature. Those responses consist of sums of exponential functions of time involving parameters pertaining to initial conditions and first-order rate constants. Values of parameters in the model were obtained from a series of isothermal experiments in which B. subtilis spores were exposed to lethal temperatures. Survivors at successive times were enumerated microbiologically, and the experimental responses were fitted to the isothermal response formulae of the model using a nonlinear regression technique. Temperature

470

Enzyme Microb. Technol., 1990, vol. 12, June

\

3

!

\

o

TIME

Figure 1 Inactivation of bacterial spores. (1) Logarithmic behavior; (2) preliminary inactivation of less heat-resistant fractions; (3) region dominated by activation; (4) predominant inactivation region

Microbial

population

dynamics:

A. A. Teixeira

and A. C, Rodriguez

99 98 97 96

95 94 93

92 91 90 89 88 87 86 85

J

I

I

0

Figure 2

Temperature

history

experienced

I

I

2

I

by B. subtilis

spores during

ates the “shoulder” of survivor curves. The third term describes inactivation of initially active spores, NZO; it corresponds to the classical single exponential model of thermal inactivation. Figure I shows the differences that can be found between use of the Rodriguez model and traditional modeling procedures. The superimposed straight line represents the traditional model that would be used as a predictor. The Rodriguez model will produce a curve that will closely follow actual data revealing the three stages that are shown in the figure. More importantly, when equation (1) is programmed for computer execution, it can more accurately predict the early response of a microbial population over time when exposed to a transient temperature process. Figure 2 is a computer plot of the input data file containing the temperaturetime history of a test spore suspension. It shows the resulting peaks and valleys in response to the heater being turned on and off at varying periods of time during the exposure process. Figure 3 shows the survivor response curve predicted by the Rodriguez two-term model along with response curves predicted by the traditional one-term model, depending upon how initial condition are chosen for the traditional model. The kinetic data that describe the population dynamics of the B. subtilis spore suspension used in this example

I

I

4 (Thousands) Time (Seconds)

6

dynamic

on-off

heating

I 8

process

are given in Table I. It should be noted that this spore suspension had no less resistant fraction, so the first term in equation (1) involving Kd3 was dropped, and the equation reduced to a two-term model for the two reactions of activation and inactivation. The response curve from this model realistically produces the initial “shoulder” during the first few minutes of heating revealing the likely predominance of the activation reaction that would be expected during early periods of exposure. Choice of initial spore population has often plagued food microbiologists in the use of the traditional oneterm model. Because of the shoulder effect, the actual number of initially active spores does not lie on the response curve describing the predominant inactivation. If this point is used as the initial condition for the traditional model, the resulting response curve will be a poor predictor of actual population behavior, as shown by the lowest response curve in Figure 3. Pretreating the spore suspension with a heat shock treatment to induce activation simply results in a larger but unknown percentage of the spore population being initially activated, but does not solve the problem completely. An alternative initial condition that can be defined for the traditional model is the pseudoinitial spore population obtained by extrapolating the Enzyme

Microb. Technol.,

1990, vol. 12, June

471

Literature Survey 210

-----

200

Model ( I n a c t i v a t i o n onl)/ NO = NIO + N 2 0 )

190 180 170

0 ©

160

c

150

0

"~

140

"4

130

b C

~

Model (Activation + InActivation)

120

C, c

110

,~ ~

loo

"5

~

8o

Q

70

k.

o .~_

60

b

40

al M o d ~

X ~ l n a c t i v a t i o n onl~ NO = N 2 0 )

3O 2O 10

0

I

0

i

I

I

i

I

4

2 Time

I

0

I

i

8

(Thousands) (Seconds)

Figure 3 S u r v i v o r response curve generated by tw o-ter m Rodriguez model sandwiched between response curves g e n e r a t e d by the traditional one-term model f o r t w o possible choices of initial population numbers

straight-line portion of the predominant inactivation curve back to the ordinate axis. This will produce a response curve that predicts the behavior of the spore populations fairly well, but only after some extended period of time into the process, after the shoulder effect caused by early activation has been exhausted. This response behavior is shown by the uppermost curve in F i g u r e 3 . In contrast, the complex two-term

model makes use of both the initial number of active spores and the initial number of inactive or dormant spores as the initial conditions. These initial conditions along with the appropriate rate constants produce a response curve that realistically reflects the initial activation reaction that occurs simultaneously with inactivation during the early stages of exposure to a lethal heat process.

Table 1 Kinetic data for normal spores of B. subtilis exposed to lethal temperature range of 87°C-99°C showing first-order rate constants at reference temperature of 93°C and activation energy constant Ea for the Arrhenius temperature dependency

Reaction"

Rate constant at 93°C k (cycles s 1)

Activation e n e r g y E a (joules k m o l e -1)

Initial n u m b e r

Activation Inactivation

/Ca = 0.000729 kd = 0.000186

1.48 x 108 2.26 x 108

N20 = 0.69 x 108 N1o = 2.26 x 108

a For this spore suspension there was no p r e l i m i n a r y inactivation of a less resistant fraction, so the rate const ant kd3 f o r this reaction was zero

472

Enzyme Microb. Technol., 1990, vol. 12, June

Microbial population dynamics: A. A. Teixeira and A. C. Rodriguez References

10 11

1 2

3 4 5 6 7 8 9

Rodriguez, A. C., Smerage, G. H., Teixeira, A. A. and Busta, F. F. Trans. A S A E 1988, 31, 1594-1601, 1606 Teixeira, A. A., Sapru V., Smerage, G. H. and Rodriquez, A. C. Thermal Sterilization Model with Complex Reaction Kinetics. Proceedings of ICEF-5. Cologn, West Germany. Elsevier Science Publishers Ltd. (in press). Ball, C. O. and Olson, F. C. W. Sterilization in Food Technology McGraw-Hill Book Company, New York, 1957 Stumbo, C. R. Thermobacteriology in Food Processing. Academic Press, New York, 1965 Teixeira, A. A., Dixon J. R., Zahradnik, J. W. and Zinsmeister, G. E. Food Technol. 1969, 23, 78-80 Lenz, M. K. and Lund, D. B. J. Food Process Eng. 1978, 2, 227-271 Chick, H. J. Hygiene 1910, 10, 237-286 Boeck, L. D., Wetzel, R. W., Burt, S. C., Huber, F. M., Fowler, G. L. and Alford, J. S., Jr. Microbiol. 1988, 3, 305310 Wang, Y. J., Leesman, G. D., Dahl, T. C. and Monkhouse, D. C. J. Parent. Sci. Technol 1984, 38, 68-82

12 13 14 15 16 17 18 19

Shull, J. J., Cargo, G. T. and Ernst, R. R. Appl. Microbiol. 1963, 11, 485-487 Kalinina, N. M. and Motina, G. L. Pharm. Chem. J. 1984, 17, 813-815 Lewis, J. C., Snell, N. S. and Alderton, G. in Spores 111 (Campbell, L. L. and Halvorson, H. O., eds.) American Society for Microbiology, Washington, DC, pp. 47-54 Berry, M. R., Jr. and Bradshaw, J. G. J. Food Sci. 1982, 47, 1698-1704 Teixeira, A. A. Report to Ross Laboratories submitted by the University of Florida, contract No. 80895-C Keynan, A., Issahary-Brand, G. and Evenchik, Z. in Spores 111 (Campbell, L. L. and Halvorson H. O., American Society for Microbiology, Washington, DC Edwards, J. L., Busta, F. F. and Speck, M. L. Appl. Microbiol. 1965, 13, 858-864 Adams, D. M. Heat injury of bacterial spores, in Advances in Applied Microbiology (Perlman, D., ed.) Academic Press, New York, 1978 Hurst, A. in Repairable Lesions in Microorganisms (Hurst, A. and Nasim, A., eds.) Associated Press, Orlando Foedgeding, P. M. and Busta, F. F. J. Food Protect. 1981, 44, 776-786

Enzyme Microb. Technol., 1990, vol. 12, June

473