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Publications - Work Done by Microbiology Reader Bioscreen C
Journal of Applied Microbiology, 2000, May,
88(5), 907-913
Disinfection kinetics: a new hypothesis and model for the tailing of
log-survivor / time curves
R.J.W. Lambert and M.D.
Johnston
ABSTRACT
A new hypothesis for the understanding of chemical disinfection, which we
have termed the Intrinsic Quenching hypothesis, is presented. This
mechanistic treatment of disinfection kinetics is based on the hypothesis
that the biocide concentration may not be in vast excess over the microbes,
as is normally assumed. A mathematical model was developed and found to be
useful in describing the observed kinetics of several disinfectants. The
model suggested that the reason for the observation of non-linear,
log-survivor curves was due to the ability of the microbes, in clean,
soil-free conditions, to intrinsically quench the bulk concentration of
biocide.
INTRODUCTION
Just over a hundred years ago Kronig and Paul (1897) reported that the
rate of chemical disinfection of bacteria was dependent on the disinfectant
concentration and the temperature of the experiment. Madsen and Nyman (1907)
and Chick (1908) suggested that disinfection was analogous to chemical
reaction processes. This became known as the Mechanistic hypothesis of
disinfection ( Lee and Gilbert 1918). However, another hypothesis was put
forward to explain disinfection. This hypothesis was based on the assumption
that there existed a distribution of resistances to the chemical
disinfectant within the microbial population. This became known as the
Vitalist hypothesis of chemical disinfection. Discussions on which
hypothesis, if either, was correct was a 'hot topic' of the time, typified
by Reichenbach (1911)'[it is] a violation of the laws of rigorous reasoning
to attempt to account, on the basis of a chemical analogy, for the
logarithmic death-rate of the micro-organisms'.
One of the principal features which the Mechanistic hypothesis could not
account for was the tailing of log-survivor time curves. The mechanistic
model of Chick-Watson, was based on first order chemical reaction kinetics (
Watson 1908; Phelps 1911). Since this mathematical model could only deal
with linear log-survivor time curves, deviations from the straight line were
explained by the presence of variations in the population resistance ( Chick
1908). The Vitalists went further and suggested that all of disinfection was
due to the 'permanent variation in the population resistance to
disinfectants' ( Lee and Gilbert 1918). In 1942 Withell described a method
for obtaining the distribution of resistances within the population and
suggested again that the Vitalist hypothesis was a more reasonable
explanation for the observations of disinfection than the Mechanistic
hypothesis.
That the issue has never been resolved can be seen in the review of
disinfection models by Prokop and Humphrey (1970). Various mathematical
models were examined from the literature and were split into two principle
classes: those supporting the Mechanistic hypothesis and those supporting
the Vitalistic hypothesis. In nearly all of the mechanistic models put
forward to take account of the non-linearity of log survivor-time curves, an
intermediate population stage was usually suggested, with different rates of
disinfection for each of the different microbial states (see Cerf 1977; for
an excellent review).
Many mathematical models for disinfection kinetics exist, but as Prokop
and Humphrey (1970) expressed 'They are for the most part too complicated to
be of practical utility'. In general, the simple Chick-Watson log-linear
model or the more useful, empirical, Hom (1972) disinfection model, which
allows a fit to non-linear log survivor-time data, are preferentially used.
The question as to whether the underlying disinfection occurs via a
Mechanistic or Vitalistic process, or neither, or both, is still open to
debate.
In a recent publication ( Johnston et al. 2000) it was shown that
the inoculum size of the disinfection test could have a very large impact on
the outcome of the test. Since, from a Vitalistic viewpoint, the
distribution of the resistance to the biocide within the population was
permanent and identical, whether there were 1 
108
microbes ml
1
or 1000 microbes ml
1,
identical survivor curves should have been obtained from different sizes of
starting inocula. Small changes in the sizes of the test inocula (from 1 107
to 5 107)
resulted in very different log reduction-time plots. This suggested that the
bacteria were altering the concentration of the disinfectant during the
course of disinfection. Although some evidence was put forward to help prove
this point, a revised mathematical model, based on Mechanistic grounds, was
lacking. Herein we report a model of disinfection, based on an advancement
of the Mechanistic hypothesis, which takes, as an assumption, the ability of
microbes to reduce the effective level of biocide during the disinfection
test itself.
MATERIALS, METHODS and MODELS
Preparation of bacterial suspensions
Staphylococcus aureus ATCC 6538, Proteus mirabilis ATCC
2937 or Pseudomonas aeruginosa ATCC 2730 were grown overnight in
flasks containing 80 ml tryptone soy broth (TSB) (Oxoid CM 129, Basingstoke,
UK) shaking at 30 °C. Cultures were centrifuged at 510 g (Sigma model 3K-1,
St Louis, MO, USA) for 10 min. The resulting cell pellets were pooled and
resuspended in 0·1% peptone water. An inoculum level of 3 108 ml
1
was used and, to ensure a good degree of reproducibility, optical density
was used via reference to a standard O.D./cell-numbers curve.
Suspension tests
All chemicals used were obtained from the Sigma-Aldrich Company (Poole,
UK). The disinfection method has been previously published ( Lambert
et al. 1998). The term log reductions, logR, used in this paper
refers to the log reductions obtained by the Bioscreen methodology.
Intrinsic Quenching Model
The basic rate model of disinfection is the Chick-Watson model ( Chick
1908; Watson 1908), equation 1.
i.e. a maximum value for the log reduction, dependent on the initial
concentration of the biocide, should be observed. This finding is equivalent
to saying that the rate of disinfection falls to zero at large time.
Shapes of the log reduction-time curves and the IQ
Model
Figure 2 displays the effect that different values of Q have on
the shape of a logR/time curve, for a given, fixed initial rate of
disinfection (equivalent to a fixed concentration of biocide). As Q
increases, the amount of tailing (curvature) also increases, such that when
Q > 1, the rate of disinfection quickly falls to zero. Linear
log-survivor curves are indicative of a low level of quenching with Q
typically < 0·005. If, however, the level of quenching is held constant and
the biocide concentration is changed, then log survivor-time curves, as
shown in Fig. 3, are predicted.
RESULTS
The disinfection of either Staph. aureus, Pr. mirabilis or
Ps. aeruginosa with a variety of biocides was examined. In each case
the disinfection data were examined using two kinetic models: the Hom (1972)
and the IQ (see Appendix for a description of the Hom model). The data set
from a Bioscreen disinfection procedure ( Lambert et al. 1998) was analysed
using equation 6 through the use of non-linear fitting procedures, as found
in statistical programs like JMP (SAS Institute, Cary, NC, USA). To prime
the non-linear fitting procedure the parameters from the Hom model
examination were routinely used and a value for Q of between 0·01 and 0·1
suggested as a starting reference value. Tables 1 and 2 give the results of
such analyses on a variety of biocides. Statistical examinations of the
models vs the observed were carried out using a residual analysis.
The mean and the standard deviation of the residuals were used as a measure
of the goodness of fit. The following three examples are used to illustrate
the methodology.
The peracetic acid disinfection of Ps. aeruginosa
An examination of this was reported in a previous publication ( Lambert
et al. 1999). The data displayed non-linear kinetics and were
examined in that publication using the Chick-Watson and Hom models. In this
work the data were also examined using the IQ model, Fig. 4. Both the Hom
and IQ models were able to describe the kinetics well. The dilution
coefficients were identical in each case (0·995) and the disinfection rate
constants of the same order. The Hom parameter h of 0·435 suggested
the presence of strong tailing and the IQ model also reflected this with a
high Q-value (0·12). In this case, as in all others examined, the IQ
model gave a lower standard deviation of the residuals than did the Hom
model.
The silver ion disinfection of Staph. aureus
Figure 5 shows the extreme non-linear disinfection kinetics observed,
with the rate of disinfection becoming zero within approximately 10 minutes
for all concentrations of silver ion used. The Hom parameter h of
0·148, suggested very strong tailing. The Q parameter of 0·378 was
indicative of strong intrinsic quenching. The Chick-Watson model, being a
log-linear model, would be incapable of describing kinetics such as this.
The IQ model gave a value of 1·038 for the dilution coefficient of silver
ions which is in accordance with that expected from a disinfectant acting in
a chemical manner as opposed to having a purely physically disruptive mode
of action ( Hugo and Denyer 1987).
Tetradecyltrimethyl ammonium bromide disinfection of
Staph. aureus
When the observed logR data were plotted against the calculated
logR data for both the IQ and Hom models ( Fig. 6) a large
discrepancy was found between the two models. The standard deviation of
residuals was 1·92 with the Hom and 0·063 with the IQ model. In this case
because there were both lags and tails present in the original data the Hom
model could not be used with confidence. Whereas with the IQ model, although
the presence of lags is not addressed with this particular form of the
model, a good fit with the observed results does suggest a greater
applicability of this methodology.
FIGURES
Fig. 1 Basis for the
Intrinsic Quenching Model of microbial and biocide inactivation
Fig. 2 Effect of
changing the Intrinsic Quenching factor, Q, with a constant rate of
disinfection (K =... 0...
Fig. 3 Effect of
changing the disinfection rate, K 0 with a constant level
of intrinsic quenching (Q = 0...·1...
Fig. 4 The
disinfection kinetics of peracetic acid (mmol l
1)
against Ps. aeruginosa
observed (symbols) ...
Fig. 5 The
disinfection kinetics of silver ion (ppm of Ag+) against
Staph. aureus
observed (symbols) a...
Fig. 6 Comparison of
the Hom and the IQ models for the disinfection of Staph. aureus by
tetradecyltrim...
Table 1 Hom model parameters
Table 2 Intrinsic
Quenching Model parameters
DISCUSSION
The basis for the current understanding of the tailing of
log-survivor/time curves is the supposed distribution of resistance
throughout a population of microbes ( Withell 1942a). In general the
analysis of such data follows a probit analysis, using the methodology given
by Withell (1942b). The hypothesis of a 'permanent variable population
resistance' is but one of two hypotheses for disinfection, the other being
based on physical chemistry ( Chick 1908; Watson 1908; Lee and Gilbert 1918)
The so-called Mechanistic hypothesis puts forward the view that
disinfection is a purely physicochemical phenomenon and is regulated in the
exact same way as are chemical reactions. The apparent exponential decay
curves of plots of survivors against disinfectant contact time are used as
proof that disinfection obeys the same laws as chemical reactions and that
the form of equation 1 can be used to describe both phenomena. Simple
integration of this equation, with N equal to the moles of reactant,
gives the log-linear curves of a first order chemical reaction. In a general
chemical reaction there are two reacting components and to make experimental
sense of a reaction one of the two components is usually present in large
excess. When this condition is met then a chemical reaction can be analysed
using equation 1. If, however, this is not the case then the above equation
may not be applicable.
In studies of disinfection it has always been assumed that the biocide is
in vast excess over the number of microbes. A 0·01% solution of a typical
biocidal quaternary ammonium compound (QAC) in a 1 108 ml
1
bacterial culture contains approximately 2 109
molecules of biocide per cell. In terms of such numbers there is a vast
excess of surfactant over a cell. However, is it a vast number of biocide
molecules over the number of potential 'target' sites? For example, an
average Escherichia coli cell contains an average of 2·2 107
lipid molecules per cell and 1·2 106
lipopolysaccharide molecules per cell ( Neidhardt et al. 1990). This
gives a 100-fold excess of surfactant biocide molecules, from a 0·01%
solution of QAC, over the lipid and lipopolysaccharide content of the cell.
QACs act by dissolving the microbial lipid membrane, but how much QAC is
required per lipid molecule? This means that even from a very simple
calculation QACs are not in vast excess over the target components of the
microbial cell. The data used to obtain Fig. 6 used concentrations as low as
0·0007% of the QAC which by this argument would suggest that assuming the
biocide to be in vast excess is erroneous. If the biocide is not in great
excess over the microbe, then non-linearity of the log survivor-time curves
must occur, in essence the reaction constant k o
becomes a variable dependent on time, equation 3.
Other scientists, such as Hom, have tried to make sense of such
non-linear log survivor-time curves by altering the dependency of time
itself. By invoking disinfection rates which operate at fractional powers of
time or powers greater than one, the rate process becomes non-physical. A
rate process which does not occur at time/minute or time/second is either
slowing down e.g. time/minute0·5, or speeding up e.g. time/minute1·5.
Rate processes like these would require input from another source, such as a
braking or an accelerating mechanism. Such a mechanism is absent from the
Hom model.
For the tailing of disinfection curves, the time exponent of the Hom
model is always less than one. This is simply signifying a rate process,
which is decelerating. One possible explanation is that the driving force of
the reaction, namely the disinfectant concentration, is diminishing as the
disinfection process continues. This removes the need for a distribution of
resistance, throughout the population, as an explanation for non-linear log
survivor time curves, which we have already shown requires revision (
Johnston et al. 2000).
There are two reasons why the biocide concentration could decrease during
the course of the disinfection process: an inherent instability or
non-microbial quenching of the disinfectant, or through
microbially-mediated, intrinsic quenching. With regards to the first process
an example would be the decomposition of ozone by heat or through the action
of metal ions. In the second case, microbial membranes, for example, would
be expected to quench surfactant biocides.
The Intrinsic Quenching model, equation 6, has been derived from known
principles and can justly be called a Mechanistic model of disinfection. The
model also allows the derivation of the Chick-Watson model, showing it to be
a 'special case'. The parameters obtained for the disinfection rate constant
and the dilution coefficient using the IQ model are similar to those
obtained from the Hom model ( Tables 1 and 2). This suggests the
compatibility of this new model with previous studies which have used the
Chick-Watson or Hom models for data analysis. A re-examination of such data
using this new model may be beneficial. The IQ model explains the tailing
features of log-survivor time plots: the active component (biocide in this
case) is inactivated, by some means, during the course of the disinfection
experiment.
In the experiments carried out here, the only possible explanation for
the quenching of the disinfectant, during the course of the test, is through
the action of the microbes themselves. Solutions of the disinfectants are
stable for periods greater than the time taken to conduct a disinfection
experiment. Thus for a given level of microbes there will be a constant
level of quenching, independent of the biocide concentration.
The IQ model also revealed the parameter Q, which we have termed
the Intrinsic Quenching parameter. Q is a measure of how quickly the
rate of disinfection slows down given a biocide inactivation rate governed
by k 2 . The IQ model suggests this to be
independent of the biocide concentration. Comparison of Figs 2 and 4
suggests the model reflects the observed tailing of disinfection tests. We
suggest that Q is therefore a physical property of the microbes with
respect to the disinfectant under investigation. We have already shown that
altering the numbers of microbes in a test dramatically alters the efficacy
of disinfection ( Johnston et al. 2000). We would expect Q to
be related to the inoculum size of the microbes used in the test. Further
experiments to examine this possibility are underway.
REFERENCES
• Cerf, O. (1977) Tailing of survival curves of bacterial spores. Journal of
Applied Bacteriology 42, 1 19.
• Chick, H. (1908) An investigation into the laws of disinfection. Journal of
Hygiene (Cambridge) 8, 92 158.
• Hom, L.W. (1972) Kinetics of chlorine disinfection in an ecosystem. Journal
of the Environmental Division of the American Society of Civil Engineering 98,
183 194.
• Hugo, W.B. & Denyer, S.P. (1987) Concentration exponent of disinfectants
and preservatives (biocides). In Preservatives in the Food, Pharmaceutical and
Environmental Industries (The Society for Applied Bacteriology Technical Series
22), pp. 281 291. Oxford: Blackwell Scientific.
• Johnston, M.D., Simons, E.-A., Lambert, R.J.W. (2000) One explanation for
the variability of the bacterial suspension test. Journal of Applied
Microbiology 88, 237 242.
• Kronig, B.anD. & Paul, T. (1897) Die chemischen Grundlagen der lehre von
der Giftwirkung und Desinfection. Zeitschrift Fur Hygiene 25, 1 112.
• Lambert, R.J.W., Johnston, M.D., Simons, E.-A. (1998) Disinfectant testing:
use of the Bioscreen Microbiological Growth Analyser for laboratory biocide
screening. Letters in Applied Microbiology 26, 288 292.
• Lambert, R.J.W., Johnston, M.D., Simons, E.-A. (1999) A kinetic study of
the effect of hydrogen peroxide and peracetic acid against Staphylococcus aureus
and Pseudomonas aeruginosa using the Bioscreen Disinfection method . Journal of
Applied Microbiology 87, 782 786.
• Lee, R.E. & Gilbert, C.A. (1918) On the application of the mass law to the
process of disinfection - being a contribution to the 'mechanistic theory' as
opposed to the 'vitalistic theory'. Journal of Physical Chemistry 22, 348 372.
• Madsen, T. & Nyman, M. (1907) Zur Theorie der Desinfektion I. Zeitschrift
Fur Hygiene 57, 388 404.
• Neidhardt, F.C., Ingraham, J.L., Schaechter, M. (1990) Physiology of the
Bacterial Cell. Sunderland, MA: Sinauer Associates.
• Phelps, E.B. (1911) The application of certain laws of physical chemistry
in the standardization of disinfectants. Journal of Infectious Diseases 8, 27
38.
• Prokop, A. & Humphrey, A.E. (1970) Kinetics of Disinfection. In
Disinfection ed. Bernarde, M.A. pp. 61 83. New York, NY: Marcel Dekker.
• Reichenbach, H. (1911) Die Absterbeordnung der Bakterian und ihre Bedeutung
fur Theorie und Praxis der Desinfektion. Zeitschrift Fur Hygiene 69, 171 222.
• Watson, H.E. (1908) A note on the variation of the rate of disinfection
with change in the concentration of the disinfectant. Journal of Hygiene
(Cambridge) 8, 536 542.
• Withell, E.R. (1942a) The significance of the variation in shape of time
survivor curves. Journal of Hygiene, (Cambridge) 42, 124 183.
• Withell, E.R. (1942b) The evaluation of bactericides. Journal of Hygiene
(Cambridge) 42, 339 353.
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