An improved model for the analysis of combined antimicrobials: a replacement for the Chou-Talalay combination index method.

AIMS: To rationalize confusion in the literature concerning the analysis of combined antimicrobials, specifically to see if the combination index (CI) method of analysis was as rigorous as claimed. METHODS AND RESULTS: Data from previous studies of the inhibition of Staphylococcus aureus by mixed antimicrobials were re-analysed using the CI method and a model which takes account of differences in the concentration exponents of individual antimicrobials. CONCLUSIONS: The Chou-Talalay combination index method for the analysis of combined antimicrobials was found to be valid only in the specific cases where concentration exponents were equal. In these cases, the CI method was found to be a function of the residuals of fitting the additive model to the observed data. Where concentration exponents were not equal, the CI method was invalid, whereas the additive model took these differences into account. SIGNIFICANCE AND IMPACT OF STUDY: The CI method can be replaced wholly by the additive model described. The model allows simple regression to be used to analyse whole data sets and provides simple graphical output.

Microbial growth parameters obtained from the analysis of time to detection data using a novel rearrangement of the Baranyi-Roberts model.

AIMS: To explore the predictions of a novel rearrangement of the Baranyi-Roberts model (BRM) with time to detection data obtained from optical density data of microbial growth. METHODS AND RESULTS: Growth of Escherichia coli and Salmonella Typhimurium under mild conditions of temperature (25-37°C), salt (0·086, 0·51 and 1·03 mol l(-1)) and pH (6·85-4·5) was examined using optical density. Time to detection (TTD) data were fitted to a model based on a rearrangement of the BRM. Observations showed compatibility with standard viable count studies and produced highly accurate specific growth rates and lag phase durations. At high salt and low pH, however, there was a substantial dependency on the initial inoculum for the observation of visible growth. At 30 and 37°C, with 1·03 mol l(-1) salt, and at pH <5·75, no visible growth was recorded for E. coli at initial inoculum levels below 10(7) CFU ml(-1). CONCLUSIONS: The rearranged BRM can be used directly with TTD data obtained from optical density measurements. SIGNIFICANCE AND IMPACT OF THE STUDY: A distinct advantage of the rearranged model is that it allows for a very simple interpretation of easily obtainable data using standard nonlinear regression. The rearranged model gives to TTD data the same modelling capability that the BRM gives to plate count data.

A new model for the effect of pH on microbial growth: an extension of the Gamma hypothesis.

AIMS: To investigate the appropriateness of the extended Lambert-Pearson model (ELPM) to model the effect of pH (as hydrogen and hydroxyl ions) over the whole biokinetic pH range in comparison with other available models. METHODS AND RESULTS: Data for the effect of pH on microbial growth were obtained from the literature or in-house. Data were examined using several models for pH. Models were compared using the residual mean of squares. Using the ELPM, pH was modelled as hydrogen ions and hydroxyl ions; hence, the model was monotonic in each. The ELPM was able to model data more successfully than the cardinal pH model (CPM) and other models in the majority of cases. CONCLUSIONS: Examining the effect of pH as hydrogen and hydroxyl ions has the advantage that the basic form of the ELPM can be retained as each is treated as a distinct antimicrobial effect. With the ELPM, each inhibitor is described by two parameters; from these parameters, the pH(min) , pH(opt) and pH(max) can be obtained. Furthermore, the idea of a dose response, absent from other models, becomes important. SIGNIFICANCE AND IMPACT OF THE STUDY: The CPM is an excellent model for certain situations - where there is a high degree of symmetry between the suboptimal pH and superoptimal pH response and where there are few data points available. The ELPM is more amenable to highly asymmetric behaviour, especially where plateaus of effect around the pH optimum are observed and where the number of data points is not restrictive.

Modelling the effect of combined antimicrobials: A base model for multiple-hurdles.

Combining antimicrobials to reduce microbial growth and to combat the potential impact of antimicrobial resistance is an important subject both in foods and in pharmaceutics. Modelling of combined treatments designed to reduce or eliminate microbial contamination in foods (microbiological predictive modelling) has become commonplace. Two main reference models are used to analyse mixtures: the Bliss Independence and the Loewe reference models (LRM). By using optical density to analyse the growth of Aeromonas hydrophila, Cronobacter sakazakii and Escherichia coli in combined NaCl/NaCl (a mock combination experiment) and combined NaCl/KCl experiments, previous models for combined antimicrobials in foods, based on the Bliss approach, were shown to be inconsistent and that models based on the LRM more applicable. The LRM was shown, however, to be valid only in the specific cases where the concentration exponents of all components in a mixture were identical. This is assured for a mock combination experiment but not for a true mixture. This, essentially, invalidates the LRM as a general reference model. A new model, based on the LRM but allowing for mixed exponents, was used to analyse the combined inhibition data, and concluded that the NaCl/KCl system gave the additive effect expected from literature studies. This study suggests the need to revise current models used to analyse combined effects.

Modelling of bacterial growth with shifts in temperature using automated methods with Listeria monocytogenes and Pseudomonas aeruginosa as examples.

Time to detection (TTD) measurements using turbidometry allow a straightforward method for the measurement of bacterial growth rates under isothermal conditions. Growth rate measurements were carried out for Listeria monocytogenes at 25, 30 and 37°C and for Pseudomonas aeruginosa over the temperature range 25 to 45°C. The classical three-parameter logistic model was rearranged to provide the theoretical foundation for the observed TTD. A model was subsequently developed for the analysis of TTD data from non-isothermal studies based on the Malthusian approximation of the logistic model. The model was able to predict the TTD for cultures of L. monocytogenes or P. aeruginosa undergoing simple temperature shunts (e.g. 25 to 37°C and vice versa), and for a multiple temperature shunt for L. monocytogenes (25-37-25-37°C and 37-25-37-25°C) over a period of 24h. In no case did a temperature shunt induce a lag.

Growth curve prediction from optical density data.

A fundamental aspect of predictive microbiology is the shape of the microbial growth curve and many models are used to fit microbial count data, the modified Gompertz and Baranyi equation being two of the most widely used. Rapid, automated methods such as turbidimetry have been widely used to obtain growth parameters, but do not directly give the microbial growth curve. Optical density (OD) data can be used to obtain the specific growth rate and if used in conjunction with the known initial inocula, the maximum population data and knowledge of the microbial number at a predefined OD at a known time then all the information required for the reconstruction of a standard growth curve can be obtained. Using multiple initial inocula the times to detection (TTD) at a given standard OD were obtained from which the specific growth rate was calculated. The modified logistic, modified Gompertz, 3-phase linear, Baranyi and the classical logistic model (with or without lag) were fitted to the TTD data. In all cases the modified logistic and modified Gompertz failed to reproduce the observed linear plots of the log initial inocula against TTD using the known parameters (initial inoculum, MPD and growth rate). The 3 phase linear model (3PLM), Baranyi and classical logistic models fitted the observed data and were able to reproduce elements of the OD incubation-time curves. Using a calibration curve relating OD and microbial numbers, the Baranyi equation was able to reproduce OD data obtained for Listeria monocytogenes at 37 and 30°C as well as data on the effect of pH (range 7.05 to 3.46) at 30°C. The Baranyi model was found to be the most capable primary model of those examined (in the absence of lag it defaults to the classic logistic model). The results suggested that the modified logistic and the modified Gompertz models should not be used as Primary models for TTD data as they cannot reproduce the observed data.

Population distributions of minimum inhibitory concentration--increasing accuracy and utility.

AIMS: To generate continuous minimum inhibitory concentration (MIC) data that describes the discrete nature of experimentally derived population MIC data. METHODS AND RESULTS: A logistic model was fitted to experimentally derived MIC population cumulative distributions from clinical isolates of Haemophilus influenzae, Moraxella catarrhalis, Streptococcus pneumoniae and Staphylococcus aureus (European Committee on Antimicrobial Susceptibility Testing, BSAC and MYSTIC population susceptibility databases). From the model continuous distributions of population susceptibility were generated. The experimentally observed population distributions based on discrete MIC could be reproduced from this underlying continuous distribution. Monte Carlo (MC) simulation was used to confirm findings. Where the discrete experimental data contained few or no isolates with MIC greater or less than the antimicrobial concentration range tested, the true mean MIC was a factor of 0.707 times that normally reported and may be of little clinical significance. Where data contained isolates beyond the range of concentration used, the true MIC was dependent on the SD and the number of isolates and could be clinically significant. Subpopulations of differing susceptibilities could be modelled successfully using a modified logistic equation: this allows a more accurate examination of the data from these databases. CONCLUSIONS: The mean MIC and SD of population data currently reported are incorrect as the method of obtaining such parameters relies on normally distributed data which current MIC population data are not. SIGNIFICANCE AND IMPACT OF THE STUDY: Obtaining the distribution parameters from the underlying continuous distribution of MIC can be carried out using a simple logistic equation. MC simulation using these values allows easy visualization of the discrete data. The analyses of subpopulations within the data should increase the usefulness of horizontal studies.

A newly developed assay to study the minimum inhibitory concentration of Satureja spinosa essential oil.

AIMS: The minimum inhibitory concentration (MIC) of Satureja spinosa essential oil against Staphylococcus aureus, Escherichia coli O157:H7, Listeria monocytogenes, Salmonella enterica, Salmonella serovar Enteritidis PT4 and Bacillus cereus was comparatively assessed with an established optical density method as well as a novel impedimetric method. METHODS AND RESULTS: The impedimetric analysis takes into account information of microbial growth, such as detection time, maximum conductance, and slope of the conductance curve. For each pathogen two levels of inoculation were studied, a high (10(5) CFU ml(-1)) and a low level (10(2) CFU ml(-1)). Non-linear regression analysis was used to fit the data using a modification of a previously published model, from which a more exact value can be obtained for the MIC. Both methods gave similar MICs as shown by t-test statistical analysis. Salm. Enteritidis seems to be the least sensitive to the action of S. spinosa essential oil followed by L. monocytogenes, E. coli, B.cereus and Staph. aureus. The MICs of low inoculum were lower than that of high inoculum. CONCLUSIONS: The new impedimetric assay of MIC of essential oils can be considered a reliable rapid method for screening antimicrobial effectiveness of natural additives. SIGNIFICANCE AND IMPACT OF THE STUDY: Determination of the minimum inhibitory concentration of an essential oil with the simple conductance technique and further study of the mode of action of its components is a good combination for obtaining additional knowledge for industrial application of such natural additives.

A model for the thermal inactivation of micro-organisms.

AIMS: To mathematically model published thermal inactivation data sets using an empirical model based on a double Arrhenius function. METHODS AND RESULTS: A mathematical model, the log R-fat, provided an excellent description of the data sets available: the thermal inactivation of Salmonella anatum at 55 degrees C, Pseudomonas viscosa at 48 degrees C and Streptococcus faecalis at 60 degrees C; Clostridium botulinum spores at various temperatures in the range of 101-121 degrees C (two data sets); thermal inactivation of Salmonella Bedford over the temperature range 50-58 degrees C, water activity range of 0.94-0.99 and a pH range of 4-7; Bacillus stearothermophilus spores from 105 to 121 degrees C and the dry heat sterilization of an indigenous mesophilic soil population over the temperature range of 120-160 degrees C. CONCLUSIONS: The log R-fat model, derived from previously published chemical inactivation studies provides as good, if not better, description of thermal inactivation kinetics as other published models. The model does not invoke either of the two hypotheses of inactivation: the mechanistic or vitalistic, although it is closely linked to descriptions of the former. SIGNIFICANCE AND IMPACT OF THE STUDY: The log R-fat double Arrhenius function provides the investigator with a relatively simple and easy mathematical model to apply to data of thermal inactivation. This model may allow a more accurate description of thermal food processing, especially when the safety of marginal heat processes are concerned.

Comparative analysis of antibiotic and antimicrobial biocide susceptibility data in clinical isolates of methicillin-sensitive Staphylococcus aureus, methicillin-resistant Staphylococcus aureus and Pseudomonas aeruginosa between 1989 and 2000.

AIMS: To analyse population minimum inhibitory concentrations (MICs) data from clinical strains of Staphylococcus aureus and Pseudomonas aeruginosa for changes over a 10-year period and to look for correlations between the antimicrobials tested. METHODS AND RESULTS: Data from the MIC study of 256 clinical isolates of Staph. aureus [169 methicillin-sensitive Staph. aureus (MSSA), 87 methicillin-resistant Staph. aureus (MRSA)] and 111 clinical isolates of Ps. aeruginosa against eight antimicrobial biocides and several clinically relevant antibiotics was analysed using anova, Spearman-Rho correlation and principal component analysis. Comparisons suggest that alterations in the mean susceptibility of Staph. aureus to antimicrobial biocides have occurred between 1989 and 2000, but that these changes were mirrored in MSSA and MRSA suggests that methicillin resistance has little to do with these changes. Between 1989 and 2000 a sub-population of MRSA has acquired a higher resistance to biocides, but this has not altered the antibiotic susceptibility of that group. In both Staph. aureus and Ps. aeruginosa several correlations (both positive and negative) between antibiotics and antimicrobial biocides were found. CONCLUSIONS: From the analyses of these clinical isolates it is very difficult to support a hypothesis that increased biocide resistance is a cause of increased antibiotic resistance either in Staph. aureus or in Ps. aeruginosa. SIGNIFICANCE AND IMPACT OF THE STUDY: The observation of negative correlations between antibiotics and biocides may be a useful reason for the continued use of biocides promoting hygiene in the hospital environment.

A model for the efficacy of combined inhibitors.

AIMS: The method of the sum of the fractional inhibitory concentrations (SigmaFIC) is used ubiquitously in the investigation of antimicrobial combinations. The inherent assumption of this simple equation is that in a mixture all antimicrobials have identical dose responses. The aim of this work was to analyse the outcome of removing this assumption. METHODS AND RESULTS: A model to describe the efficacy of combined inhibitors was produced which removed the assumption of identical dose responses. The results of several checkerboard experiments showed that the new model, termed the facomb was a more general form of the SigmaFIC method, but the features described by the SigmaFIC as either synergy or antagonism could be attributed to differences in the dose responses of antimicrobials in combination. Where the model failed to adequately describe experimental data it was suggested that these might be cases of true antagonism or synergy. CONCLUSIONS: The SigmaFIC methodology used to describe the effect of antimicrobial combinations (preservatives and antibiotics) is valid only when it is demonstrated that individual components of the mixture have identical dose responses. Otherwise the SigmaFIC method is invalid. Descriptions of antimicrobial synergy may simply be due to the mixing of antimicrobials with differing dose responses. SIGNIFICANCE AND IMPACT OF THE STUDY: Studies aimed at producing synergistic mixtures of antimicrobials, which ignore the dose response of the individual antimicrobials, may waste valuable research effort looking for a physiological explanation for an apparent synergy, where none, in-fact, exists. Conversely, mixing antimicrobials with very different dose responses might lead to mixtures with an 'apparent' synergy which may themselves be very useful therapeutically.

Adaptive resistance to benzalkonium chloride, amikacin and tobramycin: the effect on susceptibility to other antimicrobials.

AIMS: To produce strains of antimicrobial-resistant Pseudomonas aeruginosa via adaptation to benzalkonium chloride, amikacin and tobramycin and to then examine the incidence, or otherwise, of cross-resistance between antibiotics and between antibiotics and benzalkonium chloride. METHODS AND RESULTS: Adaptation was obtained by progressive subculturing in subinhibitory concentrations of the antimicrobials. Pseudomonas aeruginosa NCIMB 10421 adapted to grow in high concentrations of benzalkonium chloride (BC) had lower MIC to antibiotics than the wild type, whereas Ps. aeruginosa adapted to grow in antibiotics had greater MIC to benzalkonium by a small degree. CONCLUSIONS: Adaptive resistance to BC of Ps. aeruginosa generally produced cultures with a decrease in resistance to several antibiotics. Adaptive resistance to the aminoglycosides Ak and Tm produced a low-level increase in tolerance to BC. The adaptive mechanisms of resistance appear to be different for the different types of antimicrobials used. SIGNIFICANCE AND IMPACT OF THE STUDY: The relationships between biocide and antibiotic resistance are complex. It appears, from this study, that an organism resistant to a common biocide can become sensitive to antibiotics, but the converse was not true. Could this observation be used in a strategy to alleviate antibiotic resistance?

Membrane damage to bacteria caused by single and combined biocides.

AIMS: To examine the effect on the leakage of low molecular weight cytoplasmic constituents from Staphylococcus aureus using phenolics singly and in combination, and to see if the observations could be modelled using a non-linear dose response. METHODS AND RESULTS: The rate of potassium, phosphate and adenosine triphosphate leakage was examined in the presence of chlorocresol and m-cresol. Individually, leakage was observed only at long contact times or high concentrations. Combined at these ineffective concentrations, the cytoplasmic pool of all constituents studied was released within minutes. Both chlorocresol and m-cresol were shown to have non-linear dose responses. A rate model for the combinations, which takes account of these non-linear responses, accurately predicted the observations. CONCLUSIONS: Antimicrobials, which when used alone exhibit a non-linear dose response, will also give a non-linear dose response in combination. The simple linear-additive model ignores the concept of the dilution coefficient and will always describe the phenomenon of synergy for combinations where one or more of the components has a dilution coefficient greater than one. This has been borne out by examination of the purported prime lesion of chlorocresol and m-cresol, alone and in combination. SIGNIFICANCE AND IMPACT OF THE STUDY: Studies aimed at producing synergistic mixtures of antimicrobials, which ignore the non-linear additive effect, may waste valuable research effort looking for a physiological explanation for an apparent synergy, where none, in-fact, exists. Patents granted on the basis of analyses using the linear-additive model for combinations of compounds with non-linear dose responses may no longer be supportable.

A rapid method for assessing the suitability of quenching agents for individual biocides as well as combinations.

AIMS: To develop a novel, rapid method for testing the ability of quenching agents to neutralize disinfectants. METHODS AND RESULTS: Tests were performed to determine the suitability of different neutralizers for a range of disinfectants, using a new method based on the Bioscreen optical density analyser. Results showed that during disinfection tests, efficacy could be over-estimated due to poor, or no, neutralization of the disinfectant after a specified time of exposure to the bacteria. The failure to distinguish adequately between bacteriostatic and bactericidal effects can lead to false results during disinfectant testing. Experiments also showed that dilution of the disinfectant, following exposure to the bacteria, was not always sufficient to stop the activity of the disinfectant for chemicals with low dilution coefficients. CONCLUSIONS: The quench test proved to be very quick and easy to perform, with results being available within 18 h. Using the Bioscreen, the test is automated and determines whether dilution into a particular neutralizer is able to inactivate a disinfectant within 30 s. SIGNIFICANCE AND IMPACT OF THE STUDY: This new approach allows the efficacy of quenching agents to be determined, prior to undertaking each disinfection study, and can help in the development of more suitable quenching solutions. The test has also been used to find suitable neutralizers for mixtures of disinfectants which might be used during studies on synergistic biocide combinations.

Theory of antimicrobial combinations: biocide mixtures - synergy or addition?

AIMS: To demonstrate the effect that non-linear dose responses have on the appearance of synergy in mixtures of antimicrobials. METHODS AND RESULTS: A mathematical model, which allows the prediction of the efficacy of mixtures of antimicrobials with non-linear dose responses, was produced. The efficacy of antimicrobial mixtures that would be classified as synergistic by time-kill methodology was shown to be a natural consequence of combining antimicrobials with non-linear dose responses. CONCLUSIONS: The effectiveness of admixtures of biocides and other antimicrobials with non-linear dose responses can be predicted. If the dose response (or dilution coefficient) of any biocidal component, in a mixture, is other than one, then the time-kill methodology used to ascertain the existence of synergy in antimicrobial combinations is flawed. SIGNIFICANCE AND IMPACT OF THE STUDY: The kinetic model developed allows the prediction of the efficacy of antimicrobial combinations. Combinations of known antimicrobials, which reduce the time taken to achieve a specified level of microbial inactivation, can be easily assessed once the kinetic profile of each component has been obtained. Most patented cases of antimicrobial synergy have not taken into account the possible effect of non-linear dose responses of the component materials. That much of the earlier literature can now be predicted, suggests that future cases will require more thorough proof of the alleged synergy.

The synergistic effect of EDTA/antimicrobial combinations on Pseudomonas aeruginosa.

AIMS: To demonstrate that the nonlinear concentration-dependent inhibition of Pseudomonas aeruginosa to EDTA can be used to successfully model and predict the potentiation of antimicrobials by EDTA. METHODS AND RESULTS: A model used successfully to describe the concentration-dependent inhibition of bacterial growth caused by many antimicrobials was unable to describe the inhibition of P. aeruginosa by EDTA. Examination of the inhibition profiles for EDTA against P. aeruginosa revealed a biphasic inhibitory pattern suggesting different mechanisms of action at different concentrations. A modelled, two-stage inhibitory process was shown to fit the observations. This model was then used to examine the effect of combining EDTA with other antimicrobials. The apparent synergy of mixtures of EDTA with quaternary ammonium surfactants (QAC) and specific antibiotics was successfully modelled. Minimum inhibitory concentrations (MIC) of the QAC and that of oxacillin and cefamandole were reduced by a factor of 3-10, whereas ampicillin was reduced by a factor of 70 from an MIC of 1524 to 21 mg l(-1) in the presence of 500 mg l(-1) of EDTA. CONCLUSIONS: A nonlinear concentration-dependent inhibition of P. aeruginosa by EDTA gives rise to apparent observation of synergy with other antimicrobials. SIGNIFICANCE AND IMPACT OF THE STUDY: This is a further example where the current methodology for the examination of antimicrobial synergy (the summed fractional inhibitory concentrations) leads to false conclusions.