MIMET-04635; No of Pages 8 Journal of Microbiological Methods xxx (2015) xxx–xxx
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The Integral Method, a new approach to quantify bactericidal activity☆
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Waldemar Gottardi a, Jörg Pfleiderer b, Markus Nagl a,⁎
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Article history: Received 10 March 2015 Received in revised form 4 May 2015 Accepted 4 May 2015 Available online xxxx
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Keywords: Quantitative killing assay Killing curve Specific bactericidal activity Antimicrobial agents Antiseptic
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Department of Hygiene, Microbiology and Social Medicine, Division of Hygiene and Medical Microbiology, Medical University of Innsbruck, Schöpfstr. 41, A-6020 Innsbruck, Austria Institute of Astro- and Particle Physics, Leopold-Franzens University of Innsbruck, Technikerstr. 20, A-6020 Innsbruck, Austria
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The bactericidal activity (BA) of antimicrobial agents is generally derived from the results of killing assays. A reliable quantitative characterization and particularly a comparison of these substances, however, are impossible with this information. We here propose a new method that takes into account the course of the complete killing curve for assaying BA and that allows a clear-cut quantitative comparison of antimicrobial agents with only one number. The new Integral Method, based on the reciprocal area below the killing curve, reliably calculates an average BA [log10 CFU/min] and, by implementation of the agent's concentration C, the average specific bactericidal activity SBA = BA / C [log10 CFU/min/mM]. Based on experimental killing data, the pertaining BA and SBA values of exemplary active halogen compounds were established, allowing quantitative assertions. N-chlorotaurine (NCT), chloramine T (CAT), monochloramine (NH2Cl), and iodine (I2) showed extremely diverging SBA values of 0.0020 ± 0.0005, 1.11 ± 0.15, 3.49 ± 0.22, and 291 ± 137 log10 CFU/min/mM, respectively, against Staphylococcus aureus. This immediately demonstrates an approximately 550-fold stronger activity of CAT, 1730-fold of NH2Cl, and 150,000-fold of I2 compared to NCT. The inferred quantitative assertions and conclusions prove the new method suitable for characterizing bactericidal activity. Its application comprises the effect of defined agents on various bacteria, the consequence of temperature shifts, the influence of varying drug structure, dose–effect relationships, ranking of isosteric agents, comparison of competing commercial antimicrobial formulations, and the effect of additives. © 2015 Published by Elsevier B.V.
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1. Introduction
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The performance of killing of pathogens by antimicrobial chemicals is of considerable importance in medicine, because it indicates the usability of a given agent under conditions of practice. The results of such tests are presented by killing curves that demonstrate the surviving colony forming units (CFU) per ml in a suspension of test bacteria in the presence of a test agent after defined incubation times. The forms of killing curves substantially depend on the nature of the bacteria and their initial number as well as on the nature of the agent and its concentration. This implies that under standardized conditions, i.e., the same bacterial strain and initial log CFU, the specific activity of an agent
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Abbreviations: BA, bactericidal activity; CAT, chloramine T; CFU, colony forming units; DL, detection limit; DM-NCT, N-chloro-dimethyltaurine; NCT, N-chlorotaurine; SBA, specific bactericidal activity; tDL, killing time; tg, tangent. ☆ This article is dedicated to Professor Manfred Rotter (Medical University of Vienna), the recognized expert in the assessment of disinfecting procedures, on the occasion of his 75th birthday. ⁎ Corresponding author at: Department of Hygiene, Microbiology and Social Medicine, Division of Hygiene and Medical Microbiology, Medical University of Innsbruck, Schöpfstr. 41, 1st floor, A-6020 Innsbruck, Austria. E-mail address: [email protected] (M. Nagl).
can be determined. By visual examination of killing curves, therefore, a comparison of individual agents is possible, yielding qualitative information concerning their relative bactericidal activity (BA). For the evaluation of disinfectants and antiseptics in human medicine, the European Union has issued several norms based on the quantitative suspension test (http://www.en-standard.eu/, e.g., EN 13727 and EN 1040 for bactericidal activity in the medical area European Norm (EN) 1040, 2005; European Norm (EN) 13727, 2012, EN 12791 for surgical hand disinfection European Norm (EN) 12791, 2005, EN 1276 and EN 13697 for bactericidal activity in food, industrial, domestic and institutional areas European Norm (EN) 1276, 2009; European Norm (EN) 13697, 2002). The results of such protocols demonstrate whether a product has passed the respective EN test requirements, mostly ≥5 log reduction within 5 min. However, these standards give only a punctual account without any information about the kinetics of the bactericidal process. As a general standard for approval of disinfectants, it appears to be sufficient. However, for scientific characterization of microbicidal agents, particularly those that come directly in contact with human tissue under different conditions (antiseptics, antibiotics), a quantitative measure that would allow a more exact judgment of the microbicidal activity is of interest. Such a measure should take into account the course of killing curves, and it should be easily accessible from the curves.
http://dx.doi.org/10.1016/j.mimet.2015.05.002 0167-7012/© 2015 Published by Elsevier B.V.
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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tg α ¼ −dð log10
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K ¼ logCFU–DL:
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Under these auspices, a look on any killing curve suggests that the area between the killing curve and the detection limit, which is the integral over the killing curve with DL as abscissa level, or the integral over the relevance coordinate K, is a reciprocal measure of the average BA. It is directly apparent that the smaller the area, the faster killing occurs. The straight line that represents the average BA by its corresponding tangent is the one, which, starting from the same first data point log CFU (t = 0), provides the same integral. Mathematical details are given in Appendix A, a calculation program (Excel file) in Appendix B. It should be mentioned that the choice of the detection limit is not very critical. That is, our method works rather well even if DL is, for some reason, not securely established. Also, killing curves with not too large differences in log CFU (t = 0) can be directly compared. Nevertheless, a good experimental methodology is recommended. 2.1.1. Explanation of the Integral Method based on Fig. 1 By addition of the trapezoids 1–5 the area A of the killing curve down to the detection limit (DL = 2 log10 CFU) is found. A rectangle of equal area has the ordinate y = log10 CFU (t = 0) − DL, while the abscissa comes to x = A / y. The rectangle x × y is transformed into an orthogonal triangle with the same area. Its hypotenuse forms with the abscissa the angle α, whose tangent, tg α = y / 2x, represents the sought average BA. A calculation program (excel file) is presented in Appendix B.
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Using this parameter, results based on differing agent concentrations could be compared, where SBA values differing by a factor up to 40,000 (range 0.003 to 120 log10 CFU/min/mM) allowed a relative ranking of the investigated chlorine and bromine agents (Gottardi et al., 2014). In spite of this acceptable performance, the method exposed the shortcoming that in case of small differences in BA or SBA, a comparison of the calculated BA occasionally tended to disagree with the trend suggested by the curves. By removing the longer exposure times, slopes were obtained that finally concurred with the visual examination. This is a serious flaw. Omitting regular measuring points to obtain, or even support, a certain result is a strong indication of an inapt data interpretation. It was, therefore, of interest to find a method that approximates the average slope of killing curves without these inadequacies. For this purpose, conceivable ways for finding a suitable approximation were investigated (see Appendix A: “Theoretic considerations”) which
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Contrary to earlier methods to quantify bactericidal activity (BA) by one number we make use of not only the measurements (data points) of the killing curves but also of the detection limit (DL). It gives, by definition, the same result for any log CFU b DL, namely no detection at all. This approach allows to differentiate between relevant data (log CFU N DL) and irrelevant ones (log CFU b DL), as well as to establish a relevance order by using a “killing relevance variable” (K) as the difference of the data (log CFU) to the irrelevance level (DL),
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Instead of straight lines, such graphs in practice often show curved ones, with a high killing rate at the beginning, which gradually decreases towards the detection limit. This curvature preferably occurs with highly active agents (HOCl, active bromine compounds) (Gottardi et al., 2014), and can be explained by the depletion of the agent at the beginning of the killing process, and also by the enhanced tolerability of clumped bacteria or bacteria in a special state (e.g., small colony variants, persisters) (Glaser et al., 2014; Heras et al., 2014; Wood et al., 2013), which might be responsible for an overlong tail of the curve. As a consequence, BA (tg α) are not constant quantities, but can be specified by one characteristic number only as averaged values. The challenge was, therefore, to find a straight line that best approximates the bactericidal activity presented in the log CFU/time curve and whose slope (tg α) is a measure for BA of the tested sample. It is needless to say that the results achieved should confirm the ones of the visual comparison of killing curves. In a study dealing with isosteric chlorine and bromine compounds (Gottardi et al., 2014), extremely differing killing times were observed, which suggested quantifying them numerically. For approximating the killing curve with a straight line, whose slope equals BA, the authors used the averaged log reductions and exposure times (see method #3, Appendix A). Because the concentrations used differed by a factor of up to 1000, presentation on the same graph and visual check of the killing curves were not always possible. By including the concentration C (in mM), the specific bactericidal activity (SBA) of the agent was obtained, which enabled a reliable comparison throughout.
2.1. One-number interpretation of killing curves (Integral Method)
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finally led to the “Integral Method” as the best solution for assessing 134 tg α. 135
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A method to gain such information could consist in determining the killing time tDL necessary to reach the detection limit (DL) of CFU in quantitative killing assays. A DL of 1 log10 (2 log10), for instance, indicates that a count below 10 CFU/ml (100 CFU/ml) is not detectable. Generally, such DLs originate from small volumes plated (usually ≤ 0.1 ml) and from dilutions in solutions that inactivate the test agent. However, determination of tDL is inaccurate and even impossible if DL is not reached at all, as it is the case in incomplete killing curves (see also Section 2.1). Early investigations of the kinetics of disinfection revealed a first order reaction for the killing of living bacteria caused by heat or toxic agents (Chick, 1910). This approach indicates that within the same time intervals the same percentage of CFU will be destroyed. A semilogarithmic graph, i.e., log of surviving CFU (ordinate) vs time (abscissa), yields a straight line that intersects the abscissa with an angle α, the tangent of which suggests itself as a possible quantitative measure for the average BA.
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Fig. 1. Schematic explanation of the Integral Method. Derivation of the averaged bactericidal activity from the area below the killing curve. Killing curve (open squares and thick dotted line), detection limit (thin dotted line). A = area below the curve = sum of trapezoids 1 to 5 = 5.25 + 7.50 + 10.75 + 5.95 + 1.0 = 30.45 log10 CFU × min. Abscissa of rectangle = A / (log10 CFUt = 0 − 2) = 30.45 / 6 = 5.075 min. Abscissa of triangle = 2 × 5.075 = 10.15 min. Area below the curve = area rectangle = area triangle. tg α = 6 / 10.15 = 0.591 log10 CFU/min. tg α = (K20 − K2n) / 2A = (36 − 0) / 60.9 = 0.591 log10 CFU/min (Eq. (7)).
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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2.2. General recommendations for BA testing
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On grounds of comparability, a careful standardization of the killing tests is necessary, which comprises bacterial strain, size of the inoculum, concentration of the agent, temperature, and pH.
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2.3. Performance of BA testing in this study
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2.3.1. Test substances Active halogen compounds were applied as bactericidal test agents. Chloramine T (CAT) trihydrate, reagent grade, was from Merck (Darmstadt, Germany). N-chlorotaurine (NCT) was prepared as reported (Gottardi and Nagl, 2002), N-chloro-dimethyltaurine (DM-NCT) was kindly provided by D. Debabov and R. Najafi (NovaBay Pharmaceuticals, Inc., Emeryville, CA, USA) (Low et al., 2009; Wang et al., 2008). Monochloramine was prepared by vacuum distillation in a rotary evaporator from aqueous solutions of NCT plus ammonium chloride and quantified spectrophotometrically as published previously (Gottardi et al., 2007). Peptone (enzymatic digest from casein) was from Fluka (Buchs, Switzerland). The test compounds were freshly dissolved in 0.1 M phosphate buffer (pH 7.1). In some experiments, peptone to a final concentration of 0.1%, 1%, 3%, 5%, and 10% was added. Tests at room temperature (RT) were performed at 20–22 °C, tests at 37 °C in a water bath.
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2.3.2. Bacteria and fungi Staphylococcus aureus ATCC 25923, S. aureus ATCC 6538, and Escherichia coli ATCC 11229 were cultivated for 16 h at 37 °C in tryptic soy broth (Merck), centrifuged at 1800 ×g and washed twice with 0.9% NaCl. The suspensions contained 1–3 × 109 colony forming units (CFU)/ml. Aspergillus fumigatus ATCC 26933 was grown for 8 days on Mueller–Hinton plates. The plates were rinsed with saline to gain the conidia, which were washed twice and diluted in saline to approximately 2 × 107 CFU/ml.
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2.2.2. Procedure for quantitative killing assays The following conditions of the killing tests are defined in the respective European Standard. Bacteria grown overnight and washed twice in 0.9% sodium chloride are diluted in the test solution (prewarmed to the respective temperature, see previous Section 2.2.1) to a final concentration of approximately 1 × 107 CFU/ml. To obtain reliable tg α values, the agent concentration should be chosen such, that the detection limit is reached within a reasonable total incubation time. Anyway, this concentration will generally correspond to that used in practical circumstances. After different incubation times, aliquots of 0.1 ml are removed and diluted in a suitable inactivation solution. From this solution and further dilutions in saline as suitable, quantitative cultures are performed, preferably with a spiral plater. Respective controls are done as outlined in the guidelines. The detection limit DL must be mentioned. Test conditions and incubation times must be described in detail.
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2.3.3. Quantitative killing assays Bacterial suspensions (40 μl) were 100-fold diluted in the solutions of the antiseptics (3.96 ml) and in buffer without additives (controls) at pH 7.1 and room temperature or 37 °C as indicated in the figure legends. In some additional tests, the dilution was 10-fold, in some 1000fold to achieve start concentrations of approximately 1–3 × 106 to
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2.3.4. Calculation of tg α The parameters of the quantitative killing experiment, i.e., the incubation times and the pertaining log10 CFU values with standard deviations are transferred to the corresponding cells in the Excel program (see Appendix B) that yields the tg α value sought.
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2.2.1. Preparation of the test solution In accordance with the European Standard for quantitative killing assays (European Norm EN 1040:2005 and EN 13727:2012) (European Norm (EN) 1040, 2005; European Norm (EN) 13727, 2012), we recommend to dissolve the test agent in 0.1 M phosphate buffer at pH 7.0 ± 0.1 and at 20 °C in case of surface disinfectants or 37 °C in case of antiseptics.
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The impact of the imprecision of the log10 CFU values (±SD) on the area of the integral (Eq. (7)) and tg α (Eq. (8)) was calculated as specified previously (Sachs, 1974). If A = x ± a and B = y ± b, then applies A + B = (x + y) ± (a2 + b2)0.5, A − B = (x − y) ± (a2 + b2)0.5, A × B = x × y ± (x2 × b + y2 × a)0.5, A2 = x2 ± (2x2 × a)0.5, and A / B = x / y ± 1 / y2 (x2 × b + y2 × a)0.5. Statistical differences between killing curves were calculated with one-way analysis of variance (ANOVA) and Bonferroni's multiple comparison test (GraphPad Prism 5.02, La Jolla, CA, USA). Bartlett's test for Homogeneity of Variances was used to combine coefficients of variation, and Nalimov test to detect outliers. p-Values b 0.05 were considered significant. Linear regression was performed with GraphPad Prism software.
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3. Results
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3.1. Analytical quality of the Integral Method
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The intrinsic statistical parameters were evaluated by testing a stable standard disinfectant against a standard bacterium that revealed well reproducible results. This was realized by measuring the killing potency of chloramine T (N-chloro-4-methylbenzene sulfonamide sodium, CAT) against S. aureus at pH 7.0–7.1 and 22 °C.
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3.1.1. Repeatability Five series of SBA measurements with each 10 replicates (three series with 500 and one each with 100 and 1000 μM CAT) gave the following coefficients of variation: 5.27, 7.23, 7.30, 10.0 and 9.61. According to the Bartlett's test for Homogeneity of Variances, all five values could be combined to the average repeatability of SBA ± 7.3%.
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3.1.2. Accuracy This feature was not allocatable because no “true” reference value was available. Instead, the independency of SBA from the agent's concentration was verified by killing experiments with varying concentrations of CAT against S. aureus under otherwise identical conditions. Two stock solutions, one with CAT in 0.1 M phosphate, and the other one containing only 0.1 M buffer were mixed to obtain final concentrations of 1.000 to 0.100 mM CAT in 0.025 mM steps. From altogether 37 killing curves, the appendent BA and SBA values were calculated. One value (0.150 mM) was removed because the detection limit was not attained. According to the Nalimov test, two BA and SBA values could be removed as outliers (P b 0.05). Fig. 2 shows the outlier-freed graphs
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108 CFU/ml. Fungi were 50-fold diluted in the test solutions to final concentrations of 4 × 106 CFU/ml. After different incubation times, aliquots of 100 μl were removed and diluted 10-fold or 100-fold in 0.6% sodium thiosulfate solution to inactivate the test compound. Aliquots (50 μl) of these dilutions were spread in duplicate on tryptic soy agar plates with an automatic spiral plater (model WASP 2, Don Whitley Scientific, Shipley, UK), allowing a detection limit DL of 100 CFU/ml for all tested microorganisms taking into account both plates and the minimum dilution. The plates were incubated at 37 °C, and CFU were counted after 48 h. Special inactivation controls (addition of bacteria to sodium thiosulfate and to the active halogen compound previously inactivated by thiosulfate) were not added in this study since they were conducted in numerous previous studies, e.g., (Arnitz et al., 2009; Nagl et al., 1999).
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Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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method concerning bacterial counts. Fig. 3 shows the original killing 312 curves for S. aureus and the influence of CFU (t0) on BA (tg α). 313
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3.1.4. Range of BA and SBA values From theoretic considerations (see Appendix A) can be deduced that complete killing curves with a sufficient number of data points should be preferred, which requires appropriate test conditions. Highly reactive antimicrobial agents need low concentrations and/or short incubation times, and the reverse applies to lowly reactive ones, accordingly. The conditions for obtaining complete killing curves were investigated in view of practicability (low reactivity) and feasibility (high reactivity) concerning incubation times. Calculation of two hypothetical examples (see Appendix B) revealed a measurability of BA (tg α) in the range of approximately 0.1 to 8.0 log10 CFU/min (ratio 1:80). From these values and conceivable limiting concentrations of 1000 and 0.001 mM, the measurable SBA values can be expected in the range of 0.001 to 8000 [log10 CFU/min/mM], which means a ratio of 1:8 × 106 or nearly seven powers of ten. Up to date, the most extreme SBA values were measured with NCT and dibromoisocyanuric acid (Gottardi et al., 2014). Against E. coli and S. aureus, the SBA of NCT lays at (1.76 ± 0.27) × 10− 3 and (2.02 ± 0.47) × 10− 3, while it was (4.83 ± 0.63) × 10+ 2 and (1.95 ± 0.26) × 10+ 2 log10 CFU/min/mM with dibromoisocyanuric acid and 4 × washed bacteria. From these values, a mean SBA ratio of 1:1.70 × 10+5 can be deduced, which is more than five powers of ten.
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of the dependency of BA and SBA on the CAT concentration. BA is shown in linear presentation, while for SBA a logarithmic one was chosen, which takes into account the big span SBA values can attain (Gottardi et al., 2014). As expected, the BA values increased consistently with the concentration, showing the slope 1.275 ± 0.054 tg α/mM, and a correlation coefficient of r2 = 0.95, which indicates good linearity, while the fitting line revealed a high tendency to cross 0 mM. The regression line of SBA showed also a slope (0.127 ± 0.098), which was clearly smaller than the one of BA. Its deviation from slope zero was, however, not significant (P = 0.205). The mean of all SBA values comprising concentrations over a span of one power of ten allowed to determine an SBA of 1.11 ± 0.15 log 10 CFU/min/mM for CAT against S. aureus at 22 °C and pH 7.0–7.1. This result revealed an uncertainty of SBA determinations at varying concentrations of ±13.6%, which is nearly twice as much as the repeatability (see Section 3.1.1).
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Fig. 2. Calibration curve of BA (tg α versus concentration, open circles) (a) and of SBA (open squares) (b) in the range of 0.100–1 mM chloramine T with concentration intervals of 0.025 mM. Quantitative killing assays against S. aureus ATCC 6538 at room temperature and pH 7.1. The dotted line indicates the linear regression in (a) and (b).
3.1.3. Influence of the bacterial count on tg α Under otherwise identical conditions (37 °C, pH 7.1), BA measurements of 1% NCT against E. coli and S. aureus were conducted with bacterial suspensions of 106, 107, and 108 CFU/ml, which resulted in exact log10 CFU (t0) values of 8.15, 7.14, 6.20 and 7.33, 6.52, 5.29 for E. coli and S. aureus, respectively. The appendent tg α values were 0.309, 0.342, 0.458 (mean 0.378 ± 0.078) and 0.128, 0.158, 0.139 (mean 0.142 ± 0.015) for both strains. The dependence from log CFU (t0) was not significant in both cases, which confirms the robustness of the
Fig. 3. Influence of the CFU count at time zero (t0) on the BA of 55 mM (1%) NCT against S. aureus ATCC 25923 at 37 °C and pH 7.1. (a) Killing curves. Starting count 7.33 log10 CFU/ml (open squares, tg α = 0.128), 6.52 log10 CFU/ml (open triangles, tg α = 0.158), and 5.29 log10 CFU/ml (open diamonds, tg α = 0.139). Buffer controls (open circles). Mean values ± SD of n = 5. P b 0.01 between all three CFU-counts (0, 5, and 10 min) and between the highest count and the others (20 min), respectively. (b) Absence of a dependence of tg α on the CFU count. tg α values (open circles) and linear regression (dotted line). P N 0.05 between all three tg α values.
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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a) The individual susceptibilities of E. coli and S. aureus to the investigated preparations differed considerably. This indicates that BAbased specifications can refer only to one defined bacterial strain. b) In our example with povidone-iodine, chlorhexidine, and polyhexanide, only the latter allowed the BA measurement of the undiluted preparation, why a straight comparison (without dilution) of these commercial products was not possible. c) Nevertheless, a reasonable comparison seems conceivable with applications concerning the same target (e.g., disinfection of mucous skin) and by using the dilutions prescribed by the manufacturer.
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– A more theoretical issue concerns the evaluation of the influence of structure on BA, e.g., the effect of the methyl groups in N-chlorodimethyltaurine (DM-NCT) compared to NCT. The analysis of available data about E. coli at room temperature (Fig. 4a, Gottardi et al., 2014) gave SBA values of 0.0010 and 0.0035 log10 CFU/min/mM for NCT and DM-NCT, respectively. These results indicate a 3.5 fold increase for the di-methyl derivative. The appendent values for 37 °C (Fig. 4b) were 0.0058 and 0.0126 log10 CFU/min/mM for NCT and DM-NCT, which corresponds to a ratio of 2.17. – The evaluation of BA proved very useful to assess the impact of a variation of status parameters, e.g., pH, temperature, nature and concentration of additives, on a defined preparation. In this case, too, the agent concentration has to be kept constant. An example provides Fig. 5, which shows the surprising increase of BA in a killing test of E. coli by 0.0275 mol/l NCT in the presence of 0– 10% peptone. While the original killing curves (Fig. 5a) are hardly distinguishable, the calculated BA values in Fig. 5b give clear information about the increase of BA, which reaches its maximum with 3% peptone. The influence of temperature (derived from experiments at room temperature (20–22 °C) and 37 °C, presented in Fig. 4) revealed an
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3.2.1. BA as a relative parameter – BA could serve to specify commercial disinfection products, which suggests a comparison and a ranking of competing products and its formulations, respectively. In case of agents (preparations) with differing killing mechanisms like alcohols, quaternary ammonium or active halogen compounds, the term “concentration” is not synonymous (e.g., in the case of 70% alcohol and 1% NCT). Because BA is controlled not only by the actual concentration of the underlying agent, but also by the presence of pharmaceutical additives (e.g., to provide eudermic properties), which can influence BA, the parameter SBA is not applicable. Table 1 reveals important features:
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3.2. Results in context to fields of application of the Integral Method
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3.1.5. The problem of dilution Principally, the measurability of extremely strong agents (preparations) could be attained by dilution. However, there exist formulations which show non-linear dose–response relationships, which can cause confusing results. A well-known example concerns iodophoric preparations (e.g., based on povidone–iodine), which react on dilution with an increase of BA within a certain concentration range (Gottardi, 2001).
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Povidone iodine 10% (1% I2) 1:20,000 1.067 ± 0.104 0.363 ± 0.028 2.9 Chlorhexidine 0.012% 1:10 6.20 ± 2.94 0.084 ± 0.005 73.8 Polyhexanide 0.04% 0 0.242 ± 0.014 4.80 ± 2.26 0.0504
Fig. 4. BA of 55 mM NCT (open squares) and 55 mM DM-NCT (open triangles) against E. coli ATCC 11229 at pH 7.1. Buffer controls (open circles). Mean values ± SD. P b 0.01 between all curves. (a) Room temperature (20–22 °C); n = 3–8. (b) 37 °C; n = 3.
increase of BA of 0.057 to 0.317, and 0.190 to 0.697 for NCT and DMNCT, respectively, against E. coli. This signifies that raising the temperature by 15–17 °C increases BA by a factor of 4–6. Experiments with NCT and E. coli, where SBA values were averaged from a range of concentrations (see Table 2), revealed even an 8.1-fold higher SBA at 37 °C. These evidences emphasize that maintaining a defined constant temperature during bactericidal activity testing is an absolute must for gaining reliable and consistent results. – Dependencies between the concentration of an agent and its antimicrobial activity, i.e., dose–effect relationships, which have to be tested under the same conditions (pH, temperature, solvent, concentrations of additives), are significantly easier and more precise to attain and are more reliable if numerically based on BA values. – Another subject concerns the susceptibility of various bacterial strains to a defined agent. We found a ratio of 2:1 (E. coli:S. aureus) for NCT and 1.5:1 for DM-NCT. – A striking feature applies the BA increase of 1% NCT against A. fumigatus in the presence of up to 1% ammonium chloride. Fig. 6 shows a rise of BA with factors of 27.4, 96.8, and 568 in the presence 0.01, 0.1, and 1.0% ammonium chloride, respectively. This effect can be attributed to the formation of monochloramine (NH2Cl) according to the equilibrium NCT + NH+ 4 ↔ taurine + NH2Cl (Gottardi et al., 2007; Nagl et al., 2001).
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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Fig. 6. Enhancement of BA of 55 mM (1%) NCT against conidia of A. fumigatus ATCC 26933 in the presence of 0, 0.01, 0.1, and 1.0% ammonium chloride at 37 °C and pH 7.1. tg α mean values (open circles, full line) and linear regression (dotted line) from 5 independent experiments.
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4. Discussion
431
The assessment of BA concerns the reaction rate of bacterial kill, and therefore it is a kinetic problem. It is founded on a series of diverging occurrences like diffusion (extra- and intracellular), penetration through the cell wall, and in case of active halogen compounds of various oxidation reactions with quite differing reaction rates (Gottardi et al., 2013; Gottardi and Nagl, 2002). An exact determination of BA via kinetic laws would be nearly impossible, because no data are available for most of the underlying elementary reactions. Amazingly, the presented integral-based BA determination enables to get this information by one plain calculation. Though yielding unambiguous numerical results, a detailed examination of their scientific relevance and reliability is mandatory, and needs to discuss possible errors and inaccuracies.
432
4.1. Methodical errors
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minor differences in the absolute SBA values, while the relations were virtually the same. Multiple SBA measurements with varying concentrations can be suggested for gaining averaged values with an improved reliability. The results of experiments with CAT, NCT, NH2Cl, and I2 against E. coli and S. aureus are shown in Table 2, Figs. 2 and 7. Assayed by linear regression, a little concentration dependency of SBA was observed (slope of regression line ≠ 0), however, the departure from slope zero was not significant in most cases.
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Fig. 5. Killing of E. coli ATCC 11229 by 27.5 mM NCT at 37 °C in the presence of peptone. (a) Killing curves. Mean values ± SD, n = 3. Significantly more rapid killing in the presence of 0.1% to 5% peptone compared to 0% peptone (P b 0.01), and deceleration of killing by 10% peptone (P b 0.01). Respective tg α values are listed. Controls (filled circles) were done in plain 0.1 M phosphate buffer (pH 7.1) plus 10% peptone. (b) Increase of BA (tg α) with the peptone concentration up to 5%.
t2:1 t2:2
Table 2 Mean SBA values [log10 CFU/min/mM] obtained at pH 7.0–7.1.
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t2:3
Agent
°C
Concentration
N
E. coli
S. aureus
t2:4 t2:5 t2:6 t2:7 t2:8 t2:9 t2:10
CAT NCT
20–22 20–22
0.1–1.0 mM 12.8–55.0 mM
36 3
1.11 ± 0.15c 0.00202 ± 0.00047c
NCT
37
5.5–55.0 mM
4
NH2Cla I2 b
20–22 20–22
0.12–1.07 mM 1.2–10.7 μM
3 3
n.d. 0.00176 0.00027c 0.0142 ± ±0.0049c n.d. n.d.
t2:11 t2:12 t2:13 t2:14
426 427 428 429 430
433 434 435 436 437 438 439 440 441 442 443 444
For comparison of agents via BA, even statements as simple as “X 446 is better than Y,” i.e., “BA(X) N BA(Y),” need killing curves. These 447
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3.2.2. SBA as a specific intrinsic parameter independent on the agent's concentration The comparison of agents with extremely diverging BAs can induce a problem, because the requirement of identical concentration (C) could demand very short and therefore not practicable incubation times. In such cases it is necessary to use instead of BA the specific bacterial activity, SBA = BA / C, a parameter that enables in any case to draw a comparison. The first reference of its use was done a short time ago (Gottardi et al., 2014), but with an algorithm (see method #3 in Appendix A) that in the present study proved as minor qualified. Verification of the data with the Integral Method #5 (Appendix A) uncovered
424 425
n.d. 3.49 ± 0.22c 291 ± 137c
n.d. not determined. a According to Arnitz et al. (2009). b Pure aqueous iodine solution without additional iodide. c The deviation from slope zero was not significant.
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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Fig. 7. BA of 0.1 to 1.1 mM NH2Cl and 0.0012 to 0.011 mM iodine against S. aureus ATCC 25923 at room temperature and pH 7.1. Mean values ± SD of n = 3. (a) Killing curves by NH2Cl; 0.107 mM (open diamonds), 0.355 mM (open triangles), 1.07 mM (open squares), 0 mM (controls, open circles); P b 0.01 between all curves. (b) Killing curves by iodine, 0.0012 mM (open diamonds), 0.0036 mM (open triangles), 0.0107 mM (open squares), 0 mM (controls, open circles); P b 0.01 between all curves. (c) tg α versus concentration for NH2Cl; tg α single mean values (open circles, full line), linear regression (thick dotted line), and overall mean value (3.49 ± 0.22, thin dotted line). (d) tg α versus concentration for iodine; tg α single mean values (open circles, full line), linear regression (thick dotted line), and overall mean value (291 ± 137, thin dotted line.
468
4.2. Systematic errors
469
One example concerns the time of reaching the detection limit, which on theoretical reasons is essential for finding the correct slope (see also Section 2.1). It is obvious that tDL cannot be determined exactly because this point lies between the last two measurements. In most cases, tDL is therefore too high, which induces a somewhat too low BA. Since mixing of bacteria in the agent solution takes some time (for example 3 s), the real incubation times are somewhat shorter than the experimentally defined ones. Calculations show, however, that
455 456 457 458 459 460 461 462 463 464 465 466
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conclusively demonstrate that BA generally is not constant, but a decreasing function of time. For any quantitative comparison, as “X is ten times better than Y,” it is apparently necessary to define an average BA from the killing curve, i.e., to define an averaging straight line whose slope (= tg α) represents the essential features of the killing curve. Of the quoted methods #1 to #4, each has serious flaws that render them rather useless, even if at a quite different degree. With the introduction of the area under the curve as reciprocal measure of BA, the similarity to the visual impression is strong enough to render Eq. (7) a reasonable one-number approximation to the more complex reality. We are aware of the fact that our method is subject to a variety of uncertainties. The numerical calculation of the area under the curve (Eq. (9)) implies not only measuring errors that can be quantified by statistics on repeated measurements. It also implies a systematic error due to explicit use of the interpolating lines between single time points (Eq. (9), right side), which renders our method not entirely independent of the number and time-distance of the data. In all cases the area is overestimated, which effect should, however, partly get lost upon comparison of curves. Also, the one-number comparison of killing curves with different shapes is a further simplification.
postponing all times by the same interval has no effect upon tg α. 477 With other words, this error is of no relevance. 478
4.3. Possible experimental sources for errors
479
The reliability of tg α principally relates to the exactness of both bacterial counts and incubation times. It can be assumed that the precision of the counting process is constant and depends mainly on the skill of the operator. Concerning the impact of time, one has to distinguish between systems with rapid killing and slow ones. In the former case, short incubation times are applied whose precision decreases opposite to its duration, with the effect of higher standard deviations, but no change of tg α. Variable or undefined temperature during the killing process might also play a role in lessening precision and accuracy.
480
4.4. The high range of SBA
490
A rather astonishing feature concerns the extreme span of measured SBA, which encompasses up to more than four powers of ten. This problem was already discussed in a paper dealing with the BA of active chlorine and bromine compounds (Gottardi et al., 2014). Briefly, the authors postulated that there is a big difference in the rate of reactions of active halogen compounds with proteins in a homogeneous solution (which amounts a factor up to only 3–4) and in killing of bacteria. The latter concerns basically similar proteins which, however, are protected by a cell wall. Therefore, mainly the very complex occurrences that influence the rate of penetration were considered responsible for the observed big differences in SBA.
491
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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4.5. Significance of SBA for applications in clinical practice
Acknowledgments
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We are grateful to Andrea Windisch for excellent technical assistance. We thank Miranda Suchomel, Institute of Hygiene and Applied Immunology, Medical University of Vienna, for providing raw data on hand disinfection tests. This work was supported by the Division of Hygiene and Medical Microbiology of the Medical University of Innsbruck. We have no conflicts of interest to declare.
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Agents that are able to kill bacteria interact also with the surrounding proteins, which results in consumption effects (Gottardi et al., 2013, 2014), i.e., reduction of the agent's concentration and irritation of tissue. These features are relevant above all for oxidizing agents like active halogen compounds. Since high SBA comes along with unfavorably high consumption, SBA values don't reveal the applicability of antiseptics in practice, which is based on a compromise between sufficient BA and low irritation (Gottardi et al., 2013; Gottardi and Nagl, 2010).
References
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4.6. Why the Integral Method is of additional value to European Standards
512 513
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The Integral Method is conceived to determine the BA of a bactericidal agent against a defined microorganism. Being derived from the whole killing curve, it gives in any case more reliable information about the BA than the European Norms for evaluation of the bactericidal activity of chemical disinfectants and antiseptics, which require only one point of the killing curve. For instance, EN 13727 (Quantitative suspension test for the evaluation of bactericidal activity in the medical area) discloses not the BA but the “bactericidal concentration” for a specified application (e.g., disinfection of instruments) (European Norm (EN) 13727, 2012). Nevertheless, if the experimental data (log reduction + incubation time) necessary for finding this value include more than one incubation time, which is allowed by the norm, determination of tg α according to the Integral Method is quite possible. As an example, in a study investigating hand disinfection with npropanol versus isopropanol, the log reduction of CFU after single incubation times was compared using the European Standard EN 12791 (Suchomel et al., 2009). Taking into account all incubation times in one by the Integral Method would enhance the sensitivity to discriminate between the tested disinfectants. Our calculation revealed a highly significant difference between the BA of n-propanol versus isopropanol, which was not statistically verified in the original study (Suchomel et al., 2009). The respective BA values, calculated from the published reduction factors assuming pretreatment values of 5 log10, were 0.543 ± 0.095 for n-propanol 60% (immediate), 0.451 ± 0.073 for isopropanol 70% (immediate), 0.326 ± 0.064 for n-propanol 60% (3 h), 0.210 ± 0.056 for isopropanol 70% (3 h). One-way ANOVA and Tukey's multiple comparison tests revealed P b 0.01 between n-propanol and isopropanol for each immediate and 3 h values. The statistical outcome was identical for calculations assuming pretreatment values of 4.0 and 4.5 log10.
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The Integral Method uses for the first time an integration of a killing curve, resulting in one reliable value that is characteristic for the average BA. The clear linear relation between BA and concentration (calibration curve) and its tendency to cross zero confirm them by all means as reliable measures for relative statements. The measure SBA, on the other hand, turns out as a comprehensive parameter suitable to position agents in the extremely wide scope of chemical disinfection. The method may be useful for documentation and estimation of the microbicidal activity of antiseptics, disinfectants, and biocides in addition to present standards. Moreover, it might be helpful to characterize bactericidal antibiotics and fungicides in connection with parameters like minimum bactericidal concentration, half-life, and area under the curve. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.mimet.2015.05.002.
Arnitz, R., Nagl, M., Gottardi, W., 2009. Microbicidal activity of monochloramine and chloramine T compared. J. Hosp. Infect. 73, 164–170. Chick, H., 1910. The process of disinfection by chemical agencies and hot water. J. Hyg. (Lond.) 10, 237–286. European Norm (EN) 1040, 2005. Chemical Disinfectants and Antiseptics — Quantitative Suspension Test for the Evaluation of Basic Bactericidal Activity of Chemical Disinfectants and Antiseptics — Test Method and Requirements (Phase 1). Comité Européen de Normalisation, Brussels. European Norm (EN) 1276, 2009. Chemical Disinfectants and Antiseptics — Quantitative Suspension Test for the Evaluation of Bactericidal Activity of Chemical Disinfectants and Antiseptics Used In Food, Industrial, Domestic and Institutional Areas — Test Method and Requirements (Phase 2, Step 1). Comité Européen de Normalisation, Brussels. European Norm (EN) 12791, 2005. Chemical Disinfectants and Antiseptics — Surgical Hand Disinfection — Test Method and Requirement (Phase 2/Step 2). Comité Européen de Normalisation, Brussels. European Norm (EN) 13697, 2002. Chemical Disinfectants and Antiseptics — Quantitative Non-porous Surface Test for the Evaluation of Bactericidal and/or Fungicidal Activity of Chemical Disinfectants Used in Food, Industrial, Domestic and Institutional Areas — Test Method and Requirements Without Mechanical Action (Phase 2/Step 2). Comité Européen de Normalisation, Brussels. European Norm (EN) 13727, 2012. Chemical Disinfectants and Antiseptics — Quantitative Suspension Test for the Evaluation of Bactericidal Activity in the Medical Area — Test Method and Requirements (Phase 2/Step 1). Comité Européen de Normalisation, Brussels. Glaser, R., Becker, K., von, E.C., Meyer-Hoffert, U., Harder, J., 2014. Decreased susceptibility of Staphylococcus aureus small-colony variants toward human antimicrobial peptides. J. Investig. Dermatol. 134, 2347–2350. Gottardi, W., 2001. Iodine and iodine compounds. In: Block, S.S. (Ed.), Disinfection, Sterilization and Preservation. Lippincott Williams & Wilkins, Philadelphia, pp. 159–184. Gottardi, W., Nagl, M., 2002. Chemical properties of N-chlorotaurine sodium, a key compound in the human defence system. Arch. Pharm. Pharm. Med. Chem. 335, 411–421. Gottardi, W., Nagl, M., 2010. N-chlorotaurine, a natural antiseptic with outstanding tolerability. J. Antimicrob. Chemother. 65, 399–409. Gottardi, W., Arnitz, R., Nagl, M., 2007. N-chlorotaurine and ammonium chloride: an antiseptic preparation with strong bactericidal activity. Int. J. Pharm. 335, 32–40. Gottardi, W., Debabov, D., Nagl, M., 2013. N-chloramines: a promising class of welltolerated topical antiinfectives. Antimicrob. Agents Chemother. 57, 1107–1114. Gottardi, W., Klotz, S., Nagl, M., 2014. Superior bactericidal activity of N-bromine compounds compared to their N-chlorine analogues can be reversed under protein load. J. Appl. Microbiol. 116, 1427–1437. Heras, B., Totsika, M., Peters, K.M., Paxman, J.J., Gee, C.L., Jarrott, R.J., Perugini, M.A., Whitten, A.E., Schembri, M.A., 2014. The antigen 43 structure reveals a molecular Velcro-like mechanism of autotransporter-mediated bacterial clumping. Proc. Natl. Acad. Sci. U. S. A. 111, 457–462. Low, E., Nair, S., Shiau, T., Belisle, B., Debabov, D., Celeri, C., Zuck, M., Najafi, R., Georgopapadakou, N., Jain, R., 2009. N, N-Dichloroaminosulfonic acids as novel topical antimicrobial agents. Bioorg. Med. Chem. Lett. 19, 196–198. Nagl, M., Hengster, P., Semenitz, E., Gottardi, W., 1999. The postantibiotic effect of Nchlorotaurine on Staphylococcus aureus. Application in the mouse peritonitis model. J. Antimicrob. Chemother. 43, 805–809. Nagl, M., Lass-Flörl, C., Neher, A., Gunkel, A.R., Gottardi, W., 2001. Enhanced fungicidal activity of N-chlorotaurine in nasal secretion. J. Antimicrob. Chemother. 47, 871–874. Sachs, L., 1974. Angewandte Statistik. 4th ed. Springer, Berlin. Suchomel, M., Koller, W., Kundi, M., Rotter, M.L., 2009. Surgical hand rub: influence of duration of application on the immediate and 3-hours effects of n-propanol and isopropanol. Am. J. Infect. Control 37, 289–293. Wang, L., Khosrovi, B., Najafi, R., 2008. N-Chloro-2,2-dimethyltaurines: a new class of remarkably stable N-chlorotaurines. Tetrahedron Lett. 49, 2193–2195. Wood, T.K., Knabel, S.J., Kwan, B.W., 2013. Bacterial persister cell formation and dormancy. Appl. Environ. Microbiol. 79, 7116–7121.
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Contents lists available at ScienceDirect
Journal of Microbiological Methods journal homepage: www.elsevier.com/locate/jmicmeth
The Integral Method, a new approach to quantify bactericidal activity☆
2Q2
Waldemar Gottardi a, Jörg Pfleiderer b, Markus Nagl a,⁎
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Article history: Received 10 March 2015 Received in revised form 4 May 2015 Accepted 4 May 2015 Available online xxxx
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Keywords: Quantitative killing assay Killing curve Specific bactericidal activity Antimicrobial agents Antiseptic
a b s t r a c t
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Department of Hygiene, Microbiology and Social Medicine, Division of Hygiene and Medical Microbiology, Medical University of Innsbruck, Schöpfstr. 41, A-6020 Innsbruck, Austria Institute of Astro- and Particle Physics, Leopold-Franzens University of Innsbruck, Technikerstr. 20, A-6020 Innsbruck, Austria
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The bactericidal activity (BA) of antimicrobial agents is generally derived from the results of killing assays. A reliable quantitative characterization and particularly a comparison of these substances, however, are impossible with this information. We here propose a new method that takes into account the course of the complete killing curve for assaying BA and that allows a clear-cut quantitative comparison of antimicrobial agents with only one number. The new Integral Method, based on the reciprocal area below the killing curve, reliably calculates an average BA [log10 CFU/min] and, by implementation of the agent's concentration C, the average specific bactericidal activity SBA = BA / C [log10 CFU/min/mM]. Based on experimental killing data, the pertaining BA and SBA values of exemplary active halogen compounds were established, allowing quantitative assertions. N-chlorotaurine (NCT), chloramine T (CAT), monochloramine (NH2Cl), and iodine (I2) showed extremely diverging SBA values of 0.0020 ± 0.0005, 1.11 ± 0.15, 3.49 ± 0.22, and 291 ± 137 log10 CFU/min/mM, respectively, against Staphylococcus aureus. This immediately demonstrates an approximately 550-fold stronger activity of CAT, 1730-fold of NH2Cl, and 150,000-fold of I2 compared to NCT. The inferred quantitative assertions and conclusions prove the new method suitable for characterizing bactericidal activity. Its application comprises the effect of defined agents on various bacteria, the consequence of temperature shifts, the influence of varying drug structure, dose–effect relationships, ranking of isosteric agents, comparison of competing commercial antimicrobial formulations, and the effect of additives. © 2015 Published by Elsevier B.V.
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1. Introduction
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The performance of killing of pathogens by antimicrobial chemicals is of considerable importance in medicine, because it indicates the usability of a given agent under conditions of practice. The results of such tests are presented by killing curves that demonstrate the surviving colony forming units (CFU) per ml in a suspension of test bacteria in the presence of a test agent after defined incubation times. The forms of killing curves substantially depend on the nature of the bacteria and their initial number as well as on the nature of the agent and its concentration. This implies that under standardized conditions, i.e., the same bacterial strain and initial log CFU, the specific activity of an agent
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Abbreviations: BA, bactericidal activity; CAT, chloramine T; CFU, colony forming units; DL, detection limit; DM-NCT, N-chloro-dimethyltaurine; NCT, N-chlorotaurine; SBA, specific bactericidal activity; tDL, killing time; tg, tangent. ☆ This article is dedicated to Professor Manfred Rotter (Medical University of Vienna), the recognized expert in the assessment of disinfecting procedures, on the occasion of his 75th birthday. ⁎ Corresponding author at: Department of Hygiene, Microbiology and Social Medicine, Division of Hygiene and Medical Microbiology, Medical University of Innsbruck, Schöpfstr. 41, 1st floor, A-6020 Innsbruck, Austria. E-mail address: [email protected] (M. Nagl).
can be determined. By visual examination of killing curves, therefore, a comparison of individual agents is possible, yielding qualitative information concerning their relative bactericidal activity (BA). For the evaluation of disinfectants and antiseptics in human medicine, the European Union has issued several norms based on the quantitative suspension test (http://www.en-standard.eu/, e.g., EN 13727 and EN 1040 for bactericidal activity in the medical area European Norm (EN) 1040, 2005; European Norm (EN) 13727, 2012, EN 12791 for surgical hand disinfection European Norm (EN) 12791, 2005, EN 1276 and EN 13697 for bactericidal activity in food, industrial, domestic and institutional areas European Norm (EN) 1276, 2009; European Norm (EN) 13697, 2002). The results of such protocols demonstrate whether a product has passed the respective EN test requirements, mostly ≥5 log reduction within 5 min. However, these standards give only a punctual account without any information about the kinetics of the bactericidal process. As a general standard for approval of disinfectants, it appears to be sufficient. However, for scientific characterization of microbicidal agents, particularly those that come directly in contact with human tissue under different conditions (antiseptics, antibiotics), a quantitative measure that would allow a more exact judgment of the microbicidal activity is of interest. Such a measure should take into account the course of killing curves, and it should be easily accessible from the curves.
http://dx.doi.org/10.1016/j.mimet.2015.05.002 0167-7012/© 2015 Published by Elsevier B.V.
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
82 83 84 85 86 87 88 89
tg α ¼ −dð log10
h
i CFUÞ=dt ¼ BA min−1 :
ð1Þ
91
106 107 108 109 110 111 112 113 114 115 116
121 122 123 124 125 126 127 128 129 130 131 132 133
K ¼ logCFU–DL:
140 141 142 143 144 145
ð3Þ 147
Under these auspices, a look on any killing curve suggests that the area between the killing curve and the detection limit, which is the integral over the killing curve with DL as abscissa level, or the integral over the relevance coordinate K, is a reciprocal measure of the average BA. It is directly apparent that the smaller the area, the faster killing occurs. The straight line that represents the average BA by its corresponding tangent is the one, which, starting from the same first data point log CFU (t = 0), provides the same integral. Mathematical details are given in Appendix A, a calculation program (Excel file) in Appendix B. It should be mentioned that the choice of the detection limit is not very critical. That is, our method works rather well even if DL is, for some reason, not securely established. Also, killing curves with not too large differences in log CFU (t = 0) can be directly compared. Nevertheless, a good experimental methodology is recommended. 2.1.1. Explanation of the Integral Method based on Fig. 1 By addition of the trapezoids 1–5 the area A of the killing curve down to the detection limit (DL = 2 log10 CFU) is found. A rectangle of equal area has the ordinate y = log10 CFU (t = 0) − DL, while the abscissa comes to x = A / y. The rectangle x × y is transformed into an orthogonal triangle with the same area. Its hypotenuse forms with the abscissa the angle α, whose tangent, tg α = y / 2x, represents the sought average BA. A calculation program (excel file) is presented in Appendix B.
ð2Þ
Using this parameter, results based on differing agent concentrations could be compared, where SBA values differing by a factor up to 40,000 (range 0.003 to 120 log10 CFU/min/mM) allowed a relative ranking of the investigated chlorine and bromine agents (Gottardi et al., 2014). In spite of this acceptable performance, the method exposed the shortcoming that in case of small differences in BA or SBA, a comparison of the calculated BA occasionally tended to disagree with the trend suggested by the curves. By removing the longer exposure times, slopes were obtained that finally concurred with the visual examination. This is a serious flaw. Omitting regular measuring points to obtain, or even support, a certain result is a strong indication of an inapt data interpretation. It was, therefore, of interest to find a method that approximates the average slope of killing curves without these inadequacies. For this purpose, conceivable ways for finding a suitable approximation were investigated (see Appendix A: “Theoretic considerations”) which
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SBA ¼ BA=C ½ log10 CFU= min=mM: 118
Contrary to earlier methods to quantify bactericidal activity (BA) by one number we make use of not only the measurements (data points) of the killing curves but also of the detection limit (DL). It gives, by definition, the same result for any log CFU b DL, namely no detection at all. This approach allows to differentiate between relevant data (log CFU N DL) and irrelevant ones (log CFU b DL), as well as to establish a relevance order by using a “killing relevance variable” (K) as the difference of the data (log CFU) to the irrelevance level (DL),
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C
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Instead of straight lines, such graphs in practice often show curved ones, with a high killing rate at the beginning, which gradually decreases towards the detection limit. This curvature preferably occurs with highly active agents (HOCl, active bromine compounds) (Gottardi et al., 2014), and can be explained by the depletion of the agent at the beginning of the killing process, and also by the enhanced tolerability of clumped bacteria or bacteria in a special state (e.g., small colony variants, persisters) (Glaser et al., 2014; Heras et al., 2014; Wood et al., 2013), which might be responsible for an overlong tail of the curve. As a consequence, BA (tg α) are not constant quantities, but can be specified by one characteristic number only as averaged values. The challenge was, therefore, to find a straight line that best approximates the bactericidal activity presented in the log CFU/time curve and whose slope (tg α) is a measure for BA of the tested sample. It is needless to say that the results achieved should confirm the ones of the visual comparison of killing curves. In a study dealing with isosteric chlorine and bromine compounds (Gottardi et al., 2014), extremely differing killing times were observed, which suggested quantifying them numerically. For approximating the killing curve with a straight line, whose slope equals BA, the authors used the averaged log reductions and exposure times (see method #3, Appendix A). Because the concentrations used differed by a factor of up to 1000, presentation on the same graph and visual check of the killing curves were not always possible. By including the concentration C (in mM), the specific bactericidal activity (SBA) of the agent was obtained, which enabled a reliable comparison throughout.
2.1. One-number interpretation of killing curves (Integral Method)
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80 81
136
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2. Methods
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77 78
finally led to the “Integral Method” as the best solution for assessing 134 tg α. 135
P
75 76
A method to gain such information could consist in determining the killing time tDL necessary to reach the detection limit (DL) of CFU in quantitative killing assays. A DL of 1 log10 (2 log10), for instance, indicates that a count below 10 CFU/ml (100 CFU/ml) is not detectable. Generally, such DLs originate from small volumes plated (usually ≤ 0.1 ml) and from dilutions in solutions that inactivate the test agent. However, determination of tDL is inaccurate and even impossible if DL is not reached at all, as it is the case in incomplete killing curves (see also Section 2.1). Early investigations of the kinetics of disinfection revealed a first order reaction for the killing of living bacteria caused by heat or toxic agents (Chick, 1910). This approach indicates that within the same time intervals the same percentage of CFU will be destroyed. A semilogarithmic graph, i.e., log of surviving CFU (ordinate) vs time (abscissa), yields a straight line that intersects the abscissa with an angle α, the tangent of which suggests itself as a possible quantitative measure for the average BA.
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Fig. 1. Schematic explanation of the Integral Method. Derivation of the averaged bactericidal activity from the area below the killing curve. Killing curve (open squares and thick dotted line), detection limit (thin dotted line). A = area below the curve = sum of trapezoids 1 to 5 = 5.25 + 7.50 + 10.75 + 5.95 + 1.0 = 30.45 log10 CFU × min. Abscissa of rectangle = A / (log10 CFUt = 0 − 2) = 30.45 / 6 = 5.075 min. Abscissa of triangle = 2 × 5.075 = 10.15 min. Area below the curve = area rectangle = area triangle. tg α = 6 / 10.15 = 0.591 log10 CFU/min. tg α = (K20 − K2n) / 2A = (36 − 0) / 60.9 = 0.591 log10 CFU/min (Eq. (7)).
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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2.2. General recommendations for BA testing
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On grounds of comparability, a careful standardization of the killing tests is necessary, which comprises bacterial strain, size of the inoculum, concentration of the agent, temperature, and pH.
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2.3. Performance of BA testing in this study
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2.3.1. Test substances Active halogen compounds were applied as bactericidal test agents. Chloramine T (CAT) trihydrate, reagent grade, was from Merck (Darmstadt, Germany). N-chlorotaurine (NCT) was prepared as reported (Gottardi and Nagl, 2002), N-chloro-dimethyltaurine (DM-NCT) was kindly provided by D. Debabov and R. Najafi (NovaBay Pharmaceuticals, Inc., Emeryville, CA, USA) (Low et al., 2009; Wang et al., 2008). Monochloramine was prepared by vacuum distillation in a rotary evaporator from aqueous solutions of NCT plus ammonium chloride and quantified spectrophotometrically as published previously (Gottardi et al., 2007). Peptone (enzymatic digest from casein) was from Fluka (Buchs, Switzerland). The test compounds were freshly dissolved in 0.1 M phosphate buffer (pH 7.1). In some experiments, peptone to a final concentration of 0.1%, 1%, 3%, 5%, and 10% was added. Tests at room temperature (RT) were performed at 20–22 °C, tests at 37 °C in a water bath.
199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228
C
193 194
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192
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190 191
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188 189
N C O
186 187
2.3.2. Bacteria and fungi Staphylococcus aureus ATCC 25923, S. aureus ATCC 6538, and Escherichia coli ATCC 11229 were cultivated for 16 h at 37 °C in tryptic soy broth (Merck), centrifuged at 1800 ×g and washed twice with 0.9% NaCl. The suspensions contained 1–3 × 109 colony forming units (CFU)/ml. Aspergillus fumigatus ATCC 26933 was grown for 8 days on Mueller–Hinton plates. The plates were rinsed with saline to gain the conidia, which were washed twice and diluted in saline to approximately 2 × 107 CFU/ml.
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184 185
T
195 196
2.2.2. Procedure for quantitative killing assays The following conditions of the killing tests are defined in the respective European Standard. Bacteria grown overnight and washed twice in 0.9% sodium chloride are diluted in the test solution (prewarmed to the respective temperature, see previous Section 2.2.1) to a final concentration of approximately 1 × 107 CFU/ml. To obtain reliable tg α values, the agent concentration should be chosen such, that the detection limit is reached within a reasonable total incubation time. Anyway, this concentration will generally correspond to that used in practical circumstances. After different incubation times, aliquots of 0.1 ml are removed and diluted in a suitable inactivation solution. From this solution and further dilutions in saline as suitable, quantitative cultures are performed, preferably with a spiral plater. Respective controls are done as outlined in the guidelines. The detection limit DL must be mentioned. Test conditions and incubation times must be described in detail.
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2.3.3. Quantitative killing assays Bacterial suspensions (40 μl) were 100-fold diluted in the solutions of the antiseptics (3.96 ml) and in buffer without additives (controls) at pH 7.1 and room temperature or 37 °C as indicated in the figure legends. In some additional tests, the dilution was 10-fold, in some 1000fold to achieve start concentrations of approximately 1–3 × 106 to
229 230 231 232 233 234 235 236 237 238 239 240 241
2.3.4. Calculation of tg α The parameters of the quantitative killing experiment, i.e., the incubation times and the pertaining log10 CFU values with standard deviations are transferred to the corresponding cells in the Excel program (see Appendix B) that yields the tg α value sought.
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2.4. Statistics
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2.2.1. Preparation of the test solution In accordance with the European Standard for quantitative killing assays (European Norm EN 1040:2005 and EN 13727:2012) (European Norm (EN) 1040, 2005; European Norm (EN) 13727, 2012), we recommend to dissolve the test agent in 0.1 M phosphate buffer at pH 7.0 ± 0.1 and at 20 °C in case of surface disinfectants or 37 °C in case of antiseptics.
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The impact of the imprecision of the log10 CFU values (±SD) on the area of the integral (Eq. (7)) and tg α (Eq. (8)) was calculated as specified previously (Sachs, 1974). If A = x ± a and B = y ± b, then applies A + B = (x + y) ± (a2 + b2)0.5, A − B = (x − y) ± (a2 + b2)0.5, A × B = x × y ± (x2 × b + y2 × a)0.5, A2 = x2 ± (2x2 × a)0.5, and A / B = x / y ± 1 / y2 (x2 × b + y2 × a)0.5. Statistical differences between killing curves were calculated with one-way analysis of variance (ANOVA) and Bonferroni's multiple comparison test (GraphPad Prism 5.02, La Jolla, CA, USA). Bartlett's test for Homogeneity of Variances was used to combine coefficients of variation, and Nalimov test to detect outliers. p-Values b 0.05 were considered significant. Linear regression was performed with GraphPad Prism software.
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3. Results
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3.1. Analytical quality of the Integral Method
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The intrinsic statistical parameters were evaluated by testing a stable standard disinfectant against a standard bacterium that revealed well reproducible results. This was realized by measuring the killing potency of chloramine T (N-chloro-4-methylbenzene sulfonamide sodium, CAT) against S. aureus at pH 7.0–7.1 and 22 °C.
264
3.1.1. Repeatability Five series of SBA measurements with each 10 replicates (three series with 500 and one each with 100 and 1000 μM CAT) gave the following coefficients of variation: 5.27, 7.23, 7.30, 10.0 and 9.61. According to the Bartlett's test for Homogeneity of Variances, all five values could be combined to the average repeatability of SBA ± 7.3%.
269 270
3.1.2. Accuracy This feature was not allocatable because no “true” reference value was available. Instead, the independency of SBA from the agent's concentration was verified by killing experiments with varying concentrations of CAT against S. aureus under otherwise identical conditions. Two stock solutions, one with CAT in 0.1 M phosphate, and the other one containing only 0.1 M buffer were mixed to obtain final concentrations of 1.000 to 0.100 mM CAT in 0.025 mM steps. From altogether 37 killing curves, the appendent BA and SBA values were calculated. One value (0.150 mM) was removed because the detection limit was not attained. According to the Nalimov test, two BA and SBA values could be removed as outliers (P b 0.05). Fig. 2 shows the outlier-freed graphs
275
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173
108 CFU/ml. Fungi were 50-fold diluted in the test solutions to final concentrations of 4 × 106 CFU/ml. After different incubation times, aliquots of 100 μl were removed and diluted 10-fold or 100-fold in 0.6% sodium thiosulfate solution to inactivate the test compound. Aliquots (50 μl) of these dilutions were spread in duplicate on tryptic soy agar plates with an automatic spiral plater (model WASP 2, Don Whitley Scientific, Shipley, UK), allowing a detection limit DL of 100 CFU/ml for all tested microorganisms taking into account both plates and the minimum dilution. The plates were incubated at 37 °C, and CFU were counted after 48 h. Special inactivation controls (addition of bacteria to sodium thiosulfate and to the active halogen compound previously inactivated by thiosulfate) were not added in this study since they were conducted in numerous previous studies, e.g., (Arnitz et al., 2009; Nagl et al., 1999).
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3
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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method concerning bacterial counts. Fig. 3 shows the original killing 312 curves for S. aureus and the influence of CFU (t0) on BA (tg α). 313
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3.1.4. Range of BA and SBA values From theoretic considerations (see Appendix A) can be deduced that complete killing curves with a sufficient number of data points should be preferred, which requires appropriate test conditions. Highly reactive antimicrobial agents need low concentrations and/or short incubation times, and the reverse applies to lowly reactive ones, accordingly. The conditions for obtaining complete killing curves were investigated in view of practicability (low reactivity) and feasibility (high reactivity) concerning incubation times. Calculation of two hypothetical examples (see Appendix B) revealed a measurability of BA (tg α) in the range of approximately 0.1 to 8.0 log10 CFU/min (ratio 1:80). From these values and conceivable limiting concentrations of 1000 and 0.001 mM, the measurable SBA values can be expected in the range of 0.001 to 8000 [log10 CFU/min/mM], which means a ratio of 1:8 × 106 or nearly seven powers of ten. Up to date, the most extreme SBA values were measured with NCT and dibromoisocyanuric acid (Gottardi et al., 2014). Against E. coli and S. aureus, the SBA of NCT lays at (1.76 ± 0.27) × 10− 3 and (2.02 ± 0.47) × 10− 3, while it was (4.83 ± 0.63) × 10+ 2 and (1.95 ± 0.26) × 10+ 2 log10 CFU/min/mM with dibromoisocyanuric acid and 4 × washed bacteria. From these values, a mean SBA ratio of 1:1.70 × 10+5 can be deduced, which is more than five powers of ten.
C
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295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311
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293 294
(b)
C
291 292
N
289 290
of the dependency of BA and SBA on the CAT concentration. BA is shown in linear presentation, while for SBA a logarithmic one was chosen, which takes into account the big span SBA values can attain (Gottardi et al., 2014). As expected, the BA values increased consistently with the concentration, showing the slope 1.275 ± 0.054 tg α/mM, and a correlation coefficient of r2 = 0.95, which indicates good linearity, while the fitting line revealed a high tendency to cross 0 mM. The regression line of SBA showed also a slope (0.127 ± 0.098), which was clearly smaller than the one of BA. Its deviation from slope zero was, however, not significant (P = 0.205). The mean of all SBA values comprising concentrations over a span of one power of ten allowed to determine an SBA of 1.11 ± 0.15 log 10 CFU/min/mM for CAT against S. aureus at 22 °C and pH 7.0–7.1. This result revealed an uncertainty of SBA determinations at varying concentrations of ±13.6%, which is nearly twice as much as the repeatability (see Section 3.1.1).
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Fig. 2. Calibration curve of BA (tg α versus concentration, open circles) (a) and of SBA (open squares) (b) in the range of 0.100–1 mM chloramine T with concentration intervals of 0.025 mM. Quantitative killing assays against S. aureus ATCC 6538 at room temperature and pH 7.1. The dotted line indicates the linear regression in (a) and (b).
3.1.3. Influence of the bacterial count on tg α Under otherwise identical conditions (37 °C, pH 7.1), BA measurements of 1% NCT against E. coli and S. aureus were conducted with bacterial suspensions of 106, 107, and 108 CFU/ml, which resulted in exact log10 CFU (t0) values of 8.15, 7.14, 6.20 and 7.33, 6.52, 5.29 for E. coli and S. aureus, respectively. The appendent tg α values were 0.309, 0.342, 0.458 (mean 0.378 ± 0.078) and 0.128, 0.158, 0.139 (mean 0.142 ± 0.015) for both strains. The dependence from log CFU (t0) was not significant in both cases, which confirms the robustness of the
Fig. 3. Influence of the CFU count at time zero (t0) on the BA of 55 mM (1%) NCT against S. aureus ATCC 25923 at 37 °C and pH 7.1. (a) Killing curves. Starting count 7.33 log10 CFU/ml (open squares, tg α = 0.128), 6.52 log10 CFU/ml (open triangles, tg α = 0.158), and 5.29 log10 CFU/ml (open diamonds, tg α = 0.139). Buffer controls (open circles). Mean values ± SD of n = 5. P b 0.01 between all three CFU-counts (0, 5, and 10 min) and between the highest count and the others (20 min), respectively. (b) Absence of a dependence of tg α on the CFU count. tg α values (open circles) and linear regression (dotted line). P N 0.05 between all three tg α values.
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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a) The individual susceptibilities of E. coli and S. aureus to the investigated preparations differed considerably. This indicates that BAbased specifications can refer only to one defined bacterial strain. b) In our example with povidone-iodine, chlorhexidine, and polyhexanide, only the latter allowed the BA measurement of the undiluted preparation, why a straight comparison (without dilution) of these commercial products was not possible. c) Nevertheless, a reasonable comparison seems conceivable with applications concerning the same target (e.g., disinfection of mucous skin) and by using the dilutions prescribed by the manufacturer.
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t1:1 t1:2
Table 1 BA values of commercial antiseptics.
376 377 378 379 380 381 382 383 384 385
t1:3 t1:4 t1:5 t1:6 t1:7
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374 375
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372 373
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370 371
E
386 387
– A more theoretical issue concerns the evaluation of the influence of structure on BA, e.g., the effect of the methyl groups in N-chlorodimethyltaurine (DM-NCT) compared to NCT. The analysis of available data about E. coli at room temperature (Fig. 4a, Gottardi et al., 2014) gave SBA values of 0.0010 and 0.0035 log10 CFU/min/mM for NCT and DM-NCT, respectively. These results indicate a 3.5 fold increase for the di-methyl derivative. The appendent values for 37 °C (Fig. 4b) were 0.0058 and 0.0126 log10 CFU/min/mM for NCT and DM-NCT, which corresponds to a ratio of 2.17. – The evaluation of BA proved very useful to assess the impact of a variation of status parameters, e.g., pH, temperature, nature and concentration of additives, on a defined preparation. In this case, too, the agent concentration has to be kept constant. An example provides Fig. 5, which shows the surprising increase of BA in a killing test of E. coli by 0.0275 mol/l NCT in the presence of 0– 10% peptone. While the original killing curves (Fig. 5a) are hardly distinguishable, the calculated BA values in Fig. 5b give clear information about the increase of BA, which reaches its maximum with 3% peptone. The influence of temperature (derived from experiments at room temperature (20–22 °C) and 37 °C, presented in Fig. 4) revealed an
368 369
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F
3.2.1. BA as a relative parameter – BA could serve to specify commercial disinfection products, which suggests a comparison and a ranking of competing products and its formulations, respectively. In case of agents (preparations) with differing killing mechanisms like alcohols, quaternary ammonium or active halogen compounds, the term “concentration” is not synonymous (e.g., in the case of 70% alcohol and 1% NCT). Because BA is controlled not only by the actual concentration of the underlying agent, but also by the presence of pharmaceutical additives (e.g., to provide eudermic properties), which can influence BA, the parameter SBA is not applicable. Table 1 reveals important features:
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342
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3.2. Results in context to fields of application of the Integral Method
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3.1.5. The problem of dilution Principally, the measurability of extremely strong agents (preparations) could be attained by dilution. However, there exist formulations which show non-linear dose–response relationships, which can cause confusing results. A well-known example concerns iodophoric preparations (e.g., based on povidone–iodine), which react on dilution with an increase of BA within a certain concentration range (Gottardi, 2001).
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5
Preparation
Dilution
tg α E. coli
S. aureus
E. coli / S. aureus
Povidone iodine 10% (1% I2) 1:20,000 1.067 ± 0.104 0.363 ± 0.028 2.9 Chlorhexidine 0.012% 1:10 6.20 ± 2.94 0.084 ± 0.005 73.8 Polyhexanide 0.04% 0 0.242 ± 0.014 4.80 ± 2.26 0.0504
Fig. 4. BA of 55 mM NCT (open squares) and 55 mM DM-NCT (open triangles) against E. coli ATCC 11229 at pH 7.1. Buffer controls (open circles). Mean values ± SD. P b 0.01 between all curves. (a) Room temperature (20–22 °C); n = 3–8. (b) 37 °C; n = 3.
increase of BA of 0.057 to 0.317, and 0.190 to 0.697 for NCT and DMNCT, respectively, against E. coli. This signifies that raising the temperature by 15–17 °C increases BA by a factor of 4–6. Experiments with NCT and E. coli, where SBA values were averaged from a range of concentrations (see Table 2), revealed even an 8.1-fold higher SBA at 37 °C. These evidences emphasize that maintaining a defined constant temperature during bactericidal activity testing is an absolute must for gaining reliable and consistent results. – Dependencies between the concentration of an agent and its antimicrobial activity, i.e., dose–effect relationships, which have to be tested under the same conditions (pH, temperature, solvent, concentrations of additives), are significantly easier and more precise to attain and are more reliable if numerically based on BA values. – Another subject concerns the susceptibility of various bacterial strains to a defined agent. We found a ratio of 2:1 (E. coli:S. aureus) for NCT and 1.5:1 for DM-NCT. – A striking feature applies the BA increase of 1% NCT against A. fumigatus in the presence of up to 1% ammonium chloride. Fig. 6 shows a rise of BA with factors of 27.4, 96.8, and 568 in the presence 0.01, 0.1, and 1.0% ammonium chloride, respectively. This effect can be attributed to the formation of monochloramine (NH2Cl) according to the equilibrium NCT + NH+ 4 ↔ taurine + NH2Cl (Gottardi et al., 2007; Nagl et al., 2001).
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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Fig. 6. Enhancement of BA of 55 mM (1%) NCT against conidia of A. fumigatus ATCC 26933 in the presence of 0, 0.01, 0.1, and 1.0% ammonium chloride at 37 °C and pH 7.1. tg α mean values (open circles, full line) and linear regression (dotted line) from 5 independent experiments.
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4. Discussion
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The assessment of BA concerns the reaction rate of bacterial kill, and therefore it is a kinetic problem. It is founded on a series of diverging occurrences like diffusion (extra- and intracellular), penetration through the cell wall, and in case of active halogen compounds of various oxidation reactions with quite differing reaction rates (Gottardi et al., 2013; Gottardi and Nagl, 2002). An exact determination of BA via kinetic laws would be nearly impossible, because no data are available for most of the underlying elementary reactions. Amazingly, the presented integral-based BA determination enables to get this information by one plain calculation. Though yielding unambiguous numerical results, a detailed examination of their scientific relevance and reliability is mandatory, and needs to discuss possible errors and inaccuracies.
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4.1. Methodical errors
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minor differences in the absolute SBA values, while the relations were virtually the same. Multiple SBA measurements with varying concentrations can be suggested for gaining averaged values with an improved reliability. The results of experiments with CAT, NCT, NH2Cl, and I2 against E. coli and S. aureus are shown in Table 2, Figs. 2 and 7. Assayed by linear regression, a little concentration dependency of SBA was observed (slope of regression line ≠ 0), however, the departure from slope zero was not significant in most cases.
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Fig. 5. Killing of E. coli ATCC 11229 by 27.5 mM NCT at 37 °C in the presence of peptone. (a) Killing curves. Mean values ± SD, n = 3. Significantly more rapid killing in the presence of 0.1% to 5% peptone compared to 0% peptone (P b 0.01), and deceleration of killing by 10% peptone (P b 0.01). Respective tg α values are listed. Controls (filled circles) were done in plain 0.1 M phosphate buffer (pH 7.1) plus 10% peptone. (b) Increase of BA (tg α) with the peptone concentration up to 5%.
t2:1 t2:2
Table 2 Mean SBA values [log10 CFU/min/mM] obtained at pH 7.0–7.1.
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N
415 416
t2:3
Agent
°C
Concentration
N
E. coli
S. aureus
t2:4 t2:5 t2:6 t2:7 t2:8 t2:9 t2:10
CAT NCT
20–22 20–22
0.1–1.0 mM 12.8–55.0 mM
36 3
1.11 ± 0.15c 0.00202 ± 0.00047c
NCT
37
5.5–55.0 mM
4
NH2Cla I2 b
20–22 20–22
0.12–1.07 mM 1.2–10.7 μM
3 3
n.d. 0.00176 0.00027c 0.0142 ± ±0.0049c n.d. n.d.
t2:11 t2:12 t2:13 t2:14
426 427 428 429 430
433 434 435 436 437 438 439 440 441 442 443 444
For comparison of agents via BA, even statements as simple as “X 446 is better than Y,” i.e., “BA(X) N BA(Y),” need killing curves. These 447
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3.2.2. SBA as a specific intrinsic parameter independent on the agent's concentration The comparison of agents with extremely diverging BAs can induce a problem, because the requirement of identical concentration (C) could demand very short and therefore not practicable incubation times. In such cases it is necessary to use instead of BA the specific bacterial activity, SBA = BA / C, a parameter that enables in any case to draw a comparison. The first reference of its use was done a short time ago (Gottardi et al., 2014), but with an algorithm (see method #3 in Appendix A) that in the present study proved as minor qualified. Verification of the data with the Integral Method #5 (Appendix A) uncovered
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n.d. 3.49 ± 0.22c 291 ± 137c
n.d. not determined. a According to Arnitz et al. (2009). b Pure aqueous iodine solution without additional iodide. c The deviation from slope zero was not significant.
Please cite this article as: Gottardi, W., et al., The Integral Method, a new approach to quantify bactericidal activity, J. Microbiol. Methods (2015), http://dx.doi.org/10.1016/j.mimet.2015.05.002
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Fig. 7. BA of 0.1 to 1.1 mM NH2Cl and 0.0012 to 0.011 mM iodine against S. aureus ATCC 25923 at room temperature and pH 7.1. Mean values ± SD of n = 3. (a) Killing curves by NH2Cl; 0.107 mM (open diamonds), 0.355 mM (open triangles), 1.07 mM (open squares), 0 mM (controls, open circles); P b 0.01 between all curves. (b) Killing curves by iodine, 0.0012 mM (open diamonds), 0.0036 mM (open triangles), 0.0107 mM (open squares), 0 mM (controls, open circles); P b 0.01 between all curves. (c) tg α versus concentration for NH2Cl; tg α single mean values (open circles, full line), linear regression (thick dotted line), and overall mean value (3.49 ± 0.22, thin dotted line). (d) tg α versus concentration for iodine; tg α single mean values (open circles, full line), linear regression (thick dotted line), and overall mean value (291 ± 137, thin dotted line.
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4.2. Systematic errors
469
One example concerns the time of reaching the detection limit, which on theoretical reasons is essential for finding the correct slope (see also Section 2.1). It is obvious that tDL cannot be determined exactly because this point lies between the last two measurements. In most cases, tDL is therefore too high, which induces a somewhat too low BA. Since mixing of bacteria in the agent solution takes some time (for example 3 s), the real incubation times are somewhat shorter than the experimentally defined ones. Calculations show, however, that
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470 471 472 473 474 475 476
R
R
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E
467
conclusively demonstrate that BA generally is not constant, but a decreasing function of time. For any quantitative comparison, as “X is ten times better than Y,” it is apparently necessary to define an average BA from the killing curve, i.e., to define an averaging straight line whose slope (= tg α) represents the essential features of the killing curve. Of the quoted methods #1 to #4, each has serious flaws that render them rather useless, even if at a quite different degree. With the introduction of the area under the curve as reciprocal measure of BA, the similarity to the visual impression is strong enough to render Eq. (7) a reasonable one-number approximation to the more complex reality. We are aware of the fact that our method is subject to a variety of uncertainties. The numerical calculation of the area under the curve (Eq. (9)) implies not only measuring errors that can be quantified by statistics on repeated measurements. It also implies a systematic error due to explicit use of the interpolating lines between single time points (Eq. (9), right side), which renders our method not entirely independent of the number and time-distance of the data. In all cases the area is overestimated, which effect should, however, partly get lost upon comparison of curves. Also, the one-number comparison of killing curves with different shapes is a further simplification.
postponing all times by the same interval has no effect upon tg α. 477 With other words, this error is of no relevance. 478
4.3. Possible experimental sources for errors
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The reliability of tg α principally relates to the exactness of both bacterial counts and incubation times. It can be assumed that the precision of the counting process is constant and depends mainly on the skill of the operator. Concerning the impact of time, one has to distinguish between systems with rapid killing and slow ones. In the former case, short incubation times are applied whose precision decreases opposite to its duration, with the effect of higher standard deviations, but no change of tg α. Variable or undefined temperature during the killing process might also play a role in lessening precision and accuracy.
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4.4. The high range of SBA
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A rather astonishing feature concerns the extreme span of measured SBA, which encompasses up to more than four powers of ten. This problem was already discussed in a paper dealing with the BA of active chlorine and bromine compounds (Gottardi et al., 2014). Briefly, the authors postulated that there is a big difference in the rate of reactions of active halogen compounds with proteins in a homogeneous solution (which amounts a factor up to only 3–4) and in killing of bacteria. The latter concerns basically similar proteins which, however, are protected by a cell wall. Therefore, mainly the very complex occurrences that influence the rate of penetration were considered responsible for the observed big differences in SBA.
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4.5. Significance of SBA for applications in clinical practice
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We are grateful to Andrea Windisch for excellent technical assistance. We thank Miranda Suchomel, Institute of Hygiene and Applied Immunology, Medical University of Vienna, for providing raw data on hand disinfection tests. This work was supported by the Division of Hygiene and Medical Microbiology of the Medical University of Innsbruck. We have no conflicts of interest to declare.
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Agents that are able to kill bacteria interact also with the surrounding proteins, which results in consumption effects (Gottardi et al., 2013, 2014), i.e., reduction of the agent's concentration and irritation of tissue. These features are relevant above all for oxidizing agents like active halogen compounds. Since high SBA comes along with unfavorably high consumption, SBA values don't reveal the applicability of antiseptics in practice, which is based on a compromise between sufficient BA and low irritation (Gottardi et al., 2013; Gottardi and Nagl, 2010).
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4.6. Why the Integral Method is of additional value to European Standards
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The Integral Method is conceived to determine the BA of a bactericidal agent against a defined microorganism. Being derived from the whole killing curve, it gives in any case more reliable information about the BA than the European Norms for evaluation of the bactericidal activity of chemical disinfectants and antiseptics, which require only one point of the killing curve. For instance, EN 13727 (Quantitative suspension test for the evaluation of bactericidal activity in the medical area) discloses not the BA but the “bactericidal concentration” for a specified application (e.g., disinfection of instruments) (European Norm (EN) 13727, 2012). Nevertheless, if the experimental data (log reduction + incubation time) necessary for finding this value include more than one incubation time, which is allowed by the norm, determination of tg α according to the Integral Method is quite possible. As an example, in a study investigating hand disinfection with npropanol versus isopropanol, the log reduction of CFU after single incubation times was compared using the European Standard EN 12791 (Suchomel et al., 2009). Taking into account all incubation times in one by the Integral Method would enhance the sensitivity to discriminate between the tested disinfectants. Our calculation revealed a highly significant difference between the BA of n-propanol versus isopropanol, which was not statistically verified in the original study (Suchomel et al., 2009). The respective BA values, calculated from the published reduction factors assuming pretreatment values of 5 log10, were 0.543 ± 0.095 for n-propanol 60% (immediate), 0.451 ± 0.073 for isopropanol 70% (immediate), 0.326 ± 0.064 for n-propanol 60% (3 h), 0.210 ± 0.056 for isopropanol 70% (3 h). One-way ANOVA and Tukey's multiple comparison tests revealed P b 0.01 between n-propanol and isopropanol for each immediate and 3 h values. The statistical outcome was identical for calculations assuming pretreatment values of 4.0 and 4.5 log10.
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The Integral Method uses for the first time an integration of a killing curve, resulting in one reliable value that is characteristic for the average BA. The clear linear relation between BA and concentration (calibration curve) and its tendency to cross zero confirm them by all means as reliable measures for relative statements. The measure SBA, on the other hand, turns out as a comprehensive parameter suitable to position agents in the extremely wide scope of chemical disinfection. The method may be useful for documentation and estimation of the microbicidal activity of antiseptics, disinfectants, and biocides in addition to present standards. Moreover, it might be helpful to characterize bactericidal antibiotics and fungicides in connection with parameters like minimum bactericidal concentration, half-life, and area under the curve. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.mimet.2015.05.002.
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