Robust experimental design for optimizing the

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for the noise variables. In this study, a 23 · 22 robust. Keywords factorial analysis, logistic model, milk, penicillin, robust design, screening test. Correspondence.
Letters in Applied Microbiology ISSN 0266-8254

ORIGINAL ARTICLE

Robust experimental design for optimizing the microbial inhibitor test for penicillin detection in milk O.G. Nagel1, M.P. Molina2, J.C. Bası´lico1, M.L.Zapata1 and R.L. Althaus1 1 Ca´tedra de Biofı´sica, Departamento de Ciencias Ba´sicas, Facultad de Ciencias Veterinarias, Universidad Nacional del Litoral, Esperanza, Repu´blica Argentina 2 Departamento de Ciencia Animal, Universidad Polite´cnica de Valencia, Valencia, Spain

Abstract

Keywords factorial analysis, logistic model, milk, penicillin, robust design, screening test. Correspondence Rafael L. Althaus, Ca´tedra de Biofı´sica, Departamento de Ciencias Ba´sicas, Facultad de Ciencias Veterinarias, Universidad Nacional del Litoral, R.P.L Kreder 2804, (3080) Esperanza, Repu´blica Argentina. E-mail: [email protected]

2008 ⁄ 1393: received 12 August 2008, revised and accepted 5 February 2009 doi:10.1111/j.1472-765X.2009.02602.x

Aims: To use experimental design techniques and a multiple logistic regression model to optimize a microbiological inhibition test with dichotomous response for the detection of Penicillin G in milk. Methods and Results: A 23 · 22 robust experimental design with two replications was used. The effects of three control factors (V: culture medium volume, S: spore concentration of Geobacillus stearothermophilus, I: indicator concentration), two noise factors (Dt: diffusion time, Ip: incubation period) and their interactions were studied. The V, S, Dt, Ip factors and V · S, V · Ip, S · Ip interactions showed significant effects. Conclusions: The use of 100 ll culture medium volume, 2 · 105 spores ml)1, 60 min diffusion time and 3 h incubation period is recommended. In these elaboration conditions, the penicillin detection limit was of 3Æ9 lg l)1, similar to the maximum residue limit (MRL). Of the two noise factors studied, the incubation period can be controlled by means of the culture medium volume and spore concentration. Significance and Impact of the Study: We were able to optimize bioassays of dichotomous response using an experimental design and logistic regression model for the detection of residues at the level of MRL, aiding in the avoidance of health problems in the consumer.

Introduction Antibiotic residues in milk can cause toxicological problems affecting public health (Currie et al. 1998) and are a problem in the manufacturing of fermented products such as cheese and yoghurt (Brady and Katz 1988). Recent decades have witnessed the development of different microbial screening tests for the precise detection of antibiotic residues in milk (IDF 1991). The principle of the microbial inhibition test is the inhibition of spore outgrowth of Geobacillus stearothermophilus subsp. calidolactis (Mu¨ller and Jones 1993), by means of a colour change in an indicator in the culture medium, providing a dichotomous response in terms of ‘positive’ or ‘negative’. Many experimental design techniques have been used to optimize diverse metric variables in analytical methods (Ferreira et al. 2007) and microbiological methods of diffusion in Petri dishes (Renard et al. 1992; 744

Koenen-Dierick and De Beer 1998), by means of the anova statistical method. Nevertheless, there have been no studies on the design and optimization of variables affecting the dichotomous response of these bioassays. In consequence, the aim of the present work was to apply robust experimental design techniques and multiple logistic regression models in order to optimize the operative conditions of the bioassay that uses Geobacillus stearothermophilus to detect penicillin in milk samples. Materials and methods Experimental design The methodology for robust parameter design involves an analysis of a crossed matrix, whereby a control matrix involving control variables is crossed with a noise matrix for the noise variables. In this study, a 23 · 22 robust

ª 2009 The Authors Journal compilation ª 2009 The Society for Applied Microbiology, Letters in Applied Microbiology 48 (2009) 744–749

O.G. Nagel et al.

Penicillin detection in milk

experimental design with two replications was used to optimize the bioassay in ELISA microplates for the detection of penicillin residues in milk. The 23 matrix for the control variables and 22 matrix for the noise variables are crossed. The result is a 32-run design called a crossed matrix. In the robust design, two levels of the three ‘control factors’: Concentration of spores (S: 0Æ5 · 105–2 · 105 spores ml)1), Concentration of the indicator (I: 0Æ025– 0Æ050 mg ml)1), Volume of culture medium (V: 100– 120 ll) and two ‘noise factors’: Diffusion time (Dt: 60–90 min) and Incubation period (Ip: 3–4 h) were studied. Table 1 summarizes the combinations of the levels of each factor used in the 23 · 22 robust designs. Bioassay preparation Culture medium Plate Count Agar (PCA, Difco, ref. 247940) enriched with 20 g l)1 glucose (Sigma G-8270) was used. The culture medium was sterilized by autoclaving at 121C for 15 min. The pH of the medium was adjusted to 7Æ0 ± 0Æ1 with 1 mol l)1 NaOH. A suspension of Geobacillus stearothermophilus subsp. calidolactis (C–953 spores, Merck, ref. 1Æ11499) and Bromocresol Purple indicator solution (Sigma B-5880) were added to reach the levels detailed in Table 1. An electronic dispenser (Eppendorf Research Pro) was used to fill microplates (Deltalab, 900010, Barcelona, Spain) according to the 32-combination of Table 1. The microplates were sealed with adhesive bands and kept at 4C until use. Table 1 Design matrix used in the robust 23 · 22 experimental design Control factors

Control factors

Noise factors

Noise factors

Run

S

I

V

Dt

Ip

Run

S

I

V

Dt

Ip

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

) ) ) ) ) ) ) ) + + + + + + + +

) ) ) ) + + + + ) ) ) ) + + + +

) ) + + ) ) + + ) ) + + ) ) + +

) + ) + ) + ) + ) + ) + ) + ) +

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

+ + + + + + + + + + + + + + + +

) ) ) ) ) ) ) ) + + + + + + + +

) ) ) ) + + + + ) ) ) ) + + + +

) ) + + ) ) + + ) ) + + ) ) + +

) + ) + ) + ) + ) + ) + ) + ) +

S, spore concentration; I, Concentration of the indicator; V, volume of culture medium; Dt, diffusion time; Ip, incubation period.

Microplate analysis For each combination of the factor levels (Table 1), two microplates were used. In both microplates, 16 replicates of 12 concentrations of penicillin ‘G’ (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 lg l)1, Sigma-PEN-Na) were prepared using antibiotic-free milk samples from individual animals (IDF 1999). To each individual well we added 50 ll of milk solution fortified with penicillin. Subsequently, each microplate was sealed with adhesive bands and kept at 4C (Dt: 60 min or 90 min according to the design) in order to achieve diffusion of the antibiotic. The milk was then removed and the individual wells washed three times with distilled water. The microplates were sealed with adhesive bands and incubated in a water bath at 64 ± 1C (Ip: 3 h or 4 h, according to the design in Table 1). Interpretation of the results The antibiotic residues present in the milk samples reduce or prevent metabolic activity as well as inhibiting the growth of the micro-organism. The acidification process was used to measure metabolic activity with the help of a coloured indicator (Bromocresol Purple). The indicator changes colour (from purple to yellow) during the acidification process in response to acidic metabolic products in the culture medium. A visual interpretation was carried out by three qualified people (trained in the interpretation of dichotomous responses) and evaluated as ‘negative’ (yellow) or ‘positive’ (purple). ‘Doubtful’ (purple-yellow) qualifications were considered ‘positive’ (Suhren et al. 1996). Statistical analysis As the results were based on a categorical response variable of two levels (‘positive’ and ‘negative’), a multiple logistic regression model was used by means of the stepwise option of the logistic procedure of the SAS statistical package (SAS 2001). This was done in order to sequentially select those variables that significantly affected bioassay response. The variables were analysed using the following logistic model: Lijkl ¼ logit ½Pijkl  ¼ b0 þ b1 ½Ci þ Rbj ½Cf j þ Rbk ½Nf k þ Rbjj ½Cf j  ½Cf j þ Rbkk ½Nf k  ½Nf k þ Rbjk ½Cf j  ½Nf k þ eijkl where Lijkl = the logit model, [Pijkl] = probability for the response category (‘positive ⁄ negative’), b0 = intercept,

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Penicillin detection in milk

O.G. Nagel et al.

b1, bj, bk, bjj, bkk, bjk = estimated parameters for the model, [C]i = penicillin concentration (i:12), [Cf]j = control factors in coded terms (j:3), [Nf]k = noise factors in coded terms (k:2), [Cf]j · [Cf]j = interactions between the control factors in coded terms (jj:3), [Nf]k · [Nf]k = interactions between the noise factors in coded terms (kk:1), [Cf]j · [Nf]k = interactions between the control factors and noise factors in coded terms (jk:6), eijkl = residual error. This model allows the variability in the noise factors to be analysed by means of an appropriate selection of control factor levels. This can be done by analysing the [Cf]j · [Nf]k interactions. The concordance coefficient was applied as a rank correlation between the observed responses and predicted probabilities (SAS 2001). Detection limits of the bioassay For those factors that had a significant influence on the results of the bioassay, the detection limits of the method were established using eqn (1). Detection limits were set at the concentration that produced a 95% positive result to the bioassay (IDF 1999). Results The results from the logistic model point to significant effects (P < 0Æ05) for the V, S, Dt, Ip and V · S, V · Ti and S · Ti interactions. The equation we used for predicting the frequency of positive results to the bioassay as a function of the significantly coded variables was: Lijkl ¼ 1421 þ 382½C  347½V  090½S þ 114½Dt  077½Ip  110½V  ½S  048½V  ½Ip þ 042½S  ½Ip Concordance ¼ 992%:

ð1Þ

Increases in the values of the culture medium volume, a higher concentration of spores and a longer incubation

period produced a decrease in the frequencies of positive results to the bioassay (negative values of the ‘b’ coefficients). This is due to the fact that the increase in both the volume of the culture medium as well as in the concentration of spores requires greater concentrations of antimicrobial agents to produce a change in response. In the same way, a longer incubation period would allow a later development of the micro-organisms in individual wells containing milk fortified with greater penicillin concentrations. On the other hand, increases in the diffusion times will produce more frequent positive results (positive values of the ‘b’ coefficient), since the longer the diffusion period, more the antimicrobial agents are diffused in the individual wells of the bioassay. Detection limits calculated by means of the logistic equation for design conditions that had a significant effect on bioassay response are shown in Table 2. The arrangement of the ‘control factors’ and ‘noise factors’ in this table makes their interpretation easier since each line corresponds to a control condition that takes into account the variations from the different operative conditions (noise factors). In this way, for example, when 100 ll of culture medium and 0Æ5 · 105 spores ml)1 are used, the detection limit is between 3Æ2 lg l)1 (Dt = 90 min, Ip = 3 h) and 4Æ1 lg l)1 (Dt = 60 min, Ip = 4 h). A bioassay designed with these characteristics will present an average detection limit of 3Æ6 lg l)1 under the different operative conditions. The calculated standard deviation will be 0Æ38 lg l)1. This parameter indicates how the detection limit varies according to the different levels of the noise factors. When the value of the standard deviation is lower, the bioassay will be more robust for those factors. In Table 2, it can be seen that variations in the microplates specified with 100 ll of culture medium and 2 · 105 spores ml)1 (control factor) are hardly affected (SD: 0Æ35 lg l)1) by the different conditions in the laboratory (Dt, Ip), thus demonstrating that the bioassay was carried out in more stable conditions.

Table 2 Detection limits calculated by means of the logistic regression model for different control and noise factors Control factors

Volume (ll) 100 120

Noise factors Spores (spores ml)1)

Dt = 60 min Ip = 3 h

Dt = 60 min Ip = 4 h

Dt = 90 min Ip = 3 h

Dt = 90 min Ip = 4 h

Average

SD

50 200 50 200

3Æ7 3Æ9 4Æ7 6Æ0

4Æ1 3Æ8 5Æ6 6Æ4

3Æ2 3Æ3 4Æ1 5Æ4

3Æ5 3Æ2 5Æ0 5Æ8

3Æ6 3Æ6 4Æ9 5Æ9

0Æ38 0Æ35 0Æ62 0Æ42

000 000 000 000

Dt, diffusion time; Ip, incubation period; SD, standard deviation. Detection limits in lg l)1.

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ª 2009 The Authors Journal compilation ª 2009 The Society for Applied Microbiology, Letters in Applied Microbiology 48 (2009) 744–749

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Penicillin detection in milk

100 ll volume gave detection levels of between 3Æ2 and 4Æ1 lg l)1 penicillin ‘G’, close to the MRL. It may also be observed that inoculation with 2 · 105 spores ml)1 gave detection limits similar to the MRL. Therefore, it is more appropriate to prepare the microplates using a culture medium volume of 100 ll and a spore concentration of 2 · 105 spores ml)1. Significant interactions (Table 2 and Figs 1–3) were elaborated by means of eqn (1), using a diffusion time of 60 min. Figure 1 shows the effects that V and S produce on the dose–response curves of the penicillin for the two levels of Ip. It can clearly be seen that the logistic curves are nearest when the bioassay is performed with a lower volume of medium (100 ll) in comparison with the microplates prepared with a higher volume of medium (120 ll). Figure 2 also shows how V and Ip affect the dose– response curve of penicillin for the two levels of S. In both Figs 1 and 2, it can be observed that for different Ip levels, the logistic curves are closest when a lower volume of medium (V = 100 ll) is used in comparison with a higher volume (V = 120 ll). This shows the advantage of

The microplates specified with 120 ll of culture medium presented detection limits higher than the maximum residue limit (MRL) (4 lg l)1), with averages of 4Æ9 lg l)1 (for 0Æ5 · 105 spores ml)1) and 5Æ9 lg l)1 (for 2 · 105 spores ml)1). This fact ignores the possibility of working with this volume of culture medium. Microplates containing 100 ll of culture medium and 2 · 105 spores ml)1 presented an average detection limit of 3Æ6 lg l)1, near to the MRL of penicillin (4 lg l)1) for the different diffusion and incubation times. Of all the experimental conditions studied, the diffusion for a period of 60 min followed by an incubation period of 3 or 4 h enabled the detection of penicillin ‘G’ residues in milk at a similar level to that of the MRL, whereas the other operative conditions (Dt = 90 min and Ip = 3 or 4 h) produced lower detection limits, accompanied by an increase in ‘false violative’ results (positive result to method with an inferior level to RML). In short, it was shown that a culture medium volume of 120 ll gave a detection limit within the 4Æ1–6Æ4 lg l)1 range of penicillin ‘G’ concentration, whereas the use of a

Diffusion time = 60 min-incubation period = 4 h

-

Positive frequency (%)

Positive frequency (%)

Diffusion time = 60 min-incubation period = 3 h 100 90 80 70 60 50 40 30 20 10 0 0

1

2

3 4 5 Penicillin ‘G’ (ppb)

6

7

100 90 80 70 60 50 40 30 20 10 0

8

0

1

2

3 4 5 Penicillin ‘G’ (ppb)

6

7

8

Figure 1 Effect of volume of culture medium and concentration of spores on the dose-response curves of the penicillin in milk (h V: 100 ll – S: 0Æ5 · 105 spores ml)1; d V: 120 ll – S: 0Æ5 · 105 spores ml)1; D V: 100 ll – S: 2 · 105 spores ml)1; V: 120 ll – S: 2 · 105 spores ml)1).

Diffusion time = 60 min-Spore concentration = 2·0×105 spores ml–1

100 90 80 70 60 50 40 30 20 10 0 0

100 90 80 70 60 50 40 30 20 10 0

Positive frequency (%)

Positive frequency (%)

Diffusion time = 60 min-Spore concentration = 0·5×105 spores ml–1

1

2

3 4 5 6 Penicillin ‘G’ (ppb)

7

8

0

1

2

3 4 5 Penicillin ‘G’ (ppb)

6

7

8

Figure 2 Effect of volume of culture medium and incubation period on the dose-response curves of the penicillin in milk (h V: 100 ll – Ip: 3 h; D V: 100 ll – Ip: 4 h; d V: 120 ll – Ip: 3 h; V: 120 ll – Ip: 4 h). ª 2009 The Authors Journal compilation ª 2009 The Society for Applied Microbiology, Letters in Applied Microbiology 48 (2009) 744–749

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O.G. Nagel et al.

Diffusion time = 60 min-Culture medium volume =100 µ l Postive frequency (%)

Postive frequency (%)

100 90 80 70 60 50 40 30 20 10 0

Diffusion time = 60 min-Culture medium volume =120 µl

0

1

2

3 4 5 Penicillin ‘G’ (ppb)

6

7

8

100 90 80 70 60 50 40 30 20 10 0

0

1

2

3 4 5 Penicillin ‘G’ (ppb)

6

7

8

Figure 3 Effect of concentration of spores and incubation period on the dose-response curves of the penicillin in milk (h S: 0Æ5 · 105 spores ml)1 – Ip: 3 h; D S: 0Æ5 · 105 spores ml)1 – Ip: 4 h; d S: 2 · 105 spores ml)1 – Ip: 3 h; S: 2 · 105 spores ml)1 – Ip: 4 h).

performing the bioassay with 100 ll of medium volume, since the results are more stable (the method is more robust) for the different Ip. Similarly, Fig. 3 shows the effects of S and Ip on the dose–response curves of penicillin for the two levels of V. In both cases, the logistic curves are nearest when the bioassay is done with a high concentration of spores in comparison with those when a smaller quantity is used. For this reason, a test with a high concentration of spores will present a greater robustness for the different incubation periods used. Finally, it should be mentioned that the diffusion time (noise factor) could not be controlledfor at the moment the bioassay was being carried out, since no interactions between the control factors and Dt were significant in eqn (1). Discussion The detection limits for penicillin ‘G’ calculated for the different operative conditions of this bioassay are similar to the values obtained by other authors when using various commercial methods, Heeschen (1993), for example, obtained a detection level of 5 lg l)1 for the BRT AiM method, while Gardner et al. (1996) detected 3 lg l)1 penicillin with the Delvotest ‘SP’ method. Conclusions It is concluded that these experimental design techniques can be satisfactorily applied for the optimization of a bioassay presenting a categorical response and can be employed to detect residues of penicillin in milk that would otherwise reach the consumer. Acknowledgements This investigation was carried out as part of the CAI+D’05 ⁄ 07 no. 033-213, supported by financial 748

assistance from the Universidad Nacional del Litoral (Argentina). References Brady, M. and Katz, S. (1988) Antibiotic ⁄ antimicrobial residues in milk. J Food Prot 51, 8–11. Currie, D., Lynas, L., Kennedy, G. and Mc Caughey, J. (1998) Evaluation of modified EC four plate method to detect antimicrobial drugs. Food Addit Contam 15, 651–660. Ferreira, S., Bruns, R., Ferreira, H., Matos, G., David, J., Branda˜o, G., da Silva, E., Portugal, L. et al. (2007) Box-Behnken design: an alternative for the optimization of analytical methods. Anal Chim Acta 597, 179–186. Gardner, I.A., Cullor, J.S., Galey, F.D., Sischo, W., Salman, M., Slenning, B., Erb, H. and Tyler, J.W. (1996) Alternatives for validation of diagnostic assays used to detect antibiotic residues in milk. J Am Vet Med Assoc 209, 46–52. Heeschen, W. (1993) Residues of antibiotics and sulfonamides in milk. In Inhibitory Substances in Milk-Current Analytical Practice. IDF Bull. no. 283 ed. FIL-IDF Secretariat General. pp. 11–15. Brussels: International Dairy Federation. International Dairy Federation (IDF). (1991) Detection and Confirmation of Inhibitors in Milk and Milk Products. IDF. Bull. no. 258. Brussels, Belgium: International Dairy Federation. International Dairy Federation (IDF) (1999) Guidance for the Standardized Evaluation of Microbial Inhibitor Test. IDF Standard no. 183. Brussels, Belgium: International Dairy Federation. Koenen-Dierick, K and De Beer, J.O. (1998) Optimization of an antibiotic residue screening test, based on inhibition of Bacillus subtilis BGA, whit experimental design. Food Addit Contam 15, 528–534. Mu¨ller, F. and Jones, A. (1993) BR-Test and BRT-AS methods. In Inhibitory substances in Milk-Current Analytical Practice. IDF Bull. no. 283 ed. FIL-IDF Secretariat General. pp. 24–28. Brussels: International Dairy Federation.

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Renard, L., Moulin, G. and Sanders, P. (1992) Using experimental design to optimize a microbial diffusion assay. J Assoc Off Anal Chem Int 75, 1045–1048. SAS. (2001) SAS Users Guide: Statistics Version 9.1. Cary: SAS Institute Inc.

Penicillin detection in milk

Suhren, G., Reichmuth, J. and Walte, H.G. (1996) Detection of b-1actam antibiotics in milk by the Penzym-test. Milchwissenschaft 51, 269–273.

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