Predictive Models for Growth of Foodborne Pathogenic Spore-Formers at Temperatures Applicable to Cooling of Cooked Meat
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1 H O T T O P I C S I N M E A T P R O C E S S I N G Predictive Models for Growth of Foodborne Pthogenic Spore-Formers t Tempertures Applicble to Cooling of Cooked Met Vijy K. Junej 54 Abstrct Indequte cooling of foods in retil food opertions is mjor sfety problem. Accordingly, the objectives of these studies were to determine sfe cooling rte for cooked beef nd develop models to predict the germintion, outgrowth nd lg (GOL), nd exponentil growth rtes (EGR) of Clostridium perfringens nd from spores. C. perfringens nd C. botulinum growth from spores ws not observed t temperture of < 15 _C or > 51_ C nd < 12 _C or > 48_C, respectively, for up to three weeks. First, we demonstrted the effectiveness nd vlidity of squre- root model under non-isotherml conditions. Next, we developed two models, one ech for C. perfringens nd proteolytic C. botulinum, to predict their growth from spores t tempertures pplicble to the cooling of cooked met. It ws found tht for C. perfringens, the use of the logistic function provided better prediction of reltive growth thn the use of the Gompertz function. For C. botulinum, growth curves were determined by fitting Gompertz functions to the dt. From the prmeters of the Gompertz or logistic function the growth chrcteristics, GOL times nd EGR, were clculted. These growth chrcteristics were subsequently described by Rtkowsky functions using temperture s the independent vrible. By pplying multivrite sttisticl procedures, the stndrd errors nd confidence intervls were computed on the predictions of reltive growth for given temperture. Closed form V. K. Junej Food Sfety Reserch Unit Estern Regionl Reserch Center, USDA-ARS 600 Est Mermid Lne, Wyndmoor, PA USA Phone: ; Fx: E-mil: vjunej@rserrc.gov Mention of brnd or firm nmes does not constitute n endorsement by the U.S. Deprtment of Agriculture bove others of similr nture not mentioned. Proceedings of the 54th Reciprocl Met Conference (2001) equtions were developed tht llow prediction of growth for generl cooling scenrio. The predictive models should id in evluting the sfety of cooked product fter cooling nd thus, with the disposition of products subject to cooling devitions. Introduction Clostridium perfringens nd C. botulinum re nerobic, grm-positive, spore-forming, rod-shped, bcteri. C. perfringens continues to remin mjor cuse of foodborne illness which results fter the ingestion of lrge number of vible vegettive cells which hve grown in the implicted met or poultry product. C. botulinum is the most hzrdous spore-forming foodborne pthogen becuse it produces dedly neurotoxic protein, known s botulinum neurotoxin, which cuses neuroprlytic disese known s botulism. Improper storge nd/or indequte cooling prctices in retil food opertions hve been cited s cuse of food poisoning for 97% of C. perfringens nd 34% of C. botulinum outbreks (Ben nd Griffin 1990). Such outbreks clerly stress the importnce of cooling foods quickly fter cooking. The time/temperture complince guidelines for cooling cooked met nd poultry products recommends tht the mximum internl temperture should not remin between 130F (54.4C) nd 80F (26.7C) for more thn 1.5 h nor between 80F (26.7C) nd 40F (4.4C) for more thn 5 h (USDA 1999). The U. S. Food nd Drug Administrtion (FDA) Division of Retil Food Protection recognized tht indequte cooling ws mjor food sfety problem nd estblished recommendtion tht ll food should be cooled from 60 to 21C (140 to 70F) in 2 h nd from 21 to 5C (70 to 41F) in 4 h (FDA Code 1999). The im of the present work ws to cquire quntittive dt on the growth from spores of C. perfringens nd C. botulinum over the entire growth temperture rnge which foods must pss through during cooling fter cooking nd developed models to predict the reltive growth of the pthogens from spores t tempertures relevnt to the cooling of cooked products.
2 Mterils nd Methods Test Orgnisms nd Spore Production Three strins of Clostridium perfringens, NCTC 8238 (Hobbs serotype 2), NCTC 8239 (Hobbs serotype 3), nd NCTC (Hobbs serotype 13) nd two strins ech of Proteolytic C. botulinum type A nd B strins were used in this study. Clostridium perfringens spore were produced in Duncn nd Strong sporultion medium s described previously (Junej et l. 1993). Proteolytic C. botulinum type A nd B spores were prepred by nerobiclly growing ech strin in BAM broth (Huhtnen 1975) t 35 C for 3 weeks. Ech spore preprtion ws stored t 4 C in sterile distilled wter. Spore popultion ws enumerted by spirl plting (Spirl Biotech, Bethesd, MD; Model D) pproprite dilutions (in 0.1% peptone wter), in duplicte, on tryptose-sulfite-cycloserine gr without cycloserine, i.e., SFP gr for C. perfringens or Reinforced clostridil medium (RCM) for C. botulinum followed by incubtion of pltes nerobiclly for 48 h t 35 C. A spore cocktil ws prepred immeditely prior to experimenttion by mixing equl numbers of spores of C. perfringens (hetshocked, 20 min/ 75 C) or C. botulinum (het-shocked, 10min/ 80C) from ech suspension. Smple Preprtion nd Inocultion Cooking nd Cooling Procedures Duplicte 3 g ground beef smples were septiclly weighed into cm sterile whirl-pk smpling bgs (Model B736, NASCO Modesto, CA) nd inoculted with hetshocked C. perfringens or C. botulinum spore cocktil so tht the finl concentrtion of spores ws pproximtely 1.5 log10 cfu/g. Therefter, the bgs were mnully mixed to ensure even distribution of the orgnisms in the met smple. The bgs were evcuted to negtive pressure of 1,000 millibrs nd het seled using Multivc Model A300/16 pckging mchine (Germny). Rcks holding the ground beef smples were fully submerged in 4.4 C wter in wter circulting bth (Excl, Model Ex-251HT, NESLAB Instruments, Inc., Newington, NH). To initite cooking, the bth temperture ws rised in liner fshion to 60 C within 1 h. The cooling study ws performed through the temperture rnge of 54.4 C to 7.2 C by dding ice to the stirred wter bth t vrying rtes in order to simulte the desired cooling rte (Tble 1). Growth Medium, Inocultion nd Smpling Trypticse-peptone-glucose-yest extrct (TPGY) contining (% w/v): 5% Trypticse; 0.5% peptone 2% yest extrct; 0.1% cysteine hydrochloride (Sigm Chemicl Compny, Sint Louis, MO); nd 0.4% dextrose ws used for determintion of growth rtes of C. perfringens. The medium ws dispensed in 50 ml portions into 250 ml trypsinizing flsks equipped with rubber septum inserted in the side rm smpling port, nd sterilized by utoclving. For C. botulinum, Reinforced clostridil medium (RCM; Difco) ws used for determintion of growth rtes. The medium (50 ml) ws dispensed in tubes nd sterilized by utoclving. The medium ws supplemented with oxyrse (0.1 ml/5 ml broth medium) nd then incubted t 35 C for 30 min prior to the experiments. Ech flsk/tube received 0.5 ml of the het-shocked spores to obtin n initil count of bout 3-4 log10 spores/ml of the growth medium. The flsks were then flushed with sterile N2 for 10 min nd seled with rubber stopper. All smples were incubted t tempertures rnging from C (2 C increments). Smples were withdrwn periodiclly, seril dilutions mde in 0.1% peptone wter (wt/vol) (supplemented with oxyrse, 0.1 ml/ 5 ml, for C. botulinum), nd then surfce plted with Spirl plter (Model D, Spirl Biotech, Bethesd, MD) onto pproprite medi mentioned bove. The totl C. perfringens/c. botulinum popultion ws determined fter 48 h of incubtion t 37 C in Bctron nerobic chmber (Sheldon Mnufct. Inc., Cornelius, OR). Results nd Discussion When hot cooked food is llowed to cool, the temperture must pss through rnge tht is fvorble for pthogenic spore germintion nd multipliction of the vegettive cells. Sfe nd hzrdous cooling times nd tempertures for cooked ground beef contining C. perfringens spores re shown in Tble 1. When C. perfringens spores in cooked ground beef were cooled from54.4 to 7.2 C in 12 h, nd 15 h, no out- TABLE 1. Sfe nd Hzrdous Cooling Times nd Tempertures for Cooked Ground Beef Contining C. perfringens Spores Elpsed Cooling time-temperture 54.4 to 7.2 C 54.4 to 7.2 C Time (h) in 15 h in 18 h b Sfe cooling time b Hzrdous cooling time 54th Annul Reciprocl Met Conference 55
3 growth of the spores ws observed. However, C. perfringens spores germinted nd multiplied when 18 h cooling time ws followed. Rpid growth occurred between 22.1 C (7 h) nd 15.6 C (10 h); the genertion time ws 25.5 min (Junej et l. 1994). For generic bcteri, it hs been found by reserchers (Rtkowsky et l. 1983) tht the squre root of the exponentil growth rte, k, s the dependent vrible, nd the most generl form of the Rtkowsky model, k 1/2 (T) = (T Tmin)(1 exp(b(t Tmx)) (1) where, b, Tmin, nd Tmx, re unknown positive prmeters, is usully either 1 or ½, provides good sttisticl fit. we demonstrted the effectiveness nd vlidity of this squreroot model in predicting spore outgrowth during cooling(figure 1). In similr study, when ground beef smples inoculted with spores of C. botulinum were cooled from 54.4 to 7.2 C using cooling times vrying from 6 to 21 h, spores germinted nd grew, nd the popultion densities incresed by 1 log unit in 21 h (Junej et l.1997). Fitting Growth Curves The growth of n orgnism s function of time, cn be described by L(t) = A + (P A)f(t M,B) where L(t) is the common logrithm of N(t), the number of orgnisms t time t, f(t M, B) is non- decresing function of time between 0 nd 1, M nd B re non-negtive prmeters tht describe the slope nd loction of the curve long the t- xis nd re functions of the reltive growth rte nd the GOL time, A is n symptotic minimum vlue nd P is n symptotic mximum vlue nd represents the mximum popultion density. For exmple functions tht cn be used for f(t M, B) re the Gompertz function: g(t M, B) = exp( exp( B(t-M)), or the logistic function: h(t M, B) = 1/(1+exp( B(t M))). The concern is to limit the reltive growth of C. perfringens to no more thn certin mount, for exmple, 10-fold (1 log10) (USDA 1996). For C. perfringens, our dt nlysis did show tht the use of the Gompertz function provided, on the verge, better predictions of reltive growth for the low tempertures (< 22 C) thn use of the logistic function, but for tempertures bove 22 C (>25 C), on the verge, the logistic ws better in the primry region of concern. Thus, for predicting reltive growth s function of time nd temperture, the logistic function is used. For C. botulinum, the verges of the residuls (observed minus predicted reltive growth) were: using the logistic function nd using the Gompertz function. Thus, the Gompertz function is used for modeling the reltive growth. From estimtes of M nd B, estimtes of GOL time nd the exponentil growth rte, EGR, were computed. The exponentil growth rte, EGR, is defined to be the mximl reltive growth rte, d(l(t))/dt, with units log10(cfu/ml)/h (Gibson et l. 1988; McKeekin et l. 1993). The GOL time is defined s the vlue of time t the point of intersection of the line contining the point (M, L(M)) with slope equl to the exponentil growth rte nd the horizontl line t L(0) (McKeekin et l. 1993). The growth chrcteristics, EGR nd GOL, for the Gompertz function, g(t), cn be expressed s: egr =B(P A)/e GOL = M + (e g(0) 1)/B (3) TABLE 2. Estimted GOL Times (h) nd Exponentil Growth Rte (log10(cfu/ml)/h) of Clostridium perfringens in TPGY Broth for Gompertz nd Logistic Curves; nd in RCM broth for Gompertz Curves Approximte Exponentil GOL time Approximte growth rte Exponentil growth Temperture Gompertz GOL time logistic Gompertz rte logistic Clostridium perfringens
4 TABLE 3. Estimtes, Stndrd Errors nd 95% Confidence Intervls of Prmeters Used for Estimting Growth Chrcteristics Prmeter Estimte Stndrd error Lower limit b Upper limit b b g bg Tmin_C c Tmx_C b1 c g bg c Tmin c Tmx /GOL 1/2 = l(t-tmin)(1-exp(bl(t-tmx)) ½, where GOL is the germintion, outgrowth nd lg time (h), EGR 1/2 = g(t-tmin)(1-exp(bg(t-tmx)) ½, where EGR is exponentil growth rte(log10(cfu/ml)/h). b Confidence limits computed with 11 degrees of freedom. c Bsed on estimte of nturl log trnsformtion, to ssure positive confidence limits. where e=exp(1), while those for the logistic function, h(t), cn be expressed s: 1/GOL 1/2 = l(t Tmin)(exp(bl(T Tmx)) 1/2 (4) EGR 1/2 = g(t Tmin)(exp(bg(T Tmx)) 1/2 The estimted vlues of GOL nd EGR, ssuming A = log10(n0) (Gibson et l. 1988), derived from the experiments, using Gompertz nd logistic growth curves, re presented in Tble 2. As cn be seen from Tble 2, the estimted vlues of GOL time nd EGR re similr for the logistic nd Gompertz functions for C. perfringens. TABLE 4. Men of Estimted GOL Times (h) nd Exponentil Growth Rte, EGR, (log10(cfu/ml)/h) of Clostridium perfringens in TPGY Broth, nd Corresponding Predictions from Regressions Temperture C Estimte of Predicted Stndrd error Estimte of Predicted Stndrd error Correltion of men GOL GOL of GOL Prediction men EGR EGR of EGR Prediction EGR nd GOL Clostridium perfringens Germintion, outgrowth nd lg. 54th Annul Reciprocl Met Conference 57
5 Modeling Growth Chrcteristics The bove equtions pply for constnt temperture. However, for cooling scenrio, the temperture would be chnging, so tht, for predicting the mount of reltive growth, N(t)/N0, it is necessry to express the growth chrcteristics: GOL nd EGR, s functions of temperture. For modeling the growth chrcteristics, GOL nd EGR, there re two equtions with 6 unknown prmeters, l, bl, g, bg, Tmin, nd Tmx. egr = B(P A)/4 GOL = M + (4h(0) 2)/B (5) For ech temperture, the mens of the estimted GOL times nd exponentil growth rtes were clculted nd used to determine unknown prmeters (Tble 3 & 4). The regression nlyses were performed on the mens which could resonble be ssumed to be independent nd closer to hving norml distribution thn the individul replicte mesurements. Using the men vlues rther thn the individul replicte vlues helps simplify clcultions of stndrd errors nd confidence intervls. We found tht some of the experimentlly determined vlues were outside of the computed 95% confidence intervl. While resonble greement between the predicted nd observed trnsformed vlues ws noticed, there re lrge stndrd errors of prediction of GOL time t tempertures ner Tmin nd Tmx. To help ssure estimtes of reltive growth tht would provide n dequte mrgin of public sfety, upper confidence limits of growth should be used. In summry, this pper presents Rtkowsky type equtions (models) for predicting the effect of temperture on GOL nd EGR of C. perfringens nd C. botulinum during cooling of certin cooked met products. From these equtions nd ssumptions, the expected growth tht would occur with the chnging tempertures during cooling of met products cn be clculted. Reserch is being plnned to vlidte ssumptions nd equtions presented in this pper. References Ben, N.H.; Griffin, P.M. 1990, Food borne disese outbreks in the United Sttes, : pthogens, vehicles, nd trends. Journl of Food Protection 53, FDA Division of Retil Food Protection, 1997, Food Code. U.S. Deprtment of Helth nd Humn Services, Public Helth Service. Food nd Drug Administrtion, Pub. No. PB Wshington, DC. Gibson, A.M; Brtchell, N.; Roberts, T.A. 1988, Predicting microbil growth: Growth responses of slmonelle in lbortory medium s ffected by ph, sodium chloride, nd storge temperture. Interntionl Journl of Food Microbiology 6, Huhtnen, C.N. 1975, Some observtions on perigo-type inhibition of in simplified medium. Journl of Milk Food Technology 38, Junej, V.K.; Cll, J.E.; Miller, A.J. 1993, Evlution of methylxnthines nd relted compounds to enhnce Clostridium perfringens sporultion using modified Duncn nd Strong medium. Journl of Rpid Methods Automtion Microbiology 2, 203_218. Junej, V.K.; Snyder O.P.; Cygnrowicz-Provost, M. 1994, Influence of cooling rte on outgrowth of Clostridium perfringens spores in cooked ground beef. Journl of Food Protection 57, Junej, V.K.; Snyder, O.P., Jr.; Mrmer, B.S. 1997, Potentil for growth from spores of Bcillus cereus nd nd vegettive cells of Stphylococcus ureus, Listeri monocytogenes, nd Slmonell serotypes in cooked ground beef during cooling. Journl of Food Protection 60, McMeekin, T.A.; Olley, J.N.; Ross, T.; Rtkowsky, D.A. 1993, Predictive Microbiology: Theory nd Appliction, J. Wiley & Sons, Inc., New York. Rtkowsky, D.A.; Lowry, R.K.; McMeekin, T.A.; Stokes, A. N.; Chndler, R.E. 1983, Model for bcteril culture growth rte throughout the entire biokinetic temperture rnge. Journl of Bcteriology 154, U.S. Deprtment of Agriculture, Food Sfety nd Inspection Service., 1996, Proposed Regultion, Performnce Stndrds for the Production of Certin Met nd Poultry Products, Federl Register (61 FR ). 58
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