Non-stochastic sampling error in quantal analyses for Campylobacter species on poultry products

ORIGINAL PAPER

Non-stochastic sampling error in quantal analysesfor Campylobacter species on poultry products

Peter Irwin & Sue Reed & Jeffrey Brewster & Ly Nguyen & Yiping He

Received: 29 September 2012 /Revised: 6 December 2012 /Accepted: 12 December 2012 /Published online: 5 February 2013# Springer-Verlag Berlin Heidelberg (outside the USA) 2013

Abstract Using primers and fluorescent probes specificfor the most common food-borne Campylobacter species(Campylobacter jejuni and Campylobacter coli), we devel-oped a multiplex, most probable number (MPN) assay usingquantitative PCR (qPCR) as the determinant for binomialdetection: i.e., number of p positive pathogen growthresponses out of n=6 observations each of 4 mL (V) perdilution. Working with media washes of thrice frozen-thawed chicken pieces which had been spiked with knownlevels ofC. jejuni and C. coli, we found that about 20% of theexperiments had a significant amount of error in the form ofeither greater than 25 % MPN calculation error (Δε) and/ora low apparent recovery rate (R less than 1=MPNobserved ÷ CFU spiked). Assuming such errors were exacer-bated by an excessively small n, we examined computer-generated MPN enumeration data from the standpoint ofstochastic sampling error (Δ) and found that such binomial-based assays behaved identically to Poisson-based methods(e.g., counting data) except that fewer technical replicates (n)appeared to be required for the same number of cells per testvolume (μ). This result implies that the qPCR detection-basedMPN protocol discussed herein should accurately enumerate atest population with a μ≥1 using n=6 observations per dilu-tion. For our protocol, this equates to ≥8 cells per 400–500 g

of sampled product. Based on this analysis, the error rate wesaw in spiked experiments (where μ >>1) implied a non-stochastic source. In other experiments we present evidencethat this source was, at least in part, related to the cell concen-tration step (i.e., centrifugation). We also demonstrate that theerror rate lessened (from ∼38 % to ∼13 %) at lowerCampylobacter levels (μ≤40) as would most likely exist innature. Using this protocol, we were able to quantify 14 to1,226 MPN per 450 g of naturally contaminated chicken forskinless pieces and 11 to 244 MPN per 450 g for wings,breasts, legs, and thighs (skin on) whereupon about 50 % ofthe 29 samples tested negative for both species. Four of thesechicken wash samples did have substantially lowerCampylobacter levels (1 to 6 MPN per 450 g) which mightbe better enumerated using a larger n. However, we estab-lished that the limit of quantification of this protocol dimin-ishes for n>6 because one is ever more diluting the sample, orlessening V, to achieve the requisite n.

Keywords Food-borne pathogens .Campylobacter .

Real-time PCR . qPCR .MPN

Introduction

It is sometimes only practicable to determine the concentrationor cell density (δ) of microorganisms in solution by diluting thesample to such an extent that only a small proportion oftechnical replicates (n) display positive growth (e.g., pj =number of positive growth samples out of n observations ateach jth dilution) [1–5]. This technique is sometimes referredto as the “dilution method” inasmuch as it involves dilutingan unknown test solution to δ extinction. In particular, thisprotocol comprises repeated samplings (typically n=3–5observations per dilution with a volume per observation or Vbetween 1 and 10 mL) [6–8] from a liquid source, making

Reference to a brand or firm name does not constitute endorsement bythe U.S. Department of Agriculture (USDA) over others of a similarnature not mentioned. The USDA is an equal opportunity provider andemployer.

P. Irwin (*) : S. Reed : J. Brewster : L. Nguyen :Y. He (*)Eastern Regional Research Center, Agricultural Research Service,Molecular Characterization of Foodborne Pathogens ResearchUnit, United States Department of Agriculture,600 E. Mermaid Lane,Wyndmoor, PA 19038, USAe-mail: [email protected]: [email protected]

Anal Bioanal Chem (2013) 405:2353–2369DOI 10.1007/s00216-012-6659-2

serial dilutions from these, distributing an aliquot of each ofthe jth dilutions into separate receptacles, incubating theseunder suitable growth conditions, and observing if any growthoccurs.

Another important step in the successful application ofthe dilution method enumeration protocol is obtaining astatistically cogent estimation of the most probable number(MPN) of organisms in the original undiluted sample. Forthis reason, the dilution method is most frequently simplyreferred to as “MPN.” The MPN enumeration technique hasa lower limit of detection than other microbiological meth-ods (e.g., colony counting) because it characteristically uti-lizes a greater volume per replicate. Thus, for i replicates perdilution, the relative sensitivity advantage of MPN over

colony counting isPniVi

� �MPN

� PniVi

� �CFU

∼80 if com-

paring the method described herein (for μ=1, V=4 mL, n=6) to that of a drop plate method (for μ=1, V=10 μL, n=30)[9, 10]. We use the Greek letter “μ” to symbolize thepopulation average number of either colony forming units(CFU) or MPN per V [10].

Typically in MPN assays, pj is determined as the numberof samples (out of n) per dilution which display visualturbidity or some other growth criterion. Because of this,the method is not very specific even if utilizing a growthmedium or conditions which are touted as specific for thetarget organism. Even when immunomagnetic bead-based(IMB) capture and concentration [11–14] is carried out,MPN enumeration is not specific due to the presence of alarge non-target microflora in the food matrix which non-specifically attaches to the IMBs [15, 16]. However, in thiswork we test an MPN protocol where pj is determined usinga real-time multiplex polymerase chain reaction, detectingtwo of the most commonly occurring Campylobacter spe-cies (Campylobacter jejuni , Campylobacter coli ;Campylobacter lari can also be simultaneously detected ifdesired) [17] associated with bacterial gastroenteritis [18].We also examine this Campylobacter qPCR-MPN protocolfor various types of error associated with sample manipu-lation and random sampling [19].

PCR is one of the most sensitive and reliable qualita-tive methods available for DNA [20] identification inas-much as it can theoretically detect one gene copy pervolume tested. With a well-designed set of primers, PCRcan be used to unambiguously [21] identify organismssuch as the 2-3 most common Campylobacter specieseven in problematic matrices [17, 22]. Most end-pointPCR users rely on the detection of the reaction’s ampliconwith gel electrophoresis and a set of molecular size-basedDNA standards. When detecting two or more organisms,the multiplex end-point PCR-based amplicons must besufficiently different in molecular size in order to resolvethem using gel electrophoresis [23]. Consequently, a PCR

product of appropriate size should be apparent only if thetarget DNA is present. The quantitative version of PCRis known as real-time or quantitative PCR (qPCR). Sincea qPCR-based multiplex procedure does not rely onmolecular size standards, primers can be designed with-out concern for differentiating product size because spe-cific amplicon detection relies on the emission of afluorophore attached to the probe. However, directqPCR-based quantification of pathogens in food samplesrequires a large value for n due to low pathogen con-centration and associated large standard deviations (forcounting data the population standard deviation=σ=

ffiffiffiμ

p)

[10]. Also, direct qPCR quantification is best performedwhen polymerase reaction efficiencies are observed forboth the unknown and standard solutions in order tocorrect for disparities [24]. While cultural enrichmentalone provides binomial (i.e., presence or absence) infor-mation of an unknown sample, all initial concentrationinformation is lost [17]. However, combining binomialqPCR detection with dilution to extinction provides thespecificity of PCR with the high sensitivity of MPN[25–27]. The earliest utilization of a combined PCR(end-point) with MPN procedure we have found concernedthe “counting” of Nitrobacter populations in soil [28]which was published in 1995. In the work herein, anMPN approach combined with multiplex qPCR detectionhas been developed for simultaneous quantification of C.jejuni and C. coli cells in food samples. Some of thebenefits as well as disadvantages of MPN methods are alsodiscussed in detail with regard to specific problems associatedwith food sampling.

Materials and methods

Campylobacter growth conditions

General microbiological conditions

All Campylobacter strains were routinely grown in Brucellabroth (Becton Dickinson Co., Sparks, MD, USA) at 42 °C ina microaerobic workstation (Don Whitley Scientific, Ltd.,Shipley, UK) containing 85 %N2, 10 % CO2, 5 % O2, and82 % relative humidity. To promote the growth ofCampylobacter in the presence of other food-borne organ-isms, which can occur in high numbers in various meatproducts [15], a Campylobacter selective enrichment medi-um was prepared by adding 25 mL of “laked” horse blood(Remel, Lenexa, KS, USA) to 500 mL Bolton broth(CM0983: Oxoid, Basingstoke, Hampshire, UK) amendedwith 5 mL Bolton broth selective supplement (SR0183E:Oxoid; 10 mg of cefoperazone, vancomycin, and trimetho-prim and 25 mg of cycloheximide).

2354 P. Irwin et al.

qPCR-MPN experimental protocol

Pure culture mixtures

qPCR-MPN enumeration was first tested with an idealCampylobacter system consisting of overnight cultures di-luted in 0.1 % buffered peptone water (BPW). The numberof Campylobacter CFUmL−1 was determined on Brucellaagar using the 6×6 drop plate method (7 μL per drop, n=12drops per dilution; μ≥ca. 20 counts per drop) [9]. The initialdilutions consisted of 1 mL each of C. jejuni and C. coliovernight cultures plus 8 mL of Brucella broth as diluent;for this set of experiments only, n=12 for each dilution.Thereafter, all 1:10 dilutions were made using 1 mL fromthe previous dilution+9 mL diluent. After thorough mixing,500 μL (V in MPN calculations) of each jth dilution’s (eachdilution factor=ϕj ; ϕ is typically 0.1 [1:10 serial dilutions],j=0, 1, 2, etc.) 12 replicates was added to 4.5 mL Brucellabroth distributed into sterile, 48-well (VWR Deep WellPlates, Model 82004-674, 5 mL per well capacity) plates,covered with autoclaved aluminum foil, and incubated for16 h in the microaerobic workstation. For qPCR determina-tion of positive ( pj ) growth, 200 μL of each dilution’sreplicates was sampled after thorough mixing, cells spundown, supernatant removed, and the pellet lysed with 20 μLof PrepMan Ultra (Applied Biosystems, Foster City, CA,USA) at ∼100 °C for 15 min. After spinning down thesolids, the supernatant (2 μL) from this process was usedfor qPCR detection of C. jejuni and C. coli.

Spiked or naturally occurring Campylobacter in chickenwash media

Specific experimental details for all qPCR-MPN chickenexperiments are provided in the “Discussion” section and/or table headings. However, in general, all spiking of chick-en washes, irradiated ground chicken washes or examinationof naturally contaminated intact chicken piece washes usedthe same physical layout: VWR 48-well growth plates, V=4 mL/well, using a Campylobacter selective enrichmentmedium as diluent. Conditions for the qPCR-MPN proce-dure for chicken samples (either spiked or naturally contam-inated) are alluded to as follows. Between 150–200 mL persample (400–500 g for intact chicken pieces or ∼50 g forground chicken) of either BPW or Campylobacter selectiveenrichment medium (± centrifugation experiments only)was used to detach any surface microbes. The culture me-dium/chicken mixtures were massaged ca. 2–4 min in ster-ile, 24 ounce, Whirl-Pak Filter Bags (eNasco, Modesto, CA)taking care not to puncture these containers with protrudingbones. The liquid samples were pipetted from the bags usingthe opposing side of the “finely perforated” polyethylenefilters, deposited into sterile bottles, spiked with known

amounts of Campylobacter, balanced and centrifuged (i.e.,cells concentrated) at 16,000×g for 15 min (∼10 °C). Thesupernatants were carefully removed and each pellet (mix-ture of organisms, suspended fats, proteins, and sundrydebris) was resuspended in 3 mL BPW or, for the “+ cen-trifugation” treatment combination, resuspended in its sur-rounding Campylobacter selective enrichment medium. Theγ-irradiation-sterilized ground chicken samples (∼50 geach) were manipulated with 150 mL BPW in plastic bagsand filtered through several layers of cheesecloth afterwhich approximately 120 mL, or more, of the original liquidwas collected, spiked with C. jejuni/C. coli, and balanced/centrifuged as above; after centrifugation, part of the resus-pended pellet (in 3 mL BPW) was then used for plating onsolid media. In all chicken experiments (except for the±centrifugation tests), once the pellets were as evenly dis-persed as possible, the volume was brought up to 30 mL(Vsample) with Campylobacter selective enrichment medium(this suspension represents dilution j=0 in the MPN) andvortexed approximately 60 s to suspend the heterogeneousmixture. A small fraction of this mixture (3 mL) was used tomake the 1:10 dilution (j=1) by adding 27 mL of theselective enrichment medium; serial dilutions were contin-ued to j=3 to 5, depending on the estimated level of con-tamination; for naturally contaminated samples the greatestdilution was j=3 (i.e., 10−3). Four mL of each ith technicalreplicate (i=1, 2, ⋯ , n=6) was placed into each receptacleof the 48-well plates, covered with aluminum foil, andincubated 16 h in the microaerobic chamber. For qPCRdetermination of pj , 200 μL of each dilution’s technicalreplicates was sampled after thorough mixing whereuponthe cells were spun down, supernatant removed, and thepellet lysed with 20 μL per observation of PrepMan Ultraat ∼100 °C for 15 min. After spinning down the solids, 2 μLof the supernatant was used for qPCR detection of C. jejuniand C. coli.

Multiplex qPCR

Multiplex qPCR (Applied Biosystems 7500 Real-Time PCRsystem) was used to determine the presence/absence (+/–) ofCampylobacter DNA. Accordingly, when there was enoughspecific probe-associated fluorescence (above baseline noise),the presence of the organism was confirmed. Typically, apositive response resulted in a threshold cycle number (CT)of approximately 20 (threshold set by the instrumental soft-ware). The number of these positive occurrences out ofn observations for each jth dilution is pj.

For specific detection purposes, the fluorescent probe (5′-FAM/3′-BHQ-1 and 5′-Quasar 670/3′-BHQ-2 fluorophores/quenchers for hipO and cdtA, respectively, BiosearchTechnologies, Novato, CA, USA) consisted of the fluoro-phore covalent ly at tached to the 5’ -end of the

Non-stochastic sampling error in quantal analyses 2355

oligonucleotide moiety and a quencher at the 3′-end.These probes work by annealing within one of thesingle-stranded DNA regions being amplified and, asthe Taq polymerase extends the primer (synthesizes thenew DNA strand), the 5′-3′ exonuclease activity of thepolymerase degrades the template-annealed probe, re-leasing the fluorophore which provides the specific fluo-rescent signal which is proportional to the number oftarget DNA copies synthesized. The nucleotide sequenceof all primers and probes used were provided previously[17]. The DNA target sequences consist of short regionswithin the hipO (124 bp product) and cdtA (111 bp) genesspecific for C. jejuni and C. coli, respectively [17]. C. larican also be simultaneously identified with this techniqueusing the pepT (86 bp) gene-associated primers and detec-tion probe (5′-VIC/3′-minor groove binding for pepT,Applied Biosystems) [17]; C. lari identification was notperformed in this work since none have been found in anychicken sample tested previously in our lab.

The PCR reaction mixture was prepared using 10 μLof 2× TaqMan Gene Expression Master Mix (AppliedBiosystems) plus 2 μL of the sample DNA, 0.4 μL ofeach primer/probe from a 10 μM stock solution, andPCR-grade water to bring the reaction mixture up to20 μL. Additionally, all reaction mixtures had ∼1,200copies of an Adenovirus DNA internal amplificationcontrol (IAC) [29] template added (detected using the5′-TAMRA/3′-BHQ-2 fluorophore/quencher; BiosearchTechnologies). This DNA was included to detect anyfalse-negative results. For instance, if no IAC probe’sfluorescence was observed during the PCR thermocy-cling process, one could conclude that the CampylobacterDNA extract contained an inhibitor of the polymerase.In this work all reactions showed a positive result forIAC amplification (CT∼30). DNA polymerase reactionswere performed using optically clear 96-well plates withthermo-cycler settings as follows: “hot-start” DNA po-lymerase activation at 95 °C for 10 min, 40 cycles ofdenaturing at 95 °C for 15 s and annealing and extension at60 °C for 1 min.

MPN calculations

In previous work [30] an MPN calculation was developedwhich takes advantage of the fact that the partial first deriv-ative (with respect to δ) of ANY continuous probability

distribution function ( @P d½ �@d =@dP d½ �) when divided by itself

(i.e.,@dP d½ � � P d½ �) results in a smooth curve (or straight lineif the function is symmetrical) which passes through zerowhen P d½ � is at its maximum. For this reason, the summationin Eq. 1 (Pb dj

� �=jth dilution’s binomial probability distrib-

ution function= Exp �Vfjd0½ �� n�pj × 1� Exp �Vfjd0½ �� pjn! ÷ n� pj

� �!pj!) across j dilutions would tend toward 0

as d0 (dj ¼ fjd0) approaches theMPN (or a negative numberif d0 is too large or positive if too small)

Xj

@djPb dj� �

Pb dj� � ¼

Xj

pj � nþ pjExp Vfjd0½ � � 1

Vfj ð1Þ

Our utilization of this concept involved adding the aboveoperation to an initial guess (d0;k¼0) by inducing the calcu-lation of a new value (d0;k¼1) which after each kth recursion,

must be closer to the MPN (= Vfjd0;final ; j dilutions, kiterations) per tested volume

d0;kþ1 ¼ d0;k

þ xkXj

pj � nþ pjExp Vfjd0;k� �� 1

!Vfj ð2Þ

Normally, convergence (i.e., left-hand side≅ right-handside) occurs within 20 iterations depending upon thecloseness of d0;k¼0 to d0;final . An empirical scaling factor

(xk =d1:760;k � 10 �0:798�0:0158 n½ �) [30] was used to adjust the

summation to an appropriate level during the first fewiterations to avoid over- or undershooting the MPN.

The calculated value for p at any particular f j is

pj;calc ¼ n 1� Exp �Vdj� �� ð3Þ

This pj;calc value was used to determine deviations fromideality at each jth dilution. The normalized sum of pj ’sdeviations from pj;calc across all the appropriate dilutions is ameasure of the MPN calculation error (Eq. 4)

Δ" ¼Xj

pj � pj;calc

pj;calcð4Þ

In the calculation of either MPN (Eq. 2) or Δ" (Eq. 4)only the last dilution where pj=n and the first dilutionwhere pj =0 are included. For example, with p0 throughp5=6, 6, 4, 1, 0, 0 only p=6, 4, 1, and 0 would beincluded in the calculations. There are numerous otherprocedures available for estimating MPN when utilizinga small n [3, 31–33] but all provide identical results tothe method used here. Computer-based techniques arepreferred over MPN tables [34] because they allow forgreater experimental flexibility inasmuch as the numberof observations (n) per dilution, the total number ofdilutions, and the volume (V) used per n can all bemodified as desired [31].


Statistical comparisons

Analysis of variance (AOV, randomized complete block designwith either 3 or 4 replicates per treatment) [35] was performedon all compared data (e.g., δ0,Δε, etc.). Each experimental setof observations were replicated threefold or fourfold. Statisticalcomparisons were only made to test if differences between 2simple treatments (e.g., + or − centrifugation, recovered MPNversus applied CFU, etc.) were likely due to the treatment inquestion as opposed to random variation. The probability thattwo treatment comparisons were equivalent (P) was calculatedin Microsoft Excel as “=F.DIST.RT(F-statistic, Treatmentdegrees of freedom, Error degrees of freedom).”

Results and discussion

The dilution method applied to pure culture mixtures of C.jejuni and C. coli

Working with highly diluted overnight cultures of C. jejuniand C. coli, we investigated the performance of the qPCRdetection aspects of our proposed MPN assay. Table 1shows results from 3 experiments from combined overnightcultures of C. jejuni (Exp. 1: δ0=4.60×10

8CFUmL−1; Exp.2: δ0=4.68×10

8CFUmL−1; Exp. 3: δ0=5.06×108CFU

mL−1) and C. coli (Exp. 1: δ0=6.50×108CFUmL−1; Exp.

2: δ0=2.30×108CFUmL−1; Exp. 3: δ0=3.25×10

8CFU

Table 1 qPCR-MPN enumeration of diluted overnight Campylobacter cultures

j Dilution Experiment 1 Experiment 2 Experiment 3 Meanp pcalc p pcalc p pcalc

Campylobacter jejuni

7 10−7 12 12.0 12 12.0 12 12.0

8 10−8 11 11.9 12 11.9 12 12.0

9 10−9 7 4.27 4 4.46 8 7.79

10 10−10 1 0.517 1 0.573 1 1.19

11 10−11 0 0.0527 0 0.0586 0 0.125

12 10−12 0 0.00528 0 0.00587 0 0.0126

Log[MPNmL−1]

8.94 8.99 9.32 9.09

: 14 % 7 % 3 % 8 %

Log[CFUmL−1]

8.66 8.67 8.70 8.68

R 1.91 2.09 4.14 2.72

Campylobacter coli

7 10−7 12 12.0 12 12.0 12 12.0

8 10−8 12 12.0 11 11.0 11 11.5

9 10−9 8 7.79 3 2.66 4 3.21

10 10−10 1 1.19 0 0.297 1 0.368

11 10−11 0 0.125 0 0.0300 0 0.0373

12 10−12 0 0.0126 0 0.00300 0 0.00374

Log[MPNmL−1]:

9.32 8.70 8.79 8.94

: 3 % 7 % 7 % 6 %

Log[CFUmL−1]:

8.81 8.36 8.51 8.56

R 3.22 2.18 1.92 2.44

Δε

Δε

Each experimental replicate consisted of separately inoculated cultures of C. jejuni (Exp 1, δj=0=4.60×108 ; 2, δ0=4.68×10

8 ; 3, δ0=5.06×108 CFU

mL−1 , respectively) and C. coli (Exp 1, δ0=6.50×108 ; 2, δ0=2.30×10

8 ; 3, δ0=3.25×108 CFUmL−1 ) incubated overnight in a microaerobic chamber.

Analysis of variance (randomized complete block design) was performed on both Log-transformed and standard starting culture concentration (i.e., δj=0)data. Statistical comparisons were made to test if differences between observedMPN and inoculated CFUwere significant. The recovery rates (R) are theratio of non-Log transformed MPN mL−1 : CFUmL−1 data. P (probability that MPN-based and CFU-based Log10[δ0] values were equivalent) wascalculated in Microsoft Excel as “=F.DIST.RT(F-statistic, Treatment degrees of freedom=1, Error degrees of freedom=2).” δj=1 was created bymixing 1 mL of each species’ δ0 into 8 mL of Brucella broth; all remaining standard Campylobacter solutions were simply 1:10 serial dilution of δ1.For C. jejuni, comapring the qPCR-MPNmethod (MPNmL−1 ) with 6×6 drop plate enumeration (CFUmL−1 ), P = 0.615 (Log) or 0.154 (non-Log) andfor C. coli comparisons, P = 0.0311 (Log) or 0.225 (non-Log), respectively


mL−1) which were assessed using n=12 observations perdilution. AOV (randomized complete block design) [35]was performed on Log-transformed starting culture concen-tration (i.e., δ0) data. Comparisons were made to test ifdifferences between recovered MPN and applied CFU weresubstantial; we found that for C. jejuni, P=0.0615 and for C.coli, P=0.0311. Thus, for either organism there is a greaterthan 90 % chance that MPN enumeration results in signif-icantly better survival characteristics of the target organisms.In these somewhat idealized results, Δε (Eq. 4) was rela-tively small (C. jejuni: xΔ" =8±6 %; C. coli: xΔ" =6±3 %)and the recovery rate (R=recovered MPN ÷ applied CFU)was relatively large (C. jejuni: R varied from 1.91 to 4.14with xR=2.72±1.24; C. coli: R varied from 1.92 to 3.22 withxR =2.44±0.692). In these, and all the remaining qPCR-MPN experiments we discuss in this work, it is of value tocompare, line by line, the observed pj with the pcalc valueswhich result in a near-zero value for Eq. 1. These data arenot typically shown in MPN results but they are important inunderstanding the quantitative meaning of the observations.Accordingly, we see in Table 1 (as well as all others herein)that it does not require much of a disagreement betweenobserved and calculated values of p to produce a fairly largeΔε. In fact, the expected value of Δε due to calculation-based errors (because pcalc is real and pobs is an integer) isusually≤15 % of the j=0 concentration. However, when Δεis substantially greater than 25 %, we can safely assume thatmechanisms which make one, or more, of the MPN assump-tions (discussion in next section) false are at work. Therecovery rates (MPN observed ÷ CFU applied), or Rvalues, we observe are also subject to sampling error aswell as issues related to the physiology of the organismbeing enumerated using the MPN protocol. Table 1results show that using qPCR detection of pj in anMPN assay is actually an improvement over colonycounting methods because of the high target specificityof PCR [17] and relatively high recovery rate (R greaterthan 1). However, even in this ideal system, the Rvalues we see are fairly variable experiment to experi-ment (e.g., vary between 1.91 and 4.14).

The dilution method applied to Campylobacter-spikedchicken wash media

Table 2 displays qPCR-MPN results for spiked (6.75×103

CFU of C. jejuni: Table 2a; 6.68×103CFU of C. coli:Table 2b) chicken washes comparing both Δε and R of thetwo target organisms with or without centrifugation. Thecomparisons in Table 2 specifically address whether or notthe resuspension of a pellet after centrifugation causes great-er result heterogeneity. We present the C. jejuni (Table 2a)and C. coli (Table 2b) results in separate tables but in factthese organisms were multiplex-detected from the same

volumes and experimentally replicated thrice. For the±cen-trifugation comparisons only, Campylobacter selective en-richment medium (recovered volume: 1=133 mL; 2=139 mL; 3=141 mL) was utilized as the washing medium.These samples (336, 346, and 412 g for replicates 1, 2, and3) of commercially available chicken legs (with skin) werefrozen and thawed three separate times in order to minimizethe natural levels of Campylobacter contamination. For thewashes we used the Campylobacter selective enrichmentmedium directly so that each wash could be split into thetwo treatments: either “+” or “−” centrifugation. Thus thepellets from the “+ centrifuging” samples were resuspendedin the supernatant while the “− centrifuging” treatmentswere used directly. For C. jejuni, 2 of the 6 sets of dilutionshad largeΔε (33 % and 67 %) with both occurring in the “+centrifuging” treatment. For C. coli also, 3 of the 6 sets hadlarge Δε (26 %, 35 %, and 55 %) but one occurring in “–”and the other 2 in the “+ Centrifuging” treatment. While theR values were mostly higher for the non-centrifuged set ofobservations, they were not statistically significant becauseof between replicate variability. A similar set of experiments(Table 3) were performed (replicate: 1=474 g, 2=477 g, 3=474 g, 4=464 g; recovered volume: 1=187 mL, 2=186 mL,3=187 mL, 4=185 mL) also on thrice frozen-thawed chick-en legs but using much lower spiking concentrations(135 CFU C. jejuni: Table 3a; 304 CFU C. coli: Table 3b).In these experiments only 2 out of 8 observations showedlarge Δε (both 47 % for replicate 1: C. jejuni and C. coli “–”treatments) and small recovery rates (0.579 for replicate 1 oftheC. coli “–” treatment and 0.937 for replicate 4 of theC. coli“+” treatment). As in Table 2, there was no significant differ-ence between the±centrifuge treatments. Upon performingAOV (comparingΔε and R for C. jejuni and C. coli) on datain Tables 1–3, we found that there were no statistically signif-icant differences between the two species of Campylobacterwhereupon P=0.978 (xΔ" =17.6 % and 17.8 % for C. jejuniand C. coli, respectively) for all Δε and P=0.663 (xR =1.74and 1.94 for C. jejuni and C. coli) for all R; in this particularcase, P is the probability that all C. jejuni and C. coli resultswere the same. Because of this outcome, the species-specificdata in Tables 2 and 3 could be pooled together to, essentially,double the total number of observations.

We should mention that other PCR-MPN protocols (forCryptosporidium parvum oocyst in environmental samples;using n=3, V=10 mL from IMB-concentrated samples) [6]have shown much worse R values (R=0.15 to 0.43) thanthose reported herein and were based on less troublesomesamples (i.e., no lipids or dissolved proteins). These obser-vations by Carey and coworkers appear to be related to theirIMB cell concentration step (our cell concentration step iscentrifugation) and is perhaps associated with poor captureefficiencies which could be related to the fact that C. parvumoocysts are known to be difficult to separate from one


Table 2 Thrice frozen-thawed chicken leg (rep, 1=336 g; 2=346 g; 3=412 g) samples which were washed (4minmassage) withCampylobacterselective enrichment medium (recovered volume: 1=133 mL; 2=139 mL; 3=141 mL); each of the recovered volumes was spiked with

6.68×103CFU C. jejuni (Table 2A) as well as 6.75×103CFU C. coli(Table 2B) for testing the significance of sample concentration via cen-trifugation upon recovery of spiked cells using a qPCR-MPN method fora relatively high organism density


aCampylobacter jejuni−Centrifuging

1 0.1 6 6.00 6 6.00 6 6.00

2 0.01 6 5.40 6 6.00 5 4.96

3 0.001 0 1.23 2 3.62 1 0.97

4 0.0001 0 0.137 2 0.531 0 0.104

5 0.00001 0 0.0138 1 0.0553 0 0.0105

Log[MPN mL−1]: 1.76 2.36 1.64 1.92

%41%1%52%51:

Log[MPN per sample]: 3.88 4.51 3.79 4.06

R 1.14 4.84 0.927 2.30

1 0.1 6 6.00 5 5.98 6 6.00

2 0.01 5 5.32 5 2.66 6 5.98

3 0.001 2 1.17 2 0.341 2 5.00

4 0.0001 0 0.129 0 0.0350 1 0.330

5 0.00001 0 0.0130 1 0.00351 0 0.0338

Log[MPN mL−1]: 1.74 1.17 2.15 1.68

%73%3%76%01


R 1.08 0.306 2.99 1.46

bCampylobacter coli−Centrifuging

1 0.1 6 6.00 6 6.00 6 6.00

2 0.01 6 5.72 6 5.96 6 5.72

3 0.001 1 1.59 0 2.33 1 1.59

4 0.0001 0 0.182 2 0.288 0 0.182

5 0.00001 0 0.0185 1 0.0294 0 0.0185

Log[MPN mL−1]: 1.89 2.09 1.89 1.95

%61%8%53%7


R 1.51 2.54 1.61 1.89

Campylobacter coli+Centrifuging

Campylobacter jejuni+Centrifuging

1 0.1 6 6.00 5 5.92 6 6.00

2 0.01 5 4.50 4 2.12 5 4.96

3 0.001 0 0.777 2 0.256 1 5.00

4 0.0001 0 0.0826 0 0.0261 0 0.104

5 0.00001 0 0.00831 0 0.00261 0 0.0105

Log[MPN mL−1]: 1.54 1.04 1.64 1.41

%13%62%55%11


R 0.681 0.225 0.917 0.61

:

:

:

Δε

Δε

Δε

Δε

The pellets of the “+ centrifuging” samples were resuspended in the supernatant while the spiked recovered washes of the “− centrifuging” wereused directly without centrifugation. Analysis of variance (randomized complete block design) was performed on the Log-transformed j=0 dilutionMPN calculation (normalized as MPN per sample). P was calculated using Microsoft Excel as “=F.DIST.RT(F-statistic, Treatment degrees offreedom=1, Error degrees of freedom=2)” and is presented for both Log-transformed data and R (the probability for R is exactly equal to the non-Log-transformed MPN data for obvious reasons). MPN per Sample=MPN mL-1×Vspiked. For C. jejuni −/+ Centrifuation comparisons of Log[MPN mL−1 ] results, P = 0.682 and for R, P = 0.706; for C. coli −/+ Centrifuation comparisons, P = 0.164 and for R, P = 0.132


Table 3 Thrice frozen-thawed chicken leg (rep, 1=474 g; 2=477 g; 3=474 g; 4=464 g) samples which were each washed (4 min massage)with Campylobacter selective enrichment medium (recovered volume,1=187 mL; 2=186 mL; 3=187 mL; 4=185 mL); each of the recovered

volumes was spiked with 135 CFU C. jejuni (Table 3a) as well as304 CFU C. coli (Table 3b) for testing the significance of sampleconcentration via centrifugation upon recovery of spiked cells using aqPCR-MPN method for a relatively low organism cell density

j Dilution Experiment 1 Experiment 2 Experiment 3 Experiment 4 Meanp pcalc p pcalc p pcalc p pcalc

aCampylobacter jejuni−Centrifuging

0 1 5 5.86 6 5.98 6 6.00 6 5.98

1 0.1 4 1.88 2 2.59 3 3.35 2 2.59

2 0.01 1 0.221 1 0.330 1 0.471 1 0.330

3 0.001 0 0.0225 0 0.0338 0 0.0489 0 0.0338

MPN mL−1: 0.940 1.41 2.04 1.41 1.45

Δε

Δε

Δε

: 47 % 15 % 9 % 15 % 22 %

MPN per sample: 176 263 382 262 271

R 1.30 1.95 2.83 1.94 2.00

Campylobacter jejuni+Centrifuging

0 1 6 5.98 6 5.89 6 5.91 6 5.89

1 0.1 2 2.59 1 1.99 2 2.07 1 1.99

2 0.01 1 0.330 1 0.236 0 0.249 1 0.236

3 0.001 0 0.0338 0 0.0241 0 0.0254 0 0.0241

MPN mL−1: 1.41 1.00 1.06 1.00 1.12

: 15 % 23 % 5 % 23 % 16 %

MPN per sample: 264 187 198 186 209

R 1.96 1.38 1.47 1.38 1.55

bCampylobacter coli−Centrifuging

0 1 5 5.86 6 6.00 6 6.00 6 6.00

1 0.1 4 1.88 5 5.58 3 4.97 2 3.61

2 0.01 1 0.221 3 1.40 1 0.968 1 0.527

3 0.001 0 0.0225 0 0.158 0 0.105 0 0.0549

MPN mL-1: 0.940 6.65 4.40 2.30 3.57

: 47 % 18 % 1 % 9 % 19 %

MPN per sample: 176 1,237 822 425 665

R 0.579 4.08 2.71 1.40 2.19

Campylobacter coli+Centrifuging

0 1 6 6.00 6 6.00 6 6.00 6 5.99

1 0.1 6 5.92 6 5.73 3 3.88 3 2.76

2 0.01 2 2.09 1 1.60 2 0.593 0 0.358

3 0.001 0 0.251 0 0.183 0 0.0622 0 0.0368

MPN mL-1: 10.7 7.74 2.60 1.54 5.64

: 5 % 14 % 22 % 7 % 12 %

MPN per sample: 1,998 1,439 487 284 1,052

R 6.58 4.74 1.60 0.937 3.47

Δε

The pellets of the “+ centrifuging” samples were resuspended in the supernatant while the spiked recovered washes of the “− centrifuging” wereused directly without centrifugation. Analysis of variance (randomized complete block design) was performed on the j=0 dilution MPN calculation(normalized as MPN per sample). P was calculated using Microsoft Excel as “=F.DIST.RT(F-statistic, Treatment degrees of freedom=1, Errordegrees of freedom=2).”MPN per Sample=MPN mL−1 ×Vspiked; For C. jejuni −/+ Centrifuation comparisons of either MPN mL−1 or R results, P= 0.352; for C. coli −/+ Centrifuation comparisons, P = 488


another, or from surfaces, due to a “fluffy layer of glyco-proteins” [36]. This is yet another example of how organismrecovery can be undermined due to aspects of the targetorganism’s innate physiology. Like most of our observationsfor Campylobacter, other workers (for Listeria monocyto-genes in various foods; using n=3, V=10 mL) [7] haveshown good recovery with R values ranging from 0.94 formilk to 2.3 for pork pâté while other foods (e.g., fresh cheese,ice cream, ground beef) had recovery rates substantially lessthan one. In this case, the recovery rates are sample matrixdependent in a rather unpredictable way. Recovery rate het-erogeneity was also seen in a PCR-MPN study with Vibrioparahaemolyticus on inoculated shrimp (n=5 with V=1 mL)[8]. In this case, recovery was complicated by having toremove attached organisms from the shrimp surface.

To more thoroughly examine the effect of pellet resus-pension on our experimental measures of sampling error(Δε and R), we combined all results from Tables 2 and 3to compare only the±centrifugation treatments (n=14). Tominimize variation even more we also deleted the 2 obser-vations on either extrema (i.e., the two highest and the twolowest values) making n=10. Even with this manipulation,we found that the uncentrifuged sample’s Δε values werenearly equivalent (P=0.471) to those of the centrifugedsamples (– centrifuge xΔ" =15.6; + centrifuge xΔ" =18.4;experimental sx =2.69 %) [35]. However, when the twolargest and two smallest R values were similarly expungedand AOV performed, we found that the xR values, whichshould be inversely proportional to relative sampling error,did show greater differences (P=0.128) between thespiked+centrifuge chicken leg washes ( xR =1.44±0.201)and the – centrifuge (xR=1.89±0.201) samples than for theaveraged Δε results. As a consequence, the R values tended(i.e., 13 % chance that they were equivalent) to be smaller inthe − centrifuge samples probably due to the difficulty inevenly dispersing the pellets. This trend is confirmed by thefact that, generally, the recovery rate values in the spikedirradiation-sterilized ground chicken washes were egre-giously poorer (combined C. jejuni and C. coli xR =0.420;Table 4) than in the spiked whole chicken piece washes (xR=1.93; combined Tables 2 and 3) presumably because theground chicken washes had much larger pellet sizes (visu-ally twofold to fourfold) than the equivalent centrifugedwhole piece washes’ pellets. Part of the resuspended pelletsfrom the spiked ground chicken washes were also directlyspread-plated for comparison of recoveries via both MPNand microaerobic plate count. Based on both the total MPN(i.e., both species’ results added together; data not shown)and colony counting, the ratio (total MPN observed ÷ CFUobserved) of cells recovered determined by these two enu-meration methods was 4.19± 0.361 indicating thatCampylobacter performs significantly better in the MPN(i.e., liquid) format than that for total microaerobic plate

counting. Thus, one can conclude that the suspended mate-rials from the ground chicken inhibit Campylobacter colonyformation. When we attempted to clarify these highly turbidground chicken BPW washes (spiked with 2.13×104CFUC. jejuni+2.06×104CFU C. coli) using a blood leucocytefilter technique (data not shown) [37], we found that theoverall R values were very low (xR =0.0410±0.0601) be-cause of either the additional time the microaerophilicorganisms were exposed to air causing oxygen stress or,perhaps, the cells sticking to the membrane or membrane-bound ground chicken wash solids.

In all our combined spiked results (Tables 2–4) we sawthat 7 out of 34 of the experimental sets had Δε valuesgreater than 25 % and 9 out of 34 (most associated withTable 4) of the R values were less than 1. The more error-prone observations might occur because spun-down(concentrated) cells are surrounded by substances which,in effect, cause them not to be distributed randomly and/ornot to grow properly in the Campylobacter enrichmentmedia. In such real systems, especially when samples arecentrifuged to concentrate the test organism, one can inval-idate one, or more, of the 3 prime assumptions of thedilution method discussed in detail below. Note that in anideal system (Table 1), which neither involves food washesnor cell concentration via centrifugation, Δε≤14 % (albeitn=12) and R is always greater than 1. It is nearly impossibleto break the centrifugation-based pellet into small, homoge-neous particles: i.e., small enough that each particle wouldcontain no more than one bacterium each whereupon thelower the target concentration, the larger the particle volumecould be. Even if such homogeneous particles were formed,growth might not occur representatively if the embeddedorganisms were not experiencing the appropriate growthconditions; this could result in an R value much less than1. To what degree is this observed error due to a relativelysmall n (i.e., stochastic sampling error) and how much is dueto other sources such as the non-random distribution of thetarget bacterium? This question is addressed, in part, in thefollowing section.

The relationship between the number of replicates (n)within each dilution and stochastic sampling error (Δ)in binomial-based assays

It is self-evident that bacterial δ information gained from“quantal” assays is more precise with an ever greater n [38].However, just considering some arbitrary value of n, whatare the sources of variability associated with MPN determi-nations? Some of the variability seen in Tables 2–4 could bedue to either an excessively small n (i.e., stochastic sam-pling error) [10, 39] and/or associated with some aspect ofsample manipulation (e.g., centrifugation). The physiologyof the target organism is also a consideration inasmuch as


the time of exposure of Campylobacter species to air couldalso affect the MPN results: i.e.,Δε and/or R. At this point itis useful to examine the 3 prime assumptions, briefly men-tioned earlier, made about the dilution method or MPN[40–42] procedure: (1) microbes are volume-distributedrandomly; (2) bacteria do not tend to aggregate in dilutesolution; (3) growth will occur if any allotment or sub-sample contains even just one cell. Assumptions 1 and 2,above, could be negated if the test samples’ pellet is notdisbursed evenly and if each particle of pellet is not smallenough. Also, using PCR detection we need to somewhatamend assumption 3 inasmuch as the target genes are notgenerally extractable from bacterial cells with 100 % effi-ciency. Thus, when growth occurs it must be to such a levelthat one is assured a template upon which the primers/probes can attach. Overnight microaerobic culturing ofCampylobacter should provide this level of cell densitysince Hong and colleagues [18], using a direct (i.e., qPCRquantification using standard solutions) CampylobacterqPCR detection method, observed a limit of detection ofabout 10 CFUmL−1 using only 4 h of culture enrichment(e.g., if there are 3 population doublings in 4 hours then

10� 23 =80 CFUmL−1). For us, assuming a doubling time(τ) of 80 min (τ between ∼70–90 min) [43, 44] and a lagtime (T ) of 60 min, a 16-h enrichment of one cell should

result in approximately 2400 cells ( 2 t�Tð Þ=t ). So, evenassuming a poor extraction efficiency (e.g., 10 %), this cellconcentration level should allow enough DNA to be presentto observe a positive result even when the starting concen-tration was only 1 cell per volume tested (i.e., μ=1). Whiletrue stochastic sampling error (Δ) can only be minimized byusing more technical replicates (n) per dilution, other formsof sampling error are less easily controllable.

The first quandary to address with regard to Δ is: whatrelationship exists between Δ, μ (=δ×V) and n in quantalassays? Does Δ follow the same model as that for Poisson-distributed data (i.e., counting data) [10]? In order to addressthese issues we performed digital sampling experimentssimilar to what was done previously [10] but for a binomialresult. Thus, a large array of positive (symbolized by “1”)and negative (“0”) data was generated (using pcalc for j=0;Eq. 3) using n=96 [45] at several δ values (0.5, 0.25, 0.125,0.0625, 0.03125 MPN mL−1): e.g., for δ=0.5 MPN mL−1

and V=4 mL (i.e., μ=2) there should be, probabilistically,

Table 4 γ-irradiation sterilized ground chicken (∼50 g each) sampleseach of which was washed with 150 mL BPW (recovered V, 1=127 mL; 2=125 mL; 3=121 mL) and then spiked with both 3.96×

104CFU C. jejuni and 2.03×104CFU C. coli for testing the signifi-cance of sample concentration via centrifugation upon the qPCR-MPNenumeration technique



0 1 6 6.00 6 6.00 6 6.00

1 0.1 6 6.00 6 6.00 6 6.00

2 0.01 6 6.00 6 5.98 6 6.00

3 0.001 4 4.20 2 2.61 4 4.20

4 0.0001 1 0.680 1 0.333 1 0.680

Log[MPN mL-1]: 2.48 2.15 2.48 2.37

Δε %8%5%51%5:


R 0.456 0.216 0.456 0.376

Campylobacter coli

0 1 6 6.00 6 6.00 6 6.00

1 0.1 4 5.81 6 6.00 6 6.00

2 0.01 4 1.76 6 5.92 6 6.00

3 0.001 4 0.205 2 2.09 5 4.55

4 0.0001 0 0.0208 0 0.251 0 0.793

Log[MPN mL-1]: 0.938 2.03 2.55 1.84

Δε %42%11%5%75:


R 0.0257 0.317 1.05 0.464

Such a large spiking bacterial concentration was performed so that each sample produced could be split for both colony counting and MPN. Theground chicken BPW matrix visually contained at least 2× more suspended solids than whole piece washes


83 (nearest integer) repeats of “1” (positive: 83∼96 ×1� Exp �2½ �f g) and 13 repeats of “0” (negative: 13∼96 –

83). From each grouping of 96 “1”s and “0”s for each δ, 360of these were selected randomly from this pool of 96 basedupon random number tables generated using Mathematica(version 8) software:

Table x ¼ Random Integer; 1; 96f g½ �; x; 360f g½ � ð5ÞBriefly, this process involved arranging the 96 “0”s and “1”sin one column within a Microsoft Excel spreadsheet (cellsA1 to A96) and filling in n columns with formulas whichrefer to column “A” containing the 96 “1”s and “0”s andwhere a particular “A” row’s reference number was pro-vided by the appropriate random number table generatedfor this purpose. Each set of 360 random numbers(Eq. 5) was replicated 5 times and applied using theabove procedure. For each set of n values (n=3, 6, 9,12, 15, 18, 21, 24, 27, 30, 33), each row (360 ÷ n) wassummed across i columns to give the total number ofpositives in each row. So, the greatest computer-generated number of positive responses (p) could onlybe n, the lowest 0: i.e.,

p ¼Xni¼1

xi xi ¼ 0 or 1ð Þ: ð6Þ

Each observation of the population-based stochasticsampling error (Δm; m=1, 2, … , 5) was then deter-mined by averaging all calculations (360 ÷ n) at each δ=0.5, 0.25, 0.125, 0.0625, and 0.03125 MPN mL−1 (forV=4 mL then μ=2, 1, 0.5, 0.25, and 0.125 MPN perobservation)

Δm ¼pcalc �

Pni¼1

xi

avg

pcalcð7Þ

These data are presented in Fig. 1 as means of the 5 sets (i.e.,5 sets of results from the 5 random number tables) of

calculations (Δ=P5

m¼1 Δm � 5)±s.Since the plot of Δ versus n (Fig. 1a) was log–log linear

with a slope of about −1/2, all data were fit to the functionΔ=

Δnz ffiffiffinp

( z =−1.96±0.238; z is the average z across all 5replicates at μ=0.0625, 0.125, 0.25, 0.5, 1 and 2 MPN perobservation) based upon minimization of the sum of squaresby iteratively solving for Δn and z; the average coefficient ofdetermination (r2) was 0.994±0.0105. Likewise, since the plotof Δn versus μ was log–log linear, all Δn data were fit to thefunction Δn=A z ffiffiffi

μp

(z=-1.95±0.215; r2=0.984). All fittingparameters (z and A) are presented±asymptotic standard error[46]. Combining these two forms into one, the general

sampling error equation isΔ ¼ A �2 ffiffiffiffiffiffiffiffiffiffiffiffin� μ

pwhich is formu-

laically identical to the Δ values associated with count data[10] which are represented by a Poisson (discontinuous)probability distribution function. In this previous workwe demonstrated that it is not the value of Δ which ismeaningful but, rather, the change in Δ with respect to

n (i.e., @nΔ= � A μ½ � � 2 n μ½ �3=2n o

). Accordingly, if one

chooses some arbitrary value for n with μ=1 in the function@nΔ and solves for the real part [10] of n one achieves, uponrearrangement, the simple relationship

ncalc ¼ nμ¼1�3 ffiffiffiμp ð8Þ

where nμ¼1 is the value of n as μ approaches 1 MPN pervolume tested (i.e., the antilog of the intercept of a log-logplot). We now seek an empirical value for nμ!1. The approachwe took in this instance is illustrated in Fig. 2 which displaysthe probability of observing p positives out of n observationsfor μ=1 using various values of n. The peak in each Gaussiandistribution’s fit is the mean p which is approximately equiv-alent to pcalc (Eq. 3) and the standard deviation for eachdistribution curve in Fig. 2a is s (graphically, any Gaussians’

X axis width at 1/2 Yaxis height=2� ffiffiffiffiffiffiffiffiffiffiffiffiffi2Ln 2½ �p �s∼2:35� s).

These data were taken from the same pool as those shown inFig. 1 (filled diamond symbol in red) by combining all obser-vations of p (Eq. 6) into one probability distribution; the totalnumber of observations=360 ÷ n×5=600, 300, 200, 150, 120p values at n=3, 6, 9, 12, and 15, respectively. Each probabil-ity is merely the total number of any particular number ofpositives ÷ the total number of observations. Fig. 2b shows therelationship of the ratio of s to the mean number of positives ateach value of n which is the coefficient of variation (CV). Wehave assumed that the intersection shown at the dotted line inFig. 2b is a reasonable estimate for nμ!1 inasmuch as this isthe point where the CVwith n begins to level off. Calculationsfor ncalcwithnμ!1 ∼ 7 (Fig. 2) are shown in Fig. 3 which givesa value of about 6–7 for n at μ≥1–2. Plots of @nΔ with n areshown in the main plot and the dotted horizontal black dottedline is drawn were where A∼0.795 and μ=2, 1, 0.5, 0.25,0.125, and 0.0625 from the left-most @nΔ curve to the right-most, respectively. The corresponding intersections of thedotted black line with these @nΔ curve fits are shown with ared dotted vertical line and the respective n-data points areplotted with μ in the insert.

Since all of our previous results (Tables 2–4) use n=6 forμ values much greater than 1, our observed variability inΔεand R should be primarily related to some non-stochasticsource as alluded to previously: e.g., possibly associatedwith resuspending the pellet. The difference in spikedresults between the whole chicken piece washes and thatfor ground chicken argues for the non-random selection ofsub-samples due to the pellet not being dispersed into small


enough increments. This concept is further evidenced bythe fact that the lowest concentration sets of data in the C.jejuni/C. coli-pooled “+ centrifugation” treatments (Table 3)had the smallest percentage of high Δε values (0 of 8 Δε≥25 %) and low Rs (1 of 8 R less than 1). For instance, if eachpellet is 103μL and that the number of organisms per pelletis about 6,000 (μ∼6,000 ÷ 30 mL of suspension liquid×4 mL per observation=800) then the volume per suspended

particle, on average, needs to be <0.167 μL; however, with7–8 cells per pellet (μ∼1) the size needs only to be<133 μL.Thus, one is more likely to achieve a true random sampling ofthe target organism at lower cell densities. If these ideas aretrue then qPCR-MPN results from native Campylobacterspecies on chicken should be less likely to show muchnon-stochastic sampling error since μ values would generallybe<1.

Fig. 1 Plots of the absolute value of the average (± standard deviation)pcalc-normalized deviations (Eq. 7) of p (Eq. 6) from pcalc (Eq. 3),which is our measure of stochastic sampling error, as a function of thenumber of observations per dilution (n). The data points filled circle,filled triangle, circle, triangle, filled diamond (in red), and multiplica-tion sign (μ=0.0625, 0.125, 0.25, 0.5, 1, and 2, respectively) in Fig. 1a

represent averaged Δ calculations (Eq. 7; replicated fivefold) per-formed for various n. The curve in Fig. 1b shows a plot of the Δn (±asymptotic standard error [46]) values obtained from the fits in Fig. 1achanging with μ. Combining results from both a and b, we see thatΔeA�2 ffiffiffiffiffiffiffiffiffiffiffiffin� μ

p

Fig. 2 Empirical determination of the value of n as μ (=V×δ)approaches 1 MPN per volume tested (i.e., nμ!1). Plot 2a shows theprobability of observing p positives out of n observations calculated forμ=1 and varying n. The peak in each Gaussian distribution’s fit is themean p which is approximately equivalent to pcalc (Eq. 3) and thestandard deviation for each distribution curve in 2a is s. Data were

taken from the same pool as those shown in Fig. 1 (symbol=filleddiamond [in red]) by combining all observations of p (Eq. 6) into oneprobability distribution. Plot 2b shows the relationship of the ratio of sto the mean p at each value of n which defines the coefficient ofvariation (CV)


qPCR-MPN protocol applied to naturally occurringCampylobacter on chicken

The normal use for this qPCR-MPN protocol would be toestimate concentrations of Campylobacter which naturally

contaminate a high proportion of tested chicken samples(e.g., 24 % of sampled chicken tissues were found to beadulterated with C. coli and ∼67 % with C. jejuni) [17]. It ispresumed that the level of natural contamination is muchlower than the spiking level used in Table 3 where μ≥18.

Fig. 3 Plots of the partial first derivative of Δ (Fig. 1 assumingΔ ¼ A �2 ffiffiffiffiffiffiffiffiffiffiffiffin� μ

p) fits with respect to n (i.e., @nΔ ¼ �A μf g�

2 n μ½ �3=2n o

) at various n. The horizontal black dotted line is drawn

where A∼0.795 and μ=2, 1, 0.5, 0.25, 0.125, and 0.0625 from the left-most curve to the right-most for @nΔ. The corresponding intersections of

the dotted black line with the @nΔ curve fits are shown with a red dottedvertical line and the n-data points are plotted with μ in the insert. Fromthese data, one obtains the overall relationship shown in Eq. 8. In thisparticular case, nμ¼1 ∼ 7 (from Fig. 2 results). Any other arbitrary valuefor @nΔ would also result in Eq. 8

Table 5 qPCR-MPN protocol applied to naturally contaminated, skinless (removed prior to packaging for sale) chicken pieces

j Dilution Skinless Breasts I Skinless Breasts II Skinless Legs “Tenders”

p pcalc p pcalc p pcalc p pcalc


42.5499.56248.00010

21.1367.230090.0101.01

321.01853.0060900.00010.02

4210.008630.00709000.000100.03

815.045.18730.0MPN mL-1:

Δε %26%7%781:

3.417.9342.1:g054repNPM

Campylobacter coli

0000.6678.5510

0000.6629.151.01

0056.44822.0010.02

00238.022320.00100.03

3.73769.0MPN mL-1:

Δε %01%25:

622,10.92:g054repNPM

For these observations, 200 mL of BPW was added to Whirl-Pak Filter Bags containing approximately 450 g of each sample listed below (450, 411,523, and 488 g, respectively left to right). Samples were gently massaged∼4 min. At least 200 mL were recovered from all samples which wereloaded into large centrifuge tubes, balanced, and spun at 16,000×g for 15 min at (∼10 °C). Each pellet was suspended in 3 mL of BPWand broughtup to 30 mL with Campylobacter selective enrichment medium. All data were normalized to 450 g (∼1 lb)


Table 5 shows results from applying our qPCR-MPN pro-tocol to skinless chicken pieces picked randomly from alocal grocery store. For these observations, 200 mL ofBPW was added to Whirl-Pak Filter Bags containing ap-proximately 450 g of each sample (450, 411, 523, and488 g, for Breasts I, II, Legs, and “Tenders,” respectively).These tissue samples were washed/massaged and approxi-mately 200 mL were recovered from all samples. Thewashes were added to centrifuge tubes, balanced, and spunat 16,000×g for 15 min at (∼10 °C). Each pellet was thensuspended in 3 mL of BPW and brought up to 30 mL (=Vsample) with Campylobacter selective enrichment medium.All reported concentration data were normalized to 450 g(∼1 lb). Results show that all samples had either a C. jejunior C. coli contamination. The skinless “Breasts II” sampleexhibited both the greatest (for C. coli, δ=1226±123 MPNper 450 g=37.3 MPN per mL of Vsample; δ×V=μ∼149MPN) and least (for C. jejuni: δ=1.24±2.26 MPN per450 g=0.0378 MPN per mL of Vsample; δ×V=μ∼0.151MPN) level of natural Campylobacter contamination in thiswork. However, the C. jejuni concentration on the skinless“Breasts II” sample was positive only in the 0.1 dilution(i.e., pj=0, 1, 0, and 0 for j=0, 1, 2, and 3). While this is anunlikely circumstance, it can, and does happen [34]. It isequally apparent that, at such a low concentration and smalln, all wells could have, by chance alone, been negative aswell (false negative). This is a problem all MPN assayssuffer from due to the temporal and monetary costs ofincreasing n to a level which would all but negate suchunlikely combinations [45]. Contrariwise, the specificity ofthe qPCR detection method minimizes the possibility of afalse positive. It should also be pointed out that, based uponour analysis of @nΔ (Figs. 2 and 3), to enumerate a samplewith a concentration as low as 1 MPN per Vsample (μ∼0.133MPN) using this dilution protocol, one would have to morethan double the value of n. In reality, the utility of themethod diminishes greatly for n>6 because one is ever morediluting the sample as well. For instance, the quantitativelyminimal limit (pj=1, 0, and 0 for j=0, 1, and 2) for ourconditions (V=4 mL and n=6) is about 1.23±0.231 MPNper Vsample (μ∼0.164). Doubling n lowers this minimalMPN only slightly (1.18±0.218 per Vsample) because it alsoentails doubling Vsample. By keeping the Vsample constant andchanging V (Fig. 4), there is only a slight improvement inthe calculated limit of quantification by increasing n muchbeyond 6 and, of course, doubling the value of n more thandoubles the assay cost.

A more comprehensive set of qPCR-MPN results areshown in Table 6 for intact (with skin) chicken parts. Forthese observations, between 150–200 mL of BPW wasadded to Whirl-Pak Filter Bags with 450–600 g of eachchicken piece sample. These pieces of chicken were thenwashed/massaged and the media from all samples were

loaded into large centrifuge tubes, balanced, and spun at16,000×g for 15 min (∼10 °C). The pellet was suspended in3 mL of BPW and brought up to 30 mL (Vsample) withCampylobacter selective enrichment medium (MPN dilu-tion j=0). As before, all data were normalized to 450 g.Using this protocol, we were able to quantify as few as∼4 C.jejuni or C. coli cells per 450 g of naturally contaminatedchicken: e.g., 4 to 244 MPN per 450 g for wings, breasts,legs, and thighs (skin on) with about 50 % of the samplestesting to be negative for growth of any Campylobacterspecies. In these experiments neither wings nor breastsshowed the presence of high enough C. coli levels to showa positive growth response via qPCR. Chicken legs showedthe highest rate of contamination (67 % C. jejuni; 50 % bothC. jejuni and C. coli). Table 6 also shows that 3 of the 5 C.coli positive samples (e.g., Legs VI: 3.94±1.69 MPN per450 g; Thighs I: 6.11±1.46; Thighs II: 4.08±1.17) had verylow levels of contamination.

The benefits of using qPCR-based detection in conjunc-tion with MPN analysis is the virtual elimination of falsenegatives [29] and positives via the internal amplificationcontrol reactions and the high organismal specificity [17],respectively. This specificity is then combined with the innatesensitivity of MPN procedures and analyses. The range ofdetection is limited only by how many dilutions one desiresto make in order to achieve at least one dilution with somenegative responses. However, for pathogen enumeration, oneis typically concerned with the lower end of the analysisspectrum since fewer than 500 cells can cause gastroenteritis[47]. Most of the time required for analysis using MPN is dueto the pathogen’s growth requirement (∼16 h). The process ofperforming the chicken washes, the centrifugation, andmakingthe dilutions takes about 60 min. Performing the DNA extrac-tion is less than 1 hr and the qPCR analysis can be performed inca. 1.5 h or even less with fast-cycling instrumentation. Themajor cost above traditional MPN protocols is due to using

Fig. 4 Plot of calculated (Eq. 2) MPN (±Δε×MPN) in Vsample for {p0,p1}={1, 0} as a function of n observations per dilution


Table 6 qPCR-MPN protocol applied to naturally contaminated chicken pieces with skin intact

MPN per 450-g sample C. jejuni pobs/pcalc C. coli pobs/pcalc % positive

Observation C. jejuni C. coli j : 0 1 2 3 0 1 2 3

Wings I 244.0±16.3 nd pobs: 6 6 1 – 0 0 0 – 33 % C. jejuni; 0 % C. coli;0 % Bothpcalc: 6.00 5.77 1.67 – – – – –

Wings II nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Wings III 11.3±0.348 nd pobs: 5 1 0 – 0 0 0 –

pcalc: 4.96 0.966 0.104 – – – – –

Wings IV nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Wings V nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Wings VI nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Legs I 244±16.3 nd pobs: 6 6 1 – 0 0 0 – 67 % C. jejuni; 50 % C.coli; 50 % Bothpcalc: 6.00 5.77 1.67 – – – – –

Legs II nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Legs III nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Legs IV 27.0±12.8 21.8±3.10 pobs: 6 0 1 1 6 1 0 0

pcalc: 5.87 1.90 0.224 0.0228 5.72 1.59 0.182 0.0185

Legs V 62.9±17.4 15.0±0.463 pobs: 6 2 1 1 5 1 0 0

pcalc: 6.00 3.12 0.425 0.0439 4.96 0.966 0.104 0.0105

Legs VI 26.5±12.6 3.94±1.69 pobs: 5 3 1 1 2 1 0 0

pcalc: 5.84 1.84 0.215 0.0219 2.51 0.317 0.0325 0.00326

Thighs I 24.2±10.5 6.11±1.46 pobs: 5 4 0 – 3 1 0 – 40 % C. jejuni; 40 % C.coli; 40 % Bothpcalc: 5.76 1.65 0.190 – 3.34 0.470 0.0487 –

Thighs II 205±34.2 4.08±1.17 pobs: 6 5 3 – 2 1 0 –

pcalc: 6.00 5.61 1.44 – 2.52 0.317 0.0325 –

Thighs III nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Thighs IV nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Thighs V nd nd pobs: 0 0 0 – 0 0 0 –

pcalc: – – – – – – – –

Breasts I nd nd pobs: 0 0 0 0 0 0 0 0 50 % C. jejuni; 0 % C.coli; 0 % Bothpcalc: – – – – – – – –

Breasts II nd nd pobs: 0 0 0 0 0 0 0 0

pcalc: – – – – – – – –

Breasts III 15.4±9.50 nd pobs: 4 3 1 0 0 0 0 0

pcalc: 5.24 1.12 0.123 0.0124 – – – –

Breasts IV 139±1.96 nd pobs: 6 5 1 0 0 0 0 0

pcalc: 6.00 4.97 0.968 0.105 – – – –

For these observations, 150–200 mL of BPW was added to Whirl-Pak Filter Bags containing approximately 450–600 g of each sample listed below.Samples were gently massaged∼4 min. Typically most of the volume was recovered from all samples which was loaded into large centrifuge tubes,balanced, and spun at 16,000×g for 15 min (∼10 °C). The pellet was suspended in 3 mL of BPW and brought up to 30 mL with Campylobacterselective enrichment medium (this is MPN dilution j=0). All data were normalized to 450 g (∼1 lb)


qPCR detection technology whereupon the reagents are ∼$1per reaction (PrepMan Ultra∼$0.11; Master Mix∼$0.76; C.jejuni+C. coli+IAC probes∼$0.14); e.g., Table 6 (21 samples)would cost∼$372 for all PCR reagents.

Summary

In this work we developed a multiplex, MPN assay usingqPCR for binomial detection and analyzed some of the errorsassociated with the protocol. We demonstrated that suchqPCR-MPN enumeration methods have an excellent potentialfor quantifying extremely low levels of Campylobacter spe-cies in food using the protocol devised within. When appliedto pure cultures the results were excellent with low Δε andhigh recovery rates. However, in real food systems errorincreased substantially. We established that such errors wereprobably not stochastic but appear to be related to thesample concentration step. We also established that low-er Campylobacter spike concentrations lowers the errorrates for centrifuge-concentrated samples to a levelroughly equivalent to those assayed directly (i.e., nocentrifugation). If true, then utilization of this qPCR-MPN method for native Campylobacter on chickenshould result in even lower error rates due to lowerlevels of contamination relative to those at the lowestspiked levels (Table 3; μ≥18). Utilizing our protocolwith naturally contaminated chicken we showed thatmost of the MPN enumeration processes using qPCRdetection can be performed with n=6 observations (eachof V=4 mL) per dilution with a relatively low Δε.

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Documents

Non-stochastic sampling error in quantal analyses for Campylobacter species on poultry products