Modeling the Rate of Attachment of Listeria monocytogenes, Pantoea agglomerans, and Pseudomonas fluorescens to, and the Probability of Their Detachment from, Potato Tissue at 10°C

Abstract

The rate of attachment of bacteria to, and their subsequent detachment from, the cut surface of raw potato tissue was measured and modeled by using mathematical approaches that allowed detailed objective comparisons of adhesion processes under different conditions. Attachment was rapid and reached equilibrium after contact for 60 min. A new method to measure the probability of detachment was developed and modeled, revealing that the probability of detachment for Pseudomonas fluorescens remained unchanged for contact times between less than 5 s and 60 min. Listeria monocytogenes, however, was more easily removed initially, with the probability of detachment decreasing over the first 2 min of contact but remaining constant and equivalent to that for Pseudomonas fluorescens thereafter. For all of the bacteria tested, the number of bacteria attached after 2 min of contact was proportional to the inoculum concentration raised to the power of 0.79.

There is a growing body of literature reporting the bacterial contamination of ready-to-eat prepared vegetable tissues. Such tissues often become contaminated in the field. Despite postharvest trimming and decontamination processes, this contamination persists during commercial preparation, and the products can contain in excess of 10⁶ viable bacteria g⁻¹ at the time of packing (6). Contaminants are predominantly Pseudomonas spp. and Pantoea spp. (5, 6), but bacteria of public health significance, such as Escherichia coli, Yersinia spp., and Listeria spp., may also be present (1, 4, 5, 12, 14; K. Sizmur and C. W. Walker, Letter, Lancet i:1167, 1988).

Scanning electron microscopy of prepared leaf tissues has shown that bacteria can be found on the abaxial and adaxial surfaces. However, the bacteria preferentially occupy the cut surfaces, where they multiply throughout storage of the products to form an extensive layer, sometimes many cells thick (6). Growth of Pseudomonas spp. and Pantoea spp. on cut surfaces is followed by production by these bacteria of an extracellular polysaccharide, creating a protective layer which is resistant to chemical and physical decontamination processes (10). Colonization of the cut surface is a two-stage process; initial adhesion occurs rapidly and is followed by the production of an extracellular polysaccharide by the adhered bacteria.

Most studies of colonized vegetable tissue surfaces emphasize the mature biofilm stage, and little work has concerned the initial colonization process. However, commercial decontamination processes are typically applied to prepared vegetable tissues within a few minutes of chopping, shredding, or dicing. These processes usually involve washing in potable water with, in some countries, added biocidal compounds, such as chlorine (11). Such washing occurs considerably before the establishment of the protective extracellular polysaccharide, and yet the washing process still fails to remove all of the bacteria (2, 6, 9, 13).

Here we report studies of the measurement and modeling of the rate of adhesion of bacteria to, and the probability of their detachment from, vegetable tissue during the early stages of colonization.

MATERIALS AND METHODS

Organisms.

Listeria monocytogenes strain F4642 (Scott A) serotype 4b was supplied by R. Weaver of the Centers for Disease Control and Prevention, Atlanta, Ga. L. monocytogenes strains 10403S and DP-L189 (EGD), both serotype 1/2a, were supplied by D. A. Hodgson of the University of Warwick, Warwick, United Kingdom. Pantoea agglomerans VCM was isolated from mung bean sprouts, and Pseudomonas fluorescens A36 was isolated from green peppers; both foods were obtained from commercial vegetable processing sites.

Culture media.

Stock cultures were maintained on heart infusion agar (Difco) slants incubated at 25°C for 48 h and subsequently stored at 1°C. Fresh slants were subcultured monthly.

Cultures for measurement of the duration of the lag phase of bacteria, the rate of attachment, and the probability of detachment were grown in Pseudomonas broth F (PBF), which contained 10 g of tryptone (Difco), 10 g of proteose peptone number 3 (Difco), 1.5 g of dipotassium hydrogen phosphate (BDH), 3.1 g of magnesium sulfate heptahydrate (BDH), and 10 g of glycerol (BDH). Components were dissolved in 1 liter of glass-distilled water by boiling them and then sterilized by autoclaving them at 121 to 124°C for 15 min. Inocula were prepared in Trypticase soy broth (TSB; Baltimore Biological Laboratory).

Preparation of inocula.

Bacteria were grown successively in 10 ml of TSB at 25°C for 24 h and then at 20°C for 24 h. Inocula for measurement of the rates of attachment and probabilities of detachment were prepared by dilution of the culture in PBF, previously cooled to 10°C, to give suspensions that contained between 10⁴ and 10⁸ viable bacteria ml⁻¹.

Determination of the lag phase of bacteria.

PBF (100 ml) was transferred to sterile 250-ml Erlenmeyer flasks, which were closed with a rubber bung fitted with a filter to allow gaseous exchange and a device for aseptic sampling of the culture. The flask and its contents were then precooled to 10°C overnight. An inoculum (1 ml) grown in TSB was added to the PBF to give a suspension that contained approximately 10³ to 10⁴ viable bacteria ml⁻¹. Flasks were incubated at 10°C on an orbital platform shaker (New Brunswick Scientific, Edison, N.J.) rotating at 100 rpm. At intervals throughout incubation, a sample of culture was removed, and the number of viable bacteria was determined by spreading 50 μl of this suspension, or dilutions of it made in peptone salt dilution fluid (PSDF) (8), onto the surfaces of plates with plate count agar (PCA) (Oxoid CM325), by using a model D spiral plate maker (Spiral Systems, Inc.). The plates used for the enumeration of L. monocytogenes cells were incubated at 35°C for 24 h, and those used for the enumeration of Pseudomonas fluorescens and Pantoea agglomerans cells were incubated at 25°C for 48 h.

Growth curves were fitted using a nonautonomous differential equation (the Baranyi D model) (3) in order to estimate the lag time and the initiation of the logarithmic phase of growth. The nonautonomous differential equation was fitted to the growth data by a software program (MicroFit [www.ifr.bbsrc.ac.uk/microfit]) written specifically for this purpose.

Preparation of sterile potato disks.

Potatoes were chosen as a model vegetable tissue surface because sterile disks that were of uniform thickness and composition and had an entire surface composed of damaged plant cells could be prepared. Disks of other tissues (such as carrot, green pepper, celery, and lettuce) were also prepared, but these had differentiated tissues within them and hence were not uniform, had cut surfaces of inconsistent dimensions (for example, only along the edges of the disks in the case of lettuce leaf tissues), and were difficult to prepare aseptically. Avoidance of competing bacteria was considered important in the work reported here. Preliminary studies showed that the rates of attachment of L. monocytogenes, Pantoea agglomerans, and Pseudomonas fluorescens to potato disks were identical to their rates of attachment to green pepper disks (data not shown). However, preparation of sterile disks of green pepper was difficult and could not be achieved reliably. In contrast, potato disks were simple to prepare aseptically. Accordingly, although potato tissue is unlikely to be eaten raw, it was used as a representative model of tissues that are eaten raw.

Potatoes obtained from a local supermarket were sprayed with 70% (vol/vol) ethanol, peeled with a sterile potato peeler, sprayed again with 70% (vol/vol) ethanol, and allowed to dry in a sterile airflow on a sterile surface. A cylindrical core of potato tuber (27-mm diameter) was cut with a sterile cork borer. The core was extruded from the borer with a sterile stainless steel rod, and disks of potato tissue were cut to the desired thickness with a sterile knife. The sterility of the disks was checked by immersion of representative disks in TSB, which was incubated at 20°C and examined for turbidity.

Rate of attachment.

Sterile potato disks with a thickness of approximately 1 mm were prepared. PBF (20 ml) was cooled to 10°C in sterile, disposable plastic petri dishes (90-mm diameter). An inoculum was added to the PBF, and up to four potato disks were placed into the inoculated PBF in each petri dish and incubated without shaking at 10°C. Typically, 12 disks were incubated for each experiment. At intervals, a potato disk was removed with sterile forceps and placed in a second petri dish, where it was rinsed five times with 20 ml of PSDF in order to remove bacteria that were loosely associated with, but had not adhered to, the potato tissue. Rinsing involved tilting the petri dish three times at an angle of 10^o before decanting the rinsing liquid. Bacteria remaining on the disk were then removed by blending them with 10 ml of PSDF for 60 s by using a Stomacher Lab-Blender. The number of viable bacteria in the resultant suspension was determined by spreading 50 μl of this suspension, or dilutions of it made in PSDF, onto the surfaces of plates of PCA by using the spiral plate maker. Plates were incubated as described above.

Modeling the rate of attachment of bacteria to potato tissue.

The kinetics of adsorption were assumed to be first order, and desorption as well as adsorption was included in the model (equation 1).

(1)

Here N_B was the number of bacteria bound to the surface, N was the number concentration of bacteria free in suspension (which remained very much larger than N_B throughout the experiment and was thus taken to be constant), and t was time. The adsorption and desorption rates were k_a and k_d, respectively. For a more general solution, a term involving the surface area of the potato would need to be included, but as the potato disks used in this study were identical, no such term was required in equation 1. At equilibrium, where the rate of change of the number bound was 0, the number bound at equilibrium (N_B,eqm) was given by rearranging equation 1 to give equation 2.

(2)

It would also be possible to determine a value for the initial rate of adsorption where the initial number bound was 0 (equation 3).

(3)

Both of these quantities depended on the inoculum concentration, N. By the integration of equation 1, the insertion of boundary conditions, and rearrangement, the equation describing the number of bound bacteria with time (N_B,t) was determined (equation 4).

(4)

Probability of detachment.

Sterile potato disks were prepared as described above, with a thickness of approximately 4 mm, and care was taken to ensure that the cut surface of each was flat. An inoculum in PBF (50 ml) was poured into sterile plastic petri dishes, and potato disks were prepared and incubated, all as described above. At intervals, a potato disk was removed and rinsed as described above and then sequentially blotted facedown for 60 s onto the surface of each of a series of PCA plates. These had previously been partially dried in a fan oven at 55°C for 60 min and cooled to room temperature. After removal of the disk from each plate, the bacteria deposited on the agar were spread over the plate surface with a sterile disposable spreader. Plates were incubated as described above. The potato disk was incubated on the surface of the final PCA plate of the series in order to determine if bacteria remained on the disk after completion of the blotting series. The number of CFU on each PCA plate in the blotting series was counted, and its logarithm was plotted against the plate number in the blotting series. A straight line was fitted to each data set using the linear regression functions of Excel 2000 (Microsoft), from which a slope, an intercept, standard deviations, and the correlation coefficient, R², were determined. The gradient was a measure of the probability of removal of bacteria from the surface of the potato disk. For example, in the case of two disks with the same number of attached bacteria, a higher probability of removal resulted in a steeper gradient, resulting from a higher proportion of the bacteria being removed by the first blotting. From the gradient and the intercept, the number of bacteria initially bound to the disk before blotting was determined by an extension of the method of Eginton et al. (7).

Modeling the probability of detachment.

It was assumed that the relationship between the number of viable bacteria per plate and the plate number in the blotting series fitted an exponential decrease (equations 5 and 6) as described by Eginton et al. (7).

(5)

(6)

Here, A is a constant, C is the number of CFU per blot plate, i is the plate succession number in the blotting series, and k is the reduction exponent.

Eginton et al. (7) determined k by linear regression of the data from plots of the logarithms of the numbers of viable bacteria on the plates against the plate numbers. They interpreted the value of k as the inverse of the strength of attachment of bacteria to the surface of interest from an argument that identified k as the ease of removal of the bacteria from the surface. To arrive at a more accurate interpretation of the gradient measured in the work reported here, we have considered the probability of removal of bacteria from the surface.

The probability that any particular bacterium was removed during a blotting event was represented by x, where x took a value between 0 and 1. For an initial number of bacteria adhered to the face of a potato disk (N_F), the number removed after the first blotting event (N_d,1) and therefore the number remaining on the disk (N_r,1) were given by equations 7 and 8.

(7)

(8)

This was extended to the ith plate in the blotting sequence to give equations 9 and 10.

(9)

(10)

Taking the logarithm of equation 9 resulted in a form that was functionally identical to that obtained by Eginton et al. (7), but the parameters were defined differently (equation 11).

(11)

RESULTS

Growth in broths.

The lag times estimated by Microfit for each organism grown in PBF at 10°C were 3.1 h for L. monocytogenes Scott A, 3.6 h for Pseudomonas fluorescens A36, and 4.9 h for Pantoea agglomerans VCM. Accordingly, no attachment experiment was continued for more than 3 h in order to exclude the possibility of complication of bacterial multiplication during the experiment.

Rate of attachment of bacteria to potato tissue.

Tests confirmed that potato disks were prepared aseptically, and hence all experiments were conducted in the absence of a potentially competing microflora. The numbers of bacteria attached to the potato tissue disks increased with time for all organisms tested and reached a plateau after approximately 1 h, although all bacteria showed significant adsorption at times as short as 5 min (Fig. 1).

FIG. 1.

Effect of time of contact on the adhesion of bacterial cells to disks of raw potato tissue. Numbers of viable bacteria are the numbers per disk per inoculum concentration (numbers of cells per milliliter). ▪, L. monocytogenes Scott A; ⋄, L. monocytogenes 10403S; ♦, L. monocytogenes DP-L189; ▴, Pantoea agglomerans VCM; •, Pseudomonas fluorescens A36. Data points are from individual experiments performed either singly, in duplicate (for Pseudomonas fluorescens A36 and Pantoea agglomerans VCM), or in triplicate (for L. monocytogenes Scott A).

Curves with the form of equation 4 were fitted to the data from Fig. 1 by using curve-fitting software (Tablecurve 2D version 2.03; Jandel Scientific, Erkrath, Germany), which yielded values for the numbers of bacteria bound at equilibrium, N_B,eqm, the rates of adsorption, k_a, the rates of desorption, k_d, and the standard errors of these values (Table 1).

TABLE 1.

Coefficients determined by fitting equation 4 to the data shown in Fig. 1^a

Organism and replicate	No. of free cells (N)	NB,eqm (fitted coefficient a)	SE of NB,eqm	kd (fitted coefficient b)	SE of kd	ka	SE of ka
Pantoea agglomerans
1	5.20 × 107	0.388	0.033	2.079	0.549	1.55 × 10−8	4.30 × 10−9
2	5.60 × 107	0.501	0.033	3.151	0.729	2.82 × 10−8	6.78 × 10−9
Pseudomonas fluorescens
1	4.60 × 107	0.549	0.057	1.454	0.479	1.74 × 10−8	5.99 × 10−9
2	2.60 × 107	0.623	0.032	1.953	0.275	4.68 × 10−8	7.01 × 10−9
Listeria monocytogenes Scott A
1	1.60 × 108	0.197	0.03	1.008	0.361	1.24 × 10−9	4.83 × 10−10
2	2.26 × 108	0.326	0.033	1.618	0.451	2.33 × 10−9	6.92 × 10−10
3	2.18 × 109	0.186	0.042	1.311	0.725	1.12 × 10−10	6.68 × 10−11
Listeria monocytogenes DP-L189 (EGD)
1	1.60 × 108	0.0396	0.0028	3.266	1.091	8.08 × 10−10	2.76 × 10−10
Listeria monocytogenes 10403S
1	1.80 × 108	0.0275	0.0018	1.785	0.327	2.73 × 10−10	5.31 × 10−11

^aN_B,eqm, number of bacteria (log₁₀) bound to each potato disk at equilibrium, i.e., fitted coefficient a [(k_a/k_d)·N]; k_d, rate of desorption of bacteria from the potato disk, i.e., fitted coefficient b; k_a, rate of adsorption of bacteria from the potato disk.

Probability of detachment of bacteria from potato tissue.

The numbers of bacteria removed from the colonized potato tissue disks by the successive blotting technique is shown in Fig. 2 and 3 (for L. monocytogenes) and in Fig. 4 (for Pseudomonas fluorescens), where they are scaled for inoculum concentration. From these data, the probabilities of removal of a bacterium from the tissue during a blotting event, x, and the numbers attached to the face of the disk before blotting commenced, N_F, were obtained (Table 2), with the equation for N_F (equation 12) being equivalent to the method of summation developed by Eginton et al. (7).

(12)

Figure 2 shows the effect of varying the initial numbers of bacteria from 8.0 × 10⁴ to 7.6 × 10⁷/ml on the basis of the probability of detachment of L. monocytogenes Scott A, with a contact time of 2 min. The gradients (k), and therefore the probabilities of detachment (x) (Table 2), for the three highest inoculum concentrations were not significantly different from one another (P > 0.20), with the three replicated determinations at an inoculum of 7.6 × 10⁵ viable bacteria ml⁻¹ showing excellent agreement (P > 0.75). The apparent difference in the probabilities of detachment at the two lowest inoculum concentrations was not significant, with a P of 0.05.

FIG. 2.

Effect of inoculum concentration on the subsequent removal of L. monocytogenes Scott A from the surfaces of raw potato disks by blotting. Disks were in contact with the inoculum for 2 min. Numbers of viable bacteria are the numbers of cells per blot plate. Initial inoculum concentrations (per milliliter) were 8.0 × 10⁴ (+), 1.3 × 10⁵ (▴), 7.6 × 10⁵ (×), 7.6 × 10⁵ (•), 7.6 × 10⁵ (○), 8.0 × 10⁶ (♦), and 7.6 × 10⁷ (▪). Solid lines represent the best fit to the data obtained by linear regression.

FIG. 3.

Effect of time of contact with the inoculum on the subsequent removal of L. monocytogenes Scott A from the surfaces of raw potato disks by blotting. Numbers of viable bacteria are the numbers of cells per blot plate. The initial inoculum concentration was 1.3 × 10⁵/ml. Disks were in contact with the inoculum for <5 s (▴), 30 s (•), 2 min (×), 10 min (⧫), and 60 min (▪). Solid lines represent the best fit to the data obtained by linear regression.

FIG. 4.

Effect of inoculum concentration and time of contact with the inoculum on the subsequent removal of Pseudomonas fluorescens A36 from the surfaces of raw potato disks by blotting. Numbers of viable bacteria are the numbers per disk at each inoculum concentration, measured in cells per blot plate. The times of contact and inoculum concentrations were <5 s, 6.2 × 10⁵/ml (•); <5 s, 5.0 × 10⁴/ml (○); 1 min, 5.0 × 10⁴/ml (▪); 2 min, 5.0 × 10⁴/ml (⧫); 3 min, 5.0 × 10⁴/ml (▴); 5 min, 5.0 × 10⁴/ml (×); 10 min, 5.0 × 10⁴/ml (□); 15 min, 6.2 × 10³/ml (⋄); 30 min, 6.2 × 10³/ml (○); and 60 min, 6.2 × 10³/ml (+). Solid lines represent the best fit to the data obtained by linear regression.

TABLE 2.

Coefficients describing the probability of detachment of bacteria from disks of potato tissue

Organism	Contact time (min)	Inoculum concn (no. of viable cells ml−1)	xa	NFb	R2c
L. monocytogenes Scott A	0	1.30 × 105	0.303	97.0	0.846
	0.5	1.30 × 105	0.194	201	0.817
	2	8.00 × 104	0.158	232	0.736
	2	1.30 × 105	0.094	695	0.728
	2	7.60 × 105	0.111	1,220	0.835
	2	7.60 × 105	0.108	1,460	0.934
	2	7.60 × 105	0.112	1,760	0.902
	2	8.00 × 106	0.117	10,140	0.903
	2	7.60 × 107	0.084	71,940	0.717
	10	1.30 × 105	0.091	4,370	0.880
	60	1.30 × 105	0.123	12,310	0.978
Pseudomonas fluorescens	0	4.96 × 104	0.132	149	0.627
	0	6.18 × 105	0.121	2,070	0.715
	1	4.96 × 104	0.115	1,590	0.804
	2	4.96 × 104	0.114	2,380	0.887
	3	4.96 × 104	0.097	3,840	0.782
	5	4.96 × 104	0.077	6,860	0.812
	10	4.96 × 104	0.102	8,430	0.807
	15	6.18 × 103	0.074	2,370	0.770
	30	6.18 × 103	0.104	1,920	0.883
	60	6.18 × 103	0.079	4,980	0.839

^ax, probability of detachment of a bacterium from the vegetable tissue surface during a single blotting event (value between 0 and 1).

^bN_F, total number of bacteria attached to the face of a potato tissue disk.

^cR², coefficient of determination of the linear fit to the data (value between 0 and 1, with 1 being a perfect fit of the linear model to the data).

From inspection of Fig. 2, it is clear that the initial number of bacteria adsorbed to each face of the disk, N_F, increased with the inoculum concentration. It was assumed that the relationship obeyed a simple power law (equation 13), so the logarithm of N_F was plotted against the logarithm of the initial inoculum concentration (Fig. 5).

(13)

The coefficients a and b were determined to be 0.79 (standard error, 0.05) and 1.418, respectively, by linear regression, with an R² value of 0.979, which demonstrated that the assumption of the power law relationship was sound.

FIG. 5.

Effect of the initial inoculum concentrations on the numbers of cells of L. monocytogenes Scott A attached to the face of a raw potato disk. The solid line represents the best fit to the data obtained by linear regression.

From Fig. 3, it can be seen that the gradient, and hence the probability of detachment, x, for L. monocytogenes Scott A, decreased over the first 2 min but then remained constant up to 60 min. At the 5% probability level, the gradients of the zero time sample and the 30-s sample were not significantly different, mostly because the former was defined from only four points, which resulted in a very large uncertainty in the value of its gradient. However, the gradients of these lines were significantly different (P < 0.05) from those of all of the later samples, which showed the change in detachment probability to be real.

In the case of Pseudomonas fluorescens A36 (Fig. 4), the probability of detachment remained constant (P < 0.05) after contact times between 0 and 60 min.

The two techniques used here (the blotting of disks of tissue that had been in contact with bacteria for a given time and the enumeration of bacteria on disks of tissue during continuous contact) enabled an interesting comparison to be made: the number of bacteria calculated to populate a disk compared to the number actually enumerated by their removal with the Stomacher Lab-Blender. The results of this analysis are shown in Fig. 6. The numbers of L. monocytogenes and Pseudomonas fluorescens organisms attached to the surfaces of potato disks before blotting were calculated (equation 12), and the results showed the expected increase with time of contact. The number of L. monocytogenes organisms enumerated by removal with the Stomacher Lab-Blender and the number enumerated by blotting were comparable throughout the immersion history, once we corrected for differences in the surface areas from which the bacteria were removed (i.e., blotting was from a single face, but use of the Stomacher Lab-Blender removed bacteria from both the faces and the edge of the disk). However, the number of Pseudomonas fluorescens organisms enumerated by blotting was significantly higher than that determined by removal with a Stomacher Lab-Blender.

FIG. 6.

Effect of time of contact with raw potato disks on the numbers of cells of L. monocytogenes Scott A (▪, □), and Pseudomonas fluorescens A36 (•, ○) adhered to raw potato disks, enumerated by removal with the Stomacher Lab-Blender (filled symbols) or by the blotting technique (open symbols). Data points are from individual experiments performed either singly, in duplicate, or in triplicate.

DISCUSSION

The mathematical approaches adopted here allowed modeling of the rate of attachment of bacteria to, and their detachment from, the cut surface of raw potato tissue.

The numbers of bacteria attached to potato disks were significantly different among organisms, with Pseudomonas fluorescens and Pantoea agglomerans adsorbing in significantly higher numbers than L. monocytogenes (P < 0.001). It is possible that this difference was due to the difference in cell wall structures between the gram-positive and gram-negative bacteria, which is under further investigation. It was also clear that the two serotypes of L. monocytogenes showed considerable differences in the numbers of bacteria adsorbing, with serotype 4b (Scott A) adsorbing significantly (P < 0.001) higher numbers than serotype 1/2a (10403S and DP-L189 EDG). These differences are possibly attributable to differences in the surfaces or surface structures of the two serotypes. It was also clear that, for any particular organism, the values obtained could be very varied (e.g., two of the replicate determinations of the attachment of L. monocytogenes Scott A gave attachment numbers that were significantly higher than those from the other two determinations at the 1% level, although the values for the other two replicates were very similar to each other). This variation was possibly a function of the natural variability in the vegetable materials used, which makes these studies inherently difficult.

The assertion by Eginton et al. (7) that k (determined by linear regression of the data from the plots of the logarithms of the numbers of viable bacteria on the plates, against the plate numbers) can be interpreted as the inverse of the strength of attachment of bacteria to the surface of interest appears flawed. If this were indeed the case and the concept of a single strength of attachment were correct, then any detachment technique that has exceeded a notional threshold force required to remove one bacterium should result in the removal of all bacteria. We believe that our interpretation of the gradient, as a function of the probability of removal of bacteria from the surface, is preferable. It is of interest, however, that the k determined by Eginton et al. (7) can be equated to the negative logarithm to the base 10 of (1 − x) in the probabilistic analysis presented here. Overall, the probability of detachment, x, was not affected significantly by changes in inoculum concentration. Our simple analysis does not allow for multiple, or distributions of, detachment probabilities. If these had more than a single value, our technique would measure an average.

The power (a) of the relationship between the number of bacteria adsorbed to each face of the potato disk (N_F) and the initial inoculum concentration (i.e., where an increase in inoculum concentration would result in a directly proportional increase in attachment) was significantly different from the expected value of 1.0 (P < 0.0001). It was possible that the lower value of 0.79 occurred because the process of adsorption was saturated (i.e., the rate of adsorption was limited by diffusion of the bacteria to the surface, and then once the inoculum reached a certain concentration, the addition of more bacteria would not result in as large an increase in collision rate as at lower concentrations). Future studies will determine if this relationship between the number of bacteria attached and the inoculum concentration is true for different times, organisms, and conditions of attachment.

The number of Pseudomonas fluorescens calculated as populating a disk can be higher than the number counted on the disk by using the Stomacher Lab-Blender (Fig. 6). It is possible that because this organism attaches rapidly to vegetable tissue, bacteria removed by blending in the Stomacher Lab-Blender were able to reattach to the tissue before sampling, resulting in an underestimate of the true number of bacteria on the disk by this traditional enumeration technique. However, bacteria were being successfully removed in the turbulent liquid shear fields produced in the Stomacher Lab-Blender, in which the potato disks remained intact. This result demonstrated that, although the bacteria had attached (Fig. 3 and 4), effective removal could be achieved if sufficient force was applied. This finding suggests that commercial decontamination is possible if very vigorous washing procedures are applied to the surfaces of the vegetable tissues in order to overcome the attachment phenomena quantified here. Additional safeguards are then required to prevent reattachment of the bacteria from the washing liquid.

It is anticipated that the experimental methods and the mathematical models developed here will enable a more detailed investigation of the mechanisms responsible for the attachment of bacteria to vegetable tissues. From this will come improved decontamination protocols and methods to prevent bacterial adhesion that can be applied during commercial preparation of ready-to-eat vegetable products.