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Modeling the inhibitory effects of organic acids on bacteria
International Journal of Food Microbiology 47 (1999) 189–201
Modeling the inhibitory effects of organic acids on bacteria Chang-Ping Hsiao, Karl J. Siebert* Department of Food Science and Technology, Cornell University, Geneva, NY 14456, USA Received 20 May 1998; received in revised form 24 December 1998; accepted 15 January 1999
Abstract The inhibitory effect of acids on microbial growth has long been used to preserve foods from spoilage. While much of the effect can be accounted for by pH, it is well known that different organic acids vary considerably in their inhibitory effects. Because organic acids are not members of a homologous series, but vary in the numbers of carboxy groups, hydroxy groups and carbon–carbon double bonds in the molecule, it has typically not been possible to predict the magnitude, or in some cases even the direction, of the change in inhibitory effect upon substituting one acid for another or to predict the net result in food systems containing more than one acid. The objective of this investigation was to attempt to construct a mathematical model that would enable such prediction as a function of the physical and chemical properties of organic acids. Principal Components Analysis (PCA) was applied to 11 properties for each of 17 acids commonly found in food systems; this resulted in four significant principal components (PCs), presumably representing fundamental properties of the acids and indicating each acid’s location along each of these four scales. These properties correspond to polar groups, the number of double bonds, molecular size, and solubility in non-polar solvents. Minimum inhibitory concentrations (MICs) for each of eight acids for six test microorganisms were determined at pH 5.25. The MICs for each organism were modeled as a function of the four PCs using partial least squares (PLS) regression. This produced models with high correlations for five of the bacteria (R 2 5 0.856, 0.941, 0.968, 0.968 and 0.970) and one with a slightly lower value (R 2 5 0.785). Acid susceptible organisms (Bacillus cereus, Bacillus subtilis, and Alicyclobacillus) exhibited a similar response pattern. There appeared to be two separate response patterns for acid resistant organisms; one was exhibited by the two lactobacilli studied and the other by E. coli. Predicting the inhibitory effects of the organic acids as a function of their chemical and physical properties is clearly possible. 1999 Elsevier Science B.V. All rights reserved. Keywords: Predictive modeling; Partial least squares regression; Principal components analysis; Quantitative structure activity relationships; Microorganisms
*Corresponding author. Tel.: 1001-315-787-2299; fax: 1001-315-787-2284. E-mail address: [email protected] (K.J. Siebert) 0168-1605 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0168-1605( 99 )00012-4
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1. Introduction Preservation of foods has long employed a combination of factors in which acids have played an important role (Knochel and Gould, 1995). The fact that heat treatment regimes for high acid and low acid foods are quite different bears this out. While some foods are naturally acidic, in other cases acids are either directly added to a food or produced by the action of organisms such as lactobacilli or propionic acid bacteria. When an acid producing organism is used, the inhibitory effect may be partly due to a bacteriocin that is produced by the organism along with acids (Vandenbergh, 1993; Schillinger et al., 1996). Some acids, especially benzoic and sorbic, are very effective inhibitors of microbial growth and are intentionally added to many foods as preservatives (Dziezak, 1986). Other acids including acetic, fumaric, propionic and lactic, are often added to foods to prevent or delay the growth of pathogenic or spoilage bacteria (Dziezak, 1986; Greer and Dilts, 1995; Podolak et al., 1996). The relative effectiveness of different acids has often been expressed in terms of their minimum inhibitory concentrations or MICs. The MIC is the smallest concentration of an acid that will prevent the growth of an organism under a set of conditions (Oestling and Lindgren, 1993). The inhibitory effect of organic acids has widely been reported to be caused by their undissociated form (Lund et al., 1987; Zamora and Zaritzky, 1987; Adams and Hall, 1988). However, it has been shown that both the ionized and non-ionized forms of an acid can contribute to its inhibitory effect, although the undissociated form is generally more inhibitory (Eklund, 1983; Eklund, 1985). Since the pH determines the proportions of the dissociated and nondissociated forms of an acid near its pKa , it also has a strong influence on the MIC (Eklund, 1983). It is of considerable interest to efficiently use the combined effects of several factors that impose barriers to the growth of microbes (Chirife and Favetto, 1992). Studies that involve a particular organism and variations in several factors, such as water activity, temperature, pH and acid concentration, have frequently been carried out in model systems, and mathematical models describing the
behavior have been developed (Chen and Shelef, 1992; McMeekin et al., 1993; Houtsma et al., 1994; Zaika et al., 1994; Buchanan and Golden, 1995; Davey and Daughtry, 1995; Whiting, 1995; Clavero and Beuchat, 1996; George et al., 1996; Graham et al., 1996; Houtsma et al., 1996; Fernandez et al., 1997; Presser et al., 1997). Different organisms have demonstrated different rankings for the inhibitory effects of organic acids (Matsuda et al., 1994). As a result, it has generally not been possible to predict either the magnitude of a change produced if one organic acid is substituted for another, or in many cases even the direction of the change. Naturally, predicting what will happen in a real food with a mixture of different organic acids has not been possible. The organic acids typically found in foods are not members of a homologous series, but rather span a considerable range of structures with from one to three carboxy groups, different numbers of hydroxy groups, different numbers of carbon–carbon double bonds, either aromatic or aliphatic character, etc. As a result, it is currently not known how to numerically express the relationships of the acids to one another. A somewhat similar situation occurs with peptides, where compounds in a non-homologous series exert important biological effects. It is known in that case that the sequence of the amino acids in a peptide plays an important role. When Principal Components Analysis (PCA) was applied to a large number of chemical and physicochemical properties of the amino acids, three significant principal components (PCs) were obtained (Jonsson et al., 1989). These were used to successfully model two different biological activities, i.e., bitterness of dipeptides (R 2 5 0.88) and bradykinin potentiating activity of pentapeptides (R 2 5 0.90), as a function of the three PC’s for the amino acid in each position in the peptide. The objective of the work reported here was to apply methods used for quantitative structure activity relationship studies to attempt to develop models that would predict the inhibitory effects of particular organic acids on particular microorganisms. This feasibility study was carried out at a single pH (5.25) and a single temperature for each test bacteria. It was hoped that, if successful, this would provide information about the molecular properties that make an acid inhibitory toward an organism. Organisms
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that are known to be acid resistant presumably exhibit a different pattern of behavior than those that are acid susceptible.
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Broth and Plate Count Agar were purchased from Difco Laboratories (Detroit, MI).
2.2. Equipment Turbidity was measured with a Hach 2100AN ratio turbidimeter (Hach Co., Loveland, CO). Results were reported in nephelos turbidity units (NTU).
2. Experimental
2.1. Chemicals and materials 2.3. Organic acid data Acetic (glacial), citric (monohydrate, 99.9%), and lactic (85%, certified A.C.S.) acids were obtained from Fisher Scientific (Fair Lawn, NJ). Benzoic (potassium salt, 99%), butyric (99%), and caprylic (sodium salt, 99 1 %) acids were purchased from Sigma Chemical Co. (St. Louis, MO). DL-malic acid (practical) was obtained from Nutritional Biochemicals Corporation (Cleveland, OH) and tartaric acid (granular A.C.S.) was from Mallinckrodt Chemical Works (St. Louis, MO). A buffer, 0.8M KH 2 PO 4 , was used to maintain pH in the incubating media at 5.25. Brain Heart Infusion medium, Potato Dextrose
Physical and chemical property data for 17 organic acids commonly found in foods were collected from reference sources (Weast and Astle, 1981; Budavari et al., 1989) or obtained from inspection of structural formulae. These were the molecular weight, the number of carbon atoms, the number of carboxy groups, the number of hydroxy groups, the number of carbon–carbon double bonds, the number of conjugated double bonds, the melting point, the first pKa value, and the relative solubilities in ethanol, diethyl ether, and water (see Table 1). The solubilities were expressed as codes (see Table 2) which
Table 1 Organic acid property data a Name
MW (Da)
C NO ]
COOH
OH
CC DB ]
CONJ
MP (8C)
pKa 1
Ethanol Sol.b
Ether Sol.b
H2O Sol.b
Acetic Benzoic Butyric Capric Caproic Caprylic Citric Formic Fumaric Heptanoic Lactic Malic Propionic Sorbic Succinic Tartaric Valeric
60.1 122.1 88.1 172.3 116.2 144.2 192.1 46.0 116.1 130.2 90.1 134.1 74.1 112.1 118.1 150.01 102.1
2 7 4 10 6 8 6 1 4 7 3 4 3 6 4 4 5
1 1 1 1 1 1 3 1 2 1 1 2 1 1 2 2 1
0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 2 0
0 3 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0
0 4 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0
16.6 122.4 25.7 31.9 23.4 16.7 153 8.4 300 27.5 16.8 132 220.7 134.5 188 169 233.8
4.75 4.19 4.81 4.89 4.88 4.89 3.13 3.75 3.03 4.89 3.86 3.40 4.87 4.76 4.16 2.98 4.82
5 3 5 4 5 5 5 5 1 4 4 4 4 2 1 3 5
5 3 5 4 5 5 3 5 2 4 4 3 4 3 2 1 5
5 1 5 1 2 1 4 5 1 1 4 3 5 1 2 5 2
a
MW5molecular weight; C NO5number of carbon atoms; COOH5number of carboxy groups; OH5number of hydroxy groups; ] CC DB5number of carbon–carbon double bonds; CONJ5number of conjugated double bonds; MP5melting point; pKa 15first (lowest) ] pKa . b See solubility codes in Table 2.
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Table 2 Solubility scales used in Table 1 Code
ricultural Experiment Station. Alicyclobacillus (VF) was isolated from apple juice (Splittstoesser et al., 1994).
Solubility (g / 100 g) or description Ethanol
Diethyl ether
Water
1 2 3
0–10 .10–30 .30–70
0–1 .1–10 .10–50
4
.70 soluble freely sol. readily sol. miscible
0–0.5 .0.5–2 .2 slightly soluble soluble freely sol. readily sol. miscible
.100 miscible
5
.50–100
enabled use of descriptive (e.g. ‘slightly soluble’), as well as numeric data.
2.4. Multivariate techniques Principal Components Analysis (PCA) was applied with the Factor Analysis routine in the STATISTICA computer program ( STATISTICA for Windows Release 5.1H 1997 edition, StatSoft Inc., Tulsa, OK). In the case of the acid data, results were Varimax rotated. Cluster Analysis was applied to the Varimax rotated PC score values for the acids with the joining (tree clustering) method, using single linkage amalgamation based on the Euclidean distances ( STATISTICA).
2.5. Selection of acid subset Cluster analysis was used to display the similarities of the acid patterns of principal components. Eight acids with dissimilar patterns were selected for experimental work.
2.6. Microorganisms Six bacteria, including organisms expected to be acid susceptible and acid resistant, were used in this study. Bacillus cereus (ATCC11778), Bacillus subtilis (ATCC6633), Escherichia coli (ATCC25922), and Lactobacillus fermentum (ATCC14931) were obtained from the American Type Culture Collection (Rockville, MD). Lactobacillus plantarum (EH22G) was provided by John Churey of the Food Science and Technology Department, New York State Ag-
2.7. Growth conditions Each of the bacteria used in this study was incubated under conditions favorable for its growth. B. cereus, B. subtilis, and E. coli were incubated at 308C for 24 h in Brain Heart Infusion medium. L. fermentum and L. plantarum were incubated at 378C for 24 h in Brain Heart Infusion medium. Alicyclobacillus was incubated at 538C for 48 h in Potato Dextrose Broth.
2.8. Preparation of acid media KH 2 PO 4 was added to Type I distilled water at 10% (w / w) concentration, and this buffer solution was adjusted to pH 5.25. The incubating medium was added to the buffer solution and adjusted to pH 5.25. The organic acids were added to the buffer solution to prepare stock solutions (10% for acetic, butyric, citric, lactic, malic and tartaric acids and 1% for benzoic and caprylic acids) and adjusted to pH 5.25. The pH adjustments were made with 0.1M, 1M, or 2M HCl, or 0.1M, 1M, or 10M NaOH, as appropriate. The incubating medium, buffer solution, and organic acid (total volume 30 ml) were added to 55 ml culture tubes (Kimble Glass, Vineland, NJ) at the concentrations used for experiments. The tubes were autoclaved at 1218C for 15 min and then air-cooled to room temperature.
2.9. Growth assessment A standard curve relating light scattering results to plate counts was prepared with B. cereus. The organism was incubated in broth samples with or without benzoic or citric acid. After the incubation the light scattering intensity of one aliquot of each sample was measured. Additional aliquots (1 ml) of the same sample were plated onto Plate Count Agar in a dilution series in triplicate and incubated for 24 h at 308C. The colonies were then counted. A standard curve was prepared relating the light scattering measurements to the colony forming units.
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2.10. MIC determination Microorganisms were incubated in their selected growth environment (selected temperature and medium without added acid) for one or two days before experiments. For each test acid a series, with concentrations increasing by a constant factor, was prepared in the culture medium used for each organism. The factors and starting levels were determined by preliminary experiments with each acid / organism pair and ranged from multiples of 1.546 (L. plantarum on malic acid) to 3.68 (most organisms on most acids). The same volume (3 drops) of bacterial suspension was added to each experimental culture tube (containing 30 ml of medium), using a syringe (Becton, Dickinson and Company, Rutherford, NJ) while working in a laminar flow hood. No organisms were added to the blank culture tubes. The tubes (experimental and blank groups) were incubated for 24 or 48 h, depending on the organism. After incubation, the culture tubes were inserted into the turbidimeter to assess the sample turbidity. The blank samples were used to detect possible precipitation unrelated to bacterial growth. The minimum inhibitory concentration (MIC) was determined as the geometric mean of the lowest acid concentration at which there was no growth for an organism (turbidity equal to the non-inoculated blank for that acid and medium) and the next lower concentration.
2.11. Modeling The MICs for each bacterium (dependent variable) were modeled as a function of the four Varimax rotated principal component scores (PCs) for the acids (independent variables), using Partial Least Squares (PLS) regression. PLS was carried out with SCAN for Windows Release 1.1 (Minitab, State College, PA). PLS models were calculated using from one to four components. In each case the best fit equations (those with the highest R 2 ) and those with the best predictive ability (lowest predictive residual error sum of squares, or PRESS) were obtained.
3. Results and discussion The data for organic acids in Table 1 includes both measured properties (melting point, pKa , solubility)
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and items observed from structures (molecular weight, numbers of carbon atoms, carboxy groups, hydroxy groups, carbon–carbon double bonds, and conjugated double bonds). The solubility data available were partly numeric (typically expressed as g / 100 g) and partly descriptive (i.e., ‘slightly soluble’, ‘soluble’, ‘freely soluble’, etc.). To accommodate both, codes (numbers from 1 to 5) were used to express increasing solubility in each solvent. The numeric solubility values corresponding to each code were slightly different for ethanol, ether, and water (see Table 2) to maximize the spread of numbers representing each solubility property. Principal components analysis is a technique for concentrating the information in a data set into fewer dimensions (Massart et al., 1988). It does this by creating new variables that are linear combinations of the original property (or measurement) variables and which account for maximum possible variance in the data set. Each PC is constrained to be orthogonal to all previously extracted PCs (at right angles in multidimensional space and hence completely uncorrelated), and as a result they have no overlap in information content. Each PC thus represents a different fundamental property of a system, with properties that are partially or largely redundant in information content influencing the same PC in the same direction. This is evident in the loading plot, which shows correlations between the PCs and property variables. The number of significant PCs (usually judged from either a Scree plot or by choosing only those with eigenvalues . 1) indicates the number of fundamentally different properties exhibited by the data set. Orthogonal rotations, such as Varimax rotation, rotate the PC structure in multidimensional space to improve the alignment between the original property variables and the PCs while preserving the relationships between the PCs (Massart et al., 1988). This usually makes them easier to understand, while completely preserving their information content and modeling ability. Principal Components Analysis was applied to the data in Table 1. This resulted in the eigenvalues shown in the Scree plot in Fig. 1. A sharp break occurred at the fourth PC, so four PCs, accounting for 93.1% of the total variance in the data set, were retained. The four PCs were then subjected to Varimax rotation to bring them into closer alignment
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molecular size, and larger size results in lower water solubility. PC4 is heavily influenced by solubility in ether and alcohol, and in the opposite direction, by melting point; PC4 thus essentially represents nonpolarity. The proportion of the total variance accounted for by the four Varimax rotated PCs is the same as it was for the first four unrotated PCs, but the distribution of the variance explained over the PCs is quite different. Also resulting from the PCA are the factor score values (Table 4). These specify the location of each acid along each of the Varimax rotated PCs. This is illustrated in Figs. 2 and 3. Fig. 2 shows each acid’s location on the PC1 and PC2 axes. The PC1 axis represents high polarity toward the left and decreases toward the right. Most of the acids have similar values along PC2, but benzoic and sorbic acids, which are known to be good preservatives, have much higher values. Fumaric acid is somewhat further along this axis than most of the other acids; this is interesting in view of the relatively strong inhibitory effect of fumaric acid towards a number of microorganisms (Splittstoesser and Stoyla, 1989; Shimizu et al., 1995; Podolak et al., 1996a,b). Fig. 3 depicts the acid locations along the PC3 and PC4 axes. Here most of the acids have similar PC4 values but are separated along the PC3 axis with the smaller molecules at the right and the larger at the left. Succinic and fumaric acids have much higher PC4 values than the other acids, indicating their low solubility in organic solvents. Together, the set of four PC scores for an acid specifies its coordinates in the four dimensional
Fig. 1. Plot of the eigenvalues (showing the proportion of the variance explained) by each principal component extracted from the organic acid data.
with the original variables (Massart et al., 1988). The Varimax rotated factor loadings are shown in Table 3; these are the correlations between the PCs and the original acid characteristics. Loadings with an absolute value greater than 0.70 (shown in bold type) represent a strong influence. It can be seen that PC1 is heavily influenced by the numbers of hydroxy and carboxy groups in one direction and by the first pKa in the opposite direction. Acids with relatively large numbers of carboxy groups or hydroxy groups or with a low first pKa will have a low score on this axis. To a large extent, PC1 represents the number of polar groups. PC2 is almost entirely related to the numbers of carbon–carbon and conjugated double bonds. PC3 is loaded heavily by molecular weight, by carbon number, and, in the opposite direction, by water solubility; this means it is largely a function of
Table 3 Varimax rotated principal component factor loadings for organic acid properties Chemical and Physical Properties
PC1
PC2
PC3
PC4
Molecular weight Number of carbon atoms Number of COOH groups Number of OH groups Number of CC double bonds Number of conjugated double bonds Melting point pKa 1 Solubility in alcohol Solubility in ether Solubility in water
20.469 0.145 20.749 20.919 0.068 0.065 20.476 0.835 0.017 0.587 20.397
20.079 0.131 20.213 20.134 0.966 0.924 0.292 20.071 20.331 20.210 20.316
20.866 20.967 20.138 0.035 20.120 20.087 20.096 20.189 0.032 0.115 0.731
0.129 20.097 0.474 20.045 0.164 0.338 0.797 20.392 20.906 20.710 20.333
28.0%
20.2%
21.1%
23.8%
Proportion of total variance
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Table 4 Varimax rotated principal component factor scores for organic acid properties Organic Acid
PC1
PC2
PC3
PC4
Acetic Benzoic Butyric Capric Caproic Caprylic Citric Formic Fumaric Heptanoic Lactic Malic Propionic Sorbic Succinic Tartaric Valeric
0.539 20.0957 0.396 0.586 0.668 0.636 22.22 0.214 20.0395 0.850 20.543 21.19 0.633 0.644 0.663 22.48 0.734
20.245 3.13 20.250 20.584 20.387 20.438 20.560 20.0922 0.777 20.568 20.0259 20.402 20.392 1.79 21.22 20.156 20.368
1.45 20.488 0.726 22.02 20.492 21.37 20.997 1.94 0.277 20.967 0.882 0.00035 1.11 20.261 0.113 0.228 20.135
20.593 20.437 20.884 20.250 20.686 20.700 20.343 20.558 2.45 20.0575 20.624 0.169 20.207 0.594 2.62 0.181 20.683
Fig. 2. Plot of acid scores on varimax rotated principal component axes PC1 (representing mainly polarity) and PC2 (representing mainly numbers of double bonds).
Fig. 3. Plot of acid scores on varimax rotated principal component axes PC3 (representing mainly molecular size) and PC4 (representing mainly solubility in organic solvents).
space. Acids that are located close together (short vector distances) in this four dimensional space have similar combinations of properties. This can be represented by applying Cluster Analysis based on Euclidean distances (see Fig. 4). Acids with PC patterns that are close together are considered to be similar and are represented as joining together near the left side of the cluster diagram. Those that are more dissimilar join together closer to the right side of the figure. For modeling purposes, two acids with highly dissimilar combinations of properties provide
more information than two with similar patterns (Massart et al., 1988). As a result, when two acids have similar patterns, use of one of them is sufficient; adding data for the second provides little additional information. Of the 17 acids listed in Table 1, a set of eight acids with fairly dissimilar PC patterns (names shown in bold in Fig. 4) was selected. Six bacteria were selected for use in this study. The two Bacillus species were expected to be acid susceptible. The lactobacilli, themselves acid produc-
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Fig. 4. Cluster diagram of acid principal component scores, showing the similarity of the patterns (those joining together toward the left side are more similar than those joining together toward the right).
ers, were expected to be acid resistant. Since pathogenic E. coli has been associated with food poisoning outbreaks in cider (Mshar et al., 1997), an acidic beverage, it must be acid resistant and it might be expected that the non-pathogenic E. coli used in this study could be acid resistant as well. Alicyclobacillus has on a number of occasions been isolated from high acid fruit juices (Splittstoesser et al., 1994; Yamazaki et al., 1996; Baumgart et al., 1997; Borlinghaus and Engel, 1997; Pettipher et al., 1997) and was, as a result, expected to demonstrate acid resistance. Since most microbiologists measure ‘‘turbidity’’ with a spectrophotometer, and a turbidimeter (light scattering instrument) was used in this work, it seemed appropriate to test the linearity of response and to determine roughly how many organisms were represented by one measurement unit (nephelos turbidity unit 5 NTU). When sample turbidities (expressed in NTU) from a series of B. cereus samples
were compared with plate counting results from the same samples, a linear relationship was seen, with 1 NTU representing approximately 2 3 10 6 organisms. Turbidity values were then used directly to assess the extent of cell growth. Minimum inhibitory concentrations were determined for each of the eight selected acids for each of the six test organisms. The MICs were defined here as the geometric average between the highest concentration at which growth was observed and the lowest concentration at which no growth was seen with incubation times of 24–48 h. The geometric average should produce results that are close to the actual numerical value at which growth is inhibited, which are desirable for modeling, but it is not the most conservative approach, and food safety considerations would be better served by using the lowest concentration at which no growth occurs and longer incubation times than were employed in this feasibility study. Once the approximate inhibitory concentration of an acid for an organism was established, several nearby concentrations were prepared in which the acid was increased between samples by a constant factor. In several cases (both lactobacilli with malic acid and L. fermentum with tartaric acid), low concentrations of acid resulted in greater numbers of the test microorganisms than the no acid controls; this indicates that the acid was utilized as a nutrient. Higher acid concentrations, however, resulted in inhibition. The results are shown in Table 5. All the organisms but Alicyclobacillus were able to grow in the presence of malic acid concentrations over 10 g / l. Similar levels of citric and tartaric acids only inhibited Alicyclobacillus and B. cereus. B. subtilis, B. cereus, and Alicyclobacillus appeared to be relatively sensitive to most acids, particularly benzoic. This was a surprise in the case of Alicyclobacillus, as this bacterium was expected to
Table 5 Minimum inhibitory concentrations (g / l) for the test organic acids for the test organisms Microorganism
Acetic
Benzoic
Butyric
Caprylic
Citric
Lactic
Malic
Tartaric
B. cereus B. subtilis E. coli L. fermentum L. plantarum Alicyclobacillus
2.02 0.105 1.55 26.3 27.5 0.727
0.296 0.192 0.316 2.50 2.61 0.061
0.959 0.096 1.41 24.0 25.0 0.303
0.068 0.192 1.73 1.58 2.61 0.316
3.68 26.1 38.2 15.8 26.1 4.58
3.48 8.32 3.72 25.3 30.7 5.39
13.6 26.1 50.0 25.0 26.1 4.58
5.90 26.1 50.0 25.0 26.1 7.07
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be acid resistant. It was instead the most susceptible of all the organisms tested for three of the acids. The lactobacilli were much more resistant to acetic, benzoic, butyric and lactic acids, than the other organisms tested. E. coli was the most resistant toward citric, malic and tartaric acids, demonstrating a different pattern of acid resistance than the lactobacilli. The E. coli strain was particularly insensitive to malic acid. While different E. coli strains are known to exhibit different degrees of acid resistance (Miller and Kaspar, 1994), this finding is perhaps relevant to the outbreaks of pathogenic E. coli in cider (Mshar et al., 1997), as malic acid is, by far, the predominant organic acid in apple juice (Lee and Wrolstad, 1988). The modeling technique used in this study was Partial Least Squares Regression (PLS). This calculates principal components through the independent variables and models the dependent variable as a function of the PCs (Beebe et al., 1998). As such, the technique is robust against a number of phenomena that violate assumptions of multiple linear regression, including high correlation between independent variables and a low sample to measurement ratio (an overdetermined system). PLS also employs crossvalidation (iterative recalculation of the model omitting a different sample point each time) to test for sensitivity of the model toward a particular sample. This is used to calculate the PRESS (predictive residual error sum of squares) which allows com-
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parison of the tradeoff between better fitting with increasing complexity (more terms) and the resulting build-up of error (tending toward overfitting). Mathematical models expressing MIC as a function of the PC values of an acid: MIC 5 b 0 1 b 1 ? PC1 1 b 2 ? PC2 1 b 3 ? PC3 1 b 4 ? PC4 were constructed, where the coefficients (the b terms) were fit by Partial Least Squares (PLS) Regression using a matrix of the 4 PC scores for the eight acids as the independent variables, and the corresponding MIC values as the dependent variable. PLS is better suited than Multiple Linear Regression to situations where combinations of levels of the independent variables cannot be set at optimal levels or where the sample / measurement ratio is less than 3. The analysis resulted in the fits described in Table 6. The PLS regression best fits (highest R 2 ) were in each case for the models derived using 4 PLS components. The best prediction equations (those with the lowest PRESS), were obtained with either one (B. cereus, Alicyclobacillus), two (B. subtilis, E. coli, L. plantarum), or three (L. fermentum) PLS components. When the best prediction equations were based on 2- or 3-component models, the R 2 values were almost identical to those of the equivalent four component models. The one component model R 2 values were noticeably lower than those of the four component models. Figs. 5–10 show the
Table 6 Partial least squares (PLS) fitting results for acid minimum inhibitory concentration (g / l) data Microorganism
Best fits (highest R 2 ) R2
b0
b1
b2
b3
b4
B. cereus B. subtilis E. coli L. fermentum L. plantarum Alicyclobacillus
9.283 12.13 30.42 17.45 14.42 2.071
1.080 26.298 26.167 22.684 26.162 21.831
21.156 22.591 25.098 23.162 23.640 20.430
0.5062 20.8906 22.038 8.978 8.530 0.6521
11.74 11.73 37.39 2.464 26.488 0.7559
0.785 0.968 0.970 0.968 0.941 0.856
Microorganism
Best predictions (lowest residual PRESS)
B. cereus B. subtilis E. coli L. fermentum L. plantarum Alicyclobacillus
b0 5.28 13.60 26.32 18.58 19.79 3.398
b3 0.2258 20.9215 21.353 8.949 8.114 0.1185
b4 5.359 14.11 30.80 4.369 1.653 2.879
R2 0.621 0.966 0.964 0.966 0.898 0.831
b1 21.152 25.513 28.399 22.099 23.023 21.130
b2 20.6926 22.777 24.894 23.189 24.562 20.4812
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Fig. 5. Best fit relationship (R 2 50.785) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for B. cereus.
Fig. 6. Best fit relationship (R 2 50.968) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for B. subtilis.
relationships between the measured MICs for the test acids and those predicted from the best fit equations in Table 6. Clearly, MIC can be quite successfully predicted as a function of the four PCs. R 2 values ranged from 0.941–0.970 for four of the bacteria and were 0.785 and 0.856 for the other two. Examination of the patterns of coefficients (Table 6) reveals some similarities in signs and magnitudes. These should be informative regarding the mechanisms of acid resistance and susceptibility. Note, for example, that the b 2 values were highest (in this case less negative) for the acid susceptible organisms. This is interesting because PC2 is the axis on which the numbers of carbon–carbon and conjugated double bonds loaded heavily and along which benzoic and sorbic acids,
Fig. 7. Best fit relationship (R 2 50.970) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for E. coli.
Fig. 8. Best fit relationship (R 2 50.968) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for L. fermentum.
Fig. 9. Best fit relationship (R 2 50.941) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for L. plantarum.
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Fig. 10. Best fit relationship (R 2 50.856) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for Alicyclobacillus.
which are known to have strong antimicrobial activity, were well separated from the other acids (see Fig. 2). The lactobacilli, which exhibited one pattern of acid resistance, were highest in the coefficient b 3 , which corresponds to PC3 (heavily loaded by molecular size). It can be seen that the acids for which the Lactobacilli were particularly resistant (acetic, benzoic, butyric and lactic), were mostly relatively small (see Fig. 3). E. coli had by far the largest b 4 term, the coefficient of PC4, representing the ethanol and ether solubility (non-polarity) axis. These different patterns can be seen in Fig. 11, which shows results of PCA applied to the coefficients in Table 6. To estimate the MIC values for an acid used in the calculation of the principal components, one would take the four Varimax rotated PC score values for the acid from Table 4, and then insert these into the five-term equation for a modeled organism and compute the algebraic sum; this is the predicted MIC. For example, to estimate the MIC for fumaric acid for E. coli, look up the four PC scores for fumaric acid in Table 4: 20.0395, 0.777, 0.277, and 2.45, respectively. Look up the coefficients of the best prediction equation for E. coli in Table 6. Insert the values: MIC 5 26.32 2 8.399 ? PC1 2 4.894 ? PC2 2 1.353 ? PC3 1 30.80 ? PC4 MIC 5 26.32 2 8.399(20.0395) 2 4.894 (0.777) 2 1.353 (0.277) 1 30.80 (2.453)
Fig. 11. Depiction of relationships of the best fit models. Principal components analysis was applied to the best fit model coefficients for the six modeled bacteria.
MIC 5 98.0 g / l It is also possible to estimate the MIC for an acid not listed in Table 1 for a modeled organism, although this is more in the nature of an extrapolation than an interpolation. This is first done by obtaining the 11 needed data parameters for the acid. For the solubility data, one would convert the results into the codes according to Table 2. Using the data in Table 1, one could calculate the mean and standard deviation for each parameter. For the acid under consideration, for each of its parameter columns, one would subtract the corresponding mean and divide by the corresponding standard deviation; this results in 11 normalized parameter values. Then one would multiply each of the normalized values by the corresponding Varimax rotated factor score coefficient (from PCA analysis of Table 1) for each of the four PCs and sum algebraically. This results in the four Varimax rotated factor scores for the acid in question. One would then substitute these in the five-term equation for a modeled organism and then calculate the algebraic sum; this is the predicted MIC. The same four PCs described here were also used to model the flavor thresholds of organic acids added to beer (Siebert, 1999). This, too, produced a highly significant model (R 2 50.905). Since both biological
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activities produced good models with the same set of PCs, it appears that they represent fairly fundamental properties that are important in predicting both the fit of these molecules to flavor receptors and their ability to enter microbial cells and inhibit growth. It would clearly be of interest to expand the current data set to include more acids, more organisms, and additional growth conditions (pHs, temperatures and media). In particular, it would be interesting to know if there are only the three response patterns seen so far or if there are additional patterns of acid resistance. It would be interesting to know if the inhibitory effects of acids other than those used to construct the MIC models or even outside the set used to calculate PCs can be correctly predicted. It would also be useful to know if predictions can be made as to which acids are especially effective in inhibiting the growth of particular problem organisms. It may also be possible to predict the behavior of organisms in mixed acid systems that correspond to real food systems.
4. Conclusions Principal Components Analysis showed that four fundamental properties could represent the information contained in the 11 acid data used. These properties correspond to polar groups, the number of double bonds, molecular size, and solubility in nonpolar solvents. The six test bacteria exhibited essentially three MIC patterns, representing acid susceptibility and two different patterns of acid resistance. The lactobacilli were much more resistant to acetic, benzoic, butyric and lactic acids than the other organisms tested, while the E. coli was most resistant toward citric, malic and tartaric acids. For each organism an equation was fit that expressed the MIC for each acid as a function of its four PC scores. Four of these were very strong relationships (R 2 5 0.941–0.970), while the other two were not as strong (R 2 50.785 and 0.856). It is clearly possible to model the inhibitory effect of organic acids as a function of their molecular properties.
Acknowledgements This material is based upon work supported by the Cooperative State Research, Education and Exten-
sion Service, U.S. Department of Agriculture, under Project NYG 623-496. John Churey and Penelope Lynn of this department provided valuable advice on laboratory techniques.
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and Listeria growth by lactic, acetic and formic acids. J. Appl. Bacteriol. 75, 18–24. Pettipher, G.L., Osmundson, M.E., Murphy, J.M., 1997. Methods for the detection and enumeration of Alicyclobacillus acidoterrestris and investigation of growth and production of taint in fruit juice and fruit juice-containing drinks. Lett. Appl. Microbiol. 24, 185–189. Podolak, R.K., Zayas, J.F., Kastner, C.L., Fung, D.Y.C., 1996. Inhibition of Listeria monocytogenes and Escherichia coli O157:H7 on beef by application of organic acids. J. Food Prot. 59, 370–373. Podolak, R.K., Zayas, J.F., Kastner, C.L., Fung, D.Y.C., 1996. Reduction of bacterial populations on vacuum-packaged ground beef patties with fumaric and lactic acids. J. Food Prot. 59, 1037–1040. Presser, K.A., Ratkowsky, D.A., Ross, T., 1997. Modeling the growth rate of Escherichia coli as a function of pH and lactic acid concentration. Appl. Environ. Microbiol. 63, 2355–2360. Schillinger, U., Geisen, R., Holzapfel, W.H., 1996. Potential of antagonistic microorganisms and bacteriocins for the biological preservation of foods. Trends in Food Sci. and Technol. 7, 158–164. Shimizu, T., Takahata, T., Kato, M., 1995. Antibacterial activity of several organic acids commonly used as food additives. J. Food Hygien. Soc. Japan [Shokuhin Eiseigaku Zasshi] 36, 50–54. Siebert, K.J., 1999. Modeling the flavor thresholds of organic acids in beer as a function of their molecular properties. Food Qual. and Pref. 10, 129–137. Splittstoesser, D.F., Churey, J.J., Lee, C.Y., 1994. Growth characteristics of aciduric sporeforming bacilli isolated from fruit juices. J. Food Prot. 57, 1080–1083. Splittstoesser, D.F., Stoyla, B.O., 1989. Effect of various inhibitors on the growth of lactic acid bacteria in a model grape juice system. J. Food Prot. 52, 240–243. Vandenbergh, P.A., 1993. Lactic acid bacteria, their metabolic products and interference with microbial growth. FEMS Microbiol. Rev. 12, 221–237. CRC Handbook of Chemistry and Physics, 62nd ed, 1981. CRC Press, Inc, Boca Raton, FL. Whiting, R.C., 1995. Microbial modeling in foods. Crit. Rev. Food Sci. and Nutrit. 35, 467–494. Yamazaki, K., Teduka, H., Shinano, H., 1996. Isolation and identification of Alicyclobacillus acidoterrestris from acidic beverages. Biosci., Biotechnol. and Biochem. 60, 543–545. Zaika, L.L., Moulden, E., Weimer, L., Phillips, J.G., Buchanan, R.L., 1994. Model for the combined effects of temperature, initial pH, sodium chloride and sodium nitrite concentrations on anaerobic growth of Shigella flexneri. Int. J. Food Microbiol. 23, 345–358. Zamora, M.C., Zaritzky, N.E., 1987. Antimicrobial activity of undissociated sorbic acid in vacuum packaged beef. J. Food Sci. 52, 1449–1454.
Modeling the inhibitory effects of organic acids on bacteria Chang-Ping Hsiao, Karl J. Siebert* Department of Food Science and Technology, Cornell University, Geneva, NY 14456, USA Received 20 May 1998; received in revised form 24 December 1998; accepted 15 January 1999
Abstract The inhibitory effect of acids on microbial growth has long been used to preserve foods from spoilage. While much of the effect can be accounted for by pH, it is well known that different organic acids vary considerably in their inhibitory effects. Because organic acids are not members of a homologous series, but vary in the numbers of carboxy groups, hydroxy groups and carbon–carbon double bonds in the molecule, it has typically not been possible to predict the magnitude, or in some cases even the direction, of the change in inhibitory effect upon substituting one acid for another or to predict the net result in food systems containing more than one acid. The objective of this investigation was to attempt to construct a mathematical model that would enable such prediction as a function of the physical and chemical properties of organic acids. Principal Components Analysis (PCA) was applied to 11 properties for each of 17 acids commonly found in food systems; this resulted in four significant principal components (PCs), presumably representing fundamental properties of the acids and indicating each acid’s location along each of these four scales. These properties correspond to polar groups, the number of double bonds, molecular size, and solubility in non-polar solvents. Minimum inhibitory concentrations (MICs) for each of eight acids for six test microorganisms were determined at pH 5.25. The MICs for each organism were modeled as a function of the four PCs using partial least squares (PLS) regression. This produced models with high correlations for five of the bacteria (R 2 5 0.856, 0.941, 0.968, 0.968 and 0.970) and one with a slightly lower value (R 2 5 0.785). Acid susceptible organisms (Bacillus cereus, Bacillus subtilis, and Alicyclobacillus) exhibited a similar response pattern. There appeared to be two separate response patterns for acid resistant organisms; one was exhibited by the two lactobacilli studied and the other by E. coli. Predicting the inhibitory effects of the organic acids as a function of their chemical and physical properties is clearly possible. 1999 Elsevier Science B.V. All rights reserved. Keywords: Predictive modeling; Partial least squares regression; Principal components analysis; Quantitative structure activity relationships; Microorganisms
*Corresponding author. Tel.: 1001-315-787-2299; fax: 1001-315-787-2284. E-mail address: [email protected] (K.J. Siebert) 0168-1605 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0168-1605( 99 )00012-4
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1. Introduction Preservation of foods has long employed a combination of factors in which acids have played an important role (Knochel and Gould, 1995). The fact that heat treatment regimes for high acid and low acid foods are quite different bears this out. While some foods are naturally acidic, in other cases acids are either directly added to a food or produced by the action of organisms such as lactobacilli or propionic acid bacteria. When an acid producing organism is used, the inhibitory effect may be partly due to a bacteriocin that is produced by the organism along with acids (Vandenbergh, 1993; Schillinger et al., 1996). Some acids, especially benzoic and sorbic, are very effective inhibitors of microbial growth and are intentionally added to many foods as preservatives (Dziezak, 1986). Other acids including acetic, fumaric, propionic and lactic, are often added to foods to prevent or delay the growth of pathogenic or spoilage bacteria (Dziezak, 1986; Greer and Dilts, 1995; Podolak et al., 1996). The relative effectiveness of different acids has often been expressed in terms of their minimum inhibitory concentrations or MICs. The MIC is the smallest concentration of an acid that will prevent the growth of an organism under a set of conditions (Oestling and Lindgren, 1993). The inhibitory effect of organic acids has widely been reported to be caused by their undissociated form (Lund et al., 1987; Zamora and Zaritzky, 1987; Adams and Hall, 1988). However, it has been shown that both the ionized and non-ionized forms of an acid can contribute to its inhibitory effect, although the undissociated form is generally more inhibitory (Eklund, 1983; Eklund, 1985). Since the pH determines the proportions of the dissociated and nondissociated forms of an acid near its pKa , it also has a strong influence on the MIC (Eklund, 1983). It is of considerable interest to efficiently use the combined effects of several factors that impose barriers to the growth of microbes (Chirife and Favetto, 1992). Studies that involve a particular organism and variations in several factors, such as water activity, temperature, pH and acid concentration, have frequently been carried out in model systems, and mathematical models describing the
behavior have been developed (Chen and Shelef, 1992; McMeekin et al., 1993; Houtsma et al., 1994; Zaika et al., 1994; Buchanan and Golden, 1995; Davey and Daughtry, 1995; Whiting, 1995; Clavero and Beuchat, 1996; George et al., 1996; Graham et al., 1996; Houtsma et al., 1996; Fernandez et al., 1997; Presser et al., 1997). Different organisms have demonstrated different rankings for the inhibitory effects of organic acids (Matsuda et al., 1994). As a result, it has generally not been possible to predict either the magnitude of a change produced if one organic acid is substituted for another, or in many cases even the direction of the change. Naturally, predicting what will happen in a real food with a mixture of different organic acids has not been possible. The organic acids typically found in foods are not members of a homologous series, but rather span a considerable range of structures with from one to three carboxy groups, different numbers of hydroxy groups, different numbers of carbon–carbon double bonds, either aromatic or aliphatic character, etc. As a result, it is currently not known how to numerically express the relationships of the acids to one another. A somewhat similar situation occurs with peptides, where compounds in a non-homologous series exert important biological effects. It is known in that case that the sequence of the amino acids in a peptide plays an important role. When Principal Components Analysis (PCA) was applied to a large number of chemical and physicochemical properties of the amino acids, three significant principal components (PCs) were obtained (Jonsson et al., 1989). These were used to successfully model two different biological activities, i.e., bitterness of dipeptides (R 2 5 0.88) and bradykinin potentiating activity of pentapeptides (R 2 5 0.90), as a function of the three PC’s for the amino acid in each position in the peptide. The objective of the work reported here was to apply methods used for quantitative structure activity relationship studies to attempt to develop models that would predict the inhibitory effects of particular organic acids on particular microorganisms. This feasibility study was carried out at a single pH (5.25) and a single temperature for each test bacteria. It was hoped that, if successful, this would provide information about the molecular properties that make an acid inhibitory toward an organism. Organisms
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that are known to be acid resistant presumably exhibit a different pattern of behavior than those that are acid susceptible.
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Broth and Plate Count Agar were purchased from Difco Laboratories (Detroit, MI).
2.2. Equipment Turbidity was measured with a Hach 2100AN ratio turbidimeter (Hach Co., Loveland, CO). Results were reported in nephelos turbidity units (NTU).
2. Experimental
2.1. Chemicals and materials 2.3. Organic acid data Acetic (glacial), citric (monohydrate, 99.9%), and lactic (85%, certified A.C.S.) acids were obtained from Fisher Scientific (Fair Lawn, NJ). Benzoic (potassium salt, 99%), butyric (99%), and caprylic (sodium salt, 99 1 %) acids were purchased from Sigma Chemical Co. (St. Louis, MO). DL-malic acid (practical) was obtained from Nutritional Biochemicals Corporation (Cleveland, OH) and tartaric acid (granular A.C.S.) was from Mallinckrodt Chemical Works (St. Louis, MO). A buffer, 0.8M KH 2 PO 4 , was used to maintain pH in the incubating media at 5.25. Brain Heart Infusion medium, Potato Dextrose
Physical and chemical property data for 17 organic acids commonly found in foods were collected from reference sources (Weast and Astle, 1981; Budavari et al., 1989) or obtained from inspection of structural formulae. These were the molecular weight, the number of carbon atoms, the number of carboxy groups, the number of hydroxy groups, the number of carbon–carbon double bonds, the number of conjugated double bonds, the melting point, the first pKa value, and the relative solubilities in ethanol, diethyl ether, and water (see Table 1). The solubilities were expressed as codes (see Table 2) which
Table 1 Organic acid property data a Name
MW (Da)
C NO ]
COOH
OH
CC DB ]
CONJ
MP (8C)
pKa 1
Ethanol Sol.b
Ether Sol.b
H2O Sol.b
Acetic Benzoic Butyric Capric Caproic Caprylic Citric Formic Fumaric Heptanoic Lactic Malic Propionic Sorbic Succinic Tartaric Valeric
60.1 122.1 88.1 172.3 116.2 144.2 192.1 46.0 116.1 130.2 90.1 134.1 74.1 112.1 118.1 150.01 102.1
2 7 4 10 6 8 6 1 4 7 3 4 3 6 4 4 5
1 1 1 1 1 1 3 1 2 1 1 2 1 1 2 2 1
0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 2 0
0 3 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0
0 4 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0
16.6 122.4 25.7 31.9 23.4 16.7 153 8.4 300 27.5 16.8 132 220.7 134.5 188 169 233.8
4.75 4.19 4.81 4.89 4.88 4.89 3.13 3.75 3.03 4.89 3.86 3.40 4.87 4.76 4.16 2.98 4.82
5 3 5 4 5 5 5 5 1 4 4 4 4 2 1 3 5
5 3 5 4 5 5 3 5 2 4 4 3 4 3 2 1 5
5 1 5 1 2 1 4 5 1 1 4 3 5 1 2 5 2
a
MW5molecular weight; C NO5number of carbon atoms; COOH5number of carboxy groups; OH5number of hydroxy groups; ] CC DB5number of carbon–carbon double bonds; CONJ5number of conjugated double bonds; MP5melting point; pKa 15first (lowest) ] pKa . b See solubility codes in Table 2.
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Table 2 Solubility scales used in Table 1 Code
ricultural Experiment Station. Alicyclobacillus (VF) was isolated from apple juice (Splittstoesser et al., 1994).
Solubility (g / 100 g) or description Ethanol
Diethyl ether
Water
1 2 3
0–10 .10–30 .30–70
0–1 .1–10 .10–50
4
.70 soluble freely sol. readily sol. miscible
0–0.5 .0.5–2 .2 slightly soluble soluble freely sol. readily sol. miscible
.100 miscible
5
.50–100
enabled use of descriptive (e.g. ‘slightly soluble’), as well as numeric data.
2.4. Multivariate techniques Principal Components Analysis (PCA) was applied with the Factor Analysis routine in the STATISTICA computer program ( STATISTICA for Windows Release 5.1H 1997 edition, StatSoft Inc., Tulsa, OK). In the case of the acid data, results were Varimax rotated. Cluster Analysis was applied to the Varimax rotated PC score values for the acids with the joining (tree clustering) method, using single linkage amalgamation based on the Euclidean distances ( STATISTICA).
2.5. Selection of acid subset Cluster analysis was used to display the similarities of the acid patterns of principal components. Eight acids with dissimilar patterns were selected for experimental work.
2.6. Microorganisms Six bacteria, including organisms expected to be acid susceptible and acid resistant, were used in this study. Bacillus cereus (ATCC11778), Bacillus subtilis (ATCC6633), Escherichia coli (ATCC25922), and Lactobacillus fermentum (ATCC14931) were obtained from the American Type Culture Collection (Rockville, MD). Lactobacillus plantarum (EH22G) was provided by John Churey of the Food Science and Technology Department, New York State Ag-
2.7. Growth conditions Each of the bacteria used in this study was incubated under conditions favorable for its growth. B. cereus, B. subtilis, and E. coli were incubated at 308C for 24 h in Brain Heart Infusion medium. L. fermentum and L. plantarum were incubated at 378C for 24 h in Brain Heart Infusion medium. Alicyclobacillus was incubated at 538C for 48 h in Potato Dextrose Broth.
2.8. Preparation of acid media KH 2 PO 4 was added to Type I distilled water at 10% (w / w) concentration, and this buffer solution was adjusted to pH 5.25. The incubating medium was added to the buffer solution and adjusted to pH 5.25. The organic acids were added to the buffer solution to prepare stock solutions (10% for acetic, butyric, citric, lactic, malic and tartaric acids and 1% for benzoic and caprylic acids) and adjusted to pH 5.25. The pH adjustments were made with 0.1M, 1M, or 2M HCl, or 0.1M, 1M, or 10M NaOH, as appropriate. The incubating medium, buffer solution, and organic acid (total volume 30 ml) were added to 55 ml culture tubes (Kimble Glass, Vineland, NJ) at the concentrations used for experiments. The tubes were autoclaved at 1218C for 15 min and then air-cooled to room temperature.
2.9. Growth assessment A standard curve relating light scattering results to plate counts was prepared with B. cereus. The organism was incubated in broth samples with or without benzoic or citric acid. After the incubation the light scattering intensity of one aliquot of each sample was measured. Additional aliquots (1 ml) of the same sample were plated onto Plate Count Agar in a dilution series in triplicate and incubated for 24 h at 308C. The colonies were then counted. A standard curve was prepared relating the light scattering measurements to the colony forming units.
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2.10. MIC determination Microorganisms were incubated in their selected growth environment (selected temperature and medium without added acid) for one or two days before experiments. For each test acid a series, with concentrations increasing by a constant factor, was prepared in the culture medium used for each organism. The factors and starting levels were determined by preliminary experiments with each acid / organism pair and ranged from multiples of 1.546 (L. plantarum on malic acid) to 3.68 (most organisms on most acids). The same volume (3 drops) of bacterial suspension was added to each experimental culture tube (containing 30 ml of medium), using a syringe (Becton, Dickinson and Company, Rutherford, NJ) while working in a laminar flow hood. No organisms were added to the blank culture tubes. The tubes (experimental and blank groups) were incubated for 24 or 48 h, depending on the organism. After incubation, the culture tubes were inserted into the turbidimeter to assess the sample turbidity. The blank samples were used to detect possible precipitation unrelated to bacterial growth. The minimum inhibitory concentration (MIC) was determined as the geometric mean of the lowest acid concentration at which there was no growth for an organism (turbidity equal to the non-inoculated blank for that acid and medium) and the next lower concentration.
2.11. Modeling The MICs for each bacterium (dependent variable) were modeled as a function of the four Varimax rotated principal component scores (PCs) for the acids (independent variables), using Partial Least Squares (PLS) regression. PLS was carried out with SCAN for Windows Release 1.1 (Minitab, State College, PA). PLS models were calculated using from one to four components. In each case the best fit equations (those with the highest R 2 ) and those with the best predictive ability (lowest predictive residual error sum of squares, or PRESS) were obtained.
3. Results and discussion The data for organic acids in Table 1 includes both measured properties (melting point, pKa , solubility)
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and items observed from structures (molecular weight, numbers of carbon atoms, carboxy groups, hydroxy groups, carbon–carbon double bonds, and conjugated double bonds). The solubility data available were partly numeric (typically expressed as g / 100 g) and partly descriptive (i.e., ‘slightly soluble’, ‘soluble’, ‘freely soluble’, etc.). To accommodate both, codes (numbers from 1 to 5) were used to express increasing solubility in each solvent. The numeric solubility values corresponding to each code were slightly different for ethanol, ether, and water (see Table 2) to maximize the spread of numbers representing each solubility property. Principal components analysis is a technique for concentrating the information in a data set into fewer dimensions (Massart et al., 1988). It does this by creating new variables that are linear combinations of the original property (or measurement) variables and which account for maximum possible variance in the data set. Each PC is constrained to be orthogonal to all previously extracted PCs (at right angles in multidimensional space and hence completely uncorrelated), and as a result they have no overlap in information content. Each PC thus represents a different fundamental property of a system, with properties that are partially or largely redundant in information content influencing the same PC in the same direction. This is evident in the loading plot, which shows correlations between the PCs and property variables. The number of significant PCs (usually judged from either a Scree plot or by choosing only those with eigenvalues . 1) indicates the number of fundamentally different properties exhibited by the data set. Orthogonal rotations, such as Varimax rotation, rotate the PC structure in multidimensional space to improve the alignment between the original property variables and the PCs while preserving the relationships between the PCs (Massart et al., 1988). This usually makes them easier to understand, while completely preserving their information content and modeling ability. Principal Components Analysis was applied to the data in Table 1. This resulted in the eigenvalues shown in the Scree plot in Fig. 1. A sharp break occurred at the fourth PC, so four PCs, accounting for 93.1% of the total variance in the data set, were retained. The four PCs were then subjected to Varimax rotation to bring them into closer alignment
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molecular size, and larger size results in lower water solubility. PC4 is heavily influenced by solubility in ether and alcohol, and in the opposite direction, by melting point; PC4 thus essentially represents nonpolarity. The proportion of the total variance accounted for by the four Varimax rotated PCs is the same as it was for the first four unrotated PCs, but the distribution of the variance explained over the PCs is quite different. Also resulting from the PCA are the factor score values (Table 4). These specify the location of each acid along each of the Varimax rotated PCs. This is illustrated in Figs. 2 and 3. Fig. 2 shows each acid’s location on the PC1 and PC2 axes. The PC1 axis represents high polarity toward the left and decreases toward the right. Most of the acids have similar values along PC2, but benzoic and sorbic acids, which are known to be good preservatives, have much higher values. Fumaric acid is somewhat further along this axis than most of the other acids; this is interesting in view of the relatively strong inhibitory effect of fumaric acid towards a number of microorganisms (Splittstoesser and Stoyla, 1989; Shimizu et al., 1995; Podolak et al., 1996a,b). Fig. 3 depicts the acid locations along the PC3 and PC4 axes. Here most of the acids have similar PC4 values but are separated along the PC3 axis with the smaller molecules at the right and the larger at the left. Succinic and fumaric acids have much higher PC4 values than the other acids, indicating their low solubility in organic solvents. Together, the set of four PC scores for an acid specifies its coordinates in the four dimensional
Fig. 1. Plot of the eigenvalues (showing the proportion of the variance explained) by each principal component extracted from the organic acid data.
with the original variables (Massart et al., 1988). The Varimax rotated factor loadings are shown in Table 3; these are the correlations between the PCs and the original acid characteristics. Loadings with an absolute value greater than 0.70 (shown in bold type) represent a strong influence. It can be seen that PC1 is heavily influenced by the numbers of hydroxy and carboxy groups in one direction and by the first pKa in the opposite direction. Acids with relatively large numbers of carboxy groups or hydroxy groups or with a low first pKa will have a low score on this axis. To a large extent, PC1 represents the number of polar groups. PC2 is almost entirely related to the numbers of carbon–carbon and conjugated double bonds. PC3 is loaded heavily by molecular weight, by carbon number, and, in the opposite direction, by water solubility; this means it is largely a function of
Table 3 Varimax rotated principal component factor loadings for organic acid properties Chemical and Physical Properties
PC1
PC2
PC3
PC4
Molecular weight Number of carbon atoms Number of COOH groups Number of OH groups Number of CC double bonds Number of conjugated double bonds Melting point pKa 1 Solubility in alcohol Solubility in ether Solubility in water
20.469 0.145 20.749 20.919 0.068 0.065 20.476 0.835 0.017 0.587 20.397
20.079 0.131 20.213 20.134 0.966 0.924 0.292 20.071 20.331 20.210 20.316
20.866 20.967 20.138 0.035 20.120 20.087 20.096 20.189 0.032 0.115 0.731
0.129 20.097 0.474 20.045 0.164 0.338 0.797 20.392 20.906 20.710 20.333
28.0%
20.2%
21.1%
23.8%
Proportion of total variance
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Table 4 Varimax rotated principal component factor scores for organic acid properties Organic Acid
PC1
PC2
PC3
PC4
Acetic Benzoic Butyric Capric Caproic Caprylic Citric Formic Fumaric Heptanoic Lactic Malic Propionic Sorbic Succinic Tartaric Valeric
0.539 20.0957 0.396 0.586 0.668 0.636 22.22 0.214 20.0395 0.850 20.543 21.19 0.633 0.644 0.663 22.48 0.734
20.245 3.13 20.250 20.584 20.387 20.438 20.560 20.0922 0.777 20.568 20.0259 20.402 20.392 1.79 21.22 20.156 20.368
1.45 20.488 0.726 22.02 20.492 21.37 20.997 1.94 0.277 20.967 0.882 0.00035 1.11 20.261 0.113 0.228 20.135
20.593 20.437 20.884 20.250 20.686 20.700 20.343 20.558 2.45 20.0575 20.624 0.169 20.207 0.594 2.62 0.181 20.683
Fig. 2. Plot of acid scores on varimax rotated principal component axes PC1 (representing mainly polarity) and PC2 (representing mainly numbers of double bonds).
Fig. 3. Plot of acid scores on varimax rotated principal component axes PC3 (representing mainly molecular size) and PC4 (representing mainly solubility in organic solvents).
space. Acids that are located close together (short vector distances) in this four dimensional space have similar combinations of properties. This can be represented by applying Cluster Analysis based on Euclidean distances (see Fig. 4). Acids with PC patterns that are close together are considered to be similar and are represented as joining together near the left side of the cluster diagram. Those that are more dissimilar join together closer to the right side of the figure. For modeling purposes, two acids with highly dissimilar combinations of properties provide
more information than two with similar patterns (Massart et al., 1988). As a result, when two acids have similar patterns, use of one of them is sufficient; adding data for the second provides little additional information. Of the 17 acids listed in Table 1, a set of eight acids with fairly dissimilar PC patterns (names shown in bold in Fig. 4) was selected. Six bacteria were selected for use in this study. The two Bacillus species were expected to be acid susceptible. The lactobacilli, themselves acid produc-
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Fig. 4. Cluster diagram of acid principal component scores, showing the similarity of the patterns (those joining together toward the left side are more similar than those joining together toward the right).
ers, were expected to be acid resistant. Since pathogenic E. coli has been associated with food poisoning outbreaks in cider (Mshar et al., 1997), an acidic beverage, it must be acid resistant and it might be expected that the non-pathogenic E. coli used in this study could be acid resistant as well. Alicyclobacillus has on a number of occasions been isolated from high acid fruit juices (Splittstoesser et al., 1994; Yamazaki et al., 1996; Baumgart et al., 1997; Borlinghaus and Engel, 1997; Pettipher et al., 1997) and was, as a result, expected to demonstrate acid resistance. Since most microbiologists measure ‘‘turbidity’’ with a spectrophotometer, and a turbidimeter (light scattering instrument) was used in this work, it seemed appropriate to test the linearity of response and to determine roughly how many organisms were represented by one measurement unit (nephelos turbidity unit 5 NTU). When sample turbidities (expressed in NTU) from a series of B. cereus samples
were compared with plate counting results from the same samples, a linear relationship was seen, with 1 NTU representing approximately 2 3 10 6 organisms. Turbidity values were then used directly to assess the extent of cell growth. Minimum inhibitory concentrations were determined for each of the eight selected acids for each of the six test organisms. The MICs were defined here as the geometric average between the highest concentration at which growth was observed and the lowest concentration at which no growth was seen with incubation times of 24–48 h. The geometric average should produce results that are close to the actual numerical value at which growth is inhibited, which are desirable for modeling, but it is not the most conservative approach, and food safety considerations would be better served by using the lowest concentration at which no growth occurs and longer incubation times than were employed in this feasibility study. Once the approximate inhibitory concentration of an acid for an organism was established, several nearby concentrations were prepared in which the acid was increased between samples by a constant factor. In several cases (both lactobacilli with malic acid and L. fermentum with tartaric acid), low concentrations of acid resulted in greater numbers of the test microorganisms than the no acid controls; this indicates that the acid was utilized as a nutrient. Higher acid concentrations, however, resulted in inhibition. The results are shown in Table 5. All the organisms but Alicyclobacillus were able to grow in the presence of malic acid concentrations over 10 g / l. Similar levels of citric and tartaric acids only inhibited Alicyclobacillus and B. cereus. B. subtilis, B. cereus, and Alicyclobacillus appeared to be relatively sensitive to most acids, particularly benzoic. This was a surprise in the case of Alicyclobacillus, as this bacterium was expected to
Table 5 Minimum inhibitory concentrations (g / l) for the test organic acids for the test organisms Microorganism
Acetic
Benzoic
Butyric
Caprylic
Citric
Lactic
Malic
Tartaric
B. cereus B. subtilis E. coli L. fermentum L. plantarum Alicyclobacillus
2.02 0.105 1.55 26.3 27.5 0.727
0.296 0.192 0.316 2.50 2.61 0.061
0.959 0.096 1.41 24.0 25.0 0.303
0.068 0.192 1.73 1.58 2.61 0.316
3.68 26.1 38.2 15.8 26.1 4.58
3.48 8.32 3.72 25.3 30.7 5.39
13.6 26.1 50.0 25.0 26.1 4.58
5.90 26.1 50.0 25.0 26.1 7.07
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be acid resistant. It was instead the most susceptible of all the organisms tested for three of the acids. The lactobacilli were much more resistant to acetic, benzoic, butyric and lactic acids, than the other organisms tested. E. coli was the most resistant toward citric, malic and tartaric acids, demonstrating a different pattern of acid resistance than the lactobacilli. The E. coli strain was particularly insensitive to malic acid. While different E. coli strains are known to exhibit different degrees of acid resistance (Miller and Kaspar, 1994), this finding is perhaps relevant to the outbreaks of pathogenic E. coli in cider (Mshar et al., 1997), as malic acid is, by far, the predominant organic acid in apple juice (Lee and Wrolstad, 1988). The modeling technique used in this study was Partial Least Squares Regression (PLS). This calculates principal components through the independent variables and models the dependent variable as a function of the PCs (Beebe et al., 1998). As such, the technique is robust against a number of phenomena that violate assumptions of multiple linear regression, including high correlation between independent variables and a low sample to measurement ratio (an overdetermined system). PLS also employs crossvalidation (iterative recalculation of the model omitting a different sample point each time) to test for sensitivity of the model toward a particular sample. This is used to calculate the PRESS (predictive residual error sum of squares) which allows com-
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parison of the tradeoff between better fitting with increasing complexity (more terms) and the resulting build-up of error (tending toward overfitting). Mathematical models expressing MIC as a function of the PC values of an acid: MIC 5 b 0 1 b 1 ? PC1 1 b 2 ? PC2 1 b 3 ? PC3 1 b 4 ? PC4 were constructed, where the coefficients (the b terms) were fit by Partial Least Squares (PLS) Regression using a matrix of the 4 PC scores for the eight acids as the independent variables, and the corresponding MIC values as the dependent variable. PLS is better suited than Multiple Linear Regression to situations where combinations of levels of the independent variables cannot be set at optimal levels or where the sample / measurement ratio is less than 3. The analysis resulted in the fits described in Table 6. The PLS regression best fits (highest R 2 ) were in each case for the models derived using 4 PLS components. The best prediction equations (those with the lowest PRESS), were obtained with either one (B. cereus, Alicyclobacillus), two (B. subtilis, E. coli, L. plantarum), or three (L. fermentum) PLS components. When the best prediction equations were based on 2- or 3-component models, the R 2 values were almost identical to those of the equivalent four component models. The one component model R 2 values were noticeably lower than those of the four component models. Figs. 5–10 show the
Table 6 Partial least squares (PLS) fitting results for acid minimum inhibitory concentration (g / l) data Microorganism
Best fits (highest R 2 ) R2
b0
b1
b2
b3
b4
B. cereus B. subtilis E. coli L. fermentum L. plantarum Alicyclobacillus
9.283 12.13 30.42 17.45 14.42 2.071
1.080 26.298 26.167 22.684 26.162 21.831
21.156 22.591 25.098 23.162 23.640 20.430
0.5062 20.8906 22.038 8.978 8.530 0.6521
11.74 11.73 37.39 2.464 26.488 0.7559
0.785 0.968 0.970 0.968 0.941 0.856
Microorganism
Best predictions (lowest residual PRESS)
B. cereus B. subtilis E. coli L. fermentum L. plantarum Alicyclobacillus
b0 5.28 13.60 26.32 18.58 19.79 3.398
b3 0.2258 20.9215 21.353 8.949 8.114 0.1185
b4 5.359 14.11 30.80 4.369 1.653 2.879
R2 0.621 0.966 0.964 0.966 0.898 0.831
b1 21.152 25.513 28.399 22.099 23.023 21.130
b2 20.6926 22.777 24.894 23.189 24.562 20.4812
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Fig. 5. Best fit relationship (R 2 50.785) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for B. cereus.
Fig. 6. Best fit relationship (R 2 50.968) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for B. subtilis.
relationships between the measured MICs for the test acids and those predicted from the best fit equations in Table 6. Clearly, MIC can be quite successfully predicted as a function of the four PCs. R 2 values ranged from 0.941–0.970 for four of the bacteria and were 0.785 and 0.856 for the other two. Examination of the patterns of coefficients (Table 6) reveals some similarities in signs and magnitudes. These should be informative regarding the mechanisms of acid resistance and susceptibility. Note, for example, that the b 2 values were highest (in this case less negative) for the acid susceptible organisms. This is interesting because PC2 is the axis on which the numbers of carbon–carbon and conjugated double bonds loaded heavily and along which benzoic and sorbic acids,
Fig. 7. Best fit relationship (R 2 50.970) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for E. coli.
Fig. 8. Best fit relationship (R 2 50.968) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for L. fermentum.
Fig. 9. Best fit relationship (R 2 50.941) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for L. plantarum.
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Fig. 10. Best fit relationship (R 2 50.856) between observed minimum inhibitory concentrations and MICs predicted by the PLS model for Alicyclobacillus.
which are known to have strong antimicrobial activity, were well separated from the other acids (see Fig. 2). The lactobacilli, which exhibited one pattern of acid resistance, were highest in the coefficient b 3 , which corresponds to PC3 (heavily loaded by molecular size). It can be seen that the acids for which the Lactobacilli were particularly resistant (acetic, benzoic, butyric and lactic), were mostly relatively small (see Fig. 3). E. coli had by far the largest b 4 term, the coefficient of PC4, representing the ethanol and ether solubility (non-polarity) axis. These different patterns can be seen in Fig. 11, which shows results of PCA applied to the coefficients in Table 6. To estimate the MIC values for an acid used in the calculation of the principal components, one would take the four Varimax rotated PC score values for the acid from Table 4, and then insert these into the five-term equation for a modeled organism and compute the algebraic sum; this is the predicted MIC. For example, to estimate the MIC for fumaric acid for E. coli, look up the four PC scores for fumaric acid in Table 4: 20.0395, 0.777, 0.277, and 2.45, respectively. Look up the coefficients of the best prediction equation for E. coli in Table 6. Insert the values: MIC 5 26.32 2 8.399 ? PC1 2 4.894 ? PC2 2 1.353 ? PC3 1 30.80 ? PC4 MIC 5 26.32 2 8.399(20.0395) 2 4.894 (0.777) 2 1.353 (0.277) 1 30.80 (2.453)
Fig. 11. Depiction of relationships of the best fit models. Principal components analysis was applied to the best fit model coefficients for the six modeled bacteria.
MIC 5 98.0 g / l It is also possible to estimate the MIC for an acid not listed in Table 1 for a modeled organism, although this is more in the nature of an extrapolation than an interpolation. This is first done by obtaining the 11 needed data parameters for the acid. For the solubility data, one would convert the results into the codes according to Table 2. Using the data in Table 1, one could calculate the mean and standard deviation for each parameter. For the acid under consideration, for each of its parameter columns, one would subtract the corresponding mean and divide by the corresponding standard deviation; this results in 11 normalized parameter values. Then one would multiply each of the normalized values by the corresponding Varimax rotated factor score coefficient (from PCA analysis of Table 1) for each of the four PCs and sum algebraically. This results in the four Varimax rotated factor scores for the acid in question. One would then substitute these in the five-term equation for a modeled organism and then calculate the algebraic sum; this is the predicted MIC. The same four PCs described here were also used to model the flavor thresholds of organic acids added to beer (Siebert, 1999). This, too, produced a highly significant model (R 2 50.905). Since both biological
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activities produced good models with the same set of PCs, it appears that they represent fairly fundamental properties that are important in predicting both the fit of these molecules to flavor receptors and their ability to enter microbial cells and inhibit growth. It would clearly be of interest to expand the current data set to include more acids, more organisms, and additional growth conditions (pHs, temperatures and media). In particular, it would be interesting to know if there are only the three response patterns seen so far or if there are additional patterns of acid resistance. It would be interesting to know if the inhibitory effects of acids other than those used to construct the MIC models or even outside the set used to calculate PCs can be correctly predicted. It would also be useful to know if predictions can be made as to which acids are especially effective in inhibiting the growth of particular problem organisms. It may also be possible to predict the behavior of organisms in mixed acid systems that correspond to real food systems.
4. Conclusions Principal Components Analysis showed that four fundamental properties could represent the information contained in the 11 acid data used. These properties correspond to polar groups, the number of double bonds, molecular size, and solubility in nonpolar solvents. The six test bacteria exhibited essentially three MIC patterns, representing acid susceptibility and two different patterns of acid resistance. The lactobacilli were much more resistant to acetic, benzoic, butyric and lactic acids than the other organisms tested, while the E. coli was most resistant toward citric, malic and tartaric acids. For each organism an equation was fit that expressed the MIC for each acid as a function of its four PC scores. Four of these were very strong relationships (R 2 5 0.941–0.970), while the other two were not as strong (R 2 50.785 and 0.856). It is clearly possible to model the inhibitory effect of organic acids as a function of their molecular properties.
Acknowledgements This material is based upon work supported by the Cooperative State Research, Education and Exten-
sion Service, U.S. Department of Agriculture, under Project NYG 623-496. John Churey and Penelope Lynn of this department provided valuable advice on laboratory techniques.
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