Weak-acid preservatives: modelling microbial inhibition and response


Dr R.J. Lambert, Microbiology Section, Unilever Research, Colworth House, Sharnbrook, Bedford MK44 1LQ, UK (e-mail: RONNIE.LAMBERT@UNILEVER.COM).


Weak-acid preservatives are widely used to prevent microbial spoilage of acidic foods and beverages. Characteristically, weak-acid preservatives do not kill micro-organisms but inhibit growth, causing very extended lag phases. Preservatives are more effective at low pH values where solutions contain increased concentrations of undissociated acids. Inhibition by weak-acids involves rapid diffusion of undissociated molecules through the plasma membrane; dissociation of these molecules within cells liberates protons, thus acidifying the cytoplasm and preventing growth. By modelling preservative action in yeast, using a thermodynamic and kinetic approach, it was possible to demonstrate that: (i) inhibition depends more on the degree to which individual preservatives are concentrated within cells, rather than on undissociated acid concentration per se; (ii) it is entirely feasible for microbes to pump protons out of the cell during extended lag phase and raise internal pH (pHi), despite further influx of preservatives; (iii) the duration of the lag phase can be predicted from the model, using a Gaussian fit of proton-pumping H+-ATPase activity against pHi; (iv) theoretical ATP consumption for proton pumping can be directly correlated with the reduction in cell yield observed in glucose-limited cultures.


pHi, internal (cytoplasmic) pH; pHo, external (extracellular) pH; [HAo], external associated weak-acid concentration/mol l−1; [HAi], internal associated weak-acid concentration/mol l−1; [Ai], internal dissociated, anion concentration/mol l−1; [Ao], external dissociated anion concentration/mol l−1; K, weak acid equilibrium constant; r, rate of proton efflux, mol/ time units; t, time elapsed, arbitrary time units.


The documented use of weak-acid preservatives to inhibit growth of micro-organisms in foods and beverages extends back many centuries. John Evelyn in 1670 described the use of sulphur dioxide from burning sulphur in the preservation of cider (Rose & Pilkington 1989). Sulphur dioxide and sulphites continue to be the method of choice for the preservation of wine. Other weak-acid preservatives include acetic acid in pickles, propionic acid in bread and more recently, sorbic and benzoic acids in soft drinks (Chichester & Tanner 1972). All are targeted mainly against yeasts and moulds; low pH alone, less than pH 4·5, will prevent spore germination and growth of the great majority of bacteria (Gardner 1972; Smelt et al. 1982). Over the last few years, consumer demand for more ‘natural’ foodstuffs has caused a move away from chemical additions to food products and legislation in many parts of the world now limits their use. For example, within the EEC, sorbic acid is limited to 300 ppm in soft drinks. Preservative-resistant yeasts such as Zygosaccharomyces bailii can grow in soft drinks containing in excess of 500 ppm (Ingram 1960; Neves et al. 1994).

Weak-acid preservatives appear to share a common mode of action, despite their various chemical structures. All become increasingly potent as antimicrobial agents at more acidic pH values. In aqueous solution, weak-acids exist in pH-dependent equilibria between uncharged, acid molecules and their respective charged anions, for example acetic acid/ acetate. The proportion of undissociated acid increases as the pH declines; the pH value at which there exists equal proportions of molecular acid and charged anions, is termed the pKa. It is generally agreed that only undissociated acids have antimicrobial activity, although some activity by anions has been suggested (Eklund 1989).

Affected micro-organisms are rarely killed but growth is prevented. After very extended lag phases lasting days or even weeks, growth is poor and cell yields are greatly reduced. Inhibition of respiration and active transport have been reported (Freese et al. 1973). The mechanism of action of weak-acid preservatives is thought to involve diffusion of lipophilic acid molecules through the plasma membrane into the cytoplasm (Stratford & Rose 1986). There they encounter a pH value near to neutrality and are forced to dissociate into charged ions. Charged ions cannot return across the plasma membrane and anions are thus concentrated within the cell (Fig. 1). Dissociation of each weak-acid molecule will release a proton and the cytoplasm will become increasingly acidic. Acidification of the cytoplasm may prevent growth by inhibition of glycolysis (Krebs et al. 1983), by prevention of active transport (Freese et al. 1973) or by interference with signal transduction. pHi is increasingly recognized as having a role in signalling (Thevelein 1994). The cellular response to inhibition caused by weak-acid preservatives may involve removal of preservatives by an efflux pump (Warth 1989), although evidence for this is disputed (Cole & Keenan 1987). Of greater importance is more likely the plasma membrane H+-ATPase. This has been shown to be involved in weak-acid resistance (Cole & Keenan 1987; Vallejo & Serrano 1989), although its role remained questionable given that if pHi were raised by proton pumping, further weak-acid molecules would penetrate the cell and re-acidify the cytoplasm.

Figure 1.

Predicted medium and cytoplasmic weak-acid/anion equilibria. Only uncharged weak-acid molecules (HA) can diffuse freely across the plasma membrane. Charged anions (A) and protons (H+) are retained within the cell; cytoplasmic protons are expelled by the membrane-bound H+-ATPase

Here, a model is presented based on known principles of physical chemistry, in which cytoplasmic pH is progressively raised during the lag phase by proton pumping, despite the influx of further weak acid. This model allows the prediction of the lag time required to raise the internal pH and for growth to begin.

Materials and methods

Yeast strain

The yeast strain used in this work was Saccharomyces cerevisiae X2180–1B, MATαSUC2 mal gal2 CUP1. This is available from the National Collection of Yeast Cultures, Institute of Food Research, Norwich NR4 7UA, UK, as strain NCYC 957.

Media and culture conditions

Yeast cultures were maintained at 4 °C on YEPD agar slopes. This contained glucose 20 g l−1, yeast extract 10 g l−1, bacteriological peptone 20 g l−1 and agar 20 g l−1. Aerobically- grown, 24 h starter cultures were used to inoculate experimental cultures at 1 mg dry weight l−1 (approximately 104 cells ml−1). As indicated, potassium sorbate was added to YEPD broth and the pH adjusted with HCl prior to autoclaving. In certain experiments, a semi-defined medium (pH 4·0) was used to minimize preservative binding. This contained fructose 20 g l−1, ammonium sulphate 1 g l−1, KH2PO4 3 g l−1, citric acid 6 g l−1 and yeast extract 1 g l−1. Preservatives were added from filter-sterilized 500 mmol l−1 stock solutions. The yeast was grown in 50 ml media aliquots in 125 ml conical flasks, at 30 °C, on an orbital shaker, 150 rev min−1. Growth was monitored by optical absorbance at 600 nm and converted to dry weight using a calibration curve. The duration of the lag phase was estimated by linear regression of the semilog growth plots, and determining the intersection of the growth line with the log of the inoculum cell concentration.

Undissociated fractions of weak-acids

Proportions of dissociated and undissociated forms of weak-acid preservatives at each pH were calculated using the Henderson-Hasselbalch equation:


Undissociated fractions of sulphite, nitrite, sorbate and benzoate are shown in Table 1.

Table 1.  Percentage of undissociated acid/anions of weak-acid preservatives at pH values 4·0–6·75
  1. Values were calculated using the Henderson-Hasselbalch equation and pKa values of SO2/bisulphite, 1·77 ; nitrous acid/nitrite, 3·29 ; sorbic acid/sorbate, 4·74 ; benzoic acid/benzoate, 4·20.

4·250·33099·670 9·88190·11975·97524·02547·12552·875
4·50·18699·814 5·80894·19264·00635·99433·38666·614
4·750·10599·895 3·35196·64950·00050·00021·98778·013
5·00·05999·941 1·91398·08735·99364·00713·68186·319
5·250·03399·967 1·08598·91524·02575·975 8·18391·817
5·50·01999·981 0·61399·38715·09884·902 4·77395·227
5·750·01199·989 0·34699·654 9·09190·909 2·74197·259
6·00·00699·994 0·19599·805 5·32494·676 1·56098·440
6·250·00399·997 0·10999·891 3·06596·935 0·88399·117
6·50·00299·998 0·06299·938 1·74798·253 0·49999·501
6·750·00199·999 0·03599·965 0·99099·010 0·28199·719

Modelling pHi and proton transport

The basic model.

For the purpose of the model, activities are modelled as concentrations. This simplification holds true for low concentrations. At higher concentrations, the individual concentrations should be replaced by activities.

Consider two vessels, 1 and 2, containing weak acid, at equilibrium, from the definition of the equilibrium constant, the following holds:


Consider now a situation where one of the vessels is the interior of a cell separated from the other by a semi-permeable membrane; Equation 1 must also be satisfied in an equilibrated system. Undissociated weak-acids are capable of diffusing freely through microbial membranes and do so until equilibrium is reached (Stein 1981; Stratford & Rose 1986). The equilibrium attained will satisfy Equation 1 and due to the free movement of the weak-acid across the membrane, [HAo= [HAi]. The dissociated anion is not freely permeable and is therefore trapped inside the cell when the weak acid dissociates. This means that any difference in the pH between the internal and extracellular fluids will also be reflected in the concentrations of the dissociated anion. The assumption is made that the dissociated anion cannot leave the cell, and that the attainment of [HAo= [HAi] is faster than any other process linked to the model.

From the definition of the equilibrium constant:

-log [H+o]-log [A-o]+log [HAo] = -log [H+i]-log [A-i]+log [HAi](2)

From the definition of pH:

pHo-log [A-o]+log [HAo] = pHi-log [A-i]+log [HAi](3)

For the situation where pHo = pHi and as, for a semi-permeable membrane, [HAo= [HAi], then [Ao] = [Ai]. If pHo≠ pHi then Equation 4 must be satisfied:


With this model, a weak-acid has been added to a solution containing a microbe. The internal pH immediately falls and an equilibrium is reached such that the internal and external pH values are equal; this point is defined as time = 0. It is assumed that the diffusion of weak-acid into the cell is infinitely fast compared with any active proton pumping that may occur. The model consists of calculating the accumulation of anion coupled to the rate of proton efflux, and then using this value to calculate the internal pH (Equation 4).

Within the cell HA ↑ H+ + A.

Protons may be pumped from the cytoplasm by the H+-ATPase. For every proton removed, one anion remains accumulated. HA then diffuses in through the membrane to immediately reset the equilibrium. However, as there are now ‘extra’ anions, the equilibrium concentrations required are slightly different and the internal pH alters. From Equation 4, at t = 0, Equation 5 is obtained, where Q = log [Ho+][Ao].


The rate of proton efflux is equal to the rate of anion accumulation. Thus, the change in internal pH can be obtained from Equation 6, where r = rate of proton efflux, t = time elapsed.


Here, the rate of proton efflux is constant and independent of pHi (anion accumulation is linear with time). On a longer time-scale, as the internal pH rises above 7, anion accumulation still occurs at the same rate. This is a system lacking feedback inhibition to the proton pump. As such this is not a realistic situation and the model requires adjustment. The modification involves limiting the rate of proton efflux with respect to the internal pH. A limiting factor, f, is introduced into Equation 6:


The limiting factor must regulate the output of the proton pump. For this regulation a pH is defined, the nominal pH, pHn, at which the effectiveness of the proton pump is zero (i.e. stops pumping) and the effectiveness of the proton pump is also defined at pHi, t = 0 (=pHo) to be 100%. In this scenario, the protons are pumped out as fast as possible to begin with and then, as the internal pH rises, the pumping slows down until pHn is reached. In this model, change in internal pH is calculated over short time intervals (Equation 8), and the changes in pH summed to give the internal pH (Equation 9).

pHi = pHo+ΣΔpHi(9)

Modelling the H+-ATPase function.

To obtain a realistic model, the in vivo rate of H+-ATPase activity with respect to pH should be used as the limiting factor. The efficiency of H+-ATPase with respect to pH is known from experimental work (Willsky 1979; Eraso & Gancedo 1987). At low pH (<4·5), the enzyme was sluggish but achieved optimal performance at pH 5·5 (100% activity). At pH 7, it was shown to have 70% of optimum activity. Tests were carried out using isolated enzymes or membrane preparations. The work by Willsky (1979) gives activity at pH 10 which is obviously biologically unrealistic. In these tests, the enzyme lacked normal feedback inhibition mechanisms, and the operation of the H+-ATPase would cease at some nominal pH because of feedback inhibition, except for enzyme used to maintain a pH to power active transport. The experimental data from low pH to optimum pH were fitted to half a Gaussian curve. The bold assumption was made that the feedback inhibition followed the other half of the Gaussian curve. This means that the efficiency of the H+-ATPase approaches zero at low pH and also at the expected nominal pH (approximately pH = 7). The fit to the experimental data is portrayed in Fig. 2. The Gaussian expression for the efficiency of the enzyme is described in Equation 10:

Figure 2.

Gaussian fit of the pH profile of the plasma-membrane H+-ATPase (––-), based on the experimental data (▪) of Willsky (1979)

efficiency = 10(-1/2(pH-pHp/Gw))2(10)

where pHp = peak pH of the Gaussian curve; Gw = measure of the width of the curve. A Gaussian function with pHp = 5·5 and Gw = 0·487 (parameters from experimental data) was used as the enzyme factor in Equation 7 and modelled using the analogous form of Equation 8.


Growth inhibition by preservatives

Yeast inhibition by sulphite, nitrite, sorbic and benzoic acids was compared. At pH 4·0, the undissociated fractions of these inhibitors were 0·58% SO2, 16·3% nitrous acid, 84·9% sorbic acid and 61·3% benzoic acid (Table 1). In semi-defined medium containing increasing concentrations of preservatives, inhibition of yeast growth was found after 60 h in greater than 0·9 mmol l−1 SO2/sulphite, 0·6 mmol l−1 nitrous acid/nitrite, 0·8 mmol l−1 sorbic acid/sorbate or 1 mmol l−1 benzoic acid/ benzoate, at pH 4·0. In terms of undissociated acid, this is 5·3 μmol l−1 SO2, 98 μmol l−1 nitrous acid, 613 μmol l−1 benzoic acid or 679 μmol l−1 sorbic acid. Clearly, inhibition is not directly related to the concentration of undissociated acid in the medium.

However, undissociated acid is predicted to diffuse into the cell until the concentration is equal on both sides of the membrane. If the internal pH, pHi, is maintained by buffering at pH 6·75 or restored to this level by proton pumping, the degree to which preservatives can be concentrated within the cell can be calculated for each pH value and preservative (Fig. 3). For example, sorbic acid/sorbate at pH 4·75 are in a 1:1 ratio (Table 1). Inside the cell at pH 6·75, the ratio is 1:100. As sorbic acid is at equal concentration on both sides of the membrane, the sorbate anion will be concentrated 100-fold within the cell. The overall preservative concentration outside is 1 + 1, and inside, 1 + 100, giving a concentration ratio of 1:50·5.

Figure 3.

Predicted concentration ratios of preservatives from medium to cytoplasm, based on known proportions of undissociated acid/anion at each pH value (Table 1). Concentrations are calculated assuming pHi to be 6·75, due either to infinite buffering or to proton removal. (a) Sorbic acid/sorbate; (b) benzoic acid/benzoate; (c) nitrous acid/nitrite; (d) SO2/sulphite

Figure 3 predicts that at pH 4, sorbate will be concentrated within the cell by ×86, benzoate by ×218, nitrite by ×466 and sulphite by ×585. If inhibition is a consequence of preservative uptake, then SO2/sulphite should be most effective, followed by nitrous acid/nitrite, and sorbic acid/sorbate, benzoic acid/benzoate. Inhibitory concentrations of preservative show nitrous acid/nitrite to be marginally more effective than the others on a molar basis.

Modelling microbial response

If a microbial suspension is placed in a solution of weak-acid preservative, the internal pH will drop as weak-acids are freely permeable across microbial membranes. A possible response to this stress involves the removal of protons and consequent accumulation of anions. At first sight, raising pHi through use of the H+-ATPase appears to be a futile, ATP-wasting activity because a higher pHi will cause a further influx of preservative and consequent lowering of pHi. However, careful examination of the equilibrium shows that pHi will not be lowered back to its original position. Proton pumping by the H+-ATPase will raise the internal pH, albeit slowly and with great expense in terms of ATP. Figure 4 models the recovery of pHi in the presence of three concentrations of the sorbic acid preservative, by proton pumping. Recovery is time-dependent on preservative concentration.

Figure 4.

Modelling the rise of pHi from pH 3·5 by proton pumping, despite further weak-acid influx. Sorbic acid concentrations used were 0·5 mmol l−1 (▪), 1 mmol l−1 (e) and 2 mmol l−1 (R). Time is in arbitrary units. Increased time is required (lag phase) to raise pHi with increased preservative concentration

Calculating lag times

In the presence of a weak acid preservative, the time spent in the lag phase is increased (Table 2). Preliminary evidence suggests that to enter the exponential growth phase, the internal pH must be raised above a threshold value (Imai & Ohno 1995). Increasing the weak-acid concentrations may lead to increased lag times because the microbe has to pump out excess protons to achieve the required growth pH. The time taken to pump out this number is a direct reflection of the increased lag time observed. In the model shown here, the time taken to attain a specific internal pH (the threshold pH) would correspond to the end of lag time.

Table 2.  Duration of lag phase of Saccharomyces cerevisiae X2180-1B in YEPD containing sorbic acid at various pH values
Sorbic acid
(mmol l−1)
pH 3·0pH 3·3pH 3·6pH 3·9pH 4·2pH 4·5
  1. Lag times were calculated from the model and are expressed in arbitrary time units. Experimental data are shown within brackets and expressed in hours. Control cultures lacking preservative grew with little or no lag (less than 0·2 h).

3·016400 (20·5)
2·513700 (12·4)
2·015600 (16·7)13600 (11·2)11000 (6·9)
1·513700 (17·7)12800 (12·0)11700 (10·3)10200 (5·4) 8300 (5·1)
1·09900 (9·9) 9100 (7·8) 8500 (5·6) 7800 (4·7) 6800 (2·7) 5500 (2·9)
0·55100 (4·3) 4600 (3·4) 4300 (3·4) 4000 (3·2) 3400 (2·3) 2700 (2·1)

An internal pH of 5·8 was chosen as a reasonable estimate of the value for threshold pH. From the experimental results (Table 2), the extreme values for lag times were used to set the parameters of the Gaussian function. Using this fitted Gaussian, the time taken to reach an internal pH for a given pH and sorbic acid concentration was calculated (Table 2 and Fig. 5). In the model, the units of time are arbitrary. A correction (re-scaling) factor can be fitted to the time units as was done with the data in Table 2. Experimentally- and theoretically-derived lag times are in reasonable agreement. Figure 5 shows the calculated vs experimental data. The parameters used to fit the data are those for the H+-ATPase of Saccharomyces cerevisiae given above (pHp = 5·5, Gw = 0·489).

Figure 5.

Scatter plot of calculated and experimentally-determined lag phases of Saccharomyces cerevisiae X2180–1B

Calculating yields

If a microbe uses up energy reserves of ATP and sugars to combat the effect of a weak-acid preservative, when (or if) the microbe reaches the threshold internal pH, there will be less available for production of biomass. Physiologically, for every proton pumped out, one ATP is consumed. This model can equate the rate of protons pumped to the accumulation of anion. Therefore, the amount of anion accumulated over a set time interval reflects the ATP consumed, and therefore should relate to final biomass yield.

For this calculation, the Gaussian parameters used for the estimation of lag times are applied. However, instead of calculating the time taken to reach a specific internal pH, the amount of anion accumulated via proton efflux is calculated for a given time. For this study, yields (mg dry wt l−1) are converted into a percentage yield loss. This normalizes the data with respect to the control yield. The experimental results and the modelled results are shown in Fig. 6, and demonstrate a good correlation.

Figure 6.

Scatter plot of experimentally-determined loss of cell yield of Saccharomyces cerevisiae X2180–1B against calculated accumulation of anion. It is predicted that each anion accumulated represents expenditure of one ATP in proton extrusion. Hence, calculated ATP usage shows a linear relationship with yield loss


Freese et al. (1973) examined the antimicrobial activity of a number of lipophilic weak-acids and noted a similarity of physiological effect on micro-organisms, despite their disparate chemical structures. Growth was inhibited as was active uptake of amino acids, organic acids and phosphate. All are likely to have a common cause, namely the lowering of the internal pH caused by weak-acids. Weak-acid preservatives have been shown to be concentrated within cells (Kotyk 1962; Macris 1975; Stratford & Rose 1986). As protons are released in a 1:1 molar ratio with anions within the cell, the degree of concentration is likely to reflect the relative toxicity of each preservative, all other factors being equal. Here, it is shown that while SO2/sulphite and nitrous acid/nitrite were predicted to be most potent inhibitors (Fig. 3), in practice they showed a similar degree of inhibition to sorbic acid. Clearly, other factors impinge on weak-acid toxicity. Sulphite and nitrite may be lost due to oxidation (Hammond & Carr 1976). Sulphite is also known to be progressively detoxified by the production of binding compounds during the lag phase (Stratford et al. 1987). Alternatively, sorbic acid may be regarded as more toxic than expected. Secondary toxic actions for sorbic acid have been suggested, inhibiting glycolysis (Azukas et al. 1961) or acting on the plasma membrane (Stratford & Anslow 1996, 1998). However, an elongated lag phase did appear to be related to a weak-acid-type action by sorbic acid (Stratford & Anslow 1996).

The model shown here of the changes in internal pH of cells afflicted by weak-acid preservatives are based only on known principles of physical chemistry and a Gaussian relationship of H+-ATPase activity with pH. This demonstrates that it is entirely feasible to pump protons out of the cell, slowly raising pHi, despite the consequent influx of more weak-acid. This can most easily be explained by the fact that for any given internal and external pH, there is a defined ratio of preservative concentrated in the cell (Fig. 3, Equation 4). If pHi was raised and excess preservative entered the cell, pushing pHi back to its previous position, more preservative would now be within the cell than permitted for this pH and it would no longer be in chemical equilibrium. Some preservative must then flow out, allowing pHi to rise a little, thus restoring equilibrium. Proton pumping is therefore not a futile activity. This model also demonstrates that, having raised the pHi to a level permitting growth, no further proton pumping is required. It is therefore unnecessary to postulate continuous pumping and ATP usage throughout growth, as had previously been suggested (Warth 1988).

In this model, for convenience, the assumption is made that there is no buffering capacity within the cell and the pHi has also been allowed to fall to the external pH, following the addition of preservative. Optimum buffering is likely at pH 4·5–5·5 (Krulwich et al. 1985), and while the pHi may not fall far, the proton pumping task will remain unaltered. Internal buffering will release the same number of protons, as the pHi is raised again. Thus, this model is likely to reflect accurately the time taken to raise pHi and thereby, the duration of the lag phase.

In addition to prolonging the lag phase, weak-acid preservatives are known to diminish cell yield in batch culture (Stratford & Anslow 1996). Experimentally, a relationship between the duration of the lag phase and the loss of cell yield can be shown. A good correlation was obtained (Fig. 6) between the experimental results and those calculated assuming that the usage of ATP in proton pumping is diverted from that used in growth. This gives credence to the model and also suggests that any other inhibitory action by sorbic acid does not involve the expenditure of ATP.

To conclude, using a thermodynamic and kinetic model, it is possible for weak-acid inhibited cells to raise pHi by H+-ATPase pumping. The time required to remove protons can be used to predict the duration of the lag phase and the calculated ATP expenditure is inversely proportional to experimentally determined biomass yields.