Calorimetric Analysis of the Effects of Penicillin G, Ampicillin and Polymyxin Bon the Growth

Agric. Biol. Chem., 52 (9), 2279-2285, 1988 2279

Calorimetric Analysis of the Effects of Penicillin G, Ampicillin and Polymyxin B on the Growth of Escherichia coli Akira Katarao, Hiroshi Okuno and Katsutada Takahashi Laboratory of Biophysical Chemistry, College of Agriculture, University of Osaka Prefecture, Sakai, Osaka 591, Japan Received March 28, 1988

Calorimetric analysis was performed of the effects of penicillin G, ampicillin and polymyxin B on Escherichia coli grown on bouillon mediumat pH 6.2 and 37°C. The presence of any one of these drugs shifted the patterns of growth thermograms toward longer incubation periods, although the growth rate constant remained almost unchanged. The changes in the thermogram patterns were analyzed by means of a simple mathematical model and parameters needed to characterize the actions of the drugs on the growth ofE. coli were determined. The drug concentrations at which the number of viable cells at the start of incubation decreased by half during the incubation were 6.94, 0.46 and 0.04^moldm~3 for penicillin G, ampicillin and polymyxin B, respectively. Drug potency curves were drawn for the three drugs using the parameters determined.

In our previous study,0 we calorimetrically Antibiotics. Penicillin G (potassium salt, Lot 310081) studied the effects of streptomycin, tetracycline and polymyxin B (sulfate, Lot 510711) were purchased and chloramphenicol on the growth of from P-L Biochemicals, Inc., Milwaukee, Wis., U.S.A. Ampicillin (anhydrous, Lot KWP7495) was a product of Escherichia coli. Anincrease in the concen- Wako Pure Chemicals Industries, Ltd., Osaka. The drugs tration of all three drugs in the culture medium were used without further purification. broadened the thermogram pattern. The results have been analyzed by means of a kinetic Procedures and calorimetric measurements. The calo- model that assumes the action of the drugs to rimeter used was a conduction-type batch calorimeter with be non-competitive toward microbial cells, six calorimetric units. Thestructure and its operation were as described before.3'4) The microbes were cultured in and potency curves for these drugs have been 30 ml glass vials, that served as calorimetric vessels. They drawn. Here, the same calorimetric method contained 5 ml of test mediumcontaining one of the three was used to study three different antibiotics drugs at different concentrations. The procedures for the that bind to the cell wall and cell membraneto sub- and preliminary cultures were reported previously.1 2) inhibit their biological functions. We studied The culture mediumused in the calorimetric measure- the action patterns of penicillin G, amipicillin onementsdrugwas;at 1%a certainmeat extract,concentration.1%peptone,The heat0.5%evolutionNaCl and and polymyxin B as to the growth thermo- associated with bacterial growth was recorded for 24 to grams for cultures of E. coli cells in 1 %bouillon 72 h as described previously. mediumat 37°C and pH6.2. The results were analyzed in terms of growth kinetics. RESULTS AND DISCUSSION Figure 1 shows typical growth thermo- MATERIALS AND METHODS grams. All of the thermograms were of the same Bacterial strain and culture. Escherichia coli K-12 IFO basic shape, with parallel shifts toward longer 3301 was cultured on 1%bouillon medium at pH 6.2 and incubation times with increasing amounts of 37°C as described elsewhere.1'2) the drugs. These changes are different from 2280 A. Katarao, H. Okuno and K. Takahashi

Fig. 2. Variation in the Apparent Growth Rate Constant, pi, with the Drug Concentration, i, for Cultures of E. coli with Ampicillin. The /ij values were calculated with Eq. (1). The pH of the mediumwas 6.2 and the temperature for the measure- mentswas37°C. The growth rate constants, ju, were calculated for all growth thermograms using Eq. axá"' f(t)= ANo exp(Lit) + BNo (1) wheref(t) is the total heat evolution during the incubation time, /, 7V0 is the total number ol Fig. 1. Growth Thermograms ofE. coliGrown on 5m] viable cells at the start of incubation (the of 1% Bouillon Medium at pH 6.2 and 37°C in the inoculum size), and A and B are constants. The Presence of Various Amounts of (a) Penicillin G, (b) total heat evolution f(t) was computed as a Ampicillin and (c) Polymyxin B. function of time with Eq. (2),1~3'5'8~10) The concentrations of the drugs were; penicillin G: 1) 0. 2) 3.9, 3) 7.7, 4) ll.6, 5) 15.5 and 6) 19.3/imoldm-3, ampicillin: 1) 0, 2) 0.6, 3) 0.9, 4) 1.2 and 5) LSjumoldm"3 f(t)=g(t)+ K \ g(t)dt (2) and polymyxin B: 1) 0, 2) 0.04, 3) 0.054, 4) 0.08 and 5) 0.16/mioldm~3. where g(t) is the apparent calorimetric output The calorimeter sensitivity under the steady heat effect was signal and K is the heat leakage modulus (the cooling constant) of the calorimetric unit. The calibration value of the calorimetric unit, Ac, those observed for cultures containing strepto- was measured by means of electrical heating mycin, tetracycline or chloramphenicol.0 The and the corresponding conversion parameter results, which include a slight decrease in peak for conversion of the amplitude of the calori- height with increasing drug concentrations, metric signal to the amount of heat evolved in resemble the results of computer simulation calorimetric units was calculated with Eq. (3), (see Fig. 3 in ref. 6), in which the growth AC=PK (3) thermogram was reproduced using the inoculum size as the only adjustable param- Figure 2 shows an example of the depen- eter.6'7) This resemblance suggests that the dence of ju on the drug concentration, where growth rate constant of E. coli is not affected the growth rate constants (defined as ju,) for by the presence of any of these three drugs at cultures containing ampicillin are plotted the concentrations used here. against the drug concentration, /. Regression Calorimetry of Antibiotic Action 228 1 analysis of the plot showed that the slope is 0 centration of / as A^, and if the calorimetric within the experimental uncertainty limit of signal reaches the definite value of g{t)=a at ±0.001 h'1 fjM'1. Thus the growth rate con- the incubation time, ta(i), then stant was almost completely independent of the drug concentration. The same conclusions ^ A'Ntexp QitM (7) were drawn for cultures with penicillin G and and polymyxin B; the mean growth rate constant, averaged for the results for all cultures with the a = ^Wo exp(/ira(0)) (8) three different drugs at different concentrations, was ^.=0.55h"1 with a standard where Nois the numberof viable cells at the error of 10.03-h"1. The findings that the start of incubation in mediumwithout a drug growth rate remains unchanged and that the (true inoculum size) and /a(0) is the incubation time at which the culture without the drug gives growth process is retarded by the presence of the calorimetric signal, a. This relationship is drugs show that the three drugs tested affect schematically illustrated in Fig. 3. Comparison viable cells by reducing the effective inoculum size. ofEqs. (7) and (8) gives Eq. (9), Nowwe will consider the quantitative relationship between the parallel shifts in the growth thermograms and the decrease in the effective inoculum size. Under our experimental conditions, the cooling constant, K (the reciprocal of the time constant), of the calorimetric units is 7.60h"1 and the rate of heat leakage is much greater than that of heat evolution associated with bacterial growth, so the apparent rate of the change in calorimetric signal is negligibly small compared to the rate of heat leakage. This may be expressed in mathematical terms as dg(t)/dt<^Kg(t). In Fig. 3. Schematic Illustration Showing Parallel Shifts of Growth Thermograms in the Presence of a Drug. other words, the growth thermograms observ- /a(0) and tjf) indicate the time of incubation at which the ed practically show the actual thermogenesis calorimeter signal reaches a definite value, a, for cultures of growing cultures ofE. coli. Hence, Eq. (2) is without and with the drug, respectively. reduced to

f(t)=K \g(t)dt (4) and the apparent calorimetric output signal is expressed as the following relationship, g{t) =f\t)/K. (5) From Eqs. (1) and (5), the following relationship, g(t) = A 'No exp(tit) (6) is derived, in which A/(=A]a/K) is a constant. If we denote the effective initial cell number Fig. 4. Plots of the Fraction of Residual Viable Cells, (the number of viable cells at the start of NJNq, versus the Concentration of Polymyxin B, /, present incubation) for a culture with a drug con- in the Culture Medium. 2282 A. Katarao, H. Okuno and K. Takahashi

^ = iVo exp(/i(a0)) - a0) (9) ^ = [V][i]m/[viJ (13) Thus, the effective inoculum size in the case then we have the growth equation, of media containing drugs is expressed simply Mm (14) as a function of the extent of retardation in the iL ... time scale, ta(i)-ta(O)9 of growth thermograms. This means that one can estimate the fraction of viable cells, NJN0, for a given value where \i{ is the rate constant in the presence of of / from the growth thermogram by reading a drug at concentration / (=[1]) and \im is the the values of /a(0) and ta(i). maximumgrowth rate constant. This equation An example of the dependence of Nt on the is a practical version of Monod's equation10 drug concentration is shown in Fig. 4, where and corresponds to the equation for compet- the values of NJN0observed in the presence of itive inhibition in the case of enzyme ki- various amounts of polymyxin B are plotted netics.12* against the drug concentration. The values of Microscopicsubstrate constants are usually Nt decrease as the amount of polymyxin B of the order of 1CT3mor less and n is a large increases. This trend was also observed for the positive value, so the following approximation cultures containing penicillin G or ampicillin. is reasonable with our experimental condi- If each drug is assumed to interact non- tions: competitively with viable cells to make them [Sf>Ks (15) non-viable, the kinetic equation derived leads to the conclusion that the growth rate constant If this is assumed, Eq. (14) is reduced to Eq. is a function of the drug concentration and (16), decreases as the amount of the drug increases.1} /*å =/** (16) Thus, the results reported here indicate that the action patterns of penicillin G, ampicillin Thus, the apparent growth rate constant and polymyxin B, which affect the state of the should be independent of the drug concen- cell wall and membrane, cannot be explained tration and equal to jim. This result seems to in terms of non-competitive inhibition. agree with the findings shown in Fig. 2. If we assume that the drugs act compet- However,with the above schema we cannot itively, the drug action is expressed by the explain the decrease observed in the effective following schema; inoculum size, Nt, as the drug concentration V+ftS-VSn-2V+P (10) increases. With these schema, the effective inoculum size, Nt, for a culture at the drug V+/nI ;±VIm (ll) concentration, /, is given by where a viable microbial cell, V, takes up n ^«[V]+ [VSJ (17) moles of nutrient S to form an intermediate, VSn, which produces a new viable cell as- and Nois written as sociated with the possible formation of by- #o°c[V]+ [VSJ+ [VIJ (18) product P. The viable cell also interacts with m By using these relations, we obtain from Eqs. moles of drug I to form a non-viable state, (12) and (13): VIm, in competition with the formation of VSn. N; If the substrate constant for the interaction (19) N n between the cell and the nutrient is denoted by 1^

v K^ [S]" *s = [V] [S]7[VSJ (12) If the relation, [S]"^XS, holds, Eq. (19) is and the dissociation constant of the drug by reduced, as a good approximation, to Eq. (20), Calorimetry of Antibiotic Action 2283 portional to the raN-th power of the drug Nt/N0 = \ (20) concentration, then we have Thus, Nt should be practically independent of dNt =fc, the drug concentration and equal to Nounder (21) our experimental conditions, which is not con- sistent with the results shown in Fig. 4. This where k{ is a constant. The solution of this means that competitive inhibition, as illus- equation is trated in schema 10 and 1 1 does not occur with No - N- kiiá"" (22) the three drugs studied in this study. The problem can be discussed for a more which can be transformed into Eq. (23), empirical situation. If the decrease in the effective inoculum size is assumed to be pro- ln(1 -NJNo)=mNIn/+ln(/c^0) (23) Since the value of NJNq at a given drug concentration is known from Eq. (9), the set parameters, kt/N0 and mN,can be calculated by analysis on Eq. (23). In Fig. 5, plots of ln(l-Ni/N0) versus In/, madefor cultures with one of the three drugs, are shown. The two parameters, kt/N0 and raN, were calculated by linear regression analysis for the three drugs and the values of mNthus determined are given in Table I. From Eq. (22), the drug concentration at which the effective inoculum size decreases by 50% is given by !5o = m^Vo/2^ (24) The values obtained with the above relationship are shown in the third column of Table I. The results (Table I) indicate that the con-

Table I. Interaction of the Three Drugs with E. coli Cells, as Measured by Calorimetric Method (pH 6.2, 37°C in bouillon medium)

Drugs (/imoldm"3) (/rnioldm"3)

Penicillin G 0.38+0.04 6.94

Ampicillin 0.36 + 0.03 0.46

> 100****, 54~170***,3-14.5***,210-2100* Polymyxin0.0036**,143* B 0.54+0.05 0.04 0.015-8.5***, Fig. 5. Plots ofln(l -NJNq) versus / for the Actions of 0.006**** (a) Penicillin G, (b) Ampicillin and (c) Polymyxin B.

Open circles denote the experimental data. Solid lines were ** drawn by means of linear regression analysis, from which Taken from ref. 13. Taken from ref. 14. the parameters, mN, and kJN0, were calculated according *** Takenfromref. 15. to Eq. (23), as given in Table I. **** Taken from ref. 16. /50 MIC 2284 A. Katarao, H. Okuno and K. Takahashi

Fig. 6. Drug Potency Curves Drawn for the Actions of the Three Drugs on E. coli Growth. The data were calculated with Eq. (25). The open circles denote the experimental data. The drugs were; (a) penicillin G, (b) ampicillin and (c) polymyxin B. centration range in which a drug affects viable calculated, the fraction of residual viable cells, cells is lowest for polymyxin B and highest for NJNq, was computed as a function of / with penicillin G. Eq. (25). The results are shown in Fig. 6, from The quantity, raN, defined here is an index of which the drug action at a given concentration the cooperative nature of the drug effects. Of can be estimated. The drug potency curves the three drugs studied, penicillin G exhibits thus drawn correspond to the curves shownin the highest cooperativity and inhibits the via- Fig. 4 in an earlier paper.1} The difference ble activity of E. coli cells, with the narrowest between the two sets of curves is that the drug concentration range. potency is given as a fraction of the residual In the last column of Table I, the MIC viable cells, NJNq, here, but it was given as the values for the three drugs are cited from the relative decrease in the growth rate, jUf//xm, in literature for comparison. The MIC usually the other paper.l) This difference is due to the depends somewhat on the assay conditions, difference in the changes in the growth ther- but the values of /50 for all three drugs were in mogrampatterns due to the presence of drugs, a very muchlower concentration range than as mentioned before. the reported MIC values.13~16) This result The drug action characterized by the above together with the variable cooperative nature analysis is not invariable, but valid only for the of the drug effects mentioned above means specified assay conditions, because microbial that the MIC alone does not describe the growth is usually much influenced by the antibiotic action fully enough, and that the cultural conditions. microcalorimetric method used here provides Wedo not knowwhat the parameters de- additional information as to the drug potency fined above mean biologically. However, the in quantitative terms. drug potency curves derived here are the best Onepractical application of this methodis fits to the data and are essentially independent the drawing of drug potency curves. Equation from models of drug actions. Therefore, al- (22) was transformed into Eq. (25), though the papameters in Table I have limited biological significance, we think that they are Ni/N0 = l - (ki/N0)r- (25) useful for the quantitative characterization of Using the values of mNand kJNQ already the effects of drugs on microbial cells. Calorimetry of Antibiotic Action 2285 Penicillin Gand ampicillin are knownto 5) M. Hashimoto and K. Takahashi, Agric. Biol. interact with the cell wall and then to inhibit Chem., 46, 1559 (1982). 6) H. Yamano and K. Takahashi, Agric. Biol. Chem., their biosynthesis,17) and polymyxin B binds to 50, 3145 (1986). the cell membrane.18) It is of great interest that 7) H. Yamano and K. Takahashi, Agric. Biol. 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