SCIENTIFIC PAPER

LIPOPHILICITY AND ANTIFUNGAL ACTIVITY OF SOME

2-SUBSTITUTED BENZIMIDAZOLE DERIVATIVES

SANJA O. PODUNAVAC-KUZMANOVIĆ, DRAGOLJUB D. CVETKOVIĆ

1 Department of Applied and Engineering Chemistry, Faculty of Technology,

University of Novi Sad, Bul. Cara Lazara 1, 21000 Novi Sad, Serbia

Received 29.03.2010. Revised 23.07.2010. Accepted 30.07.2010.

Corresponding author: sanjakuzmanovic@sbb.rs

2

Abstract

In the present paper, the antifungal activity of some 2-methyl and 2-

aminobenzimidazole derivatives was evaluated against yeast Saccharomyces cerevisiae.

The tested compounds displayed in vitro antifungal activity and minimum inhibitory

concentration (MIC) was determined for all compounds. The partition coefficients of the

studied compounds were measured by the shake flask method (logP) and by theoretical

calculation (ClogP). The logP values were compared and the relationships between the

logP values and antifungal activities were investigated. The mathematical models have

been developed as a calibration models for predicting the antifungal activity of this

class of compounds. The quality of models was validated by leave one out (LOO)

technique as well as by the calculation of statistical parameters for the established

models. The results of the present study may be useful for the designing of new more

potent benzimidazole derivatives against yeast Saccharomyces cerevisiae.

Keywords: Benzimidazole, antifungal activity, lipophilicity, quantitative structure-

activity relationship, Saccharomyces cerevisiae.

3

Because of their excellent activities, benzimidazole and its derivatives have a long

history as antimicrobial agents. Several thousands of benzimidazole analogs have been

synthesized and screened for pharmacological activity. They are of wide interest

because of their diverse biological activity and clinical applications. These heterocyclic

systems have different activities as they can act as bacteriostats or bactericides, as well

as fungicides [1-5] and they are present in numerous antiparasitic, antitumoral and

antiviral drugs [6-7]. Also, some of them exhibit appreciable antiprotozoal activity [8].

They were confirmed to have a moderate in vitro anti-HIV activity [9]. The success

with this group of molecules stimulated the search for new biologically active

derivatives. Understanding the role of chemical structure on biological activity is very

important. Predictions of biological and physicochemical properties of molecules based

on their structures are the fundamental and most interesting objectives of chemistry.

The opinion that there exists a close relationship between bulk properties of

compounds and the molecular structure of those compounds is rooted in chemistry. This

idea allows one to provide a clear connection between the macroscopic and the

microscopic properties of matter, and thus has been firmly established as one of the

central foundations of chemistry. Therefore, it is the one of the aims of chemistry to

identify relationships between molecular structure and physico-chemical properties and

then to quantify them [10].

A large number of research studies are needed to analyze the pharmacophore present

in these compounds using the Three Dimensional QSAR (quantitative structure-activity

relationship) methods [11-12]. The physicochemical properties predicted from structure

are helpful in the search for new molecules of similar or increased biological activity.

QSAR studies enable the investigators to establish reliable quantitative structure-

activity relationships, to derive a QSAR model and predict the activity of novel

molecules prior to their synthesis [13-16]. These studies reduce the trial- and error

element in the design of compounds by establishing mathematical relationships between

physical, chemical, biological, or environmental activities of interest and measurable or

computable parameters such as physicochemical, electronic, topological, or

stereochemistry. 3D-QSAR methodology has been successfully used to generate models

for various chemotherapeutic agents.

4

Progress in the use of QSAR methods has shown the importance of the hydrophobic

or lipophilic nature of biologically active molecules. The lipophilicity modifies the

penetration of bioactive molecules through the apolar cell membranes. This property is

usually characterized by partition coefficient (logP), which is essentially determined

from distribution studies of the compound between an immiscible polar and non-polar

solvent pair. To measure logP by the conventional shake flask technique [17] is difficult

and time resuming. It is complicated to determine logP for substances that are not very

soluble in water or can not be detected by conventional techniques. Instead of

measuring the logP values by equilibrium methods, partition chromatographic data can

be determined.

One of the most frequently used methods for lipophilicity measuring is reversed-

phase thin-layer chromatography (RP TLC) [18-22]. Lipophilicity can be expressed in

terms of many different descriptors (logP, π, f, logkw, RM, RM0) obtained experimentally

or calculated. Most frequently used experimental parameters are retention constants,

RM0 (RP TLC) and logkw (RP HPLC), whilst the calculated factor is logP. Samples of

pure compounds are not always available, so it is important to develop QSAR methods

that can efficiently predict biological activity by using theoretical descriptors computed

from the chemical structure. logP is also used in many environmental studies to

determine the environmental fate of chemicals. By knowing the exact values for this

parameter, it is possible to predict the inhibitory activity of a drug.

In continuation of our studies on inhibitory activities of benzimidazole derivatives

[23-28], in the present work we examined the activity of different substituted 2-methyl

and 2-aminobenzimidazoles against yeast Saccharomyces cerevisiae and studied the

quantitative effect of lipophilicity on antifungal activity. The main objective was to

establish a quantitative lipophilicity-inhibitory activity relationships and derive a high-

quality model which would link the lipophilicity of these compounds with their

inhibitory activity.

5

EXPERIMENTAL

Matherial and Methods

The structures of the benzimidazoles tested in this study are presented in Table 1.

All the compounds, except (1) and (8) were synthesized by a general procedure

described by Vlaović [29]. 2-methylbenzimidazole (1) and 2-aminobenzimidazole (8)

were of analytical reagent grade, commercially available.

Table 1.

Antifungal Investigations

All the benzimidazole derivatives were tested for their in vitro growth inhibition

activity against yeast Saccharomyces cerevisiae (ATCC 24860). For the evaluation of

the antifungal activities of the samples, agar disc diffusion method was used as

described by NCCLS [30].

The strains were grown on Sabouraud Dextrose slants for 24 hours at 25 oC and

checked for purity. After incubation the cells were washed from the surface of agar and

suspended in a sterile physiological solution. The number of cells in 1 cm3 of

suspension for inoculation, measured by Mc Farland nefelometer, was 1107 cfu cm-3.

The 1 cm3 of this suspensions was homogenized with 9 cm3 of melted (45 oC)

Sabouraud Dextrose Agar and poured into Petri dishes. On the surface of the agar the

6mm diameter sterile paper discs (Hi Media, Mumbai, India) were put and impregnated

with 10-3 cm3 of samples. The plates were incubated for 24-47 hours at 25 oC, and the

diameter of the resulting inhibition zone (including the disc) was measured (in mm).

The evaluation of the antifungal activities of the samples was carried out in three

repetitions.

Minimum inhibitory concentration (MIC) was determined by the agar dilution

method according to guidelines established by the NCCLS standard M7-A5 [31]. The

MIC of the tested benzimidazoles is defined as the lowest concentration of the

compound at which no growth of the strain is observed in time and under specified

6

experimental conditions. Stock solutions of the compounds were prepared in

dimethylformamide (DMF). Further dilutions were performed with distilled water. The

inoculated plates were then incubated at 35 oC for 16-20 h. A control (using DMF

without any test compound) was included for each organism. It was determined that the

solvent had no activity against any of the test microorganisms. The negative logarithms

of molar MICs (log1/cMIC) were determined and used for further calculations.

Molecular Modelling and Calculations of Lipophilicity Parameters

Molecular modelling studies were performed using CS Chem-Office Software

version 7.0 (Cambridge software) running on a P-III processor [32]. All molecules were

constructed by using Chem Draw Ultra 7.0 and saved as the template structures. For

every compound, the template structure was suitably changed considering its structural

features, copied to Chem 3D 7.0 to create a 3-D model and, finally, the model was

cleaned up and subjected to energy minimization using molecular mechanics (MM2).

The minimization was executed until the root mean square (RMS) gradient value

reached a value smaller than 0.1 kcal/molA. The Austin Model-1 (AM-1) method was

used for re-optimization until the RMS gradient attained a value smaller than 0.0001

kcal/molA using MOPAC. The lowest energy structure was used for each molecule to

calculate ClogP values by using ChemDraw Ultra 7.0. (Table 2).

Also, for all the compounds the lipophilicity parameters, logP values, were

experimentally determined by shake flask method. Partition coefficients (P) for

benzimidazoles investigated between n-octanol and phosphate buffer were determined

at 25 oC. Before the partitioning of benzimidazoles, the buffer (0.15moldm-3, pH=7.4)

and n-octanol (99%, Sigma, USA) were saturated with each other. Benzimidazoles were

dissolved in ethanol (96%, Zorka, Serbia) at a concentration of 2mgcm-3 to give the

stock solution. Calibration was done in exactly the same manner as the partitioning,

except that n-octanol was not used. The amounts of the sample were chosen so that

absorbance (=252nm) of 0.1 to 0.8 was measured. Partitioning experiments were

performed in the systems n-octanol/phosphate buffer 1:20, 1:30, 1:70 and 1:80 (V/V).

All solutions were pipetted into glass vials; the n-octanol and stock solution were added

with a microliter sxringe. The phases were shaken together on a mechanical shaker

7

(Viggo, Sweden) for 30 minutes, centrifuged (Rotofix, Switzerland) at 2500rpm for 20

min to afford complete phase separation, and n-octanol phase was removed. Absorbance

of the buffer phase was measured using Shimadzu UV/VIS spectrophotometer (Japan)

at 252nm. logP values were calculated using Eq. 1:

oltanocn

buffer

V

V

x

xylogPlog

(1)

where: P - partition coefficient; y - total mass of benzimidazole derivative (mg); X -

mass of benzimidazole derivative in the buffer phase after partitioning (mg); Vbuffer -

volume of phosphate buffer (cm3); Vn-octanol - volume of n-octanol (cm3). Each

experimental logP value is the average of five determinations (Table 2)..

Table 2.

Statistical Methods

The complete regression analysis was carried out by PASS 2005, GESS 2006,

NCSS Statistical Softwares [33].

RESULTS AND DISCUSSION

The results of antifungal studies of benzimidazoles tested against Saccharomyces

cerevisiae are summarized in Table 3. As indicated, all the compounds show antifungal

activities against the tested yeast. Consequently, compounds with high log1/cMIC are the

best antifungals. The MICs were compared with Ketoconazole and Amphotericin B

which were screened under similar conditions as reference drugs.

Table 3.

8

In order to identify the effect of lipophilicity on the inhibitory activity, QSAR

studies of title compounds were performed. A set of benzimidazoles consisting of 14

molecules was used for multilinear regression model generation. The reference drugs

were not included in model generation as they belong to a different structural series. An

attempt has been made to find structural requirement for inhibition of Saccharomyces

cerevisiae using QSAR Hansch approach on benzimidazole derivatives. To obtain the

quantitative effects of the lipophilicity parameter of benzimidazole derivatives on their

antifungal activity, QSAR analysis with logP was operated.

It is obtained that the correlation between MICs and shake flask logP, as well as

correlation between MICs and ClogP were equally significant. In this approach, two

mathematical models were derived (Table 4). It is noteworthy that both the models were

derived using entire data set of compounds (n=14) and no outliers were identified. The

F-value obtained in Models.(1-2) is found statistically significant at 99% level since all

the calculated F values are higher as compared to tabulated values. It is apparent from

the data that fitting equations improve when resorting to second order polynomial.

Table 4.

It is well known that there are three important components in any QSAR study:

development of models, validation of models and utility of developed models.

Validation is a crucial aspect of any QSAR analysis 34. The statistical quality of the

resulting models, as depicted in Table 4, is determined by r, s, and F 35-37.

For the testing the validity of the predictive power of selected models the LOO

technique was used. The developed models were validated by the calculation of the

following statistical parameters: PRESS, SSY, SPRESS, r2CV, and r2

adj (Table 5).

Table 5.

These parameters were calculated from the following equations.

2)(PRESS calcobs YY (1)

9

2)(SSY meanobs YY (2)

n

PRESSSPRESS (3)

SSY

PRESS12

CV r (4)

1

1)(1 22

adj pn

nrr (5)

Where, Yobs, Ycalc and Ymean are observed, calculated and mean values; n, number of

compounds; p, number of independent parameters.

PRESS is an acronym for prediction sum of squares. It is used to validate a

regression model with regards to predictability. To calculate PRESS, each observation

is individually omitted. The remaining n-1 observations are used to calculate a

regression and estimate the value of the omitted observation. This is done n times, once

for each observation. The difference between the actual Y value, yobs, and the predicted

Y, ycalc, is called the prediction error. The sum of the squared prediction errors is the

PRESS value. The smaller PRESS is, the better the predictability of the model. Its value

being less than SSY points out that the model predicts better than chance and can be

considered statistically significant. SSY are the sums of squares associated with the

corresponding sources of variation. These values are in terms of the dependent variable,

y.

The PRESS value above can be used to compute an r2CV statistic, called r2 cross

validated, which reflects the prediction ability of the model. This is a good way to

validate the prediction of a regression model without selecting another sample or

splitting data. It is very possible to have a high r2 and a very low r2CV. When this occurs,

it implies that the fitted model is data dependent. This r2CV ranges from below zero to

above one. When outside the range of zero to one, it is truncated to stay within this

range. Adjusted r-squared (r2adj) is an adjusted version of r2. The adjustment seeks to

remove the distortion due to a small sample size.

In many cases r2CV and r2

adj is taken as a proof of the high predictive ability of

QSAR models. A high value of these statistical characteristic (>0.5) is considered as a

10

proof of the high predictive ability of the model. But, recent reports have proved the

opposite 38. Although, the low value of r2CV for the training set can indeed serve as an

indicator of a low predictive ability of a model, the opposite is not necessarily true.

Indeed, the high r2CV does not imply automatically a high predictive ability of the

model. Thus, the high value of LOO r2CV is the necessary condition for a model to have

a high predictive power, but it is not a sufficient condition.

The only way to estimate the true predictive power of a model is to test its ability to

predict accurately the biological activities of compounds. In order to verificate the

predictive power of the developed model, predicted log1/cMIC values of benzimidazoles

investigated were calculated by using models (1) and (2) and compared with the

experimental values (Table 3). The data presented in Table 3 show that the observed

and the estimated activities are very close to each other. The residual activity (difference

between experimentally observed log (1/cMIC) and QSAR calculated log (1/cMIC)) is less

than equal to 0.192. Further, the plot of predicted log1/cMIC values against the observed

log1/cMIC values also proves the usefulness of the derived models. (Figure 1).

Figure 1.

In order to investigate the existence of a systemic error in developing the QSAR

models, the residuals of predicted log1/cMIC were plotted against the observed log1/cMIC

values (Figure 2). The propagation of the residuals on both sides of the zero axis

indicates that no systemic error in the development of regression models exists, as

suggested by Jalali-Heravi and Kyani [39].

Figure 2.

The results of this investigation indicate that the antifungal activity exhibited by the

tested compounds is governed by the partition coefficient, logP. Lipophilicity as a

physicochemical parameter has an important effect on inhibitory activity and this

parameter is usually related to pharmacological activity [40,41]. LogP is a measure of

hydrophobicity which is important for the penetration and distribution of the drug, but

11

also for the interaction of drug with receptors. To conclude, results of this study indicate

that both shake flask logP and ClogP are equaly suitable for prediction of partition

coefficient.

CONCLUSIONS

QSAR analysis was performed to estimate the quantitative effects of the

lipophilicity parameter, logP, of the different substituted 2-methyl and 2-

aminobenzimidazole derivatives on their antifungal activity against Saccharomyces

cerevisiae. For all the studied compounds the lipophilicity parameters were

experimentally determined by shake flask method (logP) as well as by theoretical

calculation (ClogP). Accurate mathematical models were developed for predicting the

inhibitory activity of some benzimidazole derivatives. The validity of the models has

been established by the determination of suitable statistical parameters. The established

model was used to predict inhibitory activity of the benzimidazoles investigated and

close agreement between experimental and predicted values was obtained. The low

residual activity and high cross-validated r2 values (r2CV) observed indicated the

predictive ability of the developed QSAR model. It indicates that the antifungal activity

of series of 2-methyl and 2-aminobenzimidazole derivatives can be successfully

modeled using different molecular descriptors. The results of this study indicate that

both shake flask logP and ClogP are equaly suitable for prediction of partition

coefficient.

Acknowledgment

These results are part of the project No. 142028, supported by the Ministry of

Science and Technological Development of the Republic of Serbia.

12

REFERENCES

1. Z. Ates-Alagoz, S. Yildiz, E. Buyukbingol, Chemotherapy 53 (2007) 110-113.

2. P. T. M. Nguyen, J. D. Baldeck, J. Olsson, R. E. Marquis, Oral Microbiol.

Immunol. 20 (2005) 93-99.

3. G. Ayhan-Kilcigil, N. Altanlar, Turk. J. Chem. 30 (2006) 223-228.

4. H. Goker, M. Alp, S. Yildiz, Molecules 10 (2000) 1377-1386.

5. S. O. Podunavac-Kuzmanović, D. D. Cvetković, CI&CEQ 13 (2007) 68-71.

6. M. Boiani, M. Gonzalez, J. Med. Chem. 5 (2005) 409-415.

7. L. Garuti, M. Roberti, C. Cermelli, Bioorg. Med. Chem. Lett. 9 (1999) 2525-2530.

8. Z. Kazimierczuk, J. A. Upcroft, P. Upcroft, A. Gorska, B. Starosciak, A. Laudy,

Acta Biochim. Polon. 49-1 (2002) 185-195.

9. A. Akbay, I. Oren, O. Temiz-Arpaci, E. Aki-Sener, I. Yalcin, Arzneim.-

Forcsh.Drug Res. 53 (2003) 266-271.

10. G. P. Romanelli, J. C. Autino, E. A. Castro, Turk. J. Chem. 26 (2002) 335-343.

11. C. Hansch, A. Leo, D. H. Hoekman, Exploring QSAR, Hydrophobic, Electronic and

Steric Constants; American Chemical Society, Washington DC, 1995

12. C. Hansch, J. Med. Chem. 19 (1976) 1- 6.

13. P. Vasanthanathan, M. Lakshmi, M. A. Babu, A. K. Gupta, S. G. Kaskhedikar,

Chem. Pharm. Bull. 54 (2006) 583-587.

14. G. Melagraki, A. Afantitis, H. Sarimveis, O. Igglessi-Markopoulou, C. T. Supuran,

Bioorg. Med. Chem. 14 (2006) 1108-1114.

15. S. O. Podunavac-Kuzmanović, S. L. Markov, D. J. Barna, J. Theor. Comp. Chem. 6

(2007) 687-698.

16. S. O. Podunavac-Kuzmanović, D. J. Barna, D. D. Cvetković, Acta Periodica

Technologica 38 (2007) 139-147.

17. A. Leo, C. Hansch, D. Elkins, Chem. Rev. 71 (1971) 525-616.

18. A. Nasal, D. Siluk, R. Kaliszan, Curr. Med. Chem. 10 (2003) 381-426.

19. B. Tiperciuc, C. Sarbu, J. Liq. Chrom. Rel. Technol. 29 (2006) 2257-2270.

20. N. U. Perišić-Janjić, S. O. Podunavac-Kuzmanović, J. Planar. Chromatogr. 21

(2008) 135-141.

13

21. N. U. Perišić-Janjić, S. O. Podunavac-Kuzmanović, J. S. Balaž, Đ. Vlaović, J.

Planar. Chromatogr. 13 (2000) 123-129.

22. T. Slawik, B. Paw, J.Liq. Chromatogr. 27 (2004) 1043-1055.

23. S. O. Podunavac-Kuzmanović, D. D. Cvetković, D. J. Barna, J. Serb. Chem. Soc. 73

(2008) 967-978.

24. S. O. Podunavac-Kuzmanović, D. D. Cvetković, D. J. Barna, Int. J. Mol. Sci. 10

(2009) 1670-1682.

25. S. O. Podunavac-Kuzmanović, V. M. Leovac, N. U. Perišić-Janjić, J. Rogan, J.

Balaž, J. Serb. Chem. Soc. 64 (1999) 381-388.

26. S. O. Podunavac-Kuzmanović, D. D. Cvetković, J. Serb. Chem. Soc. 75 (2007) 459-

466

27. S. O. Podunavac-Kuzmanović, V. M. Leovac, D. D. Cvetković, J. Serb. Chem. Soc.

73 (2008) 1153-1160.

28. S. O. Podunavac-Kuzmanović, D. D. Cvetković, D. J. Barnaa, CICEQ 15 (2009)

125-130.

29. Đ. Vlaović, J. Čanadanović-Brunet, J. Balaž, I. Juranić, D. Đoković, K. Mackenzie,

Biosci. Biotech. Biochem. 56 (1992) 199-206.

30. National Commitee for Clinical Laboratory Standards, NCCLS Approval Standard

Document M2-A7, Vilanova, Pa, U.S.A. (2000).

31. National Commitee for Clinical Laboratory Standards, NCCLS Approval Standard

Document M7-A5, Vilanova, Pa, U.S.A. (2000).

32. CS. Chem. Office, Version 7.0, Cambridge Soft Corporation, 100 Cambridge Park

Drive, Cambridge, MA 02140-2317, U.S.A. (2001).

33. www.ncss.com.

34. J.G. Topliss, R.P. Edwards, J. Med. Chem. 22 (1979) 1238-1244.

35. G.W. Snedecor, W.G. Cochran, Statistical Methods; Oxford and IBH, New Delhi,

1967

36. S. Chaltterjee, A.S. Hadi, B. Price, Regression Analysis by Examples; Wiley VCH,

New York, 2000

37. M.V. Diudea, QSPR/QSAR Studies for Molecular Descriptors, Nova Science,

Huntingdon, New York, 2000

38. A. Golbraikh, J. Tropsha, J. Mol. Graph. Mod. 20 (2002) 269-276.

14

39. M. Jalali-Heravi, A. Kyani, J. Chem. Inf. Comput. Sci. 44 (2004) 1328-1335.

40. H. H. Meyer, Arch. Exp. Pathol. Pharmacol. 46 (1901) 338-346.

41. C. E. Overton, Studies of Narcosis, Chapman and Hall, London, 1990

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Table 1. The structures of the compounds examined

N

N

R1

R2

Compound R1 R2

1 CH3 H

2 CH3 C6H5–CH2

3 CH3 4–CH3–C6H4–CH2

4 CH3 4–Cl–C6H4–CH2

5 CH3 C6H5–CO

6 CH3 4–CH3–C6H4–CO

7 CH3 4–Cl–C6H4–CO

8 NH2 H

9 NH2 C6H5–CH2

10 NH2 4–CH3–C6H4–CH2

11 NH2 4–Cl–C6H4–CH2

12 NH2 C6H5–CO

13 NH2 4–CH3–C6H4–CO

14 NH2 4–Cl–C6H4–CO

16

Table 2. Experimentally determined and calculated lipophilicity descriptors

Compound Shake flask logP ClogP

1 1.53 1.48

2 3.51 3.45

3 4.01 3.94

4 4.07 4.01

5 3.38 3.33

6 3.87 3.81

7 3.95 3.89

8 1.05 0.99

9 3.02 2.96

10 3.50 3.44

11 3.59 3.52

12 2.90 2.84

13 3.35 3.32

14 3.45 3.39

17

Table 3. Antifungal screening summary

log1/cMIC predict. Residuals Compound log1/cMICexp.

Model 1 Model 2 Model 1 Model 2

1 4.525 4.406 4.421 0.119 0.104

2 4.325 4.411 4.413 -0.086 -0.088

3 3.277 3.439 3.456 -0.162 -0.179

4 3.313 3.296 3.289 0.017 0.024

5 4.577 4.599 4.589 -0.022 -0.012

6 3.602 3.750 3.747 -0.148 -0.145

7 3.637 3.576 3.571 0.061 0.066

8 3.425 3.479 3.468 -0.054 -0.043

9 4.854 4.982 4.989 -0.128 -0.135

10 4.579 4.426 4.428 0.153 0.151

11 4.615 4.581 4.599 0.034 0.016

12 4.88 5.065 5.072 -0.185 -0.192

13 4.604 4.639 4.603 -0.035 0.001

14 4.638 4.501 4.504 0.137 0.134

Ketoconazole 4.628 - -

Amphotericin 4.869 - -

18

Table 4. Best mathematical models for the prediction of antifungal activity.

Model Coefficient n r s F

Intercept 0.1890

Shake flask logP 3.9568 1

Shake flask logP2 -0.7846

14 0.9697 0.0257 86.7954

Intercept 0.3835

ClogP 3.8997 2

ClogP2 -0.7918

14 0.9706 0.0249 89.5498

19

Table 5. Cross-validation parameters

Model PRESS SSY PRESS/SSY SPRESS r2CV r2

adj

1 0.4350 4.7381 0.0918 0.1762 0.9082 0.9296

2 0.4152 4.7381 0.0876 0.1722 0.9124 0.9316

20

3.2 3.6 4.0 4.4 4.8 5.2

3.2

3.6

4.0

4.4

4.8

5.2

r=0.9823

Model 1

Observed log (1/cMIC

)

Pre

dic

ted

log

(1/

c MIC

)

3.2 3.6 4.0 4.4 4.8 5.2

3.2

3.6

4.0

4.4

4.8

5.2

r=0.9821

Model 2

Observed log (1/cMIC

)

Pre

dic

ted

log

(1/

c MIC

)

a)

b)

Figure 1. Plots of predicted versus experimentally observed antifungal activity against

Saccharomyces cerevisiae

21

3.2 3.6 4.0 4.4 4.8 5.2

-0.2

-0.1

0.0

0.1

0.2Model 1

Observed log (1/cMIC

)

Res

idu

e

3.2 3.6 4.0 4.4 4.8 5.2

-0.2

-0.1

0.0

0.1

0.2Model 2

Observed log (1/cMIC

)

Res

idu

e

a)

b)

Figure 2. Plots of the residual values against the experimentally observed log1/cMIC

values