THIS INVENTION relates to inhibition prediction. In particular the invention relates to a method of determining interaction between at least three agents and the probability of them having an inhibitory effect, and to the use of the method in determining the influence/interaction between agents.

BACKGROUND OF THE INVENTION

"The concept of antimicrobial synergy is based on the principle that, in combination, the formulation may enhance efficacy, reduce toxicity, decrease adverse side effects, increase bioavailability, lower the dose and reduce the advance of antimicrobial resistance. New antimicrobial combination drugs which include natural product combinations have recently become a research priority." "Multidrug therapy has become of paramount importance in the fight against multidrug resistant microbial strains." "Methods used to determine antimicrobial interactions include basic combination studies (diffusion assays), the sum of the fractional inhibitory concentration index, isobole interpretations and death kinetic (time-kill) assays." "Various authors have expressed concern over the methods used to interpret synergy" as there are vast discrepancies. "Mathematical models and statistical approaches to validate antimicrobial interactions have been developed to allow for a more reliable and quantitative assessment of pharmacological interactions." (van Vuuren & Viljoen, 201 1 ).

The inventor identified a need for a 'statistical approach' to allow for a more reliable and quantitative assessment of pharmacological interactions and to address the limited classification of synergy when looking at the influence the combination of agents has upon on one another and their effect on inhibition.

In this specification reference is made to the following documents: Eloff, J.N. 1998. A sensitive and quick microplate method to determine the minimal inhibitory concentration of plant extract for bacteria. Plant Medica, 64: 71 1— 713.

Fienberg SE: The Analysis of Cross-classified Categorical Data. 2nd edition.

Cambridge, Massachusetts: Massachusetts institute of Technology Press;

1980.

Hocking RR: The analysis and selection of variables in linear regression. Biometrics 1976, 32: 1-49.

Lall, N., Henley-Smith, C.J., De Canha, M.N., Oosthuizen, C.B. and Berrington, D.

Viability reagent, PrestoBlue, in comparison with other available reagents, utilized in cytotoxicity and antimicrobial assays. International Journal of

Microbiology, doi: 10.1 155/2013/420601

Lomovskaya O, Zgurskaya HI: Efflux Pumps from Gram-negative Bacteria: From

Structure and Function to Inhibition. In Emerging Trends in Antibacterial Discovery. Part II -4 Novel Targets and Sources. Edited by Miller AA, Millar

PF. Norfolk, UK: Caister Academic Press; 201 1 :77-105.

McFarland, J. 1907. The nephelometer: An instrument for estimating the number of bacteria in suspensions for calculating the opsonic index and for vaccines.

Journal of America Medical Association, 49: 1 176.

Nagelkerke NJD: A note on a general definition of the coefficient of determination.

Biometrika 1991 , 78:691-692.

Samaranayake LP: Essential microbiology for dentistry; with a contribution by B.M.

Jones; foreword by Crispian Scully. Edinburgh, New York: Churchill

Livingstone; 2002.

Silva, F., Ferreira, S., Duarte, A., Mendonca, D.I., Domingues, F.C. 201 1. Antifungal activity of Coriandrum sativum essential oil, its mode of action against Candida species and potential synergism with amphotericin B. Phytomedicine, 19: 42-47.

Van Vuuren, S. and Viljoen, A. 201 1. Plant-based antimicrobial studies - Methods and approaches to study the interaction between natural products. Planta

Medica, 77: 1 168-1 182.

Abbreviations ATCC, American type culture collection; CASO, Casein-peptone Soymeal-peptone; CFU, Colony forming units; CHX, Chlorhexidine gluconate; DMSO, Dimethyl sulphoxide; FIC, Fractional inhibitory concentration; MIC, Minimum inhibitory concentration; PRU, H. G.W.J. Schwelcherdt Herbarium; v/v, Volume per volume

SUMMARY OF THE INVENTION

Broadly according to an aspect of the invention there is provided a method of determining interaction between at least three agents and the probability of them having an inhibitory effect, the method including

representing outcomes of synergistic tests as at least one set of binary matrices, each set including at least a first and a second matrix, first matrices each representing binary outcomes of different concentration combinations of two agents, and second matrices each representing outcomes of the different concentration combinations of the two agents with an additional fixed concentration of a third agent, the number of sets of matrices depending on the number of agents for which synergistic activity is to be determined;

feeding the binary matrices into a qualitative response model to determine regression parameters; and

generating a prediction model based on the regression parameters, the prediction model representing approximated outcomes of the synergistic activity between the at least three agents.

Each set of binary matrices may include further binary matrices, each further binary matrix representing outcomes of the different concentration combinations of the two agents with an additional altered fixed concentration of the third agent. The number of sets of matrices may be increased by addition of additional agents, such that each set of matrices represents outcomes of synergistic tests of a combination of three of the at least three agents.

The synergistic tests may be in the form of biological inhibition tests. The synergistic tests may be in the form of microbial inhibition tests.

The outcomes of the synergistic tests may be in the form of checkerboard outcomes. The method may include the prior step of performing a plurality of synergistic tests to provide the checkerboard outcomes. The step of performing a plurality of synergistic tests may be in the form of checkerboard assays.

The checkerboard assays may be in the form of checkerboard microtiter plate assays.

The step of performing a plurality of synergistic tests may include providing a first test plate comprising a range of concentrations of a first agent in rows of a matrix of test wells; a range of concentrations of a second agent in columns of a matrix of test wells; and conducting a first biological test in each of the test wells of the first test plate; and

providing at least one additional test plate comprising a replica of the range of concentrations of the first test plate; a first fixed concentration of a third agent in all the test wells of the matrix; and conducting a second biological test in each of the test wells of the at least one additional test plate.

Conducting the biological tests may include adding a biological sample to each test well, and determining the effect the agents have on the biological sample.

Determining the effect the agents have on the biological sample may include determining whether the combination of agents in a specific well has an inhibitory effect on the biological sample in that well. The checkerboard outcomes of the first test plate and second test plate may be represented as a set of binary matrices.

The step of performing a plurality of synergistic tests may include further additional test plates comprising a replica of the range of concentrations of the first test plate and an alternative fixed concentration of a third agent in all the test wells of the matrix.

The step of performing a plurality of synergistic tests to provide the checkerboard outcomes may include

providing a set of at least four agents;

preparing sets of microtiter plates, one set of microtiter plates for each alternative combination of at least three of the agents, such that there is a set of microtiter plates for every possible combination of three agents of the set of at least four agents;

adding at least one biological sample to each well of the microtiter plates; identifying the wells in which inhibition took place; and

determining the wells that showed inhibition and wells that showed no inhibition, to provide outcomes for each plate.

The outcomes for each plate may be represented as a binary matrix, indicating wells that showed inhibition and wells that showed no inhibition.

Preparing a set of microtiter plates may include

preparing a first microtiter plate by adding a first dilution of a first agent to the wells of an end row of the microtiter plate and adding serial dilutions of the first agent to each subsequent row; and adding a second agent to the wells of an end column of the microtiter plate and adding serial dilutions of the second agent to each subsequent column such that each well contains a unique concentration combination of the first and second agent; and

preparing at least one second microtiter plate by repeating the step to prepare the first microtiter plate and following with a further step of adding a fixed concentration of a third agent to each well of the second plate, thereby forming a set of plates with the same final concentration ranges.

The first microtiter plate may include a volume of buffer solution, and in the second microtiter plate, the volume of buffer may be replaced with the same volume of the third agent.

Determining the wells in which inhibition took place may be determined by addition of a viability reagent to each well. The viability reagent may be in the form of any one of PrestoBlue and resazurin salt.

The biological sample used for the biological tests may be in the form of at least one microorganism. The at least one microorganism may be in the form of any one or more of bacteria, yeasts, algae, viruses or the like. In another embodiment the at least one biological sample may be in the form of and one of eukaryotes, yeasts, fungi, cells or the like.

The agents may be in the form of any one or more of plant extracts, medicaments, drugs, pesticides, pure compounds, antimicrobial compositions and the like.

The qualitative response model may be in the form of a logistic response model. The accuracy of the regression parameters may be evaluated by means of the Nagelkerke index. Specifically, the accuracy of the regression parameters may be evaluated by means of the Nagelkerke R ² index.

The prediction model may be generated by means of a statistical prediction tool.

The statistical prediction tool may be the "IBM SPSS" tool.

A 100% inhibition prediction by the statistical prediction tool indicates total inhibition.

The invention further extends to use of a method as described, for screening a plurality of agents to evaluate their interaction.

The use of the method may include predicting which combination of agents will have an effective inhibitory effect.

The use of the method may include selecting a combination of agents to prepare an inhibitory composition. The use of the method may include determining the contribution of each agent in the inhibitory composition.

The invention will now be described, by way of example only with reference to the following drawings:

DRAWING(S)

In the drawing(s): Figure 1 shows the checkerboard results for Prevotella intermedia. A 0 indicated no inhibition while 1 represented inhibition. Plates A and B contained Mentha piperita and Heteropyxis natalensis, while plate B had the addition of the third agent, TEAVIGO™. Plates C and D contained Melaleuca alternifolia and H. natalensis with TEAVIGO™ present in plate D. Plates E and F contained the essential oils M. piperita and M. alternifolia with Plate F additionally containing TEAVIGO™. Plates G and H contained M. alternifolia and H. natalensis with the addition of M. piperita in plate H. The MIC's for each agent are also given. Figure 2 shows the checkerboard results for Candida albicans. A 0 indicated no inhibition while 1 represented inhibition. Plates A and B contained Mentha piperita and Heteropyxis natalensis, with plate B having the addition of the third agent, TEAVIGO™ (5 mg/ml). Plates C and D contained Melaleuca alternifolia and H. natalensis with TEAVIGO™ present in plate D. Plates E and F contained the essential oils M. piperita and M. alternifolia with Plate F additionally containing TEAVIGO™. Plates G and H contained M. alternifolia and H. natalensis with the addition of M. piperita in plate H. The MIC's for each agent are also given.

Figure 3 shows The checkerboard results for Streptococcus mutans. Plates A and B contained Mentha piperita and Heteropyxis natalensis were paired, with plate B having the addition of the third agent, TEAVIGO™. Plates C and D contained Melaleuca alternifolia and H. natalensis with TEAVIGO™ present in plate D. Plates E and F contained the essential oils M. piperita and M. alternifolia with Plate F additionally containing TEAVIGO™. Plates G and H contained M. alternifolia and H. natalensis with the addition of M. piperita in plate H. The MIC's for each agent are also given.

Figure 4 Shows one set of plates with the growth indicator, PrestoBlue, in the presence of Prevotella intermedia. Plates E and F contained the essential oils Mentha piperita and Melaleuca alternfolia with plate F additionally containing TEAVIGO™. Blue-green indicated inhibition of Prevotella intermedia, while pink-red indicated growth of P. intermedia.

EMBODIMENT OF THE INVENTION

An experiment was conducted to illustrate the effectiveness of using an altered synergistic method to determine the effect various agents have upon the inhibition of a microorganism, and the ability to predict the outcome. It is to be appreciated that the invention is not in any way limited to the type of agents or microorganisms used in this experiment, and that the experiment and results are merely an example of the usefulness of the inventive method.

Materials and methods

Plant material

Aerial plant parts, comprising of leaves and twigs of H. natalensis was collected. The plant was collected from the University of Pretoria's experimental farm during January. A voucher specimen was prepared and identified at the H. G.W.J. Schwelcherdt Herbarium (PRU), University of Pretoria, (PRU 096405). Melaleuca alternifolia essential oil (Holistic Emporium cc, Gauteng, South Africa), Mentha piperita essential oil (Holistic Emporium cc, Gauteng, South Africa), and TEAVIGO™ (Chempure (Pty) Ltd, Silverton, South Africa), were purchased as well for the present investigation.

Preparation of extract

The plant material was air dried at room temperature (25°C), and ground to a fine powder using a standard food processor. The powdered material was extracted with ethanol (Merck Chemicals (Pty) Ltd Wadeville, South Africa) under pressure (100 bar) and regulated temperature of 50°C in a BUCHI Speed Extractor, E-916 (BUCHI Labortechnik AG, Switzerland). The solvent was evaporated on low boiling point in a Genevac, EZ-2 plus (Genevac SP Scientific, UK), after which the extract was subjected to antimicrobial tests.

Microbial strains

The microorganisms used in this study included Prevotella intermedia (ATCC 2561 1 ), Streptococcus mutans (ATCC 25175) and Candida albicans (ATCC 10231 ). The bacteria were grown on Casein-peptone Soymeal-peptone Agar) (CASO) (Merck Chemicals (Pty) Ltd Wadeville, South Africa) enriched with 1 % sucrose (Merck Chemicals (Pty) Ltd Wadeville, South Africa) under anaerobic conditions in an anaerobic jar with Anaerocult ^® A (Merck Chemicals (Pty) Ltd Wadeville, South Africa), at 37 °C for 48 hours. Candida albicans was grown on Sabouraud Dextrose 4% Agar (SDA) (Merck Chemicals (Pty) Ltd Wadeville, South Africa), at 37 °C for 48 hours. Sub-culturing was done every second week. Inocula were prepared by suspending bacterial test organisms in their respective broths until turbidity was compatible with McFarland Standard 1 (Merck Chemicals (Pty) Ltd Wadeville, South Africa) (McFarland, 1907).

Antimicrobial susceptibility testing

To determine the effects of combinations of H. natalensis, M. alternifolia essential oil, M. piperita essential oil and TEAVIGO™, the MIC of each component was determined first using the anti-microbial microplate method of Eloff (1998). A stock solution of the ethanol extract of H. natalensis was prepared in 20% dimethyl sulphoxide (DMSO) (Merck Chemicals (Pty) Ltd); while TEAVIGO™ was dissolved in distilled water. The stock solutions were serially diluted in enriched Casein-peptone Soymeal-peptone medium broth (Merck Chemicals (Pty) Ltd) for the bacteria and Sabouraud Dextrose 4% broth (Merck Chemicals (Pty) Ltd) for Candida; in the 96- well plate adding a McFarland Standard 1 inoculum of 48 hour old microorganisms grown at 37 ^° C. The final concentration of the extract and TEAVIGO™ ranged from 0.10-12.5 mg/ml and the positive control, 1.25% v/v chlorhexidine gluconate (CHX) (Dental Warehouse, Sandton, South Africa), ranged from 4.77 x 10 ^"6 -0.31 % v/v. The essential oils were dissolved in 10% Tween (80) (Merck Chemicals (Pty) Ltd Wadeville, South Africa). The final concentration tested of the essential oils ranged from 1.6 x 10 ^"5 — 1.25% v/v. The highest concentration of the solvent Dimethyl sulphoxide (DMSO) (5%) and Tween 80 (2%) was found to be non-toxic to the microorganisms tested. The inoculated plates were incubated at 37°C, under anaerobic and aerobic conditions respectively for 24 hours before adding the colour indicator PrestoBlue (Lall et al., 2013). The minimum inhibitory concentration (MIC) was defined as the lowest concentration that inhibited the colour change of PrestoBlue.

Synergistic assay

The synergistic activity of the samples was determined using a modified checkerboard method. The basic design is a logarithmic design with the dosages halved at each step. Full 2-factor factorial designs were used for two factors at a time with equally spaced dosages for the other factors. The individual designs were compounded in such a way that all two-way interactions and some three-way interactions could be estimated. Two 96-well plates were prepared: the first one was used to two-fold serial dilutions of H. natalensis (50 μΙ) in horizontal orientation, and the second one, was used to make five-fold serial dilutions of M. alternifolia in the vertical orientation. Both dilutions were made in enriched Casein-peptone Soymeal- peptone medium broth for the selected bacteria, and Sabouraud Dextrose 4% broth for the yeast, C. albicans (50 μΙ per well for the first plate and 200 μΙ for the second plate). Using a multichannel pipette, 50 μΙ of M. alternifolia was transferred to the first plate, 50 μΙ of the respective broth was added and then 50 μΙ of bacterial suspension was added to each well and incubated for 24 h at 37°C; after which 20 μΙ of PrestoBlue was used to indicate bacterial growth (Lall et al., 2013; Silva et al., 201 1 ). The concentration range of H. natalensis in combination ranged from 0.097 - 12.5 mg/ml, while the essential oils ranged from 1 .6 x 10 ^"5 - 1.25 % v/v. A third plate was prepared at the same time in the exact same manner as the first plate except that instead of 50 μΙ of additional broth; 50 μΙ of a third agent, M. piperita was added at a sub-MIC value at a fixed concentration to all wells. The sub-MIC concentrations of M. piperita and TEAVIGO™ were determined on the basis of MIC values previously obtained.

The MIC's of each agent tested (as previously described) were also conducted at the same time acting as controls and a comparison. The concentration range of H. natalensis and TEAVIGO™ ranged from 0.097 - 12.5 mg/ml, while the essential oils ranged from 1.6 x 10 ^"5 - 1.25 % v/v. CHX was again utilized as a positive control. This process was repeated for all 4 combinations of the 4 agents for each microorganism tested.

Once the plates were developed with PrestoBlue, each well was assigned either a 0 to indicate no inhibition or a 1 to indicate inhibition for the logistic response model. This information was used to construct a Predictive Model (IBM© SPSS© version 21 ) for each microorganism where the antimicrobial ability of the different combinations was tested as described in the antimicrobial susceptibility testing (Eloff, 1998).

Results and discussion

Antimicrobial susceptibility testing

The checkerboard method was utilized as a screening tool for the reduction of MIC values. This method also provided numerous concentration variables for the agents under investigation and their inhibition potential. The results were converted to binary code; with 0 representing no inhibition, and 1 representing inhibition. This data was then used to compute the logistic response model. Figure 1 shows the inhibitory effect of three agents on P. intermedia. In determining the antimicrobial susceptibility of P. intermedia (Figure 1 ), the addition of TEAVIGO™ (2.5 mg.ml) to plate B (of paired plates A and B) reduced the MIC of H. natalensis from 12.5 mg/ml to 3.13 mg/ml and that of M. piperita from 1.17% v/v to 0.29% v/v. In plates C and D the addition of TEAVIGO™ seemed to have little effect on either H. natalensis or M. alternifolia; however when TEAVIGO™ was added to the essential oils, M. piperita and M. alternifolia (plates E and F) both oils MIC were reduced from 1 .17% v/v to 0.29% v/v overall. In plates G and H with H. natalensis and M. alternifolia and the addition of M. piperita in plate H there is a significant decrease in both agents MIC's. Even though the pattern of inhibition to no inhibition is a little scattered the overall reduction of the MIC of H. natalensis from 12.5 mg/ml to 1.56 mg/ml and for M. alternifolia from 1 .17% v/v to 4.5 x 10 ^"3 % v/v was obtained. This is a significant decrease when compared to the MIC values of the individual agents the reduction of H. natalensis on its own (12.5 mg/ml) to as low as 1 .56 mg/ml in combination.

Figure 2 shows the inhibitory effect of three agents on C. albicans. With C. albicans (Figure 2), the addition of TEAVIGO™ at a sub-MIC (5 mg/ml) in plate B reduced the MIC of H. natalensis from 12.5 mg/ml to 3.13 mg/ml but had no impact on the MIC of M. piperita. The MIC of H. natalensis was again reduced in plate D and the essential oil M. alternifolia M. alternifolia was also reduced from 1.17% v/v to 0.29% v/v. There was virtually no difference in plates E and F containing M. alternifolia and M. piperita with the addition of TEAVIGO™. The addition of M. piperita in plate H reduced the MIC of M. alternifolia from 0.29% v/v to 0.07% v/v but had no effect on the MIC of H. natalensis.

Heteropyxis natalensis on its own inhibited C. albicans at 8.33 mg/ml; in combination with M. piperita and TEAVIGO™ this concentration is reduced to 3.13 mg/ml. In combination with H. natalensis and M. piperita the MIC of M. alternifolia on its own 0.24% v/v, is reduced to 0.07% v/v.

Figure 3 shows the inhibitory effect of three agents on S. mutans. In determining the inhibitory effect of three agents on S. mutans (Figure 3), there is a reduction in the MIC of H. natalensis from 3.13 mg/ml to 1.56 mg/ml with the addition of TEAVIGO™ but there was no effect on M. piperita (plates A and B). The same effect was exhibited with H. natalensis, M. alternifolia and the addition of TEAVIGO™ in plates C and D. There was no apparent effect of TEAVIGO™ on the essential oils, M. piperita and M. alternifolia (plates E and F). There was a marked increase in the inhibition of M. alternifolia with the addition of M. piperita; from 1.17% v/v to 0.02% v/v (plates G and H). Melaleuca alternifolia on its own inhibited S. mutans on its own at 0.29%. In combination with H. natalensis and M. piperita this inhibitory concentration was reduced to 0.02% v/v.

The combination of the agents has different effects on each of the microorganisms tested. This may indicate the possible mechanism of action of these agents. The combinations of M. piperita, H. natalensis and TEAVIGO™, against P. intermedia, C. albicans and S. mutans all had similar outcomes, resulting with an increased H. natalensis activity (plates A and B). The combination of M. alternifolia, H. natalensis and TEAVIGO™ (plates C and D) resulted in an increase in the activity of H. natalensis against S. mutans and both H. natalensis and M. alternifolia against C. albicans. However this combination had no apparent effect on P. intermedia. The reverse situation occurred for the combination of M. piperita, M. alternifolia and TEAVIGO™ (plates E and F), where an increase in activity was noted for M. piperita and M. alternifolia in P. intermedia but there were no noticeable effects in C. albicans and S. mutans. The combination of M. piperita, M. alternifolia and TEAVIGO™ may target the transenvelope efflux pump in P. intermedia which does not occur in S. mutans or the eukaryotic C. albicans. The combination of M. piperita, M. alternifolia and H. natalensis (plates G and H) all resulted in an increase in M. alternifolia activity but only in P. intermedia was the activity of H. natalensis also increased. Overall it would seem that TEAVIGO™ increases the inhibitory activity of H. natalensis; while M. piperita has a similar effect on its essential oil counterpart M. alternifolia.

Logistic Response Model

The logistic response model (Fienberg, 1980) is used to predict the probability associated with each value of the binary response (Tables 1 , 2, 3, 4, 5, 6, 7, 8, 9). A stepwise procedure (Hocking, 1976) was used to select the most important predictors. In this investigation the probability of inhibition is modelled.

The response variable is Y as follows:

Y=0 means no response

Y=1 means inhibition X=(Xi ,X ₂ ,X3,X ₄ ) is the combination of dosages with X-i representing H. natalensis, X ₂ - M. alternifolia, X ₃ - M. piperita and X ₄ - TEAVIGO™

p(X)=the probability of inhibition given the dosage combination

O(X) is the odds of obtaining inhibition

The log odds is LN{0(X)}

The logistic regression model (ref) is a linear model that links the probability to the dosage.

The function is estimated by means of maximum likelihood. In this case the estimate is

LN{0(X)}=- 6.1 +0.662X ₁ +82.473X ₂ +60.709X ₃ +1 .068X ₄ -4.795X ₁ X ₃ +35.518 X ₃ X ₄

e

The estimated probability of inhibition is then

-2 Log likelihood Nagelkerke R square ³

215.765 .864 ^a The Nagelkerke R Square is the logistic regression equivalent of the usual coefficient of determination used in multiple linear regression [16].

Table 2 Classification table for Prevoteii intermedia

Observed Predicted

Y Percentage correct

0 1

Y 0 267 1 7 94.0

1 20 336 94.4

Overall Percentage 94.2

XI .662 .072 .000

X2 82.473 1 1.501 .000

X3 60.709 7.536 .000

X4 1.068 .220 .000

XI by X3 -4.795 .690 .000

X3 by X4 35.518 18.520 .055

Constant -6.100 .638 .000 degression Co-efficient.

bStandard Error.

Significance. Table 4 Logistic model summary for Ca dida albicans

-2 Log likelihood Nagelkerke R square

92.432 .947

Table 5 Classification table for Candida albicans

Observed Predicted

Y Percentage correct

Y 0 268 9 96.8

1 1 3 350 96.4

Overall percentage 96.6

Table 6 Variables ir¾ the equation for Candida albicans

B ^a S.E. ^b Sig. ^c

X1 3.488 .852 .000

X2 770.772 207.145 .000

X3 773.1 35 212.726 .000

X4 5.946 1.620 .000

X1 by X3 -61 .807 1 7.021 .000

X2 by X4 -1 16.903 32.381 .000

X3 by X4 -4.824 2.252 .032

Constant -39.892 10.602 .000 degression Co-efficient.

bStandard Error.

Significance.

Table 7 Logsstk model summary for Streptococcus mutam

-2 Log likelihood Nagelkerke R square

162.446 .900

Table 8 Classification table for Streptococcus mutam

Observed Predicted

Y Percentage 1 correct

0

Y 0 251 13 95.1

1 23 353 93.9

Overall percentage 94.4

Table 9 Variables in the equation for Streptococcus m tans

B ^a S.E. ^b Sig. ^c

X1 2.249 .253 .000

X2 34.504 5.160 .000

X3 55.328 7.499 .000

X4 12.302 2.154 .000

X1 by X3 -5.628 .791 .000

Constant -6.086 .666 .000 degression Co-efficient.

Standard Error.

Significance.

Validation of Models

With the variables in the equation for Prevotella intermedia (Table 3), 80% of the original sample was randomly selected to be the training sample, and the remaining 20% formed the test sample. The model was fitted using the training sample and used to predict the outcomes of the training and validation samples. The outcome was that 92.4% of the training sample was correctly classified and 95.4% of the validation sample was correctly classified. This is considered satisfactory. With the variables in the equation for Candida albicans (Table 6), 80% of the original sample was randomly selected to be the training sample, and the remaining 20% formed the test sample. The model was fitted using the training sample and used to predict the outcomes of the training and validation samples. The outcome was that 96.8% of the training sample was correctly classified and 95.7% of the validation sample was correctly classified. This is considered satisfactory.

With the variables in the equation for Streptococcus mutans (Table 9), 80% of the original sample was randomly selected to be the training sample, and the remaining 20% formed the test sample. The model was fitted using the training sample and used to predict the outcomes of the training and validation samples. The outcome was that 92.7% of the training sample was correctly classified and 96.7% of the validation sample was correctly classified. This is considered satisfactory.

Predictive Inhibition Model

The results obtained from the logistic response model was used to construct a Predictive Model (IBM© SPSS© version 21 ) for each microorganism where the antimicrobial ability of the different combinations were tested.

A maximum of three components were tested on a microtiter plate using the modified checkerboard method. All possible combinations of the four components were tested this way (Figure 1 ). The log odds estimate, LN{0(X)}, obtained from the logistic regression model, combines the data of the four components in the predictive inhibition model. This enabled the probability of inhibition to be calculated utilizing all four components. The predictive inhibition model also provided information on the influence, the different components tested, had upon one another and on the probability of inhibition (Table 10).

Table 10 The influence each component had on the probability of inhibition in the Predictive Model for Prevotella intermedia

H. natalensis M. alterni folia M. piperita TEAVIGO

(mg/ml) (%) (%) (mg/ml)

3.125 0.017442 3.125 0.05 0.523084 3.125 0.05 0.05 0.915183 3.125 0.05 0.05 1 .000000

Tables 10, 1 1 and 12, show further validation of the predictive models for each microorganism tested. The models were used to predict the probability of inhibition outside the experimental area, and additional experiments were performed in the laboratory to judge the performance of the models. The performance was satisfactory.

Table 11 Predictive model showing the probability of inhibition (p) for

Prevotella intermedia

H. natalensis M. alternifolia M. piperita TEAVIGO™ P Outcome (mg/ml) (% v/v) (% v/v) (mg/ml)

0.78125 0.002 0.002 1 .25 0.02023 No inhibition

1 .5625 0.002 0.01 1 .25 0.06981 No inhibition

1 .5625 0.01 0.01 1 0.09233 No inhibition

1 .5625 0.01 0.01 2.5 0.46238 No inhibition

3.125 0.01 0.05 2.5 0.99795 No inhibition

3.125 0.05 0.05 2 0.99969 Inhibition

3.125 0.05 0.05 5 1.00000 Inhibition

6.25 0.05 0.25 5 1.00000 Inhibition

6.25 0.25 0.25 4 1.00000 Inhibition Table 12 Predictive model showing the probability of inhibition (p) for Candida albicans

H. natalensis M. alterni folia M. piperita TEAVIGO™ P Outcome

(mg/ml) (%) (%) (mg/ml)

0.78125 0.002 0.002 2.5 0.00000 No inhibition

1.5625 0.002 0.01 2 0.00000 No inhibition

1.5625 0.01 0.01 2 0.00003 No inhibition

1.5625 0.01 0.01 5 0.97528 No inhibition

3.125 0.01 0.05 4 1.00000 Inhibition

3.125 0.05 0.05 4 1.00000 Inhibition

3.125 0.05 0.05 10 1.00000 Inhibition

6.25 0.05 0.25 8 1.00000 Inhibition

6.25 0.25 0.25 8 1.00000 Inhibition

Based on the predictive inhibition model where 1 indicates the probability for 100% inhibition; P. intermedia (Table 1 1 ), C. albicans (Table 12) and S. mutans (Table 13) were successfully inhibited. At probabilities lower than 100% almost no inhibition was obtained for P. intermedia and C. albicans, while there was inhibition of S. mutans at 99%. Prevotella intermedia seemed to be sensitive to the concentration of M. alternifolia, as no inhibition was obtained when M. alternifolia was decreased to 0.01 % v/v (at a 99.8% probability).

Table 13 Predictive model showing the probability of inhibition (p) for

Streptococcus mutans

H. natalensis M. alterni folia M. piperita TEAVIGO™ P Outcome

(mg/ml) (%) (%) (mg/ml)

0.390625 0.00008 0.0004 0.390625 0.40661 No inhibition

0.390625 0.0004 0.0004 0.390625 0.40928 No inhibition

0.390625 0.002 0.002 0.390625 0.44355 No inhibition

0.78125 0.0004 0.002 0.78125 0.99549 Inhibition

0.78125 0.002 0.002 0.78125 0.99573 Inhibition

0.78125 0.01 0.01 0.78125 0.99784 Inhibition

1.5625 0.002 0.01 1 .5625 1.00000 Inhibition

1.5625 0.01 0.01 1 .5625 1.00000 Inhibition

1.5625 0.05 0.05 1 .5625 1.00000 Inhibition

There is a reduction in the MIC values of the individual components, when used in combination for each of the microorganisms tested (Table 14). And therefore, we can state that there is an overall increase in the inhibitory activity when the components are used in combination.

Table 14 Comparison of the minimum inhibitory concentrations of the tested components, individually and in combination, after utilizing the predictive model

P. intermedia C. albicans S. mutans

Alone ³ Combo ^b Alone ³ Combo ^b Alone ³ Combo ^b

H. natalensis (mg/ml) 12.50 3.13 8.33 3.13 2.60 0.78

TEAVIGO™ (mg/ml) >12.5 2.00 10.42 4.00 1.30 0.78

M. piperita (% v/v) 0.20 0.05 0.10 0.05 0.10 2 x 10 ^~3

M. alternifolia (% v/v) 0.29 0.05 0.24 0.01 0.29 4 x 10 ^{~4 a} Component tested individually.

Components tested in combination.

Discussion The synergistic combination of the components had different effects on each of the microorganisms tested. This may indicate the possible mechanism of action of these components. The combinations of M. piperita, H. natalensis and TEAVIGO™, against P. intermedia, C. albicans and S. mutans all had similar outcomes, resulting in an increased H. natalensis activity against these microorganisms (plates A and B of Figures 1 , 2 and 3). The combination of M. alternifolia, H. natalensis and TEAVIGO™ (plates C and D) resulted in an increase in the activity of H. natalensis against S. mutans and both H. natalensis and M. alternifolia against C. albicans. However, this combination had no apparent effect on P. intermedia. The reverse situation occurred for the combination of M. piperita, M. alternifolia and TEAVIGO™ (plates E and F), where an increase in antimicrobial activity was noted for M. piperita and M. alternifolia on P. intermedia but there were no noticeable effects on C. albicans and S. mutans. Both Gram-positive and Gram-negative bacteria's cell walls consist of peptidoglycan. Peptidoglycan is comprised of /V-acytyl-muramic acid and /V-acetyl-glucosamine cross linked by peptide side chains and cross-bridges; however, peptidoglycan is thicker in Gram-positive bacteria. Gram-negative bacteria also possess a periplasmic space which lies between the outer membrane and the cytoplamic membrane. It is within this space that some Gram-negative bacteria produce the lactamase enzyme that can resist drugs such as penicillin (Samaranayake, 2002). The combination of M. piperita, M. alternifolia and TEAVIGO™ may target the transenvelope efflux pump in P. intermedia which does not occur in S. mutans or the eukaryotic C. albicans (Lomovskaya, 201 1 ). The combination of M. piperita, M. alternifolia and H. natalensis (plates G and H) all resulted in an increase in M. alternifolia antimicrobial activity but only on P. intermedia was the activity of H. natalensis also increased. Overall it would seem that TEAVIGO™ increases the antimicrobial inhibitory activity of H. natalensis; while M. piperita has a similar effect on its essential oil counterpart M. alternifolia.

The predictive inhibition model provides information of the influence the different components tested have upon one another and on the probability of inhibition. This 'determination of influence' goes beyond the classification of synergism, indifference and antagonism. A probability of inhibition value was assigned to the concentration of each individual component and in various combinations of two to four. The concentrations of each component can then be adjusted to obtain a 100% probability of inhibition. The predictive inhibition model is also based on statistically significant results (p < 0.05) from the logistic response model. This has reduced the need to calculate the fractional inhibitory concentration (FIC) or equivalent values. There is a reduction in the MIC values of each individual component, when used in combination for each of the microorganisms tested (Table 14). Therefore, we can state that there is an overall increase in the inhibitory activity when the components are used in combination.

Conclusions

The use of the checkerboard method as a screening tool, utilizing the binary code to indicate inhibition and no inhibition and the input of those results into a logistic response model, lead to the successful construction of a predictive inhibition model. The predictive model not only gives the probability of 100% inhibition; but also shows the influence of those components upon one another and their ability to inhibit microbial growth. The applications of this technique are almost limitless. Not only can the inhibitory effect of different plants in combinations of more than two be determined; new multiple drug combinations can be screened too. In ethnopharmacology, where the remedies of traditional healers are tested this technique will also be useful as the healers often use combinations of a variety of different plants for a treatment. In Agriculture new pesticides can also be screened as the combination of multiple components leads to the slower development of resistance.

Specific example of the method of determining interaction between four agents and the probability of them having an inhibitory effect:

STEP 1 : Performing a plurality of synergistic tests to provide the checkerboard outcomes, as shown in Figure 4.

STEP 2: Representing the outcomes of synergistic tests as sets of binary matrices, each set including a first and a second matrix, first matrices each representing binary outcomes of different concentration combinations of two agents, and second matrices each representing outcomes of the different concentration combinations of the two agents with an additional fixed concentration of a third agent. (The binary matrices representing the checkerboard outcomes as shown in Figure 4 is shown as matrix E and F in Figure 1 ) The number of sets of matrices depends on the number of agents for which synergistic activity is to be determined, in this case four agents are used and therefore four sets of binary matrices are represented (as shown in Figure 1 ), such that each set of matrices (A and B; C and D; E and F; G and H) represents outcomes of synergistic tests of a combination of three of the four agents

STEP 3: Feeding the binary matrices into a qualitative response model to determine regression parameters

STEP 4: Generating a prediction model based on the regression parameters, the prediction model representing approximated outcomes of the synergistic activity between the at least three agents.