Analysis of Antimalarial Synergy between Bestatin and Endoprotease Inhibitors Using Statistical Response-Surface Modelling

Abstract

The pathway of hemoglobin degradation by erythrocytic stages of the human malarial parasite Plasmodium falciparum involves initial cleavages of globin chains, catalyzed by several endoproteases, followed by liberation of amino acids from the resulting peptides, probably by aminopeptidases. This pathway is considered a promising chemotherapeutic target, especially in view of the antimalarial synergy observed between inhibitors of aspartyl and cysteine endoproteases. We have applied response-surface modelling to assess antimalarial interactions between endoprotease and aminopeptidase inhibitors using cultured P. falciparum parasites. The synergies observed were consistent with a combined role of endoproteases and aminopeptidases in hemoglobin catabolism in this organism. As synergies between antimicrobial agents are often inferred without proper statistical analysis, the model used may be widely applied in studies of antimicrobial drug interactions.

Malaria remains one of the world's most important infectious diseases, and new antimalarial drugs are urgently needed, especially in areas where drug-resistant strains of the most lethal human malarial parasite, Plasmodium falciparum, are prevalent (21, 22, 30). The pathway of hemoglobin degradation by intraerythrocytic stages of P. falciparum has received a lot of attention as a potential therapeutic target (5). The parasite ingests large quantities of erythrocyte cytosol, polymerizing the heme moiety of hemoglobin into harmless crystalline inclusions (hemozoin) and digesting the globin to provide many of the amino acids required for protein synthesis. To date, most models have proposed that aspartyl proteases (plasmepsins I and II), cysteine protease (falcipain), and metalloproteases (falcilysin) are involved in hemoglobin degradation within a unique organelle, the digestive (food) vacuole (8, 10, 13, 14, 17, 25, 29). The growth-inhibitory actions of certain combinations of endoprotease inhibitors, especially those specific for aspartyl and cysteine protease classes, are synergistic on cultured parasites and possibly in animal models of malaria (1, 25, 27). The mechanism of synergy is unclear but may be related to the idea that endoproteases act sequentially in the same catabolic pathway. Accordingly, the possibility of developing combination therapy to target concomitantly more than one protease of the hemoglobinolytic pathway has become attractive.

The aminopeptidase-specific inhibitors bestatin and nitrobestatin block malarial parasite growth in culture (20), and it is thought that one or more Plasmodium aminopeptidases are required for the terminal stages of hemoglobin breakdown, exoproteolytically cleaving globin-derived peptides to liberate free amino acids for incorporation into parasite proteins (7, 12, 17). Therefore, the aim of the present study was to investigate whether aminopeptidase and endoprotease inhibitors would act synergistically on the growth of cultured P. falciparum.

A serious deficiency of the analysis of many published antimicrobial synergy and antagonism data has been the lack of adequate statistical justification for the conclusions drawn. Typically, empirically drawn isobolograms or histograms are used to suggest synergy between drug combinations, without any analysis of whether the data depart significantly from mere additivity (2, 3). We have therefore applied a statistical response-surface modelling method (19) for the rigorous analysis of the combinations used here and believe that it should have wide application in synergy and antagonism studies. This approach is superior to previously published ones (e.g., see reference 28) that analyze data for fixed ratios of the two drugs only. The method used here provides a direct quantification of the extent of synergism or antagonism between two drugs used in combination in terms of a single parameter, η, where values of η equal to 1 indicate additivity (no interaction), values of η less than 1 indicate synergy, and values of η greater than 1 indicate antagonism.

MATERIALS AND METHODS

Cultures of P. falciparum clone FCH5.C2 were maintained in human erythrocytes, and inhibitor activity was determined by a spectrophotometric parasite lactate dehydrogenase (pLDH) assay, as described previously (20). Each inhibitor was tested in a series of eight twofold dilutions, alone and in combination with another inhibitor at each of eight twofold dilutions. Dose-response curves were constructed for each drug, alone and in combination, and were used to determine the median inhibitory concentrations (IC₅₀). Results were expressed as the geometric means of the IC₅₀s from between three and five separate experiments and were used to construct isobolograms to assess drug interactions.

In addition, the individual datum points (expressed as percent growth values, where 0% was the absorbance [pLDH activity] obtained from uninfected erythrocytes and 100% was the absorbance obtained from an inhibitor-free parasite culture) were used for the statistical analysis. Specifically, the percent growth values at dose (d₁,d₂) were calculated as y(d₁,d₂) = 100[a(d₁,d₂) − a₀]/(a₁₀₀ − a₀), where a(d₁,d₂) is the observed absorbance, a₀ is the absorbance for uninfected erythrocytes, and a₁₀₀ is the absorbance for parasites in the absence of drugs.

Response-surface models that permit the assessment of synergism were fitted to the percent growth data. The notation and analysis methods parallel those of Machado and Robinson (19). The modeling assumptions were as follows. Let the expected response (percent growth) at dose (d₁,d₂) be denoted by H(d₁,d₂|Θ), where Θ is a vector of model parameters to be estimated. The single-drug dose-response functions are H₁(d₁|Θ), defined as H(d₁,0|Θ), for drug 1, and H₂(d₂|Θ), defined as H(0,d₂|Θ), for drug 2. These were modeled as decreasing logistic functions of dose: H₁(d₁|Θ) = 100 (d₁/D_1,50)^β₁/[1 + (d₁/D_1,50)^β₁] and H₂(d₂|Θ) = 100 (d₂/D_2,50)^β₂/[1 + (d₂/D_2,50)^β₂]. The parameters D_1,50 and D_2,50 are the IC₅₀s, and β₁ < 0 and β₂ < 0 determine the steepness of the curves. The logistic functional form was suggested by examination of the data. Under the assumption of zero interaction, the response-surface model is the solution H(d₁,d₂|Θ) of the equation V₁^η + V₂^η = 1, where V₁^η = d₁/H₁⁻¹[H(d₁,d₂|Θ)] and V₂^η = d₂/H₂⁻¹[H(d₁,d₂|Θ)]. The model for the response surface with a synergistic or an antagonistic interaction is the solution H(d₁,d₂|Θ) of the equation V₁^η + V₂^η = 1 (see equations 1, 2, and 9 in the report by Machado and Robinson [19]). Here, the interaction parameter η quantifies the extent of synergy (η less than 1) or antagonism (η greater than 1); setting η equal to 1 gives the zero interaction model.

Since the between-experiment standard errors increase approximately linearly with level of response, the variance of y(d₁,d₂) was modelled as ς²(d₁,d₂) = [α₁ + α₂ y(d₁,d₂)]², where α₁ and α₂ are unknown parameters to be estimated. The distribution of each percent growth value y(d₁,d₂) was assumed to be normal, with mean H(d₁,d₂) and variance ς²(d₁,d₂). For each drug pair, both the additive and interactive models were fitted by the method of maximum likelihood to the data pooled over all the respective experiments. The likelihood ratio statistic was used to compare the two models to test for significance of any synergism or antagonism, that is, to test the null hypothesis that η is equal to 1. Pooling over experiments added stability to the estimation, since the considerable variability in the data precluded separate analyses for each experiment.

RESULTS AND DISCUSSION

The method of detecting synergy or antagonism via the empirical interpretation of isobolograms dates back more than 100 years to Fraser (11) and was discussed by, among others, Loewe (18), Hewlett (16), and Berenbaum (4). More formal direct response-surface modelling approaches based on isoboles and taking of measurement error into account have only recently appeared in the literature (15, 19, 32). The models proposed by those investigators are based on somewhat different choices for model parameterization (see the discussion and comparison in reference 19), but basically should give similar answers as regards synergy or antagonism. The model of Greco et al. (15) and that used in this study (19) are both based on a single parameter to quantify the extent of interaction. The latter has the advantage that η relates by a simple one-to-one function to the degree of curvature or bowing of the isobole, whatever the level of the response, and thus is easier to interpret. In addition, we note that the parameter η is not the same as the sometimes used fractional inhibition constant (FIC) (9), although FIC values equal to 1, <1, and >1 also indicate additivity, synergy, and antagonism, respectively. There is a direct geometric interpretation for η in that the curve v₁^η + v₂^η = 1 for v₁ and v₂ values that vary between 0 and 1 is the underlying isobole; the greater the difference between η and 1 is, the greater the curvature is.

In order to demonstrate the utility of the statistical method, the combination of the aspartyl protease inhibitor pepstatin and the cysteine protease inhibitor benzyloxycarbonyl-phenylalanyl-alanyl diazomethylketone (Z-Phe-Ala-CHN₂) was tested, since from the strongly concave isobole (Fig. 1A, and in agreement with previous studies [1, 27]) we would expect highly significant synergy. The estimated value of the synergy coefficient η of 0.172 with a 95% confidence interval of (0.136, 0.216) and a likelihood ratio statistic of 300.74 (P < 0.001 by the χ² distribution with 1 degree of freedom) confirm that there is highly significant synergy between these two agents. Estimated parameters for the fitted response surfaces are given in Table 1.

FIG. 1.

Isobologram showing interactions between protease inhibitors against P. falciparum in culture: pepstatin and Z-Phe-Ala-CHN₂ (a), bestatin and pepstatin (b), bestatin and Z-Phe-Ala-CHN₂ (c), and bestatin and E-64 (d). Each point is a geometric average of three to five separate experiments (see text for details). The solid diagonals in the isobolograms represent the theoretical line of additivity (i.e., no interaction), while the values below this line indicate a synergistic effect between the two compounds. The concave isoboles (dashed lines) were fit by inspection.

TABLE 1.

Results of fitting the six-parameter (η constrained to be 1) and seven-parameter response surfaces to assess interactions between pairs of drugs

Drug pair and parameter	Six-parameter model			Seven-parameter model
	Estimate	Lower 95% CLa	Upper 95% CL	Estimate	Lower 95% CL	Upper 95% CL
Pepstatin and Z-Phe-Ala-CHN2b
D1,50	18.85	8.83	40.23	144.52	46.27	451.37
β1	−1.49	−2.86	−0.77	−1.09	−1.44	−0.82
D2,50	0.33	0.21	0.51	8.93	3.50	22.78
β2	−0.88	−1.09	−0.71	−1.65	−2.28	−1.20
α1	5.96	3.70	8.22	2.24	1.59	2.88
α2	0.630	0.490	0.809	0.582	0.498	0.681
η	1	1	1	0.172	0.136	0.216
Loglikf	−1,353.07			−1,202.70
Pepstatin and bestatinc
D1,50	46.52	39.89	54.25	62.58	44.50	88.00
β1	−1.16	−1.55	−0.87	−1.03	−2.02	−0.52
D2,50	2.28	2.05	2.53	2.69	2.24	3.23
β2	−1.26	−1.40	−1.13	−1.33	−1.58	−1.12
α1	5.08	2.62	7.53	4.89	2.72	7.06
α2	0.182	−0.129	0.255	0.182	0.134	0.247
η	1	1	1	0.645	0.482	0.862
Loglik	−1,563.18			−1,556.03
Bestatin and Z-Phe-Ala-CHN2d
D1,50	1.90	1.70	2.12	2.41	2.10	2.78
β1	−1.24	−1.35	−1.14	−1.29	−1.41	−1.18
D2,50	3.95	3.37	4.61	5.52	4.64	6.57
β2	−0.97	−1.11	−0.85	−0.99	−1.10	−0.89
α1	2.09	1.10	3.09	1.68	0.86	2.50
α2	0.261	0.224	0.305	0.263	0.229	0.302
η	1	1	1	0.597	0.529	0.675
Loglik	−1,833.73			−1,811.49
Bestatin and E-64e
D1,50	2.44	2.17	2.75	2.79	2.37	3.29
β1	−1.53	−1.77	−1.33	−1.54	−1.79	−1.32
D2,50	2.71	2.50	2.90	2.98	2.66	3.35
β2	−2.12	−2.67	−1.69	−2.07	−2.64	−1.62
α1	8.81	7.65	9.97	8.60	7.38	9.82
α2	0.075	0.044	0.130	0.080	0.046	0.140
η	1	1	1	0.780	0.655	0.929
Loglik	−1,315.92			−1,312.79

^aCL, confidence limit. 

^b311 observations; 4 experiments. 

^c388 observations; 5 experiments. 

^d480 observations; 6 experiments. 

^e347 observations; 4 experiments. 

^fLoglik denotes the maximized logarithm of the likelihood function. 

The isobolograms in Fig. 1B to D show that for combinations of bestatin and endoprotease inhibitors, it was less obvious whether there was substantial synergy. However, application of the statistical model gave a η value of 0.645 (95% confidence interval, 0.482, 0.862) and a likelihood ratio statistic of 14.3 (P < 0.001) for bestatin and pepstatin, indicating significant synergy (Table 1). For bestatin and the cysteine protease inhibitors, η was equal to 0.597 (95% confidence interval, 0.529, 0.675) and likelihood ratio statistic was 44.48 (P < 0.001) in the case of Z-Phe-Ala-CHN₂ and η was equal to 0.780 (0.655, 0.929) and the likelihood ratio statistic was 6.27 (P = 0.012) in the case of E-64 (Table 1). Therefore, in all combinations tested, statistically significant synergy was observed, but the strength of the synergy depended on the endoprotease inhibitor tested and in all cases was weaker than that with the combination of pepstatin and Z-Phe-Ala-CHN₂. This is seen in Fig. 2, which shows the fitted isoboles on a standardized scale for each of the four drug pairs. The strong synergy between pepstatin and Z-Phe-Ala-CHN₂ is evident in the concave appearance of the observed and fitted response surfaces in Fig. 3 and 4, respectively.

FIG. 2.

Fitted isoboles on a standardized scale for each drug pair.

FIG. 3.

Four views of the observed response surface (average over four experiments) for the drug pair pepstatin and Z-Phe-Ala-CHN₂.

FIG. 4.

Four views of the fitted response surface from the seven-parameter model with η equal to 0.172 for the drug pair pepstatin and Z-Phe-Ala-CHN₂.

If we assume that the synergy between inhibitors specific for different protease classes reflects the inhibition of different components of the same catabolic pathway, then these results are consistent with a role of Plasmodium aminopeptidase in hemoglobin degradation in concert with aspartyl and cysteine endoproteases. It may be relevant that aminopeptidase probably acts on globin-derived peptides transported into a separate compartment, the cytosol (7, 17). A combination drug regimen would be most advantageous in the development of novel antimalarial therapies, especially as the use of drug combinations may delay the onset of resistance (31, 33, 34). Inhibitors that concomitantly and specifically target enzymes involved in an essential metabolic process, hemoglobin breakdown, potently block parasite growth. Protease inhibitors specific for plasmepsins I and II and falcipain are being explored for the development of novel lead compounds for use in patients with malaria (5, 6, 23, 24). In view of the low mammalian toxicity of bestatin (26) and the synergies demonstrated here, it appears that aminopeptidase inhibitors, whether used alone or simultaneously with aspartyl and cysteine protease inhibitors, may also have considerable potential.