Prediction Model for Antimalarial Activities of Hemozoin Inhibitors by Using Physicochemical Properties

ABSTRACT

The rapid spread of strains of malaria parasites that are resistant to several drugs has threatened global malaria control. Hence, the aim of this study was to predict the antimalarial activity of chemical compounds that possess anti-hemozoin-formation activity as a new means of antimalarial drug discovery. After the initial in vitro anti-hemozoin-formation high-throughput screening (HTS) of 9,600 compounds, a total of 224 hit compounds were identified as hemozoin inhibitors. These 224 compounds were tested for in vitro erythrocytic antimalarial activity at 10 μM by using chloroquine-mefloquine-sensitive Plasmodium falciparum strain 3D7A. Two independent experiments were conducted. The physicochemical properties of the active compounds were extracted from the ChemSpider and SciFinder databases. We analyzed the extracted data by using Bayesian model averaging (BMA). Our findings revealed that lower numbers of S atoms; lower distribution coefficient (log D) values at pH 3, 4, and 5; and higher predicted distribution coefficient (ACD log D) values at pH 7.4 had significant associations with antimalarial activity among compounds that possess anti-hemozoin-formation activity. The BMA model revealed an accuracy of 91.23%. We report new prediction models containing physicochemical properties that shed light on effective chemical groups for synthetic antimalarial compounds and help with in silico screening for novel antimalarial drugs.

INTRODUCTION

Despite recent advances in antimalarial drug discovery and development, malaria remains one of the most serious medical burdens worldwide, resulting in 212 million new cases and 429,000 deaths in 2015 (1). According to the different stages of the parasite life cycle, several therapies can affect these stages and exert their therapeutic roles. Quinine, amodiaquine, chloroquine, and mefloquine, which contain a quinoline scaffold, are fast-acting and highly effective blood schizontocidal therapies against malaria parasites, including Plasmodium falciparum (2).

Indeed, the resistance of malaria to chloroquine and other 4-aminoquinoline-based therapies, in addition to the antifolate combination sulfadoxine-pyrimethamine, has turned the spotlight on artemisinin-based combinations to achieve higher response rates (3, 4). However, rapidly spreading resistance of P. falciparum to artemisinin-based combinations has been reported, posing a global challenge for malaria control (5, 6). Thus, it is important to discover new antimalarial drugs, especially for countries where malaria is endemic.

Recently, several new classes of antimalarials have entered clinical studies with patients with malaria, such as the fast-acting agents KAF156 (7), cipargamin (8), and artefenomel (9), whereas ferroquine remains the only long-acting novel antimalarial in clinical development (10, 11). However, these drugs have not yet been approved, and no vaccine to help in the prevention, control, elimination, and eradication of malaria has been approved yet. Only one vaccine candidate, RTS,S/AS01, reached phase III clinical trials, with relatively low efficacy (13, 14). Therefore, there is an urgent need for the discovery and development of novel antimalarial chemotherapies for which there are no preexisting resistance mechanisms.

At present, one of the most promising and ideal targets is interference with the parasite's heme detoxification pathway, which is the target for some current antimalarial drugs, such as quinine, which is still efficacious against chloroquine-resistant P. falciparum (15–19). Recently, inhibition of the heme detoxification pathway of the parasite has been highlighted as a target in several antimalarial screening projects (20–22). This target is based on the inhibition of hemozoin, which is a crystalline pigment produced by the malaria parasite as a result of the hemoglobin degradation process to protect it against the toxic heme produced as an end product of hemoglobin catabolism (23, 24).

Hemozoin formation is a protective physiochemical process that needs parasite protein (25–27) and/or food vacuole lipids or membranes (28, 29) for synthesis. Therefore, lipophilic detergents that mimic intraparasite conditions, like Nonidet P-40 and Tween 20, can be used as surrogate substances for high-throughput screening (HTS) of novel antimalarials because they have the ability to promote the crystallization of heme (20, 30). This makes hemozoin inhibition suitable for research using HTS assays to build prediction models for novel antimalarial drugs.

Recently, several studies used HTS and predicted models for β-hematin, synthetic hemozoin, inhibitors. Sandlin et al. screened 144,330 and produced 530 hits, 171 of which were active against parasites: 73 hits had parasite 50% inhibitory concentrations (IC₅₀s) of <5 μM, and 25 hits had IC₅₀s of <1 μM (31). In addition, using physiochemical properties (22), we recently developed an in silico model to predict drug-like compounds that possess antihemozoin activity.

As previously suggested, prediction models possess advantages for antimalarial design because other approaches, such as analog development based on existing agents or natural products, mainly detect new antimalarials by chemical modifications of previously known compounds (32); however, new antimalarial compounds can be discovered by the prediction equation based on a well-known metabolic target. Thus, prediction models aid in the discovery of new chemical scaffolds. Moreover, specialized labware and expensive equipment are not required for these models, so millions of library compounds can be screened in silico by using the prediction models. Also, the relationship between the compound's properties and antihemozoin activity is interpreted from the prediction models. Therefore, we continued previous work by developing new prediction models for novel antimalarial activities of hemozoin inhibitors using the physiochemical properties of these small chemical compounds.

RESULTS

In vitro antimalarial assay.

A total of 224 compounds with hemozoin inhibitory activity (22) were selected for in vitro antimalarial assays. Among them, 30 compounds with ≥45% growth-inhibitory activity at a concentration of 10 μM were further subjected to a dose-response assay to remove false-positive compounds from the initial screening (Fig. 1), resulting in only 22 compounds with a clear sigmoid dose-response curve to determine the IC₅₀ (Fig. 2 and Table 1).

FIG 1.

Workflow of this study. First, 224 compounds that showed antihemozoin activity in our previous study (22) underwent in vitro antimalarial assays at 10 μM. Second, 30 compounds with ≥45% parasite-inhibitory efficacy underwent an in vitro dose-response assay at concentrations of between 0.5 nM and 10 μM. Next, 22 compounds with IC₅₀s of ≤10 μM were identified. Subsequently, the main structures and physicochemical properties of these compounds were searched by using SciFinder. Finally, the prediction models were generated by the traditional approach versus the Bayesian approach, using their physical and chemical properties.

FIG 2.

Initial in vitro antimalarial screening of 224 compounds using the chloroquine-mefloquine-sensitive P. falciparum 3D7A strain. The circle dots represent the percentages of parasite inhibition of 224 compounds, including 30 compounds with parasite inhibition values of ≥45%.

TABLE 1.

Antimalarial and antihemozoin activities of 22 positive compounds

Compound	Compound identification	Antimalarial activity (3D7A) IC50 (μM) ± SD	Antihemozoin activity IC50 (μM)
1	UTDIF3A11	0.66 ± 0.10	78.1
2	UTDIF4A14	8.15 ± 2.60	34.67
3	UTDIF5A15	9.00 ± 1.40	14.01
4	UTDIF6C12	8	4.58
5	UTDIF7D16	10.50 ± 2.10	87.76
6	UTDIF8E4	10	38.54
7	UTDIF9E10	1.54 ± 0.07	53.44
8	UTDIF10E14	10.00 ± 1.40	41.18
9	UTDIF11F12	9	36.16
10	UTDIF12F15	8.95 ± 1.30	103.5
11	UTDIF13G5	9.26 ± 1.80	30.69
12	UTDIF14I6	7.00 ± 1.40	43.98
13	UTDIF15I15	1.01 ± 0.50	25.96
14	UTDIF16J16	9.28 ± 2.40	28.5
15	UTDIF17K7	4.80 ± 1.70	198.1
16	UTDIF18L5	3.06 ± 1.30	110
17	UTDIF19L16	6.80 ± 4.40	29.04
18	UTDIF20M7	8.00 ± 2.80	156
19	UTDIF21O9	0.56 ± 0.27	18.3
20	UTDIF22P6	0.06	42.98
21	UTDIF23P14	9.50 ± 0.70	24.72
22	UTDIF24G15	9	160

The interference of 22 compounds with SYBR Green l in the presence of malaria parasites was measured by culturing Plasmodium falciparum 3D7A for 48 h and then adding 22 compounds followed by addition of SYBR Green l with 1 h incubation in the dark. Subsequently, the fluorescence was measured by using a multiplate reader (ARVO1430; PerkinElmer, MA) in the fluorescence detection mode (excitation [Ex] at 485 nm and emission [Em] at 515 nm) for a 0.1-s exposure. The results showed that all fluorescence variations were <10%, indicating that there was almost no interference of the compounds, artemisinin, and chloroquine with SYBR green I fluorescence (see Fig. S1 in the supplemental material). Furthermore, our results demonstrated that all 22 compounds possessed antihemozoin activities, with IC₅₀s ranging from 4.58 to 198.1 μM (Table 1).

Development of prediction models for antimalarial activities.

Numbers of C and S atoms and H acceptors; the H donor-acceptor sum; log D at pH 1, 2, 3, 4, and 5; mass solubility at pH 1 and 3; and polarizability had P values of <0.1 in the univariable logistic regression (LR), and partition coefficient (log P); organic carbon-water partition coefficient (KOC) at pH 5.5 and 7.4; log D at pH 5.5 and 7.4; density; refractive index; rule-of-five violations; and numbers of freely rotatable bonds, H bond donors, and H and O atoms were significant according to the previous study (22), while the number of N atoms and surface tension were significant according to the present analysis and the previous study, respectively (22) (Table 2).

TABLE 2.

Univariable logistic regression statistics of the physicochemical properties of the compounds^a

Predictor	Univariable analysis
	OR (95% CI)	P
No. of C atoms	1.11 (0.98–1.25)	0.092
No. of H atomsb	1.07 (0.98–1.17)	0.111
No. of N atoms	1.5 (1.15–1.95)	0.003
No. of O atomsb	1.02 (0.77–1.35)	0.912
No. of S atoms	0.45 (0.19–1.06)	0.067
No. of F atoms	0 (0–Inf)	0.992
No. of Cl atoms	1.45 (0.67–3.16)	0.348
No. of Br atoms	0 (0–infinity)	0.991
Avg mass of atoms	1.01 (0.997–1.01)	0.214
No. of monoisotopic atoms	1.01 (0.998–1.01)	0.192
Densityb	0.89 (0.07–11.81)	0.929
No. of rotatable bondsb	1.03 (0.85–1.26)	0.753
No. of H acceptors	1.38 (1.08–1.77)	0.01
No. of H donorsb	1.11 (0.76–1.61)	0.605
H donor-acceptor sum	1.25 (1.03–1.52)	0.022
KOC at pH 1	1 (0.9999–1.0001)	0.647
KOC at pH 2	1 (0.9999–1.0001)	0.568
KOC at pH 3	1 (0.9998–1.0001)	0.499
KOC at pH 4	1 (0.9998–1.0001)	0.457
KOC at pH 5	1 (0.9998–1.0001)	0.469
KOC at pH 6	1 (0.9999–1.0001)	0.562
KOC at pH 7	1 (0.9999–1.0001)	0.538
KOC at pH 8	1 (0.9999–1.0001)	0.65
KOC pH 9	1 (0.9999–1.0001)	0.603
KOC at pH 10	1 (0.9998–1.0001)	0.526
Log D at pH 1b	0.73 (0.58–0.92)	0.007
Log D at pH 2	0.74 (0.59–0.93)	0.009
Log D at pH 3	0.73 (0.58–0.92)	0.008
Log D at pH 4	0.72 (0.56–0.92)	0.008
Log D at pH 5	0.76 (0.59–0.97)	0.027
Log D at pH 6	0.85 (0.66–1.09)	0.199
Log D at pH 7	0.94 (0.74–1.2)	0.643
Log D at pH 8	0.9995 (0.79–1.27)	0.997
Log D at pH 9	1.04 (0.82–1.32)	0.756
Log D at pH 10	1.09 (0.86–1.38)	0.481
Log Pb	0.85 (0.62–1.17)	0.319
Intrinsic mass	0.97 (0.79–1.19)	0.762
Mass solubility at pH 1	1.002 (0.9999–1.003)	0.067
Mass solubility at pH 2	1.001 (0.9997–1.003)	0.106
Mass solubility at pH 3	1.002 (0.9998–1.003)	0.078
Mass solubility at pH 4	1.001 (0.9991–1.004)	0.24
Mass solubility at pH 5	1.002 (0.9993–1.005)	0.136
Mass solubility at pH 6	1.001 (0.998–1.004)	0.535
Mass solubility at pH 7	0.997 (0.99–1.01)	0.616
Mass solubility at pH 8	0.97 (0.89–1.06)	0.525
Mass solubility at pH 9	0.84 (0.57–1.24)	0.376
Mass solubility at pH 10	0.97 (0.91–1.03)	0.312
Mass solubility	0.47 (0.076–2.86)	0.409
Molar vol	1.01 (0.997–1.01)	0.218
Mol wt	1 (0.997–1.01)	0.283
pKa1	1.05 (0.93–1.17)	0.444
Polar surface	1 (0.99–1.02)	0.733
Total score	1.22 (0.82–1.82)	0.334
Polarizability	1.07 (0.996–1.14)	0.066
Surface tension	1.02 (0.99–1.05)	0.256
Refractive indexc	1.36 (0.72–2.57)	0.348
Rule-of-five violations	2 (0.67–5.9)	0.212
ACD log D at pH 5.5b	0.87 (0.68–1.11)	0.256
ACD log D at pH 7.4b	1.07 (0.83–1.36)	0.617
ACD BCF at pH 5.5	1 (1–1)	0.771
ACD BCF at pH 7.4	1 (0.9998–1.0001)	0.737
ACD KOC at pH 5.5b	1 (1–1)	0.77
ACD KOC at pH 7.4b	1 (0.9999–1.0001)	0.766

^aAbbreviations: OR, odds ratio; CI, confidence interval; BCF; bioconcentration factor. Significant predictors are underlined.

^bVariables with prior significance in our previous study (22).

^cThe refractive index was multiplied by 10 to obtain a lower OR.

The Bayesian model averaging (BMA) analysis selected 37 models, from which the best 5 models had 5 variables, as the best predictors of the chemical compound activity, including the number of S atoms; log D at pH 3, 4, and 5; and ACD log D at pH 7.4 (Fig. 3 and Tables 2 and 3). This reflected that the antimalarial activity was significantly associated with a lower number of S atoms; lower log D at pH 3, 4, and 5; and higher ACD log D at pH 7.4.

FIG 3.

Models selected by Bayesian model averaging. Blue and red represent positive and negative variable estimates, respectively, while uncolored variables were not included in the model. On the x axis, models were listed in the order of the declines in the posterior probability.

TABLE 3.

The five best parsimonious models selected by BMA^a

Model	Predictor	Coefficient of predictor	BIC of model	PP of model
1	Intercept	−2.21	−648.24	0.17
	No. of S atoms	−1.26
	Log D at pH 4	−0.86
	ACD log D at pH 7.4	0.78
2	Intercept	−2.76	−647.46	0.11
	Log D at pH 4	−0.84
	ACD log D at pH 7.4	0.81
3	Intercept	−2.22	−646.94	0.09
	No. of S atoms	−1.3
	Log D at pH 3	−0.78
	ACD log D at pH 7.4	0.68
4	Intercept	−2.05	−646.02	0.06
	No. of S atoms	−1.22
	Log D at pH 5	−0.92
	ACD log D at pH 7.4	0.85
5	Intercept	−2.57	−645.61	0.05
	Log D at pH 5	−0.92
	ACD log D at pH 7.4	0.88

^aAbbreviations: BIC, Bayesian information criterion; PP, posterior probability. The cumulative posterior probability was 0.468.

Validation of the prediction model.

The BMA model, with a cutoff of 0.09, revealed a sensitivity, specificity, and maximum accuracy of 60%, 69.23%, and 91.23%, respectively.

DISCUSSION

Our BMA prediction model identified several physicochemical properties from which we can design and develop novel drugs. We found that a lower number of S atoms; lower log D values at pH 3, 4, and 5; and a higher ACD log D value at pH 7.4 could serve as good predictors for the development of novel antimalarial drugs.

Kumar et al. found that the replacement of the ring oxygen by sulfur to produce 4,5-dihydroxythioxanthone results in decreased inhibitory activity on hemozoin formation and parasite growth compared to the corresponding xanthone homolog (33).

Low log D values and low lipophilicity at pH 3, 4, and 5 through high inhibitory activities against heme crystallization (hemozoin formation) were significantly associated with better antimalarial activity. It is well known that antimalarial drugs must enter the parasite food vacuole, where the pH is around 4 to 5.5. It is noteworthy that log P is an indicator of lipophilicity and is a component of Lipinski's rule of five, a rule of thumb to predict drug-like properties. However, log D is a better indicator for specific pH environments. Because hemozoin formation occurs inside the acidic food vacuole, such compounds are expected to decrease its lipophilicity after uptake into the parasite food vacuole and to be accumulated within it.

Log P is widely used; however, it fails to take into account the variation in the lipophilicity of a drug regarding the ionic states present at key biological pH values. Given that the majority of commercial pharmaceuticals contain an ionizable moiety, Bhal et al. reported that log D is a better descriptor for lipophilicity in the context of the rule of five. It gives more physiologically relevant results, subsequently decreasing the number of potential false-negative compounds incorrectly eliminated during screening. Those authors also showed that the adapted rule of five using log D instead of log P gives a notable improvement in the pass rate for compounds that have the desired lipophilicity at a relevant physiological pH (34).

In 11 p-aminopyridine antimalarials, a quadratic association between the log lipid accumulation ratio (LAR), antilog log D at pH 7.4, and the log resistance index was confirmed, while the log(LAR/vacuolar accumulation ratio [VAR]) versus log resistance index for 12 antimalarials was linear. Both predictors might be able to predict the utility of structural adjustments (35).

This confirms for chloroquine-sensitive parasites that while the charged drug concentration in the food vacuole increases as the vacuolar pH decreases, the concentration of uncharged drug (base) in the vacuolar membrane and other lipid sites in the digestive vacuole has a constant value for each individual drug, because the proportion of drug partitioned into lipid decreases as log D (the log of [drug]_lipid/[drug]_water at equilibrium) decreases with reduced pH.

Log D can predict gastrointestinal absorption and lipophilic properties because it is a pH-dependent function. Calculated values demonstrated high gastrointestinal tract absorption (pH 3 to 7) and lipophilic properties. A good correlation between the calculated distribution coefficients at pH 7.4 and pH 5.2 (log D at pH 5.2 and 7.4) and the measured inhibition percentages for the tested compounds was observed (36).

In addition, the finding that antimalarial activity increases with increasing ACD log D values at pH 7.4 is most probably because this favors the entry of the compound into red blood cells (RBCs), the parasite, and, ultimately, the digestive vacuole. On the other hand, a low ACD log D value at a low pH (pH 3 to 5) disfavors the egress of the compound out of the digestive vacuole. The consequence would be greater accumulation in the digestive vacuole and, hence, higher concentrations at the site of action. Indeed, antilog[ACD log D (pH 7.4) − ACD log D (pH 5)] is an experimental measure of vacuolar pH trapping. It would make sense that this would apply only in the case of hemozoin inhibitors because they are the compounds that act in the digestive vacuole. Since researchers prefer to use [ACD log D (pH 7.4) − ACD log D (pH 5)] for each compound, this might weaken the correlation and undermine this argument. Hence, we built a new model with that variable, [ACD log D (pH 7.4) − ACD log D (pH 5)], to investigate its effect; however, we found that it was not significant.

It is noteworthy that we have overcome our previous limitation, in which we could not find any heavy atoms playing an important role in the refractive index used to investigate the characteristics of the material (22). The presence and even the quantity of some heavy atoms and functional groups with a high refractive index, such as sulfur (37), have an important role in increasing molar refraction. It is noteworthy that out of the 224 included compounds, there were 87 compounds that had at least 1 S atom, with a mean of 1 atom, and 131 compounds that had no S atoms. Moreover, among negative and positive compounds, there were 83 compounds and 4 compounds that had at least one atom, respectively. Additionally, among our positive antimalarial compounds, we found four compounds with quinolines that had no S atoms; hence, this suggests a negative association between S atoms and antimalarial activity. However, our results did not show an association between the refractive index and high antimalarial activities, suggesting that the refractive index is related only to antihemozoin but not antimalarial activity. Although our models have not been validated with external samples, it can be the first clue for understanding the mechanism of action of antimalarials (22). Moreover, future studies need to validate our results with a larger number of compounds, especially the positive ones.

Conclusion.

Using these physicochemical properties of compounds, we report new prediction models that can predict antimalarial activity for chemical compounds that possess antihemozoin activities. Our findings revealed that lower numbers of S atoms; lower log D values at pH 3, 4, and 5; and higher ACD log D values at pH 7.4 were independent predictors of higher antimalarial activity. This information can be used for in silico screening and modifying chemical structures to develop antimalarials.

MATERIALS AND METHODS

Ethics statement.

Experiments that required human materials, RBCs and serum, were approved by the institutional ethical review board of the Institute of Tropical Medicine (NEKKEN), Nagasaki University.

Materials.

Chloroquine (Sigma-Aldrich Chemical Company, UK) was used to monitor the assay system, stored in a 4°C freezer, and mixed well before use. Dimethyl sulfoxide (DMSO; Wako Pure Chemicals Ltd., Osaka, Japan) was used as a negative control. SYBR green I (10,000× stock concentration) was obtained from Lonza (Rockland, ME, USA) and stored at −30°C. alamarBlue was purchased from Funakoshi (Tokyo, Japan). Lysis buffer containing Tris (20 mM; pH 7.5), EDTA (10 mM), saponin (0.01%, wt/vol), and Triton X-100 (0.1%, vol/vol) was prepared in advance and kept at 4°C. Human O⁺ RBCs and serum were obtained from the Japanese Red Cross Society (reception number 28J0060). Compounds that were positively identified from our previous study (22) were obtained from the Open Innovation Center for Drug Discovery (OCDD), University of Tokyo (Tokyo, Japan). All compounds were received from the University of Tokyo at a concentration of 10 μM; however, the stock solutions were prepared in DMSO at a concentration of 2 mM. The final DMSO concentration used in the experiment was ≤0.5%, which had no inhibitory effect on parasite culture.

Parasite culture.

For this study, chloroquine-mefloquine-sensitive P. falciparum strain 3D7A was used. P. falciparum strain 3D7A was cultured and maintained as previously described (38), with slight modifications (39). In brief, parasites were maintained in RPMI 1640 medium (Thermo Fisher Scientific, MA, USA) supplemented with 5% AB⁺ human serum, 0.25% AlbuMAX I (Thermo Fisher Scientific), 12.5 μg/ml gentamicin (Sigma-Aldrich), and human RBCs (O⁺) at 2% hematocrit levels with 0.2 to 2% parasitemia in culture flasks at 37°C under an atmosphere of 5% CO₂, 5% O₂, and 90% N₂.

Asexual antimalarial assay: in vitro assay using chloroquine-mefloquine-sensitive P. falciparum strain 3D7A.

The erythrocytic antimalarial activity of the compounds was measured by growth inhibition (percent) of the parasites in the presence of compounds, using a SYBR green I assay. In brief, 50 μl of P. falciparum strains was seeded into a 96-well clear-bottom black plate (Thermo Fisher Scientific) with 0.75% parasitemia and 2% hematocrit, followed by the addition of 50 μl of the compound at a final concentration of 10 μM. Wells in the absence of parasites were considered positive controls, and parasites in DMSO (≥5%) without any treatment were considered negative controls. Plates were then incubated for 48 h at 37°C with 5% CO₂, 5% O₂, and 90% N₂ by using a closed jar. After 48 h of incubation under standard culture conditions, 100 μl of lysis buffer containing SYBR green I (1× final concentration) was directly added to the wells. Plates were then placed on a shaker with gentle mixing for incubation for 1 h at room temperature in the dark. The fluorescence of each well then measured by using a multiplate reader (ARVO1430; PerkinElmer, MA, USA) in the fluorescence detection mode (excitation [Ex] at 485 nm and emission [Em] at 515 nm) for a 0.1-s exposure. Two independent experiments were performed under similar conditions. Subsequently, an in vitro dose-response assay was performed.

In vitro antimalarial dose-response assay.

Active compounds identified by the above-described antimalarial assay were eventually subjected to an in vitro erythrocytic dose-response assay at 10 different dilutions ranging between 0.5 nM and 10 μM to exclude any false-positive compounds and measure the half-maximal inhibitory concentrations (IC₅₀s). Each experiment was conducted twice by using a 96-well clear-bottom black plate, and fluorescence was measured as described above. The data obtained were analyzed to calculate the IC₅₀ of each compound based on a typical sigmoid dose-response curve by using GraphPad Prism 6 software.

Antihemozoin dose-response assay.

The IC₅₀s of potential hit compounds against hemozoin formation were further determined, as previously described (22). Briefly, hemin solution (10 mM heme in DMSO and 100 mM acetate buffer) was incubated with the detergent NP-40 (as hemozoin formation inducer) and compounds (0 μM to 208 μM) for 250 min at 37°C, followed by the addition of pyridine solution with 10 min of shaking. Finally, the absorbance of each compound was measured at 405/705 nm. The IC₅₀s of each compound were calculated by using GraphPad Prism 6 software.

Physicochemical properties of 224 hemozoin inhibitors.

Physicochemical properties of chemical compounds were obtained from the SciFinder Scholar Database (American Chemical Society, Washington, DC) or ChemSpider (http://www.chemspider.com/), as previously described (22).

Statistical analysis.

We conducted blind experiments without knowledge of compound names or structures. The code was opened only after the antimalarial and antihemozoin results were sent to the Open Innovation Center for Drug Discovery, University of Tokyo. Moreover, the statistician who performed the analysis is not in the chemistry field and was not involved in the experiments. Variables of physical properties and compounds with many missing data, including pKa2 (negative log value of acid dissociation constant), vapor pressure (torr), flash point (degrees Celsius), enthalpy of vaporization (kilojoules per mole), and boiling point (degrees Celsius), were excluded. Finally, 206 compounds were included in our analysis.

The outcome variable was the antimalarial activity of the chemical compounds (coded as 1 for active and 0 for inactive). The predictor variables were the physicochemical properties of our chemical compounds. We performed univariable LR to examine the association between physicochemical properties and the above-mentioned outcomes. Subsequently, variables with P values of <0.1 and/or with prior significance in our previous study (22) were included in the multivariable analyses using BMA to find the independent predictors of our outcome. We multiplied the index of the refraction variable by 10 to have a lower odds ratio (OR).

Development and validation of the prediction models.

We divided the original data randomly into training and testing sets at a ratio of 70:30 (nearly 157 compounds [including 17 positive compounds] and 67 compounds [including 5 positive compounds], respectively). The training data set was constructed to develop prediction models using the model. Results are shown as the posterior probability (PP) and Bayesian information criterion (BIC) of each model (20, 40) (Tables 2 and 3). The PP, P (B ≠ 0), is the probability that a predictor variable has an effect on compound activity and that the coefficient is nonzero. The best models were then illustrated visually by depicting the variables included in them (Fig. 1).

Comparison of the best models.

The sensitivity and specificity of the best models were calculated. The discriminatory powers of the best prediction models obtained from BMA were compared according to the area under the curve (AUC) from the receiver operating characteristic (ROC) and their accuracies (Fig. 2). All analyses were performed by using RStudio software version 1.0.44 (https://www.rstudio.com/). A P value of <0.05 was considered statistically significant in all analyses. The data and R script can be obtained from M.G.K. or N.T.H.