Mathematical Modeling of Fluconazole Resistance in the Ergosterol Pathway of Candida albicans

ABSTRACT

Candidiasis is reported to be the most common fungal infection in the critical care setting. The causative agent of this infection is a commensal pathogen belonging to the genus Candida, the most common species of which is Candida albicans. The ergosterol pathway in yeast is a common target by many antifungal agents, as ergosterol is an essential component of the cell membrane. The current antifungal agent of choice for the treatment of candidiasis is fluconazole, which is classified under the azole antifungals. In recent years, the significant increase of fluconazole-resistant C. albicans in clinical samples has revealed the need for a search for other possible drug targets. In this study, we constructed a mathematical model of the ergosterol pathway of C. albicans using ordinary differential equations with mass action kinetics. From the model simulations, we found the following results: (i) a partial inhibition of the sterol-methyltransferase enzyme yields a fair amount of fluconazole resistance; (ii) the overexpression of the ERG6 gene, which leads to an increased sterol-methyltransferase enzyme, is a good target of antifungals as an adjunct to fluconazole; (iii) a partial inhibition of lanosterol yields a fair amount of fluconazole resistance; (iv) the C5-desaturase enzyme is not a good target of antifungals as an adjunct to fluconazole; (v) the C14α-demethylase enzyme is confirmed to be a good target of fluconazole; and (vi) the dose-dependent effect of fluconazole is confirmed. This study hopes to aid experimenters in narrowing down possible drug targets prior to costly and time-consuming experiments and serve as a cross-validation tool for experimental data.

IMPORTANCE Candidiasis is reported to be the most common fungal infection in the critical care setting, and it is caused by a commensal pathogen belonging to the genus Candida, the most common species of which is Candida albicans. The current antifungal agent of choice for the treatment of candidiasis is fluconazole, which is classified under the azole antifungals. There has been a significant increase in fluconazole-resistant C. albicans in recent years, which has revealed the need for a search for other possible drug targets. We constructed a mathematical model of the ergosterol pathway in C. albicans using ordinary differential equations with mass action kinetics. In our simulations, we found that by increasing the amount of the sterol-methyltransferase enzyme, C. albicans becomes more susceptible to fluconazole. This study hopes to aid experimenters in narrowing down the possible drug targets prior to costly and time-consuming experiments and to serve as a cross-validation tool for experimental data.

INTRODUCTION

Candidiasis refers to a broad range of fungal infections caused by different species of a fungal commensal pathogen belonging to the genus Candida. The following Candida species are all reported to cause cutaneous, mucosal, bloodstream, and deep-seated tissue infections: Candida albicans, C. glabrata, C. tropicalis, C. parapsilosis, and C. krusei. The most common of these is Candida albicans (1).

Invasive candidiasis is the term used for the more concerning type, which includes bloodstream yeast infections, which are also known as candidemia. Likewise, deep-seated tissue infections are infections that occur in sterile sites, such as the peritoneal cavity, and in abdominal and nonabdominal sites, namely, the bones, muscles, joints, eyes, or central nervous system (2). Surprisingly, the invasive type is the most common fungal infection in the critical care setting, with crude mortality of about 40 to 55% (3).

Logan et al. (2020) noted several risk factors for invasive candidiasis that include the use of broad-spectrum antimicrobials, immunosuppressive drugs, total parenteral nutrition, iatrogenic interventions, along with several challenges in the critical care setting, namely, the shift to more resistant Candida epidemiology and the appropriate strategies for antifungal therapy (3). Among the different classes of antifungal agents used for invasive candidiasis are agents such as azoles, polyenes, echinocandins, and allylamines. However, fluconazole, a fungistatic drug belonging to the azole group, is currently the preferred treatment for C. albicans infections due to its low cost, limited toxicity, and oral administration (4). The mechanism of action of azole drugs is the inhibition of the C14α-demethylase enzyme, which blocks the synthesis of ergosterol, an essential component of the fungal cell membrane in Candida species (5). The chemical structure of fluconazole is depicted in Fig. 1, as adopted from (6).

FIG 1.

Chemical structure of fluconazole (adopted from [6]). It is a member of the triazole class and is a five-membered ring with 3 nitrogen atoms (shown on the left and right). It is also comprised of difluorobenzene, a benzene ring with 2 fluorine atoms (shown at the bottom).

In recent years, Whaley et al. (2017) noted a high level of resistance to azoles among Candida species, and some nonalbican Candida species have already been reported to have intrinsic resistance to azoles (4). In fact, the Centers for Disease Control and Prevention (CDC), in its Antibiotic Resistance Threats in the United States, 2019 report, classifies drug-resistant Candida as a serious threat, with an estimate of 34,800 cases and 1,700 deaths (7). The CDC noted that about 7% of all Candida blood samples tested are resistant to fluconazole (7).

There is an abundance of experimental investigations into azole resistance mechanisms in C. albicans, which can be costly and time-consuming. In this study, we propose a different approach to investigating fluconazole resistance in C. albicans, namely, using mathematical models to determine possible drug targets within the ergosterol pathway. The aim of this study is to narrow down possible drug targets prior to costly and time-consuming experiments and to serve as a cross-validation tool for experimental data. To our knowledge, this is the first study to investigate the fluconazole resistance in the ergosterol pathway of Candida albicans using mathematical modeling.

The rest of the paper is organized as follows: The results of the model simulations are shown in the Results section. These are followed by a discussion on how the results compare with previous literature, the conclusions drawn, and further recommendations that are proposed in the Discussion section. Then, in the Materials and Methods section, we discuss, in detail, the mathematical modeling process.

RESULTS

The model was run to simulate several scenarios to investigate possible drug targets in the ergosterol pathway in C. albicans.

Variations in lanosterol concentration.

The lanosterol concentration was varied as follows: 0×, 0.01×, 0.1×, 1×, 10×, and 100× the baseline value (see Fig. S2), represented by cases 1 to 6, respectively. Case 1 (0×) simulates a total inhibition of lanosterol. It results in the demise of C. albicans, as no ergosterol was produced, and ergosterol is essential for yeast survival. Cases 2 (0.01×) and 3 (0.1×) simulate the partial inhibition of lanosterol. They yield a higher percentage of the toxic sterol and ergosterol as the dominant metabolite but a lower percentage of ergosterol reduction, satisfying 2 out of 3 criteria which denote fair fluconazole resistance. Case 4 (1×) denotes the default case, which serves as our baseline. Cases 5 (10×) and 6 (100×) simulate the overproduction of lanosterol. They yield a lower percentage of the toxic sterol but a higher percentage of ergosterol reduction, satisfying 1 out of 3 criteria and denoting an equivocal result. Table 1 summarizes the results pertinent to the criteria for fluconazole resistance.

TABLE 1.

Pertinent results of the variations in lanosterol concentration simulation

Metabolites	Value in μM (%)
	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
Ergosterol	0 (0%)	4.61 (45.26%)	45.48 (44.91%)	65.41 (5.22%)	40.38 (0.31%)	9.69 (0.01%)
Toxic sterol	0 (0%)	3.03 (29.74%)	29.89 (29.51%)	222.01 (17.73%)	644.09 (4.97%)	1,066.38 (0.82%)
Percent ergosterol reduction	–a	64.46%	64.93%	94.69%	96.79%	99.23%
Is ergosterol dominant?	–	Yes	Yes	No	No	No
Number of criteria satisfied	–	2	2	-	1	1

^a–, not applicable.

FIG S2

Plots generated by the simulation of variations in lanosterol concentration. The variations are as follows: 0× (red solid line), 0.01× (orange dashed line), 0.1× (yellow dotted line), 1× (green dashed dotted line), 10× (blue dense dashed dotted line), and 100× (purple dashed double dotted line). The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison. Download FIG S2, PDF file, 0.1 MB ^{(53.4KB, pdf)} .

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This content is distributed under the terms of the Creative Commons Attribution 4.0 International license.

Variations in C14α-demethylase concentration (Erg11p).

The C14α-demethylase enzyme concentration was varied as follows: 0×, 0.01×, 0.1×, 1×, 10×, and 100× the baseline value (see Fig. S3), represented by cases 1 to 6, respectively. Case 1 (0×) simulates a total inhibition of C14α-demethylase. This results in the demise of C. albicans, as no ergosterol was produced, and ergosterol is essential for yeast survival. Cases 2 (0.01×) and 3 (0.1×) simulate the partial inhibition of C14α-demethylase. They yield a higher percentage of toxic sterol and a higher percentage of ergosterol reduction, satisfying 0 out of 3 criteria, which denotes a good target for antifungals as an adjunct to fluconazole. Case 4 (1×) denotes the default case, which serves as our baseline. Cases 5 (10×) and 6 (100×) simulate the overexpression of the ERG11 gene. They yield a lower percentage of the toxic sterol and a lower percentage of ergosterol reduction, satisfying 2 out of 3 criteria and denoting fair fluconazole resistance. Table 2 summarizes the results pertinent to the criteria for fluconazole resistance.

TABLE 2.

Pertinent results of the variations in C14α-demethylase concentration simulation

Metabolites	Value in μM (%)
	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
Ergosterol	0 (0%)	0.11 (0.01%)	3.43 (0.27%)	65.41 (5.22%)	79.60 (6.36%)	81.95 (6.55%)
Toxic sterol	589.71 (46.17%)	589.63 (46.17%)	587.18 (46.08%)	222.01 (17.73%)	31.16 (2.49%)	3.64 (0.29%)
Percent ergosterol reduction	–a	99.68%	98.91%	94.69%	93.74%	93.59%
Is ergosterol dominant?	–	No	No	No	No	No
Number of criteria satisfied	–	0	0	–	2	2

^a–, not applicable.

FIG S3

Plots generated by the simulation of variations in C14α-demethylase concentration. The variations are as follows: 0× (red solid line), 0.01× (orange dashed line), 0.1× (yellow dotted line), 1× (green dashed dotted line), 10× (blue dense dashed dotted line), and 100× (purple dashed double dotted line). The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison. Download FIG S3, PDF file, 0.1 MB ^{(62.5KB, pdf)} .

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This content is distributed under the terms of the Creative Commons Attribution 4.0 International license.

Variations in fluconazole concentration.

The fluconazole concentration was varied as follows: 0×, 0.01×, 0.1×, 1×, 10×, and 100× the baseline value (see Fig. S4), represented by cases 1 to 6, respectively. Case 1 (0×) simulates a situation where no fluconazole was given. This results in the proliferation of C. albicans, as the dominant metabolite is ergosterol, and ergosterol is essential for yeast survival. Cases 2 (0.01×) and 3 (0.1×) simulate giving fluconazole with a dose lower than its minimum inhibitory concentration (MIC) (i.e., 2 μg/mL). They yield a lower percentage of toxic sterol and a lower percentage of ergosterol reduction, satisfying 2 out of 3 criteria, which denotes fair fluconazole resistance. Case 4 (1×) denotes the default case, which serves as our baseline. Cases 5 (10×) and 6 (100×) simulate giving fluconazole with a dose higher than its MIC. They yield a higher percentage of toxic sterol and a higher percentage of ergosterol reduction, satisfying 0 out of 3 criteria and denoting a good target for antifungals as an adjunct to fluconazole. Table 3 summarizes the results pertinent to the criteria for fluconazole resistance.

TABLE 3.

Pertinent results of the variations in fluconazole concentration simulation

Metabolites	Value in μM (%)
	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
Ergosterol	1,230.86 (98%)	66.73 (5.33%)	66.62 (5.32%)	65.41 (5.22%)	3.89 (0.31%)	0.11 (0.01%)
Toxic sterol	0 (0%)	204.17 (16.31%)	205.67 (16.43%)	222.01 (17.73%)	586.84 (46.06%)	589.62 (46.17%)
Percent ergosterol reduction	–a	94.58%	94.59%	94.69%	99.68%	99.99%
Is ergosterol dominant?	–	No	No	No	No	No
Number of criteria satisfied	–	2	2	–	0	0

^a–, not applicable.

FIG S4

Plots generated by the simulation of variations in fluconazole concentration. The variations are as follows: 0× (red solid line), 0.01× (orange dashed line), 0.1× (yellow dotted line), 1× (green dashed dotted line), 10× (blue dense dashed dotted line), and 100× (purple dashed double dotted line). The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison. Download FIG S4, PDF file, 0.1 MB ^{(73.7KB, pdf)} .

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This content is distributed under the terms of the Creative Commons Attribution 4.0 International license.

Variations in sterol-methyltransferase concentration (Erg6p).

The sterol-methyltransferase enzyme concentration was varied as follows: 0×, 0.01×, 0.1×, 1×, 10×, and 100× the baseline value (see Fig. S5), represented by cases 1 to 6, respectively. Case 1 (0×) simulates a total inhibition of sterol-methyltransferase. This results in the demise of C. albicans, as no ergosterol was produced, and ergosterol is essential for yeast survival. Cases 2 (0.01×) and 3 (0.1×) simulate the partial inhibition of sterol-methyltransferase. They yield a lower percentage of toxic sterol and a lower percentage of ergosterol reduction, satisfying 2 out of 3 criteria, which denotes fair fluconazole resistance. Case 4 (1×) denotes the default case, which serves as our baseline. Cases 5 (10×) and 6 (100×) simulate the overexpression of the ERG6 gene. They yield a higher percentage of toxic sterol and a higher percentage of ergosterol reduction, satisfying 0 out of 3 criteria and denoting a good target for antifungals as an adjunct to fluconazole. Table 4 summarizes the results pertinent to the criteria for fluconazole resistance.

TABLE 4.

Pertinent results of the variations in sterol-methyltransferase concentration simulation

Metabolites	Value in μM (%)
	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
Ergosterol	0 (0%)	9.31 (0.72%)	58.54 (4.67%)	65.41 (5.22%)	46.52 (3.71%)	15.07 (1.18%)
Toxic sterol	0 (0%)	3.63 (0.28%)	34.58 (2.76%)	222.01 (17.73%)	660.83 (52.70%)	796.76 (62.32%)
Percent ergosterol reduction	–a	77.83%	85.13%	94.69%	96.32%	98.81%
Is ergosterol dominant?	–	No	No	No	No	No
Number of criteria satisfied	–	2	2	–	0	0

^a–, not applicable.

FIG S5

Plots generated by the simulation of variations in sterol-methyltransferase concentration. The variations are as follows: 0× (red solid line), 0.01× (orange dashed line), 0.1× (yellow dotted line), 1× (green dashed dotted line), 10× (blue dense dashed dotted line), and 100× (purple dashed double dotted line). The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison. Download FIG S5, PDF file, 0.1 MB ^{(63.5KB, pdf)} .

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This content is distributed under the terms of the Creative Commons Attribution 4.0 International license.

Variations in C5-desaturase concentration (Erg3p).

The C5-desaturase enzyme concentration was varied as follows: 0×, 0.01×, 0.1×, 1×, 10×, and 100× the baseline value (see Fig. S6), represented by cases 1 to 6, respectively. Case 1 (0×) simulates a total inhibition of C5-desaturase. This results in the demise of C. albicans, as no ergosterol was produced, and ergosterol is essential for yeast survival. Cases 2 (0.01×) and 3 (0.1×) simulate the partial inhibition of C5-desaturase. They yield a lower percentage of the toxic sterol but a higher percentage of ergosterol reduction, satisfying 1 out of 3 criteria, which denotes an equivocal result. Case 4 (1×) denotes the default case, which serves as our baseline. Cases 5 (10×) and 6 (100×) simulate the overexpression of the ERG3 gene. They yield a higher percentage of the toxic sterol but a lower percentage of ergosterol reduction and ergosterol as the dominant metabolite, satisfying 2 out of 3 criteria and denoting fair fluconazole resistance. Table 5 summarizes the results pertinent to the criteria for fluconazole resistance.

TABLE 5.

Pertinent results of the variations in C5-desaturase concentration simulation

Metabolites	Value in μM (%)
	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
Ergosterol	0 (0%)	0.51 (0.04%)	5.37 (0.41%)	65.41 (5.22%)	431.35 (44.26%)	432.11 (44.34%)
Toxic sterol	0 (0%)	5.87 (0.45%)	52.20 (4.02%)	222.01 (17.73%)	266.99 (27.39%)	267.00 (27.40%)
Percent ergosterol reduction	–a	96.03%	95.81%	94.69%	66.36%	66.31%
Is ergosterol dominant?	–	No	No	No	Yes	Yes
Number of criteria satisfied	–	1	1	–	2	2

^a–, not applicable.

FIG S6

Plots generated by the simulation of variations in C5-desaturase concentration. The variations are as follows: 0× (red solid line), 0.01× (orange dashed line), 0.1× (yellow dotted line), 1× (green dashed dotted line), 10× (blue dense dashed dotted line), and 100× (purple dashed double dotted line). The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison. Download FIG S6, PDF file, 0.05 MB ^{(50.8KB, pdf)} .

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Sensitivity analysis.

The local one-at-a-time sensitivity analysis was plotted using a tornado chart for ergosterol, as shown in Fig. 2, and for toxic sterol, as shown in Fig. 3. The longer the bar a parameter has, the more sensitive the products (ergosterol and toxic sterol) are to it.

FIG 2.

Tornado chart of the local one-at-a-time sensitivity analysis of the model parameters to ergosterol. The y axis enumerates all of the model parameters, and the x axis represents the absolute difference of the resulting ergosterol concentration to its baseline value. The red bars indicate the sensitivity analysis of the −10% of the baseline values, whereas the blue bars indicate the sensitivity analysis of the +10% of the baseline values. The longer the bars for the parameters are, the more sensitive the ergosterol is to the parameters. See Table S1 for the parameters used in the study.

FIG 3.

Tornado chart of the local one-at-a-time sensitivity analysis of the model parameters to the toxic sterol. The y axis enumerates all of the model parameters, and the x axis represents the absolute difference of the resulting toxic sterol concentration to its baseline value. The red bars indicate the sensitivity analysis of the −10% of the baseline values, whereas the blue bars indicate the sensitivity analysis of the +10% of the baseline values. The longer the bars for the parameters are, the more sensitive the ergosterol is to the parameters. See Table S1 for the parameters used in the study.

TABLE S1

Model parameters. Download Table S1, PDF file, 0.05 MB ^{(52.2KB, pdf)} .

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DISCUSSION

The simulation for variations in lanosterol concentration showed that its total inhibition, shown in Table 1, case 1, by ERG1 gene deletion results in the demise of C. albicans due to its lack of ergosterol. This agrees with the results of the study by Pasrija et al. (2005) that the erg1 mutant showed a total lack of ergosterol and led to increased azole susceptibility (8). However, its partial inhibition, shown in Table 1, cases 2 and 3, results in fair fluconazole resistance. An example of this is the antifungal allylamine, which inhibits the squalene epoxidase enzyme in the pathway upstream of lanosterol. However, Kane and Carter showed that there is a synergistic effect when combining terbinafine (under allylamines) and fluconazole against C. albicans (9). Allylamines cause fungal cell death by depleting the ergosterol content and by accumulating squalene (10). The discrepancy may be due to our model being limited to the three implicated genes: ERG11, ERG3, and ERG6. Moreover, the overproduction of lanosterol, as shown in Table 1, cases 5 and 6, yields an equivocal result. Hence, no conclusion can be drawn. This indicates the need for further experiments or for further extension of the model to include upstream pathways, such as the squalene epoxidase enzyme.

The simulation for variations in C14α-demethylase concentration confirmed that its partial inhibition, as shown in Table 2, cases 2 and 3, is a good target of antifungals, as it should be, since it has been known that this enzyme is the target of azole drugs, such as fluconazole, leading to the demise of C. albicans (11, 12). On the other hand, the overexpression of the ERG11 gene is a known azole resistance mechanism (13). This has been confirmed by our simulation, shown in Table 2, cases 5 and 6, in that there was a lower percentage of toxic sterol and a lower percentage of ergosterol reduction.

The simulation for variations in fluconazole concentration, as shown in Table 3, confirmed that the effect of fluconazole in C. albicans is dose-dependent such that doses lower than its MIC do not fully eradicate the fungi, whereas doses greater than its MIC do eradicate them. Hence, it is crucial to have an accurate quantitative method by which to determine the MIC for antifungal susceptibility testing (14).

The simulation for variations in sterol-methyltransferase concentration showed that its partial inhibition, as shown in Table 4, cases 2 and 3, yields fair fluconazole resistance. This agrees with the findings of Kelly et al. (1997) that show that a defect in the ERG6 gene leads to toxic sterol accumulation and, hence, the resistance to fluconazole (15). This resistance mechanism is also described in the review by Bhattacharya et al. (2020) (12). On the other hand, our results showed that the overexpression of the ERG6 gene, shown in Table 4, cases 5 and 6, is a good target for antifungals as an adjunct to fluconazole. Bhattacharya et al. (2018) noted that in Saccharomyces cerevisiae, overexpression of the ERG6 gene encourages the initiation of the alternative pathway, leading to the production of toxic sterol (16). In the review by Bhattacharya et al. (2020), the ERG6 gene contributes to the formation of the toxic sterol in the presence of azoles (12). Hence, we can infer that the overexpression of the ERG6 gene can lead to an increase in the formation of the toxic sterol and can result in a hypersusceptibility to azoles. As such, this can have an additive effect when combined with fluconazole to circumvent the resistance of C. albicans against it. The overexpression of the ERG6 gene yields a higher percentage of toxic sterol and a higher percentage of ergosterol reduction. Hence, we recommend conducting further experiments on the sterol-methyltransferase enzyme to confirm that its overexpression is a possible drug target as an adjunct to fluconazole in order to validate our simulation result.

The simulation for variations in C5-desaturase concentration showed that its partial inhibition, as shown in Table 5, cases 2 and 3, leads to an equivocal result. Hence, no conclusion can be drawn. However, in the literature, it is known that its mutation is linked with azole resistance (5, 12, 17). On the other hand, our simulation of the overexpression of the ERG3 gene, shown in Table 5, cases 5 and 6, results in fair fluconazole resistance. No studies have yet been conducted regarding this in the literature; however, our results showed that it yields a lower percentage of ergosterol reduction and ergosterol as the dominant metabolite. Hence, we recommend against looking into this enzyme as a possible drug target as an adjunct to fluconazole.

The local one-at-a-time sensitivity analysis, as shown in Fig. 2 and 3, showed that the more upstream the pathway is, the less sensitive the products (ergosterol and toxic sterol) are to them, whereas the more downstream the pathway is, the more sensitive the products are to them. Also, the products (ergosterol and toxic sterol) are more sensitive to the parameters in the alternative pathway than to those in the normal pathway.

Concluding remarks.

From the model simulations, we found the following results: (i) a partial inhibition of sterol-methyltransferase yields a fair amount of fluconazole resistance; (ii) overexpression of the ERG6 gene, leading to an increased sterol-methyltransferase enzyme, is a good target of antifungals as an adjunct to fluconazole; (iii) a partial inhibition of lanosterol yields a fair amount of fluconazole resistance; (iv) C5-desaturase is not a good target of antifungals as an adjunct to fluconazole; (v) C14α-demethylase is confirmed to be a good target for fluconazole; and (vi) the dose-dependent effect of fluconazole is confirmed. This study hopes to aid experimenters in narrowing down the possible drug targets prior to costly and time-consuming experiments and to serve as a cross-validation tool for experimental data.

We recommend extending the model to include other genes involved in the ergosterol biosynthesis pathway, such as the ERG1 gene that expresses squalene epoxidase, which is the target of antifungal allylamine. Moreover, the computational approach used in our study is also applicable to other, completely different pathways involved in the azole resistance mechanism, such as the CDR1, CDR2, and MDR1 genes, which are involved in the drug efflux transporter. We also recommend doing further experiments on the sterol-methyltransferase enzyme to confirm that its overexpression is a possible target for antifungals as an adjunct to fluconazole in order to validate our simulation result.

MATERIALS AND METHODS

The model for the ergosterol biosynthesis pathway, as shown in Fig. 4, in C. albicans is built by adopting the pathways of Sanglard et al. (2003) (see Figure 1 in [5]), and Martel et al. (2010) (see Figure 1 in [17]). We noted several differences between the two studies, notably, the substrate for the C14α-demethylase enzyme is lanosterol in Sanglard et al. (2003); however, it is eburicol in the pathway presented by Martel et al. (2010). There are still disparities in the literature regarding this matter. In this study, we followed Sanglard et al. (2003) for the construction of our model. The Python programming language was used for the coding of the model equations and simulations (18).

FIG 4.

Ergosterol biosynthesis pathway. The pathway starts from lanosterol to ergosterol synthesis. It does not include the pathways upstream of lanosterol, such as the squalene epoxidase enzyme. The metabolites in green denote the ergosterol pathway in C. albicans when azole is absent, which leads to its survival, whereas those in blue represent the alternative pathway during azole inhibition, which leads to its demise, due to the production of the toxic sterol, 14α-methyl-3,6-diol. The enzymes are colored in pink. The azole drug is colored in magenta. The arrows pertain to the direction of the reaction. Bidirectional arrows indicate reversible reactions.

Due to the complexity of the calculations, the model is limited to the three genes implicated in azole resistance in the literature: ERG11, ERG3, and ERG6. Various point mutations in the ERG11 gene were shown to alter the binding abilities of azoles to the C14α-demethylase enzyme (19, 20). The deletion of the ERG3 gene resulted in the accumulation of the toxic sterol precursor 14α-methylfecosterol instead of the toxic sterol, allowing for C. albicans survival (15, 17). Disruption in the ERG6 gene was shown to cause hypersusceptible strains to antifungal agents but not to azoles (21). Moreover, Akins (2005) noted that the ERG6 gene is an attractive target for antifungals (22). Hence, we deem it worthwhile to investigate whether or not it has an additive effect with fluconazole.

Another limitation of the study is that our simulations are limited to testing drug targets as an adjunct to fluconazole, since the model calibration was based on the study by Kelly et al. (1997), which compared the sterol compositions of C. albicans before and after fluconazole treatment using gas chromatography/mass spectrometry (GC/MS) (15).

The model uses ordinary differential equations (ODEs) with mass-action kinetics, as first described in (23), which has since become a standard method for mathematical modeling. Recently, Sutradhar et al. (2021) used an ODE model to determine the drivers of the growth of antibiotic-resistant bacteria in wastewater (24). The ODEs for the model without azole (normal pathway) are shown in Equation 1, as:

$$\frac{d{R}_1}{\mathit{dt}}=k_{-1}{C}_1-k_{-2a}{C}_{2a}-k_1{R}_1{E}_1-k_{2a}{R}_1{E}_2,$$

$$\frac{d{E}_1}{\mathit{dt}}=k_{-1}{C}_1+k_4{C}_1+k_{-1a}{C}_{1a}-k_1{R}_1{E}_1-k_{1a}{R}_{1a}{E}_1,$$

$$\frac{d{C}_1}{\mathit{dt}}=k_1{R}_1{E}_1-k_{-1}{C}_1-k_4{C}_1,$$

$$\frac{d{R}_2}{\mathit{dt}}=k_4{C}_1+k_{-2}{C}_2-k_2{R}_2{E}_2,$$

$$\frac{d{E}_2}{\mathit{dt}}=k_{-2}{C}_2+k_5{C}_2+k_{-2a}{C}_{2a}+k_{4a}{C}_{2a}-k_2{R}_2{E}_2-k_{2a}{R}_1{E}_2,$$

$$\frac{d{C}_2}{\mathit{dt}}=k_2{R}_2{E}_2-k_{-2}{C}_2-k_5{C}_2,$$

$$\frac{d{R}_3}{\mathit{dt}}=k_5{C}_2+k_{-3}{C}_3-k_3{R}_3{E}_3,$$

$$\frac{d{E}_3}{\mathit{dt}}=k_{-3}{C}_3+k_6{C}_3+k_{-3a}{C}_{3a}+k_{7a}{C}_{3a}-k_3{R}_3{E}_3-k_{3a}{R}_{4a}{E}_3,$$

$$\frac{d{C}_3}{\mathit{dt}}=k_3{R}_3{E}_3-k_{-3}{C}_3-k_6{C}_3,$$

$$\frac{\mathit{dP}}{\mathit{dt}}=k_6{C}_3.$$ (1)

The ODEs for the model with azole (alternative pathway) are shown in Equation 2, as:

$$\frac{d{R}_{1a}}{\mathit{dt}}=k_{-1a}{C}_{1a}-k_{1a}{R}_{1a}{E}_1,$$

$$\frac{d{C}_{1a}}{\mathit{dt}}=k_{1a}{R}_{1a}{E}_1-k_{-1a}{C}_{1a},$$

$$\frac{d{C}_{2a}}{\mathit{dt}}=k_{2a}{R}_1{E}_2-k_{-2a}{C}_{2a}-k_{4a}{C}_{2a},$$

$$\frac{d{R}_{2a}}{\mathit{dt}}=k_{4a}{C}_{2a}-k_{5a}{R}_{2a},$$

$$\frac{d{R}_{3a}}{\mathit{dt}}=k_{5a}{R}_{2a}-k_{6a}{R}_{3a},$$

$$\frac{d{R}_{4a}}{\mathit{dt}}=k_{6a}{R}_{3a}+k_{-3a}{C}_{3a}-k_{3a}{R}_{4a}{E}_3,$$

$$\frac{d{C}_{3a}}{\mathit{dt}}=k_{3a}{R}_{4a}{E}_3-k_{-3a}{C}_{3a}-k_{7a}{C}_{3a},$$

$$\frac{d{P}_a}{\mathit{dt}}=k_{7a}{C}_{3a}.$$ (2)

The constraint equations are shown in Equation 3, as:

$$E_1=E_{1,\mathit{total}}-C_1-C_{1a},$$

$$E_2=E_{2,\mathit{total}}-C_2-C_{2a},$$

$$E_3=E_{3,\mathit{total}}-C_3-C_{3a}.$$ (3)

In the study by Hargrove et al. (2017), they used a molar ratio of 1:2:50 for the enzyme, inhibitor, and substrate, respectively (25). We tested it in our model and observed that this enzyme concentration was insufficient for the inhibitor to fully take its effect. As such, we adjusted the assignment of the molar ratio to 4:2:50 for the enzyme, inhibitor, and substrate, respectively. The fluconazole concentration is set at 16 μg/mL, following Kelly et al. (1997) (15). The parameter values, shown in Table S1, were obtained by calibrating the model to the sterol compositions described by Kelly et al. (1997) (15) such that in a fluconazole-sensitive C. albicans strain, it is mainly composed of ergosterol (98%), while the rest is classified as unknown (2%). We distribute the unknown 2% to the remaining metabolites in the pathway. In a fluconazole-resistant strain, the sterol composition is as follows: ergosterol (2%), eburicol (16.1%), obtusifoliol (34.5%), 14α-methyl-3,6-diol (45.2%), and unknown (2.2%). We again distribute the unknown 2.2% to the remaining metabolites in the pathway (see Table 8 in [15]). Following Kelly et al. (1997), the simulations were run for 24 h, and the pertinent results were tabulated thereafter. The model generated the plots shown in Fig. S1. The pertinent results are shown in Table 6.

TABLE 6.

Pertinent results of the model calibration to that of Kelly et al. (1997) (15)

Metabolites	Value in μM (%)
	(−) Azole	(+) Azole
Ergosterol	1,230.86 (98%)	25.14 (2%)
14α-methyl-3,6-diol	0 (0%)	567.29 (45.20%)
Percent ergosterol reduction	–a	97.96%

^a–, not applicable.

FIG S1

Plots generated by the model calibrated from Kelly et al., (1997) (15). The normal pathway, when azole is absent, is denoted by blue solid lines. The alternative pathway, when azole is present, is denoted by red dashed lines. The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison. Download FIG S1, PDF file, 0.04 MB ^{(41.3KB, pdf)} .

Copyright © 2022 Yu et al.

This content is distributed under the terms of the Creative Commons Attribution 4.0 International license.

The clinical breakpoints, as determined from the 24-h Clinical & Laboratory Standards Institute (CLSI) M27-A3 (26) broth microdilution method, for fluconazole against C. albicans are as follows: Susceptible (MIC ≤ 2 μg/mL), Dose-dependent (MIC = 4 μg/mL), and Resistant (MIC ≥ 8 μg/mL) (14). We recalibrated our model to accommodate the MIC breakpoint for fluconazole susceptibility (MIC = 2 μg/mL) to determine its threshold for fluconazole susceptibility. To compute the molar concentration of 2 μg/mL, we used the following calculation (molecular weight of fluconazole: 306.3 g/mol from [6]):

$$\frac{2\mathrm{\mu g}}{1\mathrm{mL}}\times \frac{1\mathrm{mol}}{306.3\text{\hspace{0.17em}g}}\times \frac{1000\mathrm{mL}}{1\text{\hspace{0.17em}L}}=6.53\mathrm{\mu M}.$$ (4)

The recalibrated model generated the plots shown in Fig. 5. This served as the baseline for the simulations in the Results section. The pertinent results are shown in Table 7.

FIG 5.

Plots generated by the model recalibrated to the MIC breakpoint for fluconazole susceptibility. The normal pathway, when azole is absent, is denoted by blue solid lines. The alternative pathway, when azole is present, is denoted by red dashed lines. The x axes denote the time in hours, and the y axes represent the concentrations in μM. The last two subplots, emphasized in dark borders, reiterate the pertinent plots of ergosterol and the toxic sterol (14α-methyl-3,6-diol) for easier comparison.

TABLE 7.

Pertinent results of the model recalibration to the MIC breakpoint for fluconazole susceptibility

Metabolites	Value in μM (%)
	(−) azole	(+) azole
Ergosterol	1,230.95 (98%)	65.41 (5.22%)
14α-methyl-3,6-diol	0 (0%)	222.01 (17.73%)
Percent ergosterol reduction	–a	94.69%

^a–, not applicable.

A local one-at-a-time sensitivity analysis was performed on the model parameters. We took −10% and +10% of the baseline values of the parameters, as shown in Table S1. Then, we gathered the absolute differences of the product (ergosterol and toxic sterol) concentrations from their baseline values.

In experimental studies, antifungal susceptibility is quantified via a visual spotting assay on yeast extract peptone dextrose (YEPD) medium (5), the disc diffusion method (19), or the broth microdilution method (27). However, these methods are not feasible to use in mathematical models because they cannot be quantified. As such, we looked for quantitative methods at the metabolite level to circumvent this limitation.

Arthington-Skaggs et al. (1999) proposed the use of percent ergosterol reduction as a quantitative method by which to evaluate antifungal susceptibility (28). However, Kelly et al. (1997) found that an accumulation of the toxic sterol causes the growth arrest of C. albicans (15). Another interesting result found by Martel et al. (2010) is that antifungal susceptibility holds when the dominant fraction of sterol is ergosterol, regardless of the amount of the toxic sterol (17).

Considering the above methods for antifungal susceptibility, we propose the following criteria, based on the data gathered in Table 7, for the determination of the threshold for fluconazole resistance in C. albicans: (i) when the percent toxic sterol (14α-methyl-3,6-diol) is less than 17.73%; (ii) when the percent ergosterol reduction is less than 94.69%; and (iii) when ergosterol is the dominant fraction among the metabolites.

When all three criteria are satisfied, we designate it as good fluconazole resistance. When two out of three are satisfied, we designate it as fair fluconazole resistance. When only one out of three is satisfied, we designate it as an equivocal result such that no conclusion can be drawn. Conversely, when none of the criteria are satisfied, we designate it as a good target for antifungals as an adjunct to fluconazole.

Data availability.

The source code is available at https://github.com/dlsu-scomb/candida-amr.