A systems biology framework for modeling metabolic enzyme inhibition of Mycobacterium tuberculosis

Background Because metabolism is fundamental in sustaining microbial life, drugs that target pathogen-specific metabolic enzymes and pathways can be very effective. In particular, the metabolic challenges faced by intracellular pathogens, such as Mycobacterium tuberculosis, residing in the infected host provide novel opportunities for therapeutic intervention. Results We developed a mathematical framework to simulate the effects on the growth of a pathogen when enzymes in its metabolic pathways are inhibited. Combining detailed models of enzyme kinetics, a complete metabolic network description as modeled by flux balance analysis, and a dynamic cell population growth model, we quantitatively modeled and predicted the dose-response of the 3-nitropropionate inhibitor on the growth of M. tuberculosis in a medium whose carbon source was restricted to fatty acids, and that of the 5'-O-(N-salicylsulfamoyl) adenosine inhibitor in a medium with low-iron concentration. Conclusion The predicted results quantitatively reproduced the experimentally measured dose-response curves, ranging over three orders of magnitude in inhibitor concentration. Thus, by allowing for detailed specifications of the underlying enzymatic kinetics, metabolic reactions/constraints, and growth media, our model captured the essential chemical and biological factors that determine the effects of drug inhibition on in vitro growth of M. tuberculosis cells.


S2. Obtaining Undetermined Parameter Values in Modelling Cell Growth Inhibition by 3-NP
We To obtain the value of K SUC,ICL1 , we varied the its value until we obtained close agreement between experimental and predicted growth data by using our mathematical framework. When we set the value to 1.5 mM, we calculated the corresponding biomass growth rates μ and propionate uptake rates v C , respectively, as obtained from the FBA of the metabolic network, for growth with 0.025 mM 3-NP inhibitor (dashed line in Figure S1A and S1B). We then applied the obtained biomass growth rates μ and propionate uptake rates v C into the population growth model (Eqs. 10-13 in Main Text), and predicted growth data which agreed with experimental data.

S3. Verification of Essentiality of Target Reactions in Modelling Cell Growth Inhibition by 3-NP
To verify that the two 3-NP-inhibited reactions, ICL and MCL, are necessary for the growth of M. tuberculosis in propionate medium, we set the fluxes associated with these reactions to zero and applying the FBA. The dotted line in Figure S1A and S1B show that the resultant biomass growth rate μ and propionate uptake rate v C , respectively, for the growth of mutant Δicl1Δicl2 were zero. Accordingly, the function g used in the population growth model (Eq. 12 in Main Text) was identical to zero, and this model predicted complete lack of bacterial growth. We did not consider maintenance fluxes (i.e., fluxes used for the viability of the bacterium but not used for growth), because FBA assumes that all possible metabolic fluxes are used to maximize cellular growth.

S4. Growth Predictions in Modelling Cell Growth Inhibition by 3-NP
We used the mathematical framework to predict the growth of M. tuberculosis at three 3-NP inhibitor concentrations (0.050, 0.100, and 0.200 mM). We used the flux ratios shown in Figure   S2A obtained from Eqs. 8 and 9 in Main Text to constrain the fluxes of the ICL and MCL reactions in the metabolic network. Next, we applied the FBA to obtain μ and ν C , for each of the three inhibitor concentrations, as shown in Figure S2B and S2C, respectively. Finally, we applied these rates for the population growth model (Eqs. 10-13 in Main Text) to simulate M. tuberculosis growth at the three different 3-NP concentrations.

S6. Verification of Essentiality of Target Reactions in Modelling Cell Growth Inhibition by sAMS
To verify the essentiality of the targeted reaction, mycobactin synthesis in the presence of sAMS, for cellular growth of M. tuberculosis in iron-deficient GAST medium, we set the flux of the mycobactin synthesis reaction to zero and applied the FBA to the metabolic network, which, as expected, yielded a biomass growth rate μ of zero. We applied this growth rate for the population growth model (Eq. 16 in Main Text) and obtained a relative cell concentration R C of zero.

S7. Growth Predictions in Modelling Cell Growth Inhibition by sAMS
To predict the response of M. tuberculosis cells growing in iron-deficient GAST medium exposed to varying sAMS inhibitor concentrations, we first used the inhibition model (Eq. 14 in Main Text), with the intracellular MbtA-enzyme concentration set to 40 μM, to calculate the flux ratio f MS of the mycobactin synthesis reaction at varying sAMS concentrations ( Figure S3A).
Next, we applied the FBA method to estimate the biomass growth rate μ as a function of f MS ( Figure S3B). Finally, we used the population growth model (Eq. 16 in Main Text) to obtain the relative cell concentration R C as a function of biomass growth rate μ ( Figure S3C). Using the functional dependencies given in Figures S3A-S3C, we mapped the relationship between inhibitor concentration [sAMS] and relative cell concentration R C of M. tuberculosis, yielding the dose-response curve.
To calculate the effect of sAMS on M. tuberculosis growth in an iron-sufficient GAST medium, we applied the FBA of the metabolic network specific to this medium to estimate the biomass growth rate μ as a function of f MS , and the resulting biomass growth rates were quite different from those of the iron-deficient medium. Figure S3B shows that the resultant biomass growth rate μ in iron-sufficient medium was always equal to the inhibitor-free growth rate μ 0 .