Mathematical modelling of polyamine metabolism in bloodstream-form Trypanosoma brucei: an application to drug target identification

Abstract

We present the first computational kinetic model of polyamine metabolism in bloodstream-form Trypanosoma brucei, the causative agent of human African trypanosomiasis. We systematically extracted the polyamine pathway from the complete metabolic network while still maintaining the predictive capability of the pathway. The kinetic model is constructed on the basis of information gleaned from the experimental biology literature and defined as a set of ordinary differential equations. We applied Michaelis-Menten kinetics featuring regulatory factors to describe enzymatic activities that are well defined. Uncharacterised enzyme kinetics were approximated and justified with available physiological properties of the system. Optimisation-based dynamic simulations were performed to train the model with experimental data and inconsistent predictions prompted an iterative procedure of model refinement. Good agreement between simulation results and measured data reported in various experimental conditions shows that the model has good applicability in spite of there being gaps in the required data. With this kinetic model, the relative importance of the individual pathway enzymes was assessed. We observed that, at low-to-moderate levels of inhibition, enzymes catalysing reactions of de novo AdoMet (MAT) and ornithine production (OrnPt) have more efficient inhibitory effect on total trypanothione content in comparison to other enzymes in the pathway. In our model, prozyme and TSHSyn (the production catalyst of total trypanothione) were also found to exhibit potent control on total trypanothione content but only when they were strongly inhibited. Different chemotherapeutic strategies against T. brucei were investigated using this model and interruption of polyamine synthesis via joint inhibition of MAT or OrnPt together with other polyamine enzymes was identified as an optimal therapeutic strategy.

Figure 1. A detailed graphical representation of total trypanothione metabolism.

Edges represent chemical conversions between model components with arrows indicating reaction directionality. Metabolites and reactions constituting the polyamine biosynthetic pathway that are considered in this model are emphasised with bold type, with time-variant metabolites shown in green and constant metabolites shown in pink. Enzymes catalysing each active elementary step in the pathway are denoted with blue boxes. The remaining modules of the network shown in grey are not modelled but help gaining an overall picture of the metabolism. Abbreviations of polyamine metabolites: Met, methionine; AdoMet, S-adenosylmethionine; dAdoMet, decarboxylated AdoMet; MTA, methylthioadenosine; AdoHcy, S-adenosylhomocysteine; Orn, ornithine; Put, putrescine; Spd, spermidine; , total trypanothione; , exogenous methionine; exogenous ornithine. Abbreviations of intra-cellular polyamine enzymes: MetPt, Met uptake enzyme; MAT, AdoMet synthase; AHS, methyltransferase; AdoMetDC, AdoMet decarboxylase; MetRcy, Met recycling enzyme; OrnPt, Orn uptake enzyme; ODC, Orn decarboxylase; SpdS, Spd synthase; TSHSyn, synthesis catalyst; TSHCpt, consumption catalyst.

Figure 2. Time-series simulation of DFMO effects on polyamine levels compared with experimental data.

Lines without symbols, model predictions; lines with symbols, experimental observations from . The maximum velocity of ODC was modelled as a time-dependent variable, with the activity decreased by more than 99% within 12-hour of treatment with DFMO. AdoMet dynamics observed by Xiao et al. were adopted. Error bars are presented where appropriate data was available in the original papers.

Figure 3. Time-series simulation of ODC inhibition on polyamine levels compared with observed values.

Lines without symbols, model predictions; lines with symbols, experimental observations from . The maximum velocity of ODC was modelled as a time-dependent variable during the simulation with equal to 0.0016, where the ODC activity was decreased by 90% within 24 hours of RNAi induction. Error bars are presented where appropriate data was available in the original papers.

Figure 4. Time-series simulation of SpdS inhibition on polyamine levels compared with observed values.

Lines without symbols, model predictions; lines with symbols, experimental observations from . The maximum velocity of SpdS was modelled as a time-dependent variable with equal to 0.0016. Error bars are presented where appropriate data was available in the original papers.

Figure 5. Time-series simulation of AdoMetDC inhibition on polyamine levels compared with observed values.

Lines without symbols, model predictions; lines with symbols, experimental observations from for (A) to (C) and for (D). In (A) to (C), during knockdown (KD) simulations, total AdoMetDC concentration ([]) was modelled as a time-dependent variable with equal to 0.0004 to represent the 70% activity down-regulation within 2 days of induction; during knockout (KO) simulations, the factor representing the percent of the complex AdoMetDC|prozyme taking up the total enzyme AdoMetDC is set to zero to represent full prozyme removal. In (D), MDL effects on Put and Spd dynamics were plotted. During the simulation, total enzyme concentration of AdoMetDC was modelled using a exponential decay function with set to 0.07 to mimic a 98% knockdown within 1 hour of induction as specified experimentally. Error bars are presented where appropriate data was available in the original papers.

Figure 6. Time-series simulation of TSHSyn inhibition on level compared with observed values.

Lines without symbols, model predictions; lines with symbols, experimental observations from . During the simulation, the maximum velocity of TSHSyn was modelled as a time-dependent variable using the exponential decay function with set to 0.00045. Percentage changes of Put and at discrete time points over a simulated time span of 8 days were extracted from and normalised to the basal conditions of respective metabolites. For Put, only the percentage change at the end of the simulated time span was shown, since percentage changes for this metabolite over other time points were not reported in .

Figure 7. Orn dynamics over 2 days after ODC activity depression.

During the simulation, the maximum velocity of ODC was modelled as a time-independent constant by multiplying the normal value by the percentage amount.

Figure 8. Studies of changes in concentration under different perturbation scenarios.

In (A) time-series concentration values are calculated over a simulated time span of 5 days subject to a 90% decrease in individual enzyme velocities. A 90% knockdown of AdoMetDC enzyme concentration and a 90% prozyme knockdown were found to follow a similar pattern of dynamics, and only prozyme inhibition is shown. In (B) concentration values at the end of the simulated time span (5 days) are calculated subject to various degrees of knockdown (KD) for individual enzymes. In both figures, the percentage of concentration under perturbed () and normal () conditions is plotted. In all cases, the maximum velocity of each enzyme is a time-dependent variable subject to specific inhibition within 24 hours of simulation.

Figure 9. Studies of combination chemotherapeutic regimens.

Percentage of concentration under perturbed (, over a simulated time span of 5 days) and normal () conditions. In individual model simulations (A) and (B), a 10% enzyme knockdown (KD) of ODC and prozyme is applied in conjunction with down-regulation of other key pathway enzymes and the simulation results from individual and combined perturbations are compared. In (C) and (D), the inhibitory effects on were examined for combinations of medium to strong depression of prozyme and TSHSyn, respectively, with different levels of knockdowns of other enzymes. In all cases, the maximum velocity of each enzyme is a time-dependent variable subject to specific inhibition within 24 hours.