Mathematical Modelling of Polyamine Metabolism in Bloodstream-Form Trypanosoma brucei: An Application to Drug Target Identification

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.


Part 1. Modelling the ODC-catalyzed reaction reversibly
One of the refinements we made during the model building procedure was to represent the ODC-catalyzed reaction with the reversible rate law, as defined in Equation 1 in the section of Materials and Methods in the main text (also given below).
In this final model (Model V5 in Supplementary Table S2), we used the best set of parameter estimates obtained from solving Model V4, based on which we analytically derived the newly-added parametersthe equilibrium constant K ODC eq and the half-saturation constant K ODC mP ut . Due to the lack of information on these two parameters, we assumed the half-saturation constant K ODC mP ut to hold the same value as the known parameter K ODC mOrn and we analytically derived the equilibrium constant K ODC eq against the experimental observations of AdoMetDC RNAi induction and prozyme knockout.
We illustrate in Figure ST1 the effect of different values of parameter K ODC eq on the dynamic behaviour of Put in the cases of AdoMetDC RNAi induction and prozyme knockdown. This figure shows that our choice of K ODC eq (which was assigned the value of 5) best reflects the dynamics and exact concentration values of Put under the perturbed conditions and when compared with simulation results from modelling ODC irreversibly, Put dynamics could reach steady state gradually over time. When AdoMetDC or prozyme were inhibited, direct downstream metabolites of the ODC-catalyzed reaction -Spd and T SH tot , were not different from the model simulations where ODC was described with the irreversible rate law, in terms of both the basal condition and dynamic behaviours (see Figure ST2), which is also the case under all other perturbed conditions considered in the manuscript. The similar effect on model behaviours exerted by varying K ODC eq was also seen on parameter K ODC mP ut (varied between 0.1 to 100 fold of the assumed value, 350 µM). We also found that there is no obvious difference in model behaviour when the term representing production inhibition by Put is present or not, which is most likely due to the weak inhibitory effect exerted by Put.

Part 2. The postulated regulatory correlation of enzyme SpdS on ODC
We postulated in the main text that the regulation of enzyme SpdS on ODC is helpful for avoiding Put accumulation.
The regulation of SpdS on ODC is reflected by the term e (−λ SpdS · t) as defined in Equation ST1. In the model where the regulatory effect is not considered, parameter λ SpdS is set to zero and the maximum velocity of ODC becomes time-invariant, whereas the model having this effect enabled allows the maximum velocity of ODC to vary with respect to changes in SpdS activity (in this case a value of 0.0016 is assigned to parameter λ SpdS as used in the main text).
We examined this postulation by comparing Put dynamics (over a simulated time span of 6 days) with ODC modelled reversibly against the situation where ODC is modelled irreversibly, which is further compared in the presence and absence of the postulated regulation of SpdS on ODC. Figure ST3 shows that, in the absence of the postulated regulation, the reversible ODC kinetics helped bring down Put level in response to SpdS knockdown compared with the result from the irreversible kinetics; however, the resulting concentration of Put still increased nearly 20 fold of the control level. These comparison results imply that the postulated regulation of SpdS on ODC is still necessary in preventing Put accumulation regardless and the conclusion remains the same with different values of the equilibrium constant.