Team:Johns Hopkins/Modeling/VitC

Vitamin C

Models

Graphical model

LBS model

Our full LBS model includes both gene expression and the metabolic pathway.

The full pathway+expression l-ascorbate model in LBS

We developed a simplified LBS model to examine the metabolic pathway in isolation from gene expression.

The l-ascorbate model in LBS

Matlab model

We chose to port our model to Matlab's SimBiology Toolbox in order to facilitate complex analysis. To speed computations, this model has been simplified by taking enzyme concentrations as constant, assuming that the gene expression component of our system has reached a steady state.

The full l-ascorbate model as exported from the Matlab SimBiology Toolbox

Note: all parameters for this model listed here.

Sensitivity Analysis

The model is equally sensitive to small changes in all k_cat values (the maximum turnover rate of saturated enzyme). This is reasonable, since our pathway is fairly simplistic and linear. A decrease in any enzyme's turnover rate will cause a bottleneck. We notice, however, that the model is significantly less sensitive to the mannose epimerase inhibition binding constant, k_i. Even though k_i is an inhibition constant, the corresponding sensitivity \[d[l-ascorbate]/d[k_{i}]\] is positive, since increasing k_i means that more inhibitor is requires to yield the same degree of inhibition, much like how increasing k_m means that more substrate is needed to drive the equilibrium towards the enzyme-substrate complex. The GDP clearance rate also has little effect on the model, suggesting that the pathway is producing a low enough amount of GDP that it can be cleared before it can inhibit the epimerase. Alternatively, it might just suggest that whatever the amount of GDP present, the effect on mannose epimerase is minor. In either case, the parameter sensitivities suggest that inhibition is of little importance in this model, at least at the substrate influx and enzyme production levels we are working with.

Optimization

For a discussion of the optimization techniques used and the nitrogen allocation analysis which follows, see our optimization techniques.

Pareto frontier

Nitrogen allocation

Marginal nitrogen allocation

Fractional marginal nitrogen allocation