###### Sensitivity Analysis

Sensitivity Analysis (SA) tries to correlate the uncertainty of the output with the variation of input conditions; in particular, the goal is to elucidate parameters that mostly influence the output of the model. This step has a twofold implication; from a biological point of view, it is important to understand the most important parts of our pathway, whereas, from a computational point of view, the identification of key parameters permits the reduction of the free variables in the system and, consequently, reduces the number of possible scenario to check (the search landscape).

In our analysis, we represent the this as \[d[vitamin]/d[parameter_i]\] We normalize these sensitivities in two ways. First, we non-dimensionalize them by dividing by the vitamin concentration and multiplying by the starting value of the parameter. Then we obtain relative sensitivities by scaling them so the maximum sensitivity is 1.

We noticed that sensitivity to the Michaelis-Menten binding constant k_{m} is nearly zero in all pathways. We can interpret this as meaning the substrate concentration is high enough to saturate the enzyme at each step of the pathway. V_{max}, which is the product of k_{cat}, and the enzyme concentration, controls the reaction rate. Thus in our analyses we show the sensitivities with respect to k_{cat}.