FIGURE 1.

Algorithm for boxing in solution space with parallelepiped and generating uniform random samples. A simple flux split was used as an example to demonstrate how the Monte Carlo sampling procedure works (A). The two-dimensional null space is constrained by the V_max planes corresponding to the three reactions in the network (B). Once the null space is capped off by the reaction V_max values, combinations choosing two of the three sets of parallel constraints leads to forming three potential parallelepipeds (C). The smallest of these parallelepipeds is chosen and uniform random points within the parallelepiped are generated (D) based on uniform weightings on the basis vectors defining the parallelepiped (shown as black arrows). Points within the solution space are kept and those that fall out of the solution space are discarded. The fraction of the points generated inside the parallelepiped that fall within the solution space is called the “hit fraction.” The hit fraction multiplied by the volume of the parallelepiped yields the volume of the solution space. Probability distributions for each of the three fluxes are calculated from the set of points within the solution space (D).