On the effects of alternative optima in context-specific metabolic model predictions
Fig 2
Pseudocode for RegrExAOS and details of the treatment of reversible reactions.
(A) RegrExAOS first finds the minimum, vmin, and maximum, vmax, allowable flux values through Flux Variability Analysis (FVA, see Methods) for each reaction in the GEM. It then repeats the following procedure until obtaining the required number of samples (nsamples). (i) Generate a random flux distribution, vrand, in which each random flux value remains within the feasible range obtained before. (ii) Change the sign of the negative entries in vrand and of the corresponding columns in the stoichiometric matrix. (iii) Generate an alternative optimal flux distribution, vAO, that is closest to vrand through OP2, which takes the modified stoichiometric matrix, S’, vmin, vmax, vrand, the previous optimum RegrEx solution, vopt and the data vector, d, as arguments. (iv) Change the sign of the entries in vAO corresponding to the original negative entries in vrand. (B) In RegrExAOS, reversible reactions are split into the forward and backward directions. The entries corresponding to reversible reactions in vrand are always non-negative (since the sign is changed if negative), and fall in the range of the corresponding forward direction (since the sign of the associated column in S is changed accordingly). Hence RegrExAOS can choose between δ+for−δ-for, quantifying the distance between vrand and an optimal flux value in the forward direction, or δback, which measures the distance between vrand and an optimal flux value in the backward direction. At the end of the optimization process (OP2), RegrExAOS selects the direction of each reversible reaction that minimizes the overall distance to vrand.