Figure 2

Algorithm for weighted least-square parameter estimation. OpenFLUX uses MATLAB's FMINCON to minimize the residual error () between the experimental MIDs () and the simulated MIDs (), by optimizing the free fluxes (), which are subjected to lower and upper boundary value constraints. is weighted by the variance matrix (D). The inverse compactification function is used to transform reverse flux from a numerical parameter (v^{←, [0,1]}) into a physical flux parameter (v^←). The null-space matrix (Ns) is then used to calculate the flux vector () from the free fluxes (). Finally, is calculated using and known MIDs of the input substrates (). FMINCON terminates when a local minimum is found, revealing the optimum free fluxes.