Flux Distribution in Bacillus subtilis: Inspection on Plurality of Optimal Solutions

Linear programming problems with alternate solutions are challenging due to the choice of multiple strategiesresulting in the same optimal value of the objective function. However, searching for these solutions is atedious task, especially when using mixed integer linear programming (MILP), as previously applied tometabolic models. Therefore, judgment on plurality of optimal metabolic flux distributions (solutions) a priorito applying MILP approach could prevent unnecessary computations. In this work for the first time, thereduced cost coefficients for the non-basic variables in a current solution of a metabolic model were utilized toinspect the possibility of multiple optimal flux distributions. If there exists at least one non-basic variablewith zero reduced cost coefficient, multiplicity of optimal solution may occur where MILP can be used tofind these solutions. This approach was implemented on a metabolic network of Bacillus subtilis aiming toreduce the cell energy requirement. Solving the model at fixed specific growth rate of 0.4 1/h resulted in minimum energy requirement of 12.67 mmol/g-h. Inspection of reduced cost coefficients showed that sixnon-basic variables had zero reduced cost coefficients at current solution, which shows that there can existmultiple optimal solutions. Subsequently, by applying MILP, five optimal flux distributions at minimized energy requirement were identified, among which one showing no acid production and minimum glucoseconsumption rate was selected as the superior solution.