Flux distribution in Bacillus subtilis: inspection on plurality of optimal solutions

Document Type : Research Paper


Biotechnology Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, P.O. Box 16846-13114, Tehran, I.R. Iran.


Linear programming problems with alternate solutions are challenging due to the choice of multiple strategies
resulting in the same optimal value of the objective function. However, searching for these solutions is a
tedious task, especially when using mixed integer linear programming (MILP), as previously applied to
metabolic models. Therefore, judgment on plurality of optimal metabolic flux distributions (solutions) a priori
to applying MILP approach could prevent unnecessary computations. In this work for the first time, the
reduced cost coefficients for the non-basic variables in a current solution of a metabolic model were utilized to
inspect the possibility of multiple optimal flux distributions. If there exists at least one non-basic variable
with zero reduced cost coefficient, multiplicity of optimal solution may occur where MILP can be used to
find these solutions. This approach was implemented on a metabolic network of Bacillus subtilis aiming to
reduce 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 six
non-basic variables had zero reduced cost coefficients at current solution, which shows that there can exist
multiple 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 glucose
consumption rate was selected as the superior solution.