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A method for tackling primal multiplicity of solutions of dynamic flux balance models

Highlights•A weighted primal-dual method is used to select a specific solution for primal multiplicity issue of linear programming problems•The method is data-driven without assumption of prior knowledge of the strain and can fit results of experiments well•The uniqueness, pointwise convergence, and continuity properties of the solution are proved•The method was used to model an industrial bacterial culture for vaccine manufacturingAbstractA method is presented to tackle primal multiplicity of Dynamic flux balance analysis (DFBA) which is a Linear Programming (LP) based modeling approach that assumes that the cell distributes fluxes such as to maximize a specific biological objective. When the LP problem has multiple optima, the LP solvers usually only report the first optimum that it is reached which may not fit well the experimental data. To tackle this primal multiplicity problem, the weighted primal-dual method with auxiliary parameters is used to calculate a unique time trajectory for a given set of initial conditions. Through tuning of these auxiliary parameters, a unique optimal solution can be obtained and calibrated to fit available experimental data. Beyond its capability to tackle multiplicity, the algorithm is shown to significantly improve the prediction of some metabolites in a case study of the fed-batch fermentation of Bordetella pertussis.

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