Multi-objective MINLP Optimization Used to Identify Theoretical Gene Knockout Strategies for E. coli Cell

G. Maria, Z. Xu and J. Sun

Abstract
Bioprocess optimization by genetically modifying the microorganism characteristics is an intensively investigated subject due to the immediate economic interest. A large variety of alternatives using elaborated experimental procedures, accompanied by in-silico cell design based on topological and dynamic models have emerged. The present study investigates the possibility of using a mixed-integer nonlinear programming (MINLP) approach to determine optimal metabolic fluxes in respect of multi-objective criteria associated to gene knockout strategies. The advantage of the proposed power-law type criterion stems from the possibility of accounting, in a simple way, for the flux nonlinear interactions and complex constraints. The combinatorial rule is included in the iterative MINLP solver, while a large number of constraints could increase the chance of obtaining a reduced set of viable gene-knockout solutions for a given metabolic network. Multiple gene deletion alternatives are thus identified, allowing a high cell growing rate with maximizing externally imposed chemical production targets. Exemplification is made for the case of designing an E. coli cell that realizes maximization of succinate production by using a reduced model from literature. Comparatively to the linear procedure that solves a combinatorial problem in a bi-level optimization approach, of dimensionality sharply increasing with the number of removed genes, the MINLP alternative considers an adjustable nonlinear influence of fluxes to the main goal, its performance being less dependent on the number of knockout genes.

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Keywords
Flux balance analysis, MINLP, gene knockout, succinate production, E. coli