k-OptForce: Integrating Kinetics with Flux Balance Analysis for Strain Design

Abstract

Computational strain design protocols aim at the system-wide identification of intervention strategies for the enhanced production of biochemicals in microorganisms. Existing approaches relying solely on stoichiometry and rudimentary constraint-based regulation overlook the effects of metabolite concentrations and substrate-level enzyme regulation while identifying metabolic interventions. In this paper, we introduce k-OptForce, which integrates the available kinetic descriptions of metabolic steps with stoichiometric models to sharpen the prediction of intervention strategies for improving the bio-production of a chemical of interest. It enables identification of a minimal set of interventions comprised of both enzymatic parameter changes (for reactions with available kinetics) and reaction flux changes (for reactions with only stoichiometric information). Application of k-OptForce to the overproduction of L-serine in E. coli and triacetic acid lactone (TAL) in S. cerevisiae revealed that the identified interventions tend to cause less dramatic rearrangements of the flux distribution so as not to violate concentration bounds. In some cases the incorporation of kinetic information leads to the need for additional interventions as kinetic expressions render stoichiometry-only derived interventions infeasible by violating concentration bounds, whereas in other cases the kinetic expressions impart flux changes that favor the overproduction of the target product thereby requiring fewer direct interventions. A sensitivity analysis on metabolite concentrations shows that the required number of interventions can be significantly affected by changing the imposed bounds on metabolite concentrations. Furthermore, k-OptForce was capable of finding non-intuitive interventions aiming at alleviating the substrate-level inhibition of key enzymes in order to enhance the flux towards the product of interest, which cannot be captured by stoichiometry-alone analysis. This study paves the way for the integrated analysis of kinetic and stoichiometric models and enables elucidating system-wide metabolic interventions while capturing regulatory and kinetic effects.

Author Summary

Computational strain design procedures aim at assisting metabolic engineering efforts by identifying metabolic interventions leading to the targeted overproduction of a desired chemical using network models of cellular metabolism. The effect of metabolite concentrations and substrate-level enzyme regulation cannot be captured with stoichiometry-only metabolic models and analysis methods. Here, we introduce k-OptForce, an optimization-based strain design framework incorporating the mechanistic details afforded by kinetic models, whenever available, into a genome-scale stoichiometric-based modeling formalism. The resulting optimization problems pose significant computational challenges due to the bilevel nature of the formulation and the nonconvex terms in the constraints. A tractable reformulation and solution procedure is introduced for solving the optimization problems. k-OptForce uses kinetic information to (re)apportion reaction fluxes in the network by identifying interventions comprised of both direct enzymatic parameter changes (for reactions with available kinetics) and reaction flux changes (for reactions with only stoichiometric information). Our results show that the introduction of kinetic expressions can significantly alter the identified interventions compared to those identified with stoichiometry-alone analysis. In particular, additional modifications are required in some cases to avoid the violation of metabolite concentration bounds, while in other cases, the kinetic constraints yield metabolic flux distributions that favor the overproduction of the desired product thereby requiring fewer direct interventions.