Multi-objective optimization of enzyme manipulations in metabolic networks considering resilience effects

Abstract

Background: Improving the synthesis rate of desired metabolites in metabolic systems is one of the main tasks in metabolic engineering. In the last decade, metabolic engineering approaches based on the mathematical optimization have been used extensively for the analysis and manipulation of metabolic networks. Experimental evidence shows that mutants reflect resilience phenomena against gene alterations. Although researchers have published many studies on the design of metabolic systems based on kinetic models and optimization strategies, almost no studies discuss the multi-objective optimization problem for enzyme manipulations in metabolic networks considering resilience phenomenon.

Results: This study proposes a generalized fuzzy multi-objective optimization approach to formulate the enzyme intervention problem for metabolic networks considering resilience phenomena and cell viability. This approach is a general framework that can be applied to any metabolic networks to investigate the influence of resilience phenomena on gene intervention strategies and maximum target synthesis rates. This study evaluates the performance of the proposed approach by applying it to two metabolic systems: S. cerevisiae and E. coli. Results show that the maximum synthesis rates of target products by genetic interventions are always over-estimated in metabolic networks that do not consider the resilience effects.

Conclusions: Considering the resilience phenomena in metabolic networks can improve the predictions of gene intervention and maximum synthesis rates in metabolic engineering. The proposed generalized fuzzy multi-objective optimization approach has the potential to be a good and practical framework in the design of metabolic networks.

Figure 1

Simple metabolic network of S. cerevisiae for ethanol production. The dashed line with an arrowhead and with a terminal bar at one end mean inhibition and activation, respectively. The optimal changed ratios of the metabolites and the optimal improved activity ratios for modulated enzymes HXT and TDH and modulated enzymes HXT and PFK are shown in red numbers and blue numbers, respectively.

Figure 2

The Pareto front and feasible solutions. The Pareto front and feasible solutions for the primal optimization problem (red data points) and the fuzzy optimization problem (green data points) obtained by the MIHDE method.

Figure 3

Percentage of over-estimation productivity for different perturbation region. The percentage of over-estimation productivity for different scale perturbation. The perturbation region for each enzyme is selected as R-fold below and above its basal value, i.e., $\left[{\gamma }_{e_i}^{LB},{\gamma }_{e_i}^{UB}\right]=\left[1∕R,R\right]$.

Figure 4

Central carbon metabolic network of Escherichia coli. The light blue boxes are metabolites and the yellow boxes are amino acid synthesis subsystems. Red circles with a number inside are used for connection.

Figure 5

Membership functions for fuzzy objective function, fuzzy equal objective, and fuzzy inequality constraint. Membership functions for fuzzy maximization objective function (blue line), fuzzy equality function (red line), and fuzzy inequality function (green line).