Abstract
Biofuel is a powerful energy source in the near future. How to produce biofuel efficiently is a sustaining challenge. In conventional studies, many engineers focused on the recombination of genes from different organisms to design the biofuel productivity and yield. However, the stochastic behaviors from random systemic switching, time-varying process delay, intrinsic molecular fluctuations, extrinsic noises and uncertain initial conditions are all affect the metabolic pathway. In this situation, a biofuel metabolic pathway in vivo can be modeled as a nonlinear Markovian jumping process. In this study, we proposed a fuzzy-based stochastic game theory approach method with GA-based design algorithm to engineer a metabolic pathway to achieve a desired yield despite stochastic behaviors. Here, the external noises and uncertainties of initial conditions are considered to be a player to maximize the deterioration as a worst-case effect on the regulation performance, while the design parameters via existing promoter libraries and datasheets are considered to be the other player to improve the regulation performance by minimizing the worst-case effect under random jumps of kinetic parameters, intrinsic fluctuations and process delays in a Markovian jumping system. Avoiding to solving the Hamilton-Jacobi inequality for the nonlinear stochastic game design problem, we solved an equivalent Linear Matrix Inequalities (LMIs)-constrained optimization problem via the help of T-S fuzzy interpolation method and Lyapunov-Krasovskii functional theory. Therefore, the robust metabolic engineering design could be easily and efficiently achieved. Our method could be applied to the progress of other metabolic engineerings like the mass production of medicinal metabolites e.g. insulin and so on.