(437f) Metabolic Pathways Optimization Using Stochastic Programming Models

In this work is presented the mathematic development of Metabolic Pathways Optimization considered under uncertainty. For this, it is necessary to reformulate the metabolic pathway representation in the S-system. It is proposed to model Metabolic Pathways Optimization as a Two-Stage Stochastic Linear Program with recourse (SLPwR). The first stage consists in an integer program, which includes all constraints related to binary variables due to regulatory loops and manipulated external parameters. After solving the first stage program, the metabolic pathway structure is defined, as well as the regulatory loops existence and the modified external parameters. In the second stage are included all the constraints for continuous variables. Kinetic coefficients for metabolic concentrations are considered the parameters under uncertainty. The case studies are solved with an implementation of the Stochastic Decomposition algorithm (SD) and it is used the Hammersley Sequence Sampling (HHS) to generate random numbers. Using the same decomposition as the one used in the implementation of the stochastic decomposition algorithm, it is proposed an alternative method to solve the Metabolic Pathways Optimization, which consist in solving the deterministic equivalent of the stochastic program. The obtained results show differences in metabolic structures and objective function values between deterministic and stochastic solutions.

Key words: Metabolic Pathways, Optimization, SLPwR, Stochastic Programming