(5m) Global Optimization in Systems Biology

During the last decade, there have been major advances in technologies for acquiring biological data and engineering desired features into organisms. Concurrently, the gap between data collection and implementation motivated many mathematical and computational approaches in analyzing biological data, inferring useful hypotheses, and systematically (re-)designing biochemical networks. Among numerous such mathematical and computational frameworks, optimization approaches based on mathematical programming can provide the most comprehensive coverage in solving biology motivated problems. This optimization approach became feasible initially due to the development of efficient local optimization algorithms, and can become an even more important approach now that rigorous global optimization techniques have been developed. This presentation reviews selected problems related to systems biology that are addressed by the authors using global optimization.

Metabolic networks are often redesigned for specific purposes such as productivity of microorganisms through steady-state optimization formulations. One of the major considerations in designing a dynamic system is stability. The stability is determined through the computation of the eigenvalues of Jacobian matrix. While it is straightforward to analyze the stability of a given system, the challenge is to redesign a metabolic network in a way that guarantees that the system will be stable around the new steady state. For this purpose, we propose to model metabolic networks through classical optimization formulations with an additional constraint to enforce stability within a prespecified neighborhood of the solution point. The proposed formulation is a bilevel optimization problem that is very difficult to solve. We develop suitable global optimization algorithms to solve this problem after transforming it to a semi-infinite optimization problem. This approach is demonstrated with a tryptophan biosynthesis problem in bacteria.

Metabolic fluxes are the key descriptor of cell's physiology, and metabolic flux analysis infers intracellular fluxes from isotopic experiments. A key question in this analysis is if the flux distribution can be uniquely determined from the measurements. While this identifiability question can be analyzed by some established methods, the challenge is to design the isotopic experiments that is capable of yielding a unique flux distribution. We propose to use incidence structure analysis to enforce the flux identifiability while designing isotopic experiments. This results in a large scale integer linear programming problem, and we exlpoit its structure to efficiently solve it. The proposed methodology was applied to both stationary and isotopically dynamic MFA experiments for E. coli strain capable of producing 1,3 propanediol to suggest critical measurements that are essential for the flux identifiability.