DFBA-LQR: An Optimal Control Approach to Flux Balance Analysis

Systems biology is becoming an emerging field, as systems science is demonstrated as an essential tool in untangling biocomplexity. While various steady-state-based methods have been developed for study of metabolic networks, the study of the network dynamics is a less explored area, as it is inherently related to the regulatory network. The difficulty of regulatory network inference opens up the possibility of employing control techniques and methods for analysis of metabolic networks. In this work, the potential for application of optimal control theory to metabolic control problems is investigated. Considering that the regulatory network in essence is a cascade control structure, the proposed modeling approach relies on the postulate that evolution is a genetic optimization scheme leading to “optimal” regulatory networks. Thus the approach utilizes a modified linear quadratic regulator formulation to evaluate the optimal regulatory network for a given flux model. Utilizing a homeostasis-type objective, the proposed dynamic flux balance analysis with linear quadratic regulator (DFBA-LQR) approach enables constructing dynamic flux balance analysis models and produces analytical descriptions of the responses of the metabolic fluxes to disturbances. The analytical description can also be used to calculate the flux control coefficients and linearized reaction kinetics for the system. The application potential of the approach is demonstrated by a sample problem of modeling of lipid accumulation in rat hepatocytes cultures.