Integrating Flux Balance Analysis into Kinetic Models to Decipher the Dynamic Metabolism of Shewanella oneidensis MR-1

Shewanella oneidensis MR-1 sequentially utilizes lactate and its waste products (pyruvate and acetate) during batch culture. To decipher MR-1 metabolism, we integrated genome-scale flux balance analysis (FBA) into a multiple-substrate Monod model to perform the dynamic flux balance analysis (dFBA). The dFBA employed a static optimization approach (SOA) by dividing the batch time into small intervals (i.e., ∼400 mini-FBAs), then the Monod model provided time-dependent inflow/outflow fluxes to constrain the mini-FBAs to profile the pseudo-steady-state fluxes in each time interval. The mini-FBAs used a dual-objective function (a weighted combination of "maximizing growth rate" and "minimizing overall flux") to capture trade-offs between optimal growth and minimal enzyme usage. By fitting the experimental data, a bi-level optimization of dFBA revealed that the optimal weight in the dual-objective function was time-dependent: the objective function was constant in the early growth stage, while the functional weight of minimal enzyme usage increased significantly when lactate became scarce. The dFBA profiled biologically meaningful dynamic MR-1 metabolisms: 1. the oxidative TCA cycle fluxes increased initially and then decreased in the late growth stage; 2. fluxes in the pentose phosphate pathway and gluconeogenesis were stable in the exponential growth period; and 3. the glyoxylate shunt was up-regulated when acetate became the main carbon source for MR-1 growth.