DFBSIM is numerical integration scheme for large-scale systems of differential equations encountered in dynamic flux balance analysis (dFBA). It provides efficient simulation of multi-culture of microbial species based on genome-scale metabolic network reconstructions for analysis, control and optimization of biochemical processes. As such, it generates dynamic predictions of substrate, biomass, and product concentrations for growth in batch or fed-batch cultures. dFBA provides a structured model of a biochemical process, where the reaction pathways within the microorganism change depending on the environmental conditions, which is effectively represented by changes in the functional dependency on the substrate concentrations.
By reformulating the dynamic flux balance model as hybrid differential algebraic equations, the embedded flux balance model, which is a linear program (LP), only has to be solved when the structure of the optimal flux distribution changes, which is a small number compared to the number of integration steps per simulation. Hierarchical optimization is required when the time evolution of some metabolic product should be predicted. Hierarchical optimization is implemented in DFBSIM to determine elements of the optimal flux distribution uniquely with minimal additional cost. The implementation makes use of the strong similarity between the primary, e.g. maximizing growth rate, and the secondary optimization problem and their respective optimal basis.
The code that has been developed to integrate general large-scale dFBA systems efficiently and accurately is a numerical integrator for a dynamical system with an embedded LP, where the dynamic states determine the right-hand side of the equality constraints and is called DSL48LPR. It employs DAEPACK component DSL48E. More information about dynamical system with an embedded LP and DSL48LPR can be found here.