dfba: Software for efficient simulation of dynamic flux-balance analysis models in Python

Flux-balance analysis (FBA) is a computational method based on linear programming (LP) that has had enormous success modeling the metabolic behaviour of organisms and cellular systems existing in steady state with their environment (Orth, Thiele, & Palsson, 2010; Varma & Palsson, 1994). Representing the corresponding biological model as an LP problem means that FBA can be used to study metabolism at genome-scale. Unfortunately, the underlying assumption of an unchanging environment means that FBA is not immediately applicable to systems with dynamics where, for example, environmental conditions may vary in time. Extensions of FBA, including dynamic FBA (DFBA)(Mahadevan, Edwards, & Doyle, 2002), have therefore been developed in order to accommodate temporal dynamics into the framework of genome-scale metabolic modeling.
Although DFBA is well-defined mathematically as an LP problem embedded in a system of ordinary differential equations (ODEs), numerical simulation of DFBA models proves particularly challenging (as described in Harwood, Höffner, & Barton (2016)). Consequently, Harwood et al.(2016) proposed an algorithm for efficiently simulating DFBA models based on reformulating the ODE system as a differential algebraic equation (DAE) with root detection and representing solutions of the LP problem using an optimal basis formulation. An initial implementation of this algorithm has been provided in the software package DFBAlab (Gomez, Höffner, & Barton, 2014) written in MATLAB and using commercial LP solvers.