Minimizing the number of optimizations for efficient community dynamic flux balance analysis

Abstract

Dynamic flux balance analysis uses a quasi-steady state assumption to calculate an organism's metabolic activity at each time-step of a dynamic simulation, using the well-know technique of flux balance analysis. For microbial communities, this calculation is especially costly and involves solving a linear constrained optimization problem for each member of the community at each time step. However, this is unnecessary and inefficient, as prior solutions can be used to inform future time steps.Here, we show that a basis for the space of internal fluxes can be chosen for each microbe in a community and this basis can be used to simulate forward by solving a relatively inexpensive system of linear equations at most time steps, instead of the full optimization problem. Using our method, we can use this solution as long as the resulting metabolic activity remains within the optimization problem's constraints (i.e. the solution remains feasible). As the solution becomes infeasible, it first becomes a feasible but degenerate solution to the optimization problem, and we can solve a different but related optimization problem to choose an appropriate basis to continue forward simulation. We show using an eight species community that this is an efficient and robust method for computing dynamic flux balance analysis simulations, and so is capable of simulating communities of organisms. We demonstrate that the method gives an approximately 85% speed-up per organism over the standard and widely used method. Our method has been implemented in the Python language and source code is available at https://github.com/jdbrunner/surfin_fba and in the Python Package Index (PyPI) as surfinFBA. Author summary.The standard method in the field for dynamic flux balance analysis carries a prohibitively high computational cost because it requires solving a linear optimization problem at each time-step. We have developed a novel method for producing solutions to this dynamical system which greatly reduces the number of optimization problems that must be solved. We prove mathematically that we can solve the optimization problem once and simulate the system forward as an ordinary differential equation for some time interval, and solutions to this ODE provide solutions to the optimization problem. Eventually, the system reaches an easily checkable condition which implies that another optimization problem must be solved. We compare our method with the classical method to validate that it provides equivalent solutions in much lower computational time.March 7, 2020 1/18 Introduction. 1 Microbial communities and human health. 2 The makeup of microbial communities is often complex, dynamic, and hard to predict. 3 However, microbial community structure has a profound effect on human health and 4 disease [1-7]. These two facts have lead to significant interest in mathematical models 5 which can predict relative abundances among microbes in a community. Recently, 6 advances in genetic sequencing have allowed the creation of genome-scale models 7 (GEMs) wh...

Experimental and computational approaches to unravel microbial community assembly

“…The former present significant predictive potential but are limited to simpler systems (e.g. Dynamic Flux Balance Analysis [85] , [86] ), while the latter provide rather qualitative insights but can be used to model complex communities (e.g. [87] , [88] ).…”

Steady state flux balance analysis game

“…Dynamic FBA (DFBA) [26] models the dynamics of the biomasses by a Lotka-Volterra model with the growth rates given by the rates of the biomass reactions as calculated by FBA at that point in time. DFBA has been extended to model cooperative community dynamics [46], and a number of efficient implementations have been developed [5, 21]. We model the dynamics of microbial communities by assuming that the instantaneous growth rates for all species are given by a generalized Nash equilibrium for the FBA problem.…”

“…Comparison of metabolite utilization and internal reaction fluxes for the second stable steady state in the right-hand part of figure(2), the third stable steady state from figure(2), and the SteadyCom steady state. The first column lists which of the four metabolites that the species are auxotrophic for are fully utilized i.e.x 1 R c 1 [j]ν ex 1 + x 2 R c 2 [j]ν ex 2 + x 3 R c 3 [j]ν ex 3 + x 4 R c 4…”