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

Nicholas Chia,Pedro Mendes,James D Brunner

doi:10.1371/journal.pcbi.1007786

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-known 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. We can use this solution as long as the resulting metabolic activity remains within the optimization problem's constraints (i.e. the solution to the linear system of equations remains a feasible to the linear program). 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 demonstrate the efficiency and robustness of our method by comparing with currently used methods on a four species community, and show that our method requires at least 91% fewer optimizations to be solved. For reproducibility, we prototyped the method using Python. Source code is available at https://github.com/jdbrunner/surfin_fba.

Highlights

Microbial communities and human healthThe makeup of microbial communities is often complex, dynamic, and hard to predict
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
Advances in genetic sequencing have allowed the creation of genome-scale models (GEMs) that reflect the internal network of cellular metabolism, and can be used to predict metabolite use and production [17,18,19]

Summary

Introduction

Microbial communities and human healthThe makeup of microbial communities is often complex, dynamic, and hard to predict. Advances in genetic sequencing have allowed the creation of genome-scale models (GEMs) that reflect the internal network of cellular metabolism, and can be used to predict metabolite use and production [17,18,19] This technique can be extended to microbial community modeling by combining GEMs of different species. One of the most basic COBRA methods, called flux balance analysis (FBA) optimizes some combination of reaction fluxes ∑γivi which correspond to increased cellular biomass, subject to the constraint that the cell’s internal metabolism is at equilibrium: ð1Þ where Γ is the stoichiometric matrix, a matrix describing the stoichiometry of the metabolic model This optimization is chosen because it reflects the optimization carried out by nature through evolution [18]. This reflects the assumption that the cell will approach an internal chemical equilibrium

Methods

Results

Conclusion