Discretised Flux Balance Analysis for Reaction-Diffusion Simulation of Single-Cell Metabolism

by Yin Hoon Chew and Fabian Spill

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Metabolism comprises thousands of biochemical reactions. It is commonly modelled using Flux Balance Analysis (FBA), a method based on linear programming, because this method requires very few parameters. However, conventional FBA implicitly assumes that all enzymatic reactions are not diffusion-limited though that may not always be the case.

To enable the exploration of diffusion effects on cellular metabolism, we present a spatial method that implements FBA on a grid-based system. The method discretises a living cell into a two-dimensional grid; creates variables that represent the rates of reactions within grid elements and diffusions between grid elements; and solves the system as a single linear programming problem.

Simulations using the method suggest that factors such as cell shape, diffusion regime and spatial distribution of enzyme can influence the variability and robustness of metabolism at both single-cell and population levels. We propose the use of this method to explore how spatiotemporal organisation of compartments and molecules in cells affect cellular behaviour.

Yin Hoon Chew is a Research Fellow and Fabian Spill is a Professor of Applied Mathematics at the University of Birmingham, UK. Yin Hoon designed and implemented the method, with feedback from Fabian.

The method can simulate living cells with different shapes and heterogeneous enzyme distribution. Simulations suggest that cell shape (perimeter-to-area ratio) does not affect cellular behaviour such as biomass growth when diffusion is fast, but there is a strong effect at low diffusion.