Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Microbiology's N-body problem: How should we estimate the rate of metabolite exchange in spatially structured populations?
Robert J Clegg, Rosemary J Dyson, Jan-Ulrich Kreft

Last modified: 2014-06-09


No microbe is an island: exchange of metabolites between microbes is crucial to nutrient cycles in both natural and man-made environments. However, even when it is experimentally possible, directly measuring or modelling the rate of exchange within observed populations is difficult. In a sense, this is comparable to the N-body problem of planetary motion, where predicting the long-term effects of gravitational pull between heavenly bodies becomes increasingly difficult the more numerous they are.

As metabolites are often transported by diffusion, reducing the physical distance between partners can greatly increase the rate of exchange and so also increase the productivity of the population. For example, degradation of organic matter to methane in lake sediments and sewage treatment plants often requires rapid transfer of acetate or hydrogen from producers to consumers. Conversely, separating cells that inhibit others may be most beneficial. Cyanobacteria are globally important species in the nitrogen and carbon cycles, but the oxygen released by photosynthesis inhibits nitrogen fixation. The two processes are performed by different cell types, which need to exchange the goods they produce without impairing nitrogen-fixers.

Ecologists and engineers interested in this problem have estimated the rate of metabolite exchange between groups using the average distance between a cell of one type and its nearest neighbour of the other. This statistic is a valid estimator in the detection and classification of spatial patterns, but its reliability in estimation of exchange rate is untested.

The uncertainty in estimating rate of exchange is an issue affecting many topics in microbial ecology and biochemical engineering, and our computational approach seeks to correct this. Marked point patterns are used as a template for populations of microbes, each performing one of two tasks: producing or consuming the intermediary diffusible metabolite. The presence of this metabolite inhibits its production by the producer cells via thermodynamic constraints, so it must diffuse to consumer cells to be catabolised at a rate given by Monod kinetics.

The rate of exchange is both solved numerically, and estimated using spatial statistics such as the distance to nearest neighbour. These estimates can then be compared to the numerical solution; Preliminary results suggest that distances to nearest neighbours is a reasonable estimator, so long as it is handled appropriately and the numbers of cells performing each task is roughly equal. The overall aim of this project is to determine the most reliable statistical estimator in a scientifically rigorous manner, so that those studying these systems in the field can make predictions in confidence.


syntrophy; spatial heterogeneity; statistics