Reproducibility, stochasticity, and geometry in a lattice of cross-feeding microbial cells

Abstract

Bacteria often exchange metabolites to achieve together what they cannot alone. Chemically-exchanging cells can survive, even as metabolic specialists in poor environments; perform decentralized chemistry; and regulate phenotypic heterogeneity. Connecting the microscopic features of transport and physiology–often stochastic and heterogeneous–with reproducible, large-scale behaviors is key to advancing microbial ecology. Here we investigate the growth of cross-feeding strains at single-cell, stochastic resolution. Using this framework, we reanalyze recently-published microscopy data on two strains of E. coli that leak an amino acid the other needs to grow. These cells thus participate in a spatially-localized mutualism. Earlier work has reported that in such a close-packed setting, a cell's mean growth rate increases with the fraction of cells of complementary type within a neighborhood of a few cell lengths. Underneath this average behavior, we find that cells grow at rates with pronounced variability over time. Part of this variability is "intrinsic;" part is registrable to the turnover of a cell's microenvironment. We study how a cell's variability scales with its typical growth rate, geometric context, and biophysical parameters. While precise trajectories of cells in growth rate (or space) are often noisy and contingent, many display canonical regularities. We reckon with these patterns, and strive to link single-cell dynamics to emergent geometric ordering in microcolonies, from the lens of simple models of timescales, lengthscales, and noise under cross-feeding. This analysis helps dissect how simple, ubiquitous forces in consortia–coupled growth, diffusion, and variability–conspire to shape complex assemblies.

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