The Physics of Spatial Differentiation in Living Systems

Abstract

Living systems exhibit spatial differentiation at every scale, from the functional compartments within cells to the biogeography of multi-species communities. In this dissertation, we investigate the emergence and consequences of spatial differentiation in two contexts: biomolecular condensates in eukaryotic cells (Chapter 1) and resource competition between territorial communities (Chapter 2). We begin at the intracellular level, where eukaryotes are able to organize important biomolecules and tasks into condensates which lack a membrane. Many such condensates are liquid droplets which phase separate due to interactions between their component molecules, but it remains difficult to bridge spatial scales and determine how molecular properties shape condensate properties. In Chapter 1, we study two important aspects of condensates' molecular architecture: 1) the role of specific interactions which are one-to-one and saturating, and 2) the sequence of interaction motifs, which is under the control of evolution and regulation. Using Monte Carlo simulations and mean-field theory, we show that the motif sequence has a dramatic effect on the thermodynamic and material properties of biomolecular condensates. Sequences with larger domains of repeated motifs phase separate under a much wider range of conditions, and the resulting condensates are much more viscous and solid-like. We find that the sequence primarily acts through the entropy of intramolecular interactions, a new mechanism for the biological control of phase separation. Having shown how spatial differentiation emerges at the intracellular level, we zoom out to the ecological level to understand how spatial structure shapes biodiversity and population dynamics. Many important ecosystems are comprised of populations which compete for both territory and diffusing resources (e.g. bacterial biofilms, terrestrial plants, coral and mussels). How diverse will such an ecosystem be, compared to a well-mixed system with the same competitors but no spatial organization? Using a model that couples mechanistic interactions to biophysical constraints, we unexpectedly find that space reduces biodiversity but renders it more robust to differences in intrinsic metabolic capacity. Finally, we conclude by asking whether these two disparate case studies offer any general lessons for theorists grappling with space and difference in biology.