Motif-pattern dependence of biomolecular phase separation driven by specific interactions.

Eukaryotic cells partition a wide variety of important materials and processes into biomolecular condensates-phase-separated droplets that lack a membrane. In addition to nonspecific electrostatic or hydrophobic interactions, phase separation also depends on specific binding motifs that link together constituent molecules. Nevertheless, few rules have been established for how these ubiquitous specific, saturating, motif-motif interactions drive phase separation. By integrating Monte Carlo simulations of lattice-polymers with mean-field theory, we show that the sequence of heterotypic binding motifs strongly affects a polymer's ability to phase separate, influencing both phase boundaries and condensate properties (e.g. viscosity and polymer diffusion). We find that sequences with large blocks of single motifs typically form more inter-polymer bonds, which promotes phase separation. Notably, the sequence of binding motifs influences phase separation primarily by determining the conformational entropy of self-bonding by single polymers. This contrasts with systems where the molecular architecture primarily affects the energy of the dense phase, providing a new entropy-based mechanism for the biological control of phase separation.

Decoding the physical principles of two-component biomolecular phase separation.

Cells possess a multiplicity of non-membrane-bound compartments, which form via liquid-liquid phase separation. These condensates assemble and dissolve as needed to enable central cellular functions. One important class of condensates is those composed of two associating polymer species that form one-to-one specific bonds. What are the physical principles that underlie phase separation in such systems? To address this question, we employed coarse-grained molecular dynamics simulations to examine how the phase boundaries depend on polymer valence, stoichiometry, and binding strength. We discovered a striking phenomenon - for sufficiently strong binding, phase separation is suppressed at rational polymer stoichiometries, which we termed the magic-ratio effect. We further developed an analytical dimer-gel theory that confirmed the magic-ratio effect and disentangled the individual roles of polymer properties in shaping the phase diagram. Our work provides new insights into the factors controlling the phase diagrams of biomolecular condensates, with implications for natural and synthetic systems.

Nutrient levels and trade-offs control diversity in a serial dilution ecosystem.

Microbial communities feature an immense diversity of species and this diversity is linked to outcomes ranging from ecosystem stability to medical prognoses. Yet the mechanisms underlying microbial diversity are under debate. While simple resource-competition models don't allow for coexistence of a large number of species, it was recently shown that metabolic trade-offs can allow unlimited diversity. Does this diversity persist with more realistic, intermittent nutrient supply? Here, we demonstrate theoretically that in serial dilution culture, metabolic trade-offs allow for high diversity. When a small amount of nutrient is supplied to each batch, the serial dilution dynamics mimic a chemostat-like steady state. If more nutrient is supplied, community diversity shifts due to an 'early-bird' effect. The interplay of this effect with different environmental factors and diversity-supporting mechanisms leads to a variety of relationships between nutrient supply and diversity, suggesting that real ecosystems may not obey a universal nutrient-diversity relationship.

In most environments, organisms compete for limited resources. The number and relative abundance of species that an ecosystem can host is referred to as 'species diversity'. The competitive-exclusion principle is a hypothesis which proposes that, in an ecosystem, competition for resources results in decreased diversity: only species best equipped to consume the available resources thrive, while their less successful competitors die off. However, many natural ecosystems foster a wide array of species despite offering relatively few resources. Researchers have proposed many competing theories to explain how this paradox can emerge, but they have mainly focused on ecosystems where nutrients are steadily supplied. By contrast, less is known about the way species diversity is maintained when nutrients are only intermittently available, for example in ecosystems that have seasons. To address this question, Erez, Lopez et al. modeled communities of bacteria in which nutrients were repeatedly added and then used up. Depending on conditions, a variety of relationships between the amount of nutrient supplied and community diversity could emerge, suggesting that ecosystems do not follow a simple, universal rule that dictates species diversity. In particular, the resulting communities displayed a higher diversity of microbes than the limit imposed by the competitive-exclusion principle. Further observations allowed Erez, Lopez et al. to suggest guiding principles for when diversity in ecosystems will be maintained or lost. In this framework, 'early-bird' species, which rapidly use a subset of the available nutrients, grow to dominate the ecosystem. Even though 'late-bird' species are more effective at consuming the remaining resources, they cannot compete with the increased sheer numbers of the 'early-birds', leading to a 'rich-get-richer' phenomenon. Oceanic plankton, arctic permafrost and many other threatened, resource-poor ecosystems across the world can dramatically influence our daily lives. Closer to home, shifts in the microbe communities that live on the surface of the human body and in the digestive system are linked to poor health. Understanding how species diversity emerges and changes will help to protect our external and internal environments.

Rigidity enhances a magic-number effect in polymer phase separation.

Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a one-to-one fashion with the binding sites of the other polymer. Biologically-motivated modeling revealed that phase separation is suppressed by a "magic-number effect" which occurs if the two polymers can form fully-bonded small oligomers by virtue of the number of binding sites in one polymer being an integer multiple of the number of binding sites of the other. Here we use lattice-model simulations and analytical calculations to show that this magic-number effect can be greatly enhanced if one of the polymer species has a rigid shape that allows for multiple distinct bonding conformations. Moreover, if one species is rigid, the effect is robust over a much greater range of relative concentrations of the two species.

Spatial ecology of territorial populations.

Many ecosystems, from vegetation to biofilms, are composed of territorial populations that compete for both nutrients and physical space. What are the implications of such spatial organization for biodiversity? To address this question, we developed and analyzed a model of territorial resource competition. In the model, all species obey trade-offs inspired by biophysical constraints on metabolism; the species occupy nonoverlapping territories, while nutrients diffuse in space. We find that the nutrient diffusion time is an important control parameter for both biodiversity and the timescale of population dynamics. Interestingly, fast nutrient diffusion allows the populations of some species to fluctuate to zero, leading to extinctions. Moreover, territorial competition spontaneously gives rise to both multistability and the Allee effect (in which a minimum population is required for survival), so that small perturbations can have major ecological effects. While the assumption of trade-offs allows for the coexistence of more species than the number of nutrients-thus violating the principle of competitive exclusion-overall biodiversity is curbed by the domination of "oligotroph" species. Importantly, in contrast to well-mixed models, spatial structure renders diversity robust to inequalities in metabolic trade-offs. Our results suggest that territorial ecosystems can display high biodiversity and rich dynamics simply due to competition for resources in a spatial community.