Noise driven phase transitions in eco-evolutionary systems.

In complex ecosystems such as microbial communities, there is constant ecological and evolutionary feedback between the residing species and the environment occurring on concurrent timescales. Species respond and adapt to their surroundings by modifying their phenotypic traits, which in turn alters their environment and the resources available. To study this interplay between ecological and evolutionary mechanisms, we develop a consumer-resource model that incorporates phenotypic mutations. In the absence of noise, we find that phase transitions require finely-tuned interaction kernels. Additionally, we quantify the effects of noise on frequency dependent selection by defining a time-integrated mutation current, which accounts for the rate at which mutations and speciation occurs. We find three distinct phases: homogeneous, patterned, and patterned traveling waves. The last phase represents one way in which co-evolution of species can happen in a fluctuating environment. Our results highlight the principal roles that noise and non-reciprocal interactions between resources and consumers play in phase transitions within eco-evolutionary systems.

Effects of linker length on phase separation: lessons from the Rubisco-EPYC1 system of the algal pyrenoid.

Biomolecular condensates are membraneless organelles formed via phase separation of macromolecules, typically consisting of bond-forming "stickers" connected by flexible "linkers". Linkers have diverse roles, such as occupying space and facilitating interactions. To understand how linker length relative to other lengths affects condensation, we focus on the pyrenoid, which enhances photosynthesis in green algae. Specifically, we apply coarse-grained simulations and analytical theory to the pyrenoid proteins of Chlamydomonas reinhardtii: the rigid holoenzyme Rubisco and its flexible partner EPYC1. Remarkably, halving EPYC1 linker lengths decreases critical concentrations by ten-fold. We attribute this difference to the molecular "fit" between EPYC1 and Rubisco. Varying Rubisco sticker locations reveals that the native sites yield the poorest fit, thus optimizing phase separation. Surprisingly, shorter linkers mediate a transition to a gas of rods as Rubisco stickers approach the poles. These findings illustrate how intrinsically disordered proteins affect phase separation through the interplay of molecular length scales.

Tuning nonequilibrium phase transitions with inertia.

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Phase-separating pyrenoid proteins form complexes in the dilute phase.

While most studies of biomolecular phase separation have focused on the condensed phase, relatively little is known about the dilute phase. Theory suggests that stable complexes form in the dilute phase of two-component phase-separating systems, impacting phase separation; however, these complexes have not been interrogated experimentally. We show that such complexes indeed exist, using an in vitro reconstitution system of a phase-separated organelle, the algal pyrenoid, consisting of purified proteins Rubisco and EPYC1. Applying fluorescence correlation spectroscopy (FCS) to measure diffusion coefficients, we found that complexes form in the dilute phase with or without condensates present. The majority of these complexes contain exactly one Rubisco molecule. Additionally, we developed a simple analytical model which recapitulates experimental findings and provides molecular insights into the dilute phase organization. Thus, our results demonstrate the existence of protein complexes in the dilute phase, which could play important roles in the stability, dynamics, and regulation of condensates.

Kinetic frustration by limited bond availability controls the LAT protein condensation phase transition on membranes.

LAT is a membrane-linked scaffold protein that undergoes a phase transition to form a two-dimensional protein condensate on the membrane during T cell activation. Governed by tyrosine phosphorylation, LAT recruits various proteins that ultimately enable condensation through a percolation network of discrete and selective protein-protein interactions. Here, we describe detailed kinetic measurements of the phase transition, along with coarse-grained model simulations, that reveal that LAT condensation is kinetically frustrated by the availability of bonds to form the network. Unlike typical miscibility transitions in which compact domains may coexist at equilibrium, the LAT condensates are dynamically arrested in extended states, kinetically trapped out of equilibrium. Modeling identifies the structural basis for this kinetic arrest as the formation of spindle arrangements, favored by limited multivalent binding interactions along the flexible, intrinsically disordered LAT protein. These results reveal how local factors controlling the kinetics of LAT condensation enable formation of different, stable condensates, which may ultimately coexist within the cell.

Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation.

Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.

Erratum: Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations [Phys. Rev. Lett. 125, 048102 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.125.048102.

Entropy production fluctuations encode collective behavior in active matter.

We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particles. We also derive optimal control forces that realize the dynamics necessary to tune dissipation and manipulate the system between phases. In so doing, we uncover a general relationship between entropy production and pattern formation in active matter, as well as ways of controlling it.

Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations.

In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.