Stoichiometry Controls the Dynamics of Liquid Condensates of Associative Proteins.

Multivalent associative proteins with strong complementary interactions play a crucial role in phase separation of intracellular liquid condensates. We study the internal dynamics of such "bond-network" condensates comprising two complementary proteins via scaling analysis and molecular dynamics. We find that when stoichiometry is balanced, relaxation slows down dramatically due to a scarcity of alternative binding partners following bond breakage.

Nucleation landscape of biomolecular condensates.

All structures within living cells must form at the right time and place. This includes condensates such as the nucleolus, Cajal bodies and stress granules, which form via liquid-liquid phase separation of biomolecules, particularly proteins enriched in intrinsically disordered regions (IDRs). In non-living systems, the initial stages of nucleated phase separation arise when thermal fluctuations overcome an energy barrier due to surface tension.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells.

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge.

Learning the dynamics of cell-cell interactions in confined cell migration.

The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive.

Learning the non-equilibrium dynamics of Brownian movies.

Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies.

Inferring the Dynamics of Underdamped Stochastic Systems.

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors.

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.

Range of geometrical frustration in lattice spin models.

The concept of geometrical frustration in condensed matter physics refers to the fact that a system has a locally preferred structure with an energy density lower than the infinite ground state. This notion is, however, often used in a qualitative sense only. In this article, we discuss a quantitative definition of geometrical frustration in the context of lattice models of binary spins.

Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks.

The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force "plucks" the fiber and induces a nonlinear tension.

Stress-dependent amplification of active forces in nonlinear elastic media.

The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that buckling in the matrix dramatically amplifies the resulting active stresses. Here we extend this result to a continuum elastic medium prone to buckling subjected to an arbitrary external stress, and derive analytical expressions for the active, nonlinear constitutive relations characterizing the full active medium.

Liquid Nuclear Condensates Mechanically Sense and Restructure the Genome.

Phase transitions involving biomolecular liquids are a fundamental mechanism underlying intracellular organization. In the cell nucleus, liquid-liquid phase separation of intrinsically disordered proteins (IDPs) is implicated in assembly of the nucleolus, as well as transcriptional clusters, and other nuclear bodies. However, it remains unclear whether and how physical forces associated with nucleation, growth, and wetting of liquid condensates can directly restructure chromatin.

Structural covariance in the hard sphere fluid.

We study the joint variability of structural information in a hard sphere fluid biased to avoid crystallisation and form five-fold symmetric geometric motifs. We show that the structural covariance matrix approach, originally proposed for on-lattice liquids [P. Ronceray and P.

Cell contraction induces long-ranged stress stiffening in the extracellular matrix.

Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here, we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel.

Suppression of crystalline fluctuations by competing structures in a supercooled liquid.

We propose a geometrical characterization of amorphous liquid structures that suppress crystallization by competing locally with crystalline order. We introduce for this purpose the crystal affinity of a liquid, a simple measure of its propensity to accumulate local crystalline structures on cooling. This quantity is explicitly related to the high-temperature structural covariance between local fluctuations in crystal order and that of competing liquid structures: favoring a structure that, due to poor overlap properties, anticorrelates with crystalline order reduces the affinity of the liquid.

The Eukaryotic CO-Concentrating Organelle Is Liquid-like and Exhibits Dynamic Reorganization.

Approximately 30%-40% of global CO fixation occurs inside a non-membrane-bound organelle called the pyrenoid, which is found within the chloroplasts of most eukaryotic algae. The pyrenoid matrix is densely packed with the CO-fixing enzyme Rubisco and is thought to be a crystalline or amorphous solid. Here, we show that the pyrenoid matrix of the unicellular alga Chlamydomonas reinhardtii is not crystalline but behaves as a liquid that dissolves and condenses during cell division.

Fiber networks amplify active stress.

Large-scale force generation is essential for biological functions such as cell motility, embryonic development, and muscle contraction. In these processes, forces generated at the molecular level by motor proteins are transmitted by disordered fiber networks, resulting in large-scale active stresses. Although these fiber networks are well characterized macroscopically, this stress generation by microscopic active units is not well understood.

Favoured local structures in liquids and solids: a 3D lattice model.

We investigate the connection between the geometry of Favoured Local Structures (FLS) in liquids and the associated liquid and solid properties. We introduce a lattice spin model - the FLS model on a face-centered cubic lattice - where this geometry can be arbitrarily chosen among a discrete set of 115 possible FLS. We find crystalline groundstates for all choices of a single FLS.

Connecting local active forces to macroscopic stress in elastic media.

In contrast with ordinary materials, living matter drives its own motion by generating active, out-of-equilibrium internal stresses. These stresses typically originate from localized active elements embedded in an elastic medium, such as molecular motors inside the cell or contractile cells in a tissue. While many large-scale phenomenological theories of such active media have been developed, a systematic understanding of the emergence of stress from the local force-generating elements is lacking.

Multiple ordering transitions in a liquid stabilized by low symmetry structures.

We present a numerical study of a lattice model of a liquid characterized by a low-symmetry favored local structure. We find that the freezing point is depressed far enough to reveal an exotic liquid-liquid transition characterized by the appearance of an extended chirality, prior to freezing. The ordered liquid can be readily supercooled to zero temperature, as the combination of critical slowing down and competing crystal polymorphs results in a dramatically slow crystallization process.

Influence of liquid structure on the thermodynamics of freezing.

The ordering transitions of a two-dimensional lattice liquid characterized by a single favored local structure (FLS) are studied using Monte Carlo simulations. All eight distinct geometries for the FLS are considered and we find a variety of ordering transitions: first order, continuous, and multistep transitions. Using an entropy-energy representation of the freezing transition we resolve the dual influence of the local structure on the ordering transition, i.

Geometry and the entropic cost of locally favoured structures in a liquid.

The role of the geometry of locally favoured structures in an equilibrium liquid is analyzed within a recently developed lattice model. The local geometry is shown to influence the liquid through the entropy and the associated density of states. We show that favoured local structures with low symmetry will, generally, incur a low entropy cost and, as a consequence, the liquid will exhibit a substantial accumulation of these low energy environments on cooling prior to the freezing transition.