Pierre Ronceray

Fiber networks amplify active stress

Significance Living organisms generate forces to move, change shape, and maintain their internal functions. These forces are typically produced by molecular motors embedded in networks of fibers. Although these motors are traditionally regarded as the defining elements of biological force generation, here we show that the surrounding network also plays a central role in this process. Indeed, rather than merely propagating forces like a simple elastic medium, fiber networks produce emergent, dramatically amplified stresses and can go so far as reversing small-scale extensile forces into large-scale contraction. Our theory quantitatively accounts for experimental measurements of contraction. 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. Here we theoretically study force transmission in these networks. We find that collective fiber buckling in the vicinity of a local active unit results in a rectification of stress towards strongly amplified isotropic contraction. This stress amplification is reinforced by the networks’ disordered nature, but saturates for high densities of active units. Our predictions are quantitatively consistent with experiments on reconstituted tissues and actomyosin networks and shed light on the role of the network microstructure in shaping active stresses in cells and tissue.

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

Significance The behavior of cells is strongly affected by the mechanics of their surroundings. In tissues, cells interact with the extracellular matrix, a 3D network of biopolymers with a highly nonlinear elastic response. We introduce a method exploiting this matrix nonlinearity to infer mechanical stresses in 3D. Using this method, we demonstrate that cell contractility induces large stresses, which generate a massive stiffness gradient over an extended region in 3D matrices of collagen, fibrin, and Matrigel. Our work highlights the importance of nonlinear matrix mechanics at the microscopic scale and suggests a concrete mechanism through which cells can control their microenvironment and mechanically communicate with each other. 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. We decipher this remarkable behavior by introducing nonlinear stress inference microscopy (NSIM), a technique to infer stress fields in a 3D matrix from nonlinear microrheology measurements with optical tweezers. Using NSIM and simulations, we reveal large long-ranged cell-generated stresses capable of buckling filaments in the matrix. These stresses give rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which can provide a mechanism for mechanical communication between cells.

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.

From liquid structure to configurational entropy: introducing structural covariance

We connect the configurational entropy of a liquid to the geometrical properties of its local energy landscape, using a high-temperature expansion. It is proposed that correlations between local structures arises from their overlap and, being geometrical in nature, can be usefully determined using the inherent structures of high temperature liquids. We show quantitatively how the high-temperature covariance of these local structural fluctuations arising from their geometrical overlap, combined with their energetic stability, control the decrease of entropy with decreasing energy. We apply this formalism to a family of Favoured Local Structure (FLS) lattice models with two low symmetry FLSs which are found to either crystallize or form a glass on cooling. The covariance, crystal energy and estimated freezing temperature are tested as possible predictors of glass-forming ability in the model system.

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. Sampling all possible FLSs, we identify the following trends: (i) low symmetry FLSs produce larger crystal unit cells but not necessarily higher energy groundstates, (ii) chiral FLSs exhibit peculiarly poor packing properties, (iii) accumulation of FLSs in supercooled liquids is linked to large crystal unit cells, and (iv) low symmetry FLSs tend to find metastable structures on cooling.

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. Using a lattice model of a liquid, we show that this quantity successfully predicts the tendency of a liquid to either accumulate or suppress local crystalline fluctuations with increasing supercooling. We demonstrate that the crystal affinity correlates strongly with the crystal nucleation rate and the crystal-liquid interfacial free energy of the low-temperature liquid, making our theory a predictive tool to determine which amorphous structures enhance glass-forming ability.

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. Harrowell, J. Stat. Mech.: Theory Exp. 2016(8), 084002], can be meaningfully employed to understand structural relationships between different motifs and can predict, within the linear-response regime, structural changes related to motifs distinct from that used to bias the system.

The free energy of a liquid when viewed as a population of overlapping clusters

The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural fluctuations arises from the local athermal constraints imposed by the overlap of adjacent coordination shells. In the context of the recently developed Favoured Local Structure model [Soft Matt. 11, 3322 (2015)], we derive explicit expressions for the structural energy and entropy in the high-temperature limit, compare this approximation with simulation data and consider the extension of this free energy to the case of spatial inhomogeneity in the distribution of local structures.