Session V37: Soft Mechanics in Biological Systems

State transitions of actin cortices in vitro and in vivo

Most animal cells are enveloped by a thin layer of actin cortex which governs the cell mechanics. A functional cortex must be rigid to provide mechanical support while being flexible to allow for rapid restructuring events such as cell division. To satisfy these requirements, the actin cortex is highly dynamic with fast actin turnover and myosin-driven contractility. The regulatory mechanism responsible for the transition between a mechanically stable state and a restructuring state is not well understood. Here, we develop a technique to map the dynamics of reconstituted actin cortices in emulsion droplets using IR fluorescent single-walled carbon nanotubes (SWNTs). By increasing crosslinker concentration, we find that a homogeneous cortex transitions to an intermediate state with broken rotational symmetry and a globally contractile state which further breaks translational symmetry. We apply this new dynamic mapping technique to cortices of live starfish oocytes in various developmental stages. To identify the regulatory mechanism for steady state transitions, we subject the oocytes to actin and myosin disrupting drugs.   

Direct measurement of local material properties within living embryonic tissues

The shaping of biological matter requires the control of its mechanical properties across multiple scales, ranging from single molecules to cells and tissues. Despite their relevance, measurements of the mechanical properties of sub-cellular, cellular and supra-cellular structures within living embryos pose severe challenges to existing techniques. We have developed a technique that uses magnetic droplets to measure the mechanical properties of complex fluids, including in situ and in vivo measurements within living embryos$, $across multiple length and time scales. By actuating the droplets with magnetic fields and recording their deformation we probe the local mechanical properties, at any length scale we choose by varying the droplets' diameter. We use the technique to determine the subcellular mechanics of individual blastomeres of zebrafish embryos, and bridge the gap to the tissue scale by measuring the local viscosity and elasticity of zebrafish embryonic tissues. Using this technique, we show that embryonic zebrafish tissues are viscoelastic with a fluid-like behavior at long time scales. This technique will enable mechanobiology and mechano-transduction studies in vivo, including the study of diseases correlated with tissue stiffness, such as cancer.   

The role of anisotropy in cell morphology

The shape of adhering cells is determined by the interplay between contractile forces, arising from the cytoskeleton, and the resistance of the underlying substrate. In particular, experiments with fibroblasts on an elastic micro-pillar array show that fibroblasts posess a high degree of orientational order of the actin stress fibers. This anisotropy causes the shape of the cell edge to deviate from the shape of cells with an isotropic cytoskeleton. We present a model that describes the contractility of the cytoskeleton as a combination of directed forces, in the direction of stress fibers, and isotropic forces. We found that cell morphology is described by an anisotropic generalization of the Young-Laplace law, which describes the cell edges as parts of an ellipse. Experiments on the shape of and adhesion forces on fibroblasts show good agreement with our model. Our work highlights the strong coupling between the organization of the internal cytoskeleton and the shapes and forces on the outside of the cell.   

Hydraulic fracture and resilience of epithelial monolayers under stretch

Epithelial monolayers are very simple and prevalent tissues. Their functions include delimiting distinct physicochemical containers and protecting us from pathogens. Epithelial fracture disrupts the mechanical integrity of this barrier, and hence compromises these functions. Here, we show that in addition to the conventional fracture resulting from excessive tissue tension, epithelia can hydraulically fracture under stretch as a result of the poroelastic nature of the matrix [1]. We will provide experimental evidence of this counterintuitive mechanism of fracture, in which cracks appear under compression. Intriguingly, unlike tensional fracture, which is localized and catastrophic, hydraulic epithelial fracture is distributed and reversible. We will also describe the active mechanisms responsible for crack healing, and the physical principles by which the poroelastic matrix contributes to this resilient behavior [2]. [1] Casares et al., Nature Materials, 14, 343-351 (2015) [2] Lucantonio et al., Physical Review Letters, 115, 188105 (2015)   

Mechanics and crack formation in the extracellular matrix with articular cartilage as a model system

We investigate the mechanical structure-function relations in the extracellular matrix (ECM) with focus on crack formation and failure. As a model system, our study focuses on the ECM in articular cartilage (AC), the tissue that covers the ends of bones, and distributes load in joints including in the knees, shoulders, and hips. The strength, toughness, and crack resistance of native articular cartilage is unparalleled in materials made by humankind. This mechanical response is mainly due to its ECM. The ECM in AC has two major mechanobiological components: a network of the biopolymer collagen and a flexible aggrecan gel. We model this system as a biopolymer network embedded in a swelling gel, and investigate the conditions for the formation and propagation of cracks using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as of biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.   

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. While fiber networks are well characterized macroscopically, this stress generation by microscopic active units is not well understood. I will present a comprehensive theoretical study of force transmission in these networks. I will show that the linear, small-force response of the networks is remarkably simple, as the macroscopic active stress depends only on the geometry of the force-exerting unit. In contrast, as non-linear buckling occurs around these units, local active forces are rectified towards isotropic contraction and strongly amplified. This stress amplification is reinforced by the networks' disordered nature, but saturates for high densities of active units. I will show that our predictions are quantitatively consistent with experiments on reconstituted tissues and actomyosin networks, and that they shed light on the role of the network microstructure in shaping active stresses in cells and tissue.   

A micro-mechanical model to determine changes of collagen fibrils under cyclic loading

Dynamic mechanical loading induces growth and remodeling in biological tissues. It can alter the degradation rate and intrinsic mechanical properties of collagen through cellular activity. Experiments showed that repeated cyclic loading of a dense collagen fibril substrate increased collagen stiffness and strength, lengthened the substrate, but did not significantly change the fibril areal fraction or fibril anisotropy (Susilo, et al. “Collagen Network Hardening Following Cyclic Tensile Loading”, Interface Focus, submitted). We developed a model for the collagen fibril substrate (Tonge, et al. “A micromechanical modeling study of the mechanical stabilization of enzymatic degradation of collagen tissues”, Biophys J, in press.) to probe whether changes in the fibril morphology and mechanical properties can explain the tissue-level properties observed during cyclic loading. The fibrils were modeled as a continuous distribution of wavy elastica, based on experimental measurements of fibril density and collagen anisotropy, and can experience damage after a critical stress threshold. Other mechanical properties in the model were fit to the stress response measured before and after the extended cyclic loading to determine changes in the strength and stiffness of collagen fibrils.   

Confined semiflexible biopolymers suppress fluctuations of soft membrane tubes

Membrane nanotubes are tubular membrane structures that contain actin and connect cells over long distances. Disrupting the actin cytoskeleton abrogates membrane nanotubes, making them an interesting model system for studying membrane-biopolymer interactions. In this study, we use Monte Carlo computer simulations to investigate tubular, elastic membrane structures with and without semiflexible polymers confined inside. At small values of membrane bending rigidity, fluid membranes adopt irregular, highly fluctuating shapes while non-fluid membranes maintain extended tube-like structures. With increasing bending rigidity, fluid membranes exhibit a local maximum in specific heat that is coincident with a transition to extended tube-like structures. We further find that confining a semiflexible polymer within a fluid membrane tube suppresses membrane shape fluctuations and reduces the specific heat of the membrane. Polymers with a sufficiently large persistence length can significantly deform the membrane tube, leading to localized bulges in the membrane that accommodate regions in which the polymer forms loops. Analytical calculations of the energies of idealized polymer-membrane configurations provide additional insight into the formation of polymer-induced membrane deformations.   

Force distributions in disordered fiber networks

Disordered filamentous networks determine the mechanical response of many materials in nature. Due to the filamentous character of these networks, the strain field, and hence the force distributions, can be highly inhomogeneous. Large local stresses can result in an increased susceptibility for local rearrangements due to rupture or unbinding events. In our study, we introduce a quantitative measure to characterize the emergence of highly stressed one-dimensional paths, so-called force chains, in three-dimensional nonlinear fiber networks. Furthermore, we provide an analytical approach, based on graph theory, that quantitatively describes the force distributions in one-dimensional periodic spring networks. Our analytical results are in excellent agreement with our extensive numerical simulations.   

Role of differential physical properties in the collective mechanics and dynamics of tissues

Living cells and tissues are highly mechanically sensitive and active. Mechanical stimuli influence the shape, motility, and functions of cells, modulate the behavior of tissues, and play a key role in several diseases. In this talk I will discuss how collective biophysical properties of tissues emerge from the interplay between differential mechanical properties and statistical physics of underlying components, focusing on two complementary tissue types whose properties are primarily determined by (1) the extracellular matrix (ECM), and (2) individual and collective cell properties. I will start with the structure-mechanics-function relationships in articular cartilage (AC), a soft tissue that has very few cells, and its mechanical response is primarily due to its ECM. AC is a remarkable tissue: it can support loads exceeding ten times our body weight and bear 60+ years of daily mechanical loading despite having minimal regenerative capacity. I will discuss the biophysical principles underlying this exceptional mechanical response using the framework of rigidity percolation theory, and compare our predictions with experiments done by our collaborators. Next I will discuss ongoing theoretical work on how the differences in cell mechanics, motility, adhesion, and proliferation in a co-culture of breast cancer cells and healthy breast epithelial cells may modulate experimentally observed differential migration and segregation. Our results may provide insights into the mechanobiology of tissues with cell populations with different physical properties present together such as during the formation of embryos or the initiation of tumors.