Frederick C. MacKintosh

Disordered fiber networks exhibit a floppy-to-rigid mechanical phase transition as a function of connectivity. Subisostatically connected networks can undergo this transition via straining. Critical exponents governing this transition have been estimated theoretically and by numerical simulations of various types of networks. In this study, we present improved results, achieved through a combination of refined numerical simulations, larger system sizes, and incorporation of theoretical predictions for better postsimulation analysis. We also report the evolution of the critical strain and critical exponents as the network is sheared while being subjected to non-volume-preserving uniaxial deformations.

We experimentally assess the nonlinear rheology of composite biopolymer hydrogels composed of thiolated hyaluronic acid, poly(ethylene glycol) diacrylate (PEGDA), and laminin-111 in varied concentrations. We focus in particular on the influence of laminin on the mechanics of the assembled hydrogels, reporting nonlinear rheological measurements for gels under applied shear and compressive load. We find that increasing the concentration of laminin in the synthesized gels reduces the linear shear modulus and gives rise to a mild strain softening regime at intermediate strains prior to the onset of strain stiffening. In the stiffening regime, we find that all gels exhibit stress-controlled mechanics with K ∝ σ ^a , with an apparent stiffening exponent of a ≈ 1, in agreement with observations of a variety of other reconstituted biopolymer gels. We discuss the possible implications of this nonlinear mechanical behavior on mechanotransduction and organoid development in biomimetic extracellular matrices.

Living systems operate far from thermodynamic equilibrium. Movements in cells are always driven by thermal forces but, more importantly, also by motor-generated active forces in the cytoplasm. How intracellular structures respond to these forces depends on their mechanical properties. Intracellular dynamics remain challenging to understand because, in most cases, neither local forces nor local material response properties are known, and imaging of fluctuations is typically not sufficient to measure both. While some subcellular structures such as actin filaments and microtubules, which form the major cytoskeletal networks, have been extensively studied , their mechanical properties in living cells where they are regulated by post-translational modifications and association with regulatory factors remain poorly understood. Here we present an alternative approach that uses nonequilibrium bending fluctuations of rod-shaped structures to characterize their mechanical properties and those of their surroundings and to estimate driving forces. We demonstrate that, when one of the three factors—two material properties and one driving force—is determined independently, the other two can be derived from observed fluctuations. By applying our method to microtubules in living cells we find that polyglutamylation, a post-translational modification enriched on microtubules that need to withstand large deformation forces like those in axons or cilia, increases microtubule stiffness. In contrast, tubelike mitochondria, lipid membrane-bounded organelles which easily deform, yielded a bending stiffness significantly lower than that of microtubules. Our method opens the door to a quantitative understanding of the effects of cellular factors on the mechanical properties of filaments and organelles in cells.

The spontaneous formation of knots in semiflexible filaments is not only a fundamental aspect of polymer physics but also plays a crucial role in biological systems, where DNA, proteins, and other macromolecules exhibit complex knotting behavior. From Brownian dynamics simulations, we examine the sedimentation of semiflexible filaments under strong fields. We show how hydrodynamics induce knotting dynamics and stabilization into tight knotted configurations. Controlling the knotting of semiflexible filaments presents opportunities to create materials with unique structural properties.

The mechanical properties of biological materials are spatially heterogeneous. Typical tissues are made up of a spanning fibrous extracellular matrix in which various inclusions, such as living cells, are embedded. While the influence of embedded inclusions on the stiffness of common elastic materials such as rubber has been studied for decades and can be understood in terms of the volume fraction and shape of inclusions, the same is not true for disordered filamentous and fibrous networks. Recent work has shown that, in isolation, such networks exhibit unusual viscoelastic behavior indicative of an underlying mechanical phase transition controlled by network connectivity and strain. How this behavior is modified when inclusions are present is unclear. Here, we present a theoretical and computational study of the influence of rigid inclusions on the mechanics of disordered elastic networks near the connectivity-controlled central-force rigidity transition. Combining scaling theory and coarse-grained simulations, we predict and confirm an anomalously strong dependence of the composite stiffness on inclusion volume fraction, beyond that seen in ordinary composites. This stiffening exceeds the well-established volume-fraction-dependent stiffening expected in conventional composites, e.g., as an elastic analog of the classic volume-fraction-dependent increase in the viscosity of liquids first identified by Einstein. We show that this enhancement is a consequence of the interplay between interparticle spacing and an emergent correlation length, leading to an effective finite-size scaling imposed by the presence of inclusions. We outline the expected scaling of the linear shear modulus and strain fluctuations with the inclusion volume fraction and network connectivity, confirm these predictions in simulations, and discuss potential experimental tests and implications for our predictions in real systems.

Plectin is a giant protein of the plakin family that crosslinks the cytoskeleton of mammalian cells. It is expressed in virtually all tissues and its dysfunction is associated with various diseases such as skin blistering. There is evidence that plectin regulates the mechanical integrity of the cytoskeleton in diverse cell and tissue types. However, it is unknown how plectin modulates the mechanical response of cells depending on the frequency and amplitude of mechanical loading. Here we demonstrate the role of plectin in the viscoelastic properties of fibroblasts at small and large deformations by quantitative single-cell compression measurements. To identify the importance of plectin, we compared the mechanical properties of wild type ( Plec ^+/+ ) fibroblasts and plectin knockout ( Plec ^−/− ) fibroblasts. We show that plectin knockout cells are nearly 2-fold softer than wild type cells, but their strain-stiffening behaviour is similar. Plectin deficiency also caused faster viscoelastic stress relaxation at long times. Fluorescence recovery after photobleaching experiments indicated that this was due to 3-fold faster actin turnover. Short-time poroelastic relaxation was also faster in Plec ^−/− cells as compared to Plec ^+/+ cells, suggesting a more sparse cytoskeletal network. Confocal imaging indicated that this was due to a marked change in the architecture of the vimentin network, from a fine meshwork in wild type cells to a bundled network in the plectin knockout cells. Our findings therefore indicate that plectin is an important regulator of the organization and viscoelastic properties of the cytoskeleton in fibroblasts. Our findings emphasize that mechanical integration of the different cytoskeletal networks present in cells is important for regulating the versatile mechanical properties of cells. SIGNIFICANCE: Mammalian cells combine superior mechanical strength with the ability to actively deform themselves. They owe this paradoxical mechanical behaviour to their cytoskeleton, an intracellular web of protein filaments that includes actin filaments and intermediate filaments. It is known that both cytoskeletal filament types contribute to cell stiffness on their own, but the impact of their mechanical integration via cytoskeletal crosslinker proteins remains unknown. Here we test the effect of crosslinking of actin and vimentin intermediate filaments by the crosslinker protein plectin in fibroblasts by single-cell compression measurements. By comparing normal cells and cells in which plectin is knocked out, we find that plectin significantly increases cell stiffness and provides a protective mechanism against actin network disruption by compressive loading.

The mechanical properties of cells are governed by the cytoskeleton, a dynamic network of actin filaments, intermediate filaments, and microtubules. Understanding the individual and collective mechanical contributions of these three different cytoskeletal elements is essential to elucidate how cells maintain mechanical integrity during deformation. Here we use a custom single-cell rheometer to identify the distinct contributions of actin and vimentin to the viscoelastic and nonlinear elastic response of cells to uniaxial compression. We used mouse embryonic fibroblasts (MEFs) isolated from wild type (WT) and vimentin knockout (vim -/-) mice in combination with chemical treatments to manipulate actin polymerization and contractility. We show through small amplitude oscillatory measurements and strain ramp tests that vimentin, often overlooked in cellular mechanics, plays a role comparable to actin in maintaining cell stiffness and resisting large compressive forces. However, actin appears to be more important than vimentin in determining cellular energy dissipation. Finally we show by comparing wild type and enucleated cells that compression stiffening originates from the actin and vimentin cytoskeleton, while the nucleus appears to play little role in this. Our findings provide insight into how cytoskeletal networks collectively determine the mechanical properties of cells, providing a basis to understand the role of the cytoskeleton in the ability of cells to resist external as well as internal forces. Significance statement A cell’s response to mechanical stress is largely governed by the actin and vimentin cytoskeletal networks, but their relative contribution to cell viscoelasticity and response to large deformations are poorly characterized. We reveal that actin and vimentin networks have an almost equal contribution to cellular stiffness and the cell’s ability to strain-stiffen under uniaxial compression. This work underscores the cytoskeleton’s central role in cellular mechanics and the mechanical synergy between the cytoskeletal networks, providing a framework for understanding how cellular components coordinate to maintain structural integrity and respond to different mechanical environments.

Fibrous networks such as collagen are common in biological systems. Recent theoretical and experimental efforts have shed light on the mechanics of single

Superparamagnetic colloids present interesting assembly dynamics and propulsion in time-varying magnetic fields due to their magnetic relaxation. However, little is known about the mechanisms governing this magnetic relaxation, which is commonly attributed to the interactions and polydispersity of the ferromagnetic nanoparticles distributed within the colloid. We measure this relaxation from the effective potential between colloids subjected to rotating magnetic fields. Remarkably, our results indicate the presence of magnetic relaxation times much longer than what has been reported, which furthers our understanding of the magnetization of colloids in complex magnetic fields.

Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.