arXiv subjects

Fred C. MacKintosh

Publications and source records attributed to Fred C. MacKintosh.

At least 37 records · Page 2Linked to original sources

arXiv2020

Compression stiffening of fibrous networks with stiff inclusions

Tissues commonly consist of cells embedded within a fibrous biopolymer network. Whereas cell-free reconstituted biopolymer networks typically soften under applied uniaxial compression, various tissues, including liver, brain, and fat, have been observed to instead stiffen when compressed. The mechanism for this compression stiffening effect is not yet clear. Here, we demonstrate that when a material composed of stiff inclusions embedded in a fibrous network is compressed, heterogeneous rearrangement of the inclusions can induce tension within the interstitial network, leading to a macroscopic crossover from an initial bending-dominated softening regime to a stretching-dominated stiffening regime, which occurs before and independently of jamming of the inclusions. Using a coarse-grained particle-network model, we first establish a phase diagram for compression-driven, stretching-dominated stress propagation and jamming in uniaxially compressed 2- and 3-dimensional systems. Then, we demonstrate that a more detailed computational model of stiff inclusions in a subisostatic semiflexible fiber network exhibits quantitative agreement with the predictions of our coarse-grained model as well as qualitative agreement with experiments.

cond-mat.soft↗

arXiv2020

Finite size effects in critical fiber networks

Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.

cond-mat.soft↗

arXiv2019

Nonlinear Poisson effect governed by mechanical critical transition

Under extensional strain, fiber networks can exhibit an anomalously large and nonlinear Poisson effect accompanied by a dramatic transverse contraction and volume reduction for applied strains as small as a few percent. We demonstrate that this phenomenon is controlled by a collective mechanical phase transition that occurs at a critical uniaxial strain that depends on network connectivity. This transition is punctuated by an anomalous peak in the apparent Poisson's ratio and other critical signatures such as diverging nonaffine strain fluctuations.

cond-mat.soft↗

arXiv2019

Stress-stabilized sub-isostatic fiber networks in a rope-like limit

The mechanics of disordered fibrous networks such as those that make up the extracellular matrix are strongly dependent on the local connectivity or coordination number. For biopolymer networks this coordination number is typically between three and four. Such networks are sub-isostatic and linearly unstable to deformation with only central force interactions, but exhibit a mechanical phase transition between floppy and rigid states under strain. Introducing weak bending interactions stabilizes these networks and suppresses the critical signatures of this transition. We show that applying external stress can also stabilize sub-isostatic networks with only tensile central force interactions, i.e., a rope-like potential. Moreover, we find that the linear shear modulus shows a power law scaling with the external normal stress, with a non-mean-field exponent. For networks with finite bending rigidity, we find that the critical stain shifts to lower values under prestress.

cond-mat.soft↗

arXiv2018

Normal stress anisotropy and marginal stability in athermal elastic networks

Hydrogels of semiflexible biopolymers such as collagen have been shown to contract axially under shear strain, in contrast to the axial dilation observed for most elastic materials. Recent work has shown that this behavior can be understood in terms of the porous, two-component nature and consequent time-dependent compressibility of hydrogels. The apparent normal stress measured by a torsional rheometer reflects only the tensile contribution of the axial component $σ_{zz}$ on long (compressible) timescales, crossing over to the first normal stress difference, $N_1 = σ_{xx}-σ_{zz}$ at short (incompressible) times. While the behavior of $N_1$ is well understood for isotropic viscoelastic materials undergoing affine shear deformation, biopolymer networks are often anisotropic and deform nonaffinely. Here, we numerically study the normal stresses that arise under shear in subisostatic, athermal semiflexible polymer networks. We show that such systems exhibit strong deviations from affine behavior and that these anomalies are controlled by a rigidity transition as a function of strain.

cond-mat.soft↗

arXiv2018

Scaling theory for mechanical critical behavior in fiber networks

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a function of strain. Experimental collagen networks were also shown to be consistent with these predictions. We develop a scaling theory for this strain-controlled transition. Using a real-space renormalization approach, we determine relations between the critical exponents governing the transition, which we verify for the strain-controlled transition using numerical simulations of both triangular lattice-based and packing-derived fiber networks.

cond-mat.soft↗

arXiv2017

A symmetrical method to obtain shear moduli from microrheology

Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacement (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformations or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function $χ(ω) = χ^{\prime}(ω)+iχ^{\prime\prime}(ω)$ as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of $χ(ω)$ relative to the use of KK transformation, which has been shown to lead to artifacts in $χ^{\prime}(ω)$. We test our method on both model data and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.

cond-mat.soft↗

arXiv2017

Force percolation of contractile active gels

Cells and tissues exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, which includes an active gel of actin filaments, crosslinks, and myosin molecular motors. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (order nN and greater) on cellular, tissue, and organismal length scales (order 10 $μ$m and greater). Experimental studies of reconstituted active-network model systems have long suggested that a mechanical interplay between the network's connectivity and motor activity dominates contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, where the network connectivity is influenced by motor activity. Here we review experimental and theoretical studies of model contractile active gels and propose a state diagram that unites a large body of experimental and theoretical observations based on concepts from percolation theory.

cond-mat.soft↗

arXiv2016

Programming filamentous network mechanics by compression

Fibrous networks are ideal functional materials since they provide mechanical rigidity at low weight. Such structures are omnipresent in natural biomaterials from cells to tissues, as well as in man-made materials from polymeric composites to paper and textiles. Here, we demonstrate that fibrous networks of the blood clotting protein fibrin undergo a strong and irreversible increase in their mechanical rigidity in response to compression. This rigidification can be precisely predetermined from the level of applied compressive strain, providing a means to program the network rigidity without having to change its composition. To identify the mechanism underlying this programmable rigidification, we measure single fiber-fiber interactions using optical tweezers. We further develop a minimal computational model of adhesive fiber networks that shows that load-induced bond formation can explain the adaptation of the fibrin networks to compressive loading. The model predicts that the network stiffness after compressive programming obeys a universal power-law dependence on the prestress built in by new bond formation, which we confirm experimentally. The generality of this functional stiffening mechanism together with our ability to quantitatively predict it provides a new powerful approach to program the stiffness of fibrous materials and dynamically adapt them to different loading conditions.

physics.bio-ph↗

arXiv2016

Porosity governs normals stresses in polymer gels

When sheared, most elastic solids such as metals, rubbers and polymer hydrogels dilate in the direction perpendicular to the shear plane. This well-known behaviour known as the Poynting effect is characterized by a positive normal stress. Surprisingly, biopolymer gels made of fibrous proteins such as fibrin and collagen, as well as many biological tissues exhibit the opposite effect, contracting under shear and displaying a negative normal stress. Here we show that this anomalous behaviour originates from the open network structure of biopolymer gels, which facilitates interstitial fluid flow during shear. Using fibrin networks with a controllable pore size as a model system, we show that the normal stress response to an applied shear is positive at short times, but decreases to negative values with a characteristic time scale set by pore size. Using a two-fluid model, we develop a quantitative theory that unifies the opposite behaviours encountered in synthetic and biopolymer gels. Synthetic polymer gels are impermeable to solvent flow and thus effectively incompressible at typical experimental time scales, whereas biopolymer gels are effectively compressible. Our findings suggest a new route to tailor elastic instabilities such as the die-swell effect that often hamper processing of polymer materials and furthermore show that poroelastic effects play a much more important role in the mechanical properties of cells and tissues than previously anticipated.

cond-mat.soft↗

arXiv2016

Self-organization of stress patterns drives state transitions in actin cortices

Biological functions rely on ordered structures and intricately controlled collective dynamics. In contrast to systems in thermodynamic equilibrium, order is typically established and sustained in stationary states by continuous dissipation of energy. Non-equilibrium dynamics is a necessary condition to make the systems highly susceptible to signals that cause transitions between different states. How cellular processes self-organize under this general principle is not fully understood. Here, we find that model actomyosin cortices, in the presence of rapid turnover, display distinct steady states, each distinguished by characteristic order and dynamics as a function of network connectivity. The different states arise from a subtle interaction between mechanical percolation of the actin network and myosin-generated stresses. Remarkably, myosin motors generate actin architectures, which in turn, force the emergence of ordered stress patterns. Reminiscent of second order phase transitions, the emergence of order is accompanied by a critical regime characterized by strongly enhanced strain fluctuations. The striking dynamics in the critical regime were revealed using fluorescent single-walled carbon nanotubes as novel probes of cortical dynamics.

physics.bio-ph↗

arXiv2016

Elasticity of fibrous networks under axial prestress

We present theoretical and experimental studies of the elastic response of fibrous networks subjected to uniaxial strain. Uniaxial compression or extension is applied to extracellular networks of fibrin and collagen using a shear rheometer with free water in/outflow. Both axial stress and the network shear modulus are measured. Prior work [van Oosten et al., Scientific Reports, 2015, 6, 19270] has shown softening/stiffening of these networks under compression/extension, together with a nonlinear response to shear, but the origin of such behaviour remains poorly understood. Here, we study how uniaxial strain influences the nonlinear mechanics of fibrous networks. Using a computational network model with bendable and stretchable fibres, we show that the softening/stiffening behaviour can be understood for fixed lateral boundaries in 2D and 3D networks with comparable average connectivities to the experimental extracellular networks. Moreover, we show that the onset of stiffening depends strongly on the imposed uniaxial strain. Our study highlights the importance of both axial strain and boundary conditions in determining the mechanical response of hydrogels.

cond-mat.soft↗

arXiv2016

On-site residence time in a driven diffusive system: violation and recovery of mean-field

We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using Domain wall theory (DWT), we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually interactive LK (TASEP + MILK). The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations.

physics.bio-ph↗

arXiv2015

Elastic regimes of sub-isostatic athermal fiber networks

Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of these systems, which include rich linear and nonlinear elasticity. Existing computational approaches have focused on both lattice-based and off-lattice networks obtained from the random placement of rods. It is not obvious, a priori, whether the two architectures have fundamentally similar or different mechanics. If they are different, it is not clear which of these represents a better model for biological networks. Here, we show that both approaches are essentially equivalent for the same network connectivity, provided the networks are sub-isostatic with respect to central force interactions. Moreover, for a given sub-isostatic connectivity, we even find that lattice-based networks in both 2D and 3D exhibit nearly identical nonlinear elastic response. We provide a description of the linear mechanics for both architectures in terms of a scaling function. We also show that the nonlinear regime is dominated by fiber bending and that stiffening originates from the stabilization of sub-isostatic networks by stress. We propose a generalized relation for this regime in terms of the self-generated normal stresses that develop under deformation. Different network architectures have different susceptibilities to the normal stress, but essentially exhibit the same nonlinear mechanics. Such stiffening mechanism has been shown to successfully capture the nonlinear mechanics of collagen networks.

cond-mat.soft↗

arXiv2015

Stress controls the mechanics of collagen networks

Collagen is the main structural and load-bearing element of various connective tissues, where it forms the extracellular matrix that supports cells. It has long been known that collagenous tissues exhibit a highly nonlinear stress-strain relationship (Fung YC, Am J Physiol 213(6),1967; Humphrey JD, Proc R Soc Lond A: Math Phys Eng Sci 459(2029),2003), although the origins of this nonlinearity remain unknown (McMahon TA, Lec Math Life Sci 13,1980). Here, we show that the nonlinear stiffening of reconstituted type I collagen networks is controlled by the applied stress, and that the network stiffness becomes surprisingly insensitive to network concentration. We demonstrate how a simple model for networks of elastic fibers can quantitatively account for the mechanics of reconstituted collagen networks. Our model points to the important role of normal stresses in determining the nonlinear shear elastic response, which can explain the approximate exponential relationship between stress and strain reported for collagenous tissues (Fung YC, Am J Physiol 213(6),1967). This further suggests new principles for the design of synthetic fiber networks with collagen-like properties, as well as a mechanism for the control of the mechanics of such networks.

cond-mat.soft↗

arXiv2015

Stability and anomalous entropic elasticity of sub isostatic random-bond networks

We study the elasticity of thermalized spring networks under an applied bulk strain. The networks considered are sub-isostatic random-bond networks that, in the athermal limit, are known to have vanishing bulk and linear shear moduli at zero bulk strain. Above a bulk strain threshold, however, these networks become rigid, although surprisingly the shear modulus remains zero until a second, higher, strain threshold. We find that thermal fluctuations stabilize all networks below the rigidity transition, resulting in systems with both finite bulk and shear moduli. Our results show a $T^{0.66}$ temperature dependence of the moduli in the region below the bulk strain threshold, resulting in networks with anomalously high rigidity as compared to ordinary entropic elasticity. Furthermore we find a second regime of anomalous temperature scaling for the shear modulus at its zero-temperature rigidity point, where it scales as $T^{0.5}$, behavior that is absent for the bulk modulus since its athermal rigidity transition is discontinuous.

cond-mat.soft↗

arXiv2013

Fluctuation-stabilized marginal networks and anomalous entropic elasticity

We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work we show that thermal networks exhibit a non-zero shear modulus $G$ well below the isostatic point, and that this modulus exhibits an anomalous, sublinear dependence on temperature $T$. At the isostatic point, $G$ increases as the square-root of $T$, while we find $G \propto T^α$ below the isostatic point, where $α \simeq 0.8$. We show that this anomalous $T$ dependence is entropic in origin.

cond-mat.soft↗

arXiv2013

Molecular motors robustly drive active gels to a critically connected state

Living systems often exhibit internal driving: active, molecular processes drive nonequilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, where molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-free size distribution. This critical behavior occurs over an unexpectedly broad range of crosslink concentrations. To understand this robustness, we develop a quantitative model of contractile networks that takes into account network restructuring: motors reduce connectivity by forcing crosslinks to unbind. Paradoxically, to coordinate global contractions, motor activity should be low. Otherwise, motors drive initially well-connected networks to a critical state where ruptures form across the entire network.

physics.bio-ph↗