Single-walled carbon nanotube reptation dynamics in submicron sized pores from randomly packed mono-sized colloids.

Studying the Brownian motion of fibers and semi-flexible filaments in porous media is the key to understanding the transport and mechanical properties in a variety of systems. The motion of semi-flexible filaments in gel-like porous media including polymer networks and cell cytoskeleton has been studied theoretically and experimentally, whereas the motion of these materials in packed-colloid porous media, advanced foams, and rock-like systems has not been thoroughly studied. Here we use video microscopy to directly visualize the reptation and transport of intrinsically fluorescent, semiflexible, semiconducting single-walled carbon nanotubes (SWCNTs) in the sub-micron pores of packed colloids as fixed obstacles of packed-colloid porous media. By visualizing the filament motion and Brownian diffusion at different locations in the pore structures, we study how the properties of the environment, like the pore shape and pore structure of the porous media, affect SWCNT mobility. These results show that the porous media structure controls SWCNT reorientation during Brownian diffusion. In packed-colloid pores, SWCNTs diffuse along straight pores and bend across pores; conversely, in gel pores, SWCNTs consistently diffuse into curved pores, displaying a faster parallel motion. In both gel and packed-colloid porous media, SWCNT finite stiffness enhances SWCNT rotational diffusion and prevents jamming, allowing for inter-pore diffusion.

Anomalous mechanics of Zn2+-modified fibrin networks.

Fibrin is the main component of blood clots. The mechanical properties of fibrin are therefore of critical importance in successful hemostasis. One of the divalent cations released by platelets during hemostasis is Zn2+; however, its effect on the network structure of fibrin gels and on the resultant mechanical properties remains poorly understood. Here, by combining mechanical measurements with three-dimensional confocal microscopy imaging, we show that Zn2+ can tune the fibrin network structure and alter its mechanical properties. In the presence of Zn2+, fibrin protofibrils form large bundles that cause a coarsening of the fibrin network due to an increase in fiber diameter and reduction of the total fiber length. We further show that the protofibrils in these bundles are loosely coupled to one another, which results in a decrease of the elastic modulus with increasing Zn2+ concentrations. We explore the elastic properties of these networks at both low and high stress: At low stress, the elasticity originates from pulling the thermal slack out of the network, and this is consistent with the thermal bending of the fibers. By contrast, at high stress, the elasticity exhibits a common master curve consistent with the stretching of individual protofibrils. These results show that the mechanics of a fibrin network are closely correlated with its microscopic structure and inform our understanding of the structure and physical mechanisms leading to defective or excessive clot stiffness.

Cofilin drives rapid turnover and fluidization of entangled F-actin.

The shape of most animal cells is controlled by the actin cortex, a thin network of dynamic actin filaments (F-actin) situated just beneath the plasma membrane. The cortex is held far from equilibrium by both active stresses and polymer turnover: Molecular motors drive deformations required for cell morphogenesis, while actin-filament disassembly dynamics relax stress and facilitate cortical remodeling. While many aspects of actin-cortex mechanics are well characterized, a mechanistic understanding of how nonequilibrium actin turnover contributes to stress relaxation is still lacking. To address this, we developed a reconstituted in vitro system of entangled F-actin, wherein the steady-state length and turnover rate of F-actin are controlled by the actin regulatory proteins cofilin, profilin, and formin, which sever, recycle, and assemble filaments, respectively. Cofilin-mediated severing accelerates the turnover and spatial reorganization of F-actin, without significant changes to filament length. We demonstrate that cofilin-mediated severing is a single-timescale mode of stress relaxation that tunes the low-frequency viscosity over two orders of magnitude. These findings serve as the foundation for understanding the mechanics of more physiological F-actin networks with turnover and inform an updated microscopic model of single-filament turnover. They also demonstrate that polymer activity, in the form of ATP hydrolysis on F-actin coupled to nucleotide-dependent cofilin binding, is sufficient to generate a form of active matter wherein asymmetric filament disassembly preserves filament number despite sustained severing.

Cell volume change through water efflux impacts cell stiffness and stem cell fate.

Cells alter their mechanical properties in response to their local microenvironment; this plays a role in determining cell function and can even influence stem cell fate. Here, we identify a robust and unified relationship between cell stiffness and cell volume. As a cell spreads on a substrate, its volume decreases, while its stiffness concomitantly increases. We find that both cortical and cytoplasmic cell stiffness scale with volume for numerous perturbations, including varying substrate stiffness, cell spread area, and external osmotic pressure. The reduction of cell volume is a result of water efflux, which leads to a corresponding increase in intracellular molecular crowding. Furthermore, we find that changes in cell volume, and hence stiffness, alter stem-cell differentiation, regardless of the method by which these are induced. These observations reveal a surprising, previously unidentified relationship between cell stiffness and cell volume that strongly influences cell biology.

Ultra-responsive soft matter from strain-stiffening hydrogels.

The stiffness of hydrogels is crucial for their application. Nature's hydrogels become stiffer as they are strained. This stiffness is not constant but increases when the gel is strained. This stiffening is used, for instance, by cells that actively strain their environment to modulate their function. When optimized, such strain-stiffening materials become extremely sensitive and very responsive to stress. Strain stiffening, however, is unexplored in synthetic gels since the structural design parameters are unknown. Here we uncover how readily tuneable parameters such as concentration, temperature and polymer length impact the stiffening behaviour. Our work also reveals the marginal point, a well-described but never observed, critical point in the gelation process. Around this point, we observe a transition from a low-viscous liquid to an elastic gel upon applying minute stresses. Our experimental work in combination with network theory yields universal design principles for future strain-stiffening materials.

Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy.

Molecular motors in cells typically produce highly directed motion; however, the aggregate, incoherent effect of all active processes also creates randomly fluctuating forces, which drive diffusive-like, nonthermal motion. Here, we introduce force-spectrum-microscopy (FSM) to directly quantify random forces within the cytoplasm of cells and thereby probe stochastic motor activity. This technique combines measurements of the random motion of probe particles with independent micromechanical measurements of the cytoplasm to quantify the spectrum of force fluctuations. Using FSM, we show that force fluctuations substantially enhance intracellular movement of small and large components. The fluctuations are three times larger in malignant cells than in their benign counterparts. We further demonstrate that vimentin acts globally to anchor organelles against randomly fluctuating forces in the cytoplasm, with no effect on their magnitude. Thus, FSM has broad applications for understanding the cytoplasm and its intracellular processes in relation to cell physiology in healthy and diseased states.

High-resolution mapping of intracellular fluctuations using carbon nanotubes.

Cells are active systems with molecular force generation that drives complex dynamics at the supramolecular scale. We present a quantitative study of molecular motions in cells over times from milliseconds to hours. Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random "stirring" that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

Stress-enhanced gelation: a dynamic nonlinearity of elasticity.

A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of filamentous actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solidlike behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior.

Nonequilibrium fluctuations of a remodeling in vitro cytoskeleton.

Motor proteins actively contract the actin cytoskeleton of cells and thereby give rise to nonequilibrium fluctuations as well as changes in the architecture of the cytoskeleton. Here, we show, by video microrheology of a reconstituted cytoskeleton, that motors generate time-dependent nonequilibrium fluctuations, which evolve as the network is remodeled. At earlier times, the fluctuation spectrum is dominated by strong non-Gaussian fluctuations, which arise from large displacements. At later times, directed displacements are infrequent and finally disappear. We show that these effects are due to contractile coarsening of the network into large actin-myosin foci.

Nonlinear viscoelasticity of actin transiently cross-linked with mutant α-actinin-4.

Filamentous actin and associated actin binding proteins play an essential role in governing the mechanical properties of eukaryotic cells. They can also play a critical role in disease; for example, mutations in α-actinin-4 (Actn4), a dynamic actin cross-linking protein, cause proteinuric disease in humans and mice. Amino acid substitutions strongly affect the binding affinity and protein structure of Actn4. To study the physical impact of such substitutions on the underlying cytoskeletal network, we examine the bulk mechanical behavior of in vitro actin networks cross-linked with wild-type and mutant Actn4. These networks exhibit a complex viscoelastic response and are characterized by fluid-like behavior at the longest timescales, a feature that can be quantitatively accounted for through a model governed by dynamic cross-linking. The elastic behavior of the network is highly nonlinear, becoming much stiffer with applied stress. This nonlinear elastic response is also highly sensitive to the mutations of Actn4. In particular, we observe that actin networks cross-linked with Actn4 bearing the disease-causing K255E mutation are more brittle, with a lower breaking stress in comparison to networks cross-linked with wild-type Actn4. Furthermore, a mutation that ablates the first actin binding site (ABS1) in Actn4 abrogates the network's ability to stress-stiffen is standard nomenclature. These changes in the mechanical properties of actin networks cross-linked with mutant Actn4 may represent physical determinants of the underlying disease mechanism in inherited focal segmental glomerulosclerosis.

Elasticity in ionically cross-linked neurofilament networks.

Neurofilaments are found in abundance in the cytoskeleton of neurons, where they act as an intracellular framework protecting the neuron from external stresses. To elucidate the nature of the mechanical properties that provide this protection, we measure the linear and nonlinear viscoelastic properties of networks of neurofilaments. These networks are soft solids that exhibit dramatic strain stiffening above critical strains of 30-70%. Surprisingly, divalent ions such as Mg(2+), Ca(2+), and Zn(2+) act as effective cross-linkers for neurofilament networks, controlling their solidlike elastic response. This behavior is comparable to that of actin-binding proteins in reconstituted filamentous actin. We show that the elasticity of neurofilament networks is entropic in origin and is consistent with a model for cross-linked semiflexible networks, which we use to quantify the cross-linking by divalent ions.

Divalent cations crosslink vimentin intermediate filament tail domains to regulate network mechanics.

Intermediate filament networks in the cytoplasm and nucleus are critical for the mechanical integrity of metazoan cells. However, the mechanism of crosslinking in these networks and the origins of their mechanical properties are not understood. Here, we study the elastic behavior of in vitro networks of the intermediate filament protein vimentin. Rheological experiments reveal that vimentin networks stiffen with increasing concentrations of Ca(2+) and Mg(2+), showing that divalent cations act as crosslinkers. We quantitatively describe the elastic response of vimentin networks over five decades of applied stress using a theory that treats the divalent cations as crosslinkers: at low stress, the behavior is entropic in origin, and increasing stress pulls out thermal fluctuations from single filaments, giving rise to a nonlinear response; at high stress, enthalpic stretching of individual filaments significantly modifies the nonlinearity. We investigate the elastic properties of networks formed by a series of protein variants with stepwise tail truncations and find that the last 11 amino acids of the C-terminal tail domain mediate crosslinking by divalent ions. We determined the single-filament persistence length, l(P) approximately 0.5 mum, and Young's modulus, Y approximately 9 MPa; both are consistent with literature values. Our results provide insight into a crosslinking mechanism for vimentin networks and suggest that divalent ions may help regulate the cytoskeletal structure and mechanical properties of cells.

Mixed microtubules steer dynein-driven cargo transport into dendrites.

BACKGROUND: To establish and maintain their polarized morphology, neurons employ active transport driven by molecular motors to sort cargo between axons and dendrites. However, the basic traffic rules governing polarized transport on neuronal microtubule arrays are unclear. RESULTS: Here we show that the microtubule minus-end-directed motor dynein is required for the polarized targeting of dendrite-specific cargo, such as AMPA receptors. To directly examine how dynein motors contribute to polarized dendritic transport, we established a trafficking assay in hippocampal neurons to selectively probe specific motor protein activity. This revealed that, unlike kinesins, dynein motors drive cargo selectively into dendrites, governed by their mixed microtubule array. Moreover, axon-specific cargos, such as presynaptic vesicle protein synaptophysin, are redirected to dendrites by coupling to dynein motors. Quantitative modeling demonstrated that bidirectional dynein-driven transport on mixed microtubules provides an efficient mechanism to establish a stable density of continuously renewing vesicles in dendrites. CONCLUSIONS: These results demonstrate a powerful approach to study specific motor protein activity inside living cells and imply a key role for dynein in dendritic transport. We propose that dynein establishes the initial sorting of dendritic cargo and additional motor proteins assist in subsequent delivery.

Active cellular materials.

The materials cells are made of are strikingly different from man-made materials. Metabolism keeps cells out of equilibrium. Motor proteins and energy-consuming polymerization drive shape changes and motion. In contrast to macroscopic machines, though, there is no clear distinction between the force generators and the structural elements. Rather, the force-generating motor proteins are mixed with the elementary building blocks of cell structure on a molecular scale. The composite ensemble presents a new type of active material which is at the focus of intense current research. Simple model systems have been used successfully in exploring fundamental phenomena. Theoretical models are extending conventional soft matter approaches, and pioneering studies strive to analyze the complex nonequilibrium dynamics of living cells.

Cross-link-governed dynamics of biopolymer networks.

Recent experiments show that networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic time scale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G ∼ ω(1/2) for low frequencies ω. This model quantitatively describes the measured rheology of actin networks cross-linked with α-actinin-4 over more than four decades in frequency.

Brownian motion of stiff filaments in a crowded environment.

The thermal motion of stiff filaments in a crowded environment is highly constrained and anisotropic; it underlies the behavior of such disparate systems as polymer materials, nanocomposites, and the cell cytoskeleton. Despite decades of theoretical study, the fundamental dynamics of such systems remains a mystery. Using near-infrared video microscopy, we studied the thermal diffusion of individual single-walled carbon nanotubes (SWNTs) confined in porous agarose networks. We found that even a small bending flexibility of SWNTs strongly enhances their motion: The rotational diffusion constant is proportional to the filament-bending compliance and is independent of the network pore size. The interplay between crowding and thermal bending implies that the notion of a filament's stiffness depends on its confinement. Moreover, the mobility of SWNTs and other inclusions can be controlled by tailoring their stiffness.

An active biopolymer network controlled by molecular motors.

We describe an active polymer network in which processive molecular motors control network elasticity. This system consists of actin filaments cross-linked by filamin A (FLNa) and contracted by bipolar filaments of muscle myosin II. The myosin motors stiffen the network by more than two orders of magnitude by pulling on actin filaments anchored in the network by FLNa cross-links, thereby generating internal stress. The stiffening response closely mimics the effects of external stress applied by mechanical shear. Both internal and external stresses can drive the network into a highly nonlinear, stiffened regime. The active stress reaches values that are equivalent to an external stress of 14 Pa, consistent with a 1-pN force per myosin head. This active network mimics many mechanical properties of cells and suggests that adherent cells exert mechanical control by operating in a nonlinear regime where cell stiffness is sensitive to changes in motor activity. This design principle may be applicable to engineering novel biologically inspired, active materials that adjust their own stiffness by internal catalytic control.

Intracellular transport by active diffusion.

All substances exhibit constant random motion at the microscopic scale. This is a direct consequence of thermal agitation, and leads to diffusion of molecules and small particles in a liquid. In addition to this nondirected motion, living cells also use active transport mechanisms, such as motor activity and polymerization forces that depend on linear biopolymers and are therefore fundamentally directed in nature. Nevertheless, it has become increasingly clear that such active processes can also drive significant random fluctuations that can appear surprisingly like thermal diffusion of particles, but faster. Here, we discuss recent progress in quantifying this behavior and identifying its origins and consequences. We suggest that it represents an important and biologically tunable mechanism for transport in living cells.

Cytoplasmic diffusion: molecular motors mix it up.

Random motion within the cytoplasm gives rise to molecular diffusion; this motion is essential to many biological processes. However, in addition to thermal Brownian motion, the cytoplasm also undergoes constant agitation caused by the activity of molecular motors and other nonequilibrium cellular processes. Here, we discuss recent work that suggests this activity can give rise to cytoplasmic motion that has the appearance of diffusion but is significantly enhanced in its magnitude and which can play an important biological role, particularly in cytoskeletal assembly.

Nonequilibrium microtubule fluctuations in a model cytoskeleton.

Biological activity gives rise to nonequilibrium fluctuations in the cytoplasm of cells; however, there are few methods to directly measure these fluctuations. Using a reconstituted actin cytoskeleton, we show that the bending dynamics of embedded microtubules can be used to probe local stress fluctuations. We add myosin motors that drive the network out of equilibrium, resulting in an increased amplitude and modified time dependence of microtubule bending fluctuations. We show that this behavior results from steplike forces on the order of 10 pN driven by collective motor dynamics.