Session B40: Focus Session: Cytoskeleton and Biomechanics - Entanglement and Crosslinking

Seeing is believing: New insight into structure-mechanics relationships in entangled and crosslinked microtubule networks

The microtubule cytoskeleton is essential in maintaining the shape, strength and organization of cells and its misregulation has been implicated in neurological disorders and cancers. To better understand the structure-mechanics relationships in microtubule networks, we measure the force-dependent viscoelastic responses of entangled and sparsely crosslinked microtubule networks to precise microscale manipulation. We use magnetic tweezers devices to apply calibrated step stresses and measure the resultant strain as a function of time. At short times the material behaves as an elastic solid. The linear regime is large, with gentle stiffening observed in entangled networks above $\sim $70{\%} strains. Crosslinked networks are stiffer, and show an extended linear regime. At longer times, we find a creeping regime, suggesting that structural rearrangements of the network dominate the mechanical response. To understand the molecular origins of this behavior, we use a newly-developed portable magnetic tweezers device to observe the network morphology using a confocal microscope while simultaneously applying point-like stresses to embedded magnetic particles. We observe substantial network compression in front of the bead with no evidence of long-length scale filament flow, and find that the spatial extent of the deformation field depends sensitively on network architecture and connectivity. Our results are important to understanding the role of the cytoskeleton in regulating cargo transport in vivo, as well as the basic physics of non-affine deformations in rigid rod polymer networks.   

Actin filament curvature biases branching direction

Actin filaments are key components of the cellular machinery, vital for a wide range of processes ranging from cell motility to endocytosis. Actin filaments can branch, and essential in this process is a protein complex known as the Arp2/3 complex, which nucleate new ``daughter'' filaments from pre-existing ``mother'' filaments by attaching itself to the mother filament. Though much progress has been made in understanding the Arp2/3-actin junction, some very interesting questions remain. In particular, F-actin is a dynamic polymer that undergoes a wide range of fluctuations. Prior studies of the Arp2/3-actin junction provides a very static notion of Arp2/3 binding. The question we ask is how differently does the Arp2/3 complex interact with a straight filament compared to a bent filament? In this study, we used Monte Carlo simulations of a surface-tethered worm-like chain to explore possible mechanisms underlying the experimental observation that there exists preferential branch formation by the Arp2/3 complex on the convex face of a curved filament. We show that a fluctuation gating model in which Arp2/3 binding to the actin filament is dependent upon a rare high-local-curvature shape fluctuation of the filament is consistent with the experimental data.   

Condensation of F-Actin by Dimensional Reduction

We present a Brownian Dynamics simulation of the equilibrium condensation of F-actin in the presence of linker molecules. The filaments are modeled as worm-like chains, using finite element analysis. At low linker concentrations, the systems forms a gel whose physical properties do not depend on the linker molecules. If the linker concentration is increased then for isotropic linkers only a single mode of condensation is encountered: bundle formation. If the linker molecules impose a preferential angle between F-actin filaments, then condensation takes place either into a either a hexatic or squaratic two-dimensional liquid crystal phase or into a heterogeneous cluster. Condensation is driven by competition between linker and filament entropy, which imposes dimensional reduction on the F-actin aggregate.   

Stress Enhanced Gelation in $\alpha$-Actinin-4 Cross-linked Actin Networks

A hallmark of biopolymer networks is their exquisite sensitivity to stress, demonstrated for example, by pronounced nonlinear elastic stiffening. Typically, they also yield under increased static load, providing a mechanism to achieve fluid-like behavior. In this talk, I will demonstrate an unexpected dynamical behavior in biopolymer networks consisting of F-actin cross-linked by a physiological actin binding protein, $\alpha$-Actinin-4. Applied stress actually enhances gelation of these networks by delaying the onset of structural relaxation and network flow, thereby extending the regime of solid-like behavior to much lower frequencies. By using human kidney disease-associated mutant cross-linkers with varying binding affinities, we propose a molecular origin for this stress-enhanced gelation: It arises from the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior. This property may have important biological implications for intracellular mechanics, representing as it does a qualitatively new class of material behavior.   

Simulations and theory of model microtubule self-assembly

We used molecular dynamics simulations to study the self-assembly of artificial microtubules. The model monomer has a wedge-shape to promote formation of rings that stack to form tubules. Attractive interaction sites are on the sides for ring formation and top/bottom for filament growth. We have studied the assembly kinetics and dynamics as a function of these lateral and vertical interaction strengths. A full structure diagram was calculated. The range of interaction strengths that best form tubules has been determined. We found that tubules form better when the lateral strength is stronger than the filamental stength, which contrast the picture for microtubules. The interaction strengths must be weak enough to allow for reformation of the clusters that initially form. Besides tubules, a variety of structures form depending on the interaction parameters. Interestingly, helical tubes and other helical structures are frequently observed despite the fact that the minimum energy substructure is a nonhelical ring. We have used a simple Flory-Huggins type theory to characterize the structure diagram.   

Dynamical Length-Regulation of Microtubules

Microtubules (MTs) are vital constituents of the cytoskeleton. These stiff filaments are not only needed for mechanical support. They also fulfill highly dynamic tasks. For instance MTs build the mitotic spindle, which pulls the doubled set of chromosomes apart during mitosis. Hence, a well-regulated and adjustable MT length is essential for cell division. Extending a recently introduced model [1], we here study length-regulation of MTs. Thereby we account for both spontaneous polymerization and depolymerization triggered by motor proteins. In contrast to the polymerization rate, the effective depolymerization rate depends on the presence of molecular motors at the tip and thereby on crowding effects which in turn depend on the MT length. We show that these antagonistic effects result in a well-defined MT length. Stochastic simulations and analytic calculations reveal the exact regimes where regulation is feasible. Furthermore, the adjusted MT length and the ensuing strength of fluctuations are analyzed. Taken together, we make quantitative predictions which can be tested experimentally. These results should help to obtain deeper insights in the microscopic mechanisms underlying length-regulation. \\[4pt] [1] L.Reese, A.Melbinger, E.Frey, Biophys. J., {\bf 101}, 9, 2190 (2011)   

On the origins and extent of mechanical variation among cells

Why would any one biological cell be mechanically different from another from the same population? Prompted by findings of broad distributions of cell stiffness within populations, we investigate possible origins of intrinsic mechanical heterogeneity among single cells. Through optical stretching, a non-contact technique for deforming cells in the suspended state, we obtain the creep compliance and complex modulus of single cells. Measurements of hundreds of human mesenchymal stem cells and murine fibroblasts in the time and frequency domains reveal that mechanical heterogeneity is not detectably dependent on cell lineage, cell cycle, cytoskeletal crosslinking, or repeated loading. However, adenosine triphosphate (ATP) depletion reduces heterogeneity of both stiffness and fluidity values. We explore the connection between these two parameters by positing that mechanical variation predominantly arises from Gaussian fluctuations in cell fluidity, which can be interpreted as emergent agitation in the energy landscape of soft glassy materials. Our findings ultimately link relatively small structural variations within cytoskeletal networks to large mechanical differences among cells and cell populations.   

Non-Equilibrium Cell Mechanics Studied with a Dual Optical Trap

Cells communicate with their surroundings biochemically, but at the same time also sense the active and passive mechanical properties of their micro-environment. Cells can ``feel'' mechanical stress and they generate contractile forces through their acto-myosin network to actively probe the mechanical response of the material they adhere to or are embedded in. These mechanosensory interactions result in cellular responses. We have used a dual optical trap to perform force measurements on cells suspended between two fibronectin-coated beads. We analyzed the correlated fluctuations of the beads with high spatial and temporal resolution. Using a combination of active and passive microrheology, we can simultaneously determine the (non-thermal) forces generated by the cells and actively probe their visco-elastic response properties. Here, we present data on contractile forces and elastic response of 3T3 fibroblasts, demonstrating that the transmitted force depends on the trap stiffness (i.e. rigidity of the environment). Using biochemical perturbations, we have studied the contributions of different cytoskeletal elements to the active and passive mechanical properties of the cell.   

M {\&} M's: Mechanosensitivity and Mechanotransduction in Myoblasts

The effect of external mechanical stimulation of muscle precursor cells (myoblasts) during exercise is a crucial step in myogenesis. This effect takes place many hours later while muscles are in a resting state; however it remains unclear to what extent the role of force application has on the promotion of myogenesis. Here, we combine Traction Force Microscopy (TFM) and Atomic Force Microscopy (AFM) to directly measure the magnitude of generated cellular traction forces (CTFs) in myoblasts, as a result of controlled mechanical loading. Precise nanonewton forces (1 {\&} 10 nN) were applied to live cells with the AFM tip while simultaneous TFM measurements were performed. The experiment was performed on substrates ranging in elastic moduli ($E)$, (16-89 kPa) mimicking resting and active muscle tissue, respectively. The results of this analysis demonstrated that the magnitude of CTFs was dependent on substrate $E,$ as expected. However, CTFs only increased in response to applied force (compared to controls) on substrates with $E$ greater than 62 kPa. Our results suggest that muscle precursor cells are most sensitive to mechanical force when the surrounding muscle tissue is stiff and contracted, whereas myogenesis itself proceeds optimally on softer, resting tissue.   

Polymer Coated Surface Acoustic Wave Biosensor for Living Cells

A shear horizontal surface acoustic wave (SH-SAW) biosensor is fabricated on quartz wafer for measurement of mechanical properties of living cells. The SAW device was fabricated with a top film of polymer (PMMA, SU-8) to avoid immense attenuation in aqueous media. Several models were designed to operate under different frequencies such as 20MHz, 40MHz and 80MHz and higher in order to identify how frequency affect the sensitivity. A network analyzer was used to capture the resonant frequency of inter-digitated transducers (IDT) of SAW, and it is found that resonant frequency shift is closely correlated to the cell deposition on the sensing area of SAW.   

Modeling spinal cord biomechanics

Regeneration after spinal cord injury is a serious health issue and there is no treatment for ailing patients. To understand regeneration of the spinal cord we used a system where regeneration occurs naturally, such as the lamprey. In this work, we analyzed the stress response of the spinal cord to tensile loading and obtained the mechanical properties of the cord both in vitro and in vivo. Physiological measurements showed that the spinal cord is pre-stressed to a strain of 10$\%$, and during sinusoidal swimming, there is a local strain of 5$\%$ concentrated evenly at the mid-body and caudal sections. We found that the mechanical properties are homogeneous along the body and independent of the meninges. The mechanical behavior of the spinal cord can be characterized by a non-linear viscoelastic model, described by a modulus of 20 KPa for strains up to 15$\%$ and a modulus of 0.5 MPa for strains above 15$\%$, in agreement with experimental data. However, this model does not offer a full understanding of the behavior of the spinal cord fibers. Using polymer physics we developed a model that relates the stress response as a function of the number of fibers.   

Matrix elasticity perturbation and Lamin-A/C expression in stem cells modulate their mechanics and lineage specification

Commitment of stem cells to different lineages is regulated by many cues in their local microenvironment. They are particularly sensitive to the mechanical properties of their extracellular matrix. Nuclear lamins are fibrous proteins providing structural function and transcriptional regulation in the cell nucleus. In particular Lamin A/C levels could influence cellular mechanical sensitivity. Here we show that perturbation of the extracellular matrix and nucleus mechanics can direct stem cells lineage specification. We studied the behavior of human mensechymal stem cells (hMSC) cultured on thin highly ordered collagen nanofilms. To tune the mechanical properties of the nanofilms we used the enzyme transglutaminase as a crosslinking agent. AFM imaging and manipulation is used to examine the nano topography and mechanical properties of the films and cells. Film stiffening affects cells morphology, cytoskeleton organization and their elastic response. hMSCs cultured for two weeks on collagen nanofilms initially tune their stiffness with matrix elasticity but later continuously change it with time. We observed upregulation of osteogenic markers on cross-linked films and increased lamin A/C expression. We show that manipulating Lamin-A/C expression in stem cells also directs cell lineage with knockdown favoring adipogenesis and over expression favoring osteogenesis. We found positive correlation between matrix and nucleus mechanics and that they have a synergistic effect on hMSCs differentiation potential.   

Simulation of Second Harmonic Generation from Heterogeneous Microtubule Structures

Second harmonic generation imaging is a coherent nonlinear microscopy with contrast arising from certain asymmetric endogenous structures in cells, including spindle microtubules. As a second-order nonlinear optical process, SHG requires a noncentrosymmetric macromolecular organization to generate signal, so it can be used as a measure of microtubule polarity within spindles or other microtubule structures. We developed a simulation of SHG microscopy accounting for 3-dimensional orientation and circularly polarized excitation in order to quantify the dependence of SHG signal on microtubule density, spacing, polarity, and rotational order. SHG can be used to assess spindle polarity in living cells using simultaneous ratio imaging with two-photon excited fluorescence from labeled tubulin. The results from simulation are used to quantify microtubule polarity from SHG and TPEF images of spindles in the one-cell C. elegans embryo and Xenopus oocyte extract.