Session J20: Physics of the Cytoskeleton Across Scales I: Mechanics and Rheology

A mechanistic view of collective filament motion in active nematic networks

Protein filament networks are structures crucial for force generation and cell shape. A central open question is how collective filament dynamics emerges from interactions between individual network constituents. To address this question we study a minimal but generic model for a nematic network where filament sliding is driven by the action of motor proteins. Our theoretical analysis shows how the interplay between viscous drag on filaments and motor-induced forces governs force propagation through such interconnected filament networks. We find that the ratio between these antagonistic forces establishes the range of filament interaction, which determines how the local filament velocity depends on the polarity of the surrounding network. This force propagation mechanism implies that the polarity-independent sliding observed in Xenopus egg extracts, and in vitro experiments with purified components, is a consequence of a large force propagation length. We suggest how our predictions can be tested by tangible in vitro experiments whose feasibility is assessed with the help of simulations and an accompanying theoretical analysis.   

Time varying mechanical response of cytoskeletal networks

Actin filaments and microtubules are critical components of the cytoskeleton, a composite network of filamentous polymers and regulatory proteins. The synergistic interplay of networks of actin filaments and microtubules and their continuous disassembly and reassembly via active de/re-polymerization play a crucial role in a wide range of mechanical properties and processes, including cell stiffness, shape change, and motility. While in-vitro actin networks have been intensely investigated over the past two decades due to their promise for understanding cell mechanics and designing smart materials, questions remain as to how the composite nature of the cytoskeleton and de/re-polymerization kinetics of individual filaments impact the collective, time-varying mechanics of cytoskeletal networks. This talk will discuss an integrated approach consisting of theory and experiments, that seeks to address these questions. In particular, we will describe the mechanical response of composites made of interconnected networks of semiflexible and stiff filaments, time-varying responses of these networks, and how they can be explained by mathematical models that couple the time-evolution of filament lengths with rigidity percolation theory. Our results provide insights into mechanisms that enable cells to exhibit a myriad of mechanical properties and can inform the general principles underlying the mechanics of a large class of dynamic systems and biomaterials of current interest.   

Microrheology of active actin-microtubule networks

The cytoskeleton, composed of actin, microtubules, and associated motor and binding proteins, self-organizes into different structures and morphologies to drive diverse mechanical processes in eukaryotic cells. While in vitro actomyosin networks are well-characterized, few studies have examined how the structure and activity of these networks are altered by the presence of microtubules. We previously synthesized steady-state actin-microtubule networks, finding that mechanical properties, such as network elasticity, depend on molecular interactions between actin and microtubules, such as the degree of crosslinking and bundling. Here, we create active actin-microtubule networks by adding the motor protein myosin. Using confocal microscopy and microrheology, we characterize how the network structure evolves during motor activity, and connect how microscopic changes in network structure affect the mechanical properties of the network. Our results shed important new light on how actin-microtubule interactions influence the structure, mechanics and activity that motor-driven cytoskeleton networks exhibit.   

Probing length scale-dependent viscoelasticity from bending fluctuations of filaments

Micron-sized beads are commonly used to perform microrheology in soft media. The size of the particles sets the length scale at which properties are probed. This can limit results when the properties of the medium vary with length scale. A typical example of such a system are living cells. Cells are constructed hierarchically, with structural elements ranging from nano- to mesoscopic scales. Here, we introduce the use of semi-flexible filaments/tubes to probe scale-dependent dynamics. We analyze shape fluctuations of semi-flexible filaments. We show that the bending dynamics of filaments can be used to probe the physical properties of such media at multiple scales, corresponding to the wavelengths of the modes analyzed.   

Triggering salt-induced contraction of cytoskeletal networks with microfluidics

The mechanical tunability and morphology of the cytoskeleton is determined by interacting networks of semiflexible actin filaments and rigid microtubules. By altering the chemical environment of the cytoskeleton, actin and microtubule networks can dynamically change and rearrange to form entanglements, crosslinks and bundles. For example, increasing the concentration of divalent salt can induce crosslinking and bundling of actin filaments. Here, we use microfluidics and confocal fluorescence microscopy to show that increasing salt concentration triggers contraction of cytoskeleton networks in the absence of motor proteins. Specifically, we use microfluidics to cyclically vary the salt concentration over the course of minutes to hours while simultaneously visualizing the triggered structural changes to the networks and measuring the contraction velocity. Our measurements shed new light on how varying environmental conditions can dynamically tune the morphology of actin-microtubule networks and trigger active contraction without motor proteins.   

Slow stress relaxation of transient-crosslinked biopolymer networks

It is well established that the unbinding of crosslinkers enables transient-crosslinked biopolymer networks to flow at long times. A recent experiment, however, shows that exerting prestress on such a network leads to near solid-like viscoelastic response. In this talk I will propose a microscopic theory for the rheology of transient networks under prestress. We show that the solid-like dynamics naturally appears as a result of the coupling between the strain-stiffening of semiflexible polymers and the transient nature of the crosslinkers. Our theory predicts the scaling behavior of shear modulus over the whole frequency regime and quantitatively fits the experimental data. This theory may also explain similar slow stress relaxation previously found in living cells.   

Electric Field Guidance of Actin Waves

Directional cell migration induced by a DC electric field (DC EF) is an important physiological process involved in wound healing, development, and regeneration. This phenomenon is modulated by the self-generating waves of signaling molecules and actin traveling on cell membranes. It has been shown that chemical perturbations of wave components lead to changes in migratory behaviors. Here we first study how a DC EF provides a unidirectional perturbation of the actin wave patterns, then study the combined perturbation by a DC EF and nanotopography. By quantifying spatial-temporal actin wave patterns, we show that DC EFs can guide actin wave propagation, lead to inhomogeneous activities of actin waves, and alter cell migratory modes.   

Exploring the effects of actin-binding proteins on the percolation of actin networks using a mean field model

The actin cytoskeleton is a dynamical system that can exert forces and transmit forces between the cell and its environment. The dynamical and rheological properties of the actin cytoskeleton are modulated by actin binding proteins (ABPs). Some ABPs, such as α-actinin or Arp2/3, connect different actin filaments thereby changing the topology of the network. Other ABPs, such as myosin, can also exert forces on the network thus altering its dynamic behavior. In this work we model an actin system and its interaction with α-actinin, myosin and Arp2/3 using ordinary differential equations and stochastic mechanochemical simulations. We then use a mean field approach to quantify how the concentrations of different ABPs affect the connectivity and rigidity of the network. We find that the presence of Arp2/3 increases the connectivity of the network. We also discuss the conditions needed for force exertion and transmission in this system. We expect that this result may provide a theoretical insight into how ABPs affect the ability of the actin cytoskeleton to exert and transmit forces.   

Mechanical stability of microtubule lattices under high crowdedness

Microtubules (MTs) are hollow cylindrical biopolymers of tubulin subunits that play key roles in cells. Understanding their functions in cilia or neurons is difficult because MTs associate in highly crowded bundled arrays. For example, it is unclear how this crowdedness or confinement and the mutual interaction between MTs chains relate to the anisotropy of MT lattices. Because of the large degree of confinement in MT bundles, the use of experimental techniques to answer such questions is not easy. In contrast, computational modeling methods do not exhibit the experimental limitations when studying MTs bundles. Still, most of the existing models treat MTs as an elastic polymer network, in which the anisotropy of the lattice is built in and which excludes the possibility of formation of cracks in the lattice during force application. Our coarse-grained molecular simulations of the response of MT lattices to applied forces allow us to study formation and propagation of cracks. We present a modified indentation protocol to determine the mechanical response of MT lattices under conditions which mimic high confinement. Our model shows that the strength of interactions between MT in bundles has substantial influence on the magnitude of the forces that induce cracks in MT lattices.   

Understanding the Topology of Microtubules

The phenomenon of dynamical instability in microtubules is of immense importance in understanding transport within the cell. In recent times, these polymeric proteins have been studied as mechanical lattices possessing a topological edge mode (Phys. Rev. Lett. 103, 248101 (2009)). We extend this idea by modelling the microtubule as a cylindrical lattice of dimers, with interactions between dimers modelled by a hopping Hamiltonian. We show the emergence of topological edge modes, and propose the modelling of dynamic instability as a phase transition. We explicitly determine the conditions for the existence of these edge modes by setting up appropriate difference equations. We speculate on the biological implications of these results, by mapping the dynamic instability of microtubules to the propagation of lattice defects, and also discuss possible methods of computational/experimental verification via microscopic network models of microtubules.   

The role of multivalent actin-binding proteins in remodeling actomyosin networks

We explore the contribution of multivalent actin-binding proteins (ABPs) in remodeling actomyosin networks by using mesoscopic computer simulations. We model ABPs as junctions with varied multi-valencies that enable bundling or branching of actin filaments, which result in diverse morphologies of actomyosin networks. We developed network theory-based order parameters that quantify connectivity between graph nodes in order to analyze emergent morphologies in actomyosin networks. First, we show that ABPs, such as calmodulin-dependent kinase II (CaMKII), with multivalency greater than two not only increase the thickness of actin bundles, but also promote their arborization. Second, myosin motor proteins accelerate the arborization of actin filaments bundled by CaMKII. Because CaMKII is as abundant as actin filaments in neurons, it plays an important role in remodeling the morphology of actin filaments in actomyosin networks; CaMKII’s chemical binding to actin filaments alters the mechanical properties of actomyosin networks that underpin the plasticity of dendritic spines.   

Mechanical properties of branched actin networks

Gels of fibrous bio-polymers are ubiquitous within cells and their rigidity is crucial for their function. Our current understanding of their elastic response is usually understood as an interplay between the bending and stretching of their filaments. This point of view however fails when applied to the weakly coordinated branched actin networks found throughout the cell. Through experiments, simulations and theory, we show that their elasticity crucially involves reversible entanglements between their filaments. Additional entanglements may get locked in during network growth, setting the final properties of the network. These properties could be key to understanding how moving cells dynamically adapt their cytoskeleton to their environment.
  

Hydrodynamic effects on the motility of crawling eukaryotic cells

Eukaryotic cell motility is crucial during development, wound healing, the immune response, and cancer metastasis. Some eukaryotic cells can swim, but cells more commonly adhere to and crawl along the extracellular matrix. We study the relationship between hydrodynamics and adhesion that describe whether a cell is swimming, crawling, or combining these motions. Our simple model of a cell, based on the three-sphere swimmer, is capable of both swimming and crawling. As cell-matrix adhesion strength increases, the influence of hydrodynamics on migration diminish. Cells with significant adhesion crawl with speeds much larger than their nonadherent, swimming counterparts. We predict that, while most eukaryotic cells are in the strong-adhesion limit, increasing environment viscosity or decreasing cell-matrix adhesion could lead to hydrodynamic effects even in crawling cells. Signatures of hydrodynamic effects include dependence of cell speed on medium viscosity or the presence of a nearby substrate as well as interactions between noncontacting cells. These signatures are suppressed at large adhesion strengths, but even strongly adherent cells will generate fluid flows advecting passive particles and swimmers.