Session A4: Physics of the Cytoskeleton I

Watching Mobility Engendered by Actin Polymerization

We have been investigating hydrodynamic flows engendered in molecular systems by active motion. In fact, active directed motion is ubiquitous as a transport mechanism within cells and other systems, sometimes by the action of molecular motors as they move along cytoskeletal filaments, sometimes by the polymerization and depolymerization of filament themselves. To probe this situation, we have employed fluorescence correlation spectroscopy (FCS) in the STED mode (stimulation emission-depletion), this super-resolution approach allowing us to investigate molecular mobility as averaged over a spectrum of space scales: from areas of the optical diffraction limit or larger, to regions as small as 30~40 nm. This comparison of FCS-STED measurements when the projected area investigated varies by a factor of >10, reveals remarkable scale dependence of the mobility that we infer.   

Modeling myosin VI stepping dynamics

Myosin VI is a molecular motor that transports intracellular cargo as well as acts as an anchor. The motor has been measured to have unusually large step size variation and it has been reported to make both long forward and short inchworm-like forward steps, as well as step backwards. We have been developing a model that incorporates this diverse stepping behavior in a consistent framework. Our model allows us to predict the dynamics of the motor under different conditions and investigate the evolutionary advantages of the large step size variation.   

Entropic Elasticity in the Giant Muscle Protein Titin

Intrinsically disordered proteins (IDPs) are a large and functionally important class of proteins that lack a fixed three-dimensional structure. Instead, they adopt a conformational ensemble of states which facilitates their biological function as molecular linkers, springs, and switches. Due to their conformational flexibility, it can be difficult to study IDPs using typical experimental methods. To overcome this challenge, we use a high-resolution single-molecule magnetic stretching technique to quantify IDP flexibility. We apply this technique to the giant muscle protein titin, measuring its elastic response at low forces. We present results demonstrating that titin's native elastic response derives from the combined entropic elasticity of its ordered and disordered domains.   

Building a Leading Edge: Influence of Gradients on Mobility and Rheology of Actin Networks

The leading edge of a migrating cell contains steep gradients in actin concentration and actin affiliated proteins. Using microfluidics and photo-uncaging of salt and ATP, we generate controlled gradients of actin concentration as well as the associated proteins fascin and Arp2/3. Tracers embedded in polymer networks with gradients do not show directed motion, but do have increased mobility compared with uniform polymer networks of the same concentration. We compare the experimental results to a dissipative dynamics simulation of the experimental conditions.   

Spectral Decomposition of Entropy Production in Acto-Myosin Gels

Active force generation at the molecular scale in living systems can result in stochastic non-equilibrium dynamics on mesoscopic scales. A characteristic feature of such non-equilibrium systems is the emergence of steady-state currents. Constant dissipation of energy is required to maintain these currents. Here, we introduce a non-invasive technique to probe non-equilibrium dynamics in active gels using single-walled carbon nanotubes (SWNTs). SWNTs are semi-flexible polymers with intrinsic fluorescence in the near infrared. We see breaking of detailed balance in the phase space spanned by the normal mode amplitudes of SWNT shape fluctuations, manifested through closed current cycles.~ These cycles imply a transfer of energy between different length scales. Using the fluctuations of phase space currents, we extract bounds on the local energy dissipation rate.~ The spectral decomposition of entropy production allows detailed examination of the spatial structure and correlations that underlie departures from thermal equilibrium.   

Fiber plucking: large emergent contractility in stiff biopolymer networks

The mechanical properties of the cell depend crucially on the tension of its cytoskeleton. Contractile stresses in this fiber network originate from the forces exerted by active motor proteins. Importantly, experimentally observed cell-scale stresses are much larger than would be expected from linear elastic transmission of the molecular forces. We have recently proposed a mechanism for this nonlinear stress amplification, involving extended filament buckling in the network\footnote{Ronceray, Broedersz and Lenz, Proc. Nat. Acad. Sci. USA, 113, 11, 2827–2832 (2016).}. We propose here an alternate mechanism: when active forces are exerted transversely on a filament, they induce a nonlinear tension in the plucked fiber. The resulting contractile response in the far-field can overwhelm dramatically the linear stress prediction. Importantly, such a \emph{plucking} force amplification relies on the surrounding network to be stiff and only moderately stressed. These conditions compete with those required to observe amplification due to fiber \emph{buckling}. Fiber networks thus provide several distinct pathways for living systems to amplify their molecular forces. Their relative importance in biological relevant situations could be assessed using experimentally testable scaling laws.   

Broken Detailed Balance of Filament Dynamics in Active Networks .

Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single- walled carbon nanotubes can be used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in biopolymer networks. We analytically calculated shape fluctuations of semi- flexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under non-equilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.   

Mechanical properties of dynamic microtubule networks

The mechanical properties of cytoskeletal networks have been studied extensively with in vitro microrheology methods to assess the effect of the composition and architecture of a network on its linear viscoelasticity, nonlinear rheology, and strength. Motor proteins have been shown to modulate mechanical response, introducing sources of athermal noise and network fluidization through driven filament sliding, while dynamic crosslinkers provide toughening and routes to self-repair. By contrast, the role of dynamic changes in filament length, which are common in cellular networks, has been largely unexplored. In this study, we demonstrate our ability to create three dimensional networks of microtubules without use of chemical stabilizers. This results in a space-spanning network of filaments that grow and shrink dynamically as a function of time. We use this platform to investigate the role of length fluctuations in determining the linear viscoelastic properties of entangled microtubule networks, as well as the ability of such networks to bear and transmit load. Using a combination of confocal microscopy and microrheology techniques, we find that the interplay between dynamic structure and mechanics plays an important role in determining the load-bearing performance of the network.   

Physical determinants of bipolar mitotic spindle assembly and stability in fission yeast

Mitotic spindles use an elegant bipolar architecture to segregate duplicated chromosomes with high fidelity. Bipolar spindles form from a monopolar initial condition; this is the most fundamental construction problem that the spindle must solve. Microtubules, motors, and crosslinkers are important for bipolarity, but the mechanisms necessary and sufficient for spindle assembly remain unknown. Here we describe a physical model that exhibits de novo bipolar spindle formation. We began with previously published data on fission-yeast spindle-pole-body size and microtubule number, kinesin-5 motors, kinesin-14 motors, and passive crosslinkers. Our model results agree quantitatively with our experiments in fission yeast, thereby establishing a minimal system with which to interrogate collective self assembly. By varying features of our model, we identify a set of functions essential for the generation and stability of spindle bipolarity. When kinesin-5 motors are present, their bidirectionality is essential, but spindles can form in the presence of passive crosslinkers alone. We also identify characteristic failed states of spindle assembly, which are avoided by creation and maintenance of antiparallel microtubule overlaps.   

Molecular crowding at microtubule plus-ends acts as a physical barrier to microtubule sliding for the organization of stable anti-parallel overlaps by PRC1 and Kif4A

The relative sliding of microtubules by motor proteins is important for the organization of specialized cellular microtubule networks. In cells, sliding filaments are likely to encounter crowded regions of microtubules, such as the plus-ends, which are densely occupied by motor and non-motor proteins. How molecular crowding impacts microtubule sliding is not well understood. Here, we reconstitute the collective activities of the non-motor protein PRC1 and the motor protein Kif4A on anti-parallel microtubules to address this question. We find that the accumulation of PRC1 and Kif4A at microtubule-plus ends (`end-tags') can act as a physical barrier to Kif4A-mediated microtubule sliding. This enables the formation of stable microtubule overlaps that persist even after the deactivation of the motor protein. Our data suggest that while end-tags stabilize anti-parallel overlaps by inhibiting relative sliding, they permit the remodeling of the microtubule bundles by external forces, as may be required for the reorganization of microtubule networks during dynamic cellular processes.   

Motor protein-induced length regulation of microtubule anti-parallel overlaps

Motor proteins moving on microtubule overlaps play an important role during cell division. The central mitotic spindle remains stable in size during anaphase due to overlap length regulation. The mechanisms by which microtubule antiparallel overlaps are regulated in length are still poorly understood. We studied length regulation system inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps. Overall motor binding is key for controlling the length. We compare our results to kinetic Monte Carlo simulations and show how the steady state length depends on bulk motor concentration and the origin of the critical concentration.