A simple active fluid model unites cytokinesis, cell crawling, and axonal outgrowth.

Axonal outgrowth, cell crawling, and cytokinesis utilize actomyosin, microtubule-based motors, cytoskeletal dynamics, and substrate adhesions to produce traction forces and bulk cellular motion. While it has long been appreciated that growth cones resemble crawling cells and that the mechanisms that drive cytokinesis help power cell crawling, they are typically viewed as unique processes. To better understand the relationship between these modes of motility, here, we developed a unified active fluid model of cytokinesis, amoeboid migration, mesenchymal migration, neuronal migration, and axonal outgrowth in terms of cytoskeletal flow, adhesions, viscosity, and force generation. Using numerical modeling, we fit subcellular velocity profiles of the motions of cytoskeletal structures and docked organelles from previously published studies to infer underlying patterns of force generation and adhesion. Our results indicate that, during cytokinesis, there is a primary converge zone at the cleavage furrow that drives flow towards it; adhesions are symmetric across the cell, and as a result, cells are stationary. In mesenchymal, amoeboid, and neuronal migration, the site of the converge zone shifts, and differences in adhesion between the front and back of the cell drive crawling. During neuronal migration and axonal outgrowth, the primary convergence zone lies within the growth cone, which drives actin retrograde flow in the P-domain and bulk anterograde flow of the axonal shaft. They differ in that during neuronal migration, the cell body is weakly attached to the substrate and thus moves forward at the same velocity as the axon. In contrast, during axonal outgrowth, the cell body strongly adheres to the substrate and remains stationary, resulting in a decrease in flow velocity away from the growth cone. The simplicity with which cytokinesis, cell crawling, and axonal outgrowth can be modeled by varying coefficients in a simple model suggests a deep connection between them.

Microtubule polarity flaws as a treatable driver of neurodegeneration.

Microtubule disruption is a common downstream mechanism leading to axonal degeneration in a number of neurological diseases. To date, most studies on this topic have focused on the loss of microtubule mass from the axon, as well as changes in the stability properties of the microtubules and/or their tubulin composition. Here we posit corruption of the normal pattern of microtubule polarity orientation as an underappreciated and yet treatable contributor to axonal degeneration. We include computational modeling to fortify the rigor of our considerations. Our simulations demonstrate that even a small deviation from the usual polarity pattern of axonal microtubules is detrimental to motor-based trafficking of organelles and other intracellular cargo. Additional modeling predicts that axons with such deviations will exhibit significantly reduced speed and reliability of organelle transport, and that localized clusters of wrongly oriented microtubules will result in traffic jams of accumulated organelles.

Model for Coordination of Microtubule and Actin Dynamics in Growth Cone Turning.

In the developing nervous system, axons are guided to their synaptic targets by motile structures at the axon tip called growth cones, which reorganize their cytoskeleton in order to steer in response to chemotactic cues. Growth cone motility is mediated by an actin-adhesion "clutch" mechanism, in which mechanical attachment to a substrate, coupled with polarized actin growth, produces leading-edge protrusion. Several studies suggest that dynamic microtubules (MTs) in the growth cone periphery play an essential role in growth cone steering. It is not yet well-understood how the MT cytoskeleton and the dynamic actin-adhesion clutch system are coordinated to promote growth cone navigation. I introduce an experimentally motivated stochastic model of the dynamic reorganization of the growth cone cytoskeleton in response to external guidance cues. According to this model, asymmetric decoupling of MTs from actin retrograde flow leads to a local influx of MTs to the growth cone leading edge, and the leading-edge MT accumulation is amplified by positive feedback between MTs and the actin-adhesion clutch system. Local accumulation of MTs at the leading edge is hypothesized to increase actin adhesion to the substrate, which attenuates actin retrograde flow and promotes leading-edge protrusion. Growth cone alignment with the chemotactic gradient is predicted to be most effective for intermediate levels of sensitivity of the adhesion strength to the presence of leading-edge MTs. Quantitative predictions of the MT distribution and the local rate of retrograde actin flow will allow the hypothetical positive feedback mechanism to be experimentally tested.

Polarity sorting of axonal microtubules: a computational study.

We present a computational model to test a "polarity sorting" mechanism for microtubule (MT) organization in developing axons. We simulate the motor-based axonal transport of short MTs to test the hypothesis that immobilized cytoplasmic dynein motors transport short MTs with their plus ends leading, so "mal-oriented" MTs with minus-end-out are transported toward the cell body while "correctly" oriented MTs are transported in the anterograde direction away from the soma. We find that dynein-based transport of short MTs can explain the predominately plus-end-out polarity pattern of axonal MTs but that transient attachments of plus-end-directed motor proteins and nonmotile cross-linker proteins are needed to explain the frequent pauses and occasional reversals observed in live-cell imaging of MT transport. Static cross-linkers increase the likelihood of a stalled "tug-of-war" between retrograde and anterograde forces on the MT, providing an explanation for the frequent pauses of short MTs and the immobility of longer MTs. We predict that inhibition of the proposed static cross-linker will produce disordered transport of short MTs and increased mobility of longer MTs. We also predict that acute inhibition of cytoplasmic dynein will disrupt the polarity sorting of MTs by increasing the likelihood of "incorrect" sorting of MTs by plus-end-directed motors.

Cytoplasmic Dynein Transports Axonal Microtubules in a Polarity-Sorting Manner.

Axonal microtubules are predominantly organized into a plus-end-out pattern. Here, we tested both experimentally and with computational modeling whether a motor-based polarity-sorting mechanism can explain this microtubule pattern. The posited mechanism centers on cytoplasmic dynein transporting plus-end-out and minus-end-out microtubules into and out of the axon, respectively. When cytoplasmic dynein was acutely inhibited, the bi-directional transport of microtubules in the axon was disrupted in both directions, after which minus-end-out microtubules accumulated in the axon over time. Computational modeling revealed that dynein-mediated transport of microtubules can establish and preserve a predominantly plus-end-out microtubule pattern as per the details of the experimental findings, but only if a kinesin motor and a static cross-linker protein are also at play. Consistent with the predictions of the model, partial depletion of TRIM46, a protein that cross-links axonal microtubules in a manner that influences their polarity orientation, leads to an increase in microtubule transport.

Model for adhesion clutch explains biphasic relationship between actin flow and traction at the cell leading edge.

Cell motility relies on the continuous reorganization of a dynamic actin-myosin-adhesion network at the leading edge of the cell, in order to generate protrusion at the leading edge and traction between the cell and its external environment. We analyze experimentally measured spatial distributions of actin flow, traction force, myosin density, and adhesion density in control and pharmacologically perturbed epithelial cells in order to develop a mechanical model of the actin-adhesion-myosin self-organization at the leading edge. A model in which the F-actin network is treated as a viscous gel, and adhesion clutch engagement is strengthened by myosin but weakened by actin flow, can explain the measured molecular distributions and correctly predict the spatial distributions of the actin flow and traction stress. We test the model by comparing its predictions with measurements of the actin flow and traction stress in cells with fast and slow actin polymerization rates. The model predicts how the location of the lamellipodium-lamellum boundary depends on the actin viscosity and adhesion strength. The model further predicts that the location of the lamellipodium-lamellum boundary is not very sensitive to the level of myosin contraction.

Membrane tension, myosin force, and actin turnover maintain actin treadmill in the nerve growth cone.

A growth cone is a motile structure at the tips of axons that is driven by the actin network and guides axon extension. Low actin adhesion to the substrate creates a stationary actin treadmill that allows leading-edge protrusion when adhesion increases in response to guidance cues. We use experimental measurements in the Aplysia bag growth cone to develop and constrain a simple mechanical model of the actin treadmill. We show that actin retrograde flow is primarily generated by myosin contractile forces, but when myosin is inhibited, leading-edge membrane tension increases and drives the flow. By comparing predictions of the model with previous experimental measurements, we demonstrate that lamellipodial and filopodial filament breaking contribute equally to the resistance to the flow. The fully constrained model clarifies the role of actin turnover in the mechanical balance driving the actin treadmill and reproduces the recent experimental observation that inhibition of actin depolymerization causes retrograde flow to slow exponentially with time. We estimate forces in the actin treadmill, and we demonstrate that measured G-actin distributions are consistent with the existence of a forward-directed fluid flow that transports G-actin to the leading edge.

Effectiveness of beads for tracking small-scale molecular motor dynamics.

Investigations into molecular motor dynamics are increasingly focused on small-scale features of the motor's motion. We define performance measures of a common type of single-molecule motility assay, the bead assay, for its ability to detect such features. Using numerical models, we explore the dependence of assay performance on a number of experimentally controllable parameters, including bead size, optical force, and the method of attaching the bead to the motor. We find that the best parameter choice depends on the objective of the experiments, and give a guide to parameter selection. Comparison of the models against experimental data from a recent bead assay of myosin V exemplifies how our methods can also be used to extract additional information from bead assays, particularly that related to small-scale features. By analyzing the experimental data we find evidence for previously undetected multiple waiting states of the bead-motor complex. Furthermore, from numerical simulations we find that equilibrium bead dynamics display features previously attributed to aborted motor steps, and that bead dynamics alone can produce multiple subphases during a step.

Mechanochemical model for myosin V.

A rigorous numerical test of a hypothetical mechanism of a molecular motor should model explicitly the diffusive motion of the motor's degrees of freedom as well as the transition rates between the motor's chemical states. We present such a Brownian dynamics, mechanochemcial model of the coarse-grain structure of the dimeric, linear motor myosin V. Compared with run-length data, our model provides strong support for a proposed strain-controlled gating mechanism that enhances processivity. We demonstrate that the diffusion rate of a detached motor head during motor stepping is self-consistent with known kinetic rate constants and can explain the motor's key performance features, such as speed and stall force. We present illustrative and realistic animations of motor stepping in the presence of thermal noise. The quantitative success and illustrative power of this type of model suggest that it will be useful in testing our understanding of a range of biological and synthetic motors.

Realization of a feedback controlled flashing ratchet.

A flashing ratchet transports diffusive particles using a time-dependent, asymmetric potential. The particle speed is predicted to increase when a feedback algorithm based on the particle position is used. We have experimentally realized such a feedback ratchet using an optical line trap, and observed that use of feedback increases velocity by up to an order of magnitude. We compare two different feedback algorithms for small particle numbers, and find good agreement with simulations. We also find that existing algorithms can be improved to be more tolerant to feedback delay times.

Mechanical coupling in flashing ratchets.

We consider the transport of rigid objects with internal structure in a flashing ratchet potential by investigating the overdamped behavior of a rodlike chain of evenly spaced point particles. In one dimension, analytical arguments show that the velocity can reverse direction multiple times in response to changing the size of the chain or the temperature of the heat bath. The physical reason is that the effective potential experienced by the mechanically coupled objects can have a different symmetry than that of individual objects. All analytical predictions are confirmed by Brownian dynamics simulations. These results may provide a route to simple, coarse-grained models of molecular motor transport that incorporate an object's size and rotational degrees of freedom into the mechanism of transport.

Single-polymer Brownian motor: a simulation study.

Numerical simulation is used to study a single polymer chain in a flashing ratchet potential to determine how the mechanism of this Brownian motor system is affected by the presence of internal degrees of freedom. The polymer is modeled by a freely jointed chain with N monomers in which the monomers interact via a repulsive Lennard-Jones potential and neighboring monomers on the chain are connected by finite extensible nonlinear elastic bonds. Each monomer is acted upon by a 1D asymmetric, piecewise linear potential of spatial period L comparable to the radius of gyration of the polymer. This potential is also characterized by a localization time, t(on), and by a free diffusion time, t(off). We characterize the average motor velocity as a function of L, t(off), and N to determine optimal parameter ranges, and we evaluate motor performance in terms of finite dispersion, Peclet number, rectification efficiency, stall force, and transportation of a load against a viscous drag. We find that the polymer motor performs qualitatively better than a single particle in a flashing ratchet: with increasing N, the polymer loses velocity much more slowly than expected in the absence of internal degrees of freedom, and the motor stall force increases linearly with N. To understand these cooperative aspects of motor operation, we analyze relevant Rouse modes. The experimental feasibility is analyzed and the parameters of the model are scaled to those of lambda-DNA. Finally, in the context of experimental realization, we present initial modeling results for a 2D flashing ratchet constructed using an electrode array, and find good agreement with the results of 1D simulations although the polymer in the 2D potential sometimes briefly "detaches" from the electrode surface.