Spatial and Temporal Sensing Limits of Microtubule Polarization in Neuronal Growth Cones by Intracellular Gradients and Forces

Neuronal growth cones are the most sensitive amongst eukaryotic cells in responding to directional chemical cues. Although a dynamic microtubule cytoskeleton has been shown to be essential for growth cone turning, the precise nature of coupling of the spatial cue with microtubule polarization is less understood. Here we present a computational model of microtubule polarization in a turning neuronal growth cone (GC). We explore the limits of directional cues in modifying the spatial polarization of microtubules by testing the role of microtubule dynamics, gradients of regulators and retrograde forces along filopodia. We analyze the steady state and transition behavior of microtubules on being presented with a directional stimulus. The model makes novel predictions about the minimal angular spread of the chemical signal at the growth cone and the fastest polarization times. A regulatory reaction-diffusion network based on the cyclic phosphorylation-dephosphorylation of a regulator predicts that the receptor signal magnitude can generate the maximal polarization of microtubules and not feedback loops or amplifications in the network. Using both the phenomenological and network models we have demonstrated some of the physical limits within which the MT polarization system works in turning neuron.Comment: 7 figures and supplementary materia

Tensegrity and Motor-Driven Effective Interactions in a Model Cytoskeleton

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.Comment: 38 pages, 13 figure

Activation of skeletal muscle is controlled by a dual-filament mechano-sensing mechanism

Contraction of skeletal muscle is triggered by a transient rise in intracellular calcium concentration leading to a structural change in the actin-containing thin filaments that allows binding of myosin motors from the thick filaments. Most myosin motors are unavailable for actin binding in resting muscle because they are folded back against the thick filament backbone. Release of the folded motors is triggered by thick filament stress, implying a positive feedback loop in the thick filaments. However, it was unclear how thin and thick filament activation mechanisms are coordinated, partly because most previous studies of the thin filament regulation were conducted at low temperatures where the thick filament mechanisms are inhibited. Here, we use probes on both troponin in the thin filaments and myosin in the thick filaments to monitor the activation states of both filaments in near-physiological conditions. We characterize those activation states both in the steady state, using conventional titrations with calcium buffers, and during activation on the physiological timescale, using calcium jumps produced by photolysis of caged calcium. The results reveal three activation states of the thin filament in the intact filament lattice of a muscle cell that are analogous to those proposed previously from studies on isolated proteins. We characterize the rates of the transitions between these states in relation to thick filament mechano-sensing and show how thin- and thick-filament-based mechanisms are coupled by two positive feedback loops that switch on both filaments to achieve rapid cooperative activation of skeletal muscle

Doctor of Philosophy

dissertationActive transport of cargoes is critical for cellular function. To accomplish this, networks of cytoskeletal filaments form highways along which small teams of mechanochemical enzymes (molecular motors) take steps to pull associated cargoes. The robustness of this transport system is juxtaposed by the stochasticity that exists at several spatial and temporal scales. For instance, individual motors stochastically step, bind, and unbind while the cargo undergoes nonnegligible thermal fluctuations. Experimental advances have produced rich quantitative measurements of each of these stochastic elements, but the interaction between them remains elusive. In this thesis, we explore the roles of stochasticity in motor-mediated transport with four specific projects at different scales. We first construct a mean-field model of a cargo transported by two teams of opposing motors. This system is known to display bidirectionality: switching between phases of transport in opposite directions. We hypothesize that thermal fluctuations of the cargo drive the switching. From our model, we predict how cargo size influences the switching time, an experimentally measurable quantity to verify the hypothesis. In the second work, we investigate the force dependence of motor stepping, formulated as a state-dependent jump-diffusion model. We prove general results regarding the computation of the statistics of this process. From this framework, we find that thermal fluctuations may provide a nonmonotonic influence on the stepping rate of motors. The remaining projects investigate the behavior of nonprocessive motors, which take few steps before detaching. In collaboration with experimentalists, we study seemingly diffusive data of motor-mediated transport. Using a jump-diffusion model, the active and passive portions of the diffusivity are disentangled, and curious higher order statistics are explained as a sampling issue. Lastly, we construct a model of cooperative transport by nonprocessive motors, which we study using reward-renewal theory. The theory provides predictions about measured quantities such as run length, which suggest that geometric effects have a large influence on the transport ability of these motors

Active liquid crystals powered by force-sensing DNA-motor clusters

Cytoskeletal active nematics exhibit striking non-equilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order. The properties of the DNA linker enable the design of force-sensing clusters. When the load across the linker exceeds a critical threshold the clusters fall apart, ceasing to generate active stresses and slowing the system dynamics. Fluorescence readout reveals the fraction of bound clusters that generate interfilament sliding. In turn, this yields the average load experienced by the kinesin motors as they step along the microtubules. DNA-motor clusters provide a foundation for understanding the molecular mechanism by which nanoscale molecular motors collectively generate mesoscopic active stresses, which in turn power macroscale non-equilibrium dynamics of active nematics.Comment: main text: text 19 pages, 6 figures. Supplementary information: text 9 pages, 12 figure

Force-Velocity Curves of Motor Proteins Cooperating In Vivo

Motor proteins convert chemical energy into work, thereby generating persistent motion of cellular and subcellular objects. The velocities of motor proteins as a function of opposing loads have been previously determined in vitro for single motors. These single molecule force-velocity curves have been useful for elucidating motor kinetics and for estimating motor performance under physiological loads due to, for example, the cytoplasmic drag force on transported organelles. Here we report forcevelocity curves for single and multiple motors measured in vivo. Using motion enhanced differential interference contrast (MEDIC) movies of living NT2 (neuron-committed teratocarcinoma) cells at 37°C, three parameters were measured-velocity (v), radius (a), and effective cytoplasmic viscosity (n1)-as they applied to moving vesicles. These parameters were combined in Stokes\u27 equation, F= 6panv1, to determine the force, F, required to transport a single intracellular particle at velocity, v. In addition, the number of active motors was inferred from the multimodal pattern seen in a normalized velocity histogram. Using this inference, the resulting in vivo force-velocity curve for a single motor agrees with previously reported in vitro single motor force-velocity curves. Interestingly, however, the curves for two and three motors lie significantly higher in both measured velocity and computed force, which suggests that motors can work cooperatively to attain higher transport forces and velocities

Understanding the Cooperative Interaction between Myosin II and Actin Cross-Linkers Mediated by Actin Filaments during Mechanosensation

AbstractMyosin II is a central mechanoenzyme in a wide range of cellular morphogenic processes. Its cellular localization is dependent not only on signal transduction pathways, but also on mechanical stress. We suggest that this stress-dependent distribution is the result of both the force-dependent binding to actin filaments and cooperative interactions between bound myosin heads. By assuming that the binding of myosin heads induces and/or stabilizes local conformational changes in the actin filaments that enhances myosin II binding locally, we successfully simulate the cooperative binding of myosin to actin observed experimentally. In addition, we can interpret the cooperative interactions between myosin and actin cross-linking proteins observed in cellular mechanosensation, provided that a similar mechanism operates among different proteins. Finally, we present a model that couples cooperative interactions to the assembly dynamics of myosin bipolar thick filaments and that accounts for the transient behaviors of the myosin II accumulation during mechanosensation. This mechanism is likely to be general for a range of myosin II-dependent cellular mechanosensory processes

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto