Dynamics of Active Semiflexible Polymers

Active fluctuations, driven by processes that consume ATP, are prevalent in living cells and are mostly driven by different forms of molecular motors. Such motors often move and transmit forces along biopolymers, which in general can be treated as semiflexible chains. We present a theoretical analysis of the active (out of thermal equilibrium) fluctuation of semiflexible polymers, using both analytical and simulation methods. We find that enhanced diffusion, even superdiffusive, occurs in a well-defined temporal regime, defined by the thermal modes of the chain and the typical timescale of the activity. In addition, we find a dynamic resonance-like condition between the elastic modes of the chain and the duration of the active force, which leads to enhanced spatial correlation of local displacements. These results are in qualitative agreement with observations of cytoskeletal biopolymers, and were recently observed for the dynamics of chromatin in interphase cells. We therefore propose that the interplay between elasticity and activity is driving long-range correlations in our model system, and may also be manifest inside living cells.     

Anterograde Microtubule Transport Drives Microtubule Bending in LLC-PK1 Epithelial Cells

Microtubules (MTs) have been proposed to act mechanically as compressive struts that resist both actomyosin contractile forces and their own polymerization forces to mechanically stabilize cell shape. To identify the origin of MT bending, we directly observed MT bending and F-actin transport dynamics in the periphery of LLC-PK1 epithelial cells. We found that F-actin is nearly stationary in these cells even as MTs are deformed, demonstrating that MT bending is not driven by actomyosin contractility. Furthermore, the inhibition of myosin II activity through the use of blebbistatin results in microtubules that are still dynamically bending. In addition, as determined by fluorescent speckle microscopy, MT polymerization rarely results, if ever, in bending. We suppressed dynamic instability using nocodazole, and we observed no qualitative change in the MT bending dynamics. Bending most often results from anterograde transport of proximal portions of the MT toward a nearly stationary distal tip. Interestingly, we found that in an in vitro kinesin-MT gliding assay, MTs buckle in a similar manner. To make quantitative comparisons, we measured curvature distributions of observed MTs and found that the in vivo and in vitro curvature distributions agree quantitatively. In addition, the measured MT curvature distribution is not Gaussian, as expected for a thermally driven semiflexible polymer, indicating that thermal forces play a minor role in MT bending. We conclude that many of the known mechanisms of MT deformation, such as polymerization and acto-myosin contractility, play an inconsequential role in mediating MT bending in LLC-PK1 cells and that MT-based molecular motors likely generate most of the strain energy stored in the MT lattice. The results argue against models in which MTs play a major mechanical role in LLC-PK1 cells and instead favor a model in which mechanical forces control the spatial distribution of the MT array.     

Transport Properties of Melanosomes along Microtubules Interpreted by a Tug-of-War Model with Loose Mechanical Coupling

In this work, we explored theoretically the transport of organelles driven along microtubules by molecular motors of opposed polarities using a stochastic model that considers a Langevin dynamics for the cargo, independent cargo-motor linkers and stepping motion for the motors. It has been recently proposed that the stiffness of the motor plays an important role when multiple motors collectively transport a cargo. Therefore, we considered in our model the recently reported values for the stiffness of the cargo-motor linker determined in living cells (～0.01 pN/nm, [1]) which is significantly lower than the motor stiffness obtained in in vitro assays and used in previous studies. Our model could reproduce the multimodal velocity distributions and typical trajectory characteristics including the properties of the reversions in the overall direction of motion observed during melanosome transport along microtubules in Xenopus laevis melanophores. Moreover, we explored the contribution of the different motility states of the cargo-motor system to the different modes of the velocity distributions and could identify the microscopic mechanisms of transport leading to trajectories compatible with those observed in living cells. Finally, by changing the attachment and detachment rates, the model could reproduce the different velocity distributions observed during melanosome transport along microtubules in Xenopus laevis melanophores stimulated for aggregation and dispersion. Our analysis suggests that active tug-of-war processes with loose mechanical coupling can account for several aspects of cargo transport along microtubules in living cells.     

Extracting the Stepping Dynamics of Molecular Motors in Living Cells from Trajectories of Single Particles

Molecular motors are responsible of transporting a wide variety of cargos in the cytoplasm. Current efforts are oriented to characterize the biophysical properties of motors in cells with the aim of elucidating the mechanisms of these nanomachines in the complex cellular environment. In this study, we present an algorithm designed to extract motor step sizes and dwell times between steps from trajectories of motors or cargoes driven by motors in cells. The algorithm is based on finding patterns in the trajectory compatible with the behavior expected for a motor step, i.e., a region of confined motion followed by a jump in the position to another region of confined motion with similar characteristics to the previous one. We show that this algorithm allows the analysis of 2D trajectories even if they present complex motion patterns such as active transport interspersed with diffusion and does not require the assumption of a given step size or dwell period. The confidence on the step detection can be easily obtained and allows the evaluation of the confidence of the dwell and step size distributions. To illustrate the possible applications of this algorithm, we analyzed trajectories of myosin-V driven organelles in living cells.     

A Highlights from MBoC Selection: Diffusion of GPI-anchored proteins is influenced by the activity of dynamic cortical actin

Molecular diffusion at the surface of living cells is believed to be predominantly driven by thermal kicks. However, there is growing evidence that certain cell surface molecules are driven by the fluctuating dynamics of cortical cytoskeleton. Using fluorescence correlation spectroscopy, we measure the diffusion coefficient of a variety of cell surface molecules over a temperature range of 24–37°C. Exogenously incorporated fluorescent lipids with short acyl chains exhibit the expected increase of diffusion coefficient over this temperature range. In contrast, we find that GPI-anchored proteins exhibit temperature-independent diffusion over this range and revert to temperature-dependent diffusion on cell membrane blebs, in cells depleted of cholesterol, and upon acute perturbation of actin dynamics and myosin activity. A model transmembrane protein with a cytosolic actin-binding domain also exhibits the temperature-independent behavior, directly implicating the role of cortical actin. We show that diffusion of GPI-anchored proteins also becomes temperature dependent when the filamentous dynamic actin nucleator formin is inhibited. However, changes in cortical actin mesh size or perturbation of branched actin nucleator Arp2/3 do not affect this behavior. Thus cell surface diffusion of GPI-anchored proteins and transmembrane proteins that associate with actin is driven by active fluctuations of dynamic cortical actin filaments in addition to thermal fluctuations, consistent with expectations from an “active actin-membrane composite” cell surface.     

Chromatin Hydrodynamics

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory—the two-fluid model—in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model—the Maxwell fluid—for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity.     

Chromatin Hydrodynamics

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory—the two-fluid model—in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model—the Maxwell fluid—for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity.     

Nonequilibrium fluctuations of mechanically stretched single red blood cells detected by optical tweezers

We study the thermal and out-of-equilibrium mechanical dynamics of single, living human red blood cells (RBCs) by combining two-probe passive and active microrheology techniques. Both experiments were performed quasisimultaneously on the same cell using two identical polystyrene probes, biochemically attached to the cell membrane. We obtained compelling evidence of nonequilibrium fluctuations in the RBCs under physiological condition and without the influence of any external chemicals. The spectral distributions of metabolically driven forces and viscoelastic response were evaluated in the relaxed and stretched states, intended to simulate the varying natural environment of the cells during blood circulation. We found that the internally generated forces are more pronounced in the stretched state, suggesting a stress-dependent RBC activity.     

Structural Hierarchy Governs Fibrin Gel Mechanics

Fibrin gels are responsible for the mechanical strength of blood clots, which are among the most resilient protein materials in nature. Here we investigate the physical origin of this mechanical behavior by performing rheology measurements on reconstituted fibrin gels. We find that increasing levels of shear strain induce a succession of distinct elastic responses that reflect stretching processes on different length scales. We present a theoretical model that explains these observations in terms of the unique hierarchical architecture of the fibers. The fibers are bundles of semiflexible protofibrils that are loosely connected by flexible linker chains. This architecture makes the fibers 100-fold more flexible to bending than anticipated based on their large diameter. Moreover, in contrast with other biopolymers, fibrin fibers intrinsically stiffen when stretched. The resulting hierarchy of elastic regimes explains the incredible resilience of fibrin clots against large deformations.     

Energy flow considerations and thermal fluctuational opening of DNA base pairs at a replicating fork: unwinding consistent with observed replication rates.

The effect of an open loop of various sizes on the thermal stability of the adjoining intact base pairs in a duplex DNA chain is studied in a lattice model of Poly(dG).Poly(dC). We find that for a Y-shaped fork configuration the thermal fluctuation at the fork is so enhanced that the life time of the adjoining base pair is much smaller than the 1 millisecond time scale associated with helicase separation of a base pair in some systems. Our analysis indicates that thermal fluctuational base pair opening may be of importance in facilitating the enzyme unwinding process during chain elongation of a replicating DNA. It is most likely that the thermal fluctuational opening of the base pair at the junction of a replicating fork is fast enough so that a DNA unwinding enzyme can encounter an unstacked base pair with reasonable probability. This conclusion can explain several experimental observations regarding the temporal relationship between ATP hydrolysis by accessory proteins and primer elongation by a holoenzyme complex in ssDNA. We also discuss a mechanism by which the energy associated with ATP hydrolysis may enhance the thermal driven base opening mechanism.     

Protein localization by actin treadmilling and molecular motors regulates stereocilia shape and treadmilling rate

We present a physical model that describes the active localization of actin-regulating proteins inside stereocilia during steady-state conditions. The mechanism of localization is through the interplay of free diffusion and directed motion, which is driven by coupling to the treadmilling actin filaments and to myosin motors that move along the actin filaments. The resulting localization of both the molecular motors and their cargo is calculated, and is found to have an exponential (or steeper) profile. This localization can be at the base (driven by actin retrograde flow and minus-end myosin motors), or at the stereocilia tip (driven by plus-end myosin motors). The localization of proteins that influence the actin depolymerization and polymerization rates allow us to describe the narrow shape of the stereocilia base, and the observed increase of the actin polymerization rate with the stereocilia height.     

Energy Flow Considerations and Thermal Fluctuational Opening of DNA Base Pairs at a Replicating Fork: Unwinding Consistent with Observed Replication Rates

Abstract

The effect of an open loop of various sizes on the thermal stability of the adjoining intact base pairs in a duplex DNA chain is studied in a lattice model of Poly(dG) · Poly(dC). We find that for a Y-shaped fork configuration the thermal fluctuation at the fork is so enhanced that the life time of the adjoining base pair is much smaller than the 1 millisecond time scale associated with helicase separation of a base pair in some systems. Our analysis indicates that thermal fluctuational base pair opening may be of importance in facilitating the enzyme unwinding process during chain elongation of a replicating DNA. It is most likely that the thermal fluctuational opening of the base pair at the junction of a replicating fork is fast enough so that a DNA unwinding enzyme can encounter an unstacked base pair with reasonable probability. This conclusion can explain several experimental observations regarding the temporal relationship between ATP hydrolysis by accessory proteins and primer elongation by a holoenzyme complex in ssDNA. We also discuss a mechanism by which the energy associated with ATP hydrolysis may enhance the thermal driven base opening mechanism.     

Autoinhibition of the kinesin-2 motor KIF17 via dual intramolecular mechanisms

Long-distance transport in cells is driven by kinesin and dynein motors that move along microtubule tracks. These motors must be tightly regulated to ensure the spatial and temporal fidelity of their transport events. Transport motors of the kinesin-1 and kinesin-3 families are regulated by autoinhibition, but little is known about the mechanisms that regulate kinesin-2 motors. We show that the homodimeric kinesin-2 motor KIF17 is kept in an inactive state in the absence of cargo. Autoinhibition is caused by a folded conformation that enables nonmotor regions to directly contact and inhibit the enzymatic activity of the motor domain. We define two molecular mechanisms that contribute to autoinhibition of KIF17. First, the C-terminal tail interferes with microtubule binding; and second, a coiled-coil segment blocks processive motility. The latter is a new mechanism for regulation of kinesin motors. This work supports the model that autoinhibition is a general mechanism for regulation of kinesin motors involved in intracellular trafficking events.     

Myosin II phosphorylation and the dynamics of stress fibers in serum-deprived and stimulated fibroblasts.

The actin-based cytomatrix generates stress fibers containing a host of proteins including actin and myosin II and whose dynamics are easily observable in living cells. We developed a dual-radioisotope-based assay of myosin II phosphorylation and applied it to serum-deprived fibroblasts treated with agents that modified the dynamic distribution of stress fibers and/or altered the phosphorylation state of myosin II. Serum-stimulation induced an immediate and sustained increase in the level of myosin II heavy chain (MHC) and 20-kDa light chain (LC20) phosphorylation over the same time course that it caused stress fiber contraction. Cytochalasin D, shown to cause stress fiber fragmentation and contraction, had little effect on myosin II phosphorylation. Okadaic acid, a protein phosphatase inhibitor, induced a delayed but massive cell shortening preceded by a large increase in MHC and LC20 phosphorylation. Staurosporine, a kinase inhibitor known to effect dissolution but not contraction of stress fibers, immediately caused an increase in MHC and LC20 phosphorylation followed within minutes by the dephosphorylation of LC20 to a level below that of untreated cells. We therefore propose that the contractility of the actin-based cytomatrix is regulated by both modulating the activity of molecular motors such as myosin II and by altering the gel structure in such a manner as to either resist or yield to the tension applied by the motors.     

Active gels: dynamics of patterning and self-organization

The actin cytoskeleton is an active gel which constantly remodels during cellular processes such as motility and division. Myosin II molecular motors are involved in this active remodeling process and therefore control the dynamic self-organization of cytoskeletal structures. Due to the complexity of in vivo systems, it is hard to investigate the role of myosin II in the reorganization process which determines the resulting cytoskeletal structures. Here we use an in vitro model system to show that myosin II actively reorganizes actin into a variety of mesoscopic patterns, but only in the presence of bundling proteins. We find that the nature of the reorganization process is complex, exhibiting patterns and dynamical phenomena not predicted by current theoretical models and not observed in corresponding passive systems (excluding motors). This system generates active networks, asters and even rings depending on motor and bundling protein concentrations. Furthermore, the motors generate the formation of the patterns, but above a critical concentration they can also disassemble them and even totally prevent the polymerization and bundling of actin filaments. These results may suggest that tuning the assembly and disassembly of cytoskeletal structures can be obtained by tuning the local myosin II concentration/activity.     

Cargos Rotate at Microtubule Intersections during Intracellular Trafficking

Intracellular cargos are transported by molecular motors along actin and microtubules, but how their dynamics depends on the complex structure of the cytoskeletal network remains unclear. In this study, we investigated this longstanding question by measuring simultaneously the rotational and translational dynamics of cargos at microtubule intersections in living cells. We engineered two-faced particles that are fluorescent on one hemisphere and opaque on the other and used their optical anisotropy to report the rotation of cargos. We show that cargos undergo brief episodes of unidirectional and rapid rotation while pausing at microtubule intersections. Probability and amplitude of the cargo rotation depend on the geometry of the intersecting filaments. The cargo rotation is not random motion due to detachment from microtubules, as revealed by statistical analyses of the translational and rotational dynamics. Instead, it is an active rotation driven by motor proteins. Although cargos are known to pause at microtubule intersections, this study reveals a different dimension of dynamics at this seemingly static state and, more importantly, provides direct evidence showing the correlation between cargo rotation and the geometry of underlying microtubule intersections.     

Anomalous Dynamics of Melanosomes Driven by Myosin-V in Xenopus laevis Melanophores

The organization of the cytoplasm is regulated by molecular motors, which transport organelles and other cargoes along cytoskeleton tracks. In this work, we use single particle tracking to study the in vivo regulation of the transport driven by myosin-V along actin filaments in Xenopus laevis melanophores. Melanophores have pigment organelles or melanosomes, which, in response to hormones, disperse in the cytoplasm or aggregate in the perinuclear region. We followed the motion of melanosomes in cells treated to depolymerize microtubules during aggregation and dispersion, focusing the analysis on the dynamics of these organelles in a time window not explored before to our knowledge. These data could not be explained by previous models that only consider active transport. We proposed a transport-diffusion model in which melanosomes may detach from actin tracks and reattach to nearby filaments to resume the active motion after a given time of diffusion. This model predicts that organelles spend ∼70% and 10% of the total time in active transport during dispersion and aggregation, respectively. Our results suggest that the transport along actin filaments and the switching from actin to microtubule networks are regulated by changes in the diffusion time between periods of active motion driven by myosin-V.     

Organelle transport along microtubules in Xenopus melanophores: evidence for cooperation between multiple motors

Xenopus melanophores have pigment organelles or melanosomes which, in response to hormones, disperse in the cytoplasm or aggregate in the perinuclear region. Melanosomes are transported by microtubule motors, kinesin-2 and cytoplasmic dynein, and an actin motor, myosin-V. We explored the regulation of melanosome transport along microtubules in vivo by using a new fast-tracking routine, which determines the melanosome position every 10 ms with 2-nm precision. The velocity distribution of melanosomes transported by cytoplasmic dynein or kinesin-2 under conditions of aggregation and dispersion presented several peaks and could not be fit with a single Gaussian function. We postulated that the melanosome velocity depends linearly on the number of active motors. According to this model, one to three dynein molecules transport each melanosome in the minus-end direction. The transport in the plus-end direction is mainly driven by one to two copies of kinesin-2. The number of dyneins transporting a melanosome increases during aggregation, whereas the number of active kinesin-2 stays the same during aggregation and dispersion. Thus, the number of active dynein molecules regulates the net direction of melanosome transport. The model also shows that multiple motors of the same polarity cooperate during the melanosome transport, whereas motors of opposite polarity do not compete.