Extended time correlation of in vitro motility by motor protein

Velocity Fluctuations in Kinesin-1 Gliding Motility Assays Originate in Motor Attachment Geometry Variations

Motor proteins such as myosin and kinesin play a major role in cellular cargo transport, muscle contraction, cell division, and engineered nanodevices. Quantifying the collective behavior of coupled motors is critical to our understanding of these systems. An excellent model system is the gliding motility assay, where hundreds of surface-adhered motors propel one cytoskeletal filament such as an actin filament or a microtubule. The filament motion can be observed using fluorescence microscopy, revealing fluctuations in gliding velocity. These velocity fluctuations have been previously quantified by a motional diffusion coefficient, which Sekimoto and Tawada explained as arising from the addition and removal of motors from the linear array of motors propelling the filament as it advances, assuming that different motors are not equally efficient in their force generation. A computational model of kinesin head diffusion and binding to the microtubule allowed us to quantify the heterogeneity of motor efficiency arising from the combination of anharmonic tail stiffness and varying attachment geometries assuming random motor locations on the surface and an absence of coordination between motors. Knowledge of the heterogeneity allows the calculation of the proportionality constant between the motional diffusion coefficient and the motor density. The calculated value (0.3) is within a standard error of our measurements of the motional diffusion coefficient on surfaces with varying motor densities calibrated by landing rate experiments. This allowed us to quantify the loss in efficiency of coupled molecular motors arising from heterogeneity in the attachment geometry.

Analysis of video-based microscopic particle trajectories using Kalman filtering

The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes.

Direction and speed of microtubule movements driven by kinesin motors arranged on catchin thick filaments

Conventional kinesin (Kinesin-1) is a microtubule-based molecular motor that supports intracellular vesicle/organelle transport in various eukaryotic cells. To arrange kinesin motors similarly to myosin motors on thick filaments in muscles, the motor domain of rat conventional kinesin (amino acid residues 1-430) fused to the C-terminal 829 amino acid residues of catchin (KHC430Cat) was bacterially expressed and attached to catchin filaments that can attach to and arrange myosin molecules in a bipolar manner on their surface. Unlike the case of myosin where actin filaments move toward the center much faster than in the opposite direction along the catchin filaments, microtubules moved at the same speed in both directions. In addition, many microtubules moved across the filaments at the same speed with various angles between the axes of the microtubule and catchin filament. Kinesin/catchin chimera proteins with a shorter kinesin neck domain were also prepared. Those without the whole hinge 1 domain and the C-terminal part of the neck helix moved microtubules toward the center of the catchin filaments significantly, but only slightly, faster than in the opposite direction, although the movements in both directions were slower than those of the KHC430Cat construct. The results suggest that kinesin has substantial mechanical flexibility within the motor domain, possibly within the neck linker, enabling its interaction with microtubules having any orientation.

Detection of fractional steps in cargo movement by the collective operation of kinesin-1 motors

The stepping behavior of single kinesin-1 motor proteins has been studied in great detail. However, in cells, these motors often do not work alone but rather function in small groups when they transport cellular cargo. Until now, the cooperative interactions between motors in such groups were poorly understood. A fundamental question is whether two or more motors that move the same cargo step in synchrony, producing the same step size as a single motor, or whether the step size of the cargo movement varies. To answer this question, we performed in vitro gliding motility assays, where microtubules coated with quantum dots were driven over a glass surface by a known number of kinesin-1 motors. The motion of individual microtubules was then tracked with nanometer precision. In the case of transport by two kinesin-1 motors, we found successive 4-nm steps, corresponding to half the step size of a single motor. Dwell-time analysis did not reveal any coordination, in the sense of alternate stepping, between the motors. When three motors interacted in collective transport, we identified distinct forward and backward jumps on the order of 10 nm. The existence of the fractional steps as well as the distinct jumps illustrate a lack of synchronization and has implications for the analysis of motor-driven organelle movement investigated in vivo.

Fluctuation of actin sliding over myosin thick filaments in vitro

It is customarily thought that myosin motors act as independent force-generators in both isotonic unloaded shortening as well as isometric contraction of muscle. We tested this assumption regarding unloaded shortening, by analyzing the fluctuation of the actin sliding movement over long native thick filaments from molluscan smooth muscle in vitro. This analysis is based on the prediction that the effective diffusion coefficient of actin, a measure of the fluctuation, is proportional to the inverse of the number of myosin motors generating the sliding movement of an actin filament, hence proportional to the inverse of the actin length, when the actions of the motors are stochastic and statistically independent. Contrary to this prediction, we found the effective diffusion coefficient to be virtually independent of, and thus not proportional to, the inverse of the actin length. This result shows that the myosin motors are not independent force-generators when generating the continuous sliding movement of actin in vitro and that the sliding motion is a macroscopic manifestation of the cooperative actions of the microscopic ensemble motors.

Fluctuations in sliding motion generated by independent and random actions of protein motors

We consider theoretical fluctuations in the in vitro sliding movement of individual cytoskeletal filaments generated by an ensemble of protein motors whose actions are assumed to be statistically independent and random. We show that the mean square deviation of the sliding distances of a filament for a given period of time around their average is proportional to the inverse of the filament length. This result provides a basis for an experimental test of the general assumption on the independent and random actions of protein motors.

Fluctuation correlation in the sliding movement generated by protein motors in vitro

The fluctuation in the sliding distance of cytoskeletal filaments driven to move by protein motors in vitro does not depend on the filament length. This is in sharp contrast to the case of Brownian movement of filamentous particles in their longitudinal directions, in which the positional fluctuation is proportional to the inverse of the length (L) of filaments. This latter 1/L dependence is a direct consequence of the central limit theorem: the statistical independence and randomness of the solvent molecule collisions with filaments, the collisions of which cause the random Brownian movement. The above length-independence in the sliding distance fluctuation found in the in vitro motility indicates the presence of correlation in the fluctuation. A possible explanation for the correlation is to assume that there is an extended time-correlation in the sliding movement, a correlation which could be produced by the actions on a sliding filament of protein motors with their heads randomly oriented in the in vitro motility assay system. We have checked this possibility by using long myosin thick filaments of molluscan smooth muscles, on which myosin heads are uniformly oriented, and have found that even with such myosin filaments with oriented myosin heads, the positional fluctuation of actin sliding distance does not depend on the actin filament length. This result thus indicates that the actions of protein motors on a sliding filament are not statistically independent or random, so that the positional fluctuation of filaments in the motor-generated sliding movement does not depend on the filament length.

Length dependence of displacement fluctuations and velocity in microtubule sliding movement driven by sea urchin sperm outer arm β dynein in vitro

We have studied the dependence on microtubule length of sliding velocity and positional fluctuation from recorded trajectories of microtubules sliding over sea urchin sperm outer arm beta dynein in a motility assay in vitro. The positional fluctuation was quantified by calculating the mean-square displacement deviation from the average, the calculation of which yields an effective diffusion coefficient. We have found that (1) the sliding velocity depends hyperbolically on the microtubule length, and (2) the effective diffusion coefficients do not depend on the length for sufficiently long microtubules. The length dependence of the sliding velocity indicates that the duty ratio, defined as the force producing period over the total cycle time of beta dynein interaction with microtubule, is very small. The length independence of the effective diffusion coefficient indicates that there is a correlation in the sliding movement fluctuation of microtubules.

Forces on chromosomal DNA during anaphase

In the course of anaphase, the chromosomal DNA is submitted to the traction of the spindle. Several physical problems are associated with this action. In particular, the sister chromatids are generally topologically intertwined at the onset of anaphase, and the removal of the intertwinings results from a coupling between the enzymatic action of type II DNA topoisomerases and the force exerted by the spindle. We propose a physical analysis of some of these problems: 1) We compare the maximum force the spindle can produce with the force required to break a DNA molecule, and define the conditions compatible with biological safety during anaphase. 2) We show that the behavior of the sister chromatids in the absence of type II DNA topoisomerases can be described by two distinct models: a chain pullout model accounts for the experimental observations made in the budding yeast, and a model of the mechanical rupture of rubbers accounts for the nondisjunction in standard cases. 3) Using the fluctuation-dissipation theorem, we introduce an effective protein friction associated with the strand-passing activity of type II DNA topoisomerases. We show that this friction can be used to describe the situation in which one chromosome passes entirely through another one. Possible experiments that could test these theoretical analyses are discussed.

Fluctuation in the microtubule sliding movement driven by kinesin in vitro

We studied the fluctuation in the translational sliding movement of microtubules driven by kinesin in a motility assay in vitro. By calculating the mean-square displacement deviation from the average as a function of time, we obtained motional diffusion coefficients for microtubules and analyzed the dependence of the coefficients on microtubule length. Our analyses suggest that 1) the motional diffusion coefficient consists of the sum of two terms, one that is proportional to the inverse of the microtubule length (as the longitudinal diffusion coefficient of a filament in Brownian movement is) and another that is independent of the length, and 2) the length-dependent term decreases with increasing kinesin concentration. This latter term almost vanishes within the length range we studied at high kinesin concentrations. From the length-dependence relationship, we evaluated the friction coefficient for sliding microtubules. This value is much larger than the solvent friction and thus consistent with protein friction. The length independence of the motional diffusion coefficient observed at sufficiently high kinesin concentrations indicates the presence of correlation in the sliding movement fluctuation. This places significant constraint on the possible mechanisms of the sliding movement generation by kinesin motors in vitro.