Yasuhiro Imafuku

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.

Kinesin: a molecular motor with a spring in its step

A key step in the processive motion of two–headed kinesin along a microtubule is the ‘docking’ of the neck linker that joins each kinesin head to the motors dimerized coiled–coil neck. This process is similar to the folding of a protein β–hairpin, which starts in a highly mobile unfolded state that has significant entropic elasticity and finishes in a more rigid folded state. We therefore suggest that neck–linker docking is mechanically equivalent to the thermally activated shortening of a spring that has been stretched by an applied load. This critical tension–dependent step utilizes Brownian motion and it immediately follows the binding of ATP, the hydrolysis of which provides the free energy that drives the kinesin cycle. A simple three–state model incorporating neck–linker docking can account quantitatively for both the kinesin force–velocity relation and the unusual tension–dependence of its Michaelis constant. However, we find that the observed randomness of the kinesin motor requires a more detailed four–state model. Monte Carlo simulations of single–molecule stepping with this model illustrate the possibility of sub–8 nm steps, the size of which is predicted to vary linearly with the applied load.

Molecular motors: thermodynamics and the random walk.

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motors ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp [−(ΔG + u0f)/kT], where −ΔG is the free energy available from ATP hydrolysis and u0 is the motors step size. A hypothetical one–state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D−v2τ, where τ is the time–constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one–state case and can be used for determining τ. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force–velocity relation and the random motion of molecular motors.

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.

Monte Carlo study for fluctuation analysis of the in vitro motility driven by protein motors

The fluctuation properties of the sliding movement of an individual cytoskeletal filament driven by protein motors in vitro can be analyzed by calculating the mean-square deviation of the displacement from the average within its single trajectory. For this purpose, a Monte Carlo simulation was used to define the conditions and limitations of a method for smoothing (curved) noisy trajectories without affecting either the steady or fluctuation characteristics inherent to the individual filament sliding movement. By applying the method to real experimental trajectory data, we show that an effective diffusion coefficient from displacement fluctuations of a sliding filament can be obtained from its single noisy trajectory even when it is curved.

Synchronous firing patterns of a set of insect neurosecretory cells

The number of active cells in each synchronous firing event in a set of 10 neurosecretory cells in the silkmoth Bombyx mori was estimated from the amplitude and waveform of compound action potentials. One to 10 cells discharged an action potential within a period of 30 ms and one to two or nine to 10 units became active more frequently in a synchronous firing event. Numbers of active cells fluctuated like a sequence of pseudo random numbers, though the same number of cells tended to fire in two successive firing events of a short interval. These patterns suggest that electrical coupling may mediate synchronous firings in the insect neurosecretory cell system.

Effect of elastic energy on the folding of an RNA hairpin

We analyse the folding and unfolding of an RNA hairpin using a conventional zipping model that includes both the free energy for RNA binding and the elastic free energy of the system. Unfolding under isotonic conditions (where we control the applied load) is known to occur at a well-defined critical load. In marked contrast, we find that unfolding under isometric conditions (where we control the extension of the hairpin) produces a series of sharp peaks in the average load as the stem of the hairpin starts to unzip base by base. A peak occurs when the elastic energy stored in the unzipped arms of the hairpin becomes so large that it is energetically favourable for the next base pair to unzip: the consequent increase in the contour length of the unzipped arms reduces their elastic energy and causes the average load to fall abruptly. However, as the contour length of the unzipped arms increases, the peaks become less distinct. Moreover, when we include the long DNA/RNA handles that have been used in single-molecule experiments, the unzipping of individual base pairs cannot be resolved at all. Instead, with the hairpin in the folded state, the average load increases with extension until the elastic energy stored in the handles makes it energetically favourable for the hairpin to unzip over a narrow range of extensions. The resultant yield point produces a mechanical hysteresis loop with a negative slope, as observed experimentally. Unfolding of the hairpin is also affected by the elastic energy stored in a compliant force transducer. We find that short, stiff handles and a stiff force transducer could improve the resolution of mechanical experiments on single molecules.

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.

Anomalous Fluctuations in Sliding Motion of Cytoskeletal Filaments Driven by Molecular Motors: Model Simulations

It has been found in in vitro experiments that cytoskeletal filaments driven by molecular motors show finite diffusion in sliding motion even in the long filament limit [Imafuku, Y. et al. Biophys. J. 1996, 70, 878-886. Noda, N. et al. Biophysics 2005, 1, 45-53]. This anomalous fluctuation can be evidence for cooperativity among the motors in action because fluctuation should be averaged out for a long filament if the action of each motor is independent. In order to understand the nature of the fluctuation in molecular motors, we perform numerical simulations and analyze velocity correlation in three existing models that are known to show some kind of cooperativity and/or large diffusion coefficient, i.e., the Sekimoto-Tawada model [Sekimoto, K.; Tawada, K. Phys. Rev. Lett. 1995, 75, 180], the Prost model [Prost, J. et al. Phys. Rev. Lett. 1994, 72, 2652], and the Duke model [Duke, T. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 2770]. It is shown that the Prost model and the Duke model do not give a finite diffusion in the long filament limit, in spite of the collective action of motors. On the other hand, the Sekimoto-Tawada model has been shown to give a diffusion coefficient that is independent of filament length, but it comes from the long time correlation whose time scale is proportional to filament length, and our simulations show that such a long correlation time conflicts with the experimental time scales. We conclude that none of the three models represent experimental findings. In order to explain the observed anomalous diffusion, we have to search for a mechanism that will allow both the amplitude and the time scale of the velocity correlation to be independent of the filament length.

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.