Neural coupling between upper and lower limbs during recumbent stepping.

During gait rehabilitation, therapists or robotic devices often supply physical assistance to a patient's lower limbs to aid stepping. The expensive equipment and intensive manual labor required for these therapies limit their availability to patients. One alternative solution is to design devices where patients could use their upper limbs to provide physical assistance to their lower limbs (i.e., self-assistance). To explore potential neural effects of coupling upper and lower limbs, we investigated neuromuscular recruitment during self-driven and externally driven lower limb motion. Healthy subjects exercised on a recumbent stepper using different combinations of upper and lower limb exertions. The recumbent stepper mechanically coupled the upper and lower limbs, allowing users to drive the stepping motion with upper and/or lower limbs. We instructed subjects to step with 1) active upper and lower limbs at an easy resistance level (active arms and legs); 2) active upper limbs and relaxed lower limbs at easy, medium, and hard resistance levels (self-driven); and 3) relaxed upper and lower limbs while another person drove the stepping motion (externally driven). We recorded surface electromyography (EMG) from six lower limb muscles. Self-driven EMG amplitudes were always higher than externally driven EMG amplitudes (P < 0.05). As resistance and upper limb exertion increased, self-driven EMG amplitudes also increased. EMG bursts during self-driven and active arms and legs stepping occurred at similar times. These results indicate that active upper limb movement increases neuromuscular activation of the lower limbs during cyclic stepping motions. Neurologically impaired humans that actively engage their upper limbs during gait rehabilitation may increase neuromuscular activation and enhance activity-dependent plasticity.     

Single-Molecule Motility: Statistical Analysis and the Effects of Track Length on Quantification of Processive Motion

In vitro, single-molecule motility assays allow for the direct characterization of molecular motor properties including stepping velocity and characteristic run length. Although application of these techniques in vivo is feasible, the challenges involved in sample preparation, as well as the added complexity of the cell and its systems, result in a reduced ability to collect large datasets, as well as difficulty in simultaneous observation of the components of the motility system, namely motor and track. To address these challenges, we have developed simulations to characterize motility datasets as a function of sample size, processive run length of the motor, and distribution of track lengths. We introduce the use of a simple bootstrapping technique that allows for the quantification of measurement uncertainty and a Monte Carlo permutation resampling scheme for the measurement of statistical significance and the estimation of required sample size. In addition, we have found that, despite conventional wisdom, the measured characteristic run length is directly coupled to the characteristic track length that describes the microtubule length distribution. To be able to make comparisons between motility experiments performed on different track populations as well as make measurements of motility when motors and tracks cannot be simultaneously resolved, we have developed a theoretical framework for the determination of the effect that track length has on observed characteristic run lengths. This shows good agreement with in vitro motility experiments on two kinesin constructs walking on microtubule populations of different characteristic track lengths.     

Engineered Myosin VI Motors Reveal Minimal Structural Determinants of Directionality and Processivity

Myosins have diverse mechanical properties reflecting a range of cellular roles. A major challenge is to understand the structural basis for generating novel functions from a common motor core. Myosin VI (M6) is specialized for processive motion toward the (−) end of actin filaments. We have used engineered M6 motors to test and refine the “redirected power stroke” model for (−) end directionality and to explore poorly understood structural requirements for processive stepping. Guided by crystal structures and molecular modeling, we fused artificial lever arms to the catalytic head of M6 at several positions, retaining varying amounts of native structure. We found that an 18-residue α-helical insert is sufficient to reverse the directionality of the motor, with no requirement for any calmodulin light chains. Further, we observed robust processive stepping of motors with artificial lever arms, demonstrating that processivity can arise without optimizing lever arm composition or mechanics.     

Processivity and Velocity for Motors Stepping on Periodic Tracks

Processive molecular motors enable cargo transportation by assembling into dimers capable of taking several consecutive steps along a cytoskeletal filament. In the well-accepted hand-over-hand stepping mechanism, the trailing motor detaches from the track and binds the filament again in the leading position. This requires fuel consumption in the form of ATP hydrolysis and coordination of the catalytic cycles between the leading and the trailing heads. Alternate stepping pathways also exist, including inchworm-like movements, backward steps, and foot stomps. Whether all the pathways are coupled to ATP hydrolysis remains to be determined. Here, to establish the principles governing the dynamics of processive movement, we present a theoretical framework that includes all of the alternative stepping mechanisms. Our theory bridges the gap between the elemental rates describing the biochemical and structural transitions in each head and the experimentally measurable quantities such as velocity, processivity, and probability of backward stepping. Our results, obtained under the assumption that the track is periodic and infinite, provide expressions that hold regardless of the topology of the network connecting the intermediate states, and are therefore capable of describing the function of any molecular motor. We apply the theory to myosin VI, a motor that takes frequent backward steps and moves forward with a combination of hand-over-hand and inchworm-like steps. Our model quantitatively reproduces various observables of myosin VI motility reported by four experimental groups. The theory is used to predict the gating mechanism, the pathway for backward stepping, and the energy consumption as a function of ATP concentration.     

Voluntary stepping behavior under single- and dual-task conditions in chronic stroke survivors: A comparison between the involved and uninvolved legs

ObjectiveIf balance is lost, quick step execution can prevent falls. Research has shown that speed of voluntary stepping was able to predict future falls in old adults. The aim of the study was to investigate voluntary stepping behavior, as well as to compare timing and leg push-off force–time relation parameters of involved and uninvolved legs in stroke survivors during single- and dual-task conditions. We also aimed to compare timing and leg push-off force–time relation parameters between stroke survivors and healthy individuals in both task conditions.MethodsTen stroke survivors performed a voluntary step execution test with their involved and uninvolved legs under two conditions: while focusing only on the stepping task and while a separate attention-demanding task was performed simultaneously. Temporal parameters related to the step time were measured including the duration of the step initiation phase, the preparatory phase, the swing phase, and the total step time. In addition, force–time parameters representing the push-off power during stepping were calculated from ground reaction data and compared with 10 healthy controls.ResultsThe involved legs of stroke survivors had a significantly slower stepping time than uninvolved legs due to increased swing phase duration during both single- and dual-task conditions. For dual compared to single task, the stepping time increased significantly due to a significant increase in the duration of step initiation. In general, the force time parameters were significantly different in both legs of stroke survivors as compared to healthy controls, with no significant effect of dual compared with single-task conditions in both groups.ConclusionsThe inability of stroke survivors to swing the involved leg quickly may be the most significant factor contributing to the large number of falls to the paretic side. The results suggest that stroke survivors were unable to rapidly produce muscle force in fast actions. This may be the mechanism of delayed execution of a fast step when balance is lost, thus increasing the likelihood of falls in stroke survivors.     

Improved hidden Markov models for molecular motors, part 2: extensions and application to experimental data

Unbiased interpretation of noisy single molecular motor recordings remains a challenging task. To address this issue, we have developed robust algorithms based on hidden Markov models (HMMs) of motor proteins. The basic algorithm, called variable-stepsize HMM (VS-HMM), was introduced in the previous article. It improves on currently available Markov-model based techniques by allowing for arbitrary distributions of step sizes, and shows excellent convergence properties for the characterization of staircase motor timecourses in the presence of large measurement noise. In this article, we extend the VS-HMM framework for better performance with experimental data. The extended algorithm, variable-stepsize integrating-detector HMM (VSI-HMM) better models the data-acquisition process, and accounts for random baseline drifts. Further, as an extension, maximum a posteriori estimation is provided. When used as a blind step detector, the VSI-HMM outperforms conventional step detectors. The fidelity of the VSI-HMM is tested with simulations and is applied to in vitro myosin V data where a small 10 nm population of steps is identified. It is also applied to an in vivo recording of melanosome motion, where strong evidence is found for repeated, bidirectional steps smaller than 8 nm in size, implying that multiple motors simultaneously carry the cargo.     

Simultaneous observation of tail and head movements of myosin V during processive motion

Processive stepping of myosin Va (myoV) has been tracked by monitoring either the tail position (center of mass) or the position of one or both heads. Here, we combine these two approaches by attaching a quantum dot to one of the motor domains and a bead to the tail. Using laser trapping and total internal reflection microscopy, the position of one head and the tail are observed simultaneously as myoV moves processively on an actin filament bundle against the resistive load of the laser trap. The head moves one step (73 ± 10 nm) for every two steps of the tail (35 ± 9 nm). One tail step occurs concurrently with quantum dot-labeled head movement, whereas the other occurs with movement of the unlabeled head, consistent with a hand-over-hand model. Load increases the probability of the motor taking a back step. The back step is triggered by the motor taking a shorter forward step (head step, 68 ± 11 nm; tail step, 32 ± 10 nm), likely one actin monomer short of its preferred binding site. During a back step, the motor reverses its hand-over-hand motion, with the leading head detaching and reattaching to one of multiple actin sites behind the trailing head. After a back step, the motor can correct its mistake and step processively forward at resistive loads <0.7 piconewton or stall or detach at higher loads. Back stepping may provide a mechanism to ensure efficient cargo delivery even when myoV encounters obstacles within the actin cytoskeletal meshwork or when other motors are attached to the same cargo.     

Dynamic motion planning for the design of robotic gait rehabilitation

In this paper we examine a method to control the stepping motion of a paralyzed person suspended over a treadmill using a robot attached to the pelvis. A leg swing motion is created by moving the pelvis without contact with the legs. The problem is formulated as an optimal control problem for an underactuated articulated chain. The optimal control problem is converted into a discrete parameter optimization and an efficient gradient-based algorithm is used to solve it. Motion capture data from an unimpaired human subject is compared to the simulation results from the dynamic motion optimization. Our results suggest that it is feasible to drive repetitive stepping on a treadmill by a paralyzed person by assisting in torso movement alone. The optimized, pelvic motion strategies are comparable to "hip-hiking" gait strategies used by people with lower limb prostheses or hemiparesis. The resulting motions can be found at the web site http://ww.eng.uci.edu/-chwang/project/stepper/stepper.html.     

Directionality of individual kinesin-5 Cin8 motors is modulated by loop 8, ionic strength and microtubule geometry

Kinesin-5 motors fulfil essential roles in mitotic spindle morphogenesis and dynamics as slow, processive microtubule (MT) plus-end directed motors. The Saccharomyces cerevisiae kinesin-5 Cin8 was found, surprisingly, to switch directionality. Here, we have examined directionality using single-molecule fluorescence motility assays and live-cell microscopy. On spindles, Cin8 motors mostly moved slowly (～25 nm/s) towards the midzone, but occasionally also faster (～55 nm/s) towards the spindle poles. In vitro, individual Cin8 motors could be switched by ionic conditions from rapid (380 nm/s) and processive minus-end to slow plus-end motion on single MTs. At high ionic strength, Cin8 motors rapidly alternated directionalities between antiparallel MTs, while driving steady plus-end relative sliding. Between parallel MTs, plus-end motion was only occasionally observed. Deletion of the uniquely large insert in loop 8 of Cin8 induced bias towards minus-end motility and affected the ionic strength-dependent directional switching of Cin8 in vitro. The deletion mutant cells exhibited reduced midzone-directed motility and efficiency to support spindle elongation, indicating the importance of directionality control for the anaphase function of Cin8.     

The Kinesin-8 Kip3 Switches Protofilaments in a Sideward Random Walk Asymmetrically Biased by Force

Molecular motors translocate along cytoskeletal filaments, as in the case of kinesin motors on microtubules. Although conventional kinesin-1 tracks a single microtubule protofilament, other kinesins, akin to dyneins, switch protofilaments. However, the molecular trajectory—whether protofilament switching occurs in a directed or stochastic manner—is unclear. Here, we used high-resolution optical tweezers to track the path of single budding yeast kinesin-8, Kip3, motor proteins. Under applied sideward loads, we found that individual motors stepped sideward in both directions, with and against loads, with a broad distribution in measured step sizes. Interestingly, the force response depended on the direction. Based on a statistical analysis and simulations accounting for the geometry, we propose a diffusive sideward stepping motion of Kip3 on the microtubule lattice, asymmetrically biased by force. This finding is consistent with previous multimotor gliding assays and sheds light on the molecular switching mechanism. For kinesin-8, the diffusive switching mechanism may enable the motor to bypass obstacles and reach the microtubule end for length regulation. For other motors, such a mechanism may have implications for torque generation around the filament axis.     

Motion Control in Saccade and Smooth Pursuit for Bionic Eye Based on Three-dimensional Coordinates

Saccade and smooth pursuit are two important functions of human eye.In order to enable bionic eye to imitate the two functions,a control method that implements saccade and smooth pursuit based on the three-dimensional coordinates of target is proposed.An optimal observation position is defined for bionic eye based on three-dimensional coordinates.A kind of motion planning method with high accuracy is developed.The motion parameters of stepper motor consisting of angle acceleration and turning time are computed according to the position deviation,the target's angular velocity and the stepper motor's current angular velocity in motion planning.The motors are controlled with the motion parameters moving to given position with desired angular velocity in schedule time.The experimental results show that the bionic eye can move to optimal observation positions in 0.6 s from initial location and the accuracy of 3D coordinates is improved.In addition,the bionic eye can track a target within the error of less than 20 pixels based on three-dimensional coordinates.It is verified that saccade and smooth pursuit of bionic eye based on three-dimensional coordinates are feasible.     

Stick insects walking on a wheel: Perturbations induced by obstruction of leg protraction

Summary Stick insects (Carausius morosus) walking on a wheel were perturbed by restricting the forward protraction of individual legs. A barrier placed before a single middle or rear leg prevented that leg from reaching its normal protraction endpoint but allowed it unimpeded retraction. Upon striking the barrier, the protracting leg attempted to get past it and thereby prolonged protraction. This prolongation increased with the extent to which the obstruction infringed upon the leg's normal step range. Barriers placed near the midpoint of this range elicited large perturbations: the blocked leg often continued its protraction throughout many step cycles of the other legs (Fig. 1 E, F). For the most part walking was irregular and smooth forward progression was disrupted. Nevertheless, the infrequent steps by the affected leg usually were coordinated with those of the adjacent ipsilateral legs.More rostral barrier positions elicited smaller perturbations: the blocked leg usually made one step in each step cycle of the other legs (Fig. 1 B, C, D, G). Measurements for these regular step sequences showed quantitatively that protraction duration increased in proportion to the severity of the infringement on normal leg movement (Figs. 3, 4). The fraction of the step period occupied by protraction increased from ca. 10% for normal walking to ca. 50% for caudal barrier positions. This proportionality is interpreted to show the importance of spatial components of the walking program.When one leg was obstructed, its extended protraction influenced the stepping of the three adjacent legs as follows. First, the ipsilateral rostral leg showed the largest change: its protraction onset was regularly delayed for the duration of the extended protraction (Figs. 4, 7, 8), demonstrating a strong, centrally mediated inhibition. The presence of a further delay of up to 100 to 140 ms suggests that peripheral input from the protracting leg may be important for releasing this inhibition. Second, steps by an adjacent caudal leg were not measurably affected. However, the method may not have sufficed to reveal such effects because during regular walking middle leg protractions rarely lasted long enough to conflict with subsequent steps by the ipsilateral rear leg. Third, contralateral effects differed between middle and rear leg obstructions. If the obstructed leg was a middle leg, its extended protraction had little effect upon stepping by the contralateral middle leg: the latter leg frequently protracted while the blocked leg continued its protraction and there was no consistent change in the phase relation of these two legs (Table 1). In contrast, if the obstructed leg was a rear leg, protractions by the contralateral rear leg tended to be delayed (Table 1).     

A model of leg coordination in the stick insect,Carausius morosus

A model of interleg coordination presented in a separate report is evaluated here by perturbing the step pattern in three ways. First, when the initial leg configuration is varied, the simulated leg movements assume a stable coordination from natural starting configurations in a natural way (Fig. 1a). They also rapidly re-establish the normal coordination when started from unnatural configurations (Fig. 1b-d). An explicit hierarchy of natural frequencies for the legs of the three thoracic segments is not required. Second, when the coordination is perturbed by assigning one or more legs a retraction velocity different from the rest, gliding coordination or various integer step ratios can be produced (Figs. 2–4). Third, when the swing of one leg is obstructed, characteristic changes in the stepping of other legs occur (Fig. 5). Overall differences between the step patterns of the model and those of the stick insect are related to the form of the coordinating mechanisms. Errors made by the model, such as overlapping swings by adjacent legs or discrepancies in step timing and step end-points, point out the limitations of a model restricted to kinematic parameters.     

A kinetic and stochastic analysis of crossbridge-type stepping mechanisms in rotary molecular motors

The bacterial flagellar motor is generally supposed to be a stepping mechanism. The main evidence for this is based on a fluctuation analysis of experiments with tethered bacteria in which rotation frequency was varied by applying an external torque: the variance in time taken for a fixed number of revolutions was found to be essentially proportional to the inverse square of the frequency. This behavior was shown to characterize a Poissonian stepper. Here we present a rigorous kinetic and stochastic analysis of elastic crossbridge stepping in tethered bacteria. We demonstrate that Poissonian stepping is a virtually unachievable limit. To the extent that a system may approach Poissonian stepping it cannot be influenced by an externally applied torque; stepping mechanisms capable of being so influenced are necessarily non-Poissonian and exhibit an approximately inverse cubic dependence. This conclusion applies whatever the torsional characteristics of the tether may be, and contrary to claims, no perceptible relaxation of the tether following each step is found. Furthermore, the inverse square dependence is a necessary but not sufficient condition for Poissonian stepping, since a nonstepping mechanism, which closely reproduces most experimental data, also fulfills this condition. Hence the inference that crossbridge-type stepping occurs is not justified.     

Directionality and processivity of molecular motors.

Analysis of a mutant with altered directionality has led to new insights into motor directionality. The prediction from current models for processivity of a two-heads-bound state has been confirmed by electron microscopy for myosin V and by unbinding experiments for kinesin. Evidence is emerging that non-processive motors bind their filament with one head, hydrolyze ATP and then release, requiring binding by a second motor to complete a step.     

Rotational locomotion by the cockroach Blattella germanica

Locomotion on complex substrata can be expressed in a plane by two geometric components of body movement: linear locomotion and rotational locomotion. This study examined pure rotation by analysing the geometry of leg movements and stepping patterns during the courtship turns of male Blattella germanica. Strict rotation or translation by an insect requires that each side of the body cover equal distance with respect to the substrate. There are three mechanisms by which the legs can maintain this equality: frequency of stepping, magnitude of the leg arcs relative to the body and the degree to which legs flex and extend during locomotion. During the courtship behaviour of Blattella germanica selected males executed turns involving body rotation along with leg movements in which the legs on the outside of the turn swung through greater average arcs than those on the inside of the turn. This difference should have resulted in a translation component. However, legs on the inside of the turn compensated by flexion and extension movements which were greater than those of opposing legs. The net effect was that both sides of the body covered equal average ground. These cockroaches used a wide variety of stepping combinations to effect rotation. The frequency of these combinations was compared to an expected frequency distribution of stepping combinations and further to an expected frequency of these stepping combinations used for straight walking. These comparisons demonstrated a similarity between interleg coordination during straight walking and that during turning in place.     

Single-Molecule Motility: Statistical Analysis and the Effects of Track Length on Quantification of Processive Motion

In vitro, single-molecule motility assays allow for the direct characterization of molecular motor properties including stepping velocity and characteristic run length. Although application of these techniques in vivo is feasible, the challenges involved in sample preparation, as well as the added complexity of the cell and its systems, result in a reduced ability to collect large datasets, as well as difficulty in simultaneous observation of the components of the motility system, namely motor and track. To address these challenges, we have developed simulations to characterize motility datasets as a function of sample size, processive run length of the motor, and distribution of track lengths. We introduce the use of a simple bootstrapping technique that allows for the quantification of measurement uncertainty and a Monte Carlo permutation resampling scheme for the measurement of statistical significance and the estimation of required sample size. In addition, we have found that, despite conventional wisdom, the measured characteristic run length is directly coupled to the characteristic track length that describes the microtubule length distribution. To be able to make comparisons between motility experiments performed on different track populations as well as make measurements of motility when motors and tracks cannot be simultaneously resolved, we have developed a theoretical framework for the determination of the effect that track length has on observed characteristic run lengths. This shows good agreement with in vitro motility experiments on two kinesin constructs walking on microtubule populations of different characteristic track lengths.     

Nanometres and piconewtons: the macromolecular mechanics of kinesin

Much of our current understanding of the molecular physiology of kinesin has come from in vitro motility assays: indeed, the discovery of kinesin relied upon such assays. By marrying in vitro assays with novel instruments capable of resolving movements on the molecular scale, it has proved possible to make measurements on single motors. Such key parameters as the step size, stepping force, and force-velocity relationship for kinesin have been determined in this fashion, and should soon contribute to a molecular model for the movement of kinesin.     

Nonprocessive Motor Dynamics at the Microtubule Membrane Tube Interface

Key cellular processes such as cell division, membrane compartmentalization, and intracellular transport rely on motor proteins. Motors have been studied in detail on the single motor level such that information on their step size, stall force, average run length, and processivity are well known. However, in vivo, motors often work together, so that the question of their collective coordination has raised great interest. Here, we specifically attach motors to giant vesicles and examine collective motor dynamics during membrane tube formation. Image correlation spectroscopy reveals directed motion as processive motors walk at typical speeds (≤500 nm/s) along an underlying microtubule and accumulate at the tip of the growing membrane tube. In contrast, nonprocessive motors exhibit purely diffusive behavior, decorating the entire length of a microtubule lattice with diffusion constants at least 1000 times smaller than a freely-diffusing lipid-motor complex in a lipid bilayer (1 μm²/s); fluorescence recovery after photobleaching experiments confirm the presence of the slower-moving motor population at the microtubule-membrane tube interface. We suggest that nonprocessive motors dynamically bind and unbind to maintain a continuous interaction with the microtubule. This dynamic and continuous interaction is likely necessary for nonprocessive motors to mediate bidirectional membrane tube dynamics reported previously.