Walking motion of an overdamped active particle in a ratchet potential

An active particle can convert its internal energy into mechanical work. We study a generalized energy-depot model of an overdamped active particle in a ratchet potential. Using well-known biological parameters for kinesin-1 and modeling ATP influx as a pulsed energy supply, we apply our model to the molecular motor system. We find that our simple model can capture the essential properties of the kinesin motor such as forward stepping, stalling, backward stepping, dependence on ATP concentration, and stall force. Our model might be quite universal in the sense that it is able to describe dynamics of various types of motors as long as realistic parameters for each motor species are adopted.     

Protein-protein ratchets: stochastic simulation and application to processive enzymes

Interaction between a protein and a series of binding sites on a cytoskeletal substrate can create a resistance, or "protein friction," as the protein is moved along the substrate. If attachment and detachment rates are specified asymmetrically, this resistance can depend on the direction of movement, and the binding interaction acts as a ratchet. Stochastic computer simulations have been used to examine this type of protein-protein interaction. The performance of a protein-protein ratchet in the piconewton and nanometer range is significantly limited by thermal fluctuations, which in experimental measurements with single molecules are evident as Brownian motion. Simulations with a two-component model combining a conventional motor enzyme model with a protein-protein ratchet confirm previous suggestions that the processive movement of a single motor enzyme molecule against a load, as seen in experiments with inner arm dynein molecules, might be made possible by an accessory protein interaction that prevents backward slippage. When this accessory protein interaction is defined so that it acts as a ratchet, backward slippage can be prevented with minimal interference with forward progression.     

A modified active Brownian dynamics model using asymmetric energy conversion and its application to the molecular motor system

We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle’s velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis–Menten relation between the energy-supply rate and the an ATP concentration, our model describes ATP-dependent stall force in contrast to kinesin-1.     

Significance of peripheral feedback in stepping movement generation under epideral spinal cord stimulation

In acute experiments on decerebrated and spinalized cats, the role of peripheral afferent input from hindlimbs in stepping patterns formation under epidural spinal cord stimulation (ESCS), was investigated. The hindlimb muscles' electromyographic activity and kinematic parameters of evoked stepping were analyzed. It has been shown that epidural stimulation (20-100 microA, 5 Hz) of L4-L5 spine segments induced coordinated stepping on the treadmill belt. In conditions of weight-bearing support (stopped treadmill, hindlimbs lifted above the treadmill), the stepping rhythmic was unstable, stepping cycle period and its internal structure having changed as well. With increased speed of locomotion the stepping frequency increased due to the duration of the support phase decreasing. Forward stepping could be reversed to backward stepping by changing the direction of the treadmill belt movement. In 2-4 hours after complete spinal transection (T8-T9), the epidural stimulation elicited stepping movements on a moving treadmill only. It was found that the influence of peripheral feedback on initiation of the stepping after spinalization increased. Peripheral feedback seems to play a major role in determining the fundamental features of motor output during the ESCS.     

Getting in sync with dimeric Eg5. Initiation and regulation of the processive run

Eg5/KSP is the kinesin-related motor protein that generates the major plus-end directed force for mitotic spindle assembly and dynamics. Recent work using a dimeric form of Eg5 has found it to be a processive motor; however, its mechanochemical cycle is different from that of conventional Kinesin-1. Dimeric Eg5 appears to undergo a conformational change shortly after collision with the microtubule that primes the motor for its characteristically short processive runs. To better understand this conformational change as well as head-head communication during processive stepping, equilibrium and transient kinetic approaches have been used. By contrast to the mechanism of Kinesin-1, microtubule association triggers ADP release from both motor domains of Eg5. One motor domain releases ADP rapidly, whereas ADP release from the other occurs after a slow conformational change at approximately 1 s(-1). Therefore, dimeric Eg5 begins its processive run with both motor domains associated with the microtubule and in the nucleotide-free state. During processive stepping however, ATP binding and potentially ATP hydrolysis signals rearward head advancement 16 nm forward to the next microtubule-binding site. This alternating cycle of processive stepping is proposed to terminate after a few steps because the head-head communication does not sufficiently control the timing to prevent both motor domains from entering the ADP-bound state simultaneously.     

An Adapting Auditory-motor Feedback Loop Can Contribute to Generating Vocal Repetition

Consecutive repetition of actions is common in behavioral sequences. Although integration of sensory feedback with internal motor programs is important for sequence generation, if and how feedback contributes to repetitive actions is poorly understood. Here we study how auditory feedback contributes to generating repetitive syllable sequences in songbirds. We propose that auditory signals provide positive feedback to ongoing motor commands, but this influence decays as feedback weakens from response adaptation during syllable repetitions. Computational models show that this mechanism explains repeat distributions observed in Bengalese finch song. We experimentally confirmed two predictions of this mechanism in Bengalese finches: removal of auditory feedback by deafening reduces syllable repetitions; and neural responses to auditory playback of repeated syllable sequences gradually adapt in sensory-motor nucleus HVC. Together, our results implicate a positive auditory-feedback loop with adaptation in generating repetitive vocalizations, and suggest sensory adaptation is important for feedback control of motor sequences.     

驱动蛋白定向运动的动力学分析

将布朗粒子的定向运动,看作是系统受到外部非平衡涨落作用的结果,并建立相应的扩散模型。通过蒙特卡罗模拟方法,得到布郎粒子定向梯跳运动曲线。结果表明：非对称锯齿势,外部含时闪烁力及加性色噪声协调与联合作用,可使布朗粒子做梯跳或锯齿运动。作为一种可能的解释,将驱动蛋白Ｋｉｎｅｓｉｎｓ沿微管定向梯跳运动看作是上述协调作用的结果。     

Controlling the ratchet effect through the symmetries of the systems: application to molecular motors

We discuss a novel generic mechanism for controlling the ratchet effect through the breaking of relevant symmetries. We review previous works on ratchets where directed transport is induced by the breaking of standard temporal symmetries f(t)=-f(t+T/2) and f(t)=f(-t) (or f(t)=-f(-t)). We find that in seemingly unrelated systems the average velocity (or the current) of particles (or solitons) exhibits common features. We show that, as a consequence of Curie's symmetry principle, the average velocity (or the current) is related to the breaking of the symmetries of the system. This relationship allows us to control the transport in a systematic way. The qualitative agreement between the present analytical predictions and previous experimental, numerical, and theoretical results leads us to suggest that for the given breaking of the temporal symmetries there is an optimal wave form for a given time-periodic force. Also, we comment on how this mechanism can be applied to the case where a ratchet effect is induced by breaking of spatial symmetries. Finally, we conjecture that the ratchet potential underlying biological motor proteins might be optimized according to the breaking of the relevant symmetries.     

Energetics of kinesin-1 stepping mechanism

Kinesin-1 is a dimeric motor protein that transports cellular cargo along microtubules by using the energy released from ATP hydrolysis and moving processively in 8-nm steps. Recent novel studies at the single molecular level have provided extensive knowledge on how kinesin-1 converts the free energy of ATP hydrolysis and uses it for “walking” along microtubules. In this review, I have discussed the important topics pertaining to the energetics of kinesin-1 stepping mechanism and the consensus walking model.     

Contextual cues are not unique for motor learning: Task-dependant switching of feedback controllers

The separation of distinct motor memories by contextual cues is a well known and well studied phenomenon of feedforward human motor control. However, there is no clear evidence of such context-induced separation in feedback control. Here we test both experimentally and computationally if context-dependent switching of feedback controllers is possible in the human motor system. Specifically, we probe visuomotor feedback responses of our human participants in two different tasks—stop and hit—and under two different schedules. The first, blocked schedule, is used to measure the behaviour of stop and hit controllers in isolation, showing that it can only be described by two independent controllers with two different sets of control gains. The second, mixed schedule, is then used to compare how such behaviour evolves when participants regularly switch from one task to the other. Our results support our hypothesis that there is contextual switching of feedback controllers, further extending the accumulating evidence of shared features between feedforward and feedback control.     

Single molecule processes on the stepwise movement of ATP-driven molecular motors

Movement is a fundamental characteristic of all living things. This biogenic function that is attributed to the molecular motors such as kinesin, dynein and myosin. Molecular motors generate forces by using chemical energy derived from the hydrolysis reaction of ATP molecules. Despite a large number of studies on this topic, the chemomechanical energy transduction mechanism is still unsolved. In this study, we have investigated the chemomechanical coupling of the ATPase cycle to the mechanical events of the molecular motor kinesin using single molecule detection (SMD) techniques. The SMD techniques allowed to detection of the movement of single kinesin molecules along a microtubule and showed that kinesin steps mainly in the forward direction, but occasionally in the backward. The stepping direction is determined by a certain load-dependent process, on which the stochastic behavior is well characterized by Feynman's thermal ratchet model. The driving force of the stepwise movement is essentially Brownian motion, but it is biased in the forward direction by using the free energy released from the hydrolysis of ATP.     

基于后推法的n维Lotka-Volterra竞争模型的稳定化设计

通过后推设计方法,研究一类两两相互竞争的n堆Lotka-Volterra模型的全局稳定化问题．在状态反馈控制下,获得了使闭环系统在正平衡点处全局渐近稳定的控制律．     

A Lightweight,Headphones-based System for Manipulating Auditory Feedback in Songbirds

Experimental manipulations of sensory feedback during complex behavior have provided valuable insights into the computations underlying motor control and sensorimotor plasticity¹. Consistent sensory perturbations result in compensatory changes in motor output, reflecting changes in feedforward motor control that reduce the experienced feedback error. By quantifying how different sensory feedback errors affect human behavior, prior studies have explored how visual signals are used to recalibrate arm movements^2,3 and auditory feedback is used to modify speech production^4-7. The strength of this approach rests on the ability to mimic naturalistic errors in behavior, allowing the experimenter to observe how experienced errors in production are used to recalibrate motor output.Songbirds provide an excellent animal model for investigating the neural basis of sensorimotor control and plasticity^8,9. The songbird brain provides a well-defined circuit in which the areas necessary for song learning are spatially separated from those required for song production, and neural recording and lesion studies have made significant advances in understanding how different brain areas contribute to vocal behavior^9-12. However, the lack of a naturalistic error-correction paradigm - in which a known acoustic parameter is perturbed by the experimenter and then corrected by the songbird - has made it difficult to understand the computations underlying vocal learning or how different elements of the neural circuit contribute to the correction of vocal errors¹³.The technique described here gives the experimenter precise control over auditory feedback errors in singing birds, allowing the introduction of arbitrary sensory errors that can be used to drive vocal learning. Online sound-processing equipment is used to introduce a known perturbation to the acoustics of song, and a miniaturized headphones apparatus is used to replace a songbird''s natural auditory feedback with the perturbed signal in real time. We have used this paradigm to perturb the fundamental frequency (pitch) of auditory feedback in adult songbirds, providing the first demonstration that adult birds maintain vocal performance using error correction¹⁴. The present protocol can be used to implement a wide range of sensory feedback perturbations (including but not limited to pitch shifts) to investigate the computational and neurophysiological basis of vocal learning.     

Analytical aspects of the Brownian motor effect in randomly flashing ratchets

The muscle contraction, operation of ATP synthase, maintaining the shape of a cell are believed to be secured by motor proteins, which can be modelled using the Brownian ratchet mechanism. We consider the randomly flashing ratchet model of a Brownian motor, where the particles can be in two states, only one of which is sensitive the applied spatially periodic potential (the mathematical setting is a pair of weakly coupled reaction-diffusion and Fokker–Planck equations). We prove that this mechanism indeed generates unidirectional transport by showing that the amount of mass in the wells of the potential decreases/increases from left to right. The direction of transport is unambiguously determined by the location of each minimum of the potential with respect to the so-called diffusive mean of its adjacent maxima. The transport can be generated not only by an asymmetric potential, but also by a symmetric potential and asymmetric transition rates, and as a consequence of the general result we derive explicit conditions when the latter happens. When the transitions are localized on narrow active sites in the protein conformation space, we find a more explicit characterization of the bulk transport direction, and infer that some common preconditions of the motor effect are redundant.     

The force exerted by a single kinesin molecule against a viscous load.

Kinesin is a motor protein that uses the energy derived from the hydrolysis of ATP to power the transport of organelles along microtubules. To probe the mechanism of this chemical-to-mechanical energy transduction reaction, the movement of microtubules across glass surfaces coated with kinesin was perturbed by raising the viscosity of the buffer solution. When the viscosity of the solution used in the low density motility assay was increased approximately 100-fold through addition of polysaccharides and polypeptides, the longer microtubules, which experienced a larger drag force from the fluid, moved more slowly than the shorter ones. The speed of movement of a microtubule depended linearly on the drag force loading the motor. At the lowest kinesin density, where dilution experiments indicated that the movement was caused by a single kinesin molecule, extrapolation of the linear relationship yielded a maximum time-averaged drag force of 4.2 +/- 0.5 pN per motor (mean +/- experimental SE). The magnitude of the force argues against one type of "ratchet" model in which the motor is hypothesized to rectify the diffusion of the microtubule; at high viscosity, diffusion is too slow to account for the observed speeds. On the other hand, our data are consistent with models in which force is a consequence of strain developed in an elastic element within the motor; these models include a different "ratchet" model (of the type proposed by A. F. Huxley in 1957) as well as "power-stroke" models.     

Limits of Feedback Control in Bacterial Chemotaxis

Inputs to signaling pathways can have complex statistics that depend on the environment and on the behavioral response to previous stimuli. Such behavioral feedback is particularly important in navigation. Successful navigation relies on proper coupling between sensors, which gather information during motion, and actuators, which control behavior. Because reorientation conditions future inputs, behavioral feedback can place sensors and actuators in an operational regime different from the resting state. How then can organisms maintain proper information transfer through the pathway while navigating diverse environments? In bacterial chemotaxis, robust performance is often attributed to the zero integral feedback control of the sensor, which guarantees that activity returns to resting state when the input remains constant. While this property provides sensitivity over a wide range of signal intensities, it remains unclear how other parameters such as adaptation rate and adapted activity affect chemotactic performance, especially when considering that the swimming behavior of the cell determines the input signal. We examine this issue using analytical models and simulations that incorporate recent experimental evidences about behavioral feedback and flagellar motor adaptation. By focusing on how sensory information carried by the response regulator is best utilized by the motor, we identify an operational regime that maximizes drift velocity along chemical concentration gradients for a wide range of environments and sensor adaptation rates. This optimal regime is outside the dynamic range of the motor response, but maximizes the contrast between run duration up and down gradients. In steep gradients, the feedback from chemotactic drift can push the system through a bifurcation. This creates a non-chemotactic state that traps cells unless the motor is allowed to adapt. Although motor adaptation helps, we find that as the strength of the feedback increases individual phenotypes cannot maintain the optimal operational regime in all environments, suggesting that diversity could be beneficial.     

Servo-controlled air pump for calibration of respiratory measurement systems

We describe a servo-controlled piston pump driven by a stepping motor. The analogue controller is a single non-linear second-order feedback loop with adjustable speed and acceleration limits. This system, designed to simulate slowly-moving active and non-linear systems, can be used as a low (0–6.5 litre s⁻¹) flow volume generator in calibration procedures.     

Listeria's right-handed helical rocket-tail trajectories: mechanistic implications for force generation in actin-based motility

Listeria monocytogenes forms right-handed helical rocket tail trajectories during actin-based motility in cell-free extracts, and this stereochemical feature is consistent with actoclampin's affinity-modulated, clamped-filament elongation model [Dickinson and Purich, 2002: Biophys J 82:605-617]. In that mechanism, right-handed torque is generated by an end-tracking molecular motor, each comprised of a filament barbed end and clamping protein that processively traces the right-handed helix of its filament partner. By contrast, torque is not a predicted property of those models (e.g., elastic propulsion, elastic Brownian ratchet, tethered ratchet, and insertional polymerization models) requiring filament barbed ends to depart/detach from the motile object's surface during/after each monomer-addition step. Helical trajectories also explain why Listeria undergoes longitudinal-axis rotation on a length-scale matching the helical periodicity of Listeria's rocket tails.     

Fly flight: a model for the neural control of complex behavior.

Flies exhibit a repertoire of aerial acrobatics unmatched in robustness and aerodynamic sophistication. The exquisite control of this complex behavior emerges from encoding intricate patterns of optic flow, and the translation of these visual signals into the mechanical language of the motor system. Recent advances in experimental design toward more naturalistic visual and mechanosensory stimuli have served to reinforce fly flight as a key model system for understanding how feedback from multiple sensory modalities is integrated to control complex and robust motor behaviors across taxa.