The tethered motor domain of a kinesin-microtubule complex catalyzes reversible synthesis of bound ATP

Step-Wise Hydration of Magnesium by Four Water Molecules Precedes Phosphate Release in a Myosin Motor

Molecular motors, such as myosin, kinesin, and dynein, convert the energy released by the hydrolysis of ATP into mechanical work, thus allowing them to undergo directional motion on cytoskeletal tracks. A pivotal step in the chemomechanical transduction in myosin motors occurs after they bind to the actin filament, which triggers the release of phosphate (P_i, product of ATP hydrolysis) and the rotation of the lever arm. Here, we investigate the mechanism of phosphate release in myosin VI using extensive molecular dynamics simulations involving multiple trajectories of several μs. Because the escape of phosphate is expected to occur on time-scales on the order of milliseconds or more in myosin VI, we observed P_i release only if the trajectories were initiated with a rotated phosphate inside the nucleotide binding pocket. We discovered that although P_i populates the traditional "back door" route, phosphate exits through various other gateways, thus establishing the heterogeneity in the escape routes. Remarkably, we observed that the release of phosphate is preceded by a stepwise hydration of the ADP-bound magnesium ion. The release of the anion occurred only after four water molecules hydrated the cation (Mg²⁺). By performing comparative structural analyses, we show that hydration of magnesium is the key step in the phosphate release in a number of ATPases and GTPases. Nature may have evolved hydration of Mg²⁺ as a general molecular switch for P_i release, which is a universal step in the catalytic cycle of many machines that share little sequence or structural similarity.

Collective intracellular cargo transport by multiple kinesins on multiple microtubules

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Signalling networks and dynamics of allosteric transitions in bacterial chaperonin GroEL: implications for iterative annealing of misfolded proteins

Signal transmission at the molecular level in many biological complexes occurs through allosteric transitions. Allostery describes the responses of a complex to binding of ligands at sites that are spatially well separated from the binding region. We describe the structural perturbation method, based on phonon propagation in solids, which can be used to determine the signal-transmitting allostery wiring diagram (AWD) in large but finite-sized biological complexes. Application to the bacterial chaperonin GroEL-GroES complex shows that the AWD determined from structures also drives the allosteric transitions dynamically. From both a structural and dynamical perspective these transitions are largely determined by formation and rupture of salt-bridges. The molecular description of allostery in GroEL provides insights into its function, which is quantitatively described by the iterative annealing mechanism. Remarkably, in this complex molecular machine, a deep connection is established between the structures, reaction cycle during which GroEL undergoes a sequence of allosteric transitions, and function, in a self-consistent manner.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Nonequilibrium Energetics of Molecular Motor Kinesin

Nonequilibrium energetics of single molecule translational motor kinesin was investigated by measuring heat dissipation from the violation of the fluctuation-response relation of a probe attached to the motor using optical tweezers. The sum of the dissipation and work did not amount to the input free energy change, indicating large hidden dissipation exists. Possible sources of the hidden dissipation were explored by analyzing the Langevin dynamics of the probe, which incorporates the two-state Markov stepper as a kinesin model. We conclude that internal dissipation is dominant.

A Unified Walking Model for Dimeric Motor Proteins

Dimeric motor proteins, kinesin-1, cytoplasmic dynein-1, and myosin-V, move stepwise along microtubules and actin filaments with a regular step size. The motors take backward as well as forward steps. The step ratio r and dwell time τ, which are the ratio of the number of backward steps to the number of forward steps and the time between consecutive steps, respectively, were observed to change with the load. To understand the movement of motor proteins, we constructed a unified and simple mathematical model to explain the load dependencies of r and of τ measured for the above three types of motors quantitatively. Our model consists of three states, and the forward and backward steps are represented by the cycles of transitions visiting different pairs of states among the three, implying that a backward step is not the reversal of a forward step. Each of r and τ is given by a simple expression containing two exponential functions. The experimental data for r and τ for dynein available in the literature are not sufficient for a quantitative analysis, which is in contrast to those for kinesin and myosin-V. We reanalyze the data to obtain r and τ of native dynein to make up the insufficient data to fit them to the model. Our model successfully describes the behavior of r and τ for all of the motors in a wide range of loads from large assisting loads to superstall loads.

Mechanochemical Model of the Power Stroke of the Single-Headed Motor Protein KIF1A

During the process of ATP binding to an apo-kinesin microtubule (MT), the kinesin core rotates on the MT, and the neck linker (NL) of the kinesin undergoes an undocked to docked transition. This has been suggested to be a power stroke of kinesin, on the basis of the structural analysis. Here, we developed a mesoscopic structure-based model and studied the power stroke of KIF1A. We quantified the underlying free energy landscape and showed the emergence of several states for the power stroke of KIF1A: UB-UR-UD (unbound, unrotating, undock), B-IR-UD (bound, initial rotating, undock), B-PR-UD (bound, partial rotating, undock), and B-R-D (bound, rotating, dock). We found that ATP binding triggered conformational fluctuations of key elements. We also explored the conformational change of key structural elements during the rotation of KIF1A and docking of the NL. In addition, we semiquantitatively and qualitatively estimated the free energy released by the ATP binding, and how much of this remains for the docking of the NL during the power stroke process at different temperatures. Finally, based on results from the thermodynamics landscape and conformational change of structural key elements, we proposed a mechanochemical model of the power stroke of KIF1A.

Energetic Costs, Precision, and Transport Efficiency of Molecular Motors

An efficient molecular motor would deliver cargo to the target site at a high speed and in a punctual manner while consuming a minimal amount of energy. According to a recently formulated thermodynamic principle, referred to as the thermodynamic uncertainty relation, the travel distance of a motor and its variance are, however, constrained by the free energy being consumed. Here we use the principle underlying the uncertainty relation to quantify the transport efficiency of molecular motors for varying ATP concentration ([ATP]) and applied load (f). Our analyses of experimental data find that transport efficiencies of the motors studied here are semioptimized under the cellular condition. The efficiency is significantly deteriorated for a kinesin-1 mutant that has a longer neck-linker, which underscores the importance of molecular structure. It is remarkable to recognize that, among many possible directions for optimization, biological motors have evolved to optimize the transport efficiency in particular.

Unbinding of Kinesin from Microtubule in the Strongly Bound States Enhances under Assisting Forces

The ability to predict the cellular dynamics of intracellular transport has enormous potential to impact human health. A key transporter is kinesin-1, an ATP-driven molecular motor that shuttles cellular cargos along microtubules (MTs). The dynamics of kinesins depends critically on their unbinding rate from MT, which varies depending on the force direction applied on the motor, i.e. the force-unbinding rate relation is asymmetric. However, it remains unclear how changing the force direction from resisting (applied against the motion direction) to assisting (applied in the motion direction) alters the kinesin's unbinding and stepping. Here, we propose a theoretical model for the influence of the force direction on the stepping dynamics of a single kinesin. The model shows that the asymmetry of the force-unbinding rate relation is independent of ATP concentration. It also reveals that the synthesis of ATP from backward stepping under assisting forces is less likely than under resisting forces. It then finds that the unbinding of kinesin in the strongly MT-bound kinetic states enhances under assisting forces.

Design principles governing chemomechanical coupling of kinesin

A systematic chemomechanical network model for the molecular motor kinesin is presented in this report. The network model is based on the nucleotide-dependent binding affinity of the heads to an microtubule (MT) and the asymmetries and similarities between the chemical transitions caused by the intramolecular strain between the front and rear heads. The network model allows for multiple chemomechanical cycles and takes into account all possible mechanical transitions between states in which one head is strongly bound and the other head is weakly bound to an MT. The results obtained from the model show the ATP-concentration dependence of the dominant forward stepping cycle and support a gated rear head mechanism in which the forward step is controlled by ATP hydrolysis and the resulting ADP-bound state of the rear head when the ATP level is saturated. When the ATP level is saturated, the energy from ATP hydrolysis is used to concentrate the chemical transition flux to a force-generating state that can produce the power stroke. In contrast, when the ATP level is low, the hydrolysis energy is consumed to avoid states in which the leading head is weakly bound to an MT and to inhibit frequent backward steps upon loading.

Review: Mechanochemistry of the kinesin-1 ATPase

Kinesins are P‐loop NTPases that can do mechanical work. Like small G‐proteins, to which they are related, kinesins execute a program of active site conformational changes that cleaves the terminal phosphate from an NTP substrate. But unlike small G‐proteins, kinesins can amplify and harness these conformational changes in order to exert force. In this short review I summarize current ideas about how the kinesin active site works and outline how the active site chemistry is coupled to the larger‐scale structural cycle of the kinesin motor domain. Focusing largely on kinesin‐1, the best‐studied kinesin, I discuss how the active site switch machinery of kinesin cycles between three distinct states, how docking of the neck linker stabilizes two of these states, and how tension‐sensitive and position‐sensitive neck linker docking may modulate both the hydrolysis step of ATP turnover and the trapping of product ADP in the active site. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 476–482, 2016.

The Kinesin-1 Chemomechanical Cycle: Stepping Toward a Consensus

Kinesin-1 serves as a model for understanding fundamentals of motor protein mechanochemistry and for interpreting functional diversity across the kinesin superfamily. Despite sustained work over the last three decades, disagreements remain regarding the events that trigger the two key transitions in the stepping cycle: detachment of the trailing head from the microtubule and binding of the tethered head to the next tubulin binding site. This review describes the conflicting views of these events and highlights recent work that sheds light on these long-standing controversies. It concludes by presenting a consensus kinesin-1 chemomechanical that incorporates recent work, resolves discrepancies, and highlights key questions for future experimental work. It is hoped that this model provides a framework for understanding how diverse kinesins are tuned for their specific cellular roles.

Effective dissipation: Breaking time-reversal symmetry in driven microscopic energy transmission

At molecular scales, fluctuations play a significant role and prevent biomolecular processes from always proceeding in a preferred direction, raising the question of how limited amounts of free energy can be dissipated to obtain directed progress. We examine the system and process characteristics that efficiently break time-reversal symmetry at fixed energy loss; in particular for a simple model of a molecular machine, an intermediate energy barrier produces unusually high asymmetry for a given dissipation. We relate the symmetry-breaking factors found in this model to recent observations of biomolecular machines.

The Kinesin-5 Chemomechanical Cycle Is Dominated by a Two-heads-bound State

Single-molecule microscopy and stopped-flow kinetics assays were carried out to understand the microtubule polymerase activity of kinesin-5 (Eg5). Four lines of evidence argue that the motor primarily resides in a two-heads-bound (2HB) state. First, upon microtubule binding, dimeric Eg5 releases both bound ADPs. Second, microtubule dissociation in saturating ADP is 20-fold slower for the dimer than for the monomer. Third, ATP-triggered mant-ADP release is 5-fold faster than the stepping rate. Fourth, ATP binding is relatively fast when the motor is locked in a 2HB state. Shortening the neck-linker does not facilitate rear-head detachment, suggesting a minimal role for rear-head-gating. This 2HB state may enable Eg5 to stabilize incoming tubulin at the growing microtubule plus-end. The finding that slowly hydrolyzable ATP analogs trigger slower nucleotide release than ATP suggests that ATP hydrolysis in the bound head precedes stepping by the tethered head, leading to a mechanochemical cycle in which processivity is determined by the race between unbinding of the bound head and attachment of the tethered head.

Direct observation of intermediate states during the stepping motion of kinesin-1

The dimeric motor protein kinesin-1 walks along microtubules by alternatingly hydrolyzing ATP and moving two motor domains ('heads'). Nanometer-precision single-molecule studies demonstrated that kinesin takes regular 8-nm steps upon hydrolysis of each ATP; however, the intermediate states between steps have not been directly visualized. Here, we employed high-temporal resolution dark-field microscopy to directly visualize the binding and unbinding of kinesin heads to or from microtubules during processive movement. Our observations revealed that upon unbinding from microtubules, the labeled heads were displaced rightward and underwent tethered diffusive movement. Structural and kinetic analyses of wild-type and mutant kinesins with altered neck linker lengths provided evidence that rebinding of the unbound head to the rear-binding site is prohibited by a tension increase in the neck linker and that ATP hydrolysis by the leading head is suppressed when both heads are bound to the microtubule, thereby explaining how the two heads coordinate to move in a hand-over-hand manner.

Kinetics of nucleotide-dependent structural transitions in the kinesin-1 hydrolysis cycle

To dissect the kinetics of structural transitions underlying the stepping cycle of kinesin-1 at physiological ATP, we used interferometric scattering microscopy to track the position of gold nanoparticles attached to individual motor domains in processively stepping dimers. Labeled heads resided stably at positions 16.4 nm apart, corresponding to a microtubule-bound state, and at a previously unseen intermediate position, corresponding to a tethered state. The chemical transitions underlying these structural transitions were identified by varying nucleotide conditions and carrying out parallel stopped-flow kinetics assays. At saturating ATP, kinesin-1 spends half of each stepping cycle with one head bound, specifying a structural state for each of two rate-limiting transitions. Analysis of stepping kinetics in varying nucleotides shows that ATP binding is required to properly enter the one-head-bound state, and hydrolysis is necessary to exit it at a physiological rate. These transitions differ from the standard model in which ATP binding drives full docking of the flexible neck linker domain of the motor. Thus, this work defines a consensus sequence of mechanochemical transitions that can be used to understand functional diversity across the kinesin superfamily.

How Dynein Moves Along Microtubules

Cytoplasmic dynein, a member of the AAA (ATPases Associated with diverse cellular Activities) family of proteins, drives the processive movement of numerous intracellular cargos towards the minus end of microtubules. Here, we summarize the structural and motile properties of dynein and highlight features that distinguish this motor from kinesin-1 and myosin V, two well-studied transport motors. Integrating information from recent crystal and cryoelectron microscopy structures, as well as high-resolution single-molecule studies, we also discuss models for how dynein biases its movement in one direction along a microtubule track, and present a movie that illustrates these principles.

The structural kinetics of switch-1 and the neck linker explain the functions of kinesin-1 and Eg5

Kinesins perform mechanical work to power a variety of cellular functions, from mitosis to organelle transport. Distinct functions shape distinct enzymologies, and this is illustrated by comparing kinesin-1, a highly processive transport motor that can work alone, to Eg5, a minimally processive mitotic motor that works in large ensembles. Although crystallographic models for both motors reveal similar structures for the domains involved in mechanochemical transduction--including switch-1 and the neck linker--how movement of these two domains is coordinated through the ATPase cycle remains unknown. We have addressed this issue by using a novel combination of transient kinetics and time-resolved fluorescence, which we refer to as "structural kinetics," to map the timing of structural changes in the switch-1 loop and neck linker. We find that differences between the structural kinetics of Eg5 and kinesin-1 yield insights into how these two motors adapt their enzymologies for their distinct functions.

Examining kinesin processivity within a general gating framework

Kinesin-1 is a dimeric motor that transports cargo along microtubules, taking 8.2-nm steps in a hand-over-hand fashion. The ATP hydrolysis cycles of its two heads are maintained out of phase by a series of gating mechanisms, which lead to processive runs averaging ∼1 μm. A key structural element for inter-head coordination is the neck linker (NL), which connects the heads to the stalk. To examine the role of the NL in regulating stepping, we investigated NL mutants of various lengths using single-molecule optical trapping and bulk fluorescence approaches in the context of a general framework for gating. Our results show that, although inter-head tension enhances motor velocity, it is crucial neither for inter-head coordination nor for rapid rear-head release. Furthermore, cysteine-light mutants do not produce wild-type motility under load. We conclude that kinesin-1 is primarily front-head gated, and that NL length is tuned to enhance unidirectional processivity and velocity.

DOI:http://dx.doi.org/10.7554/eLife.07403.001

In cells, molecules are moved from one location to another by motor proteins. Kinesins are a large family of such motors that transport their cargos along long filaments known as microtubules. Most kinesin molecules are formed from two identical protein chains. Each chain has a motor region at one end (called the head) that can attach to microtubules. The other end of each protein chain wraps around its partner to form a common stalk region (called the tail) that links to the cargo being carried.

The two kinesin heads are connected to the tail via a ‘neck linker’ region, and they advance along the microtubule in strict alternation, similar to the way our legs move when walking. During each step, the front head remains tightly associated with the filament as the trailing head releases itself, advances beyond the front head, and reattaches to become the new leading head. The two heads need to coordinate their activities, so that at any given time, they're not at the same stage in the process. For example, if both heads remained bound to the microtubule at the same time, the motor would not be able to advance. If they both released, the motor would fall off the filament and diffuse away. However, the process by which the heads coordinate is not fully understood, and different models for how this process works have been proposed.

Now, Andreasson, Milic et al. have examined the role played by the neck linker in coordinating the motor's movement using a technique known as ‘optical trapping’. The experiments involved attaching microscopic beads to the motor proteins, which serve as markers that can be tracked. The beads can also be used to exert controlled forces on the kinesin molecules, to see how they respond to different loads.

Andreasson, Milic et al. extended the length of neck linker by inserting extra amino acids (which are the building blocks of proteins) into this region of the protein. It was found that kinesins can still walk even when each neck linker was extended by up to six additional amino acids. However, introducing even a single amino acid into the linker relaxed the normal tension that exists between the heads when these are both bound to the filament. This resulted in slowed speeds, shorter distances of travel, and less ability to sustain loads. The experimental results suggest that the length of the neck linker in naturally occurring kinesins may be optimized to support maximum movement. Based on their data, Andreasson, Milic et al. propose a general framework for understanding the communication that needs to take place between the heads in order to walk in a coordinated manner. Further work is required to understand if motor proteins other than kinesins can also be understood with this same framework.

DOI:http://dx.doi.org/10.7554/eLife.07403.002

Kinesin Motor Enzymology: Chemistry, Structure, and Physics of Nanoscale Molecular Machines

Molecular motors are enzymes that convert chemical potential energy into controlled kinetic energy for mechanical work inside cells. Understanding the biophysics of these motors is essential for appreciating life as well as apprehending diseases that arise from motor malfunction. This review focuses on kinesin motor enzymology with special emphasis on the literature that reports the chemistry, structure and physics of several different kinesin superfamily members.

Processivity of the kinesin-2 KIF3A results from rear head gating and not front head gating

The kinesin-2 family motor KIF3A/B works together with dynein to bidirectionally transport intraflagellar particles, melanosomes, and neuronal vesicles. Compared with kinesin-1, kinesin-2 is less processive, and its processivity is more sensitive to load, suggesting that processivity may be controlled by different gating mechanisms. We used stopped-flow and steady-state kinetics experiments, along with single-molecule and multimotor assays to characterize the entire kinetic cycle of a KIF3A homodimer that exhibits motility similar to that of full-length KIF3A/B. Upon first encounter with a microtubule, the motor rapidly exchanges both mADP and mATP. When adenosine 5'-[(β,γ)-imido]triphosphate was used to entrap the motor in a two-head-bound state, exchange kinetics were unchanged, indicating that rearward strain in the two-head-bound state does not alter nucleotide binding to the front head. A similar lack of front head gating was found when intramolecular strain was enhanced by shortening the neck linker domain from 17 to 14 residues. In single-molecule assays in ADP, the motor dissociates at 2.1 s(-1), 20-fold slower than the stepping rate, demonstrating the presence of rear head gating. In microtubule pelleting assays, the KD(Mt) is similar in ADP and ATP. The data and accompanying simulations suggest that, rather than KIF3A processivity resulting from strain-dependent regulation of nucleotide binding (front head gating), the motor spends a significant fraction of its hydrolysis cycle in a low affinity state but dissociates only slowly from this state. This work provides a mechanism to explain differences in the load-dependent properties of kinesin-1 and kinesin-2.

Computational modeling of kinesin stepping

Kinesin is a walking motor protein that shuttles cellular cargoes along microtubules (MTs). This protein is considered as an information processor capable of sensing cellular inputs and transforming them into mechanical steps. Here, we propose a computational model to describe the mechanochemical kinetics underlying forward and backward stepping behavior of kinesin motor as a digital circuit designed based on an adenosine triphosphate (ATP)-driven finite state machine. Kinetic analysis suggests that the backward stepping of kinesin is mainly driven by ATP hydrolysis, whereas ATP synthesis rises the duration of this stepping. It is shown that kinesin pausing due to waiting for ATP binding at limiting ATP concentration ([ATP]) and low backward loads could be longer than that caused by low rate of ATP synthesis under high backward loads. These findings indicate that the pausing duration of kinesin in MT-bound (M·K) kinetic state is affected by [ATP], which in turn affects its velocity at fixed loads. We show that the proposed computational model accurately simulates the forward and backward stepping behavior of kinesin motor under different [ATP] and loads.

A stochastic automaton model for simulating kinesin processivity

MOTIVATION

Cellular interactions of kinesin-1, an adenosine triphosphate (ATP)-driven motor protein capable of undergoing multiple steps on a microtubule (MT), affect its mechanical processivity, the number of steps taken per encounter with MT. Even though the processivity of kinesin has been widely studied, a detailed study of the factors that affect the stepping of the motor along MT is still lacking.

RESULTS

We model the cellular interactions of kinesin as a probabilistic timed automaton and use the model to simulate the mechanical processivity of the motor. Theoretical analysis suggests: (i) backward stepping tends to be powered by ATP hydrolysis, rather than ATP synthesis, (ii) backward stepping powered by ATP synthesis is more likely to happen with limiting ATP concentration ([ATP]) at high loads and (iii) with increasing load the frequency of backward stepping powered by ATP hydrolysis at high [ATP] is greater than that powered by ATP synthesis at limiting [ATP]. Together, the higher frequency of backward stepping powered by ATP hydrolysis than by ATP synthesis is found to be a reason for the more dramatic falling of kinesin processivity with rising load at high [ATP] compared with that at low [ATP]. Simulation results further show that the processivity of kinesin can be determined by the number of ATP hydrolysis and synthesis kinetic cycles taken by the motor before becoming inactive. It is also found that the duration of a backward stepping cycle at high loads is more likely to be less than that of a forward stepping cycle.

CONTACT

h.r.khataee@griffithuni.edu.au or a.liew@griffith.edu.au.

A mathematical model describing the mechanical kinetics of kinesin stepping

MOTIVATION

Kinesin is a smart motor protein that steps processively forward and backward along microtubules (MTs). The mechanical kinetics of kinesin affecting its stepping behavior is not fully understood. Here, we propose a mathematical model to study the mechanical kinetics of forward and backward stepping of kinesin motor based on the four-state discrete stochastic model of the motor.

RESULTS

Results show that the probabilities of forward and backward stepping can be modeled using the mean probabilities of forward and backward kinetic transitions, respectively. We show that the backward stepping of kinesin motor starts when the probability of adenosine diphosphate (ADP) binding to the motor is much higher than that of adenosine triphosphate (ATP) binding. Furthermore, our results indicate that the backward stepping is related to both ATP hydrolysis and synthesis with rate limiting factor being ATP synthesis. Low rate of ATP synthesis under high backward loads above 10 pN is also suggested as a reason for the detachment of kinesin motor from MT in the kinetic state MTċKinesinċADPċPi.

AVAILABILITY AND IMPLEMENTATION

The code for this work is written in Visual C# and is available by request from the authors.

Motor proteins and molecular motors: how to operate machines at the nanoscale

Several classes of biological molecules that transform chemical energy into mechanical work are known as motor proteins or molecular motors. These nanometer-sized machines operate in noisy stochastic isothermal environments, strongly supporting fundamental cellular processes such as the transfer of genetic information, transport, organization and functioning. In the past two decades motor proteins have become a subject of intense research efforts, aimed at uncovering the fundamental principles and mechanisms of molecular motor dynamics. In this review, we critically discuss recent progress in experimental and theoretical studies on motor proteins. Our focus is on analyzing fundamental concepts and ideas that have been utilized to explain the non-equilibrium nature and mechanisms of molecular motors.

The load dependence of the physical properties of a molecular motor

The physical properties of a molecular motor with load changing in a wide range will be discussed in this study, in particular the mean velocity, output power and energy efficiency. The main difficulty of this study is that both the states of the molecular motor and the energy barriers between them change with the loading force. Moreover, with the change of load, the number of motor states may also change, so different models should be used to calculate the corresponding physical quantities in different ranges of load. The results show that, in contrast to the usual intuition, the mean velocity and output power of the molecular motor do not change continuously with load.

Kinesin-5: cross-bridging mechanism to targeted clinical therapy

Kinesin motor proteins comprise an ATPase superfamily that works hand in hand with microtubules in every eukaryote. The mitotic kinesins, by virtue of their potential therapeutic role in cancerous cells, have been a major focus of research for the past 28 years since the discovery of the canonical Kinesin-1 heavy chain. Perhaps the simplest player in mitotic spindle assembly, Kinesin-5 (also known as Kif11, Eg5, or kinesin spindle protein, KSP) is a plus-end-directed motor localized to interpolar spindle microtubules and to the spindle poles. Comprised of a homotetramer complex, its function primarily is to slide anti-parallel microtubules apart from one another. Based on multi-faceted analyses of this motor from numerous laboratories over the years, we have learned a great deal about the function of this motor at the atomic level for catalysis and as an integrated element of the cytoskeleton. These data have, in turn, informed the function of motile kinesins on the whole, as well as spearheaded integrative models of the mitotic apparatus in particular and regulation of the microtubule cytoskeleton in general. We review what is known about how this nanomotor works, its place inside the cytoskeleton of cells, and its small-molecule inhibitors that provide a toolbox for understanding motor function and for anticancer treatment in the clinic.

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.

Maximum power operation of interacting molecular motors

We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the noninteracting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.

Efficiency at maximum power of interacting molecular machines

We investigate the efficiency of systems of molecular motors operating at maximum power. We consider two models of kinesin motors on a microtubule: for both the simplified and the detailed model, we find that the many-body exclusion effect enhances the efficiency at maximum power of the many-motor system, with respect to the single motor case. Remarkably, we find that this effect occurs in a limited region of the system parameters, compatible with the biologically relevant range.

Oxygen isotopic exchange probes of ATP hydrolysis by RNA helicases

It is often possible to obtain a detailed understanding of the forward steps in ATP hydrolysis because they are thermodynamically favored and usually occur rapidly. However, it is difficult to obtain the reverse rates for ATP resynthesis because they are thermodynamically disfavored and little of their product, ATP, accumulates. Isotopic exchange reactions provide access to these reverse reactions because isotopic changes accumulate over time due to multiple reversals of hydrolysis, even in the absence of net resynthesis of significant amounts of ATP. Knowledge of both the forward and reverse rates allows calculation of the free energy changes at each step and how it changes when coupled to an energy-requiring conformational step such as unwinding of an RNA helix. This chapter describes the principal types of oxygen isotopic exchange reactions that are applicable to ATPases, in general, and helicases, in particular, their application and their interpretation.

Role of kinesin-1 in the pathogenesis of SPG10, a rare form of hereditary spastic paraplegia

Molecular protein motors play key roles in processes such as intracellular cargo transport and brain wiring, and failure of function can give rise to serious diseases. Kinesin-1, a member of the kinesin superfamily (also known as KIFs) is a two-headed motor protein that uses energy derived from ATP hydrolysis to transport diverse types of intracellular cargo toward the plus-ends of microtubules within axons. Recent studies at the level of a single molecule have provided extensive knowledge on how kinesin-1 moves along microtubules. Further elucidation of kinesin-1 movement may shed light on its influence on axon generation, thereby leading to therapies for diseases such as spastic paraplegia type 10 (SPG10), the subject of this review. SPG10 is an autosomal dominant form of hereditary spastic paraplegia caused by mutations in KIF5A, which encodes one of the isoforms of kinesin-1 (KIF5A, KIF5B, and KIF5C). Although little is known about the cargo of KIF5A, a recent study revealed an axonal transport defect of mitochondria in a KIF5A (-/-) mouse model. This review discusses the consensus moving model of kinesin-1 and the pathogenicity of SPG10 caused by defective KIF5A function.

Neck-linker length dependence of processive Kinesin-5 motility

Processive motility of individual molecules is essential for the function of many kinesin motors. Processivity for kinesins relies on communication between the two heads of a dimeric molecule, such that binding strictly alternates. The main communicating elements are believed to be the two neck linkers connecting the motors' stalks and heads. A proposed mechanism for coordination is the transmission of stress through the neck linkers. It is believed that the efficiency of gating depends on the length of the neck linker. Recent studies have presented support for a simple model in which the length of the neck linker directly controls the degree of processivity. Based on a previously published Kinesin-1/Kinesin-5 chimera, Eg5Kin, we have analyzed the motility of 12 motor constructs: we have varied the length of the neck linker in the range between 9 and 21 amino acids using the corresponding native Kinesin-5 sequence (Xenopus laevis Eg5). We found, surprisingly, that neither velocity nor force generation depended on neck-linker length. We also found that constructs with short neck linkers, down to 12 amino acids, were still highly processive, while processivity was lost at a length of 9 amino acids. Run lengths were maximal with neck linkers close to the native Kinesin-5 length and decreased beyond that length. This finding generally confirms the coordinating role of the neck linker for kinesin motility but challenges the simplest model postulating a motor-type-independent optimal length. Instead, our results suggest that different kinesins might be optimized for different neck-linker lengths.

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.

Dissecting the kinematics of the kinesin step

Kinesin walks processively on microtubules in an asymmetric hand-over-hand manner with each step spanning 16 nm. We used molecular simulations to determine the fraction of a single step due to conformational changes in the neck linker, and that due to diffusion of the tethered head. Stepping is determined largely by two energy scales, one favoring neck-linker docking and the other, ε(h)(MT-TH), between the trailing head (TH) and the microtubule. Neck-linker docking and an optimal value of ε(h)(MT-TH) are needed to minimize the probability that the TH takes side steps. There are three major stages in the kinematics of a step. In the first, the neck linker docks, resulting in ∼(5-6) nm movements of the trailing head. The TH moves an additional (6-8) nm in stage II by anisotropic translational diffusion. In the third stage, spanning ∼(3-4) nm, the step is complete with the TH binding to the αβ-tubulin binding site.

ATP utilization and RNA conformational rearrangement by DEAD-box proteins

RNA helicase enzymes catalyze the in vivo folding and conformational re-arrangement of RNA. DEAD-box proteins (DBPs) make up the largest family of RNA helicases and are found across all phyla. DBPs are molecular motor proteins that utilize chemical energy in cycles of ATP binding, hydrolysis, and product release to perform mechanical work resulting in reorganization of cellular RNAs. DBPs contain a highly conserved motor domain helicase core. Auxiliary domains, enzymatic adaptations, and regulatory partner proteins contribute to the diversity of DBP function throughout RNA metabolism. In this review we focus on the current understanding of the DBP ATP utilization mechanism in rearranging and unwinding RNA structures. We discuss DBP structural properties, kinetic pathways, and thermodynamic features of nucleotide-dependent interactions with RNA. We highlight recent advances in the DBP field derived from biochemical and molecular biophysical investigations aimed at developing a quantitative mechanistic understanding of DBP molecular motor function.

ACTIVE BIO-SYSTEMS: FROM SINGLE MOTOR MOLECULES TO COOPERATIVE CARGO TRANSPORT

Living cells contain a large number of molecular motors that convert the chemical energy released from nucleotide hydrolysis into mechanical work. This review focusses on stepping motors that move along cytoskeletal filaments. The behavior of these motors involves three distinct nonequilibrium processes that cover a wide range of length and time scales: (i) Directed stepping of single motors bound to a filament; (ii) Composite motor walks of single motors consisting of directed stepping interrupted by diffusive motion; and (iii) Cooperative transport by teams of several motors. On the molecular scale, the energy conversion of these motors leads to single steps along the filaments with a step size of about 10 nm. The corresponding chemomechanical coupling is governed by several distinct motor cycles, which represent the dominant pathways for different values of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses the direction of its motion. Because of thermal noise, the stepping motors unbind from the filaments after a certain run time and run length. For kinesin, the run time is about 1 s and the run length is about 1 μm for high ATP concentration and low load force. On length scales that are large compared to the run length, a single motor undergoes composite walks consisting of directed stepping interrupted by diffusive motion. The relative importance of bound and unbound motor states depends on the binding and unbinding rates of the motors. The effective transport velocity and diffusion coefficient of the motors are determined by the geometry of the compartments, in which the motors move. The effective diffusion coefficient can be enhanced by several orders of magnitude if the motors undergo active diffusion by interacting with certain filament patterns. In vivo, stepping motors are responsible for the transport of vesicles and other types of intracellular cargo particles that shuttle between the different cell compartments. This cargo transport is usually performed by teams of motors. If all motors belong to the same molecular species, the cooperative action of the motors leads to uni-directional transport with a strongly increased run length and to a characteristic force dependence of the velocity distributions. If two antagonistic species of motors pull on the cargo, they perform a stochastic tug-of-war, which is characterized by a subtle force balance between the two motor teams and leads to seven distinct patterns of uni- and bi-directional transport. So far, all experimental observations on bi-directional transport are consistent with such a tug-of-war. Finally, the traffic of interacting motors is also briefly discussed. Depending on their mutual interactions and the compartment geometry, the motors form various spatio-temporal patterns such as traffic jams, and undergo nonequilibrium phase transitions between such transport patterns.

Beyond microscopic reversibility: Are observable non-equilibrium processes precisely reversible?

Although the principle of microscopic reversibility has been studied for many decades, there remain ambiguities in its application to non-equilibrium processes of importance to chemistry, physics and biology. Examples include whether protein unfolding should follow the same pathways and in the same proportions as folding, and whether unbinding should likewise mirror binding. Using continuum-space calculations which extend previous kinetic analyses, we demonstrate formally that the precise symmetry of forward and reverse processes is expected only under certain special conditions. Approximate symmetry will be exhibited under a separate set of conditions. Exact, approximate, and broken symmetry scenarios are verified in several ways: using numerical calculations on toy and molecular systems; using exact calculations on kinetic models of induced fit in protein-ligand binding; and based on reported experimental results. The analysis highlights intrinsic challenges and ambiguities in the design and analysis of both experiments and simulations.

Mechanism of Mss116 ATPase reveals functional diversity of DEAD-Box proteins

Mss116 is a Saccharomyces cerevisiae mitochondrial DEAD-box RNA helicase protein that is essential for efficient in vivo splicing of all group I and group II introns and for activation of mRNA translation. Catalysis of intron splicing by Mss116 is coupled to its ATPase activity. Knowledge of the kinetic pathway(s) and biochemical intermediates populated during RNA-stimulated Mss116 ATPase is fundamental for defining how Mss116 ATP utilization is linked to in vivo function. We therefore measured the rate and equilibrium constants underlying Mss116 ATP utilization and nucleotide-linked RNA binding. RNA accelerates the Mss116 steady-state ATPase ∼7-fold by promoting rate-limiting ATP hydrolysis such that inorganic phosphate (P(i)) release becomes (partially) rate-limiting. RNA binding displays strong thermodynamic coupling to the chemical states of the Mss116-bound nucleotide such that Mss116 with bound ADP-P(i) binds RNA more strongly than Mss116 with bound ADP or in the absence of nucleotide. The predominant biochemical intermediate populated during in vivo steady-state cycling is the strong RNA-binding Mss116-ADP-P(i) state. Strong RNA binding allows Mss116 to fulfill its biological role in the stabilization of group II intron folding intermediates. ATPase cycling allows for transient population of the weak RNA-binding ADP state of Mss116 and linked dissociation from RNA, which is required for the final stages of intron folding. In cases where Mss116 functions as a helicase, the data collectively favor a model in which ATP hydrolysis promotes a weak-to-strong RNA binding transition that disrupts stable RNA duplexes. The subsequent strong-to-weak RNA binding transition associated with P(i) release dissociates Mss116-RNA complexes, regenerating free Mss116.

A seesaw model for intermolecular gating in the kinesin motor protein

Recent structural observations of kinesin-1, the founding member of the kinesin group of motor proteins, have led to substantial gains in our understanding of this molecular machine. Kinesin-1, similar to many kinesin family members, assembles to form homodimers that use alternating ATPase cycles of the catalytic motor domains, or "heads", to proceed unidirectionally along its partner filament (the microtubule) via a hand-over-hand mechanism. Cryo-electron microscopy has now revealed 8-Å resolution, 3D reconstructions of kinesin-1•microtubule complexes for all three of this motor's principal nucleotide-state intermediates (ADP-bound, no-nucleotide, and ATP analog), the first time filament co-complexes of any cytoskeletal motor have been visualized at this level of detail. These reconstructions comprehensively describe nucleotide-dependent changes in a monomeric head domain at the secondary structure level, and this information has been combined with atomic-resolution crystallography data to synthesize an atomic-level "seesaw" mechanism describing how microtubules activate kinesin's ATP-sensing machinery. The new structural information revises or replaces key details of earlier models of kinesin's ATPase cycle that were based principally on crystal structures of free kinesin, and demonstrates that high-resolution characterization of the kinesin-microtubule complex is essential for understanding the structural basis of the cycle. I discuss the broader implications of the seesaw mechanism within the cycle of a fully functional kinesin dimer and show how the seesaw can account for two types of "gating" that keep the ATPase cycles of the two heads out of sync during processive movement.

A coordinated molecular 'fishing' mechanism in heterodimeric kinesin

Kar3 is a kinesin motor that facilitates chromosome segregation during cell division. Unlike many members of the kinesin superfamily, Kar3 forms a heterodimer with non-motor protein Vik1 or Cik1 in vivo. The heterodimers show ATP-driven minus-end directed motility along a microtubule (MT) lattice, and also serve as depolymerase at the MT ends. The molecular mechanisms behind this dual functionality remain mysterious. Here, a molecular mechanical model for the Kar3/Vik1 heterodimer based on structural, kinetic and motility data reveals a long-range chemomechanical transmission mechanism that resembles a familiar fishing tactic. By this molecular 'fishing', ATP-binding to Kar3 dissociates catalytically inactive Vik1 off MT to facilitate minus-end sliding of the dimer on the MT lattice. When the dimer binds the frayed ends of MT, the fishing channels ATP hydrolysis energy into MT depolymerization by a mechanochemical effect. The molecular fishing thus provides a unified mechanistic ground for Kar3's dual functionality. The fishing-promoted depolymerization differs from the depolymerase mechanisms found in homodimeric kinesins. The fishing also enables intermolecular coordination with a chemomechanical coupling feature different from the paradigmatic pattern of homodimeric motors. This study rationalizes some puzzling experimental observation, and suggests new experiments for further elucidation of the fishing mechanism.

Comprehensive physical mechanism of two-headed biomotor myosin V

Two-headed biomotor myosin V autonomously coordinates its two identical heads in fuel consumption and mechanical stepping, so that the dimerized motor as a whole gains the capability of processive, unidirectional movement along cytoskeletal filament. How the dimer-level functions like sustained direction rectification and autonomous coordination emerge out of physical principles poses an outstanding question pertinent to motor protein biology as well as the nascent field of bioinspired nanomotors. Here the comprehensive physical mechanism for myosin V motor is identified by a dimer-level free-energy analysis that is methodologically calibrated against experimental data. A hallmark of the identified mechanism is a mechanically mediated symmetry breaking that occurs at the dimer level and prevails against ubiquitous thermal fluctuations. Another character is the onset of substantial free-energy gaps between major dimer-track binding configurations. The symmetry breaking is the basis for myosin V's directional rectification, and the energy gaps facilitate autonomous head-head coordination. The mechanism explains the experimental finding that myosin V makes ATP-independent consecutive steps under high opposing loads but not under pushing loads. Interestingly, myosin V and another major biomotor kinesin 1 are found to share essentially the same core mechanism but for distinctly different working regimes.

An atomic-level mechanism for activation of the kinesin molecular motors

Kinesin cytoskeletal motors convert the energy of ATP hydrolysis into stepping movement along microtubules. A partial model of this process has been derived from crystal structures, which show that movement of the motor domain relative to its major microtubule binding element, the switch II helix, is coupled to docking of kinesin's neck linker element along the motor domain. This docking would displace the cargo in the direction of travel and so contribute to a step. However, the crystal structures do not reveal how ATP binding and hydrolysis govern this series of events. We used cryoelectron microscopy to derive 8-9 A-resolution maps of four nucleotide states encompassing the microtubule-attached kinetic cycle of a kinesin motor. The exceptionally high quality of these maps allowed us to build in crystallographically determined conformations of kinesin's key subcomponents, yielding novel arrangements of kinesin's switch II helix and nucleotide-sensing switch loops. The resulting atomic models reveal a seesaw mechanism in which the switch loops, triggered by ATP binding, propel their side of the motor domain down and thereby elicit docking of the neck linker on the opposite side of the seesaw. Microtubules engage the seesaw mechanism by stabilizing the formation of extra turns at the N terminus of the switch II helix, which then serve as an anchor for the switch loops as they modulate the seesaw angle. These observations explain how microtubules activate kinesin's ATP-sensing machinery to promote cargo displacement and inform the mechanism of kinesin's ancestral relative, myosin.

Utilization of positional isotope exchange experiments to evaluate reversibility of ATP hydrolysis catalyzed by Escherichia coli Lon proteaseThis paper is one of a selection of papers published in this special issue entitled 8th International Conference on AAA Proteins and has undergone the Journal's usual peer review process

Lon protease, also known as protease La, is an ATP-dependent serine protease. Despite the presence of a proteolytic Ser–Lys dyad, the enzyme only catalyzes protein degradation in the presence of ATP. Lon possesses an intrinsic ATPase activity that is stimulated by protein and certain peptide substrates. Through sequence alignment and analysis, it is concluded that Lon belongs to the AAA+ protein family. Previous kinetic characterization of the ATPase domain of Escherichia coli Lon protease implicates a half-site reactivity model in which only 50% of the ATP bound to Lon are hydrolyzed to yield ADP; the remaining ATPase sites remain bound with ATP and are considered non-catalytic. In this model, it is implied that ATP hydrolysis is irreversible. To further evaluate the proposed half-site reactivity model, the reversibility of the ATPase activity of E. coli Lon was evaluated by positional isotope exchange experiments. The ATPase reactions were conducted in the 18O-enriched buffer such that the extent of 18O incorporation into inorganic phosphate generated from ATP hydrolysis could be used to evaluate the extent of reversibility in ATP hydrolysis. Collectively, our experimental data reveal that the ATPase reaction catalyzed by E. coli Lon in the presence and absence of peptide substrate that stimulated the enzyme’s ATPase activity is irreversible. Therefore, the half-site ATPase reactivity of E. coli Lon is validated, and can be used to account for the kinetic mechanism of the ATP-dependent peptidase activity of the enzyme.

Alternating-site mechanism of kinesin-1 characterized by single-molecule FRET using fluorescent ATP analogues

Kinesin-1 motor proteins move along microtubules in repetitive steps of 8 nm at the expense of ATP. To determine nucleotide dwell times during these processive runs, we used a Förster resonance energy transfer method at the single-molecule level that detects nucleotide binding to kinesin motor heads. We show that the fluorescent ATP analog used produces processive motility with kinetic parameters altered <2.5-fold compared with normal ATP. Using our confocal fluorescence kinesin motility assay, we obtained fluorescence intensity time traces that we then analyzed using autocorrelation techniques, yielding a time resolution of approximately 1 ms for the intensity fluctuations due to fluorescent nucleotide binding and release. To compare these experimental autocorrelation curves with kinetic models, we used Monte-Carlo simulations. We find that the experimental data can only be described satisfactorily on the basis of models assuming an alternating-site mechanism, thus supporting the view that kinesin's two motor domains hydrolyze ATP and step in a sequential way.

Kinesin's step dissected with single-motor FRET

The motor protein Kinesin-1 drives intracellular transport along microtubules, with each of its two motor domains taking 16-nm steps in a hand-over-hand fashion. The way in which a single-motor domain moves during a step is unknown. Here, we use Förster resonance energy transfer (FRET) between fluorescent labels on both motor domains of a single kinesin. This approach allows us to resolve the relative distance between the motor domains and their relative orientation, on the submillisecond timescale, during processive stepping. We observe transitions between high and low FRET values for certain kinesin constructs, depending on the location of the labels. These results reveal that, during a step, a kinesin motor domain dwells in a well-defined intermediate position for approximately 3 ms.

The ATPase cycle of the mitotic motor CENP-E

We have previously shown that the mitotic motor centrosome protein E (CENP-E) is capable of walking for more than 250 steps on its microtubule track without dissociating. We have examined the kinetics of this molecular motor to see if its enzymology explains this remarkable degree of processivity. We find that like the highly processive transport motor kinesin 1, the enzymatic cycle of CENP-E is characterized by rapid ATP binding, multiple enzymatic turnovers per diffusive encounter, and gating of nucleotide binding. These features endow CENP-E with a high duty cycle, a prerequisite for processivity. However, unlike kinesin 1, neck linker docking in CENP-E is slow, occurring at a rate closer to that for Eg5, a mitotic kinesin that takes only 5-10 steps per processive run. These results suggest that like kinesin 1, features outside of the catalytic domain of CENP-E may also play a role in regulating the processive behavior of this motor.