Mechanical control of the directional stepping dynamics of the kinesin motor

Power Strokes in Molecular Motors: Predictive, Irrelevant, or Somewhere in Between?

For several decades, molecular motor directionality has been rationalized in terms of the free energy of molecular conformations visited before and after the motor takes a step, a so-called power stroke mechanism with analogues in macroscopic engines. Despite theoretical and experimental demonstrations of its flaws, the power stroke language is quite ingrained, and some communities still value power stroke intuition. By building a catalysis-driven motor into simulated numerical experiments, we here systematically report on how directionality responds when the motor is modified accordingly to power stroke intuition. We confirm that the power stroke mechanism generally does not predict motor directionality. Nevertheless, the simulations illustrate that the relative stability of molecular conformations should be included as a potential design element to adjust the motor directional bias. Though power strokes are formally unimportant for determining directionality, we show that practical attempts to alter a power stroke have side effects that can in fact alter the bias. The change in the bias can align with what power stroke intuition would have suggested, offering a potential explanation for why the flawed power stroke mechanism can retain apparent utility when engineering specific systems.

Regulatory mechanisms of the dynein-2 motility by post-translational modification revealed by MD simulation

Intraflagellar transport for ciliary assembly and maintenance is driven by dynein and kinesins specific to the cilia. It has been shown that anterograde and retrograde transports run on different regions of the doublet microtubule, i.e., separate train tracks. However, little is known about the regulatory mechanism of this selective process. Since the doublet microtubule is known to display specific post-translational modifications of tubulins, i.e., "tubulin code", for molecular motor regulations, we investigated the motility of ciliary specific dynein-2 under different post-translational modification by coarse-grained molecular dynamics. Our setup allows us to simulate the landing behaviors of dynein-2 on un-modified, detyrosinated, poly-glutamylated and poly-glycylated microtubules in silico. Our study revealed that poly-glutamylation can play an inhibitory effect on dynein-2 motility. Our result indicates that poly-glutamylation of the B-tubule of the doublet microtubule can be used as an efficient means to target retrograde intraflagellar transport onto the A-tubule.

Tug-of-War and Coordination in Bidirectional Transport by Molecular Motors

Many cargoes in cells are transported in a bidirectional fashion by molecular motors pulling into opposite directions along a cytoskeletal filament, e.g., by kinesins and dyneins along microtubules. How opposite-polarity motors are coordinated has been under debate for a long time, with experimental evidence supporting both a tug-of-war between the motors as well as biochemical coordination mechanisms. Here we propose a model that extends a tug-of-war model by a mechanism of motor activation and inactivation and show that this model can explain some observations that are incompatible with a simple tug-of-war scenario, specifically long unidirectional runs and a directional memory after unbinding from the filament. Both features are present in two variants of the model in which motors are activated and inactivated individually and in opposite-direction pairs, respectively.

Landscape-Based View on the Stepping Movement of Myosin VI

Myosin VI dimer walks toward the minus end of the actin filament with a large and variable step size of 25–36 nm. Two competing models have been put forward to explain this large step size. The Spudich model assumes that the myosin VI dimer associates at a distal tail near the cargo-binding domain, which makes two full-length single α-helix (SAH) domains serve as long legs. In contrast, the Houdusse–Sweeney model assumes that the association occurs in the middle (between residues 913 and 940) of the SAH domain and that the three-helix bundles unfold to ensure the large step size. Their consistency with the observation of stepping motion with a large and variable step size has not been examined in detail. To compare the two proposed models of myosin VI, we computationally characterized the free energy landscape experienced by the leading head during the stepping movement along the actin filament using the elastic network model of two heads and an implicit model of the SAH domains. Our results showed that the Spudich model is more consistent with the 25–36 nm step size than the Houdusse–Sweeney model. The unfolding of the three-helix bundles gives rise to the free energy bias toward a shorter distance between two heads. Besides, the stiffness of the SAH domain is a key factor for giving strong energetic bias toward the longer distance of stepping. Free energy analysis of the stepping motion complements the visual inspection of static structures and enables a deeper understanding of underlying mechanisms of molecular motors.

Effects of Gold Nanoparticles on the Stepping Trajectories of Kinesin

A substantial increase in the temporal resolution of the stepping of dimeric molecular motors is possible by tracking the position of a large gold nanoparticle (GNP) attached to a labeled site on one of the heads. This technique was employed to measure the stepping trajectories of conventional kinesin (Kin1) using the time-dependent position of the GNP as a proxy. The trajectories revealed that the detached head always passes to the right of the head that is tightly bound to the microtubule (MT) during a step. In interpreting the results of such experiments, it is assumed that the GNP does not significantly alter the diffusive motion of the detached head. We used coarse-grained simulations of a system consisting of the MT-Kin1 complex with and without attached GNP to investigate how the stepping trajectories are affected. The two significant findings are: (1) The GNP does not faithfully track the position of the stepping head, and (2) the rightward bias is typically exaggerated by the GNP. Both these findings depend on the precise residue position to which the GNP is attached. Surprisingly, the stepping trajectories of kinesin are not significantly affected if, in addition to the GNP, a 1 μm diameter cargo is attached to the coiled coil. Our simulations suggest the effects of the large probe have to be considered when inferring the stepping mechanisms using GNP tracking experiments.

Multiscale Coarse-Grained Model for the Stepping of Molecular Motors with Application to Kinesin

Conventional kinesin, a motor protein that transports cargo within cells, walks by taking multiple steps toward the plus end of the microtubule (MT). While significant progress has been made in understanding the details of the walking mechanism of kinesin, there are many unresolved issues. From a computational perspective, a central challenge is the large size of the system, which limits the scope of time scales accessible in standard computer simulations. Here, we create a general multiscale coarse-grained model for motors that enables us to simulate the stepping process of motors on polar tracks (actin and MT) with a focus on kinesin. Our approach greatly shortens the computation times without a significant loss in detail, thus allowing us to better describe the molecular basis of the stepping kinetics. The small number of parameters, which are determined by fitting to experimental data, allows us to develop an accurate method that may be adopted to simulate stepping in other molecular motors. The model enables us to simulate a large number of steps, which was not possible previously. We show in agreement with experiments that due to the docking of the neck linker (NL) of kinesin, sometimes deemed as the power stroke, the space explored diffusively by the tethered head is severely restricted, allowing the step to be completed in tens of microseconds. We predict that increasing the interaction strength between the NL and the motor head, achievable by mutations in the NL, decreases the stepping time but reaches a saturation value. Furthermore, the full three-dimensional dynamics of the cargo are fully resolved in our model, contributing to the predictive power and allowing us to study the important aspects of cargo-motor interactions.

Computational modeling of dynein motor proteins at work

Along with various experimental methods, a combination of theoretical and computational methods is essential to explore different length-scale and time-scale processes in the biological system. The functional mechanism of a dynein, an ATP-fueled motor protein, working in a multiprotein complex, involves a wide range of length/time-scale events. It generates mechanical force from chemical energy and moves on microtubules towards the minus end direction while performing a large number of biological processes including ciliary beating, intracellular material transport, and cell division. Like in the cases of other conventional motor proteins, a combination of experimental techniques including X-crystallography, cryo-electron microscopy, and single molecular assay have provided a wealth of information about the mechanochemical cycle of a dynein. Dyneins have a large and complex structural architecture and therefore, computational modeling of different aspects of a dynein is extremely challenging. As the process of dynein movement involves varying length and timescales, it demands, like in experiments, a combination of computational methods covering such a wide range of processes for the comprehensive investigation of the mechanochemical cycle. In this review article, we will summarize how the use of state-of-the-art computational methods can provide a detailed molecular understanding of the mechanochemical cycle of the dynein. We implemented all-atom molecular dynamics simulations and hybrid quantum-mechanics/molecular-mechanics simulations to explore the ATP hydrolysis mechanisms at the primary ATPase site (AAA1) of dynein. To investigate the large-scale conformational changes we employed coarse-grained structure-based molecular dynamics simulations to capture the domain motions. Here we explored the conformational changes upon binding of ATP at AAA1, nucleotide state-dependent regulation of the mechanochemical cycle, and inter-head coordination by inter-head tension. Additionally, implementing a phenomenological theoretical model we explore the force-dependent detachment rate of a motorhead from the microtubule and the principle of multi-dynein cooperation during cargo transport.

A model of processive walking and slipping of kinesin-8 molecular motors

Kinesin-8 molecular motor can move with superprocessivity on microtubules towards the plus end by hydrolyzing ATP molecules, depolymerizing microtubules. The available single molecule data for yeast kinesin-8 (Kip3) motor showed that its superprocessive movement is frequently interrupted by brief stick-slip motion. Here, a model is presented for the chemomechanical coupling of the kinesin-8 motor. On the basis of the model, the dynamics of Kip3 motor is studied analytically. The analytical results reproduce quantitatively the available single molecule data on velocity without including the slip and that with including the slip versus external load at saturating ATP as well as slipping velocity versus external load at saturating ADP and no ATP. Predicted results on load dependence of stepping ratio at saturating ATP and load dependence of velocity at non-saturating ATP are provided. Similarities and differences between dynamics of kinesin-8 and that of kinesin-1 are discussed.

Simulations of Phage T7 Capsid Expansion Reveal the Role of Molecular Sterics on Dynamics

Molecular dynamics techniques provide numerous strategies for investigating biomolecular energetics, though quantitative analysis is often only accessible for relatively small (frequently monomeric) systems. To address this limit, we use simulations in combination with a simplified energetic model to study complex rearrangements in a large assembly. We use cryo-EM reconstructions to simulate the DNA packaging-associated 3 nm expansion of the protein shell of an initially assembled phage T7 capsid (called procapsid or capsid I). This is accompanied by a disorder-order transition and expansion-associated externalization displacement of the 420 N-terminal tails of the shell proteins. For the simulations, we use an all-atom structure-based model (1.07 million atoms), which is specifically designed to probe the influence of molecular sterics on dynamics. We find that the rate at which the N-terminal tails undergo translocation depends heavily on their position within hexons and pentons. Specifically, trans-shell displacements of the hexon E subunits are the most frequent and hexon A subunits are the least frequent. The simulations also implicate numerous tail translocation intermediates during tail translocation that involve topological traps, as well as sterically induced barriers. The presented study establishes a foundation for understanding the precise relationship between molecular structure and phage maturation.

How Kinesin-1 Utilize the Energy of Nucleotide: The Conformational Changes and Mechanochemical Coupling in the Unidirectional Motion of Kinesin-1

Kinesin-1 is a typical motile molecular motor and the founding member of the kinesin family. The most significant feature in the unidirectional motion of kinesin-1 is its processivity. To realize the fast and processive movement on the microtubule lattice, kinesin-1 efficiently transforms the chemical energy of nucleotide binding and hydrolysis to the energy of mechanical movement. The chemical and mechanical cycle of kinesin-1 are coupled to avoid futile nucleotide hydrolysis. In this paper, the research on the mechanical pathway of energy transition and the regulating mechanism of the mechanochemical cycle of kinesin-1 is reviewed.

A common chemomechanical coupling model for orphan and conventional kinesin molecular motors

Orphan and conventional kinesin dimers represent two families of the kinesin superfamily molecular motors. Conventional kinesin, having a 14-residue neck linker (NL) in each head, can step processively on microtubule (MT), with an ATP hydrolysis being coupled with a mechanical stepping under no load. Orphan kinesin phragmoplast-associated kinesin-related protein 2 (PAKRP2) dimer, despite having a NL of 32 residues in each head, can also step processively on MT and exhibits tight chemomechanical coupling under no load. However, the dynamic properties of the wild type PAKRP2 and the mutant one with each NL truncated to 14 residues are very different from those of the wild type conventional kinesin and the mutant one with each NL being replaced by the 32-residue NL from PAKRP2. Here, based on a common chemomechanical coupling model we study computationally the dynamics of the two families of the kinesin dimers, with the simulated results explaining quantitatively the available experimental data. The large differences in the dynamics between the two families of kinesin dimers arise mainly from different rate constants of NL docking and ATPase activity and different weak affinities of the head in ADP state for MT. The studies indicate that both the orphan kinesin PAKRP2 and conventional kinesin use the same mechanism for processive motility.

Protein Diffusion on Charged Biopolymers: DNA versus Microtubule

Protein diffusion in lower-dimensional spaces is used for various cellular functions. For example, sliding on DNA is essential for proteins searching for their target sites, and protein diffusion on microtubules is important for proper cell division and neuronal development. On the one hand, these linear diffusion processes are mediated by long-range electrostatic interactions between positively charged proteins and negatively charged biopolymers and have similar characteristic diffusion coefficients. On the other hand, DNA and microtubules have different structural properties. Here, using computational approaches, we studied the mechanism of protein diffusion along DNA and microtubules by exploring the diffusion of both protein types on both biopolymers. We found that DNA-binding and microtubule-binding proteins can diffuse on each other's substrates; however, the adopted diffusion mechanism depends on the molecular properties of the diffusing proteins and the biopolymers. On the protein side, only DNA-binding proteins can perform rotation-coupled diffusion along DNA, with this being due to their higher net charge and its spatial organization at the DNA recognition helix. By contrast, the lower net charge on microtubule-binding proteins enables them to diffuse more quickly than DNA-binding proteins on both biopolymers. On the biopolymer side, microtubules possess intrinsically disordered, negatively charged C-terminal tails that interact with microtubule-binding proteins, thus supporting their diffusion. Thus, although both DNA-binding and microtubule-binding proteins can diffuse on the negatively charged biopolymers, the unique molecular features of the biopolymers and of their natural substrates are essential for function.

Tubulin tails and their modifications regulate protein diffusion on microtubules

Microtubules (MTs) are essential components of the eukaryotic cytoskeleton that serve as "highways" for intracellular trafficking. In addition to the well-known active transport of cargo by motor proteins, many MT-binding proteins seem to adopt diffusional motility as a transportation mechanism. However, because of the limited spatial resolution of current experimental techniques, the detailed mechanism of protein diffusion has not been elucidated. In particular, the precise role of tubulin tails and tail modifications in the diffusion process is unclear. Here, using coarse-grained molecular dynamics simulations validated against atomistic simulations, we explore the molecular mechanism of protein diffusion along MTs. We found that electrostatic interactions play a central role in protein diffusion; the disordered tubulin tails enhance affinity but slow down diffusion, and diffusion occurs in discrete steps. While diffusion along wild-type MT is performed in steps of dimeric tubulin, the removal of the tails results in a step of monomeric tubulin. We found that the energy barrier for diffusion is larger when diffusion on MTs is mediated primarily by the MT tails rather than the MT body. In addition, globular proteins (EB1 and PRC1) diffuse more slowly than an intrinsically disordered protein (Tau) on MTs. Finally, we found that polyglutamylation and polyglycylation of tubulin tails lead to slower protein diffusion along MTs, although polyglycylation leads to faster diffusion across MT protofilaments. Taken together, our results explain experimentally observed data and shed light on the roles played by disordered tubulin tails and tail modifications in the molecular mechanism of protein diffusion along MTs.

How kinesin waits for ATP affects the nucleotide and load dependence of the stepping kinetics

Conventional kinesin, responsible for directional transport of cellular vesicles, takes multiple nearly uniform 8.2-nm steps by consuming one ATP molecule per step as it walks toward the plus end of the microtubule (MT). Despite decades of intensive experimental and theoretical studies, there are gaps in the elucidation of key steps in the catalytic cycle of kinesin. How the motor waits for ATP to bind to the leading head is controversial. Two experiments using a similar protocol have arrived at different conclusions. One asserts that kinesin waits for ATP in a state with both the heads bound to the MT, whereas the other shows that ATP binds to the leading head after the trailing head detaches. To discriminate between the 2 scenarios, we developed a minimal model, which analytically predicts the outcomes of a number of experimental observable quantities (the distribution of run length, the distribution of velocity [[Formula: see text]], and the randomness parameter) as a function of an external resistive force (F) and ATP concentration ([T]). The differences in the predicted bimodality in [Formula: see text] as a function of F between the 2 models may be amenable to experimental testing. Most importantly, we predict that the F and [T] dependence of the randomness parameters differ qualitatively depending on the waiting states. The randomness parameters as a function of F and [T] can be quantitatively measured from stepping trajectories with very little prejudice in data analysis. Therefore, an accurate measurement of the randomness parameter and the velocity distribution as a function of load and nucleotide concentration could resolve the apparent controversy.

Structural basis for power stroke vs. Brownian ratchet mechanisms of motor proteins

Two mechanisms have been proposed for the function of motor proteins: The power stroke and the Brownian ratchet. The former refers to generation of a large downhill free energy gradient over which the motor protein moves nearly irreversibly in making a step, whereas the latter refers to biasing or rectifying the diffusive motion of the motor. Both mechanisms require input of free energy, which generally involves the processing of an ATP (adenosine 5'-triphosphate) molecule. Recent advances in experiments that reveal the details of the stepping motion of motor proteins, together with computer simulations of atomistic structures, have provided greater insights into the mechanisms. Here, we compare the various models of the power stroke and the Brownian ratchet that have been proposed. The 2 mechanisms are not mutually exclusive, and various motor proteins employ them to different extents to perform their biological function. As examples, we discuss linear motor proteins Kinesin-1 and myosin-V, and the rotary motor F₁-ATPase, all of which involve a power stroke as the essential element of their stepping mechanism.

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'.

A non-tight chemomechanical coupling model for force-dependence of movement dynamics of molecular motors

Based on the available experimental evidence, we present a simple and general model to describe the movement dynamics of molecular motors that can move processively on their linear tracks by using the chemical energy derived from ATP hydrolysis. An important aspect of the model is the non-tight coupling between the ATP hydrolysis and mechanical stepping, in contrast to the prevailing models presented in the literature that assume the tight chemomechanical coupling. With kinesin as an example, based on the current model, we study in detail its movement dynamics under a backward load, reproducing well the diverse available single-molecule experimental data such as the forward to backward step ratio, velocity, dwell time, randomness, run length, etc., versus the load. Moreover, predicted results are provided on the force-dependence of the mean number of ATP molecules consumed per mechanical step. Additionally, the theoretical data for the dynamics of myosin-V obtained based on the model are also in good agreement with the available experimental data.

Investigating role of conformational changes of microtubule in regulating its binding affinity to kinesin by all-atom molecular dynamics simulation

Changes of affinity of kinesin head to microtubule regulated by changes in the nucleotide state are essential to processive movement of kinesin on microtubule. Here, using all-atom molecular dynamics simulations we show that besides the nucleotide state, large conformational changes of microtubule-tubulin heterodimers induced by strong interaction with the head in strongly binding state are also indispensable to regulate the affinity of the head to the tubulin. In strongly binding state the high affinity of the head to microtubule arises largely from mutual conformational changes of the microtubule and head induced by the specific interaction between them via an induced-fit mechanism. Moreover, the ADP-head has a much weaker affinity to the local microtubule-tubulin, whose conformation is largely altered by the interaction with the head in strongly binding state, than to other unperturbed tubulins. This indicates that upon Pi release the ADP-head temporarily has a much weaker affinity to the local tubulin than to other tubulins.

Structural consequences of hereditary spastic paraplegia disease-related mutations in kinesin

A wide range of mutations in the kinesin motor Kif5A have been linked to a neuronal disorder called hereditary spastic paraplegia (HSP). The position of these mutations can vary, and a range of different motile behaviors have been observed, indicating that the HSP mutants can alter distinct aspects of kinesin mechanochemistry. While focusing on four key HSP-associated mutants, this study examined the structural and dynamic perturbations that arise from these mutations using a series of different computational methods, ranging from bioinformatics analyses to all-atom simulations, that account for solvent effects explicitly. We show that two catalytic domain mutations (R280S and K253N) reduce the microtubule (MT) binding affinity of the kinesin head domains appreciably, while N256S has a much smaller impact. Bioinformatics analysis suggests that the stalk mutation A361V perturbs motor dimerization. Subsequent integration of these effects into a coarse-grained structure-based model of dimeric kinesin revealed that the order-disorder transition of the neck linker is substantially affected, indicating a hampered directionality and processivity of kinesin. The present analyses therefore suggest that, in addition to kinesin-MT binding and coiled-coil dimerization, HSP mutations affecting motor stepping transitions and processivity can lead to disease.

Dynamics of Allosteric Transitions in Dynein

Cytoplasmic dynein, whose motor domain belongs to the AAA+ family, walks on microtubules toward the minus end. Using the available structures in different nucleotide states, we performed simulations of a coarse-grained model to elucidate the dynamics of allosteric transitions. Binding of ATP closes the cleft between the AAA1 and AAA2 domains, triggering conformational changes in the rest of the motor domain, thus forming the pre-power stroke state. Interactions with the microtubule, modeled implicitly, enhance ADP release rate, and the formation of the post-power stroke state. The dynamics of the linker (LN), which reversibly changes from a straight to a bent state, is heterogeneous. Persistent interactions between the LN and the insert loops in the AAA2 domain prevent the formation of pre-power stroke state when ATP is bound to AAA3, thus locking dynein in a repressed non-functional state. Application of mechanical force to the LN restores motility in the repressed state.

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.

Processivity of dimeric kinesin-1 molecular motors

Kinesin‐1 is a homodimeric motor protein that can move along microtubule filaments by hydrolyzing ATP with a high processivity. How the two motor domains are coordinated to achieve such high processivity is not clear. To address this issue, we computationally studied the run length of the dimer with our proposed model. The computational data quantitatively reproduced the puzzling experimental data, including the dramatically asymmetric character of the run length with respect to the direction of external load acting on the coiled‐coil stalk, the enhancement of the run length by addition of phosphate, and the contrary features of the run length for different types of kinesin‐1 with extensions of their neck linkers compared with those without extension of the neck linker. The computational data on other aspects of the movement dynamics such as velocity and durations of one‐head‐bound and two‐head‐bound states in a mechanochemical coupling cycle were also in quantitative agreement with the available experimental data. Moreover, predicted results are provided on dependence of the run length upon external load acting on one head of the dimer, which can be easily tested in the future using single‐molecule optical trapping assays.

Parsing the roles of neck-linker docking and tethered head diffusion in the stepping dynamics of kinesin

Kinesin walks processively on microtubules (MTs) in an asymmetric hand-over-hand manner consuming one ATP molecule per 16-nm step. The individual contributions due to docking of the approximately 13-residue neck linker to the leading head (deemed to be the power stroke) and diffusion of the trailing head (TH) that contributes in propelling the motor by 16 nm have not been quantified. We use molecular simulations by creating a coarse-grained model of the MT-kinesin complex, which reproduces the measured stall force as well as the force required to dislodge the motor head from the MT, to show that nearly three-quarters of the step occurs by bidirectional stochastic motion of the TH. However, docking of the neck linker to the leading head constrains the extent of diffusion and minimizes the probability that kinesin takes side steps, implying that both the events are necessary in the motility of kinesin and for the maintenance of processivity. Surprisingly, we find that during a single step, the TH stochastically hops multiple times between the geometrically accessible neighboring sites on the MT before forming a stable interaction with the target binding site with correct orientation between the motor head and the [Formula: see text] tubulin dimer.

Molecular origin of the weak susceptibility of kinesin velocity to loads and its relation to the collective behavior of kinesins

Motor proteins are active enzymatic molecules that support important cellular processes by transforming chemical energy into mechanical work. Although the structures and chemomechanical cycles of motor proteins have been extensively investigated, the sensitivity of a motor's velocity in response to a force is not well-understood. For kinesin, velocity is weakly influenced by a small to midrange external force (weak susceptibility) but is steeply reduced by a large force. Here, we utilize a structure-based molecular dynamic simulation to study the molecular origin of the weak susceptibility for a single kinesin. We show that the key step in controlling the velocity of a single kinesin under an external force is the ATP release from the microtubule-bound head. Only under large loading forces can the motor head release ATP at a fast rate, which significantly reduces the velocity of kinesin. It underpins the weak susceptibility that the velocity will not change at small to midrange forces. The molecular origin of this velocity reduction is that the neck linker of a kinesin only detaches from the motor head when pulled by a large force. This prompts the ATP binding site to adopt an open state, favoring ATP release and reducing the velocity. Furthermore, we show that two load-bearing kinesins are incapable of equally sharing the load unless they are very close to each other. As a consequence of the weak susceptibility, the trailing kinesin faces the challenge of catching up to the leading one, which accounts for experimentally observed weak cooperativity of kinesins motors.

Allosteric conformational change cascade in cytoplasmic dynein revealed by structure-based molecular simulations

Cytoplasmic dynein is a giant ATP-driven molecular motor that proceeds to the minus end of the microtubule (MT). Dynein hydrolyzes ATP in a ring-like structure, containing 6 AAA+ (ATPases associated with diverse cellular activities) modules, which is ~15 nm away from the MT binding domain (MTBD). This architecture implies that long-distance allosteric couplings exist between the AAA+ ring and the MTBD in order for dynein to move on the MT, although little is known about the mechanisms involved. Here, we have performed comprehensive molecular simulations of the dynein motor domain based on pre- and post- power-stroke structural information and in doing so we address the allosteric conformational changes that occur during the power-stroke and recovery-stroke processes. In the power-stroke process, the N-terminal linker movement was the prerequisite to the nucleotide-dependent AAA1 transition, from which a transition cascade propagated, on average, in a circular manner on the AAA+ ring until it reached the AAA6/C-terminal module. The recovery-stroke process was initiated by the transition of the AAA6/C-terminal, from which the transition cascade split into the two directions of the AAA+ ring, occurring both clockwise and anti-clockwise. In both processes, the MTBD conformational change was regulated by the AAA4 module and the AAA5/Strut module.

The linear molecular motor dynein is an intriguing allosteric model protein. ATP hydrolysis, catalyzed by modules in the AAA+ ring, regulates the binding to the rail molecule, microtubule, which is ~15 nm away from the AAA+ ring. The molecular mechanisms underpinning this long-distance communication are unclear. Based on recently solved pre- and post- power-stroke crystal structure information, we performed, for the first time to our knowledge, molecular simulations of complete conformational changes between the two structures. The simulation revealed that module-by-module allosteric conformational changes occur. Interestingly, the transition cascade from the pre- to the post-power-stroke states propagated in a circular manner around the AAA+ ring, while that of the recovery transitions propagated in a bi-directional manner around the ring.

Kinematics of the lever arm swing in myosin VI

Myosin VI (MVI) is the only known member of the myosin superfamily that, upon dimerization, walks processively toward the pointed end of the actin filament. The leading head of the dimer directs the trailing head forward with a power stroke, a conformational change of the motor domain exaggerated by the lever arm. Using a unique coarse-grained model for the power stroke of a single MVI, we provide the molecular basis for its motility. We show that the power stroke occurs in two major steps. First, the motor domain attains the poststroke conformation without directing the lever arm forward; and second, the lever arm reaches the poststroke orientation by undergoing a rotational diffusion. From the analysis of the trajectories, we discover that the potential that directs the rotating lever arm toward the poststroke conformation is almost flat, implying that the lever arm rotation is mostly uncoupled from the motor domain. Because a backward load comparable to the largest interhead tension in a MVI dimer prevents the rotation of the lever arm, our model suggests that the leading-head lever arm of a MVI dimer is uncoupled, in accord with the inference drawn from polarized total internal reflection fluorescence (polTIRF) experiments. Without any adjustable parameter, our simulations lead to quantitative agreement with polTIRF experiments, which validates the structural insights. Finally, in addition to making testable predictions, we also discuss the implications of our model in explaining the broad step-size distribution of the MVI stepping pattern.

Quantifying the Heat Dissipation from a Molecular Motor's Transport Properties in Nonequilibrium Steady States

Theoretical analysis, which maps single-molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1, whose dynamics is confined on one-dimensional tracks, is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers a thermodynamic basis to understand the heat-enhanced self-diffusion of exothermic enzymes.

Protein dynamics and function from solution state NMR spectroscopy

It is well-established that dynamics are central to protein function; their importance is implicitly acknowledged in the principles of the Monod, Wyman and Changeux model of binding cooperativity, which was originally proposed in 1965. Nowadays the concept of protein dynamics is formulated in terms of the energy landscape theory, which can be used to understand protein folding and conformational changes in proteins. Because protein dynamics are so important, a key to understanding protein function at the molecular level is to design experiments that allow their quantitative analysis. Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited for this purpose because major advances in theory, hardware, and experimental methods have made it possible to characterize protein dynamics at an unprecedented level of detail. Unique features of NMR include the ability to quantify dynamics (i) under equilibrium conditions without external perturbations, (ii) using many probes simultaneously, and (iii) over large time intervals. Here we review NMR techniques for quantifying protein dynamics on fast (ps-ns), slow (μs-ms), and very slow (s-min) time scales. These techniques are discussed with reference to some major discoveries in protein science that have been made possible by NMR spectroscopy.

Kinesin-2 KIF3AC and KIF3AB Can Drive Long-Range Transport along Microtubules

Mammalian KIF3AC is classified as a heterotrimeric kinesin-2 that is best known for organelle transport in neurons, yet in vitro studies to characterize its single molecule behavior are lacking. The results presented show that a KIF3AC motor that includes the native helix α7 sequence for coiled-coil formation is highly processive with run lengths of ∼1.23 μm and matching those exhibited by conventional kinesin-1. This result was unexpected because KIF3AC exhibits the canonical kinesin-2 neck-linker sequence that has been reported to be responsible for shorter run lengths observed for another heterotrimeric kinesin-2, KIF3AB. However, KIF3AB with its native neck linker and helix α7 is also highly processive with run lengths of ∼1.62 μm and exceeding those of KIF3AC and kinesin-1. Loop L11, a component of the microtubule-motor interface and implicated in activating ADP release upon microtubule collision, is significantly extended in KIF3C as compared with other kinesins. A KIF3AC encoding a truncation in KIF3C loop L11 (KIF3ACΔL11) exhibited longer run lengths at ∼1.55 μm than wild-type KIF3AC and were more similar to KIF3AB run lengths, suggesting that L11 also contributes to tuning motor processivity. The steady-state ATPase results show that shortening L11 does not alter kcat, consistent with the observation that single molecule velocities are not affected by this truncation. However, shortening loop L11 of KIF3C significantly increases the microtubule affinity of KIF3ACΔL11, revealing another structural and mechanistic property that can modulate processivity. The results presented provide new, to our knowledge, insights to understand structure-function relationships governing processivity and a better understanding of the potential of KIF3AC for long-distance transport in neurons.

Strain Mediated Adaptation Is Key for Myosin Mechanochemistry: Discovering General Rules for Motor Activity

A structure-based model of myosin motor is built in the same spirit of our early work for kinesin-1 and Ncd towards physical understanding of its mechanochemical cycle. We find a structural adaptation of the motor head domain in post-powerstroke state that signals faster ADP release from it compared to the same from the motor head in the pre-powerstroke state. For dimeric myosin, an additional forward strain on the trailing head, originating from the postponed powerstroke state of the leading head in the waiting state of myosin, further increases the rate of ADP release. This coordination between the two heads is the essence of the processivity of the cycle. Our model provides a structural description of the powerstroke step of the cycle as an allosteric transition of the converter domain in response to the P_i release. Additionally, the variation in structural elements peripheral to catalytic motor domain is the deciding factor behind diverse directionalities of myosin motors (myosin V & VI). Finally, we observe that there are general rules for functional molecular motors across the different families. Allosteric structural adaptation of the catalytic motor head in different nucleotide states is crucial for mechanochemistry. Strain-mediated coordination between motor heads is essential for processivity and the variation of peripheral structural elements is essential for their diverse functionalities.

Molecular motors are perhaps the most important proteins present in the cell. The importance specifically lies with the fact that these proteins use the chemical energy source (such as ATP) of the cell to generate mechanical work and perform a wide range of functionalities. In this article, we generalize the idea of using structure-based models to explore the mechanochemistry of myosin molecular motors in structural terms. We find that a structural adaptation of the motor head domain in post-powerstroke state signals faster ADP release from the trailing head to maintain its processivity while directionality arises from a careful design of peripheral structural elements. These results along with our earlier results on other motors provide a general rule for motor activity.

Family-specific Kinesin Structures Reveal Neck-linker Length Based on Initiation of the Coiled-coil

Kinesin-1, -2, -5, and -7 generate processive hand-over-hand 8-nm steps to transport intracellular cargoes toward the microtubule plus end. This processive motility requires gating mechanisms to coordinate the mechanochemical cycles of the two motor heads to sustain the processive run. A key structural element believed to regulate the degree of processivity is the neck-linker, a short peptide of 12-18 residues, which connects the motor domain to its coiled-coil stalk. Although a shorter neck-linker has been correlated with longer run lengths, the structural data to support this hypothesis have been lacking. To test this hypothesis, seven kinesin structures were determined by x-ray crystallography. Each included the neck-linker motif, followed by helix α7 that constitutes the start of the coiled-coil stalk. In the majority of the structures, the neck-linker length differed from predictions because helix α7, which initiates the coiled-coil, started earlier in the sequence than predicted. A further examination of structures in the Protein Data Bank reveals that there is a great disparity between the predicted and observed starting residues. This suggests that an accurate prediction of the start of a coiled-coil is currently difficult to achieve. These results are significant because they now exclude simple comparisons between members of the kinesin superfamily and add a further layer of complexity when interpreting the results of mutagenesis or protein fusion. They also re-emphasize the need to consider factors beyond the kinesin neck-linker motif when attempting to understand how inter-head communication is tuned to achieve the degree of processivity required for cellular function.

Structured illumination temporal compressive microscopy

We present a compressive video microscope based on structured illumination with incoherent light source. The source-side illumination coding scheme allows the emission photons being collected by the full aperture of the microscope objective, and thus is suitable for the fluorescence readout mode. A 2-step iterative reconstruction algorithm, termed BWISE, has been developed to address the mismatch between the illumination pattern size and the detector pixel size. Image sequences with a temporal compression ratio of 4:1 were demonstrated.

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.

Exploring the mechanochemical cycle of dynein motor proteins: structural evidence of crucial intermediates

Exploration of the biologically relevant pathways of dynein's mechanochemical cycle using structure based models.

Fast or Slow, Either Head Can Start the Processive Run of Kinesin-2 KIF3AC

Mammalian KIF3AC contains two distinct motor polypeptides and is best known for its role in organelle transport in neurons. Our recent studies showed that KIF3AC is as processive as conventional kinesin-1, suggesting that their ATPase mechanochemistry may be similar. However, the presence of two different motor polypeptides in KIF3AC implies that there must be a cellular advantage for the KIF3AC heterodimer. The hypothesis tested was whether there is an intrinsic bias within KIF3AC such that either KIF3A or KIF3C initiates the processive run. To pursue these experiments, a mechanistic approach was used to compare the pre-steady-state kinetics of KIF3AC to the kinetics of homodimeric KIF3AA and KIF3CC. The results indicate that microtubule collision at 11.4 μM(-1) s(-1) coupled with ADP release at 78 s(-1) are fast steps for homodimeric KIF3AA. In contrast, KIF3CC exhibits much slower microtubule association at 2.1 μM(-1) s(-1) and ADP release at 8 s(-1). For KIF3AC, microtubule association at 6.6 μM(-1) s(-1) and ADP release at 51 s(-1) are intermediate between the constants for KIF3AA and KIF3CC. These results indicate that either KIF3A or KIF3C can initiate the processive run. Surprisingly, the kinetics of the initial event of microtubule collision followed by ADP release for KIF3AC is not equivalent to 1:1 mixtures of KIF3AA plus KIF3CC homodimers at the same motor concentration. These results reveal that the intermolecular communication within the KIF3AC heterodimer modulates entry into the processive run regardless of whether the run is initiated by the KIF3A or KIF3C motor domain.

Nucleotides regulate the mechanical hierarchy between subdomains of the nucleotide binding domain of the Hsp70 chaperone DnaK

The regulation of protein function through ligand-induced conformational changes is crucial for many signal transduction processes. The binding of a ligand alters the delicate energy balance within the protein structure, eventually leading to such conformational changes. In this study, we elucidate the energetic and mechanical changes within the subdomains of the nucleotide binding domain (NBD) of the heat shock protein of 70 kDa (Hsp70) chaperone DnaK upon nucleotide binding. In an integrated approach using single molecule optical tweezer experiments, loop insertions, and steered coarse-grained molecular simulations, we find that the C-terminal helix of the NBD is the major determinant of mechanical stability, acting as a glue between the two lobes. After helix unraveling, the relative stability of the two separated lobes is regulated by ATP/ADP binding. We find that the nucleotide stays strongly bound to lobe II, thus reversing the mechanical hierarchy between the two lobes. Our results offer general insights into the nucleotide-induced signal transduction within members of the actin/sugar kinase superfamily.

Allosteric control of kinesin's motor domain by tubulin: a molecular dynamics study

Molecular motors such as kinesin are essential for many biological processes. These motors have two motor domains, which bind to tubulin filaments, hydrolyze ATP, and transduce the released chemical energy into directed movements. The general principles of this chemomechanical coupling are now well-established but the underlying molecular mechanisms remain elusive because small conformational changes within large proteins are difficult to detect experimentally. Here, we use atomistic molecular dynamics simulations to monitor such changes within a single motor domain of KIF1A, which belongs to the kinesin-3 motor family. The nucleotide binding pocket of this domain can be empty or occupied by ATP or ADP. For these three nucleotide states, we determine the mobility of the backbone of the protein, both in solution and attached to tubulin. Only one subdomain of the motor domain is found to exhibit a strongly increased mobility upon binding to tubulin: the neck linker that presumably acts as a mechanical transmitter to the other motor domain in dimeric kinesin-3 motors. Furthermore, upon binding to tubulin, the neck linker mobility becomes sensitive to the bound nucleotide and is highly increased after phosphate release, which implies undocking of this linker from the core of the motor domain. These simulation results are consistent with experimental data from EPR spectroscopy, FRET, and cryo-electron microscopy. A detailed analysis of our simulation data also reveals that the undocking of the neck linker in the ADP-kinesin-tubulin state arises from allosteric interactions between the nucleotide and tubulin and that the β-sheet core undergoes a twist both during phosphate release and ATP binding. The computational approach used here can be applied to other motor domains and mechanoenzymes in order to identify allosteric interactions between the subdomains of these proteins.

Nucleotide-dependent structural fluctuations and regulation of microtubule-binding affinity of KIF1A

Molecular motors such as kinesin regulate affinity to a rail protein during the ATP hydrolysis cycle. The regulation mechanism, however, is yet to be determined. To understand this mechanism, we investigated the structural fluctuations of the motor head of the single-headed kinesin called KIF1A in different nucleotide states using molecular dynamics simulations of a Gō-like model. We found that the helix α4 at the microtubule (MT) binding site intermittently exhibits a large structural fluctuation when MT is absent. Frequency of this fluctuation changes systematically according to the nucleotide states and correlates strongly with the experimentally observed binding affinity to MT. We also showed that thermal fluctuation enhances the correlation and the interaction with the nucleotide suppresses the fluctuation of the helix α4. These results suggest that KIF1A regulates affinity to MT by changing the flexibility of the helix α4 during the ATP hydrolysis process: the binding site becomes more flexible in the strong binding state than in the weak binding state.

Decrypting the structural, dynamic, and energetic basis of a monomeric kinesin interacting with a tubulin dimer in three ATPase states by all-atom molecular dynamics simulation

We have employed molecular dynamics (MD) simulation to investigate, with atomic details, the structural dynamics and energetics of three major ATPase states (ADP, APO, and ATP state) of a human kinesin-1 monomer in complex with a tubulin dimer. Starting from a recently solved crystal structure of ATP-like kinesin-tubulin complex by the Knossow lab, we have used flexible fitting of cryo-electron-microscopy maps to construct new structural models of the kinesin-tubulin complex in APO and ATP state, and then conducted extensive MD simulations (total 400 ns for each state), followed by flexibility analysis, principal component analysis, hydrogen bond analysis, and binding free energy analysis. Our modeling and simulation have revealed key nucleotide-dependent changes in the structure and flexibility of the nucleotide-binding pocket (featuring a highly flexible and open switch I in APO state) and the tubulin-binding site, and allosterically coupled motions driving the APO to ATP transition. In addition, our binding free energy analysis has identified a set of key residues involved in kinesin-tubulin binding. On the basis of our simulation, we have attempted to address several outstanding issues in kinesin study, including the possible roles of β-sheet twist and neck linker docking in regulating nucleotide release and binding, the structural mechanism of ADP release, and possible extension and shortening of α4 helix during the ATPase cycle. This study has provided a comprehensive structural and dynamic picture of kinesin's major ATPase states, and offered promising targets for future mutational and functional studies to investigate the molecular mechanism of kinesin motors.

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies.

CK2 activates kinesin via induction of a conformational change

Kinesin is the canonical plus-end microtubule motor and has been the focus of intense study since its discovery in 1985. We previously demonstrated a time-dependent inactivation of kinesin in vitro that was fully reversible by the addition of purified casein kinase 2 (CK2) and showed that this inactivation/reactivation pathway was relevant in cells. Here we show that kinesin inactivation results from a conformational change that causes the neck linker to be positioned closer to the motor domain. Furthermore, we show that treatment of kinesin with CK2 prevents and reverses this repositioning. Finally, we demonstrate that CK2 treatment facilitates ADP dissociation from the motor, resulting in a nucleotide-free state that promotes microtubule binding. Thus, we propose that kinesin inactivation results from neck-linker repositioning and that CK2-mediated reactivation results from CK2's dual ability to reverse this repositioning and to promote ADP release.

Simulating movement of tRNA through the ribosome during hybrid-state formation

Biomolecular simulations provide a means for exploring the relationship between flexibility, energetics, structure, and function. With the availability of atomic models from X-ray crystallography and cryoelectron microscopy (cryo-EM), and rapid increases in computing capacity, it is now possible to apply molecular dynamics (MD) simulations to large biomolecular machines, and systematically partition the factors that contribute to function. A large biomolecular complex for which atomic models are available is the ribosome. In the cell, the ribosome reads messenger RNA (mRNA) in order to synthesize proteins. During this essential process, the ribosome undergoes a wide range of conformational rearrangements. One of the most poorly understood transitions is translocation: the process by which transfer RNA (tRNA) molecules move between binding sites inside of the ribosome. The first step of translocation is the adoption of a "hybrid" configuration by the tRNAs, which is accompanied by large-scale rotations in the ribosomal subunits. To illuminate the relationship between these rearrangements, we apply MD simulations using a multi-basin structure-based (SMOG) model, together with targeted molecular dynamics protocols. From 120 simulated transitions, we demonstrate the viability of a particular route during P/E hybrid-state formation, where there is asynchronous movement along rotation and tRNA coordinates. These simulations not only suggest an ordering of events, but they highlight atomic interactions that may influence the kinetics of hybrid-state formation. From these simulations, we also identify steric features (H74 and surrounding residues) encountered during the hybrid transition, and observe that flexibility of the single-stranded 3'-CCA tail is essential for it to reach the endpoint. Together, these simulations provide a set of structural and energetic signatures that suggest strategies for modulating the physical-chemical properties of protein synthesis by the ribosome.

Coupling of lever arm swing and biased Brownian motion in actomyosin

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (P_i) and ADP weakly binds to actin and that after releasing P_i and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

Myosin II is a molecular motor that is fueled by ATP hydrolysis and generates mechanical force by interacting with actin filament. Comparison among various myosin structures obtained by X-ray and electron microscope analyses has led to the hypothesis that structural change of myosin in ATP hydrolysis cycle is the driving mechanism of force generation. However, single-molecule experiments have suggested an alternative mechanism in which myosin moves stochastically in a biased direction along actin filament. Computer simulation serves as a platform for assessing these hypotheses by revealing the prominent features of the dynamically changing landscape of actin-myosin interaction. The calculated results show that myosin binds to actin at different locations of actin filament in the weak- and strong-binding states and that the free energy has a global gradient from the weak-binding site to the strong-binding site. Myosin relaxing into the strong-binding state therefore necessarily shows the biased Brownian motion toward the strong-binding site. Lever-arm swing is induced during this relaxation process; therefore, lever-arm swing and the biased Brownian motion are coupled to contribute to the net displacement of myosin. This coupling should affect the dynamical behaviors of muscle and cardiac systems.

Reduced model captures Mg(2+)-RNA interaction free energy of riboswitches

The stability of RNA tertiary structures depends heavily on Mg(2+). The Mg(2+)-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ2+, the number of excess Mg(2+) associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg(2+) ions interact closely and strongly with the RNA, unlike monovalent ions such as K(+), suggesting that an explicit treatment of Mg(2+) is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg(2+)-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg(2+) through the explicit representation of Mg(2+) ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K(+) and models its competition with condensed Mg(2+). The model contains one fitted parameter, the number of condensed K(+) ions in the absence of Mg(2+). Values of Γ2+ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ2+ to the Mg(2+)-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg(2+) and RNA dynamics.

From structure to function: the convergence of structure based models and co-evolutionary information

Understanding protein folding and function is one of the most important problems in biological research. Energy landscape theory and the folding funnel concept have provided a framework to investigate the mechanisms associated to these processes. Since protein energy landscapes are in most cases minimally frustrated, structure based models (SMBs) have successfully determined the geometrical features associated with folding and functional transitions. However, structural information is limited, particularly with respect to different functional configurations. This is a major limitation for SBMs. Alternatively, statistical methods to study amino acid co-evolution provide information on residue-residue interactions useful for the study of structure and function. Here, we show how the combination of these two methods gives rise to a novel way to investigate the mechanisms associated with folding and function. We use this methodology to explore the mechanistic aspects of protein translocation in the integral membrane protease FtsH. Dual basin-SBM simulations using the open and closed state of this hexameric motor reveals a functionally important paddling motion in the catalytic cycle. We also find that Direct Coupling Analysis (DCA) predicts physical contacts between AAA and peptidase domains of the motor, which are crucial for the open to close transition. Our combined method, which uses structural information from the open state experimental structure and co-evolutionary couplings, suggests that this methodology can be used to explore the functional landscape of complex biological macromolecules previously inaccessible to methods dependent on experimental structural information. This efficient way to sample the conformational space of large systems creates a theoretical/computational framework capable of better characterizing the functional landscape in large biomolecular assemblies.