Structure-based molecular simulations reveal the enhancement of biased Brownian motions in single-headed kinesin

Enhanced Coarse-Grained Molecular Dynamics Simulation with a Smoothed Hybrid Potential Using a Neural Network Model

In all-atom (AA) molecular dynamics (MD) simulations, the rugged energy profile of the force field makes it challenging to reproduce spontaneous structural changes in biomolecules within a reasonable calculation time. Existing coarse-grained (CG) models, in which the energy profile is set to a global minimum around the initial structure, are unsuitable to explore the structural dynamics between metastable states far away from the initial structure without any bias. In this study, we developed a new hybrid potential composed of an artificial intelligence (AI) potential and minimal CG potential related to the statistical bond length and excluded volume interactions to accelerate the transition dynamics while maintaining the protein character. The AI potential is trained by energy matching using a diverse structural ensemble sampled via multicanonical (Mc) MD simulation and the corresponding AA force field energy, profile of which is smoothed by energy minimization. By applying the new methodology to chignolin and TrpCage, we showed that the AI potential can predict the AA energy with significantly high accuracy, as indicated by a correlation coefficient (R-value) between the true and predicted energies exceeding 0.89. In addition, we successfully demonstrated that CGMD simulation based on the smoothed hybrid potential can significantly enhance the transition dynamics between various metastable states while preserving protein properties compared to those obtained with conventional CGMD and AAMD.

Semi-Implicit Time Integration with Hessian Eigenvalue Corrections for a Larger Time Step in Molecular Dynamics Simulations

In molecular dynamics simulations, the limited time step size has been a barrier to simulating long-time behaviors. Implicit time integration methods allow markedly larger time steps than the standard explicit time method, although they have major drawbacks such as overheads solving linear systems and instability of Newton iterations. To overcome these issues, we propose a semi-implicit time integration scheme, the semi-implicit Hessian correction (SimHec) scheme, for overdamped Langevin dynamics. The method focuses on the Hessian matrices of bonded and nonbonded interactions, where components with large negative Hessian eigenvalues are cut off in the linear approximation of momentum equations to avoid instability. The narrow band Hessian matrix enables an efficient parallelized linear solution with an overlapping approximation. We tested SimHec for the interdomain fluctuations in adenylate kinase and the powerstroke transition of myosin II using a coarse-grained protein model. SimHec reproduced the same dynamics as the explicit method, although the transition dynamics tended to be accelerated and fluctuations in bonded potentials were slightly reduced. These deviations were corrected using a hybrid method, SimHec-H, which adds explicit time steps after the semi-implicit time step. The proposed scheme allowed us to use time steps 50-200 times larger than those in explicit time integration, which resulted in a speedup factor of 7-30 taking the overhead into account.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Biased Brownian Motion of KIF1A and the Role of Tubulin's C-Terminal Tail Studied by Molecular Dynamics Simulation

KIF1A is a kinesin family protein that moves over a long distance along the microtubule (MT) to transport synaptic vesicle precursors in neurons. A single KIF1A molecule can move toward the plus-end of MT in the monomeric form, exhibiting the characteristics of biased Brownian motion. However, how the bias is generated in the Brownian motion of KIF1A has not yet been firmly established. To elucidate this, we conducted a set of molecular dynamics simulations and observed the binding of KIF1A to MT. We found that KIF1A exhibits biased Brownian motion along MT as it binds to MT. Furthermore, we show that the bias toward the plus-end is generated by the ratchet-like energy landscape for the KIF1A-MT interaction, in which the electrostatic interaction and the negatively-charged C-terminal tail (CTT) of tubulin play an essential role. The relevance to the post-translational modifications of CTT is also discussed.

Mechanistic basis of propofol-induced disruption of kinesin processivity

Propofol is a widely used general anesthetic to induce and maintain anesthesia, and its effects are thought to occur through impact on the ligand-gated channels including the GABA_A receptor. Propofol also interacts with a large number of proteins including molecular motors and inhibits kinesin processivity, resulting in significant decrease in the run length for conventional kinesin-1 and kinesin-2. However, the molecular mechanism by which propofol achieves this outcome is not known. The structural transition in the kinesin neck-linker region is crucial for its processivity. In this study, we analyzed the effect of propofol and its fluorine derivative (fropofol) on the transition in the neck-linker region of kinesin. Propofol binds at two crucial surfaces in the leading head: one at the microtubule-binding interface and the other in the neck-linker region. We observed in both the cases the order-disorder transition of the neck-linker was disrupted and kinesin lost its signal for forward movement. In contrast, there was not an effect on the neck-linker transition with propofol binding at the trailing head. Free-energy calculations show that propofol at the microtubule-binding surface significantly reduces the microtubule-binding affinity of the kinesin head. While propofol makes pi-pi stacking and H-bond interactions with the propofol binding cavity, fropofol is unable to make a suitable interaction at this binding surface. Therefore, the binding affinity of fropofol is much lower compared to propofol. Hence, this study provides a mechanism by which propofol disrupts kinesin processivity and identifies transitions in the ATPase stepping cycle likely affected.

Gō model revisited

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

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.

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.

Anchor Effect of Interactions Between Kinesin's Nucleotide-Binding Pocket and Microtubule

Microtubule not only provides the track for kinesin but also modulates kinesin's mechanochemical cycle. Microtubule binding greatly increases the rates of two chemical steps occurring inside the nucleotide-binding pocket (NBP) of kinesin, i.e., ATP hydrolysis and ADP release. Kinesin neck linker docking (the key force-generation step) is initiated by the motor head rotation induced by ATP binding which needs an anchor provided by microtubule. These functions of microtubule can only be accomplished through interactions with kinesin. Based on the newly obtained crystal structures of kinesin-microtubule complexes, we investigate the interactions between kinesin's NBP and microtubule using molecular dynamics simulations. We find that the N-3 motif of NBP has direct interactions with a group of negatively charged residues on α-tubulin through Ser235 and Lys237. These specific long-range interactions induce binding of NBP to microtubule at the right position and assist the formation of the indirect interaction between NBP and microtubule. These interactions between N-3 and microtubule have an important anchor effect for kinesin's motor domain during its rotation with Ser235 as the rotation center, and also play a crucial role in stabilizing the ATP-hydrolysis environment.

Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations

Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to emulate one ATP cycle of a molecular motor, kinesin. Second, nonspecific protein-DNA binding was studied by a combination of elaborate protein and DNA models. Third, a transcription factor, p53, that contains highly fluctuating regions was simulated on two perpendicularly arranged DNA segments, addressing intersegmental transfer of p53. Fourth, we simulated structural dynamics of dinucleosomes connected by a linker DNA finding distinct types of internucleosome docking and salt-concentration-dependent compaction. Finally, we discuss many of limitations in the current approaches and future directions. Especially, more accurate electrostatic treatment and a phospholipid model that matches our CG resolutions are of immediate importance.

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.

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.

Autoinhibitory mechanisms of ERG studied by molecular dynamics simulations

ERG, an ETS-family transcription factor, acts as a regulator of differentiation of early hematopoietic cells. It contains an autoinhibitory domain, which negatively regulates DNA-binding. The mechanism of autoinhibitory is still illusive. To understand the mechanism, we study the dynamical properties of ERG protein by molecular dynamics simulations. These simulations suggest that DNA binding autoinhibition associates with the internal dynamics of ERG. Specifically, we find that (1), The N-C terminal correlation in the inhibited ERG is larger than that in uninhibited ERG that contributes to the autoinhibition of DNA-binding. (2), DNA-binding changes the property of the N-C terminal correlation from being anti-correlated to correlated, that is, changing the relative direction of the correlated motions and (3), For the Ets-domain specifically, the inhibited and uninhibited forms exhibit essentially the same dynamics, but the binding of the DNA decreases the fluctuation of the Ets-domain. We also find from PCA analysis that the three systems, even with quite different dynamics, do have highly similar free energy surfaces, indicating that they share similar conformations.

Energetics of the single-headed kinesin KIF1A

KIF1A is a single-headed molecular motor that moves processively and unidirectionally along a microtubule by using the chemical energy released by hydrolyzing adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (P(i)). Although the movement of KIF1A seems to have successfully been explained by a simple Brownian motor model of the flashing ratchet type, this model is not suited to discuss the energetics of KIF1A. We introduce an elaborated model of the ratchet type to investigate how the chemical free energy is converted into mechanical work by taking account of the binding and release of reactant (ATP) and product (ADP and P(i)) molecules to and from the motor. The efficiency of energy transduction, the power output, and other quantities are calculated from the analytically obtained steady-state solution of the Fokker-Planck equations. It turns out that the concentrations of the reactant and product molecules that optimize both the efficiency and the power are close to those in the cell.