Mechanism of substrate translocation by a ring-shaped ATPase motor at millisecond resolution

A weak coupling mechanism for the early steps of the recovery stroke of myosin VI: A free energy simulation and string method analysis

Myosin motors use the energy of ATP to produce force and directed movement on actin by a swing of the lever-arm. ATP is hydrolysed during the off-actin re-priming transition termed recovery stroke. To provide an understanding of chemo-mechanical transduction by myosin, it is critical to determine how the reverse swing of the lever-arm and ATP hydrolysis are coupled. Previous studies concluded that the recovery stroke of myosin II is initiated by closure of the Switch II loop in the nucleotide-binding site. Recently, we proposed that the recovery stroke of myosin VI starts with the spontaneous re-priming of the converter domain to a putative pre-transition state (PTS) intermediate that precedes Switch II closing and ATPase activation. Here, we investigate the transition from the pre-recovery, post-rigor (PR) state to PTS in myosin VI using geometric free energy simulations and the string method. First, our calculations rediscover the PTS state agnostically and show that it is accessible from PR via a low free energy transition path. Second, separate path calculations using the string method illuminate the mechanism of the PR to PTS transition with atomic resolution. In this mechanism, the initiating event is a large movement of the converter/lever-arm region that triggers rearrangements in the Relay-SH1 region and the formation of the kink in the Relay helix with no coupling to the active site. Analysis of the free-energy barriers along the path suggests that the converter-initiated mechanism is much faster than the one initiated by Switch II closure, which supports the biological relevance of PTS as a major on-pathway intermediate of the recovery stroke in myosin VI. Our analysis suggests that lever-arm re-priming and ATP hydrolysis are only weakly coupled, so that the myosin recovery stroke is initiated by thermal fluctuations and stabilised by nucleotide consumption via a ratchet-like mechanism.

Characterizing ATP processing by the AAA+ protein p97 at the atomic level

The human enzyme p97 regulates various cellular pathways by unfolding hundreds of protein substrates in an ATP-dependent manner, making it an essential component of protein homeostasis and an impactful pharmacological target. The hexameric complex undergoes substantial conformational changes throughout its catalytic cycle. Here we elucidate the molecular motions that occur at the active site in the temporal window immediately before and after ATP hydrolysis by merging cryo-EM, NMR spectroscopy and molecular dynamics simulations. p97 populates a metastable reaction intermediate, the ADP·Pi state, which is poised between hydrolysis and product release. Detailed snapshots reveal that the active site is finely tuned to trap and eventually discharge the cleaved phosphate. Signalling pathways originating at the active site coordinate the action of the hexamer subunits and couple hydrolysis with allosteric conformational changes. Our multidisciplinary approach enables a glimpse into the sophisticated spatial and temporal orchestration of ATP handling by a prototype AAA+ protein.

Continuous millisecond conformational cycle of a DEAH box helicase reveals control of domain motions by atomic-scale transitions

Helicases are motor enzymes found in every living organism and viruses, where they maintain the stability of the genome and control against false recombination. The DEAH-box helicase Prp43 plays a crucial role in pre-mRNA splicing in unicellular organisms by translocating single-stranded RNA. The molecular mechanisms and conformational transitions of helicases are not understood at the atomic level. We present a complete conformational cycle of RNA translocation by Prp43 in atomic detail based on molecular dynamics simulations. To enable the sampling of such complex transition on the millisecond timescale, we combined two enhanced sampling techniques, namely simulated tempering and adaptive sampling guided by crystallographic data. During RNA translocation, the center-of-mass motions of the RecA-like domains followed the established inchworm model, whereas the domains crawled along the RNA in a caterpillar-like movement, suggesting an inchworm/caterpillar model. However, this crawling required a complex sequence of atomic-scale transitions involving the release of an arginine finger from the ATP pocket, stepping of the hook-loop and hook-turn motifs along the RNA backbone, and several others. These findings highlight that large-scale domain dynamics may be controlled by complex sequences of atomic-scale transitions.

Machines on Genes through the Computational Microscope

Macromolecular machines acting on genes are at the core of life's fundamental processes, including DNA replication and repair, gene transcription and regulation, chromatin packaging, RNA splicing, and genome editing. Here, we report the increasing role of computational biophysics in characterizing the mechanisms of "machines on genes", focusing on innovative applications of computational methods and their integration with structural and biophysical experiments. We showcase how state-of-the-art computational methods, including classical and ab initio molecular dynamics to enhanced sampling techniques, and coarse-grained approaches are used for understanding and exploring gene machines for real-world applications. As this review unfolds, advanced computational methods describe the biophysical function that is unseen through experimental techniques, accomplishing the power of the "computational microscope", an expression coined by Klaus Schulten to highlight the extraordinary capability of computer simulations. Pushing the frontiers of computational biophysics toward a pragmatic representation of large multimegadalton biomolecular complexes is instrumental in bridging the gap between experimentally obtained macroscopic observables and the molecular principles playing at the microscopic level. This understanding will help harness molecular machines for medical, pharmaceutical, and biotechnological purposes.

Integrating comparative modeling and accelerated simulations reveals conformational and energetic basis of actomyosin force generation

Muscle contraction is performed by arrays of contractile proteins in the sarcomere. Serious heart diseases, such as cardiomyopathy, can often be results of mutations in myosin and actin. Direct characterization of how small changes in the myosin-actin complex impact its force production remains challenging. Molecular dynamics (MD) simulations, although capable of studying protein structure-function relationships, are limited owing to the slow timescale of the myosin cycle as well as a lack of various intermediate structures for the actomyosin complex. Here, employing comparative modeling and enhanced sampling MD simulations, we show how the human cardiac myosin generates force during the mechanochemical cycle. Initial conformational ensembles for different myosin-actin states are learned from multiple structural templates with Rosetta. This enables us to efficiently sample the energy landscape of the system using Gaussian accelerated MD. Key myosin loop residues, whose substitutions are related to cardiomyopathy, are identified to form stable or metastable interactions with the actin surface. We find that the actin-binding cleft closure is allosterically coupled to the myosin motor core transitions and ATP-hydrolysis product release from the active site. Furthermore, a gate between switch I and switch II is suggested to control phosphate release at the prepowerstroke state. Our approach demonstrates the ability to link sequence and structural information to motor functions.

Roles of local nonequilibrium free energy in the description of biomolecules

When a system is in equilibrium, external perturbations yield a time series of nonequilibrium distributions, and recent experimental techniques give access to the nonequilibrium data that may contain critical information. Jinwoo and Tanaka [Sci. Rep. 5, 7832 (2015)2045-232210.1038/srep07832] have provided mathematical proof that such a process's nonequilibrium free energy profile over a system's substates has Jarzynski's work as content, which spontaneously dissipates while molecules perform their tasks. Here we numerically verify this fact and give a practical example where we analyze a computer simulation of RNA translocation by a ring-shaped ATPase motor. By interpreting the cyclic process of substrate translocation as a series of quenching, relaxation, and second quenching, the theory gives how the ATPase motor allocates the hydrolysis energy between individual substates until the end of the process. It turns out that the efficiency of RNA translocation is 48%-60% for most molecules, but 12% of molecules achieve 80%-100% efficiency, which is consistent with the literature. This theory would be a valuable tool for extracting quantitative information about molecular nonequilibrium behavior from experimental observations.

Computationally exploring the mechanism of bacteriophage T7 gp4 helicase translocating along ssDNA

Bacteriophage T7 gp4 helicase has served as a model system for understanding mechanisms of hexameric replicative helicase translocation. The mechanistic basis of how nucleoside 5'-triphosphate hydrolysis and translocation of gp4 helicase are coupled is not fully resolved. Here, we used a thermodynamically benchmarked coarse-grained protein force field, Associative memory, Water mediated, Structure and Energy Model (AWSEM), with the single-stranded DNA (ssDNA) force field 3SPN.2C to investigate gp4 translocation. We found that the adenosine 5'-triphosphate (ATP) at the subunit interface stabilizes the subunit-subunit interaction and inhibits subunit translocation. Hydrolysis of ATP to adenosine 5'-diphosphate enables the translocation of one subunit, and new ATP binding at the new subunit interface finalizes the subunit translocation. The LoopD2 and the N-terminal primase domain provide transient protein-protein and protein-DNA interactions that facilitate the large-scale subunit movement. The simulations of gp4 helicase both validate our coarse-grained protein-ssDNA force field and elucidate the molecular basis of replicative helicase translocation.

Revealing a Hidden Intermediate of Rotatory Catalysis with X-ray Crystallography and Molecular Simulations

The mechanism of rotatory catalysis in ATP-hydrolyzing molecular motors remains an unresolved puzzle in biological energy transfer. Notwithstanding the wealth of available biochemical and structural information inferred from years of experiments, knowledge on how the coupling between the chemical and mechanical steps within motors enforces directional rotatory movements remains fragmentary. Even more contentious is to pinpoint the rate-limiting step of a multistep rotation process. Here, using vacuolar or V₁-type hexameric ATPase as an exemplary rotational motor, we present a model of the complete 4-step conformational cycle involved in rotatory catalysis. First, using X-ray crystallography, a new intermediate or "dwell" is identified, which enables the release of an inorganic phosphate (or P_i) after ATP hydrolysis. Using molecular dynamics simulations, this new dwell is placed in a sequence with three other crystal structures to derive a putative cyclic rotation path. Free-energy simulations are employed to estimate the rate of the hexameric protein transformations and delineate allosteric effects that allow new reactant ATP entry only after hydrolysis product exit. An analysis of transfer entropy brings to light how the side-chain-level interactions transcend into larger-scale reorganizations, highlighting the role of the ubiquitous arginine-finger residues in coupling chemical and mechanical information. An inspection of all known rates encompassing the 4-step rotation mechanism implicates the overcoming of the ADP interactions with V₁-ATPase to be the rate-limiting step of motor action.

Modeling the Dynamics of Protein-Protein Interfaces, How and Why?

Protein-protein assemblies act as a key component in numerous cellular processes. Their accurate modeling at the atomic level remains a challenge for structural biology. To address this challenge, several docking and a handful of deep learning methodologies focus on modeling protein-protein interfaces. Although the outcome of these methods has been assessed using static reference structures, more and more data point to the fact that the interaction stability and specificity is encoded in the dynamics of these interfaces. Therefore, this dynamics information must be taken into account when modeling and assessing protein interactions at the atomistic scale. Expanding on this, our review initially focuses on the recent computational strategies aiming at investigating protein-protein interfaces in a dynamic fashion using enhanced sampling, multi-scale modeling, and experimental data integration. Then, we discuss how interface dynamics report on the function of protein assemblies in globular complexes, in fuzzy complexes containing intrinsically disordered proteins, as well as in active complexes, where chemical reactions take place across the protein-protein interface.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Hydrogen/Deuterium Exchange Measurements May Provide an Incomplete View of Protein Dynamics: a Case Study on Cytochrome c

Many aspects of protein function rely on conformational fluctuations. Hydrogen/deuterium exchange (HDX) mass spectrometry (MS) provides a window into these dynamics. Despite the widespread use of HDX-MS, it remains unclear whether this technique provides a truly comprehensive view of protein dynamics. HDX is mediated by H-bond-opening/closing events, implying that HDX methods provide an H-bond-centric view. This raises the question if there could be fluctuations that leave the H-bond network unaffected, thereby rendering them undetectable by HDX-MS. We explore this issue in experiments on cytochrome c (cyt c). Compared to the Fe(II) protein, Fe(III) cyt c shows enhanced deuteration on both the distal and proximal sides of the heme. Previous studies have attributed the enhanced dynamics of Fe(III) cyt c to the facile and reversible rupture of the distal M80-Fe(III) bond. Using molecular dynamics (MD) simulations, we conducted a detailed analysis of various cyt c conformers. Our MD data confirm that rupture of the M80-Fe(III) contact triggers major reorientation of the distal Ω loop. Surprisingly, this event takes place with only miniscule H-bonding alterations. In other words, the distal loop dynamics are almost "HDX-silent". Moreover, distal loop movements cannot account for enhanced dynamics on the opposite (proximal) side of the heme. Instead, enhanced deuteration of Fe(III) cyt c is attributed to sparsely populated conformers where both the distal (M80) and proximal (H18) coordination bonds have been ruptured, along with opening of numerous H-bonds on both sides of the heme. We conclude that there can be major structural fluctuations that are only weakly coupled to changes in H-bonding, making them virtually impossible to track by HDX-MS. In such cases, HDX-MS may provide an incomplete view of protein dynamics.

Spectroscopic glimpses of the transition state of ATP hydrolysis trapped in a bacterial DnaB helicase

The ATP hydrolysis transition state of motor proteins is a weakly populated protein state that can be stabilized and investigated by replacing ATP with chemical mimics. We present atomic-level structural and dynamic insights on a state created by ADP aluminum fluoride binding to the bacterial DnaB helicase from Helicobacter pylori. We determined the positioning of the metal ion cofactor within the active site using electron paramagnetic resonance, and identified the protein protons coordinating to the phosphate groups of ADP and DNA using proton-detected 31P,1H solid-state nuclear magnetic resonance spectroscopy at fast magic-angle spinning > 100 kHz, as well as temperature-dependent proton chemical-shift values to prove their engagements in hydrogen bonds. 19F and 27Al MAS NMR spectra reveal a highly mobile, fast-rotating aluminum fluoride unit pointing to the capture of a late ATP hydrolysis transition state in which the phosphoryl unit is already detached from the arginine and lysine fingers.

Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics

Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.

ATP Analogues for Structural Investigations: Case Studies of a DnaB Helicase and an ABC Transporter

Nucleoside triphosphates (NTPs) are used as chemical energy source in a variety of cell systems. Structural snapshots along the NTP hydrolysis reaction coordinate are typically obtained by adding stable, nonhydrolyzable adenosine triphosphate (ATP) -analogues to the proteins, with the goal to arrest a state that mimics as closely as possible a physiologically relevant state, e.g., the pre-hydrolytic, transition and post-hydrolytic states. We here present the lessons learned on two distinct ATPases on the best use and unexpected pitfalls observed for different analogues. The proteins investigated are the bacterial DnaB helicase from Helicobacter pylori and the multidrug ATP binding cassette (ABC) transporter BmrA from Bacillus subtilis, both belonging to the same division of P-loop fold NTPases. We review the magnetic-resonance strategies which can be of use to probe the binding of the ATP-mimics, and present carbon-13, phosphorus-31, and vanadium-51 solid-state nuclear magnetic resonance (NMR) spectra of the proteins or the bound molecules to unravel conformational and dynamic changes upon binding of the ATP-mimics. Electron paramagnetic resonance (EPR), and in particular W-band electron-electron double resonance (ELDOR)-detected NMR, is of complementary use to assess binding of vanadate. We discuss which analogues best mimic the different hydrolysis states for the DnaB helicase and the ABC transporter BmrA. These might be relevant also to structural and functional studies of other NTPases.

Free Energy Analysis of a Conformational Change of Heme ABC Transporter BhuUV-T

The heme ATP-binding cassette (ABC) transporter BhuUV-T of bacterial pathogen Burkholderia cenocepacia is required to transport heme across the inner cell membrane. The current hypothesis is that the binding of two ATPs to the nucleotide-binding domains of the transporter drives the initial steps of the transport cycle in which the empty transport sites are reoriented from the cytosol to the periplasm. Molecular details are missing because the structure of a key occluded intermediate remains hypothetical. Here we perform molecular simulations to analyze the free energy surface (FES) of the first step of the reorientation, namely the transition from an open inward-facing (IF) transport site to an occluded (Occ) conformation. We have modeled the latter structure in silico in a previous study. A simple annealing procedure removes residual bias originating from non-equilibrium targeted molecular dynamics. The calculated FES reveals the role of the ATPs in inducing the IF → Occ conformational change and validates the modeled Occ conformation.

A solid-state NMR tool box for the investigation of ATP-fueled protein engines

Motor proteins are involved in a variety of cellular processes. Their main purpose is to convert the chemical energy released during adenosine triphosphate (ATP) hydrolysis into mechanical work. In this review, solid-state Nuclear Magnetic Resonance (NMR) approaches are discussed allowing studies of structures, conformational events and dynamic features of motor proteins during a variety of enzymatic reactions. Solid-state NMR benefits from straightforward sample preparation based on sedimentation of the proteins directly into the Magic-Angle Spinning (MAS) rotor. Protein resonance assignment is the crucial and often time-limiting step in interpreting the wealth of information encoded in the NMR spectra. Herein, potentials, challenges and limitations in resonance assignment for large motor proteins are presented, focussing on both biochemical and spectroscopic approaches. This work highlights NMR tools available to study the action of the motor domain and its coupling to functional processes, as well as to identify protein-nucleotide interactions during events such as DNA replication. Arrested protein states of reaction coordinates such as ATP hydrolysis can be trapped for NMR studies by using stable, non-hydrolysable ATP analogues that mimic the physiological relevant states as accurately as possible. Recent advances in solid-state NMR techniques ranging from Dynamic Nuclear Polarization (DNP), ³¹P-based heteronuclear correlation experiments, ¹H-detected spectra at fast MAS frequencies >100 kHz to paramagnetic NMR are summarized and their applications to the bacterial DnaB helicase from Helicobacter pylori are discussed.

Weaving DNA strands: structural insight on ATP hydrolysis in RecA-induced homologous recombination

Homologous recombination is a fundamental process in all living organisms that allows the faithful repair of DNA double strand breaks, through the exchange of DNA strands between homologous regions of the genome. Results of three decades of investigation and recent fruitful observations have unveiled key elements of the reaction mechanism, which proceeds along nucleofilaments of recombinase proteins of the RecA family. Yet, one essential aspect of homologous recombination has largely been overlooked when deciphering the mechanism: while ATP is hydrolyzed in large quantity during the process, how exactly hydrolysis influences the DNA strand exchange reaction at the structural level remains to be elucidated. In this study, we build on a previous geometrical approach that studied the RecA filament variability without bound DNA to examine the putative implication of ATP hydrolysis on the structure, position, and interactions of up to three DNA strands within the RecA nucleofilament. Simulation results on modeled intermediates in the ATP cycle bring important clues about how local distortions in the DNA strand geometries resulting from ATP hydrolysis can aid sequence recognition by promoting local melting of already formed DNA heteroduplex and transient reverse strand exchange in a weaving type of mechanism.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Molecular dynamics simulations of nucleotide release from the circadian clock protein KaiC reveal atomic-resolution functional insights

The cyanobacterial clock proteins KaiA, KaiB, and KaiC form a powerful system to study the biophysical basis of circadian rhythms, because an in vitro mixture of the three proteins is sufficient to generate a robust ∼24-h rhythm in the phosphorylation of KaiC. The nucleotide-bound states of KaiC critically affect both KaiB binding to the N-terminal domain (CI) and the phosphotransfer reactions that (de)phosphorylate the KaiC C-terminal domain (CII). However, the nucleotide exchange pathways associated with transitions among these states are poorly understood. In this study, we integrate recent advances in molecular dynamics methods to elucidate the structure and energetics of the pathway for Mg·ADP release from the CII domain. We find that nucleotide release is coupled to large-scale conformational changes in the KaiC hexamer. Solvating the nucleotide requires widening the subunit interface leading to the active site, which is linked to extension of the A-loop, a structure implicated in KaiA binding. These results provide a molecular hypothesis for how KaiA acts as a nucleotide exchange factor. In turn, structural parallels between the CI and CII domains suggest a mechanism for allosteric coupling between the domains. We relate our results to structures observed for other hexameric ATPases, which perform diverse functions.

Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach

Efficient prediction and ranking of small molecule binders by their kinetic ( kon and koff) and thermodynamic ( Δ G) properties can be a valuable metric for drug lead optimization, as these quantities are often indicators of in vivo efficacy. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon's, koff's, and Δ G's. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, β-cyclodextrin, based on predicted kon's and koff's. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long time scale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and Δ G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish "best practices" for its future use.

Metal Actuated Ring Translocation Switches in Water

Among a series of metal ions in water, silver is the only one to remotely and reversibly switch cucurbit[7]uril (CB[7]) movements (translocation or uptake) on a rigid and linear three-station viologen-phenylene-imidazole ( V-P-I) derivative, avoiding undesired pH actuation. ¹H NMR, UV-vis spectroscopy, mass spectrometry, ITC, and modeling were combined to show that ring translocation or uptake along a molecular thread is possible in water by Ag⁺ as a metal stimulus.

Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

Free-energy simulations reveal molecular mechanism for functional switch of a DNA helicase

Helicases play key roles in genome maintenance, yet it remains elusive how these enzymes change conformations and how transitions between different conformational states regulate nucleic acid reshaping. Here, we developed a computational technique combining structural bioinformatics approaches and atomic-level free-energy simulations to characterize how the Escherichia coli DNA repair enzyme UvrD changes its conformation at the fork junction to switch its function from unwinding to rezipping DNA. The lowest free-energy path shows that UvrD opens the interface between two domains, allowing the bound ssDNA to escape. The simulation results predict a key metastable 'tilted' state during ssDNA strand switching. By simulating FRET distributions with fluorophores attached to UvrD, we show that the new state is supported quantitatively by single-molecule measurements. The present study deciphers key elements for the 'hyper-helicase' behavior of a mutant and provides an effective framework to characterize directly structure-function relationships in molecular machines.

Allostery in the dengue virus NS3 helicase: Insights into the NTPase cycle from molecular simulations

The C-terminus domain of non-structural 3 (NS3) protein of the Flaviviridae viruses (e.g. HCV, dengue, West Nile, Zika) is a nucleotide triphosphatase (NTPase) -dependent superfamily 2 (SF2) helicase that unwinds double-stranded RNA while translocating along the nucleic polymer. Due to these functions, NS3 is an important target for antiviral development yet the biophysics of this enzyme are poorly understood. Microsecond-long molecular dynamic simulations of the dengue NS3 helicase domain are reported from which allosteric effects of RNA and NTPase substrates are observed. The presence of a bound single-stranded RNA catalytically enhances the phosphate hydrolysis reaction by affecting the dynamics and positioning of waters within the hydrolysis active site. Coupled with results from the simulations, electronic structure calculations of the reaction are used to quantify this enhancement to be a 150-fold increase, in qualitative agreement with the experimental enhancement factor of 10–100. Additionally, protein-RNA interactions exhibit NTPase substrate-induced allostery, where the presence of a nucleotide (e.g. ATP or ADP) structurally perturbs residues in direct contact with the phosphodiester backbone of the RNA. Residue-residue network analyses highlight pathways of short ranged interactions that connect the two active sites. These analyses identify motif V as a highly connected region of protein structure through which energy released from either active site is hypothesized to move, thereby inducing the observed allosteric effects. These results lay the foundation for the design of novel allosteric inhibitors of NS3.

Non-structural protein 3 (NS3) is a Flaviviridae (e.g. Hepatitis C, dengue, and Zika viruses) helicase that unwinds double stranded RNA while translocating along the nucleic polymer during viral genome replication. As a member of superfamily 2 (SF2) helicases, NS3 utilizes the free energy of nucleotide triphosphate (NTP) binding, hydrolysis, and product unbinding to perform its functions. While much is known about SF2 helicases, the pathways and mechanisms through which free energy is transduced between the NTP hydrolysis active site and RNA binding cleft remains elusive. Here we present a multiscale computational study to characterize the allosteric effects induced by the RNA and NTPase substrates (ATP, ADP, and P_i) as well as the pathways of short-range, residue-residue interactions that connect the two active sites. Results from this body of molecular dynamics simulations and electronic structure calculations are highlighted in context to the NTPase enzymatic cycle, allowing for development of testable hypotheses for validation of these simulations. Our insights, therefore, provide novel details about the biophysics of NS3 and guide the next generation of experimental studies.

A new paradigm for atomically detailed simulations of kinetics in biophysical systems

The kinetics of biochemical and biophysical events determined the course of life processes and attracted considerable interest and research. For example, modeling of biological networks and cellular responses relies on the availability of information on rate coefficients. Atomically detailed simulations hold the promise of supplementing experimental data to obtain a more complete kinetic picture. However, simulations at biological time scales are challenging. Typical computer resources are insufficient to provide the ensemble of trajectories at the correct length that is required for straightforward calculations of time scales. In the last years, new technologies emerged that make atomically detailed simulations of rate coefficients possible. Instead of computing complete trajectories from reactants to products, these approaches launch a large number of short trajectories at different positions. Since the trajectories are short, they are computed trivially in parallel on modern computer architecture. The starting and termination positions of the short trajectories are chosen, following statistical mechanics theory, to enhance efficiency. These trajectories are analyzed. The analysis produces accurate estimates of time scales as long as hours. The theory of Milestoning that exploits the use of short trajectories is discussed, and several applications are described.

Nanoscale Dynamics and Energetics of Proteins and Protein-Nucleic Acid Complexes in Classical Molecular Dynamics Simulations

The present article describes techniques for classical simulations of proteins and protein-nucleic acid complexes, revealing their dynamics and protein-substrate binding energies. The approach is based on classical atomistic molecular dynamics (MD) simulations of the experimentally determined structures of the complexes. MD simulations can provide dynamics of complexes in realistic solvents on microsecond timescales, and the free energy methods are able to provide Gibbs free energies of binding of substrates, such as nucleic acids, to proteins. The chapter describes methodologies for the preparation of computer models of biomolecular complexes and free energy perturbation methodology for evaluating Gibbs free energies of binding. The applications are illustrated with examples of snapshots of proteins and their complexes with nucleic acids, as well as the precise Gibbs free energies of binding.

Methodology for the Simulation of Molecular Motors at Different Scales

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors-proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

Chemomechanical Coupling in Hexameric Protein-Protein Interfaces Harnesses Energy within V-Type ATPases

ATP synthase is the most prominent bioenergetic macromolecular motor in all life forms, utilizing the proton gradient across the cell membrane to fuel the synthesis of ATP. Notwithstanding the wealth of available biochemical and structural information inferred from years of experiments, the precise molecular mechanism whereby vacuolar (V-type) ATP synthase fulfills its biological function remains largely fragmentary. Recently, crystallographers provided the first high-resolution view of ATP activity in Enterococcus hirae V1-ATPase. Employing a combination of transition-path sampling and high-performance free-energy methods, the sequence of conformational transitions involved in a functional cycle accompanying ATP hydrolysis has been investigated in unprecedented detail over an aggregate simulation time of 65 μs. Our simulated pathways reveal that the chemical energy produced by ATP hydrolysis is harnessed via the concerted motion of the protein-protein interfaces in the V1-ring, and is nearly entirely consumed in the rotation of the central stalk. Surprisingly, in an ATPase devoid of a central stalk, the interfaces of this ring are perfectly designed for inducing ATP hydrolysis. However, in a complete V1-ATPase, the mechanical property of the central stalk is a key determinant of the rate of ATP turnover. The simulations further unveil a sequence of events, whereby unbinding of the hydrolysis product (ADP + Pi) is followed by ATP uptake, which, in turn, leads to the torque generation step and rotation of the center stalk. Molecular trajectories also bring to light multiple intermediates, two of which have been isolated in independent crystallography experiments.

Temperature-sensitive gating of TRPV1 channel as probed by atomistic simulations of its trans- and juxtamembrane domains

Heat-activated transient receptor potential channel TRPV1 is one of the most studied eukaryotic proteins involved in temperature sensation. Upon heating, it exhibits rapid reversible pore gating, which depolarizes neurons and generates action potentials. Underlying molecular details of such effects in the pore region of TRPV1 is of a crucial importance to control temperature responses of the organism. Despite the spatial structure of the channel in both open (O) and closed (C) states is known, microscopic nature of channel gating and mechanism of thermal sensitivity are still poorly understood. In this work, we used unrestrained atomistic molecular dynamics simulations of TRPV1 (without N- and C-terminal cytoplasmic domains) embedded into explicit lipid bilayer in its O- and C-states. We found that the pore domain with its neighboring loops undergoes large temperature-dependent conformational transitions in an asymmetric way, when fragments of only one monomer move with large amplitude, freeing the pore upon heating. Such an asymmetrical gating looks rather biologically relevant because it is faster and more reliable than traditionally proposed “iris-like” symmetric scheme of channel opening. Analysis of structural, dynamic, and hydrophobic organization of the pore domain revealed entropy growth upon TRPV1 gating, which is in line with current concepts of thermal sensitivity.

QwikMD - Integrative Molecular Dynamics Toolkit for Novices and Experts

The proper functioning of biomolecules in living cells requires them to assume particular structures and to undergo conformational changes. Both biomolecular structure and motion can be studied using a wide variety of techniques, but none offers the level of detail as do molecular dynamics (MD) simulations. Integrating two widely used modeling programs, namely NAMD and VMD, we have created a robust, user-friendly software, QwikMD, which enables novices and experts alike to address biomedically relevant questions, where often only molecular dynamics simulations can provide answers. Performing both simple and advanced MD simulations interactively, QwikMD automates as many steps as necessary for preparing, carrying out, and analyzing simulations while checking for common errors and enabling reproducibility. QwikMD meets also the needs of experts in the field, increasing the efficiency and quality of their work by carrying out tedious or repetitive tasks while enabling easy control of every step. Whether carrying out simulations within the live view mode on a small laptop or performing complex and large simulations on supercomputers or Cloud computers, QwikMD uses the same steps and user interface. QwikMD is freely available by download on group and personal computers. It is also available on the cloud at Amazon Web Services.

Molecular Mechanism of Processive 3' to 5' RNA Translocation in the Active Subunit of the RNA Exosome Complex

Recent experimental studies revealed structural details of 3' to 5' degradation of RNA molecules, performed by the exosome complex. ssRNA is channeled through its multisubunit ring-like core into the active site tunnel of its key exonuclease subunit Rrp44, which acts both as an enzyme and a motor. Even in isolation, Rrp44 can pull and sequentially cleave RNA nucleotides, one at a time, without any external energy input and release a final 3-5 nucleotide long product. Using molecular dynamics simulations, we identify the main factors that control these processes. Our free energy calculations reveal that RNA transfer from solution into the active site of Rrp44 is highly favorable, but dependent on the length of the RNA strand. While RNA strands formed by 5 nucleotides or more correspond to a decreasing free energy along the translocation coordinate toward the cleavage site, a 4-nucleotide RNA experiences a free energy barrier along the same direction, potentially leading to incomplete cleavage of ssRNA and the release of short (3-5) nucleotide products. We provide new insight into how Rrp44 catalyzes a localized enzymatic reaction and performs an action distributed over several RNA nucleotides, leading eventually to the translocation of whole RNA segments into the position suitable for cleavage.

Advances in free-energy-based simulations of protein folding and ligand binding

Free-energy-based simulations are increasingly providing the narratives about the structures, dynamics and biological mechanisms that constitute the fabric of protein science. Here, we review two recent successes. It is becoming practical: first, to fold small proteins with free-energy methods without knowing substructures and second, to compute ligand-protein binding affinities, not just their binding poses. Over the past 40 years, the timescales that can be simulated by atomistic MD are doubling every 1.3 years--which is faster than Moore's law. Thus, these advances are not simply due to the availability of faster computers. Force fields, solvation models and simulation methodology have kept pace with computing advancements, and are now quite good. At the tip of the spear recently are GPU-based computing, improved fast-solvation methods, continued advances in force fields, and conformational sampling methods that harness external information.

Coarse-Grained Simulations of Topology-Dependent Mechanisms of Protein Unfolding and Translocation Mediated by ClpY ATPase Nanomachines

Clp ATPases are powerful ring shaped nanomachines which participate in the degradation pathway of the protein quality control system, coupling the energy from ATP hydrolysis to threading substrate proteins (SP) through their narrow central pore. Repetitive cycles of sequential intra-ring ATP hydrolysis events induce axial excursions of diaphragm-forming central pore loops that effect the application of mechanical forces onto SPs to promote unfolding and translocation. We perform Langevin dynamics simulations of a coarse-grained model of the ClpY ATPase-SP system to elucidate the molecular details of unfolding and translocation of an α/β model protein. We contrast this mechanism with our previous studies which used an all-α SP. We find conserved aspects of unfolding and translocation mechanisms by allosteric ClpY, including unfolding initiated at the tagged C-terminus and translocation via a power stroke mechanism. Topology-specific aspects include the time scales, the rate limiting steps in the degradation pathway, the effect of force directionality, and the translocase efficacy. Mechanisms of ClpY-assisted unfolding and translocation are distinct from those resulting from non-allosteric mechanical pulling. Bulk unfolding simulations, which mimic Atomic Force Microscopy-type pulling, reveal multiple unfolding pathways initiated at the C-terminus, N-terminus, or simultaneously from both termini. In a non-allosteric ClpY ATPase pore, mechanical pulling with constant velocity yields larger effective forces for SP unfolding, while pulling with constant force results in simultaneous unfolding and translocation.

Cell survival is critically dependent on tightly regulated protein quality control, which includes chaperone-mediated folding and degradation. In the degradation pathway, AAA+ nanomachines, such as bacterial Clp proteases, use ATP-driven mechanisms to mechanically unfold, translocate, and destroy excess or defective proteins. Understanding these remodeling mechanisms is of central importance for deciphering the details of essential cellular processes. We perform coarse-grained computer simulations to extensively probe the effect of substrate protein topology on unfolding and translocation actions of the ClpY ATPase nanomachine. We find that, independent of SP topology, unfolding proceeds from the tagged C-terminus, which is engaged by the ATPase, and translocation involves coordinated steps. Topology-specific aspects include more complex unfolding and translocation pathways of the α/β SP compared with the all-α SP due to high stability of β-hairpins and interplay of tertiary contacts. In addition, directionality of the mechanical force applied by the Clp ATPase gives rise to distinct unfolding pathways.

Thermal unfolding simulations of NBD1 domain variants reveal structural motifs associated with the impaired folding of F508del-CFTR

The deletion of phenylalanine 508 reshapes the conformational space of the NBD1 domain that populates unique intermediate states that provide insights into the molecular events that underlie the impaired folding of F508del-NBD1.

Constraint methods that accelerate free-energy simulations of biomolecules

Atomistic molecular dynamics simulations of biomolecules are critical for generating narratives about biological mechanisms. The power of atomistic simulations is that these are physics-based methods that satisfy Boltzmann's law, so they can be used to compute populations, dynamics, and mechanisms. But physical simulations are computationally intensive and do not scale well to the sizes of many important biomolecules. One way to speed up physical simulations is by coarse-graining the potential function. Another way is to harness structural knowledge, often by imposing spring-like restraints. But harnessing external knowledge in physical simulations is problematic because knowledge, data, or hunches have errors, noise, and combinatoric uncertainties. Here, we review recent principled methods for imposing restraints to speed up physics-based molecular simulations that promise to scale to larger biomolecules and motions.

Dancing through Life: Molecular Dynamics Simulations and Network-Centric Modeling of Allosteric Mechanisms in Hsp70 and Hsp110 Chaperone Proteins

Hsp70 and Hsp110 chaperones play an important role in regulating cellular processes that involve protein folding and stabilization, which are essential for the integrity of signaling networks. Although many aspects of allosteric regulatory mechanisms in Hsp70 and Hsp110 chaperones have been extensively studied and significantly advanced in recent experimental studies, the atomistic picture of signal propagation and energetics of dynamics-based communication still remain unresolved. In this work, we have combined molecular dynamics simulations and protein stability analysis of the chaperone structures with the network modeling of residue interaction networks to characterize molecular determinants of allosteric mechanisms. We have shown that allosteric mechanisms of Hsp70 and Hsp110 chaperones may be primarily determined by nucleotide-induced redistribution of local conformational ensembles in the inter-domain regions and the substrate binding domain. Conformational dynamics and energetics of the peptide substrate binding with the Hsp70 structures has been analyzed using free energy calculations, revealing allosteric hotspots that control negative cooperativity between regulatory sites. The results have indicated that cooperative interactions may promote a population-shift mechanism in Hsp70, in which functional residues are organized in a broad and robust allosteric network that can link the nucleotide-binding site and the substrate-binding regions. A smaller allosteric network in Hsp110 structures may elicit an entropy-driven allostery that occurs in the absence of global structural changes. We have found that global mediating residues with high network centrality may be organized in stable local communities that are indispensable for structural stability and efficient allosteric communications. The network-centric analysis of allosteric interactions has also established that centrality of functional residues could correlate with their sensitivity to mutations across diverse chaperone functions. This study reconciles a wide spectrum of structural and functional experiments by demonstrating how integration of molecular simulations and network-centric modeling may explain thermodynamic and mechanistic aspects of allosteric regulation in chaperones.

ATP Hydrolysis in the RecA-DNA Filament Promotes Structural Changes at the Protein-DNA Interface

To address the mechanistic roles of ATP hydrolysis in RecA-promoted strand exchange reaction in homologous recombination, quantum mechanical calculations are performed on key parts of the RecA-DNA complex. We find that ATP hydrolysis may induce changes at the protein-DNA interface, resulting in the rearrangement of the hydrogen bond network connecting the ATP and the DNA binding sites.

Observing lysozyme's closing and opening motions by high-resolution single-molecule enzymology

Single-molecule techniques can monitor the kinetics of transitions between enzyme open and closed conformations, but such methods usually lack the resolution to observe the underlying transition pathway or intermediate conformational dynamics. We have used a 1 MHz bandwidth carbon nanotube transistor to electronically monitor single molecules of the enzyme T4 lysozyme as it processes substrate. An experimental resolution of 2 μs allowed the direct recording of lysozyme's opening and closing transitions. Unexpectedly, both motions required 37 μs, on average. The distribution of transition durations was also independent of the enzyme's state: either catalytic or nonproductive. The observation of smooth, continuous transitions suggests a concerted mechanism for glycoside hydrolysis with lysozyme's two domains closing upon the polysaccharide substrate in its active site. We distinguish these smooth motions from a nonconcerted mechanism, observed in approximately 10% of lysozyme openings and closings, in which the enzyme pauses for an additional 40-140 μs in an intermediate, partially closed conformation. During intermediate forming events, the number of rate-limiting steps observed increases to four, consistent with four steps required in the stepwise, arrow-pushing mechanism. The formation of such intermediate conformations was again independent of the enzyme's state. Taken together, the results suggest lysozyme operates as a Brownian motor. In this model, the enzyme traces a single pathway for closing and the reverse pathway for enzyme opening, regardless of its instantaneous catalytic productivity. The observed symmetry in enzyme opening and closing thus suggests that substrate translocation occurs while the enzyme is closed.