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

Absolute and Relative Binding Free Energy Calculations of Nucleotides to Multiple Protein Classes

Polyphosphate nucleotides, such as ATP, ADP, GTP, and GDP, play a crucial role in modulating protein functions through binding and/or catalytically activating proteins (enzymes). However, accurately calculating the binding free energies for these charged and flexible ligands poses challenges due to slow conformational relaxation and the limitations of force fields. In this study, we examine the accuracy and reliability of alchemical free energy simulations with fixed-charge force fields for the binding of four nucleotides to nine proteins of various classes, including kinases, ATPases, and GTPases. Our results indicate that the alchemical simulations effectively reproduce experimental binding free energies for all proteins that do not undergo significant conformational changes between their triphosphate nucleotide-bound and diphosphate nucleotide-bound states, with 87.5% (7 out of 8) of the absolute binding free energy results for 4 proteins within ±2 kcal/mol of experimental values and 88.9% (8 out of 9) of the relative binding free energy results for 9 proteins within ±3 kcal/mol of experimental values. However, our calculations show significant inaccuracies when divalent ions are included, suggesting that nonpolarizable force fields may not accurately capture interactions involving these ions. Additionally, the presence of highly charged and flexible ligands necessitates extensive conformational sampling to account for the long relaxation times associated with long-range electrostatic interactions. The simulation strategy presented here, along with its demonstrated accuracy across multiple protein classes, will be valuable for predicting the binding of nucleotides or their analogs to protein targets.

Modeling Diffusive Motion of Ferredoxin and Plastocyanin on the PSI Domain of Procholorococcus marinus MIT9313

Diffusion of mobile charge carriers, such as ferredoxin and plastocyanin, often constitutes a rate-determining step in photosynthetic energy conversion. The diffusion time scales typically exceed that of other primary bioenergetic processes and remain beyond the reach of direct simulation at the molecular level. We characterize the diffusive kinetics of ferredoxin and plastocyanin upon the photosystem I-rich domain of Prochlorococcus, the most abundant phototroph on Earth by mass. A modeling approach for ferredoxin and plastocyanin diffusion is presented that uses ensembles of coarse-grained molecular dynamics simulations in Martini 2.2P with GROMACS 2021.2. The simulation ensembles are used to construct the diffusion coefficient and drift for ferredoxin and plastocyanin as spatial functions in the photosystem I domain of the MIT9313 ecotype. Four separate models are constructed, corresponding to ferredoxin and plastocyanin in reduced and oxidized states. A single scaling constant of 0.7 is found to be sufficient to adjust the diffusion coefficient obtained from the Martini simulation ensemble to match the in vitro values for both ferredoxin and plastocyanin. A comparison of Martini versions (2.2P, 2.2, 3) is presented with respect to diffusion scaling. The diffusion coefficient and drift together quantify the inhomogeneity of diffusive behavior. Notably, a funnel-like convergence toward the corresponding putative binding positions is observed for both ferredoxin and plastocyanin, even without such a priori foreknowledge supplied in the simulation protocol. The approach presented here is of relevance for studying diffusion kinetics in photosynthetic and other bioenergetic processes.

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

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.

cpSRP43 Is Both Highly Flexible and Stable: Structural Insights Using a Combined Experimental and Computational Approach

The novel multidomain protein, cpSRP43, is a unique subunit of the post-translational chloroplast signal recognition particle (cpSRP) targeting pathway in higher plants. The cpSRP pathway is responsible for targeting and insertion of light-harvesting chlorophyll a/b binding proteins (LHCPs) to the thylakoid membrane. Upon emergence into the stroma, LHCPs form a soluble transit complex with the cpSRP heterodimer, which is composed of cpSRP43 and cpSRP54. cpSRP43 is irreplaceable as a chaperone to LHCPs in their translocation to the thylakoid membrane and remarkable in its ability to dissolve aggregates of LHCPs without the need for external energy input. In previous studies, cpSRP43 has demonstrated significant flexibility and interdomain dynamics. In this study, we explore the structural stability and flexibility of cpSRP43 using a combination of computational and experimental techniques and find that this protein is concurrently highly stable and flexible. In addition to microsecond-level unbiased molecular dynamics (MD), biased MD simulations based on system-specific collective variables are used along with biophysical experimentation to explain the basis of the flexibility and stability of cpSRP43, showing that the free and cpSRP54-bound cpSRP43 has substantially different conformations and conformational dynamics.

Physical pictures of rotation mechanisms of F1- and V1-ATPases: Leading roles of translational, configurational entropy of water

We aim to develop a theory based on a concept other than the chemo-mechanical coupling (transduction of chemical free energy of ATP to mechanical work) for an ATP-driven protein complex. Experimental results conflicting with the chemo-mechanical coupling have recently emerged. We claim that the system comprises not only the protein complex but also the aqueous solution in which the protein complex is immersed and the system performs essentially no mechanical work. We perform statistical-mechanical analyses on V₁-ATPase (the A₃B₃DF complex) for which crystal structures in more different states are experimentally known than for F₁-ATPase (the α₃β₃γ complex). Molecular and atomistic models are employed for water and the structure of V₁-ATPase, respectively. The entropy originating from the translational displacement of water molecules in the system is treated as a pivotal factor. We find that the packing structure of the catalytic dwell state of V₁-ATPase is constructed by the interplay of ATP bindings to two of the A subunits and incorporation of the DF subunit. The packing structure represents the nonuniformity with respect to the closeness of packing of the atoms in constituent proteins and protein interfaces. The physical picture of rotation mechanism of F₁-ATPase recently constructed by Kinoshita is examined, and common points and differences between F₁- and V₁-ATPases are revealed. An ATP hydrolysis cycle comprises binding of ATP to the protein complex, hydrolysis of ATP into ADP and Pi in it, and dissociation of ADP and Pi from it. During each cycle, the chemical compounds bound to the three A or β subunits and the packing structure of the A₃B₃ or α₃β₃ complex are sequentially changed, which induces the unidirectional rotation of the central shaft for retaining the packing structure of the A₃B₃DF or α₃β₃γ complex stabilized for almost maximizing the water entropy. The torque driving the rotation is generated by water with no input of chemical free energy. The presence of ATP is indispensable as a trigger of the torque generation. The ATP hydrolysis or synthesis reaction is tightly coupled to the rotation of the central shaft in the normal or inverse direction through the water-entropy effect.

Molecular mechanism and energetics of coupling between substrate binding and product release in the F1-ATPase catalytic cycle

F1-ATPase is a motor protein that couples the rotation of its rotary [Formula: see text] subunit with ATP synthesis or hydrolysis. Single-molecule experiments indicate that nucleotide binding and release events occur almost simultaneously during the synthesis cycle, allowing the energy gain due to spontaneous binding of ADP to one catalytic [Formula: see text] subunit to be directly harnessed for driving the release of ATP from another rather than being dissipated as heat. Here, we examine the unknown mechanism of this coupling that is critical for an exceptionally high mechanochemical efficiency of F1-ATPase by means of all-atom free-energy simulations. We find that nondissipative and kinetically fast progression of the motor in the synthesis direction requires a concerted conformational change involving the closure of the ADP-binding [Formula: see text] subunit followed by the gradual opening of the ATP-releasing [Formula: see text] subunit over the course of the 30 to 40° rotary substep of the [Formula: see text] subunit. This rotary substep, preceding the ATP-dependent metastable state, allows for the recovery of a large portion of the ADP binding energy in the conformation of ATP-bound [Formula: see text] that gradually adopts the low-affinity conformation, captured also by the recent cryo-EM structure of this elusive state. The release of ATP from this nearly open conformation leads to its further opening, which enables the progression of the motor to the next catalytic metastable state. Our simulations explain this energy conversion mechanism in terms of intersubunit and ligand-protein interactions.

Atomic-level characterization of the conformational transition pathways in SARS-CoV-1 and SARS-CoV-2 spike proteins

Severe acute respiratory syndrome (SARS) coronaviruses 1 and 2 (SARS-CoV-1 and SARS-CoV-2) derive transmissibility from spike protein activation in the receptor binding domain (RBD) and binding to the host cell angiotensin converting enzyme 2 (ACE2). However, the mechanistic details that describe the large-scale conformational changes associated with spike protein activation or deactivation are still somewhat unknown. Here, we have employed an extensive set of nonequilibrium all-atom molecular dynamics (MD) simulations, utilizing a novel protocol, for the SARS-CoV-1 (CoV-1) and SARS-CoV-2 (CoV-2) prefusion spike proteins in order to characterize the conformational pathways associated with the active-to-inactive transition. Our results indicate that both CoV-1 and CoV-2 spike proteins undergo conformational transitions along pathways unique to each protein. We have identified a number of key residues that form various inter-domain saltbridges, suggesting a multi-stage conformational change along the pathways. We have also constructed the free energy profiles along the transition pathways for both CoV-1 and CoV-2 spike proteins. The CoV-2 spike protein must overcome larger free energy barriers to undergo conformational changes towards protein activation or deactivation, when compared to CoV-1.

Perspective: Path Sampling Methods Applied to Enzymatic Catalysis

This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.

Meta-Analysis Reveals That Absolute Binding Free-Energy Calculations Approach Chemical Accuracy

Systematic and quantitative analysis of the reliability of formally exact methods that in silico calculate absolute protein-ligand binding free energies remains lacking. Here, we provide, for the first time, evidence-based information on the reliability of these methods by statistically studying 853 cases from 34 different research groups through meta-analysis. The results show that formally exact methods approach chemical accuracy (error = 1.58 kcal/mol), even if people are challenging difficult tasks such as blind drug screening in recent years. The geometrical-pathway-based methods prove to possess a better convergence ability than the alchemical ones, while the latter have a larger application range. We also reveal the importance of always using the latest force fields to guarantee reliability and discuss the pros and cons of turning to an implicit solvent model in absolute binding free-energy calculations. Moreover, based on the meta-analysis, an evidence-based guideline for in silico binding free-energy calculations is provided.

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.

Accurate determination of protein:ligand standard binding free energies from molecular dynamics simulations

Designing a reliable computational methodology to calculate protein:ligand standard binding free energies is extremely challenging. The large change in configurational enthalpy and entropy that accompanies the association of ligand and protein is notoriously difficult to capture in naive brute-force simulations. Addressing this issue, the present protocol rests upon a rigorous statistical mechanical framework for the determination of protein:ligand binding affinities together with the comprehensive Binding Free-Energy Estimator 2 (BFEE2) application software. With the knowledge of the bound state, available from experiments or docking, application of the BFEE2 protocol with a reliable force field supplies in a matter of days standard binding free energies within chemical accuracy, for a broad range of protein:ligand complexes. Limiting undesirable human intervention, BFEE2 assists the end user in preparing all the necessary input files and performing the post-treatment of the simulations towards the final estimate of the binding affinity.

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Anionic Lipids Confine Cytochrome c2 to the Surface of Bioenergetic Membranes without Compromising Its Interaction with Redox Partners

Cytochrome c2 (cyt. c2) is a major element in electron transfer between redox proteins in bioenergetic membranes. While the interaction between cyt. c2 and anionic lipids abundant in bioenergetic membranes has been reported, their effect on the shuttling activity of cyt. c2 remains elusive. Here, the effect of anionic lipids on the interaction and binding of cyt. c2 to the cytochrome bc1 complex (bc1) is investigated using a combination of molecular dynamics (MD) and Brownian dynamics (BD) simulations. MD is used to generate thermally accessible conformations of cyt. c2 and membrane-embedded bc1, which were subsequently used in multireplica BD simulations of diffusion of cyt. c2 from solution to bc1, in the presence of various lipids. We show that, counterintuitively, anionic lipids facilitate association of cyt. c2 with bc1 by localizing its diffusion to the membrane surface. The observed lipid-mediated bc1 association is further enhanced by the oxidized state of cyt. c2, in line with its physiological function. This lipid-mediated enhancement is salinity-dependent, and anionic lipids can disrupt cyt. c2-bc1 interaction at nonphysiological salt levels. Our data highlight the importance of the redox state of cyt. c2, the lipid composition of the chromatophore membrane, and the salinity of the chromatophore in regulating the efficiency of the electron shuttling process mediated by cyt. c2. The conclusions can be extrapolated to mitochondrial systems and processes, or any bioenergetic membrane, given the structural similarity between cyt. c2 and bc1 and their mitochondrial counterparts.

MLCV: Bridging Machine-Learning-Based Dimensionality Reduction and Free-Energy Calculation

Importance-sampling algorithms leaning on the definition of a model reaction coordinate (RC) are widely employed to probe processes relevant to chemistry and biology alike, spanning time scales not amenable to common, brute-force molecular dynamics (MD) simulations. In practice, the model RC often consists of a handful of collective variables (CVs) chosen on the basis of chemical intuition. However, constructing manually a low-dimensional RC model to describe an intricate geometrical transformation for the purpose of free-energy calculations and analyses remains a daunting challenge due to the inherent complexity of the conformational transitions at play. To solve this issue, remarkable progress has been made in employing machine-learning techniques, such as autoencoders, to extract the low-dimensional RC model from a large set of CVs. Implementation of the differentiable, nonlinear machine-learned CVs in common MD engines to perform free-energy calculations is, however, particularly cumbersome. To address this issue, we present here a user-friendly tool (called MLCV) that facilitates the use of machine-learned CVs in importance-sampling simulations through the popular Colvars module. Our approach is critically probed with three case examples consisting of small peptides, showcasing that through hard-coded neural network in Colvars, deep-learning and enhanced-sampling can be effectively bridged with MD simulations. The MLCV code is versatile, applicable to all the CVs available in Colvars, and can be connected to any kind of dense neural networks. We believe that MLCV provides an effective, powerful, and user-friendly platform accessible to experts and nonexperts alike for machine-learning (ML)-guided CV discovery and enhanced-sampling simulations to unveil the molecular mechanisms underlying complex biochemical processes.

String Method with Swarms-of-Trajectories, Mean Drifts, Lag Time, and Committor

The kinetics of a dynamical system comprising two metastable states is formulated in terms of a finite-time propagator in phase space (position and velocity) adapted to the underdamped Langevin equation. Dimensionality reduction to a subspace of collective variables yields familiar expressions for the propagator, committor, and steady-state flux. A quadratic expression for the steady-state flux between the two metastable states can serve as a robust variational principle to determine an optimal approximate committor expressed in terms of a set of collective variables. The theoretical formulation is exploited to clarify the foundation of the string method with swarms-of-trajectories, which relies on the mean drift of short trajectories to determine the optimal transition pathway. It is argued that the conditions for Markovity within a subspace of collective variables may not be satisfied with an arbitrary short time-step and that proper kinetic behaviors appear only when considering the effective propagator for longer lag times. The effective propagator with finite lag time is amenable to an eigenvalue-eigenvector spectral analysis, as elaborated previously in the context of position-based Markov models. The time-correlation functions calculated by swarms-of-trajectories along the string pathway constitutes a natural extension of these developments. The present formulation provides a powerful theoretical framework to characterize the optimal pathway between two metastable states of a system.

Poor Person's pH Simulation of Membrane Proteins

pH conditions are central to the functioning of all biomolecules. However, implications of pH changes are nontrivial on a molecular scale. Though a rigorous microscopic definition of pH exists, its implementation in classical molecular dynamics (MD) simulations is cumbersome, and more so in large integral membrane systems. In this chapter, an integrative pipeline is described that combines Multi-Conformation Continuum Electrostatics (MCCE) computations with MD simulations to capture the effect of transient protonation states on the coupled conformational changes in transmembrane proteins. The core methodologies are explained, and all the software required to set up this pipeline are outlined with their key parameters. All associated analyses of structure and function are provided using two case studies, namely those of bioenergetic complexes: NADH dehydrogenase (complex I) and V_o domain of V-type ATPase. The hybrid MCCE-MD pipeline has allowed the discovery of hydrogen bond networks, ligand binding pathways, and disease-causing mutations.

Molecular Dynamics-Based Thermodynamic and Kinetic Characterization of Membrane Protein Conformational Transitions

Molecular dynamics (MD) simulations are routinely used to study structural dynamics of membrane proteins. However, conventional MD is often unable to sample functionally important conformational transitions of membrane proteins such as those involved in active membrane transport or channel activation process. Here we describe a combination of multiple MD based techniques that allows for a rigorous characterization of energetics and kinetics of large-scale conformational changes in membrane proteins. The methodology is based on biased, nonequilibrium, collective-variable based simulations including nonequilibrium pulling, string method with swarms of trajectories, bias-exchange umbrella sampling, and rate estimation techniques.

Data-guided Multi-Map variables for ensemble refinement of molecular movies

Driving molecular dynamics simulations with data-guided collective variables offer a promising strategy to recover thermodynamic information from structure-centric experiments. Here, the three-dimensional electron density of a protein, as it would be determined by cryo-EM or x-ray crystallography, is used to achieve simultaneously free-energy costs of conformational transitions and refined atomic structures. Unlike previous density-driven molecular dynamics methodologies that determine only the best map-model fits, our work employs the recently developed Multi-Map methodology to monitor concerted movements within equilibrium, non-equilibrium, and enhanced sampling simulations. Construction of all-atom ensembles along the chosen values of the Multi-Map variable enables simultaneous estimation of average properties, as well as real-space refinement of the structures contributing to such averages. Using three proteins of increasing size, we demonstrate that biased simulation along the reaction coordinates derived from electron densities can capture conformational transitions between known intermediates. The simulated pathways appear reversible with minimal hysteresis and require only low-resolution density information to guide the transition. The induced transitions also produce estimates for free energy differences that can be directly compared to experimental observables and population distributions. The refined model quality is superior compared to those found in the Protein Data Bank. We find that the best quantitative agreement with experimental free-energy differences is obtained using medium resolution density information coupled to comparatively large structural transitions. Practical considerations for probing the transitions between multiple intermediate density states are also discussed.

Cryo-EM and MD infer water-mediated proton transport and autoinhibition mechanisms of Vo complex

Rotary vacuolar adenosine triphosphatases (V-ATPases) drive transmembrane proton transport through a V_o proton channel subcomplex. Despite recent high-resolution structures of several rotary ATPases, the dynamic mechanism of proton pumping remains elusive. Here, we determined a 2.7-Å cryo-electron microscopy (cryo-EM) structure of yeast V_o proton channel in nanodisc that reveals the location of ordered water molecules along the proton path, details of specific protein-lipid interactions, and the architecture of the membrane scaffold protein. Moreover, we uncover a state of V_o that shows the c-ring rotated by ~14°. Molecular dynamics simulations demonstrate that the two rotary states are in thermal equilibrium and depict how the protonation state of essential glutamic acid residues couples water-mediated proton transfer with c-ring rotation. Our cryo-EM models and simulations also rationalize a mechanism for inhibition of passive proton transport as observed for free V_o that is generated as a result of V-ATPase regulation by reversible disassembly in vivo.

Charge Transfer and Chemo-Mechanical Coupling in Respiratory Complex I

The mitochondrial respiratory chain, formed by five protein complexes, utilizes energy from catabolic processes to synthesize ATP. Complex I, the first and the largest protein complex of the chain, harvests electrons from NADH to reduce quinone, while pumping protons across the mitochondrial membrane. Detailed knowledge of the working principle of such coupled charge-transfer processes remains, however, fragmentary due to bottlenecks in understanding redox-driven conformational transitions and their interplay with the hydrated proton pathways. Complex I from Thermus thermophilus encases 16 subunits with nine iron-sulfur clusters, reduced by electrons from NADH. Here, employing the latest crystal structure of T. thermophilus complex I, we have used microsecond-scale molecular dynamics simulations to study the chemo-mechanical coupling between redox changes of the iron-sulfur clusters and conformational transitions across complex I. First, we identify the redox switches within complex I, which allosterically couple the dynamics of the quinone binding pocket to the site of NADH reduction. Second, our free-energy calculations reveal that the affinity of the quinone, specifically menaquinone, for the binding-site is higher than that of its reduced, menaquinol form-a design essential for menaquinol release. Remarkably, the barriers to diffusive menaquinone dynamics are lesser than that of the more ubiquitous ubiquinone, and the naphthoquinone headgroup of the former furnishes stronger binding interactions with the pocket, favoring menaquinone for charge transport in T. thermophilus. Our computations are consistent with experimentally validated mutations and hierarchize the key residues into three functional classes, identifying new mutation targets. Third, long-range hydrogen-bond networks connecting the quinone-binding site to the transmembrane subunits are found to be responsible for proton pumping. Put together, the simulations reveal the molecular design principles linking redox reactions to quinone turnover to proton translocation in complex I.

Multiscale modeling and cinematic visualization of photosynthetic energy conversion processes from electronic to cell scales

Conversion of sunlight into chemical energy, namely photosynthesis, is the primary energy source of life on Earth. A visualization depicting this process, based on multiscale computational models from electronic to cell scales, is presented in the form of an excerpt from the fulldome show Birth of Planet Earth. This accessible visual narrative shows a lay audience, including children, how the energy of sunlight is captured, converted, and stored through a chain of proteins to power living cells. The visualization is the result of a multi-year collaboration among biophysicists, visualization scientists, and artists, which, in turn, is based on a decade-long experimental-computational collaboration on structural and functional modeling that produced an atomic detail description of a bacterial bioenergetic organelle, the chromatophore. Software advancements necessitated by this project have led to significant performance and feature advances, including hardware-accelerated cinematic ray tracing and instanced visualizations for efficient cell-scale modeling. The energy conversion steps depicted feature an integration of function from electronic to cell levels, spanning nearly 12 orders of magnitude in time scales. This atomic detail description uniquely enables a modern retelling of one of humanity's earliest stories-the interplay between light and life.

Insights into directional movement in molecular machines from free-energy calculations

A rotaxane composed of a symmetrical axle containing three binding stations and a cone-like macrocycle containing two secondary amines has been investigated at the atomic level. At high pH, the macrocycle binds to the intermediate di(quaternary ammonium) site, while at low pH, the protonated macrocycle selectively moves along the axle to one of the two symmetrical phenyl triazole binding sites facing its upper rim, but does not shuttle backward. The determined free-energy profile characterizing the translocation of the macrocycle indicates that the selected binding site is energetically more favorable than the one facing the lower rim of the macrocycle and the free-energy barrier against translocation to the former site is lower than to the latter one, rationalizing the directional movement. This selectivity mainly stems from the asymmetry of the macrocycle shape. The strong electrostatic repulsion between the ring and the axle is found to constitute the driving force for the shuttling of the ring and also the resistance for its reverse motion. Moreover, the effect of the solvent on the shuttling has been examined, suggesting that increasing the solvent polarity may weaken the directional preference of shuttling, due to the shielding effect of polar solvents on electrostatic interactions. Our study provides a theoretical framework for tuning the selectivity of directional movement in molecular machines.

XFEL and NMR Structures of Francisella Lipoprotein Reveal Conformational Space of Drug Target against Tularemia

Francisella tularensis is the causative agent for the potentially fatal disease tularemia. The lipoprotein Flpp3 has been identified as a virulence determinant of tularemia with no sequence homology outside the Francisella genus. We report a room temperature structure of Flpp3 determined by serial femtosecond crystallography that exists in a significantly different conformation than previously described by the NMR-determined structure. Furthermore, we investigated the conformational space and energy barriers between these two structures by molecular dynamics umbrella sampling and identified three low-energy intermediate states, transitions between which readily occur at room temperature. We have also begun to investigate organic compounds in silico that may act as inhibitors to Flpp3. This work paves the road to developing targeted therapeutics against tularemia and aides in our understanding of the disease mechanisms of tularemia.

Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism

We report a 100-million atom-scale model of an entire cell organelle, a photosynthetic chromatophore vesicle from a purple bacterium, that reveals the cascade of energy conversion steps culminating in the generation of ATP from sunlight. Molecular dynamics simulations of this vesicle elucidate how the integral membrane complexes influence local curvature to tune photoexcitation of pigments. Brownian dynamics of small molecules within the chromatophore probe the mechanisms of directional charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore's structural integrity and robust energy conversion. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence molecular-scale insights into the mechanism of cellular aging are inferred. Together, our integrative method and spectroscopic experiments pave the way to first-principles modeling of whole living cells.

The Role of a Crystallographically Unresolved Cytoplasmic Loop in Stabilizing the Bacterial Membrane Insertase YidC2

YidC, a bacterial member of the YidC/Alb3/Oxa1 insertase family, mediates membrane protein assembly and insertion. Cytoplasmic loops are known to have functional significance in membrane proteins such as YidC. Employing microsecond-level molecular dynamics (MD) simulations, we show that the crystallographically unresolved C2 loop plays a crucial role in the structural dynamics of Bacillus halodurans YidC2. We have modeled the C2 loop and used all- atom MD simulations to investigate the structural dynamics of YidC2 in its apo form, both with and without the C2 loop. The C2 loop was found to stabilize the entire protein and particularly the C1 region. C2 was also found to stabilize the alpha-helical character of the C-terminal region. Interestingly, the highly polar or charged lipid head groups of the simulated membranes were found to interact with and stabilize the C2 loop. These findings demonstrate that the crystallographically unresolved loops of membrane proteins could be important for the stabilization of the protein despite the apparent lack of structure, which could be due to the absence of the relevant lipids to stabilize them in crystallographic conditions.

Dynamic Structural Differences between Human and Mouse STING Lead to Differing Sensitivity to DMXAA

The stimulator-of-interferon-genes (STING) protein is involved in innate immunity. It has recently been shown that modulation of STING can lead to an aggressive antitumor response. DMXAA is an antitumor agent that had shown great promise in murine models but failed in human clinical trials. The molecular target of DMXAA was subsequently shown to be murine STING (mSTING); however, human STING (hSTING) is insensitive to DMXAA. Molecular dynamics simulations were employed to investigate the differences between hSTING and mSTING that could influence DMXAA binding. An initial set of simulations was performed to investigate a single lid region mutation G230I in hSTING (corresponding residue in mSTING is an Ile), which rendered the protein sensitive to DMXAA. The simulations found that an Ile side chain was enough to form a steric barrier that prevents exit of DMXAA, whereas in WT hSTING, the Gly residue that lacks a side chain formed a porous lid region that allowed DMXAA to exit. A second set of molecular dynamics simulations compared the tendency of STING to be in an open-inactive conformation or a closed-active conformation. The results show that hSTING prefers to be in an open-inactive conformation even with cGAMP, the native ligand, bound. On the other hand, mSTING prefers a closed-active conformation even without a ligand bound. These results highlight the challenges in translating a mouse active STING compound into a human active compound, while also providing avenues to pursue for designing a small-molecule drug targeting human STING.

Rotational Mechanism Model of the Bacterial V1 Motor Based on Structural and Computational Analyses

V₁-ATPase exemplifies the ubiquitous rotary motor, in which a central shaft DF complex rotates inside a hexagonally arranged catalytic A₃B₃ complex, powered by the energy from ATP hydrolysis. We have recently reported a number of crystal structures of the Enterococcus hirae A₃B₃DF (V₁) complex corresponding to its nucleotide-bound intermediate states, namely the forms waiting for ATP hydrolysis (denoted as catalytic dwell), ATP binding (ATP-binding dwell), and ADP release (ADP-release dwell) along the rotatory catalytic cycle of ATPase. Furthermore, we have performed microsecond-scale molecular dynamics simulations and free-energy calculations to investigate the conformational transitions between these intermediate states and to probe the long-time dynamics of the molecular motor. In this article, the molecular structure and dynamics of the V₁-ATPase are reviewed to bring forth a unified model of the motor’s remarkable rotational mechanism.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Kinetics of Huperzine A Dissociation from Acetylcholinesterase via Multiple Unbinding Pathways

The dissociation of huperzine A (hupA) from Torpedo californica acetylcholinesterase ( TcAChE) was investigated by 4 μs unbiased and biased all-atom molecular dynamics (MD) simulations in explicit solvent. We performed our study using memetic sampling (MS) for the determination of reaction pathways (RPs), metadynamics to calculate free energy, and maximum-likelihood estimation (MLE) to recover kinetic rates from unbiased MD simulations. Our simulations suggest that the dissociation of hupA occurs mainly via two RPs: a front door along the axis of the active-site gorge (pwf) and through a new transient side door (pws), i.e., formed by the Ω-loop (residues 67-94 of TcAChE). An analysis of the inhibitor unbinding along the RPs suggests that pws is opened transiently after hupA and the Ω-loop reach a low free-energy transition state characterized by the orientation of the pyridone group of the inhibitor directed toward the Ω-loop plane. Unlike pws, pwf does not require large structural changes in TcAChE to be accessible. The estimated free energies and rates agree well with available experimental data. The dissociation rates along the unbinding pathways are similar, suggesting that the dissociation of hupA along pws is likely to be relevant. This indicates that perturbations to hupA- TcAChE interactions could potentially induce pathway hopping. In summary, our results characterize the slow-onset inhibition of TcAChE by hupA, which may provide the structural and energetic bases for the rational design of the next-generation slow-onset inhibitors with optimized pharmacokinetic properties for the treatment of Alzheimer's disease.

Elastic coupling power stroke mechanism of the F1-ATPase molecular motor

The angular velocity profile of the 120° F₁-ATPase power stroke was resolved as a function of temperature from 16.3 to 44.6 °C using a Δμ_ATP = -31.25 k_BT at a time resolution of 10 μs. Angular velocities during the first 60° of the power stroke (phase 1) varied inversely with temperature, resulting in negative activation energies with a parabolic dependence. This is direct evidence that phase 1 rotation derives from elastic energy (spring constant, κ = 50 k_BT·rad^-2). Phase 2 of the power stroke had an enthalpic component indicating that additional energy input occurred to enable the γ-subunit to overcome energy stored by the spring after rotating beyond its 34° equilibrium position. The correlation between the probability distribution of ATP binding to the empty catalytic site and the negative E_a values of the power stroke during phase 1 suggests that this additional energy is derived from the binding of ATP to the empty catalytic site. A second torsion spring (κ = 150 k_BT·rad^-2; equilibrium position, 90°) was also evident that mitigated the enthalpic cost of phase 2 rotation. The maximum ΔG^ǂ was 22.6 k_BT, and maximum efficiency was 72%. An elastic coupling mechanism is proposed that uses the coiled-coil domain of the γ-subunit rotor as a torsion spring during phase 1, and then as a crankshaft driven by ATP-binding-dependent conformational changes during phase 2 to drive the power stroke.

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.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm.

Alanine mutation of the catalytic sites of Pantothenate Synthetase causes distinct conformational changes in the ATP binding region

The enzyme Pantothenate synthetase (PS) represents a potential drug target in Mycobacterium tuberculosis. Its X-ray crystallographic structure has demonstrated the significance and importance of conserved active site residues including His44, His47, Asn69, Gln72, Lys160 and Gln164 in substrate binding and formation of pantoyl adenylate intermediate. In the current study, molecular mechanism of decreased affinity of the enzyme for ATP caused by alanine mutations was investigated using molecular dynamics (MD) simulations and free energy calculations. A total of seven systems including wild-type + ATP, H44A + ATP, H47A + ATP, N69A + ATP, Q72A + ATP, K160A + ATP and Q164A + ATP were subjected to 50 ns MD simulations. Docking score, MM-GBSA and interaction profile analysis showed weak interactions between ATP (substrate) and PS (enzyme) in H47A and H160A mutants as compared to wild-type, leading to reduced protein catalytic activity. However, principal component analysis (PCA) and free energy landscape (FEL) analysis revealed that ATP was strongly bound to the catalytic core of the wild-type, limiting its movement to form a stable complex as compared to mutants. The study will give insight about ATP binding to the PS at the atomic level and will facilitate in designing of non-reactive analogue of pantoyl adenylate which will act as a specific inhibitor for PS.

Multiscale molecular dynamics simulations of rotary motor proteins

Protein functions require specific structures frequently coupled with conformational changes. The scale of the structural dynamics of proteins spans from the atomic to the molecular level. Theoretically, all-atom molecular dynamics (MD) simulation is a powerful tool to investigate protein dynamics because the MD simulation is capable of capturing conformational changes obeying the intrinsically structural features. However, to study long-timescale dynamics, efficient sampling techniques and coarse-grained (CG) approaches coupled with all-atom MD simulations, termed multiscale MD simulations, are required to overcome the timescale limitation in all-atom MD simulations. Here, we review two examples of rotary motor proteins examined using free energy landscape (FEL) analysis and CG-MD simulations. In the FEL analysis, FEL is calculated as a function of reaction coordinates, and the long-timescale dynamics corresponding to conformational changes is described as transitions on the FEL surface. Another approach is the utilization of the CG model, in which the CG parameters are tuned using the fluctuation matching methodology with all-atom MD simulations. The long-timespan dynamics is then elucidated straightforwardly by using CG-MD simulations.

The FOF1 ATP synthase: from atomistic three-dimensional structure to the rotary-chemical function

Molecular motors are multi-subunit complexes that are indispensable for accomplishing various tasks of the living cells. One such molecular motor is the F_OF₁ ATP synthase that synthesizes ATP at the expense of the membrane proton gradient. Elucidating the molecular origin of the motor function is challenging despite significant advances in various experimental fields. Currently atomic simulations of whole motor complexes cannot reach to functionally relevant time scales that extend beyond the millisecond regime. Moreover, to reveal the underlying molecular origin of the function, one must model the coupled chemical and conformational events using physically and chemically meaningful multiscaling techniques. In this review, we discuss our approach to model the action of the F₁ and F_O molecular motors, where emphasis is laid on elucidating the molecular origin of the driving force that leads to directional rotation at the expense of ATP hydrolysis or proton gradients. We have used atomic structures of the motors and used hierarchical multiscaling techniques to generate low dimensional functional free energy surfaces of the complete mechano-chemical process. These free energy surfaces were studied further to calculate important characteristics of the motors, such as, rotational torque, temporal dynamics, occurrence of intermittent dwell states, etc. We also studied the result of mutating various parts of the motor domains and our observations correspond very well with the experimental findings. Overall, our studies have generated a cumulative understanding of the motor action, and especially highlight the crucial role of electrostatics in establishing the mechano-chemical coupling.

The lubricating role of water in the shuttling of rotaxanes

We have investigated at the atomic level amide-based rotaxanes set in motion in four different solvents, namely, ethyl ether, acetonitrile, ethanol and water. In three non-aqueous solvents, shuttling of the macrocycle between two binding sites separated by a free-energy barrier is coupled with a conformational change and rotation, driven primarily by hydrogen-bonding interactions. The mechanism that underlies the shuttling is completely altered when the non-aqueous solvent is replaced by water. In aqueous solution, hydrophobic interactions chiefly control shuttling of the rotaxane, leading to a sharp decrease of the free-energy barrier, thereby speeding up the process. The binding sites and the reaction pathway describing shuttling vary significantly in water compared with in the other three solvents. We found that the high polarity, the hydrogen-bond donor and acceptor ability, and the minimal steric hindrance of water conspire to modify the mechanism. These three physicochemical properties are also responsible for the lubrication by water. That water completely changes the mechanism underlying the shuttling of rotaxanes, is addressed for the first time in this study, and provides valuable guidelines for the de novo design of molecular machines.

Mechanochemical Energy Transduction during the Main Rotary Step in the Synthesis Cycle of F1-ATPase

F₁-ATPase is a highly efficient molecular motor that can synthesize ATP driven by a mechanical torque. Its ability to function reversibly in either direction requires tight mechanochemical coupling between the catalytic domain and the rotating central shaft, as well as temporal control of substrate binding and product release. Despite great efforts and significant progress, the molecular details of this synchronized and fine-tuned energy conversion mechanism are not fully understood. Here, we use extensive molecular dynamics simulations to reconcile recent single-molecule experiments with structural data and provide a consistent thermodynamic, kinetic and mechanistic description of the main rotary substep in the synthetic cycle of mammalian ATP synthase. The calculated free energy profiles capture a discrete pattern in the rotation of the central γ-shaft, with a metastable intermediate located-consistently with recent experimental findings-at 70° relative to the X-ray position. We identify this rotary step as the ATP-dependent substep, and find that the associated free energy input supports the mechanism involving concurrent nucleotide binding and release. During the main substep, our simulations show no significant opening of the ATP-bound β subunit; instead, we observe that mechanical energy is transmitted to its nucleotide binding site, thus lowering the affinity for ATP. Simultaneously, the empty subunit assumes a conformation that enables the enzyme to harness the free energy of ADP binding to drive ATP release. Finally, we show that ligand exchange is regulated by a checkpoint mechanism, an apparent prerequisite for high efficiency in protein nanomotors.