Insights into the molecular mechanism of rotation in the Fo sector of ATP synthase

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.

Keratan sulfate, an electrosensory neurosentient bioresponsive cell instructive glycosaminoglycan

The roles of keratan sulfate (KS) as a proton detection glycosaminoglycan in neurosensory processes in the central and peripheral nervous systems is reviewed. The functional properties of the KS-proteoglycans aggrecan, phosphacan, podocalyxcin as components of perineuronal nets in neurosensory processes in neuronal plasticity, cognitive learning and memory are also discussed. KS-glycoconjugate neurosensory gels used in electrolocation in elasmobranch fish species and KS substituted mucin like conjugates in some tissue contexts in mammals need to be considered in sensory signalling. Parallels are drawn between KS's roles in elasmobranch fish neurosensory processes and its roles in mammalian electro mechanical transduction of acoustic liquid displacement signals in the cochlea by the tectorial membrane and stereocilia of sensory inner and outer hair cells into neural signals for sound interpretation. The sophisticated structural and functional proteins which maintain the unique high precision physical properties of stereocilia in the detection, transmittance and interpretation of acoustic signals in the hearing process are important. The maintenance of the material properties of stereocilia are essential in sound transmission processes. Specific, emerging roles for low sulfation KS in sensory bioregulation are contrasted with the properties of high charge density KS isoforms. Some speculations are made on how the molecular and electrical properties of KS may be of potential application in futuristic nanoelectronic, memristor technology in advanced ultrafast computing devices with low energy requirements in nanomachines, nanobots or molecular switches which could be potentially useful in artificial synapse development. Application of KS in such innovative areas in bioregulation are eagerly awaited.

Mechanism of proton-powered c-ring rotation in a mitochondrial ATP synthase

Proton-powered c-ring rotation in mitochondrial ATP synthase is crucial to convert the transmembrane protonmotive force into torque to drive the synthesis of adenosine triphosphate (ATP). Capitalizing on recent cryo-EM structures, we aim at a structural and energetic understanding of how functional directional rotation is achieved. We performed multi-microsecond atomistic simulations to determine the free energy profiles along the c-ring rotation angle before and after the arrival of a new proton. Our results reveal that rotation proceeds by dynamic sliding of the ring over the a-subunit surface, during which interactions with conserved polar residues stabilize distinct intermediates. Ordered water chains line up for a Grotthuss-type proton transfer in one of these intermediates. After proton transfer, a high barrier prevents backward rotation and an overall drop in free energy favors forward rotation, ensuring the directionality of c-ring rotation required for the thermodynamically disfavored ATP synthesis. The essential arginine of the a-subunit stabilizes the rotated configuration through a salt bridge with the c-ring. Overall, we describe a complete mechanism for the rotation step of the ATP synthase rotor, thereby illuminating a process critical to all life at atomic resolution.

Coulombic Organization in Membrane-Embedded Rotary Motor of ATP Synthase

The electrochemical potential difference of protons across the membrane is used to synthesize ATP through the proton-motive rotatory motion of the membrane-embedded region of ATP synthase called F_o. In this study, we illuminate the unsolved proton-motive rotary mechanism of F_o on the basis of atomistic simulation with full description of protein, lipid, and water molecules, and highlight the underlying Coulombic design. We first show that a water channel is spontaneously formed at the interfacial region between the rotor (c-ring) and the stator (a-subunit). The observed water channel is a full channel penetrating the membrane, but a Coulomb barrier by a strictly conserved arginine of the a-subunit dominates at the midpoint of the full channel, preventing proton leakage. Our molecular dynamics simulation further demonstrates that the Coulomb attraction between the arginine and the essential glutamic acid of the c-subunit drives the c-ring rotation. We finally illustrate that the charge-state changes of the glutamic acids, enabled by the electrochemical potential difference of proton and the thermal motion, can produce unidirectional rotation of the c-ring.

Rotational Mechanism of FO Motor in the F-Type ATP Synthase Driven by the Proton Motive Force

In FOF1 ATP synthase, driven by the proton motive force across the membrane, the FO motor rotates the central rotor and induces conformational changes in the F1 motor, resulting in ATP synthesis. Recently, many near-atomic resolution structural models have been obtained using cryo-electron microscopy. Despite high resolution, however, static information alone cannot elucidate how and where the protons pass through the FO and how proton passage is coupled to FO rotation. Here, we review theoretical and computational studies based on FO structure models. All-atom molecular dynamics (MD) simulations elucidated changes in the protonation/deprotonation of glutamate—the protein-carrier residue—during rotation and revealed the protonation states that form the “water wire” required for long-range proton hopping. Coarse-grained MD simulations unveiled a free energy surface based on the protonation state and rotational angle of the rotor. Hybrid Monte Carlo and MD simulations showed how proton transfer is coupled to rotation.

Determinants of Directionality and Efficiency of the ATP Synthase Fo Motor at Atomic Resolution

F_o subcomplex of ATP synthase is a membrane-embedded rotary motor that converts proton motive force into mechanical energy. Despite a rapid increase in the number of high-resolution structures, the mechanism of tight coupling between proton transport and motion of the rotary c-ring remains elusive. Here, using extensive all-atom free energy simulations, we show how the motor's directionality naturally arises from the interplay between intraprotein interactions and energetics of protonation of the c-ring. Notably, our calculations reveal that the strictly conserved arginine in the a-subunit (R176) serves as a jack-of-all-trades: it dictates the direction of rotation, controls the protonation state of the proton-release site, and separates the two proton-access half-channels. Therefore, arginine is necessary to avoid slippage between the proton flux and the mechanical output and guarantees highly efficient energy conversion. We also provide mechanistic explanations for the reported defective mutations of R176, reconciling the structural information on the F_o motor with previous functional and single-molecule data.

Sequence and structure comparison of ATP synthase F0 subunits 6 and 8 in notothenioid fish

Mitochondrial changes such as tight coupling of the mitochondria have facilitated sustained oxygen and respiratory activity in haemoglobin-less icefish of the Channichthyidae family. We aimed to characterise features in the sequence and structure of the proteins directly involved in proton transport, which have potential physiological implications. ATP synthase subunit a (ATP6) and subunit 8 (ATP8) are proteins that function as part of the F0 component (proton pump) of the F0F1complex. Both proteins are encoded by the mitochondrial genome and involved in oxidative phosphorylation. To explore mitochondrial sequence variation for ATP6 and ATP8 we analysed sequences from C. gunnari and C. rastrospinosus and compared them with their closely related red-blooded species and eight other vertebrate species. Our comparison of the amino acid sequence of these proteins reveals important differences that could underlie aspects of the unique physiology of the icefish. In this study we find that changes in the sequence of subunit a of the icefish C. gunnari at position 35 where there is a hydrophobic alanine which is not seen in the other notothenioids we analysed. An amino acid change of this type is significant since it may have a structural impact. The biology of the haemoglobin-less icefish is necessarily unique and any insights about these animals will help to generate a better overall understanding of important physiological pathways.

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.

Cryo-EM structures provide insight into how E. coli F1Fo ATP synthase accommodates symmetry mismatch

F₁F_o ATP synthase functions as a biological rotary generator that makes a major contribution to cellular energy production. It comprises two molecular motors coupled together by a central and a peripheral stalk. Proton flow through the F_o motor generates rotation of the central stalk, inducing conformational changes in the F₁ motor that catalyzes ATP production. Here we present nine cryo-EM structures of E. coli ATP synthase to 3.1-3.4 Å resolution, in four discrete rotational sub-states, which provide a comprehensive structural model for this widely studied bacterial molecular machine. We observe torsional flexing of the entire complex and a rotational sub-step of F_o associated with long-range conformational changes that indicates how this flexibility accommodates the mismatch between the 3- and 10-fold symmetries of the F₁ and F_o motors. We also identify density likely corresponding to lipid molecules that may contribute to the rotor/stator interaction within the F_o motor.

Molecular dynamics simulation of proton-transfer coupled rotations in ATP synthase FO motor

The F_O motor in F_OF₁ ATP synthase rotates its rotor driven by the proton motive force. While earlier studies elucidated basic mechanisms therein, recent advances in high-resolution cryo-electron microscopy enabled to investigate proton-transfer coupled F_O rotary dynamics at structural details. Here, taking a hybrid Monte Carlo/molecular dynamics simulation method, we studied reversible dynamics of a yeast mitochondrial F_O. We obtained the 36°-stepwise rotations of F_O per one proton transfer in the ATP synthesis mode and the proton pumping in the ATP hydrolysis mode. In both modes, the most prominent path alternatively sampled states with two and three deprotonated glutamates in c-ring, by which the c-ring rotates one step. The free energy transduction efficiency in the model F_O motor reached ~ 90% in optimal conditions. Moreover, mutations in key glutamate and a highly conserved arginine increased proton leakage and markedly decreased the coupling, in harmony with previous experiments. This study provides a simple framework of simulations for chemical-reaction coupled molecular dynamics calling for further studies in ATP synthase and others.

Assembly of Spinach Chloroplast ATP Synthase Rotor Ring Protein-Lipid Complex

Rotor ATPases are large multisubunit membrane protein complexes found in all kingdoms of life. The membrane parts of these ATPases include a ring-like assembly, so-called c-ring, consisting of several subunits c, plugged by a patch of phospholipids. In this report, we use a nature-inspired approach to model the assembly of the spinach (Spinacia oleracea) c₁₄ ring protein-lipid complex, where partially assembled oligomers are pulled toward each other using a biasing potential. The resulting assemblies contain 23 to 26 encapsulated plug lipids, general position of which corresponds well to experimental maps. However, best fit to experimental data is achieved with 15 to 17 lipids inside the c-ring. In all of the simulations, the lipids from one leaflet (loop side of the c subunit) are ordered and static, whereas the lipids from the other leaflet are disordered and dynamic. Spontaneous permeation of water molecules toward Glu61 at the active site is also observed. The presented assembly approach is expected to be generalizable to other protein complexes with encapsulated lipid patches.

Revisiting the protomotive vectorial motion of F0-ATPase

The elucidation of the detailed mechanism used by F₀ to convert proton gradient to torque and rotational motion presents a major puzzle despite significant biophysical and structural progress. Although the conceptual model has advanced our understanding of the working principles of such systems, it is crucial to explore the actual mechanism using structure-based models that actually reproduce a unidirectional proton-driven rotation. Our previous work used a coarse-grained (CG) model to simulate the action of F₀ However, the simulations were based on a very tentative structural model of the interaction between subunit a and subunit c. Here, we again use a CG model but with a recent cryo-EM structure of cF₁F₀ and also explore the proton path using our water flooding and protein dipole Langevin dipole semimacroscopic formalism with its linear response approximation version (PDLD/S-LRA) approaches. The simulations are done in the combined space defined by the rotational coordinate and the proton transport coordinate. The study reproduced the effect of the protomotive force on the rotation of the F₀ while establishing the electrostatic origin of this effect. Our landscape reproduces the correct unidirectionality of the synthetic direction of the F₀ rotation and shows that it reflects the combined electrostatic coupling between the proton transport path and the c-ring conformational change. This work provides guidance for further studies in other proton-driven mechanochemical systems and should lead (when combined with studies of F₁) to a complete energy transduction picture of the F₀F₁-ATPase system.

Dielectric Properties of a Protein Probed by Reversal of a Buried Ion Pair

Thirty years ago, Hwang and Warshel suggested that a microenvironment preorganized to stabilize an ion pair would be incapable of reorganizing to stabilize the reverse ion pair. The implications were that (1) proteins have a limited capacity to reorganize, even under the influence of strong interactions, such as those present when ionizable groups are buried in the hydrophobic interior of a protein, and (2) the inability of proteins to tolerate the reversal of buried ion pairs demonstrates the limitations inherent to continuum electrostatic models of proteins. Previously we showed that when buried individually in the interior of staphylococcal nuclease, Glu23 and Lys36 have p K_a values near pH 7, but when buried simultaneously, they establish a strong interaction of ∼5 kcal/mol and have p K_a values shifted toward more normal values. Here, using equilibrium thermodynamic measurements, crystal structures, and NMR spectroscopy experiments, we show that although the reversed, individual substitutions-Lys23 and Glu36-also have p K_a values near 7, when buried together, they neither establish a strong interaction nor promote reorganization of their microenvironment. These experiments both confirm Warshel's original hypothesis and expand it by showing that it applies to reorganization, as demonstrated by our artificial ion pairs, as well as to preorganization as is commonly argued for motifs that stabilize naturally occurring ion pairs in polar microenvironments. These data constitute a challenging benchmark useful to test the ability of structure-based algorithms to reproduce the compensation between self-energy, Coulomb and polar interactions in hydrophobic environments of proteins.

Geometric somersaults of a polymer chain through cyclic twisting motions

This study explores the significance of geometric angle shifts, which we call geometric somersaults, arising from cyclic twisting motions of a polymer chain. A five-bead polymer chain serves as a concise and minimal model of a molecular shaft throughout this study. We first show that this polymer chain can change its orientation about its longitudinal axis largely, e.g., 120^{∘}, under conditions of zero total angular momentum by changing the two dihedral angles in a cyclic manner. This phenomenon is an example of the so-called "falling cat" phenomenon, where a falling cat undergoes a geometric somersault by changing its body shape under conditions of zero total angular momentum. We then extend the geometric somersault of the polymer chain to a noisy and viscous environment, where the polymer chain is steered by external driving forces. This extension shows that the polymer chain can achieve an orientation change keeping its total angular momentum and total external torque fluctuating around zero in a noisy and viscous environment. As an application, we argue that the geometric somersault of the polymer chain by 120^{∘} may serve as a prototypical and coarse-grained model for the rotary motion of the central shaft of ATP synthase (F_{O}F_{1}-ATPase). This geometric somersault is in clear contrast to the standard picture for the rotary motion of the central shaft as a rigid body, which generally incurs nonzero total angular momentum and nonzero total external torque. The power profile of the geometric somersault implies a preliminary mechanism for elastic power transmission. The results of this study may be of fundamental interest in twisting and rotary motions of biomolecules.

Cryo-EM structures of the autoinhibited E. coli ATP synthase in three rotational states

A molecular model that provides a framework for interpreting the wealth of functional information obtained on the E. coli F-ATP synthase has been generated using cryo-electron microscopy. Three different states that relate to rotation of the enzyme were observed, with the central stalk’s ε subunit in an extended autoinhibitory conformation in all three states. The F_o motor comprises of seven transmembrane helices and a decameric c-ring and invaginations on either side of the membrane indicate the entry and exit channels for protons. The proton translocating subunit contains near parallel helices inclined by ~30° to the membrane, a feature now synonymous with rotary ATPases. For the first time in this rotary ATPase subtype, the peripheral stalk is resolved over its entire length of the complex, revealing the F₁ attachment points and a coiled-coil that bifurcates toward the membrane with its helices separating to embrace subunit a from two sides.

DOI:http://dx.doi.org/10.7554/eLife.21598.001

ATP synthase is a biological motor that produces a molecule called adenosine tri-phosphate (ATP for short), which acts as the major store of chemical energy in cells. A single molecule of ATP contains three phosphate groups: the cell can remove one of these phosphates to make a molecule called adenosine di-phosphate (ADP) and release energy to drive a variety of biological processes.

ATP synthase sits in the membranes that separate cell compartments or form barriers around cells. When cells break down food they transport hydrogen ions across these membranes so that each side of the membrane has a different level (or “concentration”) of hydrogen ions. Movement of hydrogen ions from an area with a high concentration to a low concentration causes ATP synthase to rotate like a turbine. This rotation of the enzyme results in ATP synthase adding a phosphate group to ADP to make a new molecule of ATP. In certain conditions cells need to switch off the ATP synthase and this is done by changing the shape of the central shaft in a process called autoinhibition, which blocks the rotation.

The ATP synthase from a bacterium known as E. coli – which is commonly found in the human gut –has been used as a model to study how this biological motor works. However, since the precise details of the three-dimensional structure of ATP synthase have remained unclear it has been difficult to interpret the results of these studies.

Sobti et al. used a technique called Cryo-electron microscopy to investigate the structure of ATP synthase from E. coli. This made it possible to develop a three-dimensional model of the ATP synthase in its autoinhibited form. The structural data could also be split into three distinct shapes that relate to dwell points in the rotation of the motor where the rotation has been inhibited. These models further our understanding of ATP synthases and provide a template to understand the findings of previous studies.

Further work will be needed to understand this essential biological process at the atomic level in both its inhibited and uninhibited form. This will reveal the inner workings of a marvel of the natural world and may also lead to the discovery of new antibiotics against related bacteria that cause diseases in humans.

DOI:http://dx.doi.org/10.7554/eLife.21598.002

Predicted Structures of the Proton-Bound Membrane-Embedded Rotor Rings of the Saccharomyces cerevisiae and Escherichia coli ATP Synthases

Recent years have witnessed a renewed interest in the ATP synthase as a drug target against human pathogens. Indeed, clinical, biochemical, and structural data indicate that hydrophobic inhibitors targeting the membrane-embedded proton-binding sites of the c-subunit ring could serve as last-resort antibiotics against multidrug resistant strains. However, because inhibition of the mitochondrial ATP synthase in humans is lethal, it is essential that these inhibitors be not only potent but also highly selective for the bacterial enzyme. To this end, a detailed understanding of the structure of this protein target is arguably instrumental. Here, we use computational methods to predict the atomic structures of the proton-binding sites in two prototypical c-rings: that of the ATP synthase from Saccharomyces cerevisiae, which is a model system for mitochondrial enzymes, and that from Escherichia coli, which can be pathogenic for humans. Our study reveals the structure of these binding sites loaded with protons and in the context of the membrane, that is, in the state that would mediate the recognition of a potential inhibitor. Both structures reflect a mode of proton coordination unlike those previously observed in other c-ring structures, whether experimental or modeled.

Ultrafast proton transport in sub-1-nm diameter carbon nanotube porins

Proton transport plays an important role in many biological processes due to the ability of protons to rapidly translocate along chains of hydrogen-bonded water molecules. Molecular dynamics simulations have predicted that confinement in hydrophobic nanochannels should enhance the rate of proton transport. Here, we show that 0.8-nm-diameter carbon nanotube porins, which promote the formation of one-dimensional water wires, can support proton transport rates exceeding those of bulk water by an order of magnitude. The transport rates in these narrow nanotube pores also exceed those of biological channels and Nafion. With larger 1.5-nm-diameter nanotube porins, proton transport rates comparable to bulk water are observed. We also show that the proton conductance of these channels can be modulated by the presence of Ca(2+) ions. Our results illustrate the potential of small-diameter carbon nanotube porins as a proton conductor material and suggest that strong spatial confinement is a key factor in enabling efficient proton transport.

The Phylogenetic Signature Underlying ATP Synthase c-Ring Compliance

The proton-driven ATP synthase (FOF1) is comprised of two rotary, stepping motors (FO and F1) coupled by an elastic power transmission. The elastic compliance resides in the rotor module that includes the membrane-embedded FO c-ring. Proton transport by FO is firmly coupled to the rotation of the c-ring relative to other FO subunits (ab2). It drives ATP synthesis. We used a computational method to investigate the contribution of the c-ring to the total elastic compliance. We performed principal component analysis of conformational ensembles built using distance constraints from the bovine mitochondrial c-ring x-ray structure. Angular rotary twist, the dominant ring motion, was estimated to show that the c-ring accounted in part for the measured compliance. Ring rotation was entrained to rotation of the external helix within each hairpin-shaped c-subunit in the ring. Ensembles of monomer and dimers extracted from complete c-rings showed that the coupling between collective ring and the individual subunit motions was independent of the size of the c-ring, which varies between organisms. Molecular determinants were identified by covariance analysis of residue coevolution and structural-alphabet-based local dynamics correlations. The residue coevolution gave a readout of subunit architecture. The dynamic couplings revealed that the hinge for both ring and subunit helix rotations was constructed from the proton-binding site and the adjacent glycine motif (IB-GGGG) in the midmembrane plane. IB-GGGG motifs were linked by long-range couplings across the ring, while intrasubunit couplings connected the motif to the conserved cytoplasmic loop and adjacent segments. The correlation with principal collective motions shows that the couplings underlie both ring rotary and bending motions. Noncontact couplings between IB-GGGG motifs matched the coevolution signal as well as contact couplings. The residue coevolution reflects the physiological importance of the dynamics that may link proton transfer to ring compliance.

Molecular Dynamics Simulation of DNA Capture and Transport in Heated Nanopores

The integration of local heat sources with solid-state nanopores offers new means for controlling the transmembrane transport of charged biomacromolecules. In the case of electrophoretic transport of DNA, recent experimental studies revealed unexpected temperature dependences of the DNA capture rate, the DNA translocation velocity, and the ionic current blockades produced by the presence of DNA in the nanopore. Here, we report the results of all-atom molecular dynamics simulations that elucidated the effect of temperature on the key microscopic processes governing electric field-driven transport of DNA through nanopores. Mimicking the experimental setup, we simulated the capture and subsequent translocation of short DNA duplexes through a locally heated nanopore at several temperatures and electrolyte conditions. The temperature dependence of ion mobility at the DNA surface was found to cause the dependence of the relative conductance blockades on temperature. To the first order, the effective force on DNA in the nanopore was found to be independent of temperature, despite a considerable reduction of solution viscosity. The temperature dependence of the solution viscosity was found to make DNA translocations faster for a uniformly heated system but not in the case of local heating that does not affect viscosity of solution surrounding the untranslocated part of the molecule. Increasing solution temperature was also found to reduce the lifetime of bonds formed between cations and DNA. Using a flow suppression algorithm, we were able to separate the effects of electro-osmotic flow and direct ion binding, finding the reduced durations of DNA-ion bonds to increase, albeit weakly, the effective force experienced by DNA in an electric field. Unexpectedly, our simulations revealed a considerable temperature dependence of solvent velocity at the DNA surface-slip velocity, an effect that can alter hydrodynamic coupling between the motion of DNA and the surrounding fluid.

Effect of a buried ion pair in the hydrophobic core of a protein: An insight from constant pH molecular dynamics study

Constant pH molecular dynamics (CpHMD) is a commonly used sampling method, which incorporates the coupling of conformational flexibility and protonation state of a protein during the simulation by using pH as an external parameter. The effects on the structure and stability of a hyperstable variant of staphylococcal nuclease (Δ+PHS) protein of an artificial charge pair buried in its hydrophobic core are investigated by applying both CpHMD and accelerated molecular dynamics coupled with constant pH (CpHaMD) methods. Generalized Born electrostatics is used to model the solvent water. Two sets of starting coordinates of V23E/L36K variant of Δ+PHS, namely, Maestro generated coordinates from Δ+PHS and crystal structure coordinates of the same are considered for detail investigations. On the basis of root mean square displacement (RMSD) and root mean square fluctuations (RMSF) calculations, it is observed that this variant is stable over a wide range of pH. The calculated pKa values for aspartate and glutamate residues based on both CpHMD and CpHaMD simulations are consistent with the reported experimental values (within ± 0.5 to ± 1.5 pH unit), which clearly indicates that the local chemical environment of the carboxylic acids in V23E/L36K variant are comparable to the parent form. The strong salt bridge interaction between the mutated pair, E23/K36 and additional hydrogen bonds formed in the V23E/L36K variant, may help to compensate for the unfavorable self-energy experienced by the burial of these residues in the hydrophobic core. However, from RMSD, RMSF, and pKa analysis, no significant change in the global conformation of V23E/L36K variant with respect to the parent form, Δ+PHS is noticed.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

Resolution Exchange Simulation with Incremental Coarsening

We previously developed an algorithm, called "resolution exchange", which improves canonical sampling of atomic resolution models by swapping conformations between high- and low-resolution simulations. Here, we demonstrate a generally applicable incremental coarsening procedure and apply the algorithm to a larger peptide, met-enkephalin. In addition, we demonstrate a combination of resolution and temperature exchange, in which the coarser simulations are also at elevated temperatures. Both simulations are implemented in a "top-down" mode, to allow efficient allocation of CPU time among the different replicas.

ATP Synthesis by Oxidative Phosphorylation

The F1F0-ATP synthase (EC 3.6.1.34) is a remarkable enzyme that functions as a rotary motor. It is found in the inner membranes of Escherichia coli and is responsible for the synthesis of ATP in response to an electrochemical proton gradient. Under some conditions, the enzyme functions reversibly and uses the energy of ATP hydrolysis to generate the gradient. The ATP synthase is composed of eight different polypeptide subunits in a stoichiometry of α3β3γδεab2c10. Traditionally they were divided into two physically separable units: an F1 that catalyzes ATP hydrolysis (α3β3γδε) and a membrane-bound F0 sector that transports protons (ab2c10). In terms of rotary function, the subunits can be divided into rotor subunits (γεc10) and stator subunits (α3β3δab2). The stator subunits include six nucleotide binding sites, three catalytic and three noncatalytic, formed primarily by the β and α subunits, respectively. The stator also includes a peripheral stalk composed of δ and b subunits, and part of the proton channel in subunit a. Among the rotor subunits, the c subunits form a ring in the membrane, and interact with subunit a to form the proton channel. Subunits γ and ε bind to the c-ring subunits, and also communicate with the catalytic sites through interactions with α and β subunits. The eight subunits are expressed from a single operon, and posttranscriptional processing and translational regulation ensure that the polypeptides are made at the proper stoichiometry. Recent studies, including those of other species, have elucidated many structural and rotary properties of this enzyme.

ATP synthase

Oxygenic photosynthesis is the principal converter of sunlight into chemical energy. Cyanobacteria and plants provide aerobic life with oxygen, food, fuel, fibers, and platform chemicals. Four multisubunit membrane proteins are involved: photosystem I (PSI), photosystem II (PSII), cytochrome b6f (cyt b6f), and ATP synthase (FOF1). ATP synthase is likewise a key enzyme of cell respiration. Over three billion years, the basic machinery of oxygenic photosynthesis and respiration has been perfected to minimize wasteful reactions. The proton-driven ATP synthase is embedded in a proton tight-coupling membrane. It is composed of two rotary motors/generators, FO and F1, which do not slip against each other. The proton-driven FO and the ATP-synthesizing F1 are coupled via elastic torque transmission. Elastic transmission decouples the two motors in kinetic detail but keeps them perfectly coupled in thermodynamic equilibrium and (time-averaged) under steady turnover. Elastic transmission enables operation with different gear ratios in different organisms.

Fo-driven Rotation in the ATP Synthase Direction against the Force of F1 ATPase in the FoF1 ATP Synthase

Living organisms rely on the FoF1 ATP synthase to maintain the non-equilibrium chemical gradient of ATP to ADP and phosphate that provides the primary energy source for cellular processes. How the Fo motor uses a transmembrane electrochemical ion gradient to create clockwise torque that overcomes F1 ATPase-driven counterclockwise torque at high ATP is a major unresolved question. Using single FoF1 molecules embedded in lipid bilayer nanodiscs, we now report the observation of Fo-dependent rotation of the c10 ring in the ATP synthase (clockwise) direction against the counterclockwise force of ATPase-driven rotation that occurs upon formation of a leash with Fo stator subunit a. Mutational studies indicate that the leash is important for ATP synthase activity and support a mechanism in which residues aGlu-196 and cArg-50 participate in the cytoplasmic proton half-channel to promote leash formation.

Constant pH molecular dynamics study on the doubly mutated staphylococcal nuclease: capturing the microenvironment

Small rearrangements of residues in the microenvironment of V23E/L36K variant of staphylococcal nuclease can effectively be captured by CpHMD method.

S. AK, Meena G, Sethi KP, Sharma R, Trivedi P, Khan SR, Verma AS, Singh S, Sharma S, Roy KK, Kant R, Krishnan MY, Singh BN, Sinha S, Chaturvedi V, Saxena AK, Dikshit DK. Synthesis and anti-tubercular activity of conformationally-constrained and bisquinoline analogs of TMC207

Conformationally-constrained and bisquinoline analogs of TMC207 as antitubercular agents.

Experimental and theoretical investigations on temperature modulated translocation of IgG molecules through nanopore arrays

In this work, the temperature modulated translocation of IgG molecules through nanopore arrays has been investigated. Our results show that the IgG concentration corresponding to the maximum influence on the modulated ionic current by the physical place-holding effect shifts to a higher value with the system temperature rising.

Molecular interactions and residues involved in force generation in the T4 viral DNA packaging motor

Many viruses utilize molecular motors to package their genomes into preformed capsids. A striking feature of these motors is their ability to generate large forces to drive DNA translocation against entropic, electrostatic, and bending forces resisting DNA confinement. A model based on recently resolved structures of the bacteriophage T4 motor protein gp17 suggests that this motor generates large forces by undergoing a conformational change from an extended to a compact state. This transition is proposed to be driven by electrostatic interactions between complementarily charged residues across the interface between the N- and C-terminal domains of gp17. Here we use atomistic molecular dynamics simulations to investigate in detail the molecular interactions and residues involved in such a compaction transition of gp17. We find that although electrostatic interactions between charged residues contribute significantly to the overall free energy change of compaction, interactions mediated by the uncharged residues are equally if not more important. We identify five charged residues and six uncharged residues at the interface that play a dominant role in the compaction transition and also reveal salt bridging, van der Waals, and solvent hydrogen-bonding interactions mediated by these residues in stabilizing the compact form of gp17. The formation of a salt bridge between Glu309 and Arg494 is found to be particularly crucial, consistent with experiments showing complete abrogation in packaging upon Glu309Lys mutation. The computed contributions of several other residues are also found to correlate well with single-molecule measurements of impairments in DNA translocation activity caused by site-directed mutations.

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

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

A "nano-windmill" driven by a flux of water vapour: a comparison to the rotating ATPase

We measure the frequency of collective molecular precession as a function of temperature in the ferroelectric liquid crystalline monolayer at the water-air interface. This movement is driven by the unidirectional flux of evaporating water molecules. The collective rotation in the monolayer with angular velocities ω ~ 1 s(-1) (at T = 312 K) to 10(-2) s(-1) (at T = 285.8 K) is 9 to 14 orders of magnitude slower than rotation of a single molecule (typically ω ~ 10(9) to 10(12) s(-1)). The angular velocity reaches 0 upon approach to the two dimensional liquid-to-solid transition in the monolayer at T = 285.8 K. We estimate the rotational viscosity, γ1, in the monolayer and the torque, Γ, driving this rotation. The torque per molecule equals Γ = 5.7 × 10(-8) pN nm at 310 K (γ1 = 0.081 Pa s, ω = 0.87 s(-1)). The energy generated during one turn of the molecule at the same temperature is W = 3.5 × 10(-28) J. Surprisingly, although this energy is 7 orders of magnitude smaller than the thermal energy, kBT (310 K) = 4.3 × 10(-21) J, the rotation is very stable. The potential of the studied effect lies in the collective motion of many (>10(12)) "nano-windmills" acting "in concerto" at the scale of millimetres. Therefore, such systems are candidates for construction of artificial molecular engines, despite the small energy density per molecular volume (5 orders of magnitude smaller than for a single ATPase).

Energy transfer in a molecular motor in the Kramers regime

We present a theoretical treatment of energy transfer in a molecular motor described in terms of overdamped Brownian motion on a multidimensional tilted periodic potential. The tilt represents a thermodynamic force driving the system out of equilibrium and, for nonseparable potentials, energy transfer occurs between degrees of freedom. For deep potential wells, the continuous theory transforms to a discrete master equation that is tractable analytically. We use this master equation to derive formal expressions for the hopping rates, drift and diffusion, and the efficiency and rate of energy transfer in terms of the thermodynamic force. These results span both strong and weak coupling between degrees of freedom, describe the near and far from equilibrium regimes, and are consistent with generalized detailed balance and the Onsager relations. We thereby derive a number of diverse results for molecular motors within a single theoretical framework.

Theoretical study of a molecular turbine

We present an analytic and stochastic simulation study of a molecular engine working with a flux of particles as a turbine. We focus on the physical observables of velocity, flux, power, and efficiency. The control parameters are the external conservative force and the particle densities. We revise a simpler previous study by using a more realistic model containing multiple equidistant vanes complemented by stochastic simulations of the particles and the turbine. Here we show that the effect of the thermal fluctuations into the flux and the efficiency of these nanometric devices are relevant to the working scale of the system. The stochastic simulations of the Brownian motion of the particles and turbine support the simplified analytical calculations performed.

Electric field driven torque in ATP synthase

F_O-ATP synthase (F_O) is a rotary motor that converts potential energy from ions, usually protons, moving from high- to low-potential sides of a membrane into torque and rotary motion. Here we propose a mechanism whereby electric fields emanating from the proton entry and exit channels act on asymmetric charge distributions in the c-ring, due to protonated and deprotonated sites, and drive it to rotate. The model predicts a scaling between time-averaged torque and proton motive force, which can be hindered by mutations that adversely affect the channels. The torque created by the c-ring of F_O drives the γ-subunit to rotate within the ATP-producing complex (F₁) overcoming, with the aid of thermal fluctuations, an opposing torque that rises and falls with angular position. Using the analogy with thermal Brownian motion of a particle in a tilted washboard potential, we compute ATP production rates vs. proton motive force. The latter shows a minimum, needed to drive ATP production, which scales inversely with the number of proton binding sites on the c-ring.

Combined mathematical methods in the description of the F(o)F(1)-ATP synthase catalytic cycle

The FoF1-ATP synthase is one of the key enzymes in supplying energy production in almost all living systems. In this paper, we provide a theoretical description of its catalytic cycle using combined mathematical methods. These methods include Langevin dynamics for the rotation of the central protein core and the Monte-Carlo method to model nucleotide and proton binding. This model is the first in which ATP synthesis and hydrolysis can occur depending on the nucleotide concentration and system conditions. The main advantage of the presented model is the possibility of obtaining results for both single-molecular protein-machines and large ensembles of proteins. The calculated rates are close to the experimentally measured rates for a single enzyme. The model has been formalised as a computer simulation that allows researchers to evaluate ATP production in different types of living cells.

Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase

The molecular origin of the action of the F(0) proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challenging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F(0)-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunit-a. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems.

BROMOC-D: Brownian Dynamics/Monte-Carlo Program Suite to Study Ion and DNA Permeation in Nanopores

A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion-ion and ion-DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)(n) and ss-poly(dC)(n). The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.

A rotary nano ion pump: a molecular dynamics study

The dynamics of a rotary nano ion pump, inspired by the F (0) part of the F(0)F(1)-ATP synthase biomolecular motor, were investigated. This nanopump is composed of a rotor, which is constructed of two carbon nanotubes with benzene rings, and a stator, which is made of six graphene sheets. The molecular dynamics (MD) method was used to simulate the dynamics of the ion nanopump. When the rotor of the nanopump rotates mechanically, an ion gradient will be generated between the two sides of the nanopump. It is shown that the ion gradient generated by the nanopump is dependant on parameters such as the rotary frequency of the rotor, temperature and the amounts and locations of the positive and negative charges of the stator part of the nanopump. Also, an electrical potential difference is generated between the two sides of the pump as a result of its operation.

Diarylquinolines, synthesis pathways and quantitative structure--activity relationship studies leading to the discovery of TMC207

The emergence of multidrug-resistant strains of Mycobacterium tuberculosis and resistance to current anti-TB drugs call for the discovery and development of new effective anti-TB drugs. TMC207 is the lead candidate of a novel class of antimycobacterial agents, the diarylquinolines, which specifically inhibit mycobacterial ATP synthase and displays high activity against both drug-susceptible and multidrug-resistant strains of Mycobacterium tuberculosis. This article covers both synthesis pathways as well as qualitative and quantitative analyses of the structure-activity relationships of the diarylquinoline series on Mycobacterium smegmatis activity.

Uptake and translocation mechanisms of cationic amino derivatives functionalized on pristine C60 by lipid membranes: a molecular dynamics simulation study

Bioactive molecules, cationic peptides among them, are nowadays well-recognized in modern pharmacology for their drug potential. However, they usually suffer from poor translocation across cell membranes, and specific drug carriers should be designed to circumvent this problem. In the present study, the uptake mechanism of fullerene bearing cationic ammonium groups by membranes modeled as lipid bilayers is investigated using extensive molecular dynamics simulations and free-energy calculations. Three main results issued from this work can be drawn. First, the fullerene core appears to be a good drug vector since it greatly enhances the uptake of the cationic groups by the membrane. Second, we show that the amino derivatives should be deprotonated at the lipid headgroup level in order to fully translocate the membrane by passive diffusion. Finally, the fullerenes bearing too many cationic groups display mostly a hydrophilic character; thus, the lipophilic fullerene core is not anymore effective as an insertion enhancer. Therefore, the lipid bilayer appears to be very selective with respect to the amount of amino groups conjugated with C(60).

Torsional elasticity and energetics of F1-ATPase

F(o)F(1)-ATPase is a rotary motor protein synthesizing ATP from ADP driven by a cross-membrane proton gradient. The proton flow through the membrane-embedded F(o) generates the rotary torque that drives the rotation of the asymmetric shaft of F(1). Mechanical energy of the rotating shaft is used by the F(1) catalytic subunit to synthesize ATP. It was suggested that elastic power transmission with transient storage of energy in some compliant part of the shaft is required for the observed high turnover rate. We used atomistic simulations to study the spatial distribution and structural determinants of the F(1) torsional elasticity at the molecular level and to comprehensively characterize the elastic properties of F(1)-ATPase. Our fluctuation analysis revealed an unexpected heterogeneity of the F(1) shaft elasticity. Further, we found that the measured overall torsional moduli of the shaft arise from two distinct contributions, the intrinsic elasticity and the effective potential imposed on the shaft by the catalytic subunit. Separation of these two contributions provided a quantitative description of the coupling between the rotor and the catalytic subunit. This description enabled us to propose a minimal quantitative model of the F(1) energetics along the rotary degrees of freedom near the resting state observed in the crystal structures. As opposed to the usually employed models where the motor mechanical progression is described by a single angular variable, our multidimensional treatment incorporates the spatially inhomogeneous nature of the shaft and its interactions with the stator and offers new insight into the mechanoenzymatics of F(1)-ATPase.

Keep It Flexible: Driving Macromolecular Rotary Motions in Atomistic Simulations with GROMACS

We describe a versatile method to enforce the rotation of subsets of atoms, e.g., a protein subunit, in molecular dynamics (MD) simulations. In particular, we introduce a "flexible axis" technique that allows realistic flexible adaptions of both the rotary subunit as well as the local rotation axis during the simulation. A variety of useful rotation potentials were implemented for the GROMACS 4.5 MD package. Application to the molecular motor F(1)-ATP synthase demonstrates the advantages of the flexible axis approach over the established fixed axis rotation technique.

Modeling nanopores for sequencing DNA

Using nanopores to sequence DNA rapidly and at a low cost has the potential to radically transform the field of genomic research. However, despite all the exciting developments in the field, sequencing DNA using a nanopore has yet to be demonstrated. Among the many problems that hinder development of the nanopore sequencing methods is the inability of current experimental techniques to visualize DNA conformations in a nanopore and directly relate the microscopic state of the system to the measured signal. We have recently shown that such tasks could be accomplished through computation. This chapter provides step-by-step instructions of how to build atomic scale models of biological and solid-state nanopore systems, use the molecular dynamics method to simulate the electric field-driven transport of ions and DNA through the nanopores, and analyze the results of such computational experiments.

The ATP synthase a-subunit of extreme alkaliphiles is a distinct variant: mutations in the critical alkaliphile-specific residue Lys-180 and other residues that support alkaliphile oxidative phosphorylation

A lysine residue in the putative proton uptake pathway of the ATP synthase a-subunit is found only in alkaliphilic Bacillus species and is proposed to play roles in proton capture, retention and passage to the synthase rotor. Here, Lys-180 was replaced with alanine (Ala), glycine (Gly), cysteine (Cys), arginine (Arg), or histidine (His) in the chromosome of alkaliphilic Bacillus pseudofirmus OF4. All mutants exhibited octylglucoside-stimulated ATPase activity and β-subunit levels at least as high as wild-type. Purified mutant F(1)F(0)-ATP synthases all contained substantial a-subunit levels. The mutants exhibited diverse patterns of native (no octylglucoside) ATPase activity and a range of defects in malate growth and in vitro ATP synthesis at pH 10.5. ATP synthesis by the Ala, Gly, and His mutants was also impaired at pH 7.5 in the presence of a protonophoric uncoupler. Thus Lys-180 plays a role when the protonmotive force is reduced at near neutral, not just at high pH. The Arg mutant exhibited no ATP synthesis activity in the alkaliphile setting although activity was reported for a K180R mutant of a thermoalkaliphile synthase (McMillan, D. G., Keis, S., Dimroth, P., and Cook, G. M. (2007) J. Biol. Chem. 282, 17395-17404). The hypothesis that a-subunits from extreme alkaliphiles and the thermoalkaliphile represent distinct variants was supported by demonstration of the importance of additional alkaliphile-specific a-subunit residues, not found in the thermoalkaliphile, for malate growth of B. pseudofirmus OF4. Finally, a mutant B. pseudofirmus OF4 synthase with switched positions of Lys-180 (helix 4) and Gly-212 (helix 5) retained significant coupled synthase activity accompanied by proton leakiness.

Essential arginine residue of the F(o)-a subunit in F(o)F(1)-ATP synthase has a role to prevent the proton shortcut without c-ring rotation in the F(o) proton channel

In F(o)F(1) (F(o)F(1)-ATP synthase), proton translocation through F(o) drives rotation of the oligomer ring of F(o)-c subunits (c-ring) relative to F(o)-a. Previous reports have indicated that a conserved arginine residue in F(o)-a plays a critical role in the proton transfer at the F(o)-a/c-ring interface. Indeed, we show in the present study that thermophilic F(o)F(1s) with substitution of this arginine (aR169) to other residues cannot catalyse proton-coupled reactions. However, mutants with substitution of this arginine residue by a small (glycine, alanine, valine) or acidic (glutamate) residue mediate the passive proton translocation. This translocation requires an essential carboxy group of F(o)-c (cE56) since the second mutation (cE56Q) blocks the translocation. Rotation of the c-ring is not necessary because the same arginine mutants of the 'rotation-impossible' (c(10)-a)F(o)F(1), in which the c-ring and F(o)-a are fused to a single polypeptide, also exhibits the passive proton translocation. The mutant (aR169G/Q217R), in which the arginine residue is transferred to putatively the same topological position in the F(o)-a structure, can block the passive proton translocation. Thus the conserved arginine residue in F(o)-a ensures proton-coupled c-ring rotation by preventing a futile proton shortcut.