Conformational free-energy landscapes of a Na+/Ca2+ exchanger explain its alternating-access mechanism and functional specificity.

Secondary-active transporters catalyze the movement of myriad substances across all cellular membranes, typically against opposing concentration gradients, and without consuming any ATP. To do so, these proteins employ an intriguing structural mechanism evolved to be activated only upon recognition or release of the transported species. We examine this self-regulated mechanism using a homolog of the cardiac Na+/Ca2+ exchanger as a model system. Using advanced computer simulations, we map out the complete functional cycle of this transporter, including unknown conformations that we validate against existing experimental data. Calculated free-energy landscapes reveal why this transporter functions as an antiporter rather than a symporter, why it specifically exchanges Na+ and Ca2+, and why the stoichiometry of this exchange is exactly 3:1. We also rationalize why the protein does not exchange H+ for either Ca2+ or Na+, despite being able to bind H+ and its high similarity with H+/Ca2+ exchangers. Interestingly, the nature of this transporter is not explained by its primary structural states, known as inward- and outward-open conformations; instead, the defining factor is the feasibility of conformational intermediates between those states, wherein access pathways leading to the substrate binding sites become simultaneously occluded from both sides of the membrane. This analysis offers a physically coherent, broadly transferable route to understand the emergence of function from structure among secondary-active membrane transporters.

Conformational free-energy landscapes of a Na+/Ca2+ exchanger explain its alternating-access mechanism and functional specificity.

Secondary-active transporters catalyze the movement of myriad substances across all cellular membranes, typically against opposing concentration gradients, and without consuming any ATP. To do so, these proteins employ an intriguing structural mechanism evolved to be activated only upon recognition or release of the transported species. We examine this self-regulated mechanism using a homolog of the cardiac Na+/Ca2+ exchanger as a model system. Using advanced computer simulations, we map out the complete functional cycle of this transporter, including unknown conformations that we validate against existing experimental data. Calculated free-energy landscapes reveal why this transporter functions as an antiporter rather than a symporter, why it specifically exchanges Na+ and Ca2+, and why the stoichiometry of this exchange is exactly 3:1. We also rationalize why the protein does not exchange H+ for either Ca2+ or Na+, despite being able to bind H+ and its high similarity with H+/Ca2+ exchangers. Interestingly, the nature of this transporter is not explained by its primary structural states, known as inward- and outward-open conformations; instead, the defining factor is the feasibility of conformational intermediates between those states, wherein access pathways leading to the substrate binding sites become simultaneously occluded from both sides of the membrane. This analysis offers a physically-coherent, broadly transferable route to understand the emergence of function from structure among secondary-active membrane transporters.

Differential ion dehydration energetics explains selectivity in the non-canonical lysosomal K+ channel TMEM175.

Structures of the human lysosomal K+ channel transmembrane protein 175 (TMEM175) in open and closed states revealed a novel architecture lacking the canonical K+ selectivity filter motif present in previously known K+ channel structures. A hydrophobic constriction composed of four isoleucine residues was resolved in the pore and proposed to serve as the gate in the closed state, and to confer ion selectivity in the open state. Here, we achieve higher-resolution structures of the open and closed states and employ molecular dynamics simulations to analyze the conducting properties of the putative open state, demonstrating that it is permeable to K+ and, to a lesser degree, also Na+. Both cations must dehydrate significantly to penetrate the narrow hydrophobic constriction, but ion flow is assisted by a favorable electrostatic field generated by the protein that spans the length of the pore. The balance of these opposing energetic factors explains why permeation is feasible, and why TMEM175 is selective for K+ over Na+, despite the absence of the canonical selectivity filter. Accordingly, mutagenesis experiments reveal an exquisite sensitivity of the channel to perturbations that mitigate the constriction. Together, these data reveal a novel mechanism for selective permeation of ions by TMEM175 that is unlike that of other K+ channels.

Force-Correction Analysis Method for Derivation of Multidimensional Free-Energy Landscapes from Adaptively Biased Replica Simulations.

A methodology is proposed for the calculation of multidimensional free-energy landscapes of molecular systems, based on analysis of multiple molecular dynamics trajectories wherein adaptive biases have been applied to enhance the sampling of different collective variables. In this approach, which we refer to as the Force-Correction Analysis Method (FCAM), local averages of the total and biasing forces are evaluated post hoc, and the latter are subtracted from the former to obtain unbiased estimates of the mean force across collective-variable space. Multidimensional free-energy surfaces and minimum free-energy pathways are then derived by integrating the mean-force landscape with a kinetic Monte Carlo algorithm. To evaluate the proposed method, a series of numerical tests and comparisons with existing approaches were carried out for small molecules, peptides, and proteins, based on all-atom trajectories generated with standard, concurrent, and replica-exchange metadynamics in collective-variable spaces ranging from one to six dimensional. The tests confirm the correctness of the FCAM formulation and demonstrate that calculated mean forces and free energies converge rapidly and accurately, outperforming other methods used to unbias this kind of simulation data.

Interpreting Hydrogen-Deuterium Exchange Experiments with Molecular Simulations: Tutorials and Applications of the HDXer Ensemble Reweighting Software [Article v1.0].

Hydrogen-deuterium exchange (HDX) is a comprehensive yet detailed probe of protein structure and dynamics and, coupled to mass spectrometry, has become a powerful tool for investigating an increasingly large array of systems. Computer simulations are often used to help rationalize experimental observations of exchange, but interpretations have frequently been limited to simple, subjective correlations between microscopic dynamical fluctuations and the observed macroscopic exchange behavior. With this in mind, we previously developed the HDX ensemble reweighting approach and associated software, HDXer, to aid the objective interpretation of HDX data using molecular simulations. HDXer has two main functions; first, to compute H-D exchange rates that describe each structure in a candidate ensemble of protein structures, for example from molecular simulations, and second, to objectively reweight the conformational populations present in a candidate ensemble to conform to experimental exchange data. In this article, we first describe the HDXer approach, theory, and implementation. We then guide users through a suite of tutorials that demonstrate the practical aspects of preparing experimental data, computing HDX levels from molecular simulations, and performing ensemble reweighting analyses. Finally we provide a practical discussion of the capabilities and limitations of the HDXer methods including recommendations for a user's own analyses. Overall, this article is intended to provide an up-to-date, pedagogical counterpart to the software, which is freely available at https://github.com/Lucy-Forrest-Lab/HDXer.

Interpretation of HDX Data by Maximum-Entropy Reweighting of Simulated Structural Ensembles.

Hydrogen-deuterium exchange combined with mass spectrometry (HDX-MS) is a widely applied biophysical technique that probes the structure and dynamics of biomolecules without the need for site-directed modifications or bio-orthogonal labels. The mechanistic interpretation of HDX data, however, is often qualitative and subjective, owing to a lack of quantitative methods to rigorously translate observed deuteration levels into atomistic structural information. To help address this problem, we have developed a methodology to generate structural ensembles that faithfully reproduce HDX-MS measurements. In this approach, an ensemble of protein conformations is first generated, typically using molecular dynamics simulations. A maximum-entropy bias is then applied post hoc to the resulting ensemble such that averaged peptide-deuteration levels, as predicted by an empirical model, agree with target values within a given level of uncertainty. We evaluate this approach, referred to as HDX ensemble reweighting (HDXer), for artificial target data reflecting the two major conformational states of a binding protein. We demonstrate that the information provided by HDX-MS experiments and by the model of exchange are sufficient to recover correctly weighted structural ensembles from simulations, even when the relevant conformations are rarely observed. Degrading the information content of the target data-e.g., by reducing sequence coverage, by averaging exchange levels over longer peptide segments, or by incorporating different sources of uncertainty-reduces the structural accuracy of the reweighted ensemble but still allows for useful insights into the distinctive structural features reflected by the target data. Finally, we describe a quantitative metric to rank candidate structural ensembles according to their correspondence with target data and illustrate the use of HDXer to describe changes in the conformational ensemble of the membrane protein LeuT. In summary, HDXer is designed to facilitate objective structural interpretations of HDX-MS data and to inform experimental approaches and further developments of theoretical exchange models.

Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics.

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this "Multi-Map" variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich-Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.

Molecular mechanisms of human P2X3 receptor channel activation and modulation by divalent cation bound ATP.

P2X3 receptor channels expressed in sensory neurons are activated by extracellular ATP and serve important roles in nociception and sensory hypersensitization, making them attractive therapeutic targets. Although several P2X3 structures are known, it is unclear how physiologically abundant Ca2+-ATP and Mg2+-ATP activate the receptor, or how divalent cations regulate channel function. We used structural, computational and functional approaches to show that a crucial acidic chamber near the nucleotide-binding pocket in human P2X3 receptors accommodates divalent ions in two distinct modes in the absence and presence of nucleotide. The unusual engagement between the receptor, divalent ion and the γ-phosphate of ATP enables channel activation by ATP-divalent complex, cooperatively stabilizes the nucleotide on the receptor to slow ATP unbinding and recovery from desensitization, a key mechanism for limiting channel activity. These findings reveal how P2X3 receptors recognize and are activated by divalent-bound ATP, aiding future physiological investigations and drug development.

Structural Characterization of Biomolecules through Atomistic Simulations Guided by DEER Measurements.

Double electron-electron resonance (DEER) is a popular technique that exploits attached spin labels to probe the collective dynamics of biomolecules in a native environment. Like most spectroscopic approaches, DEER detects an ensemble of states accounting for biomolecular dynamics as well as the labels' intrinsic flexibility. Hence, the DEER data alone do not provide high-resolution structural information. To disentangle this variability, we introduce a minimally biased simulation method to sample a structural ensemble that reproduces multiple experimental signals within the uncertainty. In contrast to previous approaches, our method targets the raw data themselves, and thereby it brings forth an unbiased molecular interpretation of the experiments. After validation on the T4 lysozyme, we apply this technique to interpret recent DEER experiments on a membrane transporter binding protein (VcSiaP). The results highlight the large-scale conformational movement that occurs upon substrate binding and reveal that the unbound VcSiaP is more open in solution than the X-ray structure.

Confidence Analysis of DEER Data and Its Structural Interpretation with Ensemble-Biased Metadynamics.

Given its ability to measure multicomponent distance distributions between electron-spin probes, double electron-electron resonance (DEER) spectroscopy has become a leading technique to assess the structural dynamics of biomolecules. However, methodologies to evaluate the statistical error of these distributions are not standard, often hampering a rigorous interpretation of the experimental results. Distance distributions are often determined from the experimental DEER data through a mathematical method known as Tikhonov regularization, but this approach makes rigorous error estimates difficult. Here, we build upon an alternative, model-based approach in which the distance probability distribution is represented as a sum of Gaussian components, and use propagation of errors to calculate an associated confidence band. Our approach considers all sources of uncertainty, including the experimental noise, the uncertainty in the fitted background signal, and the limited time span of the data collection. The resulting confidence band reveals the most and least reliable features of the probability distribution, thereby informing the structural interpretation of DEER experiments. To facilitate this interpretation, we also generalize the molecular simulation method known as ensemble-biased metadynamics (EBMetaD). This method, originally designed to generate maximal-entropy structural ensembles consistent with one or more probability distributions, now also accounts for the uncertainty in those target distributions exactly as dictated by their confidence bands. After careful benchmarks, we demonstrate the proposed techniques using DEER results from spin-labeled T4 lysozyme.

The prokaryotic Na+/Ca2+ exchanger NCX_Mj transports Na+ and Ca2+ in a 3:1 stoichiometry.

Intracellular Ca2+ signals control a wide array of cellular processes. These signals require spatial and temporal regulation of the intracellular Ca2+ concentration, which is achieved in part by a class of ubiquitous membrane proteins known as sodium-calcium exchangers (NCXs). NCXs are secondary-active antiporters that power the translocation of Ca2+ across the cell membrane by coupling it to the flux of Na+ in the opposite direction, down an electrochemical gradient. Na+ and Ca2+ are translocated in separate steps of the antiport cycle, each of which is thought to entail a mechanism whereby ion-binding sites within the protein become alternately exposed to either side of the membrane. The prokaryotic exchanger NCX_Mj, the only member of this family with known structure, has been proposed to be a good functional and structural model of mammalian NCXs; yet our understanding of the functional properties of this protein remains incomplete. Here, we study purified NCX_Mj reconstituted into liposomes under well-controlled experimental conditions and demonstrate that this homologue indeed shares key functional features of the NCX family. Transport assays and reversal-potential measurements enable us to delineate the essential characteristics of this antiporter and establish that its ion-exchange stoichiometry is 3Na+:1Ca2+ Together with previous studies, this work confirms that NCX_Mj is a valid model system to investigate the mechanism of ion recognition and membrane transport in sodium-calcium exchangers.

Atomistic simulations indicate the c-subunit ring of the F1Fo ATP synthase is not the mitochondrial permeability transition pore.

Pathological metabolic conditions such as ischemia induce the rupture of the mitochondrial envelope and the release of pro-apoptotic proteins, leading to cell death. At the onset of this process, the inner mitochondrial membrane becomes depolarized and permeable to osmolytes, proposedly due to the opening of a non-selective protein channel of unknown molecular identity. A recent study purports that this channel, referred to as Mitochondrial Permeability Transition Pore (MPTP), is formed within the c-subunit ring of the ATP synthase, upon its dissociation from the catalytic domain of the enzyme. Here, we examine this claim for two c-rings of different lumen width, through calculations of their ion conductance and selectivity based on all-atom molecular dynamics simulations. We also quantify the likelihood that the lumen of these c-rings is in a hydrated, potentially conducting state rather than empty or blocked by lipid molecules. These calculations demonstrate that the structure and biophysical properties of a correctly assembled c-ring are inconsistent with those attributed to the MPTP.

Mechanism of extracellular ion exchange and binding-site occlusion in a sodium/calcium exchanger.

Na(+)/Ca(2+) exchangers use the Na(+) electrochemical gradient across the plasma membrane to extrude intracellular Ca(2+) and play a central role in Ca(2+) homeostasis. Here, we elucidate their mechanisms of extracellular ion recognition and exchange through a structural analysis of the exchanger from Methanococcus jannaschii (NCX_Mj) bound to Na(+), Ca(2+) or Sr(2+) in various occupancies and in an apo state. This analysis defines the binding mode and relative affinity of these ions, establishes the structural basis for the anticipated 3:1 Na(+)/Ca(2+)-exchange stoichiometry and reveals the conformational changes at the onset of the alternating-access transport mechanism. An independent analysis of the dynamics and conformational free-energy landscape of NCX_Mj in different ion-occupancy states, based on enhanced-sampling molecular dynamics simulations, demonstrates that the crystal structures reflect mechanistically relevant, interconverting conformations. These calculations also reveal the mechanism by which the outward-to-inward transition is controlled by the ion occupancy, thereby explaining the emergence of strictly coupled Na(+)/Ca(2+) antiport.

Atomic-resolution dissection of the energetics and mechanism of isomerization of hydrated ATP-Mg(2+) through the SOMA string method.

The atomic mechanisms of isomerization of ATP-Mg(2+) in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg(2+) complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg(2+) ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.

Ensemble-Biased Metadynamics: A Molecular Simulation Method to Sample Experimental Distributions.

We introduce an enhanced-sampling method for molecular dynamics (MD) simulations referred to as ensemble-biased metadynamics (EBMetaD). The method biases a conventional MD simulation to sample a molecular ensemble that is consistent with one or more probability distributions known a priori, e.g., experimental intramolecular distance distributions obtained by double electron-electron resonance or other spectroscopic techniques. To this end, EBMetaD adds an adaptive biasing potential throughout the simulation that discourages sampling of configurations inconsistent with the target probability distributions. The bias introduced is the minimum necessary to fulfill the target distributions, i.e., EBMetaD satisfies the maximum-entropy principle. Unlike other methods, EBMetaD does not require multiple simulation replicas or the introduction of Lagrange multipliers, and is therefore computationally efficient and straightforward in practice. We demonstrate the performance and accuracy of the method for a model system as well as for spin-labeled T4 lysozyme in explicit water, and show how EBMetaD reproduces three double electron-electron resonance distance distributions concurrently within a few tens of nanoseconds of simulation time. EBMetaD is integrated in the open-source PLUMED plug-in (www.plumed-code.org), and can be therefore readily used with multiple MD engines.

Sodium recognition by the Na+/Ca2+ exchanger in the outward-facing conformation.

Na(+)/Ca(2+) exchangers (NCXs) are ubiquitous membrane transporters with a key role in Ca(2+) homeostasis and signaling. NCXs mediate the bidirectional translocation of either Na(+) or Ca(2+), and thus can catalyze uphill Ca(2+) transport driven by a Na(+) gradient, or vice versa. In a major breakthrough, a prokaryotic NCX homolog (NCX_Mj) was recently isolated and its crystal structure determined at atomic resolution. The structure revealed an intriguing architecture consisting of two inverted-topology repeats, each comprising five transmembrane helices. These repeats adopt asymmetric conformations, yielding an outward-facing occluded state. The crystal structure also revealed four putative ion-binding sites, but the occupancy and specificity thereof could not be conclusively established. Here, we use molecular-dynamics simulations and free-energy calculations to identify the ion configuration that best corresponds to the crystallographic data and that is also thermodynamically optimal. In this most probable configuration, three Na(+) ions occupy the so-called Sext, SCa, and Sint sites, whereas the Smid site is occupied by one water molecule and one H(+), which protonates an adjacent aspartate side chain (D240). Experimental measurements of Na(+)/Ca(2+) and Ca(2+)/Ca(2+) exchange by wild-type and mutagenized NCX_Mj confirm that transport of both Na(+) and Ca(2+) requires protonation of D240, and that this side chain does not coordinate either ion at Smid. These results imply that the ion exchange stoichiometry of NCX_Mj is 3:1 and that translocation of Na(+) across the membrane is electrogenic, whereas transport of Ca(2+) is not. Altogether, these findings provide the basis for further experimental and computational studies of the conformational mechanism of this exchanger.

Following easy slope paths on a free energy landscape: the case study of the Trp-cage folding mechanism.

In this work a new method for the automatic exploration and calculation of multidimensional free energy landscapes is proposed. Inspired by metadynamics, it uses several collective variables that are relevant for the investigated process and a bias potential that discourages the sampling of already visited configurations. The latter potential allows escaping a local free energy minimum following the direction of slow motions. This is different from metadynamics in which there is no specific direction of the biasing force and the computational effort increases significantly with the number of collective variables. The method is tested on the Ace-Ala3-Nme peptide, and then it is applied to investigate the Trp-cage folding mechanism. For this protein, within a few hundreds of nanoseconds, a broad range of conformations is explored, including nearly native ones, initiating the simulation from a completely unfolded conformation. Finally, several folding/unfolding trajectories give a systematic description of the Trp-cage folding pathways, leading to a unified view for the folding mechanisms of this protein. The proposed mechanism is consistent with NMR chemical shift data at increasing temperature and recent experimental observations pointing to a pivotal role of secondary structure elements in directing the folding process toward the native state.

Two-state dynamics of the SH3-SH2 tandem of Abl kinase and the allosteric role of the N-cap.

The regulation and localization of signaling enzymes is often mediated by accessory modular domains, which frequently function in tandems. The ability of these tandems to adopt multiple conformations is as important for proper regulation as the individual domain specificity. A paradigmatic example is Abl, a ubiquitous tyrosine kinase of significant pharmacological interest. SH3 and SH2 domains inhibit Abl by assembling onto the catalytic domain, allosterically clamping it in an inactive state. We investigate the dynamics of this SH3-SH2 tandem, using microsecond all-atom simulations and differential scanning calorimetry. Our results indicate that the Abl tandem is a two-state switch, alternating between the conformation observed in the structure of the autoinhibited enzyme and another configuration that is consistent with existing scattering data for an activated form. Intriguingly, we find that the latter is the most probable when the tandem is disengaged from the catalytic domain. Nevertheless, an amino acid stretch preceding the SH3 domain, the so-called N-cap, reshapes the free-energy landscape of the tandem and favors the interaction of this domain with the SH2-kinase linker, an intermediate step necessary for assembly of the autoinhibited complex. This allosteric effect arises from interactions between N-cap and the SH2 domain and SH3-SH2 connector, which involve a phosphorylation site. We also show that the SH3-SH2 connector plays a determinant role in the assembly equilibrium of Abl, because mutations thereof hinder the engagement of the SH2-kinase linker. These results provide a thermodynamic rationale for the involvement of N-cap and SH3-SH2 connector in Abl regulation and expand our understanding of the principles of modular domain organization.

Molecular description of the propagation of chirality from molecules to complex systems: different mechanisms controlled by hydrophobic interactions.

In this work a combined theoretical and experimental approach was used to elucidate and describe at the molecular level the basic interactions that drive the transfer of the chiral information from chiral surfactant molecules to dye/surfactant assemblies. It was found that both hydrophobic interactions and relative concentrations strongly influence the chiroptical features of the heteroaggregates. In particular it was observed that, depending on the length of the surfactant hydrophobic chain, the chiral information is transferred to the dye by stabilizing an enantiomer either of a chiral conformer or of a chiral topological arrangement. These findings underline the role of hydrophobic interactions in the transfer of chirality and provide an example of the potential of in silico simulations for providing an accurate description of the process of chirality propagation.

Evidence for an allosteric mechanism of substrate release from membrane-transporter accessory binding proteins.

Numerous membrane importers rely on accessory water-soluble proteins to capture their substrates. These substrate-binding proteins (SBP) have a strong affinity for their ligands; yet, substrate release onto the low-affinity membrane transporter must occur for uptake to proceed. It is generally accepted that release is facilitated by the association of SBP and transporter, upon which the SBP adopts a conformation similar to the unliganded state, whose affinity is sufficiently reduced. Despite the appeal of this mechanism, however, direct supporting evidence is lacking. Here, we use experimental and theoretical methods to demonstrate that an allosteric mechanism of enhanced substrate release is indeed plausible. First, we report the atomic-resolution structure of apo TeaA, the SBP of the Na(+)-coupled ectoine TRAP transporter TeaBC from Halomonas elongata DSM2581(T), and compare it with the substrate-bound structure previously reported. Conformational free-energy landscape calculations based upon molecular dynamics simulations are then used to dissect the mechanism that couples ectoine binding to structural change in TeaA. These insights allow us to design a triple mutation that biases TeaA toward apo-like conformations without directly perturbing the binding cleft, thus mimicking the influence of the membrane transporter. Calorimetric measurements demonstrate that the ectoine affinity of the conformationally biased triple mutant is 100-fold weaker than that of the wild type. By contrast, a control mutant predicted to be conformationally unbiased displays wild-type affinity. This work thus demonstrates that substrate release from SBPs onto their membrane transporters can be facilitated by the latter through a mechanism of allosteric modulation of the former.