Search

Kinetic and thermodynamic models of biological systems have been used to connect microscopic features to system function. The parameters of such models—free energy differences for equilibrium properties and in general rates for equilibrium and out-of-equilibrium observables—have to be measured by different experiments or calculated by multiple computer simulations. All such parameters necessarily come with uncertainties so that when they are naively combined in a full model of the process of interest, they will generally violate fundamental statistical mechanical equalities, namely detailed balance and an equality of forward/backward rate products in cycles due to T. Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here we develop a formalism (namedmultibind) to combine kinetic or thermodynamic measurements to yield state resolved models that are thermodynamically consistent. For equilibrium thermodynamic models, we transform the graph of given free energy differences between states to the potential graph of free energies of states using a maximum likelihood approach; the potential graph obeys path-independence of free energies and detailed balance by construction. Based on the thermodynamically consistent potential graph, we project the given rates of an equilibrium system onto a new set of rates that by construction obeys Hill’s rate cycle-product equality. This approach produces thermodynamically consistent models that are most consistent with the provided data and their uncertainties. We show examples for how observables can be calculated from these models to interpret the effects of microscopic features on system function for two toy systems: A two-proton binding site is modeled as a four-state model and we demonstrate how cooperative or anti-cooperative behavior emerges as a function of the microscopic pKas. For simplified model of an electroneutral sodium/proton antiporter we compute the turnover number (sodium ions transported across the membrane per second) as a function of sodium concentration, pH, and membrane potential to show the strong effect of the membrane potential on transport in this system. We also describe an algorithm to use themultibindapproach to solve the inverse problem of determining microscopic quantities from macroscopic measurements. As an example we predict the microscopic pKas and protonation states of a small organic molecule from 1D NMR data. Themultibindapproach is applicable to any thermodynamic or kinetic model that describes a system as transitions between well defined states with associated free energy differences or rates between these states. A Python packagemultibind, which implements the approach described here, is made publicly available under the MIT Open Source license.WHY IT MATTERSThe increase in computational efficiency and rapid advances in methodology for quantitative free energy and rate calculations has allowed for the construction of increasingly complex thermodynamic or kinetic “bottom-up” models of chemical and biological processes. These multi-scale models serve as a framework for analyzing aspects of cellular function in terms of microscopic, molecular properties and provide an opportunity to connect molecular mechanisms to cellular function. The underlying model parameters—free energy differences or rates—are constrained by thermodynamic identities over cycles of states but these identities are not necessarily obeyed during model construction, thus potentially leading to inconsistent models. We address these inconsistencies through the use of a maximum likelihood approach for free energies and an exact projection for rates to adjust the model parameters in such a way that they are maximally consistent with the input parameters and exactly fulfill the thermodynamic cycle constraints. This approach enables formulation of thermodynamically consistent multi-scale models from simulated or experimental measurements.

YiiP is a prokaryotic Zn2+/H+antiporter that serves as a model for the Cation Diffusion Facilitator (CDF) superfamily, members of which are generally responsible for homeostasis of transition metal ions. Previous studies of YiiP as well as related CDF transporters have established a homodimeric architecture and the presence of three distinct Zn2+binding sites named A, B, and C. In this study, we use cryo-EM, microscale thermophoresis and molecular dynamics simulations to address the structural and functional roles of individual sites and the interplay between Zn2+binding and protonation. Structural studies indicate that site C in the cytoplasmic domain is primarily responsible for stabilizing the dimer and that site B at the cytoplasmic membrane surface controls the structural transition from an inward facing conformation to an occluded conformation. Binding data show that intramembrane site A, which is directly responsible for transport, has a dramatic pH dependence consistent with coupling to the proton motive force. A comprehensive thermodynamic model encompassing Zn2+binding and protonation states of individual residues indicates a transport stoichiometry of 1 Zn2+to 2-3 H+depending on the external pH. This stoichiometry would be favorable in a physiological context, allowing the cell to use the proton gradient as well as the membrane potential to drive the export of Zn2+.

International audience; OXA-48 carbapenemase has rapidly spread in many countries worldwide with several OXA-48-variants being described, differing by a few amino acid (AA) substitutions or deletions, mostly in the β5-β6 loop. While single AA substitutions have only a minor impact on OXA-48 hydrolytic profiles, others with 4 AA deletions result in loss of carbapenem hydrolysis and gain of expanded-spectrum cephalosporin (ESC) hydrolysis. We have replaced the β5-β6 loop of OXA-48 with that of OXA-18, a clavulanic-acid inhibited oxacillinase capable of hydrolyzing ESCs but not carbapenems. The hybrid enzyme OXA-48Loop18 was able to hydrolyze ESCs and carbapenems (although with a lower kcat), even though the β5-β6 loop was longer and its sequence quite different from that of OXA-48. The kinetic parameters of OXA-48Loop18 were in agreement with the MIC values. X-ray crystallography and molecular modeling suggest that the conformation of the grafted loop allows the binding of bulkier substrates, unlike that of the native loop, expanding the hydrolytic profile. This seems to be due not only to differences in AA sequence, but also to the backbone conformation the loop can adopt. Finally, our results provide further experimental evidence for the role of the β5-β6 loop in substrate selectivity of OXA-48-like enzymes and additional details on the structure-function relationship of β-lactamases, demonstrating how localized changes in these proteins can alter or expand their function, highlighting their plasticity.

The strict exchange of protons for sodium ions across cell membranes by Na

Na+/H+ exchangers catalyse an ion-exchange activity that is carried out in most, if not all cells. SLC9B2, also known as NHA2, correlates with the long-sought after sodium/lithium (Na+/Li+) exchanger linked to the pathogenesis of diabetes mellitus and essential hypertension in humans. Despite its functional importance, structural information and the molecular basis of its ion-exchange mechanism have been lacking. Here, we report the cryo EM structures of bison NHA2 in detergent and in nanodiscs at 3.0 and 3.5 Å resolution, respectively. NHA2 shares closest structural similarity to the bacterial electrogenic Na+/H+ antiporter NapA, rather than other mammalian SLC9A members. Nevertheless, SSM-based electrophysiology results with NHA2 show the catalysis of electroneutral rather than electrogenic ion exchange, and the ion-binding site is quite distinctive, with a tryptophan-arginine- glutamate triad separated from the well-established ion-binding aspartates. These triad residues fine-tune ion binding specificity, as demonstrated by a salt-bridge swap mutant that converts NHA2 into a Li+-specific transporter. Strikingly, an additional N-terminal helix in NHA2 establishes a unique homodimer with a large ∼ 25 Å intracellular gap between protomers. In the presence of phosphatidylinositol lipids, the N-terminal helix rearranges and closes this gap. We confirm that dimerization of NHA2 is required for activity in vivo, and propose that the N- terminal helix has evolved as a lipid-mediated remodelling switch for regulation of transport activity.

The Na

YiiP is a secondary transporter that couples Zn2+ transport to the proton motive force. Structural studies of YiiP from prokaryotes as well as Znt8 from humans revealed three different Zn2+ sites and a conserved homodimeric architecture. These structures define the inward-facing and outward-facing states that characterize the archetypal alternating access mechanism of transport. To study effects of Zn2+ binding on the conformational transition, we have used a YiiP/Fab complex for single-particle cryo-EM together with Molecular Dynamics simulation to compare structures of YiiP from S. oneidensis in presence and absence of Zn2+. Without Zn2+, YiiP exhibits enhanced flexibility and adopts a novel conformation that appears to be an intermediate state. The transition closes a hydrophobic gate and is controlled by the Zn2+ site at the cytoplasmic membrane interface. This work enhances our understanding of individual Zn2+ binding sites and their role in the conformational dynamics that governs the transport cycle.

Escherichia coli NhaA is a prototypical sodium–proton antiporter responsible for maintaining cellular ion and volume homeostasis by exchanging two protons for one sodium ion; despite two decades of research, the transport mechanism of NhaA remains poorly understood. Recent crystal structure and computational studies suggested Lys300 as a second proton-binding site; however, functional measurements of several K300 mutants demonstrated electrogenic transport, thereby casting doubt on the role of Lys300. To address the controversy, we carried out state-of-the-art continuous constant pH molecular dynamics simulations of NhaA mutants K300A, K300R, K300Q/D163N, and K300Q/D163N/D133A. Simulations suggested that K300 mutants maintain the electrogenic transport by utilizing an alternative proton-binding residue Asp133. Surprisingly, while Asp133 is solely responsible for binding the second proton in K300R, Asp133 and Asp163 jointly bind the second proton in K300A, and Asp133 and Asp164 jointly bind two protons in K300Q/D163N. Intriguingly, the coupling between Asp133 and Asp163 or Asp164 is enabled through the proton-coupled hydrogen-bonding network at the flexible intersection of two disrupted helices. These data resolve the controversy and highlight the intricacy of the compensatory transport mechanism of NhaA mutants. Alternative proton-binding site and proton sharing between distant aspartates may represent important general mechanisms of proton-coupled transport in secondary active transporters.

All-atom molecular dynamics simulations with stratified alchemical free energy calculations were used to predict the octanol-water partition coefficient [Formula: see text] of eleven small molecules as part of the SAMPL6-[Formula: see text] blind prediction challenge using four different force field parametrizations: standard OPLS-AA with transferable charges, OPLS-AA with non-transferable CM1A charges, AMBER/GAFF, and CHARMM/CGenFF. Octanol parameters for OPLS-AA, GAFF and CHARMM were validated by comparing the density as a function of temperature, the chemical potential, and the hydration free energy to experimental values. The partition coefficients were calculated from the solvation free energy for the compounds in water and pure ("dry") octanol or "wet" octanol with 27 mol% water dissolved. Absolute solvation free energies were computed by thermodynamic integration (TI) and the multistate Bennett acceptance ratio with uncorrelated samples from data generated by an established protocol using 5-ns windowed alchemical free energy perturbation (FEP) calculations with the Gromacs molecular dynamics package. Equilibration of sets of FEP simulations was quantified by a new measure of convergence based on the analysis of forward and time-reversed trajectories. The accuracy of the [Formula: see text] predictions was assessed by descriptive statistical measures such as the root mean square error (RMSE) of the data set compared to the experimental values. Discarding the first 1 ns of each 5-ns window as an equilibration phase had a large effect on the GAFF data, where it improved the RMSE by up to 0.8 log units, while the effect for other data sets was smaller or marginally worsened the agreement. Overall, CGenFF gave the best prediction with RMSE 1.2 log units, although for only eight molecules because the current CGenFF workflow for Gromacs does not generate files for certain halogen-containing compounds. Over all eleven compounds, GAFF gave an RMSE of 1.5. The effect of using a mixed water/octanol solvent slightly decreased the accuracy for CGenFF and GAFF and slightly increased it for OPLS-AA. The GAFF and OPLS-AA results displayed a systematic error where molecules were too hydrophobic whereas CGenFF appeared to be more balanced, at least on this small data set.

Na+/H+ exchangers (NHEs) are ancient membrane‐bound nanomachines that work to regulate intracellular pH, sodium levels and cell volume. NHE activities contribute to the control of the cell cycle, cell proliferation, cell migration and vesicle trafficking. NHE dysfunction has been linked to many diseases, and they are targets of pharmaceutical drugs. Despite their fundamental importance to cell homeostasis and human physiology, structural information for the mammalian NHE was lacking. Here, we report the cryogenic electron microscopy structure of NHE isoform 9 (SLC9A9) from Equus caballus at 3.2 Å resolution, an endosomal isoform highly expressed in the brain and associated with autism spectrum (ASD) and attention deficit hyperactivity (ADHD) disorders. Despite low sequence identity, the NHE9 architecture and ion‐binding site are remarkably similar to distantly related bacterial Na+/H+ antiporters with 13 transmembrane segments. Collectively, we reveal the conserved architecture of the NHE ion‐binding site, their elevator‐like structural transitions, the functional implications of autism disease mutations and the role of phosphoinositide lipids to promote homodimerization that, together, have important physiological ramifications., Cryo‐EM structures reveal conserved architecture and exchange mechanism of the horse endosomal Na+/H+ exchanger NHE9.

G protein-coupled receptors (GPCRs) are known to be modulated by membrane cholesterol levels, but whether or not the effects are caused by specific receptor-cholesterol interactions or cholesterol’s general effects on the membrane is not well-understood. We performed coarse-grained molecular dynamics (CGMD) simulations coupled with structural bioinformatics approaches on the β(2)-adrenergic receptor (β(2)AR) and the cholecystokinin (CCK) receptor subfamily. The β(2)AR has been shown to be sensitive to membrane cholesterol and cholesterol molecules have been clearly resolved in numerous β(2)AR crystal structures. The two CCK receptors are highly homologous and preserve similar cholesterol recognition motifs but despite their homology, CCK(1)R shows functional sensitivity to membrane cholesterol while CCK(2)R does not. Our results offer new insights into how cholesterol modulates GPCR function by showing cholesterol interactions with β(2)AR that agree with previously published data; additionally, we observe differential and specific cholesterol binding in the CCK receptor subfamily while revealing a previously unreported Cholesterol Recognition Amino-acid Consensus (CRAC) sequence that is also conserved across 38% of class A GPCRs. A thermal denaturation assay (LCP-T(m)) shows that mutation of a conserved CRAC sequence on TM7 of the β(2)AR affects cholesterol stabilization of the receptor in a lipid bilayer. The results of this study provide a better understanding of receptor-cholesterol interactions that can contribute to novel and improved therapeutics for a variety of diseases.

Transport of ions and small molecules across the cell membrane against electrochemical gradients is catalyzed by integral membrane proteins that use a source of free energy to drive the energetically uphill flux of the transported substrate. Secondary active transporters couple the spontaneous influx of a "driving" ion such as Na$^+$ or H$^+$ to the flux of the substrate. The thermodynamics of such cyclical non-equilibrium systems are well understood and recent work has focused on the molecular mechanism of secondary active transport. The fact that these transporters change their conformation between an inward-facing and outward-facing conformation in a cyclical fashion, called the alternating access model, is broadly recognized as the molecular framework in which to describe transporter function. High resolution structures and detailed computer simulations lead to the recognition of common molecular-level principles between disparate transporter families. Inverted repeat symmetry in secondary active transporters has shed light on how protein structures can encode a bi-stable two-state system. Three broad classes of alternating access transitions have been described as rocker-switch, rocking-bundle, and elevator mechanisms. Transporters can be understood as gated pores with at least two coupled gates that map to distinct parts of the transporter protein. Enumerating all distinct gate states naturally includes occluded states in the alternating access picture and suggests observable protein conformations. By connecting the possible conformational states and ion/substrate bound states in a kinetic model, a unified picture emerges in which symporter, antiporter, and uniporter function are extremes in a continuum of functionality. We briefly discuss how biological complexity may be integrated in quantitative kinetic models to provide a bridge from structure to function., accepted for publication in Biophysics Reviews

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

The performance of biomolecular molecular dynamics simulations has steadily increased on modern high performance computing resources but acceleration of the analysis of the output trajectories has lagged behind so that analyzing simulations is becoming a bottleneck. To close this gap, we studied the performance of parallel trajectory analysis with MPI and the Python MDAnalysis library on three different XSEDE supercomputers where trajectories were read from a Lustre parallel file system. Strong scaling performance was impeded by stragglers, MPI processes that were slower than the typical process. Stragglers were less prevalent for compute-bound workloads, thus pointing to file reading as a bottleneck for scaling. However, a more complicated picture emerged in which both the computation and the data ingestion exhibited close to ideal strong scaling behavior whereas stragglers were primarily caused by either large MPI communication costs or long times to open the single shared trajectory file. We improved overall strong scaling performance by either subfiling (splitting the trajectory into separate files) or MPI-IO with Parallel HDF5 trajectory files. The parallel HDF5 approach resulted in near ideal strong scaling on up to 384 cores (16 nodes), thus reducing trajectory analysis times by two orders of magnitude compared to the serial approach., Comment: accepted manuscript, to appear in 'Concurrency and Computation: Practice and Experience'