Structure and elevator mechanism of the mammalian sodium/proton exchanger NHE9.

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.

Alternative proton-binding site and long-distance coupling in Escherichia coli sodium-proton antiporter NhaA.

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.

Precise force-field-based calculations of octanol-water partition coefficients for the SAMPL7 molecules.

We predicted water-octanol partition coefficients for the molecules in the SAMPL7 challenge with explicit solvent classical molecular dynamics (MD) simulations. Water hydration free energies and octanol solvation free energies were calculated with a windowed alchemical free energy approach. Three commonly used force fields (AMBER GAFF, CHARMM CGenFF, OPLS-AA) were tested. Special emphasis was placed on converging all simulations, using a criterion developed for the SAMPL6 challenge. In aggregate, over 1000 [Formula: see text]s of simulations were performed, with some free energy windows remaining not fully converged even after 1 [Formula: see text]s of simulation time. Nevertheless, the amount of sampling produced [Formula: see text] estimates with a precision of 0.1 log units or better for converged simulations. Despite being probably as fully sampled as can expected and is feasible, the agreement with experiment remained modest for all force fields, with no force field performing better than 1.6 in root mean squared error. Overall, our results indicate that a large amount of sampling is necessary to produce precise [Formula: see text] predictions for the SAMPL7 compounds and that high precision does not necessarily lead to high accuracy. Thus, fundamental problems remain to be solved for physics-based [Formula: see text] predictions.

Correction: Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways.

[This corrects the article DOI: 10.1371/journal.pcbi.1004568.].

Prediction of octanol-water partition coefficients for the SAMPL6-[Formula: see text] molecules using molecular dynamics simulations with OPLS-AA, AMBER and CHARMM force fields.

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.

A two-domain elevator mechanism for sodium/proton antiport.

Sodium/proton (Na(+)/H(+)) antiporters, located at the plasma membrane in every cell, are vital for cell homeostasis. In humans, their dysfunction has been linked to diseases, such as hypertension, heart failure and epilepsy, and they are well-established drug targets. The best understood model system for Na(+)/H(+) antiport is NhaA from Escherichia coli, for which both electron microscopy and crystal structures are available. NhaA is made up of two distinct domains: a core domain and a dimerization domain. In the NhaA crystal structure a cavity is located between the two domains, providing access to the ion-binding site from the inward-facing surface of the protein. Like many Na(+)/H(+) antiporters, the activity of NhaA is regulated by pH, only becoming active above pH 6.5, at which point a conformational change is thought to occur. The only reported NhaA crystal structure so far is of the low pH inactivated form. Here we describe the active-state structure of a Na(+)/H(+) antiporter, NapA from Thermus thermophilus, at 3 Å resolution, solved from crystals grown at pH 7.8. In the NapA structure, the core and dimerization domains are in different positions to those seen in NhaA, and a negatively charged cavity has now opened to the outside. The extracellular cavity allows access to a strictly conserved aspartate residue thought to coordinate ion binding directly, a role supported here by molecular dynamics simulations. To alternate access to this ion-binding site, however, requires a surprisingly large rotation of the core domain, some 20° against the dimerization interface. We conclude that despite their fast transport rates of up to 1,500 ions per second, Na(+)/H(+) antiporters operate by a two-domain rocking bundle model, revealing themes relevant to secondary-active transporters in general.

Molecular mechanism of ligand recognition by membrane transport protein, Mhp1.

The hydantoin transporter Mhp1 is a sodium-coupled secondary active transport protein of the nucleobase-cation-symport family and a member of the widespread 5-helix inverted repeat superfamily of transporters. The structure of Mhp1 was previously solved in three different conformations providing insight into the molecular basis of the alternating access mechanism. Here, we elucidate detailed events of substrate binding, through a combination of crystallography, molecular dynamics, site-directed mutagenesis, biochemical/biophysical assays, and the design and synthesis of novel ligands. We show precisely where 5-substituted hydantoin substrates bind in an extended configuration at the interface of the bundle and hash domains. They are recognised through hydrogen bonds to the hydantoin moiety and the complementarity of the 5-substituent for a hydrophobic pocket in the protein. Furthermore, we describe a novel structure of an intermediate state of the protein with the external thin gate locked open by an inhibitor, 5-(2-naphthylmethyl)-L-hydantoin, which becomes a substrate when leucine 363 is changed to an alanine. We deduce the molecular events that underlie acquisition and transport of a ligand by Mhp1.

Ligandbook: an online repository for small and drug-like molecule force field parameters.

SUMMARY: Ligandbook is a public database and archive for force field parameters of small and drug-like molecules. It is a repository for parameter sets that are part of published work but are not easily available to the community otherwise. Parameter sets can be downloaded and immediately used in molecular dynamics simulations. The sets of parameters are versioned with full histories and carry unique identifiers to facilitate reproducible research. Text-based search on rich metadata and chemical substructure search allow precise identification of desired compounds or functional groups. Ligandbook enables the rapid set up of reproducible molecular dynamics simulations of ligands and protein-ligand complexes. AVAILABILITY AND IMPLEMENTATION: Ligandbook is available online at https://ligandbook.org and supports all modern browsers. Parameters can be searched and downloaded without registration, including access through a programmatic RESTful API. Deposition of files requires free user registration. Ligandbook is implemented in the PHP Symfony2 framework with TCL scripts using the CACTVS toolkit. CONTACT: oliver.beckstein@asu.edu or bogdan.iorga@cnrs.fr ; contact@ligandbook.org . SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SAMPL6: calculation of macroscopic pKa values from ab initio quantum mechanical free energies.

Macroscopic pKa values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pKa values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pKas with a maximum likelihood estimator and appropriately summed to yield macroscopic pKa values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pKas: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pKa. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pKa units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pKa values for novel compounds with reasonable accuracy.

Topological Dissection of the Membrane Transport Protein Mhp1 Derived from Cysteine Accessibility and Mass Spectrometry.

Cys accessibility and quantitative intact mass spectrometry (MS) analyses have been devised to study the topological transitions of Mhp1, the membrane protein for sodium-linked transport of hydantoins from Microbacterium liquefaciens. Mhp1 has been crystallized in three forms (outward-facing open, outward-facing occluded with substrate bound, and inward-facing open). We show that one natural cysteine residue, Cys327, out of three, has an enhanced solvent accessibility in the inward-facing (relative to the outward-facing) form. Reaction of the purified protein, in detergent, with the thiol-reactive N-ethylmalemide (NEM), results in modification of Cys327, suggesting that Mhp1 adopts predominantly inward-facing conformations. Addition of either sodium ions or the substrate 5-benzyl-l-hydantoin (L-BH) does not shift this conformational equilibrium, but systematic co-addition of the two results in an attenuation of labeling, indicating a shift toward outward-facing conformations that can be interpreted using conventional enzyme kinetic analyses. Such measurements can afford the Km for each ligand as well as the stoichiometry of ion-substrate-coupled conformational changes. Mutations that perturb the substrate binding site either result in the protein being unable to adopt outward-facing conformations or in a global destabilization of structure. The methodology combines covalent labeling, mass spectrometry, and kinetic analyses in a straightforward workflow applicable to a range of systems, enabling the interrogation of changes in a protein's conformation required for function at varied concentrations of substrates, and the consequences of mutations on these conformational transitions.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways.

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.

Prediction of cyclohexane-water distribution coefficients for the SAMPL5 data set using molecular dynamics simulations with the OPLS-AA force field.

All-atom molecular dynamics simulations were used to predict water-cyclohexane distribution coefficients [Formula: see text] of a range of small molecules as part of the SAMPL5 blind prediction challenge. Molecules were parameterized with the transferable all-atom OPLS-AA force field, which required the derivation of new parameters for sulfamides and heterocycles and validation of cyclohexane parameters as a solvent. The distribution coefficient was calculated from the solvation free energies of the compound in water and cyclohexane. Absolute solvation free energies were computed by an established protocol using windowed alchemical free energy perturbation with thermodynamic integration. This protocol resulted in an overall root mean square error in [Formula: see text] of almost 4 log units and an overall signed error of -3 compared to experimental data. There was no substantial overall difference in accuracy between simulating in NVT and NPT ensembles. The signed error suggests a systematic error but the experimental [Formula: see text] data on their own are insufficient to uncover the source of this error. Preliminary work suggests that the major source of error lies in the hydration free energy calculations.

Understanding thermosensitive transient receptor potential channels as versatile polymodal cellular sensors.

Transient receptor potential (TRP) ion channels are eukaryotic polymodal sensors that function as molecular cellular signal integrators. TRP family members sense and are modulated by a wide array of inputs, including temperature, pressure, pH, voltage, chemicals, lipids, and other proteins. These inputs induce signal transduction events mediated by nonselective cation passage through TRP channels. In this review, we focus on the thermosensitive TRP channels and highlight the emerging view that these channels play a variety of significant roles in physiology and pathophysiology in addition to sensory biology. We attempt to use this viewpoint as a framework to understand the complexity and controversy of TRP channel modulation and ultimately suggest that the complex functional behavior arises inherently because this class of protein is exquisitely sensitive to many diverse and distinct signal inputs. To illustrate this idea, we primarily focus on TRP channel thermosensing. We also offer a structural, biochemical, biophysical, and computational perspective that may help to bring more coherence and consensus in understanding the function of this important class of proteins.

Peptide Folding in Translocon-Like Pores.

The cellular translocon, present in all three domains of life, is one of the most versatile and important biological nanopores. This complex molecular apparatus is directly responsible for the secretion of globular proteins across membranes as well as the insertion of integral membrane proteins into lipid bilayers. Recently determined structures of the archaean SecY translocon reveal an hour-glass-shaped pore, which accommodates the nascent peptide chain during translocation. While these structures provide important insights into ribosome binding to the translocon, threading of the nascent chain into the channel, and lateral gate opening for releasing the folded helical peptide into the membrane bilayer, the exact folding pathway of the peptide inside the protein-conducting channel during translocation and prior to the lateral release into the bilayer remains elusive. In the present study, we use molecular dynamics simulations to investigate atomic resolution peptide folding in hour-glass-shaped pore models that are based on the SecY translocon channel structure. The theoretical setup allows systematic variation of key determinants of folding, in particular the degree of confinement of the peptide and the hydration level of the pore. A 27-residue hydrophobic peptide was studied that is preferentially inserted into membranes by the translocon. Our results show that both pore diameter as well as channel hydration are important determinants for folding efficiency and helical stability of the peptide, therefore providing important insights into translocon gating and lateral peptide partitioning.

Prediction of hydration free energies for the SAMPL4 diverse set of compounds using molecular dynamics simulations with the OPLS-AA force field.

All-atom molecular dynamics computer simulations were used to blindly predict the hydration free energies of a range of small molecules as part of the SAMPL4 challenge. Compounds were parametrized on the basis of the OPLS-AA force field using three different protocols for deriving partial charges: (1) using existing OPLS-AA atom types and charges with minor adjustments of partial charges on equivalent connecting atoms and derivation of new parameters for a number of distinct chemical groups (N-alkyl imidazole, nitrate) that were not present in the published force field; (2) calculation of quantum mechanical charges via geometry optimization, followed by electrostatic potential (ESP) fitting, using Jaguar at the LMP2/cc-pVTZ(-F) level; and (3) via geometry optimization and CHelpG charges (Gaussian09 at the HF/6-31G* level), followed by two-stage RESP fitting. The absolute hydration free energy was computed by an established protocol including alchemical free energy perturbation with thermodynamic integration. The use of standard OPLS-AA charges (protocol 1) with a number of newly parametrized charges and the use of histidine derived parameters for imidazole yielded an overall root mean square deviation of the prediction from the experimental data of 1.75 kcal/mol. The precision of our results appears to be mainly limited by relatively poor reproducibility of the Lennard-Jones contribution towards the solvation free energy, for which we observed large variability that could be traced to a strong dependence on the initial system conditions.

Kinetic Diagram Analysis: A Python Library for Calculating Steady-State Observables of Kinetic Systems Analytically.

Kinetic diagrams are commonly used to represent biochemical systems in order to study phenomena such as free energy transduction and ion selectivity. While numerical methods are commonly used to analyze such kinetic networks, the diagram method by King, Altman and Hill makes it possible to construct exact algebraic expressions for steady-state observables in terms of the rate constants of the kinetic diagram. However, manually obtaining these expressions becomes infeasible for models of even modest complexity as the number of the required intermediate diagrams grows with the factorial of the number of states in the diagram. We developed Kinetic Diagram Analysis (KDA), a Python library that programmatically generates the relevant diagrams and expressions from a user-defined kinetic diagram. KDA outputs symbolic expressions for state probabilities and cycle fluxes at steady-state that can be symbolically manipulated and evaluated to quantify macroscopic system observables. We demonstrate the KDA approach for examples drawn from the biophysics of active secondary transmembrane transporters. For a generic 6-state antiporter model, we show how the introduction of a single leakage transition reduces transport efficiency by quantifying substrate turnover. We apply KDA to a real-world example, the 8-state free exchange model of the small multidrug resistance transporter EmrE of Hussey et al (J General Physiology 152 (2020), e201912437), where a change in transporter phenotype is achieved by biasing two different subsets of kinetic rates: alternating access and substrate unbinding rates. KDA is made available as open source software under the GNU General Public License version 3.

Chloride binding and cholesterol effects on high frequency complex nonlinear capacitance (cNLC) in the mouse outer hair cell: experiment and molecular dynamics.

The function of prestin (SLC26a5), an anion transport family member, has evolved to enhance auditory sensitivity and frequency selectivity by providing mechanical feedback via outer hair cells (OHC) into the organ of Corti. The frequency extent of this boost is governed by the voltage-dependent kinetics of the protein's charge movements, otherwise known as nonlinear capacitance (NLC) that we measure in membrane patches under voltage clamp. Here we extend our previous studies on guinea pig OHCs by studying the frequency response of NLC in the mouse OHC, a species with higher frequency auditory needs. We find that the characteristic frequency cut-off (F is ) for the mouse surpasses that of the guinea pig, being 27 kHz vs. 19 kHz, respectively; nevertheless, each shows significant activity in the ultrasonic range. We also evaluate the influence of anion binding on prestin frequency response. Several single point mutations within the chloride binding pocket of prestin (e.g., S396E, S398E) lack anion influence. In agreement, we show absence of anion binding through molecular dynamics (MD) simulations. NLC F is in the S396E knock-in mouse remains the same as controls, indicating that high frequency activity is likely governed by viscoelastic loads within the membrane characterized by stretched-exponential frequency roll-off. Accordingly, treatment with MßCD, which removes membrane cholesterol, possibly from prestin itself, and can alter membrane fluidity, augments NLC F is out to 39 kHz. Although interactions between membrane lipid and prestin have been suggested from structural studies to arise at their interfacial boundaries within the membrane, our MD simulations suggest that phospholipids can insert within transmembrane domains of prestin during voltage perturbation. Such novel lipid-protein interactions could account for our observed changes in the phase of prestin's voltage-sensor charge movements across frequency. We hypothesize that because prestin tertiary structures of all species studied to-date are indistinguishable, it is likely that any special auditory requirements of individual species for cochlear amplification have evolved to capitalize on prestin performance by modifying, not the protein itself, but the external loads on the protein, including those within the membrane and organ of Corti. Significance: Prestin is believed to provide cochlear amplification in mammals that possess a wide range of frequency sensitivities, yet its tertiary structure is indistinguishable among those species studied. We find that prestin kinetics is faster in mice than in guinea pigs, mice showing higher frequency auditory capabilities. Chloride binding is not influential, but membrane lipids/viscosity is. We suggest that the evolution of prestin's species performance involves modifications of impinging loads, not the protein itself.

A novel congenital myasthenic syndrome due to decreased acetylcholine receptor ion-channel conductance.

Muscle acetylcholine receptor ion channels mediate neurotransmission by depolarizing the postsynaptic membrane at the neuromuscular junction. Inherited disorders of neuromuscular transmission, termed congenital myasthenic syndromes, are commonly caused by mutations in genes encoding the five subunits of the acetylcholine receptor that severely reduce endplate acetylcholine receptor numbers and/or cause kinetic abnormalities of acetylcholine receptor function. We tracked the cause of the myasthenic disorder in a female with onset of first symptoms at birth, who displayed mildly progressive bulbar, respiratory and generalized limb weakness with ptosis and ophthalmoplegia. Direct DNA sequencing revealed heteroallelic mutations in exon 8 of the acetylcholine receptor ε-subunit gene. Two alleles were identified: one with the missense substitution p.εP282R, and the second with a deletion, c.798_800delCTT, which result in the loss of a single amino acid, residue F266, within the M2 transmembrane domain. When these acetylcholine receptor mutations were expressed in HEK 293 cells, the p.εP282R mutation caused severely reduced expression on the cell surface, whereas p.εΔF266 gave robust surface expression. Single-channel analysis for p.εΔF266 acetylcholine receptor channels showed the longest burst duration population was not different from wild-type acetylcholine receptor (4.39 ± 0.6 ms versus 4.68 ± 0.7 ms, n = 5 each) but that the amplitude of channel openings was reduced. Channel amplitudes at different holding potentials showed that single-channel conductance was significantly reduced in p.εΔF266 acetylcholine receptor channels (42.7 ± 1.4 pS, n = 8, compared with 70.9 ± 1.6 pS for wild-type, n = 6). Although a phenylalanine residue at this position within M2 is conserved throughout ligand-gated excitatory cys-loop channel subunits, deletion of equivalent residues in the other subunits of muscle acetylcholine receptor did not have equivalent effects. Modelling the impact of p.εΔF266 revealed only a minor alteration to channel structure. In this study we uncover the novel mechanism of reduced acetylcholine receptor channel conductance as an underlying cause of congenital myasthenic syndrome, with the 'low conductance' phenotype that results from the p.εΔF266 deletion mutation revealed by the coinheritance of the low-expressor mutation p.εP282R.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models.

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. 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 from 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 Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here, we develop a maximum likelihood approach (named multibind) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state-resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and, as an example, we predict the microscopic pKa values and protonation states of a small organic molecule from 1D NMR data. The multibind approach 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 package multibind, which implements the approach described here, is made publicly available under the MIT Open Source license.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models.

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. 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 from 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 maximum likelihood approach (named multibind ) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and as an example we predict the microscopic p K a s and protonation states of a small organic molecule from 1D NMR data. The multibind approach 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 package multibind , which implements the approach described here, is made publicly available under the MIT Open Source license. WHY IT MATTERS: The 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 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.