Alchemical Free Energy Calculations on Membrane-Associated Proteins

Membrane proteins have diverse functions within cells and are well-established drug targets. The advances in membrane protein structural biology have revealed drug and lipid binding sites on membrane proteins, while computational methods such as molecular simulations can resolve the thermodynamic basis of these interactions. Particularly, alchemical free energy calculations have shown promise in the calculation of reliable and reproducible binding free energies of protein-ligand and protein-lipid complexes in membrane-associated systems. In this review, we present an overview of representative alchemical free energy studies on G-protein-coupled receptors, ion channels, transporters as well as protein-lipid interactions, with emphasis on best practices and critical aspects of running these simulations. Additionally, we analyze challenges and successes when running alchemical free energy calculations on membrane-associated proteins. Finally, we highlight the value of alchemical free energy calculations calculations in drug discovery and their applicability in the pharmaceutical industry.

Unwrapping NPT Simulations to Calculate Diffusion Coefficients

In molecular dynamics simulations in the NPT ensemble at constant pressure, the size and shape of the periodic simulation box fluctuate with time. For particle images far from the origin, the rescaling of the box by the barostat results in unbounded position displacements. Special care is thus required when a particle trajectory is unwrapped from a projection into the central box under periodic boundary conditions to a trajectory in full three-dimensional space, e.g., for the calculation of translational diffusion coefficients. Here, we review and compare different schemes in use for trajectory unwrapping. We also specify the corresponding rewrapping schemes to put an unwrapped trajectory back into the central box. On this basis, we then identify a scheme for the calculation of diffusion coefficients from NPT simulations, which is a primary application of trajectory unwrapping. In this scheme, the wrapped and unwrapped trajectory are mutually consistent and their statistical properties are preserved. We conclude with advice on best practice for the consistent unwrapping of constant-pressure simulation trajectories and the calculation of accurate translational diffusion coefficients.

Molecular determinants of inhibition of UCP1-mediated respiratory uncoupling

Brown adipose tissue expresses uncoupling protein 1 (UCP1), which dissipates energy as heat, making it a target for treating metabolic disorders. Here, we investigate how purine nucleotides inhibit respiration uncoupling by UCP1. Our molecular simulations predict that GDP and GTP bind UCP1 in the common substrate binding site in an upright orientation, where the base moiety interacts with conserved residues R92 and E191. We identify a triplet of uncharged residues, F88/I187/W281, forming hydrophobic contacts with nucleotides. In yeast spheroplast respiration assays, both I187A and W281A mutants increase the fatty acid-induced uncoupling activity of UCP1 and partially suppress the inhibition of UCP1 activity by nucleotides. The F88A/I187A/W281A triple mutant is overactivated by fatty acids even at high concentrations of purine nucleotides. In simulations, E191 and W281 interact with purine but not pyrimidine bases. These results provide a molecular understanding of the selective inhibition of UCP1 by purine nucleotides.

Consistent Picture of Phosphate-Divalent Cation Binding from Models with Implicit and Explicit Electronic Polarization

The binding of divalent cations to the ubiquitous phosphate group is essential for a number of key biological processes, such as DNA compaction, RNA folding, or interactions of some proteins with membranes. Yet, probing their binding sites, modes, and associated binding free energy is a challenge for both experiments and simulations. In simulations, standard force fields strongly overestimate the interaction between phosphate groups and divalent cations. Here, we examine how different strategies to include electronic polarization effects in force fields─implicitly, through the use of scaled charges or pair-specific Lennard-Jones parameters, or explicitly, with the polarizable force fields Drude and AMOEBA─capture the interactions of a model phosphate compound, dimethyl phosphate, with calcium and magnesium divalent cations. We show that both implicit and explicit approaches, when carefully parameterized, are successful in capturing the overall binding free energy and that common trends emerge from the comparison of different simulation approaches. Overall, the binding is very moderate, slightly weaker for Ca²⁺ than Mg²⁺, and the solvent-shared ion pair is slightly more stable than the contact monodentate ion pair. The bidentate ion pair is higher in energy (or even fully unstable for Mg²⁺). Our results thus suggest practical ways to capture the divalent cations with biomolecular phosphate groups in complex biochemical systems. In particular, the computational efficiency of implicit models makes them ideally suited for large-scale simulations of biological assemblies, with improved accuracy compared to state-of-the-art fixed-charge force fields.

Symmetry-Adapted Restraints for Binding Free Energy Calculations

Binding free energy calculations rely critically on a precise definition of the bound state and well-designed ligand restraints to ensure that binding free energy calculations converge rapidly and yield estimates of well-defined thermodynamic quantities. The distance-to-bound-configuration (DBC) is a single variable that can precisely delineate the bound state of a ligand including translational, rotational and conformational degrees of freedom and has been successfully used to capture binding modes with complex geometries. DBC is defined as the root-mean-square deviation (RMSD) of ligand coordinates in the frame of reference of the binding site. In the special case where the ligand features symmetry-equivalent atoms, a standard RMSD arbitrarily distinguishes equivalent poses, mixing equivalent and nonequivalent degrees of freedom, and preventing the precise delineation of the bound state ensemble, which negates the benefits of defining a flat-bottom binding restraint. To remedy this, we introduce a symmetry-adapted DBC coordinate where the RMSD is minimized over permutations of equivalent ligand atoms. This coordinate is implemented in a portable software library, the Collective Variables Module. We tested the approach by computing the absolute binding free energy of benzene to the engineered site of a mutant lysozyme (L99A/M102H) using alchemical free energy perturbation. We found that the symmetry-adapted restraint leads to well-behaved convergence of both the decoupling free energy in the binding site and the restrained free energy in the gas phase, recovering the affinity computed using a classic center-of-mass restraint. Thus, symmetry-adapted DBC seamlessly generalizes the benefits of DBC restraints to the case of symmetric ligands. The underlying symmetric RMSD coordinate can also be used for analyzing or biasing simulations in other contexts than affinity predictions.

Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD

The Collective Variables Dashboard is a software tool for real-time, seamless exploration of molecular structures and trajectories in a customizable space of collective variables. The Dashboard arises from the integration of the Collective Variables Module (also known as Colvars) with the visualization software VMD, augmented with a fully discoverable graphical interface offering interactive workflows for the design and analysis of collective variables. Typical use cases include a priori design of collective variables for enhanced sampling and free energy simulations as well as analysis of any type of simulation or collection of structures in a collective variable space. A combination of those cases commonly occurs when preliminary simulations, biased or unbiased, reveal that an optimized set of collective variables is necessary to improve sampling in further simulations. Then the Dashboard provides an efficient way to intuitively explore the space of likely collective variables, validate them on existing data, and use the resulting collective variable definitions directly in further biased simulations using the Collective Variables Module. Visualization of biasing energies and forces is proposed to help analyze or plan biased simulations. We illustrate the use of the Dashboard on two applications: discovering coordinates to describe ligand unbinding from a protein binding site and designing volume-based variables to bias the hydration of a transmembrane pore.

Multiscale Computational Study of the Conformation of the Full-Length Intrinsically Disordered Protein MeCP2

The malfunction of the methyl-CpG binding protein 2 (MeCP2) is associated with the Rett syndrome, one of the most common causes of cognitive impairment in females. MeCP2 is an intrinsically disordered protein (IDP), making its experimental characterization a challenge. There is currently no structure available for the full-length MeCP2 in any of the databases, and only the structure of its MBD domain has been solved. We used this structure to build a full-length model of MeCP2 by completing the rest of the protein via ab initio modeling. Using a combination of all-atom and coarse-grained simulations, we characterized its structure and dynamics as well as the conformational space sampled by the ID and transcriptional repression domain (TRD) domains in the absence of the rest of the protein. The present work is the first computational study of the full-length protein. Two main conformations were sampled in the coarse-grained simulations: a globular structure similar to the one observed in the all-atom force field and a two-globule conformation. Our all-atom model is in good agreement with the available experimental data, predicting amino acid W104 to be buried, amino acids R111 and R133 to be solvent-accessible, and having a 4.1% α-helix content, compared to the 4% found experimentally. Finally, we compared the model predicted by AlphaFold to our Modeller model. The model was not stable in water and underwent further folding. Together, these simulations provide a detailed (if perhaps incomplete) conformational ensemble of the full-length MeCP2, which is compatible with experimental data and can be the basis of further studies, e.g., on mutants of the protein or its interactions with its biological partners.

Fast and Accurate Multidimensional Free Energy Integration

Enhanced sampling and free energy calculation algorithms of the thermodynamic integration family (such as the adaptive biasing force (ABF) method) are not based on the direct computation of a free energy surface but rather of its gradient. Integrating the free energy surface is nontrivial in dimensions higher than one. Here, the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimensions 2 and 3 using any combination of periodic and nonperiodic (Neumann) boundary conditions. The algorithm is implemented in portable C++ and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as umbrella integration as a post-treatment of umbrella sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradient estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Leliévre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.

Building intuition for binding free energy calculations: Bound state definition, restraints, and symmetry

The theory behind computation of absolute binding free energies using explicit-solvent molecular simulations is well-established, yet somewhat complex, with counter-intuitive aspects. This leads to frequent frustration, common misconceptions, and sometimes erroneous numerical treatment. To improve this, we present the main practically relevant segments of the theory with constant reference to physical intuition. We pinpoint the role of the implicit or explicit definition of the bound state (or the binding site) to make a robust link between an experimental measurement and a computational result. We clarify the role of symmetry and discuss cases where symmetry number corrections have been misinterpreted. In particular, we argue that symmetry corrections as classically presented are a source of confusion and could be advantageously replaced by restraint free energy contributions. We establish that contrary to a common intuition, partial or missing sampling of some modes of symmetric bound states does not affect the calculated decoupling free energies. Finally, we review these questions and pitfalls in the context of a few common practical situations: binding to a symmetric receptor (equivalent binding sites), binding of a symmetric ligand (equivalent poses), and formation of a symmetric complex, in the case of homodimerization.

Mechanistic Insights on Heme-to-Heme Transmembrane Electron Transfer Within NADPH Oxydases From Atomistic Simulations

NOX5 is a member of the NADPH oxidase family which is dedicated to the production of reactive oxygen species. The molecular mechanisms governing transmembrane electron transfer (ET) that permits to shuttle electrons over the biological membrane have remained elusive for a long time. Using computer simulations, we report conformational dynamics of NOX5 embedded within a realistic membrane environment. We assess the stability of the protein within the membrane and monitor the existence of cavities that could accommodate dioxygen molecules. We investigate the heme-to-heme electron transfer. We find a reaction free energy of a few tenths of eV (ca. −0.3 eV) and a reorganization free energy of around 1.1 eV (0.8 eV after including electrostatic induction corrections). The former indicates thermodynamically favorable ET, while the latter falls in the expected values for transmembrane inter-heme ET. We estimate the electronic coupling to fall in the range of the μeV. We identify electron tunneling pathways showing that not only the W378 residue is playing a central role, but also F348. Finally, we reveal the existence of two connected O₂₋binding pockets near the outer heme with fast exchange between the two sites on the nanosecond timescale. We show that when the terminal heme is reduced, O₂ binds closer to it, affording a more efficient tunneling pathway than when the terminal heme is oxidized, thereby providing an efficient mechanism to catalyze superoxide production in the final step. Overall, our study reveals some key molecular mechanisms permitting reactive oxygen species production by NOX5 and paves the road for further investigation of ET processes in the wide family of NADPH oxidases by computer simulations.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Binding of divalent cations to acetate: molecular simulations guided by Raman spectroscopy

We combine Raman-MCR vibrational spectroscopy experiments with ab initio and classical MD simulations to gain molecular insights into carboxylate–cation binding.

A Streamlined, General Approach for Computing Ligand Binding Free Energies and Its Application to GPCR-Bound Cholesterol

The theory of receptor-ligand binding equilibria has long been well-established in biochemistry, and was primarily constructed to describe dilute aqueous solutions. Accordingly, few computational approaches have been developed for making quantitative predictions of binding probabilities in environments other than dilute isotropic solution. Existing techniques, ranging from simple automated docking procedures to sophisticated thermodynamics-based methods, have been developed with soluble proteins in mind. Biologically and pharmacologically relevant protein-ligand interactions often occur in complex environments, including lamellar phases like membranes and crowded, nondilute solutions. Here, we revisit the theoretical bases of ligand binding equilibria, avoiding overly specific assumptions that are nearly always made when describing receptor-ligand binding. Building on this formalism, we extend the asymptotically exact Alchemical Free Energy Perturbation technique to quantifying occupancies of sites on proteins in a complex bulk, including phase-separated, anisotropic, or nondilute solutions, using a thermodynamically consistent and easily generalized approach that resolves several ambiguities of current frameworks. To incorporate the complex bulk without overcomplicating the overall thermodynamic cycle, we simplify the common approach for ligand restraints by using a single distance-from-bound-configuration (DBC) ligand restraint during AFEP decoupling from protein. DBC restraints should be generalizable to binding modes of most small molecules, even those with strong orientational dependence. We apply this approach to compute the likelihood that membrane cholesterol binds to known crystallographic sites on three GPCRs (β₂-adrenergic, 5HT-2B, and μ-opioid) at a range of concentrations. Nonideality of cholesterol in a binary cholesterol:phosphatidylcholine (POPC) bilayer is characterized and consistently incorporated into the interpretation. We find that the three sites exhibit very different affinities for cholesterol: The site on the adrenergic receptor is predicted to be high affinity, with 50% occupancy for 1:10⁹ CHOL:POPC mixtures. The sites on the 5HT-2B and μ-opioid receptor are predicted to be lower affinity, with 50% occupancy for 1:10³ CHOL:POPC and 1:10² CHOL:POPC, respectively. These results could not have been predicted from the crystal structures alone.

Smoothed Biasing Forces Yield Unbiased Free Energies with the Extended-System Adaptive Biasing Force Method

We report a theoretical description and numerical tests of the extended-system adaptive biasing force method (eABF), together with an unbiased estimator of the free energy surface from eABF dynamics. Whereas the original ABF approach uses its running estimate of the free energy gradient as the adaptive biasing force, eABF is built on the idea that the exact free energy gradient is not necessary for efficient exploration, and that it is still possible to recover the exact free energy separately with an appropriate estimator. eABF does not directly bias the collective coordinates of interest, but rather fictitious variables that are harmonically coupled to them; therefore is does not require second derivative estimates, making it easily applicable to a wider range of problems than ABF. Furthermore, the extended variables present a smoother, coarse-grain-like sampling problem on a mollified free energy surface, leading to faster exploration and convergence. We also introduce CZAR, a simple, unbiased free energy estimator from eABF trajectories. eABF/CZAR converges to the physical free energy surface faster than standard ABF for a wide range of parameters.

A Novel Bifunctional Alkylphenol Anesthetic Allows Characterization of γ-Aminobutyric Acid, Type A (GABAA), Receptor Subunit Binding Selectivity in Synaptosomes

Propofol, an intravenous anesthetic, is a positive modulator of the GABA_A receptor, but the mechanistic details, including the relevant binding sites and alternative targets, remain disputed. Here we undertook an in-depth study of alkylphenol-based anesthetic binding to synaptic membranes. We designed, synthesized, and characterized a chemically active alkylphenol anesthetic (2-((prop-2-yn-1-yloxy)methyl)-5-(3-(trifluoromethyl)-3H-diazirin-3-yl)phenol, AziPm-click (1)), for affinity-based protein profiling (ABPP) of propofol-binding proteins in their native state within mouse synaptosomes. The ABPP strategy captured ∼4% of the synaptosomal proteome, including the unbiased capture of five α or β GABA_A receptor subunits. Lack of γ2 subunit capture was not due to low abundance. Consistent with this, independent molecular dynamics simulations with alchemical free energy perturbation calculations predicted selective propofol binding to interfacial sites, with higher affinities for α/β than γ-containing interfaces. The simulations indicated hydrogen bonding is a key component leading to propofol-selective binding within GABA_A receptor subunit interfaces, with stable hydrogen bonds observed between propofol and α/β cavity residues but not γ cavity residues. We confirmed this by introducing a hydrogen bond-null propofol analogue as a protecting ligand for targeted-ABPP and observed a lack of GABA_A receptor subunit protection. This investigation demonstrates striking interfacial GABA_A receptor subunit selectivity in the native milieu, suggesting that asymmetric occupancy of heteropentameric ion channels by alkylphenol-based anesthetics is sufficient to induce modulation of activity.

Evolution of Pentameric Ligand-Gated Ion Channels: Pro-Loop Receptors

Pentameric ligand-gated ion channels (pLGICs) are ubiquitous neurotransmitter receptors in Bilateria, with a small number of known prokaryotic homologues. Here we describe a new inventory and phylogenetic analysis of pLGIC genes across all kingdoms of life. Our main finding is a set of pLGIC genes in unicellular eukaryotes, some of which are metazoan-like Cys-loop receptors, and others devoid of Cys-loop cysteines, like their prokaryotic relatives. A number of such “Cys-less” receptors also appears in invertebrate metazoans. Together, those findings draw a new distribution of pLGICs in eukaryotes. A broader distribution of prokaryotic channels also emerges, including a major new archaeal taxon, Thaumarchaeota. More generally, pLGICs now appear nearly ubiquitous in major taxonomic groups except multicellular plants and fungi. However, pLGICs are sparsely present in unicellular taxa, suggesting a high rate of gene loss and a non-essential character, contrasting with their essential role as synaptic receptors of the bilaterian nervous system. Multiple alignments of these highly divergent sequences reveal a small number of conserved residues clustered at the interface between the extracellular and transmembrane domains. Only the “Cys-loop” proline is absolutely conserved, suggesting the more fitting name “Pro loop” for that motif, and “Pro-loop receptors” for the superfamily. The infered molecular phylogeny shows a Cys-loop and a Cys-less clade in eukaryotes, both containing metazoans and unicellular members. This suggests new hypotheses on the evolutionary history of the superfamily, such as a possible origin of the Cys-loop cysteines in an ancient unicellular eukaryote. Deeper phylogenetic relationships remain uncertain, particularly around the split between bacteria, archaea, and eukaryotes.

Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory

Membrane proteins mediate processes that are fundamental for the flourishing of biological cells. Membrane-embedded transporters move ions and larger solutes across membranes; receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. We present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function, and dynamics of membrane proteins.

A predicted binding site for cholesterol on the GABAA receptor

Modulation of the GABA type A receptor (GABAAR) function by cholesterol and other steroids is documented at the functional level, yet its structural basis is largely unknown. Current data on structurally related modulators suggest that cholesterol binds to subunit interfaces between transmembrane domains of the GABAAR. We construct homology models of a human GABAAR based on the structure of the glutamate-gated chloride channel GluCl of Caenorhabditis elegans. The models show the possibility of previously unreported disulfide bridges linking the M1 and M3 transmembrane helices in the α and γ subunits. We discuss the biological relevance of such disulfide bridges. Using our models, we investigate cholesterol binding to intersubunit cavities of the GABAAR transmembrane domain. We find that very similar binding modes are predicted independently by three approaches: analogy with ivermectin in the GluCl crystal structure, automated docking by AutoDock, and spontaneous rebinding events in unbiased molecular dynamics simulations. Taken together, the models and atomistic simulations suggest a somewhat flexible binding mode, with several possible orientations. Finally, we explore the possibility that cholesterol promotes pore opening through a wedge mechanism.

Role of Internal Water on Protein Thermal Stability: The Case of Homologous G Domains

In this work, we address the question of whether the enhanced stability of thermophilic proteins has a direct connection with internal hydration. Our model systems are two homologous G domains of different stability: the mesophilic G domain of the elongation factor thermal unstable protein from E. coli and the hyperthermophilic G domain of the EF-1α protein from S. solfataricus. Using molecular dynamics simulation at the microsecond time scale, we show that both proteins host water molecules in internal cavities and that these molecules exchange with the external solution in the nanosecond time scale. The hydration free energy of these sites evaluated via extensive calculations is found to be favorable for both systems, with the hyperthermophilic protein offering a slightly more favorable environment to host water molecules. We estimate that, under ambient conditions, the free energy gain due to internal hydration is about 1.3 kcal/mol in favor of the hyperthermophilic variant. However, we also find that, at the high working temperature of the hyperthermophile, the cavities are rather dehydrated, meaning that under extreme conditions other molecular factors secure the stability of the protein. Interestingly, we detect a clear correlation between the hydration of internal cavities and the protein conformational landscape. The emerging picture is that internal hydration is an effective observable to probe the conformational landscape of proteins. In the specific context of our investigation, the analysis confirms that the hyperthermophilic G domain is characterized by multiple states and it has a more flexible structure than its mesophilic homologue.

The adaptive biasing force method: everything you always wanted to know but were afraid to ask

In the host of numerical schemes devised to calculate free energy differences by way of geometric transformations, the adaptive biasing force algorithm has emerged as a promising route to map complex free-energy landscapes. It relies upon the simple concept that as a simulation progresses, a continuously updated biasing force is added to the equations of motion, such that in the long-time limit it yields a Hamiltonian devoid of an average force acting along the transition coordinate of interest. This means that sampling proceeds uniformly on a flat free-energy surface, thus providing reliable free-energy estimates. Much of the appeal of the algorithm to the practitioner is in its physically intuitive underlying ideas and the absence of any requirements for prior knowledge about free-energy landscapes. Since its inception in 2001, the adaptive biasing force scheme has been the subject of considerable attention, from in-depth mathematical analysis of convergence properties to novel developments and extensions. The method has also been successfully applied to many challenging problems in chemistry and biology. In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions. Through free-energy calculations of prototypical molecular systems, many methodological aspects are examined, from stratification strategies to overcoming the so-called hidden barriers in orthogonal space, relevant not only to the adaptive biasing force algorithm but also to other importance-sampling schemes. On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.

Lipid concentration and molar ratio boundaries for the use of isotropic bicelles

Bicelles are model membranes generally made of long-chain dimyristoylphosphatidylcholine (DMPC) and short-chain dihexanoyl-PC (DHPC). They are extensively used in the study of membrane interactions and structure determination of membrane-associated peptides, since their composition and morphology mimic the widespread PC-rich natural eukaryotic membranes. At low DMPC/DHPC (q) molar ratios, fast-tumbling bicelles are formed in which the DMPC bilayer is stabilized by DHPC molecules in the high-curvature rim region. Experimental constraints imposed by techniques such as circular dichroism, dynamic light scattering, or microscopy may require the use of bicelles at high dilutions. Studies have shown that such conditions induce the formation of small aggregates and alter the lipid-to-detergent ratio of the bicelle assemblies. The objectives of this work were to determine the exact composition of those DMPC/DHPC isotropic bicelles and study the lipid miscibility. This was done using (31)P nuclear magnetic resonance (NMR) and exploring a wide range of lipid concentrations (2-400 mM) and q ratios (0.15-2). Our data demonstrate how dilution modifies the actual DMPC/DHPC molar ratio in the bicelles. Care must be taken for samples with a total lipid concentration ≤250 mM and especially at q ∼ 1.5-2, since moderate dilutions could lead to the formation of large and slow-tumbling lipid structures that could hinder the use of solution NMR methods, circular dichroism or dynamic light scattering studies. Our results, supported by infrared spectroscopy and molecular dynamics simulations, also show that phospholipids in bicelles are largely segregated only when q > 1. Boundaries are presented within which control of the bicelles' q ratio is possible. This work, thus, intends to guide the choice of q ratio and total phospholipid concentration when using isotropic bicelles.

Type VI secretion and bacteriophage tail tubes share a common assembly pathway

The Type VI secretion system (T6SS) is a widespread macromolecular structure that delivers protein effectors to both eukaryotic and prokaryotic recipient cells. The current model describes the T6SS as an inverted phage tail composed of a sheath-like structure wrapped around a tube assembled by stacked Hcp hexamers. Although recent progress has been made to understand T6SS sheath assembly and dynamics, there is no evidence that Hcp forms tubes in vivo. Here we show that Hcp interacts with TssB, a component of the T6SS sheath. Using a cysteine substitution approach, we demonstrate that Hcp hexamers assemble tubes in an ordered manner with a head-to-tail stacking that are used as a scaffold for polymerization of the TssB/C sheath-like structure. Finally, we show that VgrG but not TssB/C controls the proper assembly of the Hcp tubular structure. These results highlight the conservation in the assembly mechanisms between the T6SS and the bacteriophage tail tube/sheath.

CHARMM36 united atom chain model for lipids and surfactants

Molecular simulations of lipids and surfactants require accurate parameters to reproduce and predict experimental properties. Previously, a united atom (UA) chain model was developed for the CHARMM27/27r lipids (Hénin, J., et al. J. Phys. Chem. B. 2008, 112, 7008-7015) but suffers from the flaw that bilayer simulations using the model require an imposed surface area ensemble, which limits its use to pure bilayer systems. A UA-chain model has been developed based on the CHARMM36 (C36) all-atom lipid parameters, termed C36-UA, and agreed well with bulk, lipid membrane, and micelle formation of a surfactant. Molecular dynamics (MD) simulations of alkanes (heptane and pentadecane) were used to test the validity of C36-UA on density, heat of vaporization, and liquid self-diffusion constants. Then, simulations using C36-UA resulted in accurate properties (surface area per lipid, X-ray and neutron form factors, and chain order parameters) of various saturated- and unsaturated-chain bilayers. When mixed with the all-atom cholesterol model and tested with a series of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/cholesterol mixtures, the C36-UA model performed well. Simulations of self-assembly of a surfactant (dodecylphosphocholine, DPC) using C36-UA suggest an aggregation number of 53 ± 11 DPC molecules at 0.45 M of DPC, which agrees well with experimental estimates. Therefore, the C36-UA force field offers a useful alternative to the all-atom C36 lipid force field by requiring less computational cost while still maintaining the same level of accuracy, which may prove useful for large systems with proteins.

Allosteric regulation of pentameric ligand-gated ion channels: an emerging mechanistic perspective

Pentameric ligand-gated ion channels (pLGICs) play a central role in intercellular communications in the nervous system by converting the binding of a chemical messenger—a neurotransmitter—into an ion flux through the postsynaptic membrane. They are oligomeric assemblies that provide prototypical examples of allosterically regulated integral membrane proteins. Here, we present an overview of the most recent advances on the signal transduction mechanism based on the X-ray structures of both prokaryotic and invertebrate eukaryotic pLGICs and atomistic Molecular Dynamics simulations. The present results suggest that ion gating involves a large structural reorganization of the molecule mediated by two distinct quaternary transitions, a global twisting and the blooming of the extracellular domain, which can be modulated by ligand binding at the topographically distinct orthosteric and allosteric sites. The emerging model of gating is consistent with a wealth of functional studies and will boost the development of novel pharmacological strategies.

Single-spanning transmembrane domains in cell growth and cell-cell interactions: More than meets the eye?

As a whole, integral membrane proteins represent about one third of sequenced genomes, and more than 50% of currently available drugs target membrane proteins, often cell surface receptors. Some membrane protein classes, with a defined number of transmembrane (TM) helices, are receiving much attention because of their great functional and pharmacological importance, such as G protein-coupled receptors possessing 7 TM segments. Although they represent roughly half of all membrane proteins, bitopic proteins (with only 1 TM helix) have so far been less well characterized. Though they include many essential families of receptors, such as adhesion molecules and receptor tyrosine kinases, many of which are excellent targets for biopharmaceuticals (peptides, antibodies, et al.). A growing body of evidence suggests a major role for interactions between TM domains of these receptors in signaling, through homo and heteromeric associations, conformational changes, assembly of signaling platforms, etc. Significantly, mutations within single domains are frequent in human disease, such as cancer or developmental disorders. This review attempts to give an overview of current knowledge about these interactions, from structural data to therapeutic perspectives, focusing on bitopic proteins involved in cell signaling.

An atomistic model for simulations of the general anesthetic isoflurane

An atomistic model of isoflurane is constructed and calibrated to describe its conformational preferences and intermolecular interactions. The model, which is compatible with the CHARMM force field for biomolecules, is based on target quantities including bulk liquid properties, molecular conformations, and local interactions with isolated water molecules. Reference data is obtained from tabulated thermodynamic properties and high-resolution structural information from gas-phase electron diffraction, as well as DFT calculations at the B3LYP level. The model is tested against experimentally known solvation properties in water and oil, and shows quantitative agreement. In particular, isoflurane is faithfully described as lipophilic, yet nonhydrophobic, a combination of properties critical to its pharmacological activity. Intermolecular interactions of the model are further probed through simulations of the binding of isoflurane to a binding site in horse spleen apoferritin (HSAF). The observed binding mode compares well with crystallographic data, and the calculated binding affinities are compatible with experimental results, although both computational and experimental measurements are challenging and provide results with limited precision. The model is expected to be useful for detailed simulations of the elementary molecular processes associated with anesthesia. Full parameters are provided as Supporting Information.

Models for phosphatidylglycerol lipids put to a structural test

Three atomistic empirical models for phosphatidylglycerol (PG) lipids are tested against structural data in the crystal and liquid crystal states. Simulations of the anhydrous crystal of dimyristoyl-phosphatidylglycerol (DMPG) show that only the CHARMM force field describes the conformation and interactions of PG head groups accurately. The other two models do not reproduce the native network of hydrogen bonds, suggesting the presence of biases in their conformational and nonbonded interaction properties. The CHARMM model is further validated in the biologically relevant liquid crystal phase by comparing experimental small-angle X-ray scattering spectra from DMPG unilamellar vesicles with data calculated from fluid bilayer simulations. The good agreement found in this model-free comparison implies that liquid crystal PG bilayers as described by CHARMM exhibit realistic bilayer thickness and lateral packing. Last, this model is used to simulate a fluid bilayer of palmitoyl-oleoyl-phosphatidylglycerol (POPG). The resulting view of the POPG bilayer structure is at variance with that proposed previously based on simulations, in particular, with respect to lateral packing of head groups and the role of counterions.

United-atom acyl chains for CHARMM phospholipids

In all-atom simulations of lipid membranes, explicit hydrogen atoms contained in the hydrocarbon region are described by a large number of degrees of freedom, although they convey only limited physical information. We propose an implicit-hydrogen model for saturated and monounsaturated acyl chains, aimed at complementing the all-atom CHARMM27 model for phospholipid headgroups. Torsional potentials and nonbonded parameters were fitted to reproduce experimental data and free energy surfaces of all-atom model systems. Comparative simulations of fluid-phase POPC bilayers were performed using the all-hydrogen force field and the present model. The hybrid model accelerates a typical bilayer simulation by about 50% while sacrificing a minimal amount of detail with respect to the fully atomistic description. In addition, the united-atom description is energetically compatible with all-atom CHARMM models, making it suitable for simulations of complex membrane systems.

Conformational Equilibrium in Alanine-Rich Peptides Probed by Reversible Stretching Simulations

Reversible stretching of the alanine-rich peptide 3K (Proc. Natl. Acad. Sci. USA 1989, 86, 5286-5290) and its analogue MW (Nature 1992, 359, 653-655) is examined using molecular dynamics simulations in explicit water. In both cases, sampling of the extension pathway is obtained on the 10 ns time scale by applying an adaptive biasing force. The free energy profile reveals a single minimum associated with a contiguous alpha-helix. Short 3(10)-helical motifs are observed in folded as well as extended conformations, in accordance with their proposed role as folding intermediates. The native 3(10)-helical content of both peptides is found, however, to be no higher than a few percent. Difficulties in both the definition and the detection of secondary structure motifs, most notably in relation to bifurcated hydrogen bonds, are proposed to account for the discrepancy between 3(10)-helical propensities reported by several authors, based on experimental and computational results.

Exploring the free-energy landscape of a short peptide using an average force

The reversible folding of deca-alanine is chosen as a test case for characterizing a method that uses an adaptive biasing force (ABF) to escape from the minima and overcome the barriers of the free-energy landscape. This approach relies on the continuous estimation of a biasing force that yields a Hamiltonian in which no average force is exerted along the ordering parameter xi. Optimizing the parameters that control how the ABF is applied, the method is shown to be extremely effective when a nonequivocal ordering parameter can be defined to explore the folding pathway of the peptide. Starting from a beta-turn motif and restraining xi to a region of the conformational space that extends from the alpha-helical state to an ensemble of extended structures, the ABF scheme is successful in folding the peptide chain into a compact alpha helix. Sampling of this conformation is, however, marginal when the range of xi values embraces arrangements of greater compactness, hence demonstrating the inherent limitations of free-energy methods when ambiguous ordering parameters are utilized.

Probing a model of a GPCR/ligand complex in an explicit membrane environment: the human cholecystokinin-1 receptor

A three-dimensional model structure of a complex formed by a G-protein-coupled receptor (GPCR) and an agonist ligand is probed and refined using molecular-dynamics simulations and free energy calculations in a realistic environment. The model of the human receptor of cholecystokinin associated to agonist ligand CCK9 was obtained from a synergistic procedure combining site-directed mutagenesis experiments and in silico modeling. The 31-ns molecular-dynamics simulation in an explicit membrane environment indicates that both the structure of the receptor and its interactions with the ligand are robust. Whereas the secondary structure of the alpha-helix bundle is well preserved, the region of the intracellular loops exhibits a significant flexibility likely to be ascribed to the absence of G-protein subunits in the model. New insight into the structural features of the binding pocket is gained, in particular, the interplay of the ligand with both the receptor and internal water molecules. Water-mediated interactions are shown to participate in the binding, hence, suggesting additional site-directed mutagenesis experiments. Accurate free energy calculations on mutated ligands provide differences in the receptor-ligand binding affinity, thus offering a direct, quantitative comparison to experiment. We propose that this detailed consistency-checking procedure be used as a routine refinement step of in vacuo GPCR models, before further investigation and application to structure-based drug design.

Insights into the Recognition and Association of Transmembrane α-Helices. The Free Energy of α-Helix Dimerization in Glycophorin A

The free energy of alpha-helix dimerization of the transmembrane (TM) region of glycophorin A was estimated from a 125-ns molecular dynamics (MD) simulation in a membrane mimetic. The free energy profile was obtained by allowing the TM helical segments to diffuse reversibly along the reaction pathway. Partition of the potential of mean force into free energy components illuminates the critical steps of alpha-helix recognition and association. At large separations, the TM segments are pushed together by the solvent, allowing initial, but not necessarily native, interhelical interactions to occur. This early recognition stage precedes the formation of native contacts, which is accompanied by a tilt of the helices, characteristic of the dimeric structure. This step is primarily driven by the van der Waals helix-helix interactions. Free energy perturbation calculations of the L75A and I76A point mutations reveal a disruption in helix-helix association due to a loss of favorable dispersion interactions. Additional MD simulations of the native TM dimer and of a single alpha-helix confirm that, prior to association, individual alpha-helices are independently stable, in agreement with the "two-stage" model of integral membrane protein folding.

Overcoming free energy barriers using unconstrained molecular dynamics simulations

Association of unconstrained molecular dynamics (MD) and the formalisms of thermodynamic integration and average force [Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)] have been employed to determine potentials of mean force. When implemented in a general MD code, the additional computational effort, compared to other standard, unconstrained simulations, is marginal. The force acting along a chosen reaction coordinate xi is estimated from the individual forces exerted on the chemical system and accumulated as the simulation progresses. The estimated free energy derivative computed for small intervals of xi is canceled by an adaptive bias to overcome the barriers of the free energy landscape. Evolution of the system along the reaction coordinate is, thus, limited by its sole self-diffusion properties. The illustrative examples of the reversible unfolding of deca-L-alanine, the association of acetate and guanidinium ions in water, the dimerization of methane in water, and its transfer across the water liquid-vapor interface are examined to probe the efficiency of the method.