Jérôme Hénin

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.

Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables

A new implementation of the adaptive biasing force (ABF) method is described. This implementation supports a wide range of collective variables and can be applied to the computation of multidimensional energy profiles. It is provided to the community as part of a code that implements several analogous methods, including metadynamics. ABF and metadynamics have not previously been tested side by side on identical systems. Here, numerical tests are carried out on processes including conformational changes in model peptides and translocation of a halide ion across a lipid membrane through a peptide nanotube. On the basis of these examples, we discuss similarities and differences between the ABF and metadynamics schemes. Both approaches provide enhanced sampling and free energy profiles in quantitative agreement with each other in different applications. The method of choice depends on the dimension of the reaction coordinate space, the height of the barriers, and the relaxation times of degrees of freedom in the orthogonal space, which are not explicitly described by the chosen collective variables.

Using collective variables to drive molecular dynamics simulations

A software framework is introduced that facilitates the application of biasing algorithms to collective variables of the type commonly employed to drive massively parallel molecular dynamics (MD) simulations. The modular framework that is presented enables one to combine existing collective variables into new ones, and combine any chosen collective variable with available biasing methods. The latter include the classic time-dependent biases referred to as steered MD and targeted MD, the temperature-accelerated MD algorithm, as well as the adaptive free-energy biases called metadynamics and adaptive biasing force. The present modular software is extensible, and portable between commonly used MD simulation engines.

Embedded cholesterol in the nicotinic acetylcholine receptor

The nicotinic acetylcholine receptor (nAChR) is a cation-selective channel central to both neuronal and muscular processes and is considered the prototype for ligand-gated ion channels, motivating a structural determination effort that spanned several decades [Unwin N (2005) Refined structure of the nicotinic acetylcholine receptor at 4 Å resolution. J Mol Biol 346:967–989]. Purified nAChR must be reconstituted in a mixture containing cholesterol to function. Proposed modes of interaction between cholesterol and the protein range from specific binding to indirect membrane-mediated mechanisms. However, the underlying cause of nAChR sensitivity to cholesterol remains controversial, in part because the vast majority of functional studies were conducted before a medium resolution structure was reported. We show that the nAChR contains internal sites capable of containing cholesterol, whose occupation stabilizes the protein structure. We detect sites at the protein–lipid interface as conventionally predicted from functional data, as well as deeply buried sites that are not usually considered. Molecular dynamics simulations reveal that occupation of both superficial and deeply buried sites most effectively preserves the experimental structure; the structure collapses in the absence of bound cholesterol. In particular, we find that bound cholesterol directly supports contacts between the agonist-binding domain and the pore that are thought to be essential for activation of the receptor. These results likely apply to those other ion channels within the Cys-loop superfamily that depend on cholesterol, such as the GABA receptor.

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.

Multiple binding sites for the general anesthetic isoflurane identified in the nicotinic acetylcholine receptor transmembrane domain.

An extensive search for isoflurane binding sites in the nicotinic acetylcholine receptor (nAChR) and the proton gated ion channel from Gloebacter violaceus (GLIC) has been carried out based on molecular dynamics (MD) simulations in fully hydrated lipid membrane environments. Isoflurane introduced into the aqueous phase readily partitions into the lipid membrane and the membrane-bound protein. Specifically, isoflurane binds persistently to three classes of sites in the nAChR transmembrane domain: (i) An isoflurane dimer occludes the pore, contacting residues identified by previous mutagenesis studies; analogous behavior is observed in GLIC. (ii) Several nAChR subunit interfaces are also occupied, in a site suggested by photoaffinity labeling and thought to positively modulate the receptor; these sites are not occupied in GLIC. (iii) Isoflurane binds to the subunit centers of both nAChR α chains and one of the GLIC chains, in a site that has had little experimental targeting. Interpreted in the context of existing structural and physiological data, the present MD results support a multisite model for the mechanism of receptor-channel modulation by anesthetics.

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.

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.

General anesthetics predicted to block the GLIC pore with micromolar affinity.

Although general anesthetics are known to modulate the activity of ligand-gated ion channels in the Cys-loop superfamily, there is at present neither consensus on the underlying mechanisms, nor predictive models of this modulation. Viable models need to offer quantitative assessment of the relative importance of several identified anesthetic binding sites. However, to date, precise affinity data for individual sites has been challenging to obtain by biophysical means. Here, the likely role of pore block inhibition by the general anesthetics isoflurane and propofol of the prokaryotic pentameric channel GLIC is investigated by molecular simulations. Microscopic affinities are calculated for both single and double occupancy binding of isoflurane and propofol to the GLIC pore. Computations are carried out for an open-pore conformation in which the pore is restrained to crystallographic radius, and a closed-pore conformation that results from unrestrained molecular dynamics equilibration of the structure. The GLIC pore is predicted to be blocked at the micromolar concentrations for which inhibition by isofluorane and propofol is observed experimentally. Calculated affinities suggest that pore block by propofol occurs at signifcantly lower concentrations than those for which inhibition is observed: we argue that this discrepancy may result from binding of propofol to an allosteric site recently identified by X-ray crystallography, which may cause a competing gain-of-function effect. Affinities of isoflurane and propofol to the allosteric site are also calculated, and shown to be 3 mM for isoflurane and for propofol; both anesthetics have a lower affinity for the allosteric site than for the unoccupied pore.

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.