Parameterization of a coarse-grained model of cholesterol with point-dipole electrostatics

We present a new coarse-grained (CG) model of cholesterol (CHOL) for the electrostatic-based ELBA force field. A distinguishing feature of our CHOL model is that the electrostatics is modeled by an explicit point dipole which interacts through an ideal vacuum permittivity. The CHOL model parameters were optimized in a systematic fashion, reproducing the electrostatic and nonpolar partitioning free energies of CHOL in lipid/water mixtures predicted by full-detailed atomistic molecular dynamics simulations. The CHOL model has been validated by comparison to structural, dynamic and thermodynamic properties with experimental and atomistic simulation reference data. The simulation of binary DPPC/cholesterol mixtures covering the relevant biological content of CHOL in mammalian membranes is shown to correctly predict the main lipid behavior as observed experimentally.     

Anisotropic solvent model of the lipid bilayer. 2. Energetics of insertion of small molecules, peptides, and proteins in membranes

A new computational approach to calculating binding energies and spatial positions of small molecules, peptides, and proteins in the lipid bilayer has been developed. The method combines an anisotropic solvent representation of the lipid bilayer and universal solvation model, which predicts transfer energies of molecules from water to an arbitrary medium with defined polarity properties. The universal solvation model accounts for hydrophobic, van der Waals, hydrogen-bonding, and electrostatic solute-solvent interactions. The lipid bilayer is represented as a fluid anisotropic environment described by profiles of dielectric constant (ε), solvatochromic dipolarity parameter (π*), and hydrogen bonding acidity and basicity parameters (α and β). The polarity profiles were calculated using published distributions of quasi-molecular segments of lipids determined by neutron and X-ray scattering for DOPC bilayer and spin-labeling data that define concentration of water in the lipid acyl chain region. The model also accounts for the preferential solvation of charges and polar groups by water and includes the effect of the hydrophobic mismatch for transmembrane proteins. The method was tested on calculations of binding energies and preferential positions in membranes for small-molecules, peptides and peripheral membrane proteins that have been experimentally studied. The new theoretical approach was implemented in a new version (2.0) of our PPM program and applied for the large-scale calculations of spatial positions in membranes of more than 1000 peripheral and integral proteins. The results of calculations are deposited in the updated OPM database ( http://opm.phar.umich.edu ).     

Testing the semi-explicit assembly model of aqueous solvation in the SAMPL4 challenge

Here, we test a method, called semi-explicit assembly (SEA), that computes the solvation free energies of molecules in water in the SAMPL4 blind test challenge. SEA was developed with the intention of being as accurate as explicit-solvent models, but much faster to compute. It is accurate because it uses pre-simulations of simple spheres in explicit solvent to obtain structural and thermodynamic quantities, and it is fast because it parses solute free energies into regionally additive quantities. SAMPL4 provided us the opportunity to make new tests of SEA. Our tests here lead us to the following conclusions: (1) The newest version, called Field-SEA, which gives improved predictions for highly charged ions, is shown here to perform as well as the earlier versions (dipolar and quadrupolar SEA) on this broad blind SAMPL4 test set. (2) We find that both the past and present SEA models give solvation free energies that are as accurate as TIP3P. (3) Using a new approach for force field parameter optimization, we developed improved hydroxyl parameters that ensure consistency with neat-solvent dielectric constants, and found that they led to improved solvation free energies for hydroxyl-containing compounds in SAMPL4. We also learned that these hydroxyl parameters are not just fixing solvent exposed oxygens in a general sense, and therefore do not improve predictions for carbonyl or carboxylic-acid groups. Other such functional groups will need their own independent optimizations for potential improvements. Overall, these tests in SAMPL4 indicate that SEA is an accurate, general and fast new approach to computing solvation free energies.     

Adsorption of phenyltin compounds onto phosphatidylcholine / cholesterol bilayers

Phenyltin compounds are known to be biologically active and, whan widely spread, are potentially hazardous. As their chemical structure suggests, they interact with the lipid fraction of the cell membrane. Their effect on the model phosphatidylcholine/cholesterol bilayer has been studied using fluorescence and ¹H NMR techniques. The change in the fluorescein‐PE fluorescence intensity indicates the amount of charge added by phenyltin compounds to the membrane surface. Although the presence of cholesterol alone does not alter membrane interface properties measured with fluorescein‐PE, ¹H NMR measurements show that lipid mobility is altered throughout the hydrophobic core of the membrane. Cholesterol in the phosphatidylcholine bilayer does not alter tetraphenyltin interaction with the membrane, though the effect of diphenyltin dichloride, penetrating deeply into the hydrophobic core of the membrane, is reduced when the amount of cholesterol in the membrane is increased, suggesting decreased compound adsorption. Triphenyltin chloride has a qualitatively different effect on the lipid bilayer, when observed using this fluorescence technique. The adsorption of triphenyltin onto the phosphatidylcholine/cholesterol membrane induces a lateral phase separation of membrane components. Since triphenyltin chloride is known to be adsorbed onto the interface of the lipid bilayer, this separation mechanism must originate in this region and does not seem to be electrostatic in origin. ¹H NMR measurements have confirmed the observation that these two active phenyltin compounds interact with the phosphatidylcholine/cholesterol membrane differently, disrupting different regions of the bilayer to a different degree. Copyright © 2000 John Wiley & Sons, Ltd.     

A multiscale coarse-graining method for biomolecular systems

A new approach is presented for obtaining coarse-grained (CG) force fields from fully atomistic molecular dynamics (MD) trajectories. The method is demonstrated by applying it to derive a CG model for the dimyristoylphosphatidylcholine (DMPC) lipid bilayer. The coarse-graining of the interparticle force field is accomplished by an application of a force-matching procedure to the force data obtained from an explicit atomistic MD simulation of the biomolecular system of interest. Hence, the method is termed a "multiscale" CG (MS-CG) approach in which explicit atomistic-level forces are propagated upward in scale to the coarse-grained level. The CG sites in the lipid bilayer application were associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic data. The resulting CG lipid bilayer model is shown to accurately reproduce the structural properties of the phospholipid bilayer.     

Modifying the OPLS-AA force field to improve hydration free energies for several amino acid side chains using new atomic charges and an off-plane charge model for aromatic residues

The hydration free energies of amino acid side chains are an important determinant of processes that involve partitioning between different environments, including protein folding, protein complex formation, and protein-membrane interactions. Several recent papers have shown that calculated hydration free energies for polar and aromatic residues (Trp, His, Tyr, Asn, Gln, Asp, Glu) in several common molecular dynamics force fields differ significantly from experimentally measured values. We have attempted to improve the hydration energies for these residues by modifying the partial charges of the OPLS-AA force field based on natural population analysis of density functional theory calculations. The resulting differences between calculated hydration free energies and experimental results for the seven side chain analogs are less than 0.1 kcal/mol. Simulations of the synthetic Trp-rich peptide Trpzip2 show that the new charges lead to significantly improved geometries for interacting Trp-side chains. We also investigated an off-plane charge model for aromatic rings that more closely mimics their electronic configuration. This model results in an improved free energy of hydration for Trp and a somewhat altered benzene-sodium potential of mean force with a more favorable energy for direct benzene-sodium contact.     

Direct calculation of the binding free energies of FKBP ligands

Direct calculations of the absolute free energies of binding for eight ligands to FKBP protein were performed using the Fujitsu BioServer massively parallel computer. Using the latest version of the general assisted model building with energy refinement (AMBER) force field for ligand model parameters and the Bennett acceptance ratio for computing free-energy differences, we obtained an excellent linear fit between the calculated and experimental binding free energies. The rms error from a linear fit is 0.4 kcal/mol for eight ligand complexes. In comparison with a previous study of the binding energies of these same eight ligand complexes, these results suggest that the use of improved model parameters can lead to more predictive binding estimates, and that these estimates can be obtained with significantly less computer time than previously thought. These findings make such direct methods more attractive for use in rational drug design.     

Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations

Molecular dynamics simulations in explicit solvent were applied to predict the hydration free energies for 23 small organic molecules in blind SAMPL2 test. We found good agreement with experimental results, with an RMS error of 2.82 kcal/mol over the whole set and 1.86 kcal/mol over all the molecules except several hydroxyl-rich compounds where we find evidence for a systematic error in the force field. We tested two different solvent models, TIP3P and TIP4P-Ew, and obtained very similar hydration free energies for these two models; the RMS difference was 0.64 kcal/mol. We found that preferred conformation of the carboxylic acids in water differs from that in vacuum. Surprisingly, this conformational change is not adequately sampled on simulation timescales, so we apply an umbrella sampling technique to include free energies associated with the conformational change. Overall, the results of this test reveal that the force field parameters for some groups of molecules (such as hydroxyl-rich compounds) still need to be improved, but for most compounds, accuracy was consistent with that seen in our previous tests.     

Water Permeation Through DMPC Lipid Bilayers using Polarizable Charge Equilibration Force Fields

We investigate permeation energetics of water entering a model dimyristoylphosphatidylcholine (DMPC) bilayer via molecular dynamics simulations using polarizable Charge Equilibration (CHEQ) models. Potentials of mean force show 4.5-5.5 kcal/mol barriers for water permeation into bilayers. Barriers are highest when water coordination within the bilayer is prevented, and also when using force fields that accurately reproduce experimental alkane hydration free energies. The magnitude of the average water dipole moment decreases from 2.6 Debye (in bulk) to 1.88 Debye (in membrane interior). This variation correlates with the change in a water molecule's coordination number.     

Amine hydration: a united-atom force-field solution.

The free energies of hydration for ammonia and mono-, di-, and trimethylated amines experimentally show an unexpected trend that has, in the past, been difficult to reproduce computationally. Absolute and relative free energies of hydration of these compounds were calculated using the OPLS all-atom and the united-atom GROMOS force fields. Both force fields reproduce the relative free energy of hydration, but the absolute free energies of hydration were only reproduced within kBT when using the recently developed GROMOS parameter set 53A6. Relative free energies of solvation in chloroform could also be reproduced indicating a proper partitioning of the compounds between polar and apolar media. Overall we conclude that it is possible to resolve the amine hydration problem using a simple united-atom force field.     

Molecular level investigation of organization in ternary lipid bilayer: a computational approach

The differential organization of lipid components in a multicomponent membrane leads to formation of domains having diverse composition and size. Cholesterol and glycosphingolipids are known to be important components of such lateral assembly. We report here the ordering of cholesterol around ganglioside GM1 and the nature of the cluster from an all-atom simulation of a ternary lipid system. The results are compared with a binary bilayer and a pure phospholipid bilayer. The difference in molecular rearrangements in ternary and binary lipid mixture shows the role of GM1 in the rearrangement of cholesterol. Calculation of the radial distribution function, rotational reorientation, and residence time analysis of cholesterol shows that cholesterol is preferentially accumulating near gangliosides, while the lateral translational motion, rotational diffusion, and order parameter of phospholipids characterize the amount of rigidity imparted on the phospholipid bilayer.     

Additive empirical force field for hexopyranose monosaccharides

We present an all-atom additive empirical force field for the hexopyranose monosaccharide form of glucose and its diastereomers allose, altrose, galactose, gulose, idose, mannose, and talose. The model is developed to be consistent with the CHARMM all-atom biomolecular force fields, and the same parameters are used for all diastereomers, including both the alpha- and beta-anomers of each monosaccharide. The force field is developed in a hierarchical manner and reproduces the gas-phase and condensed-phase properties of small-molecule model compounds corresponding to fragments of pyranose monosaccharides. The resultant parameters are transferred to the full pyranose monosaccharides, and additional parameter development is done to achieve a complete hexopyranose monosaccharide force field. Parametrization target data include vibrational frequencies, crystal geometries, solute-water interaction energies, molecular volumes, heats of vaporization, and conformational energies, including those for over 1800 monosaccharide conformations at the MP2/cc-pVTZ//MP2/6-31G(d) level of theory. Although not targeted during parametrization, free energies of aqueous solvation for the model compounds compare favorably with experimental values. Also well-reproduced are monosaccharide crystal unit cell dimensions and ring pucker, densities of concentrated aqueous glucose systems, and the thermodynamic and dynamic properties of the exocyclic torsion in dilute aqueous systems. The new parameter set expands the CHARMM additive force field to allow for simulation of heterogeneous systems that include hexopyranose monosaccharides in addition to proteins, nucleic acids, and lipids.     

Simulating the Physiological Phase of Hydrated DPPC Bilayers: The Ester Moiety

Abstract

The charge on the ester oxygen of the sn2 group of the dipalmitoylphosphatidylcholine (DPPC) has a remarkable effect on the square area per lipid in simulations of a hydrated bilayer. This is in contrast to simulations of nonpolar, neutral lipids, where it has been found to have little effect. The charges associated with the GROMOS96 45A3 and 45A4 biomolecular force fields have been previously shown to cause significant membrane shrinkage. We find that the use of larger charges at the ester groups alone (as opposed to on all the polar moieties in the head group) remedies the shrinkage. The source of this effect in DPPC lies in the fact that the charge distribution of this polar group profoundly influences its free energy of hydration and, correspondingly, the water distribution around it. In an attempt to rationally tune the ester parameters, the repulsive Lennard–Jones parameters that represent the van der Waals interaction have been refined to reproduce the experimental density and heat of vaporization, and the charges of the ester groups have been tuned to reproduce the experimental free energies of hydration of a series of alkane esters. The new parameters form part of the GROMOS96 53A5 and 53A6 force fields. However, with the new force‐field parameters, the area per lipid in simulations of hydrated DPPC bilayers lies below that of the physiological liquid‐crystalline phase, the implications of which are discussed.     

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

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

A reoptimized GROMOS force field for hexopyranose-based carbohydrates accounting for the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers

This article presents a reoptimization of the GROMOS 53A6 force field for hexopyranose-based carbohydrates (nearly equivalent to 45A4 for pure carbohydrate systems) into a new version 56A(CARBO) (nearly equivalent to 53A6 for non-carbohydrate systems). This reoptimization was found necessary to repair a number of shortcomings of the 53A6 (45A4) parameter set and to extend the scope of the force field to properties that had not been included previously into the parameterization procedure. The new 56A(CARBO) force field is characterized by: (i) the formulation of systematic build-up rules for the automatic generation of force-field topologies over a large class of compounds including (but not restricted to) unfunctionalized polyhexopyranoses with arbritrary connectivities; (ii) the systematic use of enhanced sampling methods for inclusion of experimental thermodynamic data concerning slow or unphysical processes into the parameterization procedure; and (iii) an extensive validation against available experimental data in solution and, to a limited extent, theoretical (quantum-mechanical) data in the gas phase. At present, the 56A(CARBO) force field is restricted to compounds of the elements C, O, and H presenting single bonds only, no oxygen functions other than alcohol, ether, hemiacetal, or acetal, and no cyclic segments other than six-membered rings (separated by at least one intermediate atom). After calibration, this force field is shown to reproduce well the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers. As a result, the 56A(CARBO) force field should be suitable for: (i) the characterization of the dynamics of pyranose ring conformational transitions (in simulations on the microsecond timescale); (ii) the investigation of systems where alternative ring conformations become significantly populated; (iii) the investigation of anomerization or epimerization in terms of free-energy differences; and (iv) the design of simulation approaches accelerating the anomerization process along an unphysical pathway.     

Development of the CHARMM Force Field for Lipids

The development of the CHARMM additive all-atom lipid force field (FF) is traced from the early 1990's to the most recent version (C36) published in 2010. Though simulations with early versions yielded useful results, they failed to reproduce two important quantities: a zero surface tension at the experimental bilayer surface area, and the signature splitting of the deuterium order parameters in the glycerol and upper chain carbons. Systematic optimization of parameters based on high level quantum mechanical data and free energy simulations have resolved these issues, and bilayers with a wide range of lipids can be simulated in tensionless ensembles using C36. Issues associated with other all-atom lipid FFs, success and limitations in the C36 FF and ongoing developments are also discussed.     

Impact of cholesterol on voids in phospholipid membranes

Free volume pockets or voids are important to many biological processes in cell membranes. Free volume fluctuations are a prerequisite for diffusion of lipids and other macromolecules in lipid bilayers. Permeation of small solutes across a membrane, as well as diffusion of solutes in the membrane interior are further examples of phenomena where voids and their properties play a central role. Cholesterol has been suggested to change the structure and function of membranes by altering their free volume properties. We study the effect of cholesterol on the properties of voids in dipalmitoylphosphatidylcholine (DPPC) bilayers by means of atomistic molecular dynamics simulations. We find that an increasing cholesterol concentration reduces the total amount of free volume in a bilayer. The effect of cholesterol on individual voids is most prominent in the region where the steroid ring structures of cholesterol molecules are located. Here a growing cholesterol content reduces the number of voids, completely removing voids of the size of a cholesterol molecule. The voids also become more elongated. The broad orientational distribution of voids observed in pure DPPC is, with a 30% molar concentration of cholesterol, replaced by a distribution where orientation along the bilayer normal is favored. Our results suggest that instead of being uniformly distributed to the whole bilayer, these effects are localized to the close vicinity of cholesterol molecules.