Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

Molecular Dynamics Simulations of a DMPC Bilayer Using Nonadditive Interaction Models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.     

A Novel Implicit Solvent Model for Simulating the Molecular Dynamics of?RNA

Although molecular dynamics simulations can be accelerated by more than an order of magnitude by implicitly describing the influence of the solvent with a continuum model, most currently available implicit solvent simulations cannot robustly simulate the structure and dynamics of nucleic acids. The difficulties become exacerbated especially for RNAs, suggesting the presence of serious physical flaws in the prior continuum models for the influence of the solvent and counter ions on the nucleic acids. We present a novel, to our knowledge, implicit solvent model for simulating nucleic acids by combining the Langevin–Debye model and the Poisson–Boltzmann equation to provide a better estimate of the electrostatic screening of both the water and counter ions. Tests of the model involve comparisons of implicit and explicit solvent simulations for three RNA targets with 20, 29, and 75 nucleotides. The model provides reasonable agreement with explicit solvent simulations, and directions for future improvement are noted.     

A Novel Implicit Solvent Model for Simulating the Molecular Dynamics of RNA

Although molecular dynamics simulations can be accelerated by more than an order of magnitude by implicitly describing the influence of the solvent with a continuum model, most currently available implicit solvent simulations cannot robustly simulate the structure and dynamics of nucleic acids. The difficulties become exacerbated especially for RNAs, suggesting the presence of serious physical flaws in the prior continuum models for the influence of the solvent and counter ions on the nucleic acids. We present a novel, to our knowledge, implicit solvent model for simulating nucleic acids by combining the Langevin–Debye model and the Poisson–Boltzmann equation to provide a better estimate of the electrostatic screening of both the water and counter ions. Tests of the model involve comparisons of implicit and explicit solvent simulations for three RNA targets with 20, 29, and 75 nucleotides. The model provides reasonable agreement with explicit solvent simulations, and directions for future improvement are noted.     

Effect of membrane tension on the electric field and dipole potential of lipid bilayer membrane

The dipole potential of lipid bilayer membrane controls the difference in permeability of the membrane to oppositely charged ions. We have combined molecular dynamics (MD) simulations and experimental studies to determine changes in electric field and electrostatic potential of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer in response to applied membrane tension. MD simulations based on CHARMM36 force field showed that electrostatic potential of DOPC bilayer decreases by ~45mV in the physiologically relevant range of membrane tension values (0 to 15dyn/cm). The electrostatic field exhibits a peak (~0.8×10(9)V/m) near the water/lipid interface which shifts by 0.9? towards the bilayer center at 15dyn/cm. Maximum membrane tension of 15dyn/cm caused 6.4% increase in area per lipid, 4.7% decrease in bilayer thickness and 1.4% increase in the volume of the bilayer. Dipole-potential sensitive fluorescent probes were used to detect membrane tension induced changes in DOPC vesicles exposed to osmotic stress. Experiments confirmed that dipole potential of DOPC bilayer decreases at higher membrane tensions. These results are suggestive of a potentially new mechanosensing mechanism by which mechanically induced structural changes in the lipid bilayer membrane could modulate the function of membrane proteins by altering electrostatic interactions and energetics of protein conformational states.     

Molecular origin of the internal dipole potential in lipid bilayers: calculation of the electrostatic potential.

The finite difference linearized Poisson-Boltzmann equation was solved for a segment of bilayer for two lipids (phosphatidylcholine dihydrate and phosphatidylethanolamine-acetic acid) in order to obtain the transbilayer electrostatic potential. Atomic coordinates derived from the crystal structures of these lipids were used, and partial changes were assigned to all atoms in the polar parts of the molecules. These calculations confirmed that a dipole potential exists in the uncharged hydrophobic interior of a bilayer. The phosphocholine and phosphoethanolamine groups make negative contributions to the internal potential, and the glycerol acyl esters make positive contributions, but the sum of these terms is negative. The water of hydration in phosphatidylcholine, and the acetic acid which is present in the phosphatidylethanolamine crystal structure, make positive contributions to the internal potential. It is concluded that the water of hydration in fully hydrated lipid bilayers is mainly responsible for the experimentally inferred positive sign of the internal potential.     

Stability of an ion channel in lipid bilayers: implicit solvent model calculations with gramicidin

Gramicidin is a helical peptide, 15 residues in length, which dimerizes to form ion-conducting channels in lipid bilayers. Here we report calculations of its free energy of transfer from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the desolvation free energy were calculated using implicit solvent models, in which gramicidin was described in atomic detail and the hydrocarbon region of the membrane was described as a slab of hydrophobic medium embedded in water. The free energy penalties from the lipid perturbation and membrane deformation effects, and the entropy loss associated with gramicidin immobilization in the bilayer, were estimated from a statistical thermodynamic model of the bilayer. The calculations were carried out using two classes of experimentally observed conformations: a head-to-head dimer of two single-stranded (SS) beta-helices and a double-stranded (DS) intertwined double helix. The calculations showed that gramicidin is likely to partition into the bilayer in all of these conformations. However, the SS conformation was found to be significantly more stable than the DS in the bilayer, in agreement with most of the experimental data. We tested numerous transmembrane and surface orientations of gramicidin in bilayers of various widths. Our calculations indicate that the most favorable orientation is transmembrane, which is indeed to be expected from a channel-forming peptide. The calculations demonstrate that gramicidin insertion into the membrane is likely to involve a significant deformation of the bilayer to match the hydrophobic width of the peptide (22 A), again in good agreement with experimental data. Interestingly, deformation of the bilayer was induced by all of the gramicidin conformations.     

Structure refinement of membrane proteins via molecular dynamics simulations

A refinement protocol based on physics‐based techniques established for water soluble proteins is tested for membrane protein structures. Initial structures were generated by homology modeling and sampled via molecular dynamics simulations in explicit lipid bilayer and aqueous solvent systems. Snapshots from the simulations were selected based on scoring with either knowledge‐based or implicit membrane‐based scoring functions and averaged to obtain refined models. The protocol resulted in consistent and significant refinement of the membrane protein structures similar to the performance of refinement methods for soluble proteins. Refinement success was similar between sampling in the presence of lipid bilayers and aqueous solvent but the presence of lipid bilayers may benefit the improvement of lipid‐facing residues. Scoring with knowledge‐based functions (DFIRE and RWplus) was found to be as good as scoring using implicit membrane‐based scoring functions suggesting that differences in internal packing is more important than orientations relative to the membrane during the refinement of membrane protein homology models.     

Parameterization and Application of an Implicit Solvent Model for Macromolecules

Abstract

As the field of theoretical biophysics begins to recognize systems of longer timescales and larger magnitude, rapid approaches for investigating these systems are required. One promising simplification of the typical system of a solute surrounded by water is the use of implicit solvation models. The generalized Born implicit solvent offers a rapid approach for computing the electrostatic effects of bulk solvent without the explicit representation of water molecules. This report describes the parameterization of a generalized Born (GB) model for protein and nucleic acid structures. As a demonstration of the usefulness of this approach, the GB model is applied toward the discrimination of misfolded and properly folded protein structures. This study attempts to illustrate the potential of the GB model for molecular dynamics simulations over longer timescales as well as for screening large structural databases.     

Molecular dynamics simulations of local anesthetic articaine in a lipid bilayer

In order to investigate structural and dynamical properties of local anesthetic articaine in a model lipid bilayer, a series of molecular dynamics simulations have been performed. Simulations were carried out for neutral and charged (protonated) forms of articaine inserted in fully hydrated dimyristoylphosphatidylcholine (DMPC) lipid bilayer. For comparison purpose, a fully hydrated DMPC bilayer without articaine was also simulated. The length of each simulation was 200 ns. Various properties of the lipid bilayer systems in the presence of both charged and uncharged forms of articaine taken at two different concentrations have been examined: membrane area per lipid, mass density distributions, order parameters, radial distribution functions, head group tilt, diffusion coefficients, electrostatic potential, etc, and compared with results of previous simulations of DMPC bilayer in the presence of lidocaine. It was shown that addition of both charged and neutral forms of articaine causes increase of the dipole electrostatic potential in the membrane interior.     

Solvation Effects on the Conformational Behaviour of Gellan and Calcium Ion Binding to Gellan Double Helices

The contribution of the presence of solvent to the conformations adopted by disaccharide fragments within the repeat unit of gellan have been studied by molecular modelling techniques. Initial conformational energy searches, using a dielectric continuum to represent the solvent, provided starting geometries for a series of molecular dynamics simulations. The solution behaviour from these simulations was subsequently compared to fibre diffraction data of the potassium gellan salt. The present calculations indicate considerable flexibility of the glycosidic linkages, and this is discussed in relation to its effect on gel formation. One of the fragments was solvated with explicit water molecules. These calculations showed the same conformational behaviour as those simulations conducted in implicit solvent.Finally, a series of molecular dynamics (MD) simulations were performed to study the calcium binding to gellan. The results from this clearly showed a well defined binding site for this ion.Abbreviations MM molecular mechanics - MD molecular dynamics     

A method to determine dielectric constants in nonhomogeneous systems: application to biological membranes

Continuum electrostatic models have had quantitative success in describing electrostatic-mediated phenomena on atomistic scales; however, there continues to be significant disagreement about how to assign dielectric constants in mixed, nonhomogeneous systems. We introduce a method for determining a position-dependent dielectric profile from molecular dynamics simulations. In this method, the free energy of introducing a test charge is computed two ways: from a free energy perturbation calculation and from a numerical solution to Poisson's Equation. The dielectric profile of the system is then determined by minimizing the discrepancy between these two calculations simultaneously for multiple positions of the test charge. We apply this method to determine the dielectric profile of a lipid bilayer surrounded by water. We find good agreement with dielectric models for lipid bilayers obtained by other approaches. The free energy of transferring an ion from bulk water to the lipid bilayer computed from the atomistic simulations indicates that large errors are introduced when the bilayer is represented as a single slab of low dielectric embedded in the higher-dielectric solvent. Significant improvement results from introducing an additional layer of intermediate dielectric (∼3) on each side of the low dielectric core extending from ∼12 Å to 18 Å. A small dip in transfer free energy just outside the lipid headgroups indicates the presence of a very high dielectric. These results have implications for the design of implicit membrane models and our understanding of protein-membrane interactions.     

Characterization of the outer membrane protein OprF of Pseudomonas aeruginosa in a lipopolysaccharide membrane by computer simulation

The N-terminal domain of outer membrane protein OprF of Pseudomonas aeruginosa forms a membrane spanning eight-stranded antiparallel beta-barrel domain that folds into a membrane channel with low conductance. The structure of this protein has been modeled after the crystal structure of the homologous protein OmpA of Escherichia coli. A number of molecular dynamics simulations have been carried out for the homology modeled structure of OprF in an explicit molecular model for the rough lipopolysaccharide (LPS) outer membrane of P. aeruginosa. The structural stability of the outer membrane model as a result of the strong electrostatic interactions compared with simple lipid bilayers is restricting both the conformational flexibility and the lateral diffusion of the porin in the membrane. Constricting side-chain interactions within the pore are similar to those found in reported simulations of the protein in a solvated lipid bilayer membrane. Because of the strong interactions between the loop regions of OprF and functional groups in the saccharide core of the LPS, the entrance to the channel from the extracellular space is widened compared with the lipid bilayer simulations in which the loops are extruding in the solvent. The specific electrostatic signature of the LPS membrane, which results in a net intrinsic dipole across the membrane, is found to be altered by the presence of OprF, resulting in a small electrically positive patch at the position of the channel.     

Continuum dielectric modelling of the protein-solvent system, and calculation of the long-range electrostatic field of the enzyme phosphoglycerate mutase

The numerical continuum electrostatic method presented previously (Warwicker, J. & Watson, H. C. (1982) J. Mol. Biol., 157, 671-679), is developed with an improved analysis of the protein-solvent system. Inclusion in the model of saturable solvent dielectric, and counterions is discussed and presented. A number of long-range electrostatic field calculations are made on bovine pancreatic trypsin inhibitor to demonstrate the differences between various solvent and counterion models. The long-range potential field, due to polar side-chain and alpha-helix dipole charge, is calculated for the glycolytic enzyme phosphoglycerate mutase. The positive potential in and around the catalytic cleft region is sufficiently large to suggest that it may play a role in long-range attraction of the enzyme's negatively charged substrates. Analogous systems with charge-charge interactions in solvent water are considered. It is suggested that a long-range enzyme-substrate attractive force-field may, in part, offset the repulsive energy arising from overlap of hydration shells between enzyme and substrate.     

Solvent impact on the aromaticity of benzene analogues: implicit versus explicit solvent approach

Solvent impact on the structural index of aromaticity was modelled by polarised continuum field approximation (IEFPCM) and hybrid quantum chemistry (QM/MM) method. Significant solvent related relaxation of the solutes geometries were noticed especially for highly polar species. The significant reduction of the aromaticity was observed for some aromatic compounds in water solution compared to gas phase. The rationale of this fact was provided based on dipole moment changes, energy penalty for polarisation of solute and the distribution of frontier orbital densities. The incoherent predictions of explicit and implicit solvation models are noticed since in some cases the PCM approach artificially exaggerate the geometry relaxation in solution which is not observed if explicit solvent molecules are taken into account.     

Probing the role of interfacial waters in protein–DNA recognition using a hybrid implicit/explicit solvation model

When proteins bind to their DNA target sites, ordered water molecules are often present at the protein–DNA interface bridging protein and DNA through hydrogen bonds. What is the role of these ordered interfacial waters? Are they important determinants of the specificity of DNA sequence recognition, or do they act in binding in a primarily nonspecific manner, by improving packing of the interface, shielding unfavorable electrostatic interactions, and solvating unsatisfied polar groups that are inaccessible to bulk solvent? When modeling details of structure and binding preferences, can fully implicit solvent models be fruitfully applied to protein–DNA interfaces, or must the individualistic properties of these interfacial waters be accounted for? To address these questions, we have developed a hybrid implicit/explicit solvation model that specifically accounts for the locations and orientations of small numbers of DNA‐bound water molecules, while treating the majority of the solvent implicitly. Comparing the performance of this model with that of its fully implicit counterpart, we find that explicit treatment of interfacial waters results in a modest but significant improvement in protein side‐chain placement and DNA sequence recovery. Base‐by‐base comparison of the performance of the two models highlights DNA sequence positions whose recognition may be dependent on interfacial water. Our study offers large‐scale statistical evidence for the role of ordered water for protein–DNA recognition, together with detailed examination of several well‐characterized systems. In addition, our approach provides a template for modeling explicit water molecules at interfaces that should be extensible to other systems. Proteins 2013; 81:1318–1329. © 2013 Wiley Periodicals, Inc.     

Constant-pressure molecular dynamics investigation of cholesterol effects in a dipalmitoylphosphatidylcholine bilayer.

We report a 1.4-ns constant-pressure molecular dynamics simulation of cholesterol at 12.5 mol% in a dipalmitoylphosphatidylcholine (DPPC) bilayer at 50 degrees C and compare the results to our previous simulation of a pure DPPC bilayer. The interlamellar spacing was increased by 2.5 A in the cholesterol-containing bilayer, consistent with x-ray diffraction results, whereas the bilayer thickness was increased by only 1 A. The bilayer/water interface was more abrupt because the lipid headgroups lie flatter to fill spaces left by the cholesterol molecules. This leads to less compensation by the lipid headgroups of the oriented water contribution to the membrane dipole potential and could explain the experimentally observed increase in the magnitude of the dipole potential by cholesterol. Our calculations suggested that 12.5 mol% cholesterol does not significantly affect the conformations and packing of the hydrocarbon chains and produces only a slight reduction in the empty free volume. However, cholesterol has a significant influence on the subnanosecond time scale lipid dynamics: the diffusion constant for the center-of-mass "rattling" motion was reduced by a factor of 3, and the reorientational motion of the methylene groups was slowed along the entire length of the hydrocarbon chains.     

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.     

On Calculation of the Electrostatic Potential of a Phosphatidylinositol Phosphate-Containing Phosphatidylcholine Lipid Membrane Accounting for Membrane Dynamics

Many signaling events require the binding of cytoplasmic proteins to cell membranes by recognition of specific charged lipids, such as phosphoinositol-phosphates. As a model for a protein-membrane binding site, we consider one charged phosphoinositol phosphate (PtdIns(3)P) embedded in a phosphatidylcholine bilayer. As the protein-membrane binding is driven by electrostatic interactions, continuum solvent models require an accurate representation of the electrostatic potential of the phosphoinositol phosphate-containing membrane. We computed and analyzed the electrostatic potentials of snapshots taken at regular intervals from molecular dynamics simulations of the bilayer. We observe considerable variation in the electrostatic potential of the bilayer both along a single simulation and between simulations performed with the GAFF or CHARMM c36 force fields. However, we find that the choice of GAFF or CHARMM c36 parameters has little effect on the electrostatic potential of a given configuration of the bilayer with a PtdIns(3)P embedded in it. From our results, we propose a remedian averaging method for calculating the electrostatic potential of a membrane system that is suitable for simulations of protein-membrane binding with a continuum solvent model.     

The barrier for proton transport in aquaporins as a challenge for electrostatic models: the role of protein relaxation in mutational calculations

The origin of the barrier for proton transport through the aquaporin channel is a problem of general interest. It is becoming increasingly clear that this barrier is not attributable to the orientation of the water molecules across the channel but rather to the electrostatic penalty for moving the proton charge to the center of the channel. However, the reason for the high electrostatic barrier is still rather controversial. It has been argued by some workers that the barrier is due to the so-called NPA motif and/or to the helix macrodipole or to other specific elements. However, our works indicated that the main reason for the high barrier is the loss of the generalized solvation upon moving the proton charge from the bulk to the center of the channel and that this does not reflect a specific repulsive electrostatic interaction but the absence of sufficient electrostatic stabilization. At this stage it seems that the elucidation and clarification of the origin of the electrostatic barrier can serve as an instructive test case for electrostatic models. Thus, we reexamine the free-energy surface for proton transport in aquaporins using the microscopic free-energy perturbation/umbrella sampling (FEP/US) and the empirical valence bond/umbrella sampling (EVB/US) methods as well as the semimacroscopic protein dipole Langevin dipole model in its linear response approximation version (the PDLD/S-LRA). These extensive studies help to clarify the nature of the barrier and to establish the "reduced solvation effect" as the primary source of this barrier. That is, it is found that the barrier is associated with the loss of the generalized solvation energy (which includes of course all electrostatic effects) upon moving the proton charge from the bulk solvent to the center of the channel. It is also demonstrated that the residues in the NPA region and the helix dipole cannot be considered as the main reasons for the electrostatic barrier. Furthermore, our microscopic and semimacroscopic studies clarify the problems with incomplete alternative calculations, illustrating that the effects of various electrostatic elements are drastically overestimated by macroscopic calculations that use a low dielectric constant and do not consider the protein reorganization. Similarly, it is pointed out that microscopic potential of mean force calculations that do not evaluate the electrostatic barrier relative to the bulk water cannot be used to establish the origin of the electrostatic barrier. The relationship between the present study and calculations of pK(a)s in protein interiors is clarified, pointing out that approaches that are applied to study the aquaporin barrier should be validated by pK(a)s calculations. Such calculations also help to clarify the crucial role of solvation energies in establishing the barrier in aquaporins.