Distance and exposure dependent effective dielectric function

Computer simulation of molecular recognition in biomolecular system: from in silico screening to generalized ensembles

Prediction of ligand-receptor complex structure is important in both the basic science and the industry such as drug discovery. We report various computation molecular docking methods: fundamental in silico (virtual) screening, ensemble docking, enhanced sampling (generalized ensemble) methods, and other methods to improve the accuracy of the complex structure. We explain not only the merits of these methods but also their limits of application and discuss some interaction terms which are not considered in the in silico methods. In silico screening and ensemble docking are useful when one focuses on obtaining the native complex structure (the most thermodynamically stable complex). Generalized ensemble method provides a free-energy landscape, which shows the distribution of the most stable complex structure and semi-stable ones in a conformational space. Also, barriers separating those stable structures are identified. A researcher should select one of the methods according to the research aim and depending on complexity of the molecular system to be studied.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.

A New Mixed All-Atom/Coarse-Grained Model: Application to Melittin Aggregation in Aqueous Solution

We introduce a new mixed resolution, all-atom/coarse-grained approach (AACG), for modeling peptides in aqueous solution and apply it to characterizing the aggregation of melittin. All of the atoms in peptidic components are represented, while a single site is used for each water molecule. With the full flexibility of the peptide retained, our AACG method achieves speedups by a factor of 3-4 for CPU time reduction and another factor of roughly 7 for diffusion. An Ewald treatment permits the inclusion of long-range electrostatic interactions. These characteristics fit well with the requirements for studying peptide association and aggregation, where the system sizes and time scales require considerable computational resources with all-atom models. In particular, AACG is well suited for biologics since changes in peptide shape and long-range electrostatics may play an important role. The application of AACG to melittin, a 26-residue peptide with a well-known propensity to aggregate in solution, serves as an initial demonstration of this technology for studying peptide aggregation. We observed the formation of melittin aggregates during our simulations and characterized the time-evolution of aggregate size distribution, buried surface areas, and residue contacts. Key interactions including π-cation and π-stacking involving TRP19 were also examined. Our AACG simulations demonstrated a clear salt effect and a moderate temperature effect on aggregation and support the molten globule model of melittin aggregates. As a showcase, this work illustrates the useful role for AACG in investigations of peptide aggregation and its potential to guide formulation and design of biologics.

A Monte-Carlo simulation of ionic conductivity and viscosity of highly concentrated electrolytes based on a pseudo-lattice model

Simulating three transport phenomena-ionic conductivity, viscosity, and self-diffusion coefficient-in a common Monte-Carlo framework, we discuss their relationship to the intermolecular interactions of electrolyte solutions at high concentrations (C/mol l^-1 ∼ 1). The simulation is predicated on a pseudolattice model of the solution. The ions and solvents (collectively termed "molecules") are considered dimensionless points occupying the lattice sites. The molecular transport is realized by a repetition of swapping two adjacent molecules by the stochastic Gibbs sampling process based on simple intermolecular interactions. The framework has been validated by the fact that the simulated ionic conductivity and dynamic viscosity of 1:1- and 2:1-salts qualitatively well represent the experimental data. The magnitude of the Coulombic interaction itself is not reflected in the ionic conductivity, but the extent to which the Coulombic interaction is shielded by the dielectric constant has a significant influence. On the other hand, the dielectric constant barely influences the viscosity, while the magnitude of the Coulombic interaction is directly reflected in the viscosity.

Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid

We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

Water-exclusion and liquid-structure forces in implicit solvation

A continuum model of solvation is proposed to describe (i) long-range electrostatic effects of water exclusion resulting from incomplete and anisotropic hydration in crowded environments and (ii) short-range effects of liquid-structure forces on the hydrogen-bond interactions at solute/water interfaces. The model is an extension of the phenomenological screened coulomb potential-based implicit model of solvation. The developments reported here allow a more realistic representation of highly crowded and spatially heterogeneous environments, such as those in the interior of a living cell. Only the solvent is treated as a continuum medium. It is shown that the electrostatic effects of long-range water-exclusion can strongly affect protein-protein binding energies and are then related to the thermodynamics of complex formation. Hydrogen-bond interactions modulated by the liquid structure at interfaces are calibrated based on systematic calculations of potentials of mean force in explicit water. The electrostatic component of the model is parametrized for monovalent, divalent and trivalent ions. The conceptual and practical aspects of the model are discussed based on simulations of protein complexation and peptide folding. The current implementation is ~1.5 times slower than the gas-phase force field and exhibits good parallel performance.

PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions

In this study, we have revised the rules and parameters for one of the most commonly used empirical pKa predictors, PROPKA, based on better physical description of the desolvation and dielectric response for the protein. We have introduced a new and consistent approach to interpolate the description between the previously distinct classifications into internal and surface residues, which otherwise is found to give rise to an erratic and discontinuous behavior. Since the goal of this study is to lay out the framework and validate the concept, it focuses on Asp and Glu residues where the protein pKa values and structures are assumed to be more reliable. The new and improved implementation is evaluated and discussed; it is found to agree better with experiment than the previous implementation (in parentheses): rmsd = 0.79 (0.91) for Asp and Glu, 0.75 (0.97) for Tyr, 0.65 (0.72) for Lys, and 1.00 (1.37) for His residues. The most significant advance, however, is in reducing the number of outliers and removing unreasonable sensitivity to small structural changes that arise from classifying residues as either internal or surface.

Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics

Polar liquids like water carry a characteristic nanometric length scale, the correlation length of orientation polarizations. Continuum theories that can capture this feature commonly run under the name of "nonlocal" electrostatics since their dielectric response is characterized by a scale-dependent dielectric function ε(q), where q is the wave vector; the Poisson(-Boltzmann) equation then turns into an integro-differential equation. Recently, "local" formulations have been put forward for these theories and applied to water, solvated ions, and proteins. We review the local formalism and show how it can be applied to a structured liquid in slit and plate geometries, and solve the Poisson-Boltzmann theory for a charged plate in a structured solvent with counterions. Our results establish a coherent picture of the local version of nonlocal electrostatics and show its ease of use when compared to the original formulation.

Electrostatic solvation energy for two oppositely charged ions in a solvated protein system: salt bridges can stabilize proteins

Born-type electrostatic continuum methods have been an indispensable ingredient in a variety of implicit-solvent methods that reduce computational effort by orders of magnitude compared to explicit-solvent MD simulations and thus enable treatment using larger systems and/or longer times. An analysis of the limitations and failures of the Born approaches serves as a guide for fundamental improvements without diminishing the importance of prior works. One of the major limitations of the Born theory is the lack of a liquidlike description of the response of solvent dipoles to the electrostatic field of the solute and the changes therein, a feature contained in the continuum Langevin-Debye (LD) model applied here to investigate how Coulombic interactions depend on the location of charges relative to the protein/water boundary. This physically more realistic LD model is applied to study the stability of salt bridges. When compared head to head using the same (independently measurable) physical parameters (radii, dielectric constants, etc.), the LD model is in good agreement with observations, whereas the Born model is grossly in error. Our calculations also suggest that a salt bridge on the protein's surface can be stabilizing when the charge separation is < or =4 A.

Docking flexible ligands in proteins with a solvent exposure- and distance-dependent dielectric function

Physics-based force fields for ligand-protein docking usually determine electrostatic energy with distance-dependent dielectric (DDD) functions, which do not fully account for the dielectric permittivity variance between approximately 2 in the protein core and approximately 80 in bulk water. Here we propose an atom-atom solvent exposure- and distance-dependent dielectric (SEDDD) function, which accounts for both electrostatic and dehydration energy components. Docking was performed using the ZMM program, the AMBER force field, and precomputed libraries of ligand conformers. At the seeding stage, hundreds of thousands of positions and orientations of conformers from the libraries were sampled within the rigid protein. At the refinement stage, the ten lowest-energy structures from the seeding stage were Monte Carlo-minimized with the flexible ligand and flexible protein. A search was considered a success if the root mean square deviation (RMSD) of the ligand atoms in the apparent global minimum from the x-ray structure was <2 A. Calculations on an examining set of 60 ligand-protein complexes with different DDD functions and solvent-exclusion energy revealed outliers in most of which the ligand-binding site was located at the protein surface. Using a training set of 16 ligand-protein complexes, which did not overlap with the examining set, we parameterized the SEDDD function to minimize the RMSD of the apparent global minima from the x-ray structures. Recalculation of the examining set with the SEDDD function demonstrated a 20% increase in the success rate versus the best-performing DDD function.

ABSINTH: a new continuum solvation model for simulations of polypeptides in aqueous solutions

A new implicit solvation model for use in Monte Carlo simulations of polypeptides is introduced. The model is termed ABSINTH for self-Assembly of Biomolecules Studied by an Implicit, Novel, and Tunable Hamiltonian. It is designed primarily for simulating conformational equilibria and oligomerization reactions of intrinsically disordered proteins in aqueous solutions. The paradigm for ABSINTH is conceptually similar to the EEF1 model of Lazaridis and Karplus (Proteins 1999, 35, 133). In ABSINTH, the transfer of a polypeptide solute from the gas phase into a continuum solvent is the sum of a direct mean field interaction (DMFI), and a term to model the screening of polar interactions. Polypeptide solutes are decomposed into a set of distinct solvation groups. The DMFI is a sum of contributions from each of the solvation groups, which are analogs of model compounds. Continuum-mediated screening of electrostatic interactions is achieved using a framework similar to the one used for the DMFI. Promising results are shown for a set of test cases. These include the calculation of NMR coupling constants for short peptides, the assessment of the thermal stability of two small proteins, reversible folding of both an alpha-helix and a beta-hairpin forming peptide, and the polymeric properties of intrinsically disordered polyglutamine peptides of varying lengths. The tests reveal that the computational expense for simulations with the ABSINTH implicit solvation model increase by a factor that is in the range of 2.5-5.0 with respect to gas-phase calculations.

Langevin-Debye model for nonlinear electrostatic screening of solvated ions

Ion-ion interactions are central to numerous phenomena in geology, biology, and material science, but current understanding is based on linear theories of limited physical applicability. Using the Langevin-Debye model, we investigate how nonlinear dielectric saturation alters screening of electrostatic interactions between solvated charges and show that charge screening in liquids strongly depends on the charge magnitudes but negligibly on the ion radii. Qualitatively different universal screening functions are predicted for ions with charges of the same or opposite signs.

Accelerating molecular dynamic simulation on the cell processor and Playstation 3

Implementation of molecular dynamics (MD) calculations on novel architectures will vastly increase its power to calculate the physical properties of complex systems. Herein, we detail algorithmic advances developed to accelerate MD simulations on the Cell processor, a commodity processor found in PlayStation 3 (PS3). In particular, we discuss issues regarding memory access versus computation and the types of calculations which are best suited for streaming processors such as the Cell, focusing on implicit solvation models. We conclude with a comparison of improved performance on the PS3's Cell processor over more traditional processors.

Methods for Monte Carlo simulations of biomacromolecules

The state-of-the-art for Monte Carlo (MC) simulations of biomacromolecules is reviewed. Available methodologies for sampling conformational equilibria and associations of biomacromolecules in the canonical ensemble, given a continuum description of the solvent environment, are reviewed. Detailed sections are provided dealing with the choice of degrees of freedom, the efficiencies of MC algorithms and algorithmic peculiarities, as well as the optimization of simple movesets. The issue of introducing correlations into elementary MC moves, and the applicability of such methods to simulations of biomacromolecules is discussed. A brief discussion of multicanonical methods and an overview of recent simulation work highlighting the potential of MC methods are also provided. It is argued that MC simulations, while underutilized biomacromolecular simulation community, hold promise for simulations of complex systems and phenomena that span multiple length scales, especially when used in conjunction with implicit solvation models or other coarse graining strategies.

Scoring functions for de novo protein structure prediction revisited

De novo protein structure prediction methods attempt to predict tertiary structures from sequences based on general principles that govern protein folding energetics and/or statistical tendencies of conformational features that native structures acquire, without the use of explicit templates. A general paradigm for de novo prediction involves sampling the conformational space, guided by scoring functions and other sequence-dependent biases, such that a large set of candidate ("decoy") structures are generated, and then selecting native-like conformations from those decoys using scoring functions as well as conformer clustering. High-resolution refinement is sometimes used as a final step to fine-tune native-like structures. There are two major classes of scoring functions. Physics-based functions are based on mathematical models describing aspects of the known physics of molecular interaction. Knowledge-based functions are formed with statistical models capturing aspects of the properties of native protein conformations. We discuss the implementation and use of some of the scoring functions from these two classes for de novo structure prediction in this chapter.

Benchmarking implicit solvent folding simulations of the amyloid beta(10-35) fragment

A pathogenetic feature of Alzhemier disease is the aggregation of monomeric beta-amyloid proteins (Abeta) to form oligomers. Usually these oligomers of long peptides aggregate on time scales of microseconds or longer, making computational studies using atomistic molecular dynamics models prohibitively expensive and making it essential to develop computational models that are cheaper and at the same time faithful to physical features of the process. We benchmark the ability of our implicit solvent model to describe equilibrium and dynamic properties of monomeric Abeta(10-35) using all-atom Langevin dynamics (LD) simulations, since Alphabeta(10-35) is the only fragment whose monomeric properties have been measured. The accuracy of the implicit solvent model is tested by comparing its predictions with experiment and with those from a new explicit water MD simulation, (performed using CHARMM and the TIP3P water model) which is approximately 200 times slower than the implicit water simulations. The dependence on force field is investigated by running multiple trajectories for Alphabeta(10-35) using the CHARMM, OPLS-aal, and GS-AMBER94 force fields, whereas the convergence to equilibrium is tested for each force field by beginning separate trajectories from the native NMR structure, a completely stretched structure, and from unfolded initial structures. The NMR order parameter, S2, is computed for each trajectory and is compared with experimental data to assess the best choice for treating aggregates of Alphabeta. The computed order parameters vary significantly with force field. Explicit and implicit solvent simulations using the CHARMM force fields display excellent agreement with each other and once again support the accuracy of the implicit solvent model. Alphabeta(10-35) exhibits great flexibility, consistent with experiment data for the monomer in solution, while maintaining a general strand-loop-strand motif with a solvent-exposed hydrophobic patch that is believed to be important for aggregation. Finally, equilibration of the peptide structure requires an implicit solvent LD simulation as long as 30 ns.

Solvation effect on conformations of 1,2:dimethoxyethane: charge-dependent nonlinear response in implicit solvent models

The physical content of and, in particular, the nonlinear contributions from the Langevin-Debye model are illustrated using two applications. First, we provide an improvement in the Langevin-Debye model currently used in some implicit solvent models for computer simulations of solvation free energies of small organic molecules, as well as of biomolecular folding and binding. The analysis is based on the implementation of a charge-dependent Langevin-Debye (qLD) model that is modified by subsequent corrections due to Onsager and Kirkwood. Second, the physical content of the model is elucidated by discussing the general treatment within the LD model of the self-energy of a charge submerged in a dielectric medium for three different limiting conditions and by considering the nonlinear response of the medium. The modified qLD model is used to refine an implicit solvent model (previously applied to protein dynamics). The predictions of the modified implicit solvent model are compared with those from explicit solvent molecular dynamics simulations for the equilibrium conformational populations of 1,2-dimethoxyethane (DME), which is the shortest ether molecule to reproduce the local conformational properties of polyethylene oxide, a polymer with tremendous technological importance and a wide variety of applications. Because the conformational population preferences of DME change dramatically upon solvation, DME is a good test case to validate our modified qLD model. The present analysis of the modified qLD model provides the motivation and tools for studying a wide variety of other interesting systems with heterogeneous dielectric properties and spatial anisotropy.

Dielectric permittivity profiles of confined polar fluids

The dielectric response of a simple model of a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivity tensor epsilon(r) are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of epsilon exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of "electrostatic double layers" signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules.

Factors influencing the energetics of electron and proton transfers in proteins. What can be learned from calculations

A protein structure should provide the information needed to understand its observed properties. Significant progress has been made in developing accurate calculations of acid/base and oxidation/reduction reactions in proteins. Current methods and their strengths and weaknesses are discussed. The distribution and calculated ionization states in a survey of proteins is described, showing that a significant minority of acidic and basic residues are buried in the protein and that most of these remain ionized. The electrochemistry of heme and quinones are considered. Proton transfers in bacteriorhodopsin and coupled electron and proton transfers in photosynthetic reaction centers, 5-coordinate heme binding proteins and cytochrome c oxidase are highlighted as systems where calculations have provided insight into the reaction mechanism.

Exploring peptide energy landscapes: a test of force fields and implicit solvent models

A biased Monte Carlo-minimization/annealing conformational search was used to characterize five descriptions of the energy landscape for each of three model systems: the 20-residue "trp-cage" miniprotein, the 20-residue "BS1" peptide, and the 17-residue "U(1-17)T9D" peptide. The EEF1 and SASA energy landscapes were studied as well as those defined by using the GB/ACE implicit water model with one of three protein force fields: CHARMM19, CHARMM22, and CHARMM22/CMAP. The lowest-energy structures of the trp-cage and BS1 peptides found for the EEF1 landscape have main-chain root-mean-square deviations (rmsds) from the respective NMR structures of less than 2 A; for U(1-17)T9D, the deviation is less than 3 A using EEF1. The main-chain rmsd of the minimum-energy trp-cage conformation obtained for the GB/ACE/CHARMM22/CMAP landscape is less than 1 A. However, this energy function strongly favored helical structures for the two peptides shown by NMR to form beta-sheet structures. Brief annealing of the system following main-chain conformational changes was found to enhance the exploration of low-energy states. The thousands of simulations reported here suggest that the prediction of protein structure might be improved by the simultaneous use of a CMAP-like description of the main chain and an EEF1-like description of the solvent.

Electrostatics in computational protein design

Catalytic activity and protein-protein recognition have proven to be significant challenges for computational protein design. Electrostatic interactions are crucial for these and other protein functions, and therefore accurate modeling of electrostatics is necessary for successfully advancing protein design into the realm of protein function. This review focuses on recent progress in modeling electrostatic interactions in computational protein design, with particular emphasis on continuum models.

Transitions in microtubule C-termini conformations as a possible dendritic signaling phenomenon

We model the dynamical states of the C-termini of tubulin dimers that comprise neuronal microtubules. We use molecular dynamics and other computational tools to explore the time-dependent behavior of conformational states of a C-terminus of tubulin within a microtubule and assume that each C-terminus interacts via screened Coulomb forces with the surface of a tubulin dimer, with neighboring C-termini and also with any adjacent microtubule-associated protein 2 (MAP2). Each C-terminus can either bind to the tubulin surface via one of the several positively charged regions or can be allowed to explore the space available in the solution surrounding the dimer. We find that the preferential orientation of each C-terminus is away from the tubulin surface but binding to the surface may also take place, albeit at a lower probability. The results of our model suggest that perturbations generated by the C-termini interactions with counterions surrounding a MAP2 may propagate over distances greater than those between adjacent microtubules. Thus, the MAP2 structure is able to act as a kind of biological wire (or a cable) transmitting local electrostatic perturbations resulting in ionic concentration gradients from one microtubule to another. We briefly discuss the implications the current dynamic modeling may have on synaptic activation and potentiation.

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.

Energy functions for protein design I: efficient and accurate continuum electrostatics and solvation

Electrostatics and solvation energies are important for defining protein stability, structural specificity, and molecular recognition. Because these energies are difficult to compute quickly and accurately, they are often ignored or modeled very crudely in computational protein design. To address this problem, we have developed a simple, fast, and accurate approximation for calculating Born radii in the context of protein design calculations. When these approximate Born radii are used with the generalized Born continuum dielectric model, energies calculated by the 10(6)-fold slower finite difference Poisson-Boltzmann model are faithfully reproduced. A similar approach can be used for estimating solvent-accessible surface areas (SASAs). As an independent test, we show that these approximations can be used to accurately predict the experimentally determined pK(a)s of >200 ionizable groups from 15 proteins.

Efficient evaluation of the effective dielectric function of a macromolecule in aqueous solution

We propose an analytical approach to calculate the effective dielectric function of proteins in aqueous solution. The screening effect if quantified by a measure of enclosure which is based on the distribution of solute atomic volumes around a pair of charges in a macromolecule. For protein conformations that vary significantly in size and shape, a comparison with finite difference Poisson calculations shows that pair interaction energies, their sums and solvation energies are well reproduced. The approach rivals the speed of simple distance dependent dielectric functions and the accuracy of the generalized Born model.

Effective energy function for proteins in lipid membranes

A simple extension of the EEF1 energy function to heterogeneous membrane-aqueous media is proposed. The extension consists of (a) development of solvation parameters for a nonpolar phase using experimental data for the transfer of amino acid side-chains from water to cyclohexane, (b) introduction of a heterogeneous membrane-aqueous system by making the reference solvation free energy of each atom dependent on the vertical coordinate, (c) a modification of the distance-dependent dielectric model to account for reduced screening of electrostatic interactions in the membrane, and (d) an adjustment of the EEF1 aqueous model in light of recent calculations of the potential of mean force between amino acid side-chains in water. The electrostatic model is adjusted to match experimental observations for polyalanine, polyleucine, and the glycophorin A dimer. The resulting energy function (IMM1) reproduces the preference of Trp and Tyr for the membrane interface, gives reasonable energies of insertion into or adsorption onto a membrane, and allows stable 1-ns MD simulations of the glycophorin A dimer. We find that the lowest-energy orientation of melittin in bilayers varies, depending on the thickness of the hydrocarbon layer.