Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

Energetics of the native and non-native states of the glycophorin transmembrane helix dimer

Using an implicit membrane model (IMM1), we examine whether the structure of the transmembrane domain of Glycophorin A (GpA) could be predicted based on energetic considerations alone. The energetics of native GpA shows that van der Waals interactions make the largest contribution to stability. Although specific electrostatic interactions are stabilizing, the overall electrostatic contribution is close to zero. The GXXXG motif contributes significantly to stability, but residues outside this motif contribute almost twice as much. To generate non-native states a global conformational search was done on two segments of GpA: an 18-residue peptide (GpA74-91) that is embedded in the membrane and a 29-residue peptide (GpA70-98) that has additional polar residues flanking the transmembrane region. Simulated annealing was done on a large number of conformations generated from parallel, antiparallel, left- and right-handed starting structures by rotating each helix at 20 degrees intervals around its helical axis. Several crossing points along the helix dimer were considered. For 18-residue parallel topology, an ensemble of native-like structures was found at the lowest effective energy region; the effective energy is lowest for a right-handed structure with an RMSD of 1.0 A from the solid-state NMR structure with correct orientation of the helices. For the 29-residue peptide, the effective energies of several left-handed structures were lower than that of the native, right-handed structure. This could be due to deficiencies in modeling the interactions between charged sidechains and/or omission of the sidechain entropy contribution to the free energy. For 18-residue antiparallel topology, both IMM1 and a Generalized Born model give effective energies that are lower than that of the native structure. In contrast, the Poisson-Boltzmann solvation model gives lower effective energy for the parallel topology, largely because the electrostatic solvation energy is more favorable for the parallel structure. IMM1 seems to underestimate the solvation free energy advantage when the CO and NH dipoles just outside the membrane are parallel. This highlights the importance of electrostatic interactions even when these are not obvious by looking at the structures.     

An implicit membrane generalized born theory for the study of structure, stability, and interactions of membrane proteins

Exploiting recent developments in generalized Born (GB) electrostatics theory, we have reformulated the calculation of the self-electrostatic solvation energy to account for the influence of biological membranes. Consistent with continuum Poisson-Boltzmann (PB) electrostatics, the membrane is approximated as an solvent-inaccessible infinite planar low-dielectric slab. The present membrane GB model closely reproduces the PB electrostatic solvation energy profile across the membrane. The nonpolar contribution to the solvation energy is taken to be proportional to the solvent-exposed surface area (SA) with a phenomenological surface tension coefficient. The proposed membrane GB/SA model requires minor modifications of the pre-existing GB model and appears to be quite efficient. By combining this implicit model for the solvent/bilayer environment with advanced computational sampling methods, like replica-exchange molecular dynamics, we are able to fold and assemble helical membrane peptides. We examine the reliability of this model and approach by applications to three membrane peptides: melittin from bee venom, the transmembrane domain of the M2 protein from Influenza A (M2-TMP), and the transmembrane domain of glycophorin A (GpA). In the context of these proteins, we explore the role of biological membranes (represented as a low-dielectric medium) in affecting the conformational changes in melittin, the tilt of transmembrane peptides with respect to the membrane normal (M2-TMP), helix-to-helix interactions in membranes (GpA), and the prediction of the configuration of transmembrane helical bundles (GpA). The present method is found to perform well in each of these cases and is anticipated to be useful in the study of folding and assembly of membrane proteins as well as in structure refinement and modeling of membrane proteins where a limited number of experimental observables are available.     

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.     

A generalized born implicit-membrane representation compared to experimental insertion free energies

An implicit-membrane representation based on the generalized Born theory of solvation has been developed. The method was parameterized against the water-to-cyclohexane insertion free energies of hydrophobic side-chain analogs. Subsequently, the membrane was compared with experimental data from translocon inserted polypeptides and validated by comparison with an independent dataset of six membrane-associated peptides and eight integral membrane proteins of known structure and orientation. Comparison of the insertion energy of alpha-helical model peptides with the experimental values from the biological hydrophobicity scale of Hessa et al. gave a correlation of 93% with a mean unsigned error of 0.64 kcal/mol, when charged residues were ignored. The membrane insertion energy was found to be dependent on residue position. This effect is particularly pronounced for charged and polar residues, which strongly prefer interfacial locations. All integral membrane proteins investigated orient and insert correctly into the implicit-membrane model. Remarkably, the membrane model correctly predicts a partially inserted configuration for the monotopic membrane protein cyclooxygenase, matching experimental and theoretical predictions. To test the applicability and usefulness of the implicit-membrane method, molecular simulations of influenza A M2 as well as the glycophorin A dimer were performed. Both systems remain structurally stable and integrated into the membrane.     

Position-resolved free energy of solvation for amino acids in lipid membranes from molecular dynamics simulations

Studies of insertion and interactions of amino acids in lipid membranes are pivotal to our understanding of membrane protein structure and function. Calculating the insertion cost as a function of transmembrane helix sequence is thus an important step towards improved membrane protein prediction and eventually drug design. Here, we present position-dependent free energies of solvation for all amino acid analogs along the membrane normal. The profiles cover the entire region from bulk water to hydrophobic core, and were produced from all-atom molecular dynamics simulations. Experimental differences corresponding to mutations and costs for entire segments match experimental data well, and in addition the profiles provide the spatial resolution currently not available from experiments. Polar side-chains largely maintain their hydration and assume quite ordered conformations, which indicates the solvation cost is mainly entropic. The cost of solvating charged side-chains is not only significantly lower than for implicit solvation models, but also close to experiments, meaning these could well maintain their protonation states inside the membrane. The single notable exception to the experimental agreement is proline, which is quite expensive to introduce in vivo despite its hydrophobicity--a difference possibly explained by kinks making it harder to insert helices in the translocon.     

Influence of proline residues in transmembrane helix packing

Integral membrane proteins often contain proline residues in their alpha-helical transmembrane (TM) fragments, which may strongly influence their folding and association. Pro-scanning mutagenesis of the helical domain of glycophorin A (GpA) showed that replacement of the residues located at the center abrogates helix packing while substitution of the residues forming the ending helical turns allows dimer formation. Synthetic TM peptides revealed that a point mutation of one of the residues of the dimerization motif (L75P) located at the N-terminal helical turn of the GpA TM fragment, adopts a secondary structure and oligomeric state similar to the wild-type sequence in detergents. In addition, both glycosylation mapping in biological membranes and molecular dynamics showed that the presence of a proline residue at the lipid/water interface has as an effect the extension of the helical end. Thus, helix packing can be an important factor that determines appearance of proline in TM helices. Membrane proteins might accumulate proline residues at the two ends of their TM segments in order to modulate the exposition of key amino acid residues at the interface for molecular recognition events while allowing stable association and native folding.     

Implications of threonine hydrogen bonding in the glycophorin A transmembrane helix dimer

The transmembrane helix of glycophorin A contains a seven-residue motif, LIxxGVxxGVxxT, that mediates protein dimerization. Threonine is the only polar amino acid in this motif with the potential to stabilize the dimer through hydrogen-bonding interactions. Polarized Fourier transform infrared spectroscopy is used to establish a robust protocol for incorporating glycophorin A transmembrane peptides into membrane bilayers. Analysis of the dichroic ratio of the 1655-cm(-1) amide I vibration indicates that peptides reconstituted by detergent dialysis have a transmembrane orientation with a helix crossing angle of <35 degrees. Solid-state nuclear magnetic resonance spectroscopy is used to establish high resolution structural restraints on the conformation and packing of Thr-87 in the dimer interface. Rotational resonance measurement of a 2.9-A distance between the gamma-methyl and backbone carbonyl carbons of Thr-87 is consistent with a gauche- conformation for the chi1 torsion angle. Rotational-echo double-resonance measurements demonstrate close packing (4.0 +/- 0.2 A) of the Thr-87 gamma-methyl group with the backbone nitrogen of Ile-88 across the dimer interface. The short interhelical distance places the beta-hydroxyl of Thr-87 within hydrogen-bonding range of the backbone carbonyl of Val-84 on the opposing helix. These results refine the structure of the glycophorin A dimer in membrane bilayers and highlight the complementary role of small and polar residues in the tight association of transmembrane helices in membrane proteins.     

Sequence context modulates the stability of a GxxxG-mediated transmembrane helix-helix dimer

To quantify the relationship between sequence and transmembrane dimer stability, a systematic mutagenesis and thermodynamic study of the protein-protein interaction residues in the glycophorin A transmembrane helix-helix dimer was carried out. The results demonstrate that the glycophorin A transmembrane sequence dimerizes when its GxxxG motif is abolished by mutation to large aliphatic residues, suggesting that the sequence encodes an intrinsic propensity to self-associate independent of a GxxxG motif. In the presence of an intact GxxxG motif, the glycophorin A dimer stability can be modulated over a span of -0.5 kcal mol(-1) to +3.2 kcal mol(-1) by mutating the surrounding sequence context. Thus, these flanking residues play an active role in determining the transmembrane dimer stability. To assess the structural consequences of the thermodynamic effects of mutations, molecular models of mutant transmembrane domains were constructed, and a structure-based parameterization of the free energy change due to mutation was carried out. The changes in association free energy for glycophorin A mutants can be explained primarily by changes in packing interactions at the protein-protein interface. The energy cost of removing favorable van der Waals interactions was found to be 0.039 kcal mol(-1) per A2 of favorable occluded surface area. The value corresponds well with estimates for mutations in bacteriorhodopsin as well as for those mutations in the interiors of soluble proteins that create packing defects.     

Nonlinear poisson equation for heterogeneous media

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects.     

Modeling of peptides and proteins in a membrane environment: II. Structural and energetic aspects of glycophorin A in a lipid bilayer

The conformational space of a hydrophobic peptide fragment of glycophorin A in a lipid membrane was studied with the Monte Carlo method using the solvation model described in the first communication of this series. The simulation was performed for various starting orientations of the peptide relative the membrane bilayer: outside, inside, partially immersed, and transbilayer. We showed that the membrane substantially stabilizes the α-helical conformation of the central hydrophobic part of the glycophorin A molecule, which for the most part is immersed in the apolar core of the bilayer. For various conformational states, energy values were calculated and the orientations of the peptide relative to the membrane were characterized. Depending on the thickness of the bilayer, either an entirely α-helical conformation in transbilayer orientation or a conformation with a kink in the central part of the helix with theN- andC-termini exposed on one side of the membrane corresponds to the minimal-energy structure. The transmembrane orientation of glycophorin A is energetically advantageous when the membrane thickness is close to the length of its hydrophobic helical portion, which is consistent with the effect ofhydrophobic match observed experimentally. The prospects for further refinement of the model are discussed. For communication I, see [1].     

The role of a hydrogen bonding network in the transmembrane beta-barrel OMPLA

The hydrogen bonding of polar side-chains has emerged as an important theme for membrane protein interactions. The crystal structure of the dimeric state of the transmembrane beta-barrel protein outer membrane phospholipase A (OMPLA) revealed an intermolecular hydrogen bond mediated by a highly conserved glutamine side-chain (Q94). It has been shown that the introduction of a polar residue can drive the association of model helices, and by extension it was presumed that the glutamine hydrogen bond played a key role in stabilizing the OMPLA dimer. However, a thermodynamic investigation using sedimentation equilibrium ultracentrifugation in detergent micelles reveals that the hydrogen bond plays only a very modest role in stabilizing the dimer. The Q94 side-chain is hydrogen bonded intramolecularly to residues Y92 and S96, but amino acid substitutions at these positions suggest these intramolecular interactions are not responsible for attenuating the strength of the intermolecular Q94 hydrogen bond. Other substitutions suggested that hydration of the local environment around Q94 may be responsible for the modest strength of the hydrogen bond. Heat inactivation experiments with the variants suggest that the Y92-Q94-S96 network may instead be important for thermal stability of the monomer. These results highlight the context dependence and broad range of interactions that can be mediated by polar residues in membrane proteins.     

Lipid solvation effects contribute to the affinity of Gly-xxx-Gly motif-mediated helix-helix interactions

Interactions between transmembrane helices are mediated by the concave Gly-xxx-Gly motif surface. Whether Gly residues per se are sufficient for selection of this motif has not been established. Here, we used the in vivo TOXCAT assay to measure the relative affinities of all 18 combinations of Gly, Ala, and Ser "small-xxx-small" mutations in glycophorin A (GpA) and bacteriophage M13 major coat protein (MCP) homodimers. Affinity values were compared with the accessibility to a methylene-sized probe of the total surface area of each helix monomer as a measure of solvation by membrane components. A strong inverse correlation was found between nonpolar-group lipid accessibility and dimer affinity (R = 0.75 for GpA, p = 0.013, and R = 0.81 for MCP, p = 0.004), suggesting that lipid as a poor membrane protein solvent, conceptually analogous to water in soluble protein folding, can contribute to dimer stability and help to define helix-helix interfaces.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Energetics and stability of transmembrane helix packing: a replica-exchange simulation with a knowledge-based membrane potential

The energetics and stability of the packing of transmembrane helices were investigated by Monte Carlo simulations with the replica-exchange method. The helices were modeled with a united atom representation, and the CHARMM19 force field was employed. Based on known experimental structures of membrane proteins, an implicit knowledge-based potential was developed to describe the helix-membrane interactions at the residue level, whose validity was tested through prediction of the orientations when single helices were inserted into a membrane. Two systems were studied in this article, namely the glycophorin A dimer, and helices A and B of Bacteriorhodopsin. For the glycophorin A dimer, the most stable structure (0.5 A away from the experimental structure) is mainly stabilized by the favorable helix-helix interactions, and has the most population regardless of the helix-membrane interaction. However, for helices A and B of Bacteriorhodopsin, it was found that the packing determined by helix-helix interactions is nonspecific, and a native-like structure (0.2 A from the experimental one) can be identified from several structural analogs as the most stable one only after applying the membrane potential. Our results suggest that the contribution from the helix-membrane interaction could be critical in the correct packing of transmembrane helices in the membrane.     

Unfolding a transmembrane helix dimer: A FRET study in mixed micelles

The exact nature of membrane protein folding and assembly is not understood in detail yet. Addition of SDS to a membrane protein dissolved in mild, non-polar detergent results in formation of mixed micelles and in subsequent denaturation of higher ordered membrane protein structures. The exact nature of this denaturation event is, however, enigmatic, and separation of an individual helix pair in mixed micelles has also not been reported yet. Here we followed unfolding of the human glycophorin A transmembrane helix dimer in mixed micelles by fluorescence spectroscopy. Energy transfer between differently labelled glycophorin A transmembrane helices decreased with increasing SDS mole fractions albeit without modifying the helicity of the peptides. The energetics and kinetics of the dimer dissociation in mixed micelles is analyzed and discussed, and the experimental data demonstrate that mixed micelles can be used as a general method to investigate unfolding of α-helical membrane proteins.     

A solvent model for simulations of peptides in bilayers. I. Membrane-promoting alpha-helix formation

We describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting alpha-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides-poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation-were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of alpha-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed.     

Hydrophilicity of polar amino acid side-chains is markedly reduced by flanking peptide bonds

Several amino acid side-chain hydropathy scales have been devised on the basis of solubility and water/organic solvent partitioning data obtained with free amino acids or side-chain analogs. In nearly all cases, these scales are based upon the structure-additivity assumption; it has been assumed that the transfer free energies of the amino acid side-chains are the same in these model compounds as they are in a polypeptide. This assumption is probably wrong. In the present study, deviations from additivity for amino acid side-chains are demonstrated by comparing a theoretically derived scale, which N-acetylamino acid amides. The results show that the flanking peptide bonds dramatically reduce the hydrophilicity of the polar side-chains, with deviations up to several kilocalories (1 kcal = 4.184 kJ) for the charged side-chains at pH 7.0. Further calculation shows that these deviations are due to reductions of 40 to 85% in the unfavorable transfer free energy of the polar functional groups. In addition, proximity of the neighboring amide bonds in the parent molecule (N-acetylglycine amide) decreases the hydrophilicity of the -CONH-backbone unit by 36%. This decrease is expected to be twice as large for -CONH- units in the interior of a polypeptide backbone. The significance of these observations is: (1) valid hydropathy scales can be obtained only with model peptides; (2) deviations from additivity are expected in all solvent systems, including non-polar solvents that are thought to mimic the interior of a membrane; (3) the spontaneous insertion of polypeptides into membranes is likely to occur much more readily than has been previously thought. In order to estimate the free energy of transferring the side-chains and the polypeptide backbone from water to the interior of a lipid bilayer, the results of this study are used to construct a hydropathy scale based upon the partitioning of solutes between water and non-polar solvents. The validity of hydropathy scales that are based on criteria other than solubility and water/organic solvent partitioning data is also discussed.