Validation of an All-Atom Protein Force Field: From Dipeptides to Larger Peptides

The relevance of short peptides for an understanding of unfolded and intrinsically disordered proteins

Over the last thirty years the unfolded state of proteins has attracted considerable interest owing to the discovery of intrinsically disordered proteins which perform a plethora of functions despite resembling unfolded proteins to a significant extent. Research on both, unfolded and disordered proteins has revealed that their conformational properties can deviate locally from random coil behavior. In this context results from work on short oligopeptides suggest that individual amino acid residues sample the sterically allowed fraction of the Ramachandran plot to a different extent. Alanine has been found to exhibit a peculiarity in that it has a very high propensity for adopting polyproline II like conformations. This Perspectives article reviews work on short peptides aimed at exploring the Ramachandran distributions of amino acid residues in different contexts with experimental and computational means. Based on the thus provided overview the article discussed to what extent short peptides can serve as tools for exploring unfolded and disordered proteins and as benchmarks for the development of a molecular dynamics force field.

Exploring Nearest Neighbor Interactions and Their Influence on the Gibbs Energy Landscape of Unfolded Proteins and Peptides

The Flory isolated pair hypothesis (IPH) is one of the corner stones of the random coil model, which is generally invoked to describe the conformational dynamics of unfolded and intrinsically disordered proteins (IDPs). It stipulates, that individual residues sample the entire sterically allowed space of the Ramachandran plot without exhibiting any correlations with the conformational dynamics of its neighbors. However, multiple lines of computational, bioinformatic and experimental evidence suggest that nearest neighbors have a significant influence on the conformational sampling of amino acid residues. This implies that the conformational entropy of unfolded polypeptides and proteins is much less than one would expect based on the Ramachandran plots of individual residues. A further implication is that the Gibbs energies of residues in unfolded proteins or polypeptides are not additive. This review provides an overview of what is currently known and what has yet to be explored regarding nearest neighbor interactions in unfolded proteins.

Randomizing of Oligopeptide Conformations by Nearest Neighbor Interactions between Amino Acid Residues

Flory’s random coil model assumes that conformational fluctuations of amino acid residues in unfolded poly(oligo)peptides and proteins are uncorrelated (isolated pair hypothesis, IPH). This implies that conformational energies, entropies and solvation free energies are all additive. Nearly 25 years ago, analyses of coil libraries cast some doubt on this notion, in that they revealed that aromatic, but also β-branched side chains, could change the ³J(H^NH^Cα) coupling of their neighbors. Since then, multiple bioinformatical, computational and experimental studies have revealed that conformational propensities of amino acids in unfolded peptides and proteins depend on their nearest neighbors. We used recently reported and newly obtained Ramachandran plots of tetra- and pentapeptides with non-terminal homo- and heterosequences of amino acid residues to quantitatively determine nearest neighbor coupling between them with a Ising type model. Results reveal that, depending on the choice of amino acid residue pairs, nearest neighbor interactions either stabilize or destabilize pairs of polyproline II and β-strand conformations. This leads to a redistribution of population between these conformations and a reduction in conformational entropy. Interactions between residues in polyproline II and turn(helix)-forming conformations seem to be cooperative in most cases, but the respective interaction parameters are subject to large statistical errors.

Repeating Aspartic Acid Residues Prefer Turn-like Conformations in the Unfolded State: Implications for Early Protein Folding

Protein folding can be described as a motion of the polypeptide chain in a potential energy funnel, where the conformational manifold is narrowed as the chain traverses from a completely unfolded state until it reaches the folded (native) state. The initial folding stages set the tone for this process by substantially narrowing the manifold of accessible conformations. In an ideally unfolded state with no long-range stabilizing forces, local conformations (i.e., residual structures) are likely to drive the folding process. While most amino acid residues tend to predominantly adopt extended structures in unfolded proteins and peptides, aspartic acid exhibits a relatively high intrinsic preference for turn-forming conformations. Regions in an unfolded polypeptide or protein that are rich in aspartic acid residues may therefore be crucial sites for protein folding steps. By combining NMR and vibrational spectroscopies, we observed that the conformational sampling of multiple sequentially neighbored aspartic acid residues in the model peptides GDDG and GDDDG even show an on average higher propensity for turn-forming structures than the intrinsic reference system D in GDG, which suggests that nearest neighbor interactions between adjacent aspartic acid residues stabilize local turn-forming structures. In the presence of the unlike neighbor phenylalanine, nearest neighbor interactions are of a totally different nature in that it they decrease the turn-forming propensities and mutually increase the sampling of polyproline II (pPII) conformations. We hypothesize the structural role of aspartic residues in intrinsically disordered proteins in general, and particularly in small linear motifs, that are very much determined by their respective neighbors.

On the Role of Entropy in the Stabilization of α-Helices

Protein folding evolves by exploring the conformational space with a subtle balance between enthalpy and entropy changes which eventually leads to a decrease of free energy upon reaching the folded structure. A complete understanding of this process requires, therefore, a deep insight into both contributions to free energy. In this work, we clarify the role of entropy in favoring the stabilization of folded structures in polyalanine peptides with up to 12 residues. We use a novel method referred to as K2V that allows us to obtain the potential-energy landscapes in terms of residue conformations extracted from molecular dynamics simulations at conformational equilibrium and yields folding thermodynamic magnitudes, which are in agreement with the experimental data available. Our results demonstrate that the folded structures of the larger polyalanine chains are stabilized with respect to the folded structures of the shorter chains by both an energetic contribution coming from the formation of the intramolecular hydrogen bonds and an entropic contribution coming from an increase of the entropy of the solvent with approximate weights of 60 and 40%, respectively, thus unveiling a key piece in the puzzle of protein folding. In addition, the ability of the K2V method to provide the enthalpic and entropic contributions for individual residues along the peptide chain makes it clear that the energetic and entropic stabilizations are basically governed by the nearest neighbor residue conformations, with the folding propensity being rationalized in terms of triads of residues.

Native-Based Dissipative Particle Dynamics Approach for α-Helical Folding

We developed a dissipative particle dynamics (DPD) approach that captures polyalanine folding into a stable helical conformation. Within the proposed native-based approach, the DPD parameters are derived based on the contact map constructed from the molecular dynamics (MD) simulations. We show that the proposed approach reproduces the folding of polypeptides of various lengths, including bundle formation for sufficiently long polypeptides. The proposed approach also allows one to capture the folding of the helical segments of the lysozyme. With further development of computationally efficient native-based DPD approaches for folding, modeling of a range of biomaterials incorporating α-helical segments could be extended to time and length scales far beyond those accessible in molecular dynamics simulations.

Glycine in Water Favors the Polyproline II State

Conformational preferences of amino acid residues in water are determined by the backbone and side-chain properties. Alanine is known for its high polyproline II (pPII) propensity. The question of relative contributions of the backbone and side chain to the conformational preferences of alanine and other amino acid residues in water is not fully resolved. Because glycine lacks a heavy-atom side chain, glycine-based peptides can be used to examine to which extent the backbone properties affect the conformational space. Here, we use published spectroscopic data for the central glycine residue of cationic triglycine in water to demonstrate that its conformational space is dominated by the pPII state. We assess three commonly used molecular dynamics (MD) force fields with respect to their ability to capture the conformational preferences of the central glycine residue in triglycine. We show that pPII is the mesostate that enables the functional backbone groups of the central residue to form the most hydrogen bonds with water. Our results indicate that the pPII propensity of the central glycine in GGG is comparable to that of alanine in GAG, implying that the water-backbone hydrogen bonding is responsible for the high pPII content of these residues.

Raman optical activity of tetra-alanine in the poly(l-proline) II type peptide conformation

The poly(l-proline) II (PPII) helix is considered to be a major conformation in disordered polypeptides and unfolded proteins in aqueous solution. The PPII conformation can be identified by using Raman optical activity (ROA), which measures the different intensities of right- and left-circularly polarized Raman scattered light from chiral molecules and provides information on stereochemistry associated with vibrational motions. In the present study, we used tetra-alanine (Ala₄) as a model system, since its central amide bond adopts the PPII conformation. The predominance of the PPII conformation was supported by 11 ns molecular dynamics (MD) simulations at 300 K. The MD snapshots were used for subsequent quantum mechanical/molecular mechanical (QM/MM) calculations to compute the Raman and ROA spectra. The present MD + QM/MM analysis leads to a good agreement between the observed and simulated spectra, allowing us to assign most of the spectral features including the ROA band near 1320 cm^-1, which has been used as a marker for the PPII conformation. This positive ROA band has three components. The lower frequency component near 1310 cm^-1 arises from an internal peptide bond, whereas the higher frequency components around 1320-1335 cm^-1 appear due to N- and C-terminal peptide groups. The MD + QM/MM calculations also reproduced the electronic circular dichroism spectra of Ala₄. The present results provide a satisfactory framework for future investigations of unfolded/disordered proteins as well as peptides in solutions by chiral spectroscopic methods.

Sensitivity of Folding Molecular Dynamics Simulations to Even Minor Force Field Changes

We examine the sensitivity of folding molecular dynamics simulations on the choice between three variants of the same force field (the AMBER99SB force field and its ILDN, NMR-ILDN, and STAR-ILDN variants). Using two different peptide systems (a marginally stable helical peptide and a β-hairpin) and a grand total of more than 20 μs of simulation time we show that even relatively minor force field changes can lead to appreciable differences in the peptide folding behavior.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Demixing of water and ethanol causes conformational redistribution and gelation of the cationic GAG tripeptide

The cationic tripeptide GAG undergoes three conformational changes in binary mixtures of water and ethanol. At 17 mol% of ethanol conformational sampling is shifted from pPII towards β-strands. A more pronounced shift in the same direction occurs at 40 mol%. At ca. 55 mol% of ethanol and above a peptide concentration of ca. 0.2 M the ternary peptide-water-ethanol mixture forms a hydrogel which is comprised of unusually large crystalline like non-β sheet fibrils forming a sample spanning matrix.

Assessing backbone solvation effects in the conformational propensities of amino acid residues in unfolded peptides

Conformational ensembles of individual amino acid residues within model GxG peptides (x representing different amino acid residues) are dominated by a mixture of polyproline II (pPII) and β-strand like conformations. We recently discovered rather substantial differences between the enthalpic and entropic contributions to this equilibrium for different amino acid residues. Isoleucine and valine exceed all other amino acid residues in terms of their rather large enthalpic stabilization and entropic destabilization of polyproline II. In order to shed light on these underlying physical mechanisms, we performed high-level DFT calculations to explore the energetics of four representative GxG peptides where x = alanine (A), leucine (L), valine (V), and isoleucine (I) in explicit water (10 H2O molecules with a polarizable continuum water model) and in vacuo. We found that the large energetic contributions to the stabilization of pPII result, to a major extent, from peptide-water, water-water interactions, and changes of the solvent self-energy. Differences between the peptide-solvent interaction energies of hydration in pPII and β-strand peptides are particularly important for the pPII ⇌ β equilibria of the more aliphatic peptides GIG and GLG. Furthermore, we performed a vibrational analysis of the four peptides in both conformations and discovered a rather substantial mixing between water motions and peptide vibrations below 700 cm(-1). We found that the respective vibrational entropies are substantially different for the considered conformations, and their contributions to the Gibbs/Helmholtz energy stabilize β-strand conformations. Taken together, our results underscore the notion of the solvent being the predominant determinant of peptide (and protein) conformations in the unfolded state.

Application of two-dimensional infrared spectroscopy to benchmark models for the amide I band of proteins

In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinations of molecular dynamics force fields, vibrational frequency mappings, and coupling models. We find that two-dimensional infrared spectra provide a much stronger test of the models than linear absorption does. The best modelling approach in the present study still leaves significant room for future improvement. The presented benchmarking scheme, thus, provides a way of validating future protocols for modelling the amide I band in proteins.

Conformational Interconversions of Amino Acid Derivatives

Exhaustive conformational interconversions including transition structure analyses of N-acetyl-l-glycine-N-methylamide as well as its alanine, serine, and cysteine analogues have been investigated at the MP2/6-31G** level, yielding a total of 142 transition states. Improved estimates of relative energies were obtained by separately extrapolating the Hartree-Fock and MP2 energies to the basis set limit and adding the difference between CCSD(T) and MP2 results with the cc-pVDZ basis set to the extrapolated MP2 results. The performance of eight empirical force fields (AMBER94, AMBER14SB, MM2, MM3, MMFFs, CHARMM22_CMAP, OPLS_2005, and AMOEBAPRO13) in reproducing ab initio energies of transition states was tested. Our results indicate that commonly used class I force fields employing a fixed partial charge model for the electrostatic interaction provide mean errors in the ∼10 kJ/mol range for energies of conformational transition states for amino acid conformers. Modern reparametrized versions, such as CHARMM22_CMAP, and polarizable force fields, such as AMOEBAPRO13, have slightly lower mean errors, but maximal errors are still in the 35 kJ/mol range. There are differences between the force fields in their ability for reproducing conformational transitions classified according to backbone/side-chain or regions in the Ramachandran angles, but the data set is likely too small to draw any general conclusions. Errors in conformational interconversion barriers by ∼10 kJ/mol suggest that the commonly used force field may bias certain types of transitions by several orders of magnitude in rate and thus lead to incorrect dynamics in simulations. It is therefore suggested that information for conformational transition states should be included in parametrizations of new force fields.

Water-Centered Interpretation of Intrinsic pPII Propensities of Amino Acid Residues: In Vitro-Driven Molecular Dynamics Study

Amino acid residues of unfolded peptides in water sample only a few basins in the Ramachandran plot, including prominent polyproline II-like (pPII) conformations. Dynamics of guest residues, X, in GXG peptides in water were recently reported to be dominated by pPII and β-strand-like (β) conformations, resulting in an enthalpy-entropy compensation at ∼300 K. Using molecular dynamics (MD) in explicit solvent, we here examine pPII and β conformational ensembles of 15 guest residues in GXG peptides, quantify local orientation of water around their side chains through novel water orientation plots, and study their hydration and hydrogen bonding properties. We show that pPII and β ensembles are characterized by distinct water orientations: pPII ensembles are associated with an increased population of water oriented in parallel to the side chain surface whereas β ensembles exhibit more heterogeneous water orientations. The backbone hydration is significantly higher in pPII than in β ensembles. Importantly, pPII to β hydration differences and the solvent accessible surface area of Cβ hydrogens both correlate with experimental pPII propensities. We propose that pPII conformations are stabilized by a local, hydrogen-bonded clathrate-like water structure and that residue-specific intrinsic pPII propensities reflect distinct abilities of side chains to template this water structure.

Free Energy Landscapes of Alanine Oligopeptides in Rigid-Body and Hybrid Water Models

Replica exchange molecular dynamics is used to study the effect of different rigid-body (mTIP3P, TIP4P, SPC/E) and hybrid (H1.56, H3.00) water models on the conformational free energy landscape of the alanine oligopeptides (acAnme and acA5nme), in conjunction with the CHARMM22 force field. The free energy landscape is mapped out as a function of the Ramachandran angles. In addition, various secondary structure metrics, solvation shell properties, and the number of peptide-solvent hydrogen bonds are monitored. Alanine dipeptide is found to have similar free energy landscapes in different solvent models, an insensitivity which may be due to the absence of possibilities for forming i-(i + 4) or i-(i + 3) intrapeptide hydrogen bonds. The pentapeptide, acA5nme, where there are three intrapeptide backbone hydrogen bonds, shows a conformational free energy landscape with a much greater degree of sensitivity to the choice of solvent model, though the three rigid-body water models differ only quantitatively. The pentapeptide prefers nonhelical, non-native PPII and β-sheet populations as the solvent is changed from SPC/E to the less tetrahedral liquid (H1.56) to an LJ-like liquid (H3.00). The pentapeptide conformational order metrics indicate a preference for open, solvent-exposed, non-native structures in hybrid solvent models at all temperatures of study. The possible correlations between the properties of solvent models and secondary structure preferences of alanine oligopeptides are discussed, and the competition between intrapeptide, peptide-solvent, and solvent-solvent hydrogen bonding is shown to be crucial in the relative free energies of different conformers.

Peptide Conformation Analysis Using an Integrated Bayesian Approach

Unlike native proteins that are amenable to structural analysis at atomic resolution, unfolded proteins occupy a manifold of dynamically interconverting structures. Defining the conformations of unfolded proteins is of significant interest and importance, for folding studies and for understanding the properties of intrinsically disordered proteins. Short chain protein fragments, i.e., oligopeptides, provide an excellent test-bed in efforts to define the conformational ensemble of unfolded chains. Oligomers of alanine in particular have been extensively studied as minimalist models of the intrinsic conformational preferences of the peptide backbone. Even short alanine peptides occupy an ensemble of substates that are distinguished by small free energy differences, so that the problem of quantifying the conformational preferences of the backbone remains a fundamental challenge in protein biophysics. Here, we demonstrate an integrated computational-experimental-Bayesian approach to quantify the conformational ensembles of the model trialanine peptide in water. In this approach, peptide conformational substates are first determined objectively by clustering molecular dynamics snapshots based on both structural and dynamic information. Next, a set of spectroscopic data for each conformational substate is computed. Finally, a Bayesian statistical analysis of both experimentally measured spectroscopic data and computational results is carried out to provide a current best estimate of the substate population ensemble together with corresponding confidence intervals. This distribution of substates can be further systematically refined with additional high-quality experimental data and more accurate computational modeling. Using an experimental data set of NMR coupling constants, we have also applied this approach to characterize the conformation ensemble of trivaline in water.

Local order in the unfolded state: conformational biases and nearest neighbor interactions

The discovery of Intrinsically Disordered Proteins, which contain significant levels of disorder yet perform complex biologically functions, as well as unwanted aggregation, has motivated numerous experimental and theoretical studies aimed at describing residue-level conformational ensembles. Multiple lines of evidence gathered over the last 15 years strongly suggest that amino acids residues display unique and restricted conformational preferences in the unfolded state of peptides and proteins, contrary to one of the basic assumptions of the canonical random coil model. To fully understand residue level order/disorder, however, one has to gain a quantitative, experimentally based picture of conformational distributions and to determine the physical basis underlying residue-level conformational biases. Here, we review the experimental, computational and bioinformatic evidence for conformational preferences of amino acid residues in (mostly short) peptides that can be utilized as suitable model systems for unfolded states of peptides and proteins. In this context particular attention is paid to the alleged high polyproline II preference of alanine. We discuss how these conformational propensities may be modulated by peptide solvent interactions and so called nearest-neighbor interactions. The relevance of conformational propensities for the protein folding problem and the understanding of IDPs is briefly discussed.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

On the foldability of tryptophan-containing tetra- and pentapeptides: an exhaustive molecular dynamics study

Short peptides serve as minimal model systems to decipher the determinants of foldability due to their simplicity arising from their smaller size, their ability to echo protein-like structural characteristics, and their direct implication in force field validation. Here, we describe an effort to identify small peptides that can still form stable structures in aqueous solutions. We followed the in silico folding of a selected set of 8640 tryptophan-containing tetra- and pentapeptides through 15 210 molecular dynamics simulations amounting to a total of 272.46 μs using explicit representation of the solute and full treatment of the electrostatics. The evaluation and sorting of peptides is achieved through scoring functions, which include terms based on interatomic vector distances, atomic fluctuations, and rmsd matrices between successive frames of a trajectory. Highly scored peptides are studied further via successive simulation rounds of increasing simulation length and using different empirical force fields. Our method suggested only a handful of peptides with strong foldability prognosis. The discrepancies between the predictions of the various force fields for such short sequences are also extensively discussed. We conclude that the vast majority of such short peptides do not adopt significantly stable structures in water solutions, at least based on our computational predictions. The present work can be utilized in the rational design and engineering of bioactive peptides with desired molecular properties.

pH-Independence of trialanine and the effects of termini blocking in short peptides: a combined vibrational, NMR, UVCD, and molecular dynamics study

Several lines of evidence now well establish that unfolded peptides in general, and alanine in specific, have an intrinsic preference for the polyproline II (pPII) conformation. Investigation of local order in the unfolded state is, however, complicated by experimental limitations and the inherent dynamics of the system, which has in some cases yielded inconsistent results from different types of experiments. One method of studying these systems is the use of short model peptides, and specifically short alanine peptides, known for predominantly sampling pPII structure in aqueous solution. Recently, He et al. ( J. Am. Chem. Soc. 2012 , 134 , 1571 - 1576 ) proposed that unblocked tripeptides may not be suitable models for studying conformational propensities in unfolded peptides due to the presence of end effect, that is, electrostatic interactions between investigated amino acid residues and terminal charges. To determine whether changing the protonation states of the N- and C-termini influence the conformational manifold of the central amino acid residue in tripeptides, we have examined the pH-dependence of unblocked trialanine and the conformational preferences of alanine in the alanine dipeptide. To this end, we measured and globally analyzed amide I' band profiles and NMR J-coupling constants. We described conformational distributions as the superposition of two-dimensional Gaussian distributions assignable to specific subspaces of the Ramachandran plot. Results show that the conformational ensemble of trialanine as a whole, and the pPII content (χpPII = 0.84) in particular, remains practically unaffected by changing the protonation state. We found that compared to trialanine, the alanine dipeptide has slightly lower pPII content (χpPII = 0.74) and an ensemble more reminiscent of the unblocked Gly-Ala-Gly model peptide. In addition, a two-state thermodynamic analysis of the conformational sensitive Δε(T) and (3)J(H(N)H(α))(T) data obtained from electronic circular dichroism and H NMR spectra indicate that the free energy landscape of trialanine is similar in all protonation states. MD simulations for the investigated peptides corroborate this notion and show further that the hydration shell around unblocked trialanine is unaffected by the protonation/deprotonation of the C-terminal group. In contrast, the alanine dipeptide shows a reduced water density around the central residue as well as a less ordered hydration shell, which decreases the pPII propensity and reduces the lifetime of sampled conformations.

Reduced atomic pair-interaction design (RAPID) model for simulations of proteins

Increasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses all-atom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solvent-free model matches the relevant pair-distribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into β-sheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly.

Dimer formation enhances structural differences between amyloid β-protein (1-40) and (1-42): an explicit-solvent molecular dynamics study

Amyloid β-protein (Aβ) is central to the pathology of Alzheimer's disease. A 5% difference in the primary structure of the two predominant alloforms, Aβ(1-40) and Aβ(1-42), results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD) studies of Aβ(1-40) and Aβ(1-42) assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD-derived Aβ(1-40) and Aβ(1-42) monomers and dimers was subjected to fully atomistic molecular dynamics (MD) simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower β-strand propensities than those predicted by DMD. Fully atomistic Aβ(1-40) and Aβ(1-42) monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of Aβ(1-42) dimers indicated a larger conformational variability in comparison to that of Aβ(1-40) dimers. Aβ(1-42) dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to Aβ(1-40) dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of Aβ(1-42) dimers and was significantly lower than in Aβ(1-40) dimers. The potential relevance of the three positively charged amino acids in mediating the Aβ oligomer toxicity is discussed in the light of available experimental data.

Using J-coupling constants for force field validation: application to hepta-alanine

A computational solution to the protein folding problem is the holy grail of biomolecular simulation and of the corresponding force fields. The complexity of the systems used for folding simulations precludes a direct feedback between the simulations and the force fields, thus necessitating the study of simpler systems with sufficient experimental data to allow force field optimization and validation. Recent studies on short polyalanine peptides of increasing length (up to penta-alanine) indicated the presence of a systematic deviation between the experimental (NMR-derived) J-couplings and the great majority of biomolecular force fields, with the χ(2) values for even the best-performing force fields being in the 1.4-1.8 range. Here we show that by increasing the number of residues to seven and by achieving convergence through an increase of the simulation time to 2 μs, we can identify one force field (the AMBER99SB force field, out of the three force fields studied) which when compared with the experimental J-coupling data (and for a specific set of Karplus equation parameters and estimated J-coupling errors previously used in the literature) gave a value of χ(2) = 0.99, indicating that full statistical consistency between experiment and simulation is feasible. However, and as a detailed analysis of the effects of estimated errors shows, the χ(2) values may be unsuitable as indicators of the goodness of fit of the various biomolecular force fields.

Specific interactions of sodium salts with alanine dipeptide and tetrapeptide in water: insights from molecular dynamics

We examine computationally the dipeptide and tetrapeptide of alanine in pure water and solutions of sodium chloride (NaCl) and iodide (NaI), with salt concentrations up to 3 M. Enhanced sampling of the configuration space is achieved by the replica exchange method. In agreement with other works, we observe preferential sodium interactions with the peptide carbonyl groups, which are enhanced in the NaI solutions due to the increased affinity of the less hydrophilic iodide anion for the peptide methyl side-chains and terminal blocking groups. These interactions have been associated with a decrease in the helicities of more complex peptides. In our simulations, both salts have a small effect on the dipeptide, but consistently stabilize the intramolecular hydrogen-bonding interactions and "α-helical" conformations of the tetrapeptide. This behavior, and an analysis of the intermolecular interaction energies show that ion-peptide interactions, or changes in the peptide hydration due to salts, are not sufficient determining factors of the peptide conformational preferences. Additional simulations suggest that the observed stabilizing effect is not due to the employed force-field, and that it is maintained in short peptides but is reversed in longer peptides. Thus, the peptide conformational preferences are determined by an interplay of energetic and entropic factors, arising from the peptide sequence and length and the composition of the solution.

Comparison between molecular dynamic based and knowledge based potentials for protein side chains

Parameterizing protein coarse-grained models from atomic-level force fields is a relatively new and promising approach in protein modeling. Here, dihedral angle potentials for the amino acid side chains are derived using molecular dynamic simulations. These are compared to those obtained using the traditional knowledge based approach, where the potentials are obtained from known protein structures. Side chain potentials consist of two- or three-dimensional dihedral angle histograms with a 20 degrees resolution. The simulations for the amino acids are carried out in explicit water using variants of the united atom Gromos force field, in the all-atom OPLS-AA/L force field, and in implicit solvent using variants of the Amber force field. It was found that the knowledge-based and molecular dynamic potentials are significantly correlated, with correlation coefficients in the upper 0.70. Nevertheless, in energy minimization tests performed on a group of proteins keeping the backbones fixed, the knowledge-based potentials generate angles that correspond closer to the angles in native structures (about 20% closer), for either buried and solvent exposed residues. Furthermore, in tests using high-resolution proteins, the prediction accuracy for buried residues reached 88%. Among the molecular dynamic-based potentials, the one derived using the G43A2 force field resulted in the highest prediction accuracy.

Conformations of phenylalanine in the tripeptides AFA and GFG probed by combining MD simulations with NMR, FTIR, polarized Raman, and VCD spectroscopy

Conformational properties of small, flexible peptides are a matter of ongoing interest since they can be considered as models for unfolded proteins. However, the investigation of the conformations of small peptides is challenging as they are ensembles of rapidly interconverting conformers; moreover, the different methods used are prone to different approximations and errors. In order to obtain more reliable results, it is prudent to combine different techniques; here, molecular dynamics (MD) simulations together with nuclear magnetic resonance (NMR), Fourier transform IR (FTIR), polarized Raman, and vibrational circular dichroism (VCD) measurements were used to study the conformational propensity of phenylalanine in the tripeptides AFA and GFG, motivated by the relevance of phenylalanine for the self-aggregation of peptides. The results of this analysis indicate that the F residue predominantly populates the beta-strand (beta) and polyproline II (PPII) conformations in both AFA and GFG. However, while phenylalanine exhibits a propensity for beta-strand conformations in GFG (0.40 < or = beta population < or = 0.69 and 0.29 < or = PPII population < or = 0.42), the substitution of terminal glycines with alanine residues induces a higher population of PPII (0.31 < or = beta population < or = 0.50 and 0.37 < or = PPII population < or = 0.57).

UV resonance Raman investigation of the conformations and lowest energy allowed electronic excited states of tri- and tetraalanine: charge transfer transitions

UV resonance Raman excitation profiles and Raman depolarization ratios were measured for trialanine and tetraalanine between 198 and 210 nm. Excitation within the pi --> pi* electronic transitions of the peptide bond results in UVRR spectra dominated by amide peptide bond vibrations. In addition to the resonance enhancement of the normal amide vibrations, we find enhancement of the symmetric terminal COO(-) vibration. The Ala(3) UVRR AmIII(3) band frequencies indicate that poly-proline II and 2.5(1) helix conformations and type II turns are present in solution. We also find that the conformation of the interior peptide bond of Ala(4) is predominantly poly-proline-II-like. The Raman excitation profiles of both Ala(3) and Ala(4) reveal a charge transfer electronic transition at 202 nm, where electron transfer occurs from the terminal nonbonding carboxylate orbital to the adjacent peptide bond pi* orbital. Raman depolarization ratio measurements support this assignment. An additional electronic transition is found in Ala(4) at 206 nm.

Intrinsic propensities of amino acid residues in GxG peptides inferred from amide I' band profiles and NMR scalar coupling constants

A reliable intrinsic propensity scale of amino acid residues is indispensable for an assessment of how local conformational distributions in the unfolded state can affect the folding of peptides and proteins. Short host-guest peptides, such as GxG tripeptides, are suitable tools for probing such propensities. To explore the conformational distributions sampled by the central amino acid residue in these motifs, we combined vibrational (IR, Raman, and VCD) with NMR spectroscopy. The data were analyzed in terms of a superposition of two-dimensional Gaussian distribution functions in the Ramachandran space pertaining to subensembles of polyproline II, beta-strand, right- and left-handed helical, and gamma-turn-like conformations. The intrinsic propensities of eight amino acid residues (x = A, V, F, L, S, E, K, and M) in GxG peptides were determined as mole fractions of these subensembles. Our results show that alanine adopts primarily (approximately 80%) a PPII-like conformation, while valine and phenylalanine were found to sample PPII and beta-strand-like conformations equally. The centers of the respective beta-strand distributions generally do not coincide with canonical values of dihedral angles of residues in parallel or antiparallel beta-strands. In fact, the distributions for most residues found in the beta-region significantly overlap the PPII-region. A comparison with earlier reported results for trivaline reveals that the terminal valines increase the beta-strand propensity of the central valine residue even further. Of the remaining investigated amino acids, methionine preferred PPII the most (0.64), and E, S, L, and K exhibit moderate (0.56-0.45) PPII propensities. Residues V, F, S, E, and L sample, to a significant extent, a region between the canonical PPII and (antiparallel) beta-strand conformations. This region coincides with the sampling reported for L and V using theoretical predictions (Tran et al. Biochemistry 2005, 44, 11369). The distributions of all investigated residues differ from coil library and computationally predicted distributions in that they do not exhibit a substantial sampling of helical conformations. We conclude that this sampling of helical conformations arises from the context dependence, for example, neighboring residues, in proteins and longer peptides, some of which is long-range.

Probing the folding of mini-protein Beta3s by two-dimensional infrared spectroscopy; simulation study

We propose to use infrared coherent two-dimensional correlation spectroscopy (2DCS) to characterize the folding mechanism of the mini-protein Beta3s. In this study Beta3s was folded by molecular dynamics (MD) simulation and intermediate conformational ensembles were identified. The one and two-dimensional correlation spectrum was calculated for the intermediate and native states of the mini-protein. A direct structure-spectra relationship was determined by analysis of conformational properties and specific residue contributions. We identified the structural origin of diagonal and off-diagonal peaks in the 2DCS spectra for the native and intermediate conformational ensembles in the folding mechanism. This work supports the implementation of computational techniques in conjunction with experimental 2DCS to study the folding mechanism of proteins. In addition to exploring the folding mechanism the work presented here can be applied in combination with experiment to refine and validate current molecular dynamics force fields.

PACS Codes: 87.15.Cc, 87.15.hm, 87.15.hp

Influence of ionization on the conformational preferences of peptide models. Ramachandran surfaces of N-formyl-glycine amide and N-formyl-alanine amide radical cations

Ramachandran maps of neutral and ionized HCO-Gly-NH2 and HCO-Ala-NH2 peptide models have been built at the B3LYP/6-31++G(d,p) level of calculation. Direct optimizations using B3LYP and the recently developed MPWB1K functional have also been carried out, as well as single-point calculations at the CCSD(T) level of theory with the 6-311++G(2df,2p) basis set. Results indicate that for both peptide models ionization can cause drastic changes in the shape of the PES in such a way that highly disallowed regions in neutral PES become low-energy regions in the radical cation surface. The structures localized in such regions, epsilonL+* and epsilonD+* are highly stabilized due to the formation of 2-centre-3-electron interactions between the two carbonyl oxygens. Inclusion of solvent effects by the conductor-like polarizable continuum model (CPCM) shows that the solute-solvent interaction energy plays an important role in determining the stability order.

Distribution of conformations sampled by the central amino acid residue in tripeptides inferred from amide I band profiles and NMR scalar coupling constants

The conformational preference of individual amino acid residues in the unfolded state of peptides and proteins is the subject of a continuous debate. Research has mostly been focused on alanine, owing to its abundance in proteins and its relevance for the understanding of helix <----> coil transitions. In the current study, we have analyzed the amide I band profiles of the IR, isotropic and anisotropic Raman, and VCD profiles of trialanine in terms of a conformational model which, for the first time, explicitly considers the entire ensemble of possible conformations rather than representative structures. The distribution function utilized for a satisfactory simulation of the amide I band profiles was found to also reproduce a set of five J coupling constants reported by Graf et al. (Graf, J.; et al. J. Am. Chem. Soc. 2007, 129, 1179). The results of our analysis reveal a PPII fraction of approximately 0.84 for the central alanine residue, which strongly corroborates the notion that alanine has a very high PPII propensity, exceeding the values obtained from restricted coil libraries. We performed a similar analysis for trivaline and found that the dominant fraction of its central residue is a beta-strand. The fraction of the respective distribution is 0.68. The remaining fraction contains contributions from helical and PPII conformations. The results of our analysis enable us to decide on the suitability of force fields used for MD simulations of short alanine-containing peptides. The paper establishes vibrational spectroscopy as a suitable method to explore the energy landscape of amino acid residues.

Multidimensional Langevin modeling of biomolecular dynamics

A systematic computational approach to describe the conformational dynamics of biomolecules in reduced dimensionality is presented. The method is based on (i) the decomposition of a high-dimensional molecular dynamics trajectory into a few "system" and (many) "bath" degrees of freedom and (ii) a Langevin simulation of the resulting model. Employing principal component analysis, the dimension of the system is chosen such that it contains all slow large-amplitude motions of the molecule, while the bath coordinates only account for its high-frequency fluctuations. It is shown that a sufficiently large dimension of the model is essential to ensure a clear time scale separation of system and bath variables, which warrants the validity of the memory-free Langevin equation. Applying methods from nonlinear time series analysis, a practical Langevin algorithm is presented which performs a local estimation of the multidimensional Langevin vector fields describing deterministic drift and stochastic driving. Adopting a 800 ns molecular dynamics simulation of the folding of heptaalanine in explicit water, it is shown that a five-dimensional Langevin model correctly reproduces the structure and conformational dynamics of the system. The virtues and limits of the approach are discussed in some detail.

Blind test of physics-based prediction of protein structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.