Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: comparisons with IR and vibrational circular dichroism spectra

Vibrational circular dichroism spectra of proline in water at different pH values

Recording VCD spectra of aqueous solution poses a particular challenge as water is a strong infrared absorber. Likewise, the computational analysis of VCD spectra by means of DFT-based spectral calculations requires the consideration of explicit solvent molecules, thus posing an even greater challenge. Several studies suggested that by modeling the solvent environment with a few water molecules in a micro-solvation approach would be sufficient to describe experimental spectra. For example, using proline at different pH values, we herein show that a change in the relative spatial orientation of a single water molecule in five-fold solvated structures strongly affects the computed VCD spectral signatures and that Boltzmann-weighted spectra do not correctly reproduce the experiment. We thus explored an approach based on molecular dynamics and subsequent DFT-calculations, in which we considered 30 water molecules (about 1.5 solvation shells). Once again, it was found that the Boltzmann-weighted spectra obtained on the basis of several hundred structures did not correctly reproduce experimental signatures, and a simple averaging scheme resulted in well-matching spectra with comparable bandwidths. The rationale behind the procedure was that sampling the configurational space of the solvent molecules is as equally important as the conformational sampling of the solute. For conformationally more flexible molecules, it is assumed that a much larger set of structures will have to be computed in order to properly sample the conformational space of both solute and solvent.

Vibrational Circular Dichroism Spectroscopy with a Classical Polarizable Force Field: Alanine in the Gas and Condensed Phases

Polarizable force fields are an essential component for the chemically accurate modeling of complex molecular systems with a significant degree of fluxionality, beyond harmonic or perturbative approximations. In this contribution we examine the performance of such an approach for the vibrational spectroscopy of the alanine amino acid, in the gas and condensed phases, from the Fourier transform of appropriate time correlation functions generated along molecular dynamics (MD) trajectories. While the infrared (IR) spectrum only requires the electric dipole moment, the vibrational circular dichroism (VCD) spectrum further requires knowledge of the magnetic dipole moment, for which we provide relevant expressions to be used with polarizable force fields. The AMOEBA force field was employed here to model alanine in the neutral and zwitterionic isolated forms, solvated by water or nitrogen, and as a crystal. Within this framework, comparison of the electric and magnetic dipole moments to those obtained with nuclear velocity perturbation theory based on density-functional theory for the same MD trajectories are found to agree well with one another. The statistical convergence of the IR and VCD spectra is examined and found to be more demanding in the latter case. Comparisons with experimental frequencies are also provided for the condensed phases.

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.

Competition between inter and intramolecular hydrogen bond evidenced by vibrational circular dichroism spectroscopy: The case of (1S,2R)-(-)-cis-1-amino-2-indanol

The infrared (IR) absorption and vibrational circular dichroism (VCD) spectra of an intramolecularly hydrogen-bonded chiral amino-alcohol, (1S,2R)-(-)-cis-1-amino-2-indanol, are studied in DMSO-d₆ . The spectra are simulated at the density functional theory (DFT) level within the frame of the cluster-in-the-liquid model. Both IR and VCD spectra show a clear signature of the formation of intermolecular hydrogen bonds at the detriment of the intramolecular OH … N interaction present in the isolated molecule. Two solvent molecules are necessary to reproduce the experimental spectra. Whereas the first DMSO molecule captures the main spectral modifications due to hydrogen bond formation between the solute and the solvent, the second DMSO molecule is necessary for a good description of the Boltzmann contribution of the different complexes, based on their Gibbs free energy.

A Proposed Method to Obtain Surface Specificity with Pump-Probe and 2D Spectroscopies

Surfaces and interfaces are ubiquitous in nature. From cell membranes, to photovoltaic thin films, surfaces have important function in both biological and materials systems. Spectroscopic techniques have been developed to probe systems like these, such as sum frequency generation (SFG) spectroscopies. The advantage of SFG spectroscopy, a second-order spectroscopy, is that it can distinguish between signals produced from molecules in the bulk versus on the surface. We propose a polarization scheme for third-order spectroscopy experiments, such as pump-probe and 2D spectroscopy, to select for surface signals and not bulk signals. This proposed polarization condition uses one pulse perpendicular compared to the other three to isolate cross-peaks arising from molecules with polar and uniaxial (i.e., biaxial) order at a surface, while removing the signal from bulk isotropic molecules. In this work, we focus on two of these cases: XXXY and YYYX, which differ by the sign of the cross-peak they create. We compare this technique to SFG spectroscopy and vibrational circular dichroism to provide insight to the behavior of the cross-peak signal. We propose that these singularly cross-polarized schemes provide odd-ordered spectroscopies the surface-specificity typically associated with even-ordered techniques.

Conformational preference of bicyclic β-amino acid dipeptides

Bridged bicyclic amino acids have high potential applicability as self-organized, conformationally constrained synthetic building blocks that do not require assistance from hydrogen bond formation. We systematically investigated the intrinsic conformational propensities of dipeptides of bridged bicyclic β-amino acids by means of accelerated molecular dynamics simulation and density functional theory (DFT) calculations in methanol, chloroform, and water. While the main-chain conformation, represented by φ and θ values, is fixed by the nature of the bicyclic ring structure, rotation of the C-terminal carbonyl group (ψ) is also restricted, converging to one or two minima. In endo-type dipeptides, in which the two N- and C-terminal amides are spatially close to each other, the C-terminal amide plane is placed horizontally. In exo-type dipeptides, in which the two amides are on opposite sides of the ring plane, the C-terminal carbonyl group can take two types of positions: either parallel/antiparallel with the N-terminal carbonyl or beneath the bicyclic ring, forcing the amide NHMe moiety to lie outside of the ring. We also examined the cis-trans preference of model bicyclic amides. Although the parent amides exhibit cis-trans equilibrium without any preference, addition of a methyl group on one of the bridgehead positions tips the equilibrium towards trans.

Assessing cluster models of solvation for the description of vibrational circular dichroism spectra: synergy between static and dynamic approaches

Solvation effects are essential for defining the shape of vibrational circular dichroism (VCD) spectra.

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Insight into vibrational circular dichroism of proteins by density functional modeling

Vibrational circular dichroism (VCD) spectroscopy is an excellent method to determine the secondary structure of proteins in solution. Comparison of experimental spectra with quantum-chemical simulations represents a convenient and objective way to extract information on the structure. This has been difficult for such large molecules where approximate theoretical models have to be used. In the present study we applied the Cartesian-coordinate based tensor transfer (CCT) making it possible to extend the density functional theory (DFT) and model spectral intensities of large globular proteins nearly at quantum-chemical precision. Indeed, comparison with experiment provided a better understanding of the dependence of VCD spectral shapes on the geometry, their sensitivity to fine structural details and interactions with the environment. On a model set of globular proteins the simulated spectra correlated well with experimental data and revealed which structural information can (and cannot) be obtained from this kind of spectroscopy. Although the VCD technique has been regarded as being rather insensitive to side-chain variations, we found that the spectra of human and hen lysozyme differing by a few amino acids only are quite distinct. This has been explained by long-distance coupling of the amide vibrations. Likewise, the modeling reproduced some spectral changes caused by protein deuteration even when the protein structure was conserved.

Construction and comparison of the statistical coil states of unfolded and intrinsically disordered proteins from nearest-neighbor corrected conformational propensities of short peptides

Assessing the influence of nearest neighbors on the conformational ensemble of amino acid residues in unfolded and intrinsically disordered proteins and peptides is pivotal for a thorough understanding of the statistical coil state of unfolded proteins as well as of the energetics of the folding process. Research aimed at exploring nearest neighbor interactions has mostly focused on the analysis of restricted coil libraries that reflect conformational distributions in loops connecting more regular secondary structure segments. Recently, however, Toal et al. reported an experimentally based structural analysis of selected xy-pairs in GxyG tetrapeptides, which revealed quantitative information about conformational changes induced by nearest-neighbor interactions (Eur. J. Chem., 2015, 21, 5173-5192). Here, we perform analyses of Ramachandran plots of xy-pairs in GxyG and in coil libraries (Ting et al., PLOS CompBiol, 2010, 6, e1000763) using Hellinger distances as a quantitative measure of dissimilarities between Ramachandran distributions. Our analysis reveals that nearest-neighbor effects inferred from the above coil library are much less pronounced than corresponding structural changes observed for GxyG peptides. To determine whether nearest-neighbor induced conformational changes observed for GxyG can be utilized for the analysis of unfolded proteins, we analyzed sets of ³J(H^HH^α) coupling constants of three different unfolded proteins, namely the 130-residue fragment of the Staphylococcus aureus fibronectin-binding protein (FnBPc), denatured hen lysozyme, and the htau40 protein. For the first two proteins we found statistically meaningful correlations between predicted nearest-neighbor induced changes of ³J(H^HH^α) and experimentally observed deviations from corresponding coupling constants of GxG peptides in water, which we used as reference system with minimal nearest-neighbor interactions. This observation is in line with the NMR based understanding of these proteins being predominantly statistical coils. For htau40, however, which is known to exhibit residual structure and large deviations form statistical coil expectations, these correlations are weak or absent. Our results thus underscore the importance of nearest-neighbor interactions for a complete physical description of an ideal statistical coil state of a protein.

Quantum Mechanics Approach to Hydration Energies and Structures of Alanine and Dialanine

A systematic approach to the phenomena related to hydration of biomolecules is reported at the state of the art of electronic-structure methods. Large-scale CCSD(T), MP4-SDQ, MP2, and DFT(M06-2X) calculations for some hydrated complexes of alanine and dialanine (Ala⋅13 H₂ O, Ala₂ H⁺ ⋅18 H₂ O, and Ala₂ ⋅18 H₂ O) are compared with experimental data and other elaborate modeling to assess the reliability of a simple bottom-up approach. The inclusion of a minimal number of water molecules for microhydration of the polar groups together with the polarizable continuum model is sufficient to reproduce the relative bulk thermodynamic functions of the considered biomolecules. These quantities depend on the adopted electronic-structure method, which should be chosen with great care. Nevertheless, the computationally feasible MP2 and M06-2X functionals with the aug-cc-pVTZ basis set satisfactorily reproduce values derived by high-level CCSD(T) and MP4-SDQ methods, and thus they are suitable for future developments of more elaborate and hence more biochemically significant peptides.

Conformational analysis of short polar side-chain amino-acids through umbrella sampling and DFT calculations

Molecular and quantum mechanics calculations were carried out in a series of tripeptides (GXG, where X = D, N and C) as models of the unfolded states of proteins. The selected central amino acids, especially aspartic acid (D) and asparagine (N) are known to present significant average conformations in partially allowed areas of the Ramachandran plot, which have been suggested to be important in unfolded protein regions. In this report, we present the calculation of the propensity values through an umbrella sampling procedure in combination with the calculation of the NMR J-coupling constants obtained by a DFT model. The experimental NMR observations can be reasonably explained in terms of a conformational distribution where PP_II and β basins sum up propensities above 0.9. The conformational analysis of the side chain dihedral angle (χ₁), along with the computation of ³J(H^αH^β), revealed a preference for the g _- and g ₊ rotamers. These may be connected with the presence of intermolecular H-bonding and carbonyl-carbonyl interactions sampled in the PP_II and β basins. Taking into account all those results, it can be established that these residues show a similar behavior to other amino acids in short peptides regarding backbone φ,ψ dihedral angle distribution, in agreement with some experimental analysis of capped dipeptides.

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.

Anharmonic Infrared Spectroscopy through the Fourier Transform of Time Correlation Function Formalism in ONETEP

Density functional theory molecular dynamics (DFT-MD) provides an efficient framework for accurately computing several types of spectra. The major benefit of DFT-MD approaches lies in the ability to naturally take into account the effects of temperature and anharmonicity, without having to introduce any ad hoc or a posteriori corrections. Consequently, computational spectroscopy based on DFT-MD approaches plays a pivotal role in the understanding and assignment of experimental peaks and bands at finite temperature, particularly in the case of floppy molecules. Linear-scaling DFT methods can be used to study large and complex systems, such as peptides, DNA strands, amorphous solids, and molecules in solution. Here, we present the implementation of DFT-MD IR spectroscopy in the ONETEP linear-scaling code. In addition, two methods for partitioning the dipole moment within the ONETEP framework are presented. Dipole moment partitioning allows us to compute spectra of molecules in solution, which fully include the effects of the solvent, while at the same time removing the solvent contribution from the spectra.

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.

Randomizing the unfolded state of peptides (and proteins) by nearest neighbor interactions between unlike residues

To explore the influence of nearest neighbors on conformational biases in unfolded peptides, we combined vibrational and 2D NMR spectroscopy to obtain the conformational distributions of selected "GxyG" host-guest peptides in aqueous solution: GDyG, GSyG, GxLG, GxVG, where x/y=A, K, L, V. Large changes of conformational propensities were observed due to nearest-neighbor interactions, at variance with the isolated pair hypothesis. We found that protonated aspartic acid and serine lose their above-the-average preference for turn-like structures in favor of polyproline II (pPII) populations in the presence of neighbors with bulky side chains. Such residues also decrease the above-the-average pPII preference of alanine. These observations suggest that the underlying mechanism involves a disruption of the hydration shell. Thermodynamic analysis of (3) J(H(N) ,H(α) ) (T) data for each x,y residue reveals that modest changes in the conformational ensemble masks larger changes of enthalpy and entropy governing the pPII↔β equilibrium indicating a significant residue dependent temperature dependence of the peptides' conformational ensembles. These results suggest that nearest-neighbor interactions between unlike residues act as conformational randomizers close to the enthalpy-entropy compensation temperature, eliminating intrinsic biases in favor of largely balanced pPII/β dominated ensembles at physiological temperatures.

Interfacial water at the trialanine hydrophilic surface: a DFT electronic structure and bottom-up investigation

A model describing a network of hydrogen bonded water-trialanine has been developed to estimate hydration effects on various conformers of the peptide.

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

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.

Intrinsic α-helical and β-sheet conformational preferences: a computational case study of alanine

A fundamental question in protein science is what is the intrinsic propensity for an amino acid to be in an α-helix, β-sheet, or other backbone dihedral angle ( ϕ-ψ) conformation. This question has been hotly debated for many years because including all protein crystal structures from the protein database, increases the probabilities for α-helical structures, while experiments on small peptides observe that β-sheet-like conformations predominate. We perform molecular dynamics (MD) simulations of a hard-sphere model for Ala dipeptide mimetics that includes steric interactions between nonbonded atoms and bond length and angle constraints with the goal of evaluating the role of steric interactions in determining protein backbone conformational preferences. We find four key results. For the hard-sphere MD simulations, we show that (1) β-sheet structures are roughly three and half times more probable than α-helical structures, (2) transitions between α-helix and β-sheet structures only occur when the backbone bond angle τ (NCα C) is greater than 110°, and (3) the probability distribution of τ for Ala conformations in the "bridge" region of ϕ-ψ space is shifted to larger angles compared to other regions. In contrast, (4) the distributions obtained from Amber and CHARMM MD simulations in the bridge regions are broader and have increased τ compared to those for hard sphere simulations and from high-resolution protein crystal structures. Our results emphasize the importance of hard-sphere interactions and local stereochemical constraints that yield strong correlations between ϕ-ψ conformations and τ.

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.

Ramachandran Plot for Alanine Dipeptide as Determined from Raman Optical Activity

Accessible values of the φ and ψ torsional angles determining peptide main chain conformation are traditionally displayed in the form of Ramachandran plots. The number of experimental methods making it possible to determine such conformational distribution is limited. In the present study, Raman optical activity (ROA) spectra of Ac-Ala-NHMe were measured and fit by theoretical curves. This revealed the most favored conformers and a large part of the potential energy surface (PES) of this model dipeptide. Such experimental PES compares well to quantum chemical computations, whereas molecular dynamics (MD) modeling reproduces it less faithfully. The surface shape is consistent with the temperature dependence of the spectra, as observed experimentally and predicted by MD. Despite errors associated with spectral modeling and the measurement, the results are likely to facilitate future applications of ROA spectroscopy.

A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

Reliable oligonucleotide conformational ensemble generation in explicit solvent for force field assessment using reservoir replica exchange molecular dynamics simulations

Molecular dynamics force field development and assessment requires a reliable means for obtaining a well-converged conformational ensemble of a molecule in both a time-efficient and cost-effective manner. This remains a challenge for RNA because its rugged energy landscape results in slow conformational sampling and accurate results typically require explicit solvent which increases computational cost. To address this, we performed both traditional and modified replica exchange molecular dynamics simulations on a test system (alanine dipeptide) and an RNA tetramer known to populate A-form-like conformations in solution (single-stranded rGACC). A key focus is on providing the means to demonstrate that convergence is obtained, for example, by investigating replica RMSD profiles and/or detailed ensemble analysis through clustering. We found that traditional replica exchange simulations still require prohibitive time and resource expenditures, even when using GPU accelerated hardware, and our results are not well converged even at 2 μs of simulation time per replica. In contrast, a modified version of replica exchange, reservoir replica exchange in explicit solvent, showed much better convergence and proved to be both a cost-effective and reliable alternative to the traditional approach. We expect this method will be attractive for future research that requires quantitative conformational analysis from explicitly solvated simulations.

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.

Disorder and order in unfolded and disordered peptides and proteins: a view derived from tripeptide conformational analysis. II. Tripeptides with short side chains populating asx and β-type like turn conformations

In the preceding paper, we found that ensembles of tripeptides with long or bulky chains can include up to 20% of various turns. Here, we determine the structural and thermodynamic characteristics of GxG peptides with short polar and/or ionizable central residues (D, N, C), whose conformational distributions exhibit higher than average percentage (>20%) of turn conformations. To probe the side-chain conformations of these peptides, we determined the (3)J(H(α),H(β)) coupling constants and derived the population of three rotamers with χ1 -angles of -60°, 180° and 60°, which were correlated with residue propensities by DFT-calculations. For protonated GDG, the rotamer distribution provides additional evidence for asx-turns. A comparison of vibrational spectra and NMR coupling constants of protonated GDG, ionized GDG, and the protonated aspartic acid dipeptide revealed that side chain protonation increases the pPII content at the expense of turn populations. The charged terminal groups, however, have negligible influence on the conformational properties of the central residue. Like protonated GDG, cationic GCG samples asx-turns to a significant extent. The temperature dependence of the UVCD spectra and (3)J(H(N)H(α)) constants suggest that the turn populations of GDG and GNG are practically temperature-independent, indicating enthalpic and entropic stabilization. The temperature-independent J-coupling and UVCD spectra of GNG require a three-state model. Our results indicate that short side chains with hydrogen bonding capability in GxG segments of proteins may serve as hinge regions for establishing compact structures of unfolded proteins and peptides.

QM and QM/MM simulations of proteins

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

Assessment of the intrinsic conformational preferences of dipeptide amino acids in aqueous solution by combined umbrella sampling/MBAR statistics. A comparison with experimental results

The propensities of 19 amino acid dipeptides have been calculated by a distributed umbrella sampling molecular dynamics simulation procedure using the OPLS-AA force field. The potential of mean force maps was estimated with the multiple Bennett acceptance ratio statistics. The resulting propensities compare satisfactorily well with very recently published experimental data on equivalent systems. In particular, α conformation-probabilities for all of the dipeptides remain much lower than either β or P(II) propensities. This result is in agreement with most experimental data for dipeptides. However, it is also in contrast with most simulation studies performed so far with other force fields, where α conformations result even more probable than P(II) or β ones. We discuss the behavior of the OPLS-AA force field, which can be useful for the improvement of this model in reproducing the recent experimental observations on amino acid dipeptides.

Axial chirality of donor-donor, donor-acceptor, and tethered 1,1'-binaphthyls: a theoretical revisit with dynamics trajectories

The circular dichroism (CD) spectra of (R)-2,2'-dimethoxy-1,1'-binaphthyl (DD) and its untethered and tethered donor-acceptor analogues (DA and DA7-DA9) were investigated experimentally and theoretically. The experimental CD spectra of DD and DA resembled each other in several aspects, displaying a positive-positive-negative Cotton effect pattern in the (1)L(b)-(1)L(a) region and a strong negative couplet at the (1)B(b) band, but significantly differed in transition energy and rotatory strength. The couplet amplitude (A) of the main band was 1.6 times larger in DA than in DD, despite the comparable extinction coefficients and seemingly analogous conformations. An additional positive Cotton effect was observed at the CT (CT) band for donor-acceptor binaphthyl DA. Our theoretical prediction of the CD spectra of binaphthyls involves three sequential first principle quantum mechanics (QM) calculations. Thus, the geometry optimizations of a series of conformers with varying dihedral angles were performed by the dispersion-corrected DFT-D method using the B97-D functional and the TZV2P basis set. The potential curve as a function of the dihedral angle (θ) was obtained by using the SCS-MP2/TZVPP single-point energy calculations with and without application of the solvent correction. The CD spectrum of each conformer was independently calculated by the second-order approximate coupled cluster calculation (CC2 method) using the TZVPP basis sets and the resolution of the identity (RI-J) approximation. The (net) theoretical CD spectrum was obtained by averaging over all possible conformers, where the dynamics trajectories based on the relative SCS-MP2 energies were taken into account. By using 17 possible conformers at θ varying from 50 to 130° by 5° intervals, the experimental CD spectra were successfully reproduced in a quantitative manner, enabling us to characterize properly almost all of the important spectral features and chiroptical properties. The two-state model, reported previously, turned out to have led to the right answer with wrong reasons. The couplet sign and amplitude A are critical functions of θ and can be used not only for (qualitatively) determining the absolute configuration but also for quantitatively analyzing the binaphthyl conformations. The angle dependence of A was already argued in the classical coupled oscillator and exciton chirality theories to provide reasonable structure elucidations but only in a qualitative or semiquantitative manner. Our method is able to predict the A value quantitatively as a function of θ. For tethered binaphthyls DA7-DA9, particular care should be exercised in the conformational assessment based on the classical treatment because the amplitude A was shown to be significantly affected by the existence of the tether itself. In the present method, the couplet amplitude A was nicely related to the dihedral angle θ of DA and DD by the state-of-the-art ab initio calculations, enabling us to gain the quantitative information about the conformation of axially chiral binaphthyls. The Cotton effect at the CT band also serves as a complementary clue for elucidating the conformation of donor-acceptor binaphthyls.

Isolated monohydrates of a model peptide chain: effect of a first water molecule on the secondary structure of a capped phenylalanine

The formation of monohydrates of capped phenylalanine model peptides, CH(3)-CO-Phe-NH(2) and CH(3)-CO-Phe-NH-CH(3), in a supersonic expansion has been investigated using laser spectroscopy and quantum chemistry methods. Conformational distributions of the monohydrates have been revealed by IR/UV double-resonance spectroscopy and their structures assigned by comparison with DFT-D calculations. A careful analysis of the final hydrate distribution together with a detailed theoretical investigation of the potential energy surface of the monohydrates demonstrates that solvation occurs from the conformational distribution of the isolated peptide monomers. The distribution of the monohydrates appears to be strongly dependent on both the initial monomer conformation (extended or folded backbone) and the solvation site initially occupied by the water molecule. The solvation processes taking place during the cooling can be categorized as follows: (a) solvation without significant structural changes of the peptide, (b) solvation inducing significant distortions of the backbone but retaining the secondary structure, and (c) solvation triggering backbone isomerizations, leading to a modification of the peptide secondary structure. It is observed that solvation by a single water molecule can fold a β-strand into a γ-turn structure (type c) or induce a significant opening of a γ-turn characterized by an elongated C(7) hydrogen bond (type b). These structural changes can be considered as a first step toward the polyproline II condensed-phase structure, illustrating the role played by the very first water molecule in the solvation process.

Modeling the infrared and circular dichroism spectroscopy of a bridged cyclic diamide

Density functional theory based molecular dynamics simulations are used to study the structure, infrared (IR) spectroscopy, circular dichroism (CD) spectroscopy, and coupling between the amide I vibrations of a bridged cyclic diamide in the gas phase and in aqueous solution. IR spectra computed via the dipole moment time correlation function show a large red-shift of 30 cm(-1) in the amide I vibration in solution compared to the gas phase, and are in good agreement with experiment. Conformationally averaged CD spectra computed using the CIS(D) method are highly sensitive to the structures used, and structures sampled in the aqueous phase simulation are required to obtain qualitatively correct CD spectra. Analysis of the coupling between the amide I modes shows that in the aqueous phase there is an increased localization of the vibrations on the individual peptide groups and a reduction in the mode coupling parameter compared to the gas phase. Overall, the results illustrate the significance of incorporating molecular dynamics in the simulation of IR and CD spectra.

Quantitative Assessment of Force Fields on Both Low-Energy Conformational Basins and Transition-State Regions of the (ϕ-ψ) Space

The free energy surfaces (FESs) of alanine dipeptide are studied to illustrate a new strategy to assess the performance of classical molecular mechanics force field on the full range of the (ϕ-ψ) conformational space. The FES is obtained from metadynamics simulations with five commonly used force fields and from ab initio density functional theory calculations in both gas phase and aqueous solution. The FESs obtained at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d,p) level of theory are validated by comparison with previously reported MP2 and LMP2 results as well as with experimentally obtained probability distribution between the C5-β (or β-PPII) and αR states. A quantitative assessment is made for each force field in three conformational basins, LeRI (C5-β-C7eq), LeRII (β2-αR), and LeRIII(αL-C7ax-αD) as well as three transition-state regions linking the above conformational basins. The performance of each force field is evaluated in terms of the average free energy of each region in comparison with that of the ab initio results. We quantify how well a force field FES matches the ab initio FES through the calculation of the standard deviation of a free energy difference map between the two FESs. The results indicate that the performance varies largely from region to region or from force field to force field. Although not one force field is able to outperform all others in all conformational areas, the OPLSAA/L force field gives the best performance overall, followed by OPLSAA and AMBER03. For the three top performers, the average free energies differ from the corresponding ab initio values from within the error range (<0.4 kcal/mol) to ∼1.5 kcal/mol for the low-energy regions and up to ∼2.0 kcal/mol for the transition-state regions. The strategy presented and the results obtained here should be useful for improving the parametrization of force fields targeting both accuracy in the energies of conformers and the transition-state barriers.