Peptide Conformation Analysis Using an Integrated Bayesian Approach

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Multipolar Force Fields for Amide-I Spectroscopy from Conformational Dynamics of the Alanine Trimer

The dynamics and spectroscopy of N-methyl-acetamide (NMA) and trialanine in solution are characterized from molecular dynamics simulations using different energy functions, including a conventional point charge (PC)-based force field, one based on a multipolar (MTP) representation of the electrostatics, and a semiempirical DFT method. For the 1D infrared spectra, the frequency splitting between the two amide-I groups is 10 cm^-1 from the PC, 13 cm^-1 from the MTP, and 47 cm^-1 from self-consistent charge density functional tight-binding (SCC-DFTB) simulations, compared with 25 cm^-1 from experiment. The frequency trajectory required for the frequency fluctuation correlation function (FFCF) is determined from individual normal mode (INM) and full normal mode (FNM) analyses of the amide-I vibrations. The spectroscopy, time-zero magnitude of the FFCF C(t = 0), and the static component Δ₀² from simulations using MTP and analysis based on FNM are all consistent with experiments for (Ala)₃. Contrary to this, for the analysis excluding mode-mode coupling (INM), the FFCF decays to zero too rapidly and for simulations with a PC-based force field, the Δ₀² is too small by a factor of two compared with experiments. Simulations with SCC-DFTB agree better with experiment for these observables than those from PC-based simulations. The conformational ensemble sampled from simulations using PCs is consistent with the literature (including P_II, β, α_R, and α_L), whereas that covered by the MTP-based simulations is dominated by P_II with some contributions from β and α_R. This agrees with and confirms recently reported Bayesian-refined populations based on 1D infrared experiments. FNM analysis together with a MTP representation provides a meaningful model to correctly describe the dynamics of hydrated trialanine.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala-Ala-Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala-Ala-Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.

Integrative Approaches in Structural Biology: A More Complete Picture from the Combination of Individual Techniques

With the recent technological and computational advancements, structural biology has begun to tackle more and more difficult questions, including complex biochemical pathways and transient interactions among macromolecules. This has demonstrated that, to approach the complexity of biology, one single technique is largely insufficient and unable to yield thorough answers, whereas integrated approaches have been more and more adopted with successful results. Traditional structural techniques (X-ray crystallography and Nuclear Magnetic Resonance (NMR)) and the emerging ones (cryo-electron microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS)), together with molecular modeling, have pros and cons which very nicely complement one another. In this review, three examples of synergistic approaches chosen from our previous research will be revisited. The first shows how the joint use of both solution and solid-state NMR (SSNMR), X-ray crystallography, and cryo-EM is crucial to elucidate the structure of polyethylene glycol (PEG)ylated asparaginase, which would not be obtainable through any of the techniques taken alone. The second deals with the integrated use of NMR, X-ray crystallography, and SAXS in order to elucidate the catalytic mechanism of an enzyme that is based on the flexibility of the enzyme itself. The third one shows how it is possible to put together experimental data from X-ray crystallography and NMR restraints in order to refine a protein model in order to obtain a structure which simultaneously satisfies both experimental datasets and is therefore closer to the ‘real structure’.

Quantum Mechanics Study on Hydrophilic and Hydrophobic Interactions in the Trivaline-Water System

With the aim to elucidate hydrophobic effects in the unfolded state of peptides, DFT-M062X computations on the Val₃H⁺· nH₂O ( n up to 22) clusters have been accomplished. As far as the main chain is concerned, four conformers with β-strand and/or polyproline type II conformations, PPII (indicated as β-β, β-PPII, PPII-β, and PPII-PPII), have been found by changing the ϕ and ψ angles. For bare peptide, the side chain (isopropyl) of each residue can independently take on three different orientations with negligible effects on energetics. The great isopropyl spatial separations in β-β and β-PPII conformers allow for the construction of synergic and extensive water-water and water-peptide H-bonding in the minimal hydration Val₃H⁺·22H₂O models without significant steric encumbrance. Conversely, due to the proximity of the isopropyl of the central residue with the other two, some restrictions in the water shell construction around the peptide become evident for the PPII-PPII conformer and the number of energetically accessible structures decreases. This is indicative of correlated motion involving isopropyls and backbone mediated by water molecules, the origin of the nearest neighbor effects. Comparing the thermodynamic data of Ala₃H⁺·22H₂O and Val₃H⁺·22H₂O, what emerges is that both hydration enthalpy and entropy drive the β-strand stability of the latter.

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.

Principles of protein structural ensemble determination

The biological functions of protein molecules are intimately dependent on their conformational dynamics. This aspect is particularly evident for disordered proteins, which constitute perhaps one-third of the human proteome. Therefore, structural ensembles often offer more useful representations of proteins than individual conformations. Here, we describe how the well-established principles of protein structure determination should be extended to the case of protein structural ensembles determination. These principles concern primarily how to deal with conformationally heterogeneous states, and with experimental measurements that are averaged over such states and affected by a variety of errors. We first review the growing literature of recent methods that combine experimental and computational information to model structural ensembles, highlighting their similarities and differences. We then address some conceptual problems in the determination of structural ensembles and define future goals towards the establishment of objective criteria for the comparison, validation, visualization and dissemination of such ensembles.

Predicting protein backbone chemical shifts from Cα coordinates: extracting high resolution experimental observables from low resolution models

Given the demonstrated utility of coarse-grained modeling and simulations approaches in studying protein structure and dynamics, developing methods that allow experimental observables to be directly recovered from coarse-grained models is of great importance. In this work, we develop one such method that enables protein backbone chemical shifts (¹HN, ¹Hα, ¹³Cα, ¹³C, ¹³Cβ, and ¹⁵N) to be predicted from Cα coordinates. We show that our Cα-based method, LARMOR^Cα, predicts backbone chemical shifts with comparable accuracy to some all-atom approaches. More importantly, we demonstrate that LARMOR^Cα predicted chemical shifts are able to resolve native structure from decoy pools that contain both native and non-native models, and so it is sensitive to protein structure. As an application, we use LARMOR^Cα to characterize the transient state of the fast-folding protein gpW using recently published NMR relaxation dispersion derived backbone chemical shifts. The model we obtain is consistent with the previously proposed model based on independent analysis of the chemical shift dispersion pattern of the transient state. We anticipate that LARMOR^Cα will find utility as a tool that enables important protein conformational substates to be identified by “parsing” trajectories and ensembles generated using coarse-grained modeling and simulations.

Molecular Dynamics Simulations of 441 Two-Residue Peptides in Aqueous Solution: Conformational Preferences and Neighboring Residue Effects with the Amber ff99SB-ildn-NMR Force Field

Understanding the intrinsic conformational preferences of amino acids and the extent to which they are modulated by neighboring residues is a key issue for developing predictive models of protein folding and stability. Here we present the results of 441 independent explicit-solvent MD simulations of all possible two-residue peptides that contain the 20 standard amino acids with histidine modeled in both its neutral and protonated states. (3)J(HNHα) coupling constants and δ(Hα) chemical shifts calculated from the MD simulations correlate quite well with recently published experimental measurements for a corresponding set of two-residue peptides. Neighboring residue effects (NREs) on the average (3)J(HNHα) and δ(Hα) values of adjacent residues are also reasonably well reproduced, with the large NREs exerted experimentally by aromatic residues, in particular, being accurately captured. NREs on the secondary structure preferences of adjacent amino acids have been computed and compared with corresponding effects observed in a coil library and the average β-turn preferences of all amino acid types have been determined. Finally, the intrinsic conformational preferences of histidine, and its NREs on the conformational preferences of adjacent residues, are both shown to be strongly affected by the protonation state of the imidazole ring.

Experimental Inferential Structure Determination of Ensembles for Intrinsically Disordered Proteins

We develop a Bayesian approach to determine the most probable structural ensemble model from candidate structures for intrinsically disordered proteins (IDPs) that takes full advantage of NMR chemical shifts and J-coupling data, their known errors and variances, and the quality of the theoretical back-calculation from structure to experimental observables. Our approach differs from previous formulations in the optimization of experimental and back-calculation nuisance parameters that are treated as random variables with known distributions, as opposed to structural or ensemble weight optimization or use of a reference ensemble. The resulting experimental inferential structure determination (EISD) method is size extensive with O(N) scaling, with N = number of structures, that allows for the rapid ranking of large ensemble data comprising tens of thousands of conformations. We apply the EISD approach on singular folded proteins and a corresponding set of ∼25 000 misfolded states to illustrate the problems that can arise using Boltzmann weighted priors. We then apply the EISD method to rank IDP ensembles most consistent with the NMR data and show that the primary error for ranking or creating good IDP ensembles resides in the poor back-calculation from structure to simulated experimental observable. We show that a reduction by a factor of 3 in the uncertainty of the back-calculation error can improve the discrimination among qualitatively different IDP ensembles for the amyloid-beta peptide.

Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode

Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechano-energetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.

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.