Correct folding of an α-helix and a β-hairpin using a polarized 2D torsional potential

Decoding the dynamics of BCL9 triazole stapled peptide

BCL9 is a key protein in Wnt signaling pathway. It acts as a transcriptional co-activator to β-catenin, and dysregulation in this pathway leads to tumor growth. Inhibiting such a protein-protein interaction is considered as a therapeutic challenge. The interaction between β-catenin and BCL9 is facilitated by a 23-residue helical domain from BCL9 and a hydrophobic groove of β-catenin. To prevent this interaction, a peptide that mimics the alpha-helical domain of BCL9 can be designed. Stapling is considered a successful strategy in the pursuit of designing such peptides in which amino acids side are stitched together using chemical moieties. Among the various types of cross-linkers, triazole is the most rapid and effective one synthesized via click reaction. However, the underlying interactions behind maintaining the secondary structure of stapled peptides remain less explored. In the current work, we employed the molecular dynamics simulation to study the conformational behavior of the experimentally synthesized single and double triazole stapled BCL9 peptide. Upon the addition of a triazole staple, there is a significant reduction in the conformational space of BCL9. The helical character of the stapled peptide increases with an increase in separation between the triazole cross-linkers. Also, we encompassed the Replica Exchange with Solute Tempering (REST2) simulation to validate the high-temperature response of the stapled peptide. From REST2, the PCA and t-SNE show the reduction in distinct cluster formation on the addition of triazole staple. Our study infers further development of these triazole-stapled BCL9 peptides into effective inhibitors to target the interaction between β-catenin and BCL9.

Multifaceted folding-unfolding landscape of the TrpZip2 β-hairpin and the role of external sub-piconewton mechanical tensions

Proteins can experience uneven tensions of the order of tens of piconewtons when exposed to different solvent environment due to the thermal motion of the solvent. It is also true that biomolecules, especially proteins, are subjected to a variety of mechanical tensions generated by several factors, including mechanically assisted translocation and pressure gradients within living systems. Here, we use metadynamics simulations to revisit the folding-unfolding of the TrpZip2 β-hairpin and redefine it from the perspective of an external force of a sub-piconewton magnitude acting on the ends of the hairpin. The chosen forces, while preserving the morphology of the β-hairpin chain when it is pulled, are capable of influencing the conformational behavior of the chain during folding and unfolding. Our investigations confirm that the TrpZip2 β-hairpin exhibits a zipper (zip-out) mechanism for folding-unfolding in both mechanically unbiased and biased (with a 30 pN end force) situations. However, it is important to note that they present marked differences in their folding and unfolding paths, with the mechanically biased system capable of becoming trapped in various intermediate states. Both unbiased and biased scenarios of the hairpin indicate that the hairpin turn is highly stable during the folding-unfolding event and initiates folding. More importantly we confirm that the existing heterogeneity in the TrpZip2 β-hairpin folding-unfolding is a consequence of the wide range of conformations observed, owing to the different trapped intermediates caused by the uneven forces it may experience in solution.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρ_liq and vaporization enthalpies ΔH_vap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κ_T, the isobaric thermal-expansion coefficient α_P, the isobaric heat capacity c_P, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔG_wat, and the free energy of solvation ΔG_che in cyclohexane. For the target properties ρ_liq and ΔH_vap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κ_T, α_P, ϵ, D, and ΔG_che; and less accurate results in terms of c_P and ΔG_wat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Extraction of kinetics from equilibrium distributions of states using the Metropolis Monte Carlo method

The Metropolis Monte Carlo (MMC) method is used to extract reaction kinetics from a given equilibrium distribution of states of a complex system. The approach is illustrated by the folding/unfolding reaction for two proteins: a model β-hairpin and α-helical protein α_{3}D. For the β-hairpin, the free energy surfaces (FESs) and free energy profiles (FEPs) are employed as the equilibrium distributions of states, playing a role of the potentials of mean force to determine the acceptance probabilities of new states in the MMC simulations. Based on the FESs and PESs for a set of temperatures that were simulated with the molecular dynamics (MD) method, the MMC simulations are performed to extract folding/unfolding rates. It has been found that the rate constants and first-passage time (FPT) distributions obtained in the MMC simulations change with temperature in good agreement with those from the MD simulations. For α_{3}D protein, whose equilibrium folding/unfolding was studied with the single-molecule FRET method [Chung et al., J. Phys. Chem. A 115, 3642 (2011)1089-563910.1021/jp1009669], the FRET-efficiency histograms at different denaturant concentrations were used as the equilibrium distributions of protein states. It has been found that the rate constants for folding and unfolding obtained in the MMC simulations change with denaturant concentration in reasonable agreement with the constants that were extracted from the photon trajectories on the basis of theoretical models. The simulated FPT distributions are single-exponential, which is consistent with the assumption of two-state kinetics that was made in the theoretical models. The promising feature of the present approach is that it is based solely on the equilibrium distributions of states, without introducing any additional parameters to perform simulations, which suggests its applicability to other complex systems.

First-passage times in protein folding: exploring the native-like states vs. overcoming the free energy barrier

Using a model β-hairpin protein as a representative example of simple two-state folders whose kinetics are uncomplicated by the presence of on- and off-pathway intermediates, it is studied how the search for the protein's native state among native-like states affects the folding kinetics. It is revealed that the first-passage time (FPT) distributions are essentially single-exponential not only for the times to overcome the free energy barrier between the unfolded and native-like states but also for the times to find the native state among the native-like ones. The FPT distributions of this type are observed through all studied two-state-like regimes of protein folding, varying from a regime close to two-state folding to a regime close to downhill folding. If the protein explores native-like states for a time much longer than the time to overcome the free energy barrier, which is characteristic of high temperatures, the resulting FPT distribution to reach the native state remains close to exponential but the mean FPT (MFPT) is determined not by the height of the free energy barrier but by the time to explore native-like states. In particular, the mean time to overcome the free energy barrier is in reasonable agreement with the Kramers rate formula and generally far shorter than the overall MFPT to reach the native state. The observed increase of the overall MFPT, as a result of longer exploration of native-like states, may lead to an overestimate of the height of the free energy barrier between the unfolded and folded states when it is calculated from the overall MFPT.

Effect of Stapling on the Thermodynamics of mdm2-p53 Binding

Protein-protein interaction (PPI) is one of the key regulatory features driving biomolecular processes and hence is targeted for designing therapeutics against diseases. Small peptides are a new and emerging class of therapeutics owing to their high specificity and low toxicity. For achieving efficient targeting of the PPI, amino acid side chains are often stapled together, resulting in the rigidification of these peptides. Exploring the scope of these peptides demands a comprehensive understanding of their working principle. In this work, two stapled p53 peptides have been considered to delineate their binding mechanism with mdm2 using computational approaches. The addition of stapling agent protects the secondary structure of the peptides even in the case of thermal and chemical denaturation. Although the introduction of a stapling agent increases the hydrophobicity of the peptide, the enthalpic stabilization decreases. This is overcome by the lowering of the entropic penalty, and the overall binding affinity improves. The mechanistic insights into the benefit of peptide stapling can be adopted for further improvement of peptide therapeutics.

Advances in Molecular Dynamics Simulations and Enhanced Sampling Methods for the Study of Protein Systems

Molecular dynamics (MD) simulation is a rigorous theoretical tool that when used efficiently could provide reliable answers to questions pertaining to the structure-function relationship of proteins. Data collated from protein dynamics can be translated into useful statistics that can be exploited to sieve thermodynamics and kinetics crucial for the elucidation of mechanisms responsible for the modulation of biological processes such as protein-ligand binding and protein-protein association. Continuous modernization of simulation tools enables accurate prediction and characterization of the aforementioned mechanisms and these qualities are highly beneficial for the expedition of drug development when effectively applied to structure-based drug design (SBDD). In this review, current all-atom MD simulation methods, with focus on enhanced sampling techniques, utilized to examine protein structure, dynamics, and functions are discussed. This review will pivot around computer calculations of protein-ligand and protein-protein systems with applications to SBDD. In addition, we will also be highlighting limitations faced by current simulation tools as well as the improvements that have been made to ameliorate their efficiency.

Unfavorable regions in the ramachandran plot: Is it really steric hindrance? The interacting quantum atoms perspective

Accurate description of the intrinsic preferences of amino acids is important to consider when developing a biomolecular force field. In this study, we use a modern energy partitioning approach called Interacting Quantum Atoms to inspect the cause of the φ and ψ torsional preferences of three dipeptides (Gly, Val, and Ile). Repeating energy trends at each of the molecular, functional group, and atomic levels are observed across both (1) the three amino acids and (2) the φ/ψ scans in Ramachandran plots. At the molecular level, it is surprisingly electrostatic destabilization that causes the high-energy regions in the Ramachandran plot, not molecular steric hindrance (related to the intra-atomic energy). At the functional group and atomic levels, the importance of key peptide atoms (Oi-1 , Ci , Ni , Ni+1 ) and some sidechain hydrogen atoms (Hγ ) are identified as responsible for the destabilization seen in the energetically disfavored Ramachandran regions. Consistently, the Oi-1 atoms are particularly important for the explanation of dipeptide intrinsic behavior, where electrostatic and steric destabilization unusually complement one another. The findings suggest that, at least for these dipeptides, it is the peptide group atoms that dominate the intrinsic behavior, more so than the sidechain atoms. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

N-terminal diproline and charge group effects on the stabilization of helical conformation in alanine-based short peptides: CD studies with water and methanol as solvent

Protein folding problem remains a formidable challenge as main chain, side chain and solvent interactions remain entangled and have been difficult to resolve. Alanine-based short peptides are promising models to dissect protein folding initiation and propagation structurally as well as energetically. The effect of N-terminal diproline and charged side chains is assessed on the stabilization of helical conformation in alanine-based short peptides using circular dichroism (CD) with water and methanol as solvent. A1 (Ac-Pro-Pro-Ala-Lys-Ala-Lys-Ala-Lys-Ala-NH₂ ) is designed to assess the effect of N-terminal homochiral diproline and lysine side chains to induce helical conformation. A2 (Ac-Pro-Pro-Glu-Glu-Ala-Ala-Lys-Lys-Ala-NH₂ ) and A3 (Ac-dPro-Pro-Glu-Glu-Ala-Ala-Lys-Lys-Ala-NH₂ ) with N-terminal homochiral and heterochiral diproline, respectively, are designed to assess the effect of Glu...Lys (i, i + 4) salt bridge interactions on the stabilization of helical conformation. The CD spectra of A1, A2 and A3 in water manifest different amplitudes of the observed polyproline II (PPII) signals, which indicate different conformational distributions of the polypeptide structure. The strong effect of solvent substitution from water to methanol is observed for the peptides, and CD spectra in methanol evidence A2 and A3 as helical folds. Temperature-dependent CD spectra of A1 and A2 in water depict an isodichroic point reflecting coexistence of two conformations, PPII and β-strand conformation, which is consistent with the previous studies. The results illuminate the effect of N-terminal diproline and charged side chains in dictating the preferences for extended-β, semi-extended PPII and helical conformation in alanine-based short peptides. The results of the present study will enhance our understanding on stabilization of helical conformation in short peptides and hence aid in the design of novel peptides with helical structures. Copyright © 2017 European Peptide Society and John Wiley & Sons, Ltd.

Evaluation of the Coupled Two-Dimensional Main Chain Torsional Potential in Modeling Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) carry out crucial biological functions in essential biological processes of life. Because of the highly dynamic and conformationally heterogeneous nature of the disordered states of IDPs, molecular dynamics simulations are becoming an indispensable tool for the investigation of the conformational ensembles and dynamic properties of IDPs. Nevertheless, there is still no consensus on the most reliable force field in molecular dynamics simulations for IDPs hitherto. In this work, the recently proposed AMBER99SB^2D force field is evaluated in modeling some disordered polypeptides and proteins by checking its ability to reproduce experimental NMR data. The results highlight that when the ildn side-chain corrections are included, AMBER99SB^2D-ildn exhibits reliable results that agree with experiments compared with its predecessors, the AMBER14SB, AMBER99SB, AMBER99SB-ildn, and AMBER99SB^2D force fields, and that decreasing the overall magnitude of protein-protein interactions in favor of protein-water interactions is a key ingredient behind the improvement.

Probing the role of electrostatics of polypeptide main-chain in protein folding by perturbing N-terminal residue stereochemistry: DFT study with oligoalanine models

Energetics of folding (ΔH_E→F, in kcal mol⁻¹) from the extended (E) structure to the folded (F) structure for Ia and Ib critically depend on the geometrical relationship between the backbone peptide units of the polypeptide structure.