Folding thermodynamics ofβ-hairpins studied by replica-exchange molecular dynamics simulations

A study of ab initio folding of chignolins using replica-exchange molecular dynamics simulations

More and more studies have confirmed the importance of polarization effects in hydrogen bonding interactions in protein folding simulations. In this paper, a recently developed charge update scheme termed polarized structure-specific backbone charge (PSBC) model was applied to the folding of 10-residue chignolin. A comparison between simulations performed using PSBC and a nonpolarizable (AMBER99SB) force field demonstrably showed the importance of the electrostatic polarization effect in the folding of the short β-hairpin peptide by a series of analyses such as DSSP, free-energy landscape, hydrogen bond occupancy, and melting curve. The PSBC model was further validated by folding two other chignolin variants.

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.

Polyelectrolyte Influence on Beta-Hairpin Peptide Stability: A Simulation Study

Assemblies of proteins and charged macromolecules (polyelectrolytes) find important applications as pharmaceutical formulations, biocatalysts, and cell-contacting substrates. A key question is how the polymer component influences the structure and function of the protein. The present paper addresses the influence of charged polymers on the thermal stability of two model beta-hairpin-forming peptides through an all-atom, replica exchange molecular dynamics simulation. The (negatively charged) peptides consist of the terminal 16 amino acids of the B1 domain of Protein G (GB1) and a variant with three of the GB1 residues substituted with tryptophan (Tryptophan Zipper 4, or TZ4). A (cationic) lysine polymer is seen to thermally stabilize TZ4 and destabilize GB1, while a (also cationic) chitosan polymer slightly stabilizes GB1 but has essentially no effect on TZ4. Free energy profiles reveal folded and unfolded conformations to be separated by kinetic barriers generally acting in the direction of the thermodynamically favored state. Through application of an Ising-like statistical mechanical model, a mechanism is proposed based on competition between (indirect) entropic stabilization of folded versus unfolded states and (direct) competition for hydrogen-bonding and hydrophobic interactions. These findings have important implications to the design of polyelectrolyte-based materials for biomedical and biotechnological applications.

Granger Causality Analysis of Chignolin Folding

Constantly advancing computer simulations of biomolecules provide huge amounts of data that are difficult to interpret. In particular, obtaining insights into functional aspects of macromolecular dynamics, often related to cascades of transient events, calls for methodologies that depart from the well-grounded framework of equilibrium statistical physics. One of the approaches toward the analysis of complex temporal data which has found applications in the fields of neuroscience and econometrics is Granger causality analysis. It allows determining which components of multidimensional time series are most influential for the evolution of the entire system, thus providing insights into causal relations within the dynamic structure of interest. In this work, we apply Granger analysis to a long molecular dynamics trajectory depicting repetitive folding and unfolding of a mini β-hairpin protein, CLN025. We find objective, quantitative evidence indicating that rearrangements within the hairpin turn region are determinant for protein folding and unfolding. On the contrary, interactions between hairpin arms score low on the causality scale. Taken together, these findings clearly favor the concept of zipperlike folding, which is one of two postulated β-hairpin folding mechanisms. More importantly, the results demonstrate the possibility of a conclusive application of Granger causality analysis to a biomolecular system.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

The relative stability of trpzip1 and its mutants determined by computation and experiment

The single-point mutations of tprzip1 are indicated at left, and their relative energetics are compared at right.

Distinct and Nonadditive Effects of Urea and Guanidinium Chloride on Peptide Solvation

Using enhanced-sampling replica exchange fully atomistic molecular dynamics simulations, we show that, individually, urea and guanidinium chloride (GdmCl) denature the Trpcage protein, but remarkably, the helical segment ¹NLYIQWL⁷ of the protein is stabilized in mixed denaturant solutions. GdmCl induces protein denaturation via a combination of direct and indirect effects involving dehydration of the protein and destabilization of stabilizing salt bridges. In contrast, urea denatures the protein through favorable protein-urea preferential interactions, with peptide-specific indirect effects of urea on the water structure around the protein. In the case of the helical segment of Trpcage, urea "oversolvates" the peptide backbone by reorganizing water molecules from the peptide side chains to the peptide backbone. An intricate nonadditive thermodynamic balance between GdmCl-induced dehydration of the peptide and the urea-induced changes in solvation structure triggers partial counteraction to urea denaturation and stabilization of the helix.

Computational investigation of retro-isomer equilibrium structures: Intrinsically disordered, foldable, and cyclic peptides

We use all-atom modeling and advanced-sampling molecular dynamics simulations to investigate quantitatively the effect of peptide bond directionality on the equilibrium structures of four linear (two foldable, two disordered) and two cyclic peptides. We find that the retro forms of cyclic and foldable linear peptides adopt distinctively different conformations compared to their parents. While the retro form of a linear intrinsically disordered peptide with transient secondary structure fails to reproduce a secondary structure content similar to that of its parent, the retro form of a shorter disordered linear peptide shows only minor differences compared to its parent.

Effect of heterochiral inversions on the structure of a β-hairpin peptide

We study computationally a family of β-hairpin peptides with systematically introduced chiral inversions, in explicit water, and we investigate the extent to which the backbone structure is able to fold in the presence of heterochiral perturbations. In contrast to the recently investigated case of a helical peptide, we do not find a monotonic change in secondary structure content as a function of the number of L- to D-inversions. The effects of L- to D-inversions are instead found to be highly position-specific. Additionally, in contrast to the helical peptide, some inversions increase the stability of the folded peptide: in such cases, we compute an increase in β-sheet content in the aqueous solution equilibrium ensemble. However, the tertiary structures of the stable (folded) configurations for peptides for which inversions cause an increase in β-sheet content show differences from one another, as well as from the native fold of the nonchirally perturbed β-hairpin. Our results suggest that although some chiral perturbations can increase folding stability, chirally perturbed proteins may still underperform functionally, given the relationship between structure and function.

Atomistic Peptide Folding Simulations Reveal Interplay of Entropy and Long-Range Interactions in Folding Cooperativity

Understanding how proteins fold has remained a problem of great interest in biophysical research. Atomistic computer simulations using physics-based force fields can provide important insights on the interplay of different interactions and energetics and their roles in governing the folding thermodynamics and mechanism. In particular, generalized Born (GB)-based implicit solvent force fields can be optimized to provide an appropriate balance between solvation and intramolecular interactions and successfully recapitulate experimental conformational equilibria for a set of helical and β-hairpin peptides. Here, we further demonstrate that key thermodynamic properties and their temperature dependence obtained from replica exchange molecular dynamics simulations of these peptides are in quantitative agreement with experimental results. Useful lessons can be learned on how the interplay of entropy and sequentially long-range interactions governs the mechanism and cooperativity of folding. These results highlight the great potential of high-quality implicit solvent force fields for studying protein folding and large-scale conformational transitions.

Computational Investigation of the Effect of Backbone Chiral Inversions on Polypeptide Structure

Studying a set of helix-folding polyalanine peptides with systematically inserted chiral inversions in explicit water, we investigate quantitatively the effect of chiral perturbations on the structural ensembles of the peptides, thereby assessing the extent to which the backbone structure is able to fold in the presence of systematic heterochiral perturbations. Starting from the homochiral l-Ala₂₀ peptide, we invert the backbone chiralities of Ala residues one by one along a specific perturbation pathway, until reaching the homochiral d-Ala₂₀ peptide. Analysis of the helical contents of the simulated structural ensembles of the peptides shows that even a single inversion in the middle of the peptide completely breaks the helical structure in its vicinity and drastically reduces the helical content of the peptide. Further inversions in the middle of the peptide monotonically decrease the original helical content, that is, the right-handed helical content for l-Ala, and increase the helical content of the opposite chirality. Further analysis of the peptide ensembles using several size- and shape-related order parameters also indicate the drastic global changes in the peptide structure due to the local effects caused by the chiral inversions, such as formation of a reverse turn. However, the degree of the structural changes introduced by opposite chirality substitutions depends on the position of the inversion.

An adaptive bias - hybrid MD/kMC algorithm for protein folding and aggregation

In this paper, we present a novel hybrid Molecular Dynamics/kinetic Monte Carlo (MD/kMC) algorithm and apply it to protein folding and aggregation in explicit solvent. The new algorithm uses a dynamical definition of biases throughout the MD component of the simulation, normalized in relation to the unbiased forces. The algorithm guarantees sampling of the underlying ensemble in dependency of one average linear coupling factor 〈α〉_τ. We test the validity of the kinetics in simulations of dialanine and compare dihedral transition kinetics with long-time MD-simulations. We find that for low 〈α〉_τ values, kinetics are in good quantitative agreement. In folding simulations of TrpCage and TrpZip4 in explicit solvent, we also find good quantitative agreement with experimental results and prior MD/kMC simulations. Finally, we apply our algorithm to study growth of the Alzheimer Amyloid Aβ 16-22 fibril by monomer addition. We observe two possible binding modes, one at the extremity of the fibril (elongation) and one on the surface of the fibril (lateral growth), on timescales ranging from ns to 8 μs.

The sensitivity of folding free energy landscapes of trpzips to mutations in the hydrophobic core

The sensitivity of the stability of folded states and free energy landscapes to the differences in the hydrophobic content of the core residues has been studied for the set of 16-residue trpzips, namely, Trpzip4, Trpzip5 and Trpzip6.

Determining the Energetics of Small β-Sheet Peptides using Adaptive Steered Molecular Dynamics

Mechanically driven unfolding is a useful computational tool for extracting the energetics and stretching pathway of peptides. In this work, two representative β-hairpin peptides, chignolin (PDB: 1UAO ) and trpzip1 (PDB: 1LE0 ), were investigated using an adaptive variant of the original steered molecular dynamics method called adaptive steered molecular dynamics (ASMD). The ASMD method makes it possible to perform energetic calculations on increasingly complex biological systems. Although the two peptides are similar in length and have similar secondary structures, their unfolding energetics are quite different. The hydrogen bonding profile and specific residue pair interaction energies provide insight into the differing stabilities of these peptides and reveal which of the pairs provides the most significant stabilization.

Effect of O-Linked Glycosylation on the Equilibrium Structural Ensemble of Intrinsically Disordered Polypeptides

Glycosylation is one of the most common post-translational modifications (PTMs), which provides a large proteome diversity. Previous work on glycosylation of globular proteins has revealed remarkable effects of glycosylation on protein function, altering the folding stability and structure and/or altering the protein surface which affects their binding characteristics. Intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs) of large proteins are also frequently glycosylated, yet how glycosylation affects their function remains to be elucidated. An important open question is, does glycosylation affect IDP structure or binding characteristics or both? In this work, we particularly address the structural effects of O-linked glycosylation by investigating glycosylated and unglycosylated forms of two different IDPs, tau174-183 and human islet amyloid polypeptide (hIAPP), by all-atom explicit solvent simulations. We simulate these IDPs in aqueous solution for O-linked glycosylated and unglycosylated forms by employing two modern all-atom force fields for which glycan parameters are also available. We find that O-linked glycosylation only has a modest effect on equilibrium structural ensembles of IDPs, for the cases studied here, which suggests that the functional role of glycosylation may be primarily exerted by modulation of the protein binding characteristics rather than structure.