Unfolding and folding internal friction of β-hairpins is smaller than that of α-helices

Probing the Energy Landscape of Spectrin R15 and R16 and the Effects of Non-native Interactions

Understanding the details of a protein folding mechanism can be a challenging and complex task. One system with an interesting folding behavior is the α-spectrin domain, where the R15 folds three-orders of magnitude faster than its homologues R16 and R17, despite having similar structures. The molecular origins that explain these folding rate differences remain unclear, but our previous work revealed that a combined effect produced by non-native interactions could be a reasonable cause for these differences. In this study, we explore further the folding process by identifying the molecular paths, metastable states, and the collective motions that lead these unfolded proteins to their native state conformation. Our results uncovered the differences between the folding pathways for the wild-type R15 and R16 and an R16 mutant. The metastable ensembles that speed down the folding were identified using an energy landscape visualization method (ELViM). These ensembles correspond to similar experimentally reported configurations. Our observations indicate that the non-native interactions are also associated with secondary structure misdocking. This computational methodology can be used as a fast, straightforward protocol for shedding light on systems with unclear folding or conformational traps.

Molecular Origin of Driving-Dependent Friction in Fluids

The friction coefficient of fluids may become a function of the velocity at increased external driving. This non-Newtonian behavior is of general theoretical interest and of great practical importance, for example, for the design of lubricants. Although the effect has been observed in large-scale atomistic simulations of bulk liquids, its theoretical formulation and microscopic origin are not well understood. Here, we use dissipation-corrected targeted molecular dynamics, which pulls apart two tagged liquid molecules in the presence of surrounding molecules, and analyze this nonequilibrium process via a generalized Langevin equation. The approach is based on a second-order cumulant expansion of Jarzynski's identity, which is shown to be valid for fluids and therefore allows for an exact computation of the friction profile as well of the underlying memory kernel. We show that velocity-dependent friction in fluids results from an intricate interplay of near-order structural effects and the non-Markovian behavior of the friction memory kernel. For complex fluids such as the model lubricant C₄₀H₈₂, the memory kernel exhibits a stretched-exponential long-time decay, which reflects the multitude of timescales of the system.

How important are fluctuations in the treatment of internal friction in polymers?

The Rouse model with internal friction (RIF), a widely used theoretical framework to interpret the effects of internal friction on conformational transitions in biomolecules, is shown to be an approximate treatment that is based on preaveraging internal friction. By comparison with Brownian dynamics simulations of an exact coarse-grained model that incorporates fluctuations in internal friction, the accuracy of the preaveraged model predictions is examined both at and away from equilibrium. While the two models predict intrachain autocorrelations that approach each other for long enough chain segments, they differ in their predictions for shorter segments. Furthermore, the two models differ qualitatively in their predictions for the chain extension and viscosity in shear flow, which is taken to represent a prototypical out-of-equilibrium condition.

Temperature Dependence of Internal Friction of Peptides

Internal friction is a valuable concept to describe the kinetics of proteins. As is well known, internal friction can be modulated by solvent features (such as viscosity). How can internal friction be affected by environmental temperature? The answer to this question is not evident. In the present work, we approach this problem with simulations on two model peptides. The thermodynamics and relaxation kinetics are characterized through long molecular dynamics simulations, with the viscosity modulated by varying the mass of solvent molecules. Based on the extrapolation to zero viscosity together with scaling of the relaxation time scales, we discover that internal friction is almost invariant at various temperatures. Controlled simulations further support the idea that internal friction is independent of environmental temperature. Comparisons between the two model peptides help us to understand the diverse phenomena in experiments.

Friction-Limited Folding of Disulfide-Reduced Monomeric SOD1

The folding reaction of a stable monomeric variant of Cu/Zn superoxide dismutase (mSOD1), an enzyme responsible for the conversion of superoxide free radicals into hydrogen peroxide and oxygen, is known to be among the slowest folding processes that adhere to two-state behavior. The long lifetime, ∼10 s, of the unfolded state presents ample opportunities for the polypeptide chain to transiently sample nonnative structures before the formation of the productive folding transition state. We recently observed the formation of a nonnative structure in a peptide model of the C-terminus of SOD1, a sequence that might serve as a potential source of internal chain friction-limited folding. To test for friction-limited folding, we performed a comprehensive thermodynamic and kinetic analysis of the folding mechanism of mSOD1 in the presence of the viscogens glycerol and glucose. Using a, to our knowledge, novel analysis of the folding reactions, we found the disulfide-reduced form of the protein that exposes the C-terminal sequence, but not its disulfide-oxidized counterpart that protects it, experiences internal chain friction during folding. The sensitivity of the internal friction to the disulfide bond status suggests that one or both of the cross-linked regions play a critical role in driving the friction-limited folding. We speculate that the molecular mechanisms giving rise to the internal friction of disulfide-reduced mSOD1 might play a role in the amyotrophic lateral sclerosis-linked aggregation of SOD1.

The role of solvent quality and chain stiffness on the end-to-end contact kinetics of semiflexible polymers

Motivated by loop closure during protein folding and DNA packing, we systemically studied the effects of the solvent quality and chain stiffness on the thermodynamics and kinetics of the end-to-end contact formation for semiflexible polymer chains with reactive ends by Langevin dynamics simulations. In thermodynamics, a rich variety of products of the end-to-end contact have been discovered, such as loop, hairpin, toroid, and rodlike bundle, the populations of which are dependent on the solvent quality and chain stiffness. In kinetics, the overall pathways to form the end-to-end contact have been identified. The change of solvent quality and chain stiffness can tune the roughness of energy landscape and modulate the kinetic partitioning of the end-to-end contact formation pathways, leading to differing kinetic behaviors. In good or poor solvents, the first end-to-end contact rate k _c decreases with increasing the strength of bending stiffness k _θ monotonically. In very poor solvents, however, the dependence of the logarithm of the first end-to-end contact rate ln k _c on k _θ exhibits erratic behavior, which stems from more rugged energy landscape due to the polymer chain getting trapped into the intermediate state composed of the rodlike bundles with two ends in separation. For semiflexible chains, with increasing chain length N, the rate k _c increases initially and then decreases: in good solvents, the rate k _c exhibits a power-law relationship to chain length N with an exponent of ∼-1.50 in the region of long chains, which is in good agreement with the value derived from the experiment in the asymptotic limit of large N; and in poor solvents, the rate k _c exhibits a significantly stronger chain length dependence than those observed in good solvents in the region of long chains due to frustration to form the end-to-end contact along a specific path, especially the scaling exponent between the rate k _c and chain length N is ∼-3.62 for the case of polymer chains with k _θ = 4 at the solvent quality ε _ij = 1, in accord with the value obtained from the experiments.

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.

Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations

Internal friction is an important contribution to protein dynamics at all stages along the folding reaction. Even in unfolded and intrinsically disordered proteins, internal friction has a large influence, as demonstrated with several experimental techniques and in simulations. However, these methods probe different facets of internal friction and have been applied to disparate molecular systems, raising questions regarding the compatibility of the results. To obtain an integrated view, we apply here the combination of two complementary experimental techniques, simulations, and theory to the same system: unfolded protein L. We use single-molecule Förster resonance energy transfer (FRET) to measure the global reconfiguration dynamics of the chain, and photoinduced electron transfer (PET), a contact-based method, to quantify the rate of loop formation between two residues. This combination enables us to probe unfolded-state dynamics on different length scales, corresponding to different parts of the intramolecular distance distribution. Both FRET and PET measurements show that internal friction dominates unfolded-state dynamics at low denaturant concentration, and the results are in remarkable agreement with recent large-scale molecular dynamics simulations using a new water model. The simulations indicate that intrachain interactions and dihedral angle rotation correlate with the presence of internal friction, and theoretical models of polymer dynamics provide a framework for interrelating the contribution of internal friction observed in the two types of experiments and in the simulations. The combined results thus provide a coherent and quantitative picture of internal friction in unfolded proteins that could not be attained from the individual techniques.

Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations

Internal friction is an important contribution to protein dynamics at all stages along the folding reaction. Even in unfolded and intrinsically disordered proteins, internal friction has a large influence, as demonstrated with several experimental techniques and in simulations. However, these methods probe different facets of internal friction and have been applied to disparate molecular systems, raising questions regarding the compatibility of the results. To obtain an integrated view, we apply here the combination of two complementary experimental techniques, simulations, and theory to the same system: unfolded protein L. We use single-molecule Förster resonance energy transfer (FRET) to measure the global reconfiguration dynamics of the chain, and photoinduced electron transfer (PET), a contact-based method, to quantify the rate of loop formation between two residues. This combination enables us to probe unfolded-state dynamics on different length scales, corresponding to different parts of the intramolecular distance distribution. Both FRET and PET measurements show that internal friction dominates unfolded-state dynamics at low denaturant concentration, and the results are in remarkable agreement with recent large-scale molecular dynamics simulations using a new water model. The simulations indicate that intrachain interactions and dihedral angle rotation correlate with the presence of internal friction, and theoretical models of polymer dynamics provide a framework for interrelating the contribution of internal friction observed in the two types of experiments and in the simulations. The combined results thus provide a coherent and quantitative picture of internal friction in unfolded proteins that could not be attained from the individual techniques.

Modulation of Folding Internal Friction by Local and Global Barrier Heights

Recent experiments have revealed an unexpected deviation from a first power dependence of protein relaxation times on solvent viscosity, an effect that has been attributed to "internal friction". One clear source of internal friction in protein dynamics is the isomerization of dihedral angles. A key outstanding question is whether the global folding barrier height influences the measured internal friction, based on the observation that the folding rates of fast-folding proteins, with smaller folding free energy barriers, tend to exhibit larger internal friction. Here, by studying two alanine-based peptides, we find that systematic variation of global folding barrier heights has little effect on the internal friction for folding rates. On the other hand, increasing local torsion angle barriers leads to increased internal friction, which is consistent with solvent memory effects being the origin of the viscosity dependence. Thus, it appears that local torsion transitions determine the viscosity dependence of the diffusion coefficient on the global coordinate and, in turn, internal friction effects on the folding rate.

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.

Using Kinetic Network Models To Probe Non-Native Salt-Bridge Effects on α-Helix Folding

Salt-bridge interactions play an important role in stabilizing many protein structures, and have been shown to be designable features for protein design. In this work, we study the effects of non-native salt bridges on the folding of a soluble alanine-based peptide (Fs peptide) using extensive all-atom molecular dynamics simulations performed on the Folding@home distributed computing platform. Using Markov State Models, we show how non-native salt-bridges affect the folding kinetics of Fs peptide by perturbing specific conformational states. Furthermore, we present methods for the automatic detection and analysis of such states. These results provide insight into helix folding mechanisms and useful information to guide simulation-based computational protein design.