Simulations of the pressure and temperature unfolding of an alpha-helical peptide

PQBP5/NOL10 maintains and anchors the nucleolus under physiological and osmotic stress conditions

Polyglutamine binding protein 5 (PQBP5), also called nucleolar protein 10 (NOL10), binds to polyglutamine tract sequences and is expressed in the nucleolus. Using dynamic imaging of high-speed atomic force microscopy, we show that PQBP5/NOL10 is an intrinsically disordered protein. Super-resolution microscopy and correlative light and electron microscopy method show that PQBP5/NOL10 makes up the skeletal structure of the nucleolus, constituting the granule meshwork in the granular component area, which is distinct from other nucleolar substructures, such as the fibrillar center and dense fibrillar component. In contrast to other nucleolar proteins, which disperse to the nucleoplasm under osmotic stress conditions, PQBP5/NOL10 remains in the nucleolus and functions as an anchor for reassembly of other nucleolar proteins. Droplet and thermal shift assays show that the biophysical features of PQBP5/NOL10 remain stable under stress conditions, explaining the spatial role of this protein. PQBP5/NOL10 can be functionally depleted by sequestration with polyglutamine disease proteins in vitro and in vivo, leading to the pathological deformity or disappearance of the nucleolus. Taken together, these findings indicate that PQBP5/NOL10 is an essential protein needed to maintain the structure of the nucleolus.

Volumetric Properties of the Transition State Ensemble for Protein Folding

Understanding how high hydrostatic pressure affects biomacromolecular interaction is important for deciphering the molecular mechanisms by which organisms adapt to live at the bottom of the ocean. The relative effect of hydrostatic pressure on the rates of folding/unfolding reactions is defined by the volumetric properties of the transition state ensemble relative to the folded and unfolded states. All-atom structure-based molecular dynamics simulations combined with quantitative computational protocol to compute volumes from three-dimensional coordinates allow volumetric mapping of protein folding landscape. This, is turn, provides qualitative understanding of the effects of hydrostatic pressure on energy landscape of proteins. The computational results for six different proteins are directly benchmark against experimental data and show an excellent agreement. Both experiments and computation show that the transition-state ensemble volume appears to be in-between the folded and unfolded state volumes, and thus the hydrostatic pressure accelerates protein unfolding.

Raman spectroscopic insight into osteoarthritic cartilage regeneration by mRNA therapeutics encoding cartilage-anabolic transcription factor Runx1

While joint arthroplasty remains nowadays the most popular option available to repair chronically degenerated osteoarthritic joints, possibilities are recently emerging for regeneration of damaged cartilage rather than its replacement with artificial biomaterials. This latter strategy could allow avoiding the quite intrusive surgical procedures associated with total joint replacement. Building upon this notion, we first apply Raman spectroscopy to characterize diseased cartilage in a mice model of instability-induced knee osteoarthritis (OA) upon medial collateral ligament (MCL) and medial meniscus (MM) transections. Then, we examine the same OA model after cartilage regeneration by means of messenger RNA (mRNA) delivery of a cartilage-anabolic runt-related transcription factor 1 (RUNX1). Raman spectroscopy is shown to substantiate at the molecular scale the therapeutic effect of the Runx1 mRNA cartilage regeneration approach. This study demonstrates how the Raman spectroscopic method could support and accelerate the development of new therapies for cartilage diseases.

Quantum chemistry for molecules at extreme pressure on graphical processing units: Implementation of extreme-pressure polarizable continuum model

Pressure plays essential roles in chemistry by altering structures and controlling chemical reactions. The extreme-pressure polarizable continuum model (XP-PCM) is an emerging method with an efficient quantum mechanical description of small- and medium-sized molecules at high pressure (on the order of GPa). However, its application to large molecular systems was previously hampered by a CPU computation bottleneck: the Pauli repulsion potential unique to XP-PCM requires the evaluation of a large number of electric field integrals, resulting in significant computational overhead compared to the gas-phase or standard-pressure polarizable continuum model calculations. Here, we exploit advances in graphical processing units (GPUs) to accelerate the XP-PCM-integral evaluations. This enables high-pressure quantum chemistry simulation of proteins that used to be computationally intractable. We benchmarked the performance using 18 small proteins in aqueous solutions. Using a single GPU, our method evaluates the XP-PCM free energy of a protein with over 500 atoms and 4000 basis functions within half an hour. The time taken by the XP-PCM-integral evaluation is typically 1% of the time taken for a gas-phase density functional theory (DFT) on the same system. The overall XP-PCM calculations require less computational effort than that for their gas-phase counterpart due to the improved convergence of self-consistent field iterations. Therefore, the description of the high-pressure effects with our GPU-accelerated XP-PCM is feasible for any molecule tractable for gas-phase DFT calculation. We have also validated the accuracy of our method on small molecules whose properties under high pressure are known from experiments or previous theoretical studies.

High-pressure small-angle X-ray scattering cell for biological solutions and soft materials

Pressure is a fundamental thermodynamic parameter controlling the behavior of biological macromolecules. Pressure affects protein denaturation, kinetic parameters of enzymes, ligand binding, membrane permeability, ion trans-duction, expression of genetic information, viral infectivity, protein association and aggregation, and chemical processes. In many cases pressure alters the molecular shape. Small-angle X-ray scattering (SAXS) is a primary method to determine the shape and size of macromolecules. However, relatively few SAXS cells described in the literature are suitable for use at high pressures and with biological materials. Described here is a novel high-pressure SAXS sample cell that is suitable for general facility use by prioritization of ease of sample loading, temperature control, mechanical stability and X-ray background minimization. Cell operation at 14 keV is described, providing a q range of 0.01 < q < 0.7 Å-1, pressures of 0-400 MPa and an achievable temperature range of 0-80°C. The high-pressure SAXS cell has recently been commissioned on the ID7A beamline at the Cornell High Energy Synchrotron Source and is available to users on a peer-reviewed proposal basis.

Molecular dynamics simulation of proteins under high pressure: Structure, function and thermodynamics

BACKGROUND

Molecular dynamics (MD) simulation is well-recognized as a powerful tool to investigate protein structure, function, and thermodynamics. MD simulation is also used to investigate high pressure effects on proteins. For conducting better MD simulation under high pressure, the main issues to be addressed are: (i) protein force fields and water models were originally developed to reproduce experimental properties obtained at ambient pressure; and (ii) the timescale to observe the pressure effect is often much longer than that of conventional MD simulations.

SCOPE OF REVIEW

First, we describe recent developments in MD simulation methodologies for studying the high-pressure structure and dynamics of protein molecules. These developments include force fields for proteins and water molecules, and enhanced simulation techniques. Then, we summarize recent studies of MD simulations of proteins in water under high pressure.

MAJOR CONCLUSIONS

Recent MD simulations of proteins in solution under pressure have reproduced various phenomena identified by experiments using high pressure, such as hydration, water penetration, conformational change, helix stabilization, and molecular stiffening.

GENERAL SIGNIFICANCE

MD simulations demonstrate differences in the properties of proteins and water molecules between ambient and high-pressure conditions. Comparing the results obtained by MD calculations with those obtained experimentally could reveal the mechanism by which biological molecular machines work well in collaboration with water molecules.

Theoretical analysis on thermodynamic stability of chignolin

Understanding the dominant factor in thermodynamic stability of proteins remains an open challenge. Kauzmann’s hydrophobic interaction hypothesis, which considers hydrophobic interactions between nonpolar groups as the dominant factor, has been widely accepted for about sixty years and attracted many scientists. The hypothesis, however, has not been verified or disproved because it is difficult, both theoretically and experimentally, to quantify the solvent effects on the free energy change in protein folding. Here, we developed a computational method for extracting the dominant factor behind thermodynamic stability of proteins and applied it to a small, designed protein, chignolin. The resulting free energy profile quantitatively agreed with the molecular dynamics simulations. Decomposition of the free energy profile indicated that intramolecular interactions predominantly stabilized collapsed conformations, whereas solvent-induced interactions, including hydrophobic ones, destabilized them. These results obtained for chignolin were consistent with the site-directed mutagenesis and calorimetry experiments for globular proteins with hydrophobic interior cores.

Temperature-induced collapse of a disordered peptide observed by three sampling methods in molecular dynamics simulations

The conformational ensembles of a disordered peptide, polyglutamine Q15, over a wide temperature range were sampled using multiple replicates of conventional molecular dynamics (cMD) simulations as well as two enhanced sampling methods, temperature replica exchange (TREMD) and replica exchange with solute tempering (REST). The radius of gyration, asphericity, secondary structure, and hydrogen bonding patterns were used for the comparison of the sampling methods. Overall, the three sampling methods generated similar conformational ensembles, with progressive collapse at higher temperatures. Although accumulating the longest simulation time (90 μs), cMD at room temperature missed a small subspace that was sampled by both TREMD and REST. This subspace was high in α-helical content and separated from the main conformational space by an energy barrier. REST used less simulation time than TREMD (36 μs versus 42 μs), and this gap is expected to widen significantly for larger disordered proteins. We conclude that REST is the method of choice for conformational sampling of intrinsically disordered proteins.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Resolution Exchange Simulation with Incremental Coarsening

We previously developed an algorithm, called "resolution exchange", which improves canonical sampling of atomic resolution models by swapping conformations between high- and low-resolution simulations. Here, we demonstrate a generally applicable incremental coarsening procedure and apply the algorithm to a larger peptide, met-enkephalin. In addition, we demonstrate a combination of resolution and temperature exchange, in which the coarser simulations are also at elevated temperatures. Both simulations are implemented in a "top-down" mode, to allow efficient allocation of CPU time among the different replicas.

How Efficient Is Replica Exchange Molecular Dynamics? An Analytic Approach

Replica exchange molecular dynamics (REMD) has become a standard technique for accelerating relaxation in biosimulations. Despite its widespread use, questions remain about its efficiency compared with conventional, constant temperature molecular dynamics (MD). An analytic approach is taken to describe the relative efficiency of REMD with respect to MD. This is applied to several simple two-state models and to several real proteins-protein L and the B domain of protein A-to predict the relative efficiency of REMD with respect to MD in actual applications. In agreement with others, we find the following: as long as there is a positive activation energy for folding, REMD is more efficient than MD; the effectiveness of REMD is strongly dependent on the activation enthalpy; and the efficiency of REMD for actual proteins is a strong function of the maximum temperature. Choosing the maximum temperature too high can result in REMD becoming significantly less efficient than conventional MD. A good rule of thumb appears to be to choose the maximum temperature of the REMD simulation slightly above the temperature at which the enthalpy for folding vanishes. Additionally, we find that the number of replicas in REMD, while important for simulations shorter than one or two relaxation times, has a minimal effect on the asymptotic efficiency of the method.

Contribution of Water to Pressure and Cold Denaturation of Proteins

The mechanisms of cold and pressure denaturation of proteins are matter of debate and are commonly understood as due to water-mediated interactions. Here, we study several cases of proteins, with or without a unique native state, with or without hydrophilic residues, by means of a coarse-grain protein model in explicit solvent. We show, using Monte Carlo simulations, that taking into account how water at the protein interface changes its hydrogen bond properties and its density fluctuations is enough to predict protein stability regions with elliptic shapes in the temperature-pressure plane, consistent with previous theories. Our results clearly identify the different mechanisms with which water participates to denaturation and open the perspective to develop advanced computational design tools for protein engineering.

Role of solvation in pressure-induced helix stabilization

In contrast to the well-known destabilization of globular proteins by high pressure, recent work has shown that pressure stabilizes the formation of isolated α-helices. However, all simulations to date have obtained a qualitatively opposite result within the experimental pressure range. We show that using a protein force field (Amber03w) parametrized in conjunction with an accurate water model (TIP4P/2005) recovers the correct pressure-dependence and an overall stability diagram for helix formation similar to that from experiment; on the other hand, we confirm that using TIP3P water results in a very weak pressure destabilization of helices. By carefully analyzing the contributing factors, we show that this is not merely a consequence of different peptide conformations sampled using TIP3P. Rather, there is a critical role for the solvent itself in determining the dependence of total system volume (peptide and solvent) on helix content. Helical peptide structures exclude a smaller volume to water, relative to non-helical structures with both the water models, but the total system volume for helical conformations is higher than non-helical conformations with TIP3P water at low to intermediate pressures, in contrast to TIP4P/2005 water. Our results further emphasize the importance of using an accurate water model to study protein folding under conditions away from standard temperature and pressure.

Transition state and ground state properties of the helix-coil transition in peptides deduced from high-pressure studies

Volume changes associated with protein folding reactions contain valuable information about the folding mechanism and the nature of the transition state. However, meaningful interpretation of such data requires that overall volume changes be deconvoluted into individual contributions from different structural components. Here we focus on one type of structural element, the α-helix, and measure triplet-triplet energy transfer at high pressure to determine volume changes associated with the helix-coil transition. Our results reveal that the volume of a 21-amino-acid alanine-based peptide shrinks upon helix formation. Thus, helices, in contrast with native proteins, become more stable with increasing pressure, explaining the frequently observed helical structures in pressure-unfolded proteins. Both helix folding and unfolding become slower with increasing pressure. The volume changes associated with the addition of a single helical residue to a preexisting helix were obtained by comparing the experimental results with Monte Carlo simulations based on a kinetic linear Ising model. The reaction volume for adding a single residue to a helix is small and negative (-0.23 cm(3) per mol = -0.38 Å(3) per molecule) implying that intrahelical hydrogen bonds have a smaller volume than peptide-water hydrogen bonds. In contrast, the transition state has a larger volume than either the helical or the coil state, with activation volumes of 2.2 cm(3)/mol (3.7 Å(3) per molecule) for adding and 2.4 cm(3)/mol (4.0 Å(3) per molecule) for removing one residue. Thus, addition or removal of a helical residue proceeds through a transitory high-energy state with a large volume, possibly due to the presence of unsatisfied hydrogen bonds, although steric effects may also contribute.

Pressure-Induced Helical Structure of a Peptide Studied by Simulated Tempering Molecular Dynamics Simulations

It is known experimentally that an AK16 peptide forms more α-helix structures with increasing pressure while proteins unfold in general. In order to understand this abnormality, molecular dynamics (MD) simulations with the simulated tempering method for the isobaric-isothermal ensemble were performed in a wide pressure range from 1.0 × 10(-4) GPa to 1.4 GPa. From the results of the simulations, it is found that the fraction of the folded state decreases once and increases after that with increasing pressure. The partial molar volume change from the folded state to unfolded state increases monotonically from a negative value to a positive value with pressure. The behavior under high pressure conditions is consistent with the experimental results. The radius of gyration of highly helical structures decreases with increasing pressure, which indicates that the helix structure shrinks with pressure. This is the reason why the fraction of the folded state increases as pressure increases.

Misplaced helix slows down ultrafast pressure-jump protein folding

Using a newly developed microsecond pressure-jump apparatus, we monitor the refolding kinetics of the helix-stabilized five-helix bundle protein λ*YA, the Y22W/Q33Y/G46,48A mutant of λ-repressor fragment 6-85, from 3 μs to 5 ms after a 1,200-bar P-drop. In addition to a microsecond phase, we observe a slower 1.4-ms phase during refolding to the native state. Unlike temperature denaturation, pressure denaturation produces a highly reversible helix-coil-rich state. This difference highlights the importance of the denatured initial condition in folding experiments and leads us to assign a compact nonnative helical trap as the reason for slower P-jump-induced refolding. To complement the experiments, we performed over 50 μs of all-atom molecular dynamics P-drop refolding simulations with four different force fields. Two of the force fields yield compact nonnative states with misplaced α-helix content within a few microseconds of the P-drop. Our overall conclusion from experiment and simulation is that the pressure-denatured state of λ*YA contains mainly residual helix and little β-sheet; following a fast P-drop, at least some λ*YA forms misplaced helical structure within microseconds. We hypothesize that nonnative helix at helix-turn interfaces traps the protein in compact nonnative conformations. These traps delay the folding of at least some of the population for 1.4 ms en route to the native state. Based on molecular dynamics, we predict specific mutations at the helix-turn interfaces that should speed up refolding from the pressure-denatured state, if this hypothesis is correct.

Cosolvent effects on protein stability

Proteins are marginally stable, and the folding/unfolding equilibrium of proteins in aqueous solution can easily be altered by the addition of small organic molecules known as cosolvents. Cosolvents that shift the equilibrium toward the unfolded ensemble are termed denaturants, whereas those that favor the folded ensemble are known as protecting osmolytes. Urea is a widely used denaturant in protein folding studies, and the molecular mechanism of its action has been vigorously debated in the literature. Here we review recent experimental as well as computational studies that show an emerging consensus in this problem. Urea has been shown to denature proteins through a direct mechanism, by interacting favorably with the peptide backbone as well as the amino acid side chains. In contrast, the molecular mechanism by which the naturally occurring protecting osmolyte trimethylamine N-oxide (TMAO) stabilizes proteins is not clear. Recent studies have established the strong interaction of TMAO with water. Detailed molecular simulations, when used with force fields that incorporate these interactions, can provide insight into this problem. We present the development of a model for TMAO that is consistent with experimental observations and that provides physical insight into the role of cosolvent-cosolvent interaction in determining its preferential interaction with proteins.

High-pressure NMR reveals close similarity between cold and alcohol protein denaturation in ubiquitin

Proteins denature not only at high, but also at low temperature as well as high pressure. These denatured states are not easily accessible for experiment, because usually heat denaturation causes aggregation, whereas cold or pressure denaturation occurs at temperatures well below the freezing point of water or pressures above 5 kbar, respectively. Here we have obtained atomic details of the pressure-assisted, cold-denatured state of ubiquitin at 2,500 bar and 258 K by high-resolution NMR techniques. Under these conditions, a folded, native-like and a disordered state exist in slow exchange. Secondary chemical shifts show that the disordered state has structural propensities for a native-like N-terminal β-hairpin and α-helix and a nonnative C-terminal α-helix. These propensities are very similar to the previously described alcohol-denatured (A-)state. Similar to the A-state, (15)N relaxation data indicate that the secondary structure elements move as independent segments. The close similarity of pressure-assisted, cold-denatured, and alcohol-denatured states with native and nonnative secondary elements supports a hierarchical mechanism of folding and supports the notion that similar to alcohol, pressure and cold reduce the hydrophobic effect. Indeed, at nondenaturing concentrations of methanol, a complete transition from the native to the A-state can be achieved at ambient temperature by varying the pressure from 1 to 2,500 bar. The methanol-assisted pressure transition is completely reversible and can also be induced in protein G. This method should allow highly detailed studies of protein-folding transitions in a continuous and reversible manner.

Enhanced sampling algorithms

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.

Role of hydrophobic hydration in protein stability: a 3D water-explicit protein model exhibiting cold and heat denaturation

We investigate the microscopic mechanism of cold and heat denaturation using a 3D lattice model of a hydrated protein in which water is represented explicitly. The water model, which incorporates directional bonding and tetrahedral geometry, captures many aspects of water thermodynamics and properly describes hydrophobic hydration around apolar solutes because the hydrogen bonding rules in the model were gleaned from off-lattice atomistic simulations of water around representative protein structures. By incorporating local chain stiffness in the protein model, a homopolymer can fold into a β-hairpin. It is shown that the homopolymer can be folded by either attractive interactions between the monomers or as a direct consequence of the entropic cost of forming interfacial hydrogen bonds in the solvent. However, cold denaturation is not observed if the collapse transition is induced by intramolecular attractions. We further find that it is the changes in hydrophobic hydration with decreasing temperature that drive cold unfolding and that the overall process is enthalpically driven, whereas heat denaturation is entropically driven.

Temperature dependence of water interactions with the amide carbonyls of α-helices

Hydration is a key determinant of the folding, dynamics, and function of proteins. In this study, temperature-dependent Fourier transform infrared (FTIR) spectroscopy combined with singular value decomposition (SVD) and global fitting were used to investigate both the interaction of water with α-helical proteins and the cooperative thermal unfolding of these proteins. This methodology has been applied to an isolated α-helix (Fs peptide) and to globular α-helical proteins including the helical subdomain and full-length villin headpiece (HP36 and HP67). The results suggest a unique IR signature for the interaction of water with the helical amide carbonyl groups of the peptide backbone. The IR spectra indicate a weakening of the net hydrogen bond strength of water to the backbone carbonyls with increasing temperature. This weakening of the backbone solvation occurs as a discrete transition near the maximum of the temperature-dependent hydrophobic effect, not a continuous change with increasing temperature. Possible molecular origins of this effect are discussed with respect to previous molecular dynamics simulations of the temperature-dependent solvation of the helix backbone.

Atomistic molecular simulations of protein folding

Theory and experiment have provided answers to many of the fundamental questions of protein folding; a remaining challenge is an accurate, high-resolution picture of folding mechanism. Atomistic molecular simulations with explicit solvent are the most promising method for providing this information, by accounting more directly for the physical interactions that stabilize proteins. Although simulations of folding with such force fields are extremely challenging, they have become feasible as a result of recent advances in computational power, accuracy of the energy functions or 'force fields', and methods for improving sampling of folding events. I review the recent progress in these areas, and highlight future challenges and questions that we may hope to address with these methods. I also attempt to place atomistic models into the context of the energy landscape view of protein folding, and coarse-grained simulations.

MOLECULAR DYNAMICS SIMULATION OF FOLDING OF A SHORT HELICAL TOXIN PEPTIDE

A molecular dynamics simulation of the folding of a short helical toxin peptide was carried out. The simulation gave a folding time of ~10 ns, which is longer than typical time of ~1 ns for the formation of 1–2 helical turns. The simulation demonstrates that a helical peptide with disulfide bonds, which may encounter extra steric hindrance compared with the peptide without disulfide bonds, can fold in nanosecond timescale. An analysis shows that this folding time should correspond to the folding time in weak denaturation condition in experiment. Interactions and factors affecting folding pathways are analyzed and discussed.

Possible mechanism underlying high-pressure unfolding of proteins: formation of a short-period high-density hydration shell

Hydration effects on high-pressure unfolding of a hydrophobic polymer chain are investigated through a multiscale simulation based on density-functional theory. The results strongly suggest the following: a thermodynamic origin for high-pressure denaturation, i.e., the decrease in volume due to the unfolding can be explained by the formation of a short-period high-density hydration shell.

What is the time scale for α-helix nucleation?

Helix formation is an elementary process in protein folding, influencing both the rate and mechanism of the global folding reaction. Yet, because helix formation is less cooperative than protein folding, the kinetics are often multiexponential, and the observed relaxation times are not straightforwardly related to the microscopic rates for helix nucleation and elongation. Recent ultrafast spectroscopic measurements on the peptide Ac-WAAAH(+)-NH(2) were best fit by two relaxation modes on the ∼0.1-1 ns time scale, (1) apparently much faster than had previously been experimentally inferred for helix nucleation. Here, we use replica-exchange molecular dynamics simulations with an optimized all-atom protein force field (Amber ff03w) and an accurate water model (TIP4P/2005) to study the kinetics of helix formation in this peptide. We calculate temperature-dependent microscopic rate coefficients from the simulations by treating the dynamics between helical states as a Markov process using a recently developed formalism. The fluorescence relaxation curves obtained from simulated temperature jumps are in excellent agreement with the experimentally determined results. We find that the kinetics are multiphasic but can be approximated well by a double-exponential function. The major processes contributing to the relaxation are the shrinking of helical states at the C-terminal end and a faster re-equilibration among coil states. Despite the fast observed relaxation, the helix nucleation time is estimated from our model to be 20-70 ns at 300 K, with a dependence on temperature well described by Arrhenius kinetics.

Unique features of the folding landscape of a repeat protein revealed by pressure perturbation

The volumetric properties of proteins yield information about the changes in packing and hydration between various states along the folding reaction coordinate and are also intimately linked to the energetics and dynamics of these conformations. These volumetric characteristics can be accessed via pressure perturbation methods. In this work, we report high-pressure unfolding studies of the ankyrin domain of the Notch receptor (Nank1-7) using fluorescence, small-angle x-ray scattering, and Fourier transform infrared spectroscopy. Both equilibrium and pressure-jump kinetic fluorescence experiments were consistent with a simple two-state folding/unfolding transition under pressure, with a rather small volume change for unfolding compared to proteins of similar molecular weight. High-pressure fluorescence, Fourier transform infrared spectroscopy, and small-angle x-ray scattering measurements revealed that increasing urea over a very small range leads to a more expanded pressure unfolded state with a significant decrease in helical content. These observations underscore the conformational diversity of the unfolded-state basin. The temperature dependence of pressure-jump fluorescence relaxation measurements demonstrated that at low temperatures, the folding transition state ensemble (TSE) lies close in volume to the folded state, consistent with significant dehydration at the barrier. In contrast, the thermal expansivity of the TSE was found to be equivalent to that of the unfolded state, indicating that the interactions that constrain the folded-state thermal expansivity have not been established at the folding barrier. This behavior reveals a high degree of plasticity of the TSE of Nank1-7.

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This "unfolding-up-on-squeezing" is counter-intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results-that pressure denatured states are water-swollen, and theoretical results-that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states-their water-swollen nature, retention of secondary structure, and overall compactness-mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure-dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately -60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500-2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water-swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies.

Tuning the globular assembly of hydrophobic/hydrophilic heteropolymer sequences

We propose a heteropolymer design scheme to tune monomer distributions that stabilize or destabilize the collapsed globular conformation relative to random sequencing. Polymer sequences trained via globular templating are mapped to a one-dimensional Ising-like model, and inverse Monte Carlo simulations are performed to determine an effective interaction between monomers that reproduces intrasequence correlations. Heteropolymer sequences generated using this effective interaction quantitatively reproduce the coil-to-globule transition with increasing polymer hydrophobicity observed for templated sequences. Through potential scaling, the range of transition hydrophobic fractions required to collapse the polymer opens up by a factor of 2, from a minimum fraction of 17% to a maximum of 32% for the longest polymers simulated. Collapsed conformations are favored by sequences in which there is intermediate segregation of hydrophobic and hydrophilic units along the backbone, while monomer integration favors coils.