Characterization of Heparin's Conformational Ensemble by Molecular Dynamics Simulations and Nuclear Magnetic Resonance Spectroscopy

Heparin is a highly charged, polysulfated polysaccharide and serves as an anticoagulant. Heparin binds to multiple proteins throughout the body, suggesting a large range of potential therapeutic applications. Although its function has been characterized in multiple physiological contexts, heparin's solution conformational dynamics and structure-function relationships are not fully understood. Molecular dynamics (MD) simulations facilitate the analysis of a molecule's underlying conformational ensemble, which then provides important information necessary for understanding structure-function relationships. However, for MD simulations to afford meaningful results, they must both provide adequate sampling and accurately represent the energy properties of a molecule. The aim of this study is to compare heparin's conformational ensemble using two well-developed force fields for carbohydrates, known as GLYCAM06 and CHARMM36, using replica exchange molecular dynamics (REMD) simulations, and to validate these results with NMR experiments. The anticoagulant sequence, an ultra-low-molecular-weight heparin, known as Arixtra (fondaparinux, sodium), was simulated with both parameter sets. The results suggest that GLYCAM06 matches experimental nuclear magnetic resonance three-bond J-coupling values measured for Arixtra better than CHARMM36. In addition, NOESY and ROESY experiments suggest that Arixtra is very flexible in the sub-millisecond time scale and does not adopt a unique structure at 25 C. Moreover, GLYCAM06 affords a much more dynamic conformational ensemble for Arixtra than CHARMM36.

Anionic Lipids Impact RAS-Binding Site Accessibility and Membrane Binding Affinity of CRAF RBD-CRD

CRAF activation requires binding to membrane-anchored and active GTP-bound RAS. Whereas its RAS-binding domain (RBD) contains the main binding interface to the RAS G domain, its cysteine-rich domain (CRD) is responsible for association to anionic lipid-rich membranes. Both RAF domains are connected by a short linker, and it remains unclear if the two domains act independently or if one domain can impact the function of the other. Here, we used a combination of coarse-grained and all-atom molecular dynamics simulations of a CRAF RBD-CRD construct to investigate the dynamics of the RBD when it is tethered to CRD that is anchored to a POPC:POPS model membrane. First, we show that the RBD positioning is very dynamic with a preferential localization near the membrane surface. Next, we show that membrane-localized RBD has its RAS-binding interface mostly inaccessible because of its proximity to the membrane. Several positively charged residues in this interface were identified from simulations as important for driving RBD association to the membrane. Surface plasmon resonance (SPR) measurements confirmed that mutations of these RBD residues reduced the liposome partitioning of RBD-CRD. Last, simulations indicated that the presence of RBD near the membrane led to a local enrichment of anionic lipids that could potentially enhance the membrane affinity of the entire RBD-CRD construct. This was supported by SPR measurements that showed stronger liposome partitioning of RBD-CRD relative to CRD alone. These findings thus suggest that the RBD and CRD have synergistic effects on their membrane dynamics, with CRD bringing RBD closer to the membrane that impacts its accessibility to RAS and with RBD causing local anionic lipid enrichment that enhances the overall affinity between the membrane and RBD-CRD. These mechanisms have potential implications on the order of events of the interactions between RAS and CRAF at the membrane.

Presence or Absence of Ras Dimerization Shows Distinct Kinetic Signature in Ras-Raf Interaction

Initiations of cell signaling pathways often occur through the formation of multiprotein complexes that form through protein-protein interactions. Therefore, detecting their presence is central to understanding the function of a cell signaling pathway, aberration of which often leads to fatal diseases, including cancers. However, the multiprotein complexes are often difficult to detect using microscopes due to their small sizes. Therefore, currently, their presence can be only detected through indirect means. In this article, we propose to investigate the presence or absence of protein complexes through some easily measurable kinetic parameters, such as activation rates. As a proof of concept, we investigate the Ras-Raf system, a well-characterized cell signaling system. It has been hypothesized that Ras dimerization is necessary to create activated Raf dimers. Although there are circumstantial evidences supporting the Ras dimerization hypothesis, direct proof of Ras dimerization is still inconclusive. In the absence of conclusive direct experimental proof, this hypothesis can only be examined through indirect evidences of Ras dimerization. In this article, using a multiscale simulation technique, we provide multiple criteria that distinguishes an activation mechanism involving Ras dimerization from another mechanism that does not involve Ras dimerization. The provided criteria will be useful in the investigation of not only Ras-Raf interaction but also other two-protein interactions.

The Plasma Membrane as a Competitive Inhibitor and Positive Allosteric Modulator of KRas4B Signaling

Mutant Ras proteins are important drivers of human cancers, yet no approved drugs act directly on this difficult target. Over the last decade, the idea has emerged that oncogenic signaling can be diminished by molecules that drive Ras into orientations in which effector-binding interfaces are occluded by the cell membrane. To support this approach to drug discovery, we characterize the orientational preferences of membrane-bound K-Ras4B in 1.45-ms aggregate time of atomistic molecular dynamics simulations. Individual simulations probe active or inactive states of Ras on membranes with or without anionic lipids. We find that the membrane orientation of Ras is relatively insensitive to its bound guanine nucleotide and activation state but depends strongly on interactions with anionic phosphatidylserine lipids. These lipids slow Ras' translational and orientational diffusion and promote a discrete population in which small changes in orientation control Ras' competence to bind multiple regulator and effector proteins. Our results suggest that compound-directed conversion of constitutively active mutant Ras into functionally inactive forms may be accessible via subtle perturbations of Ras' orientational preferences at the membrane surface.

Methionine 170 is an Environmentally Sensitive Membrane Anchor in the Disordered HVR of K-Ras4B

Ras protein colocalization at the plasma membrane is implicated in the activation of signaling cascades that promote cell growth, survival, and motility. However, the mechanisms that underpin Ras self-association remain unclear. We use molecular dynamics simulations to show how basic and hydrophobic components of the disordered C-terminal membrane tether of K-Ras4B combine to regulate its membrane interactions. Specifically, anionic lipids attract lysine residues to the membrane surface, thereby splitting the peptide population into two states that exchange on the microsecond time scale. These states differ in the membrane insertion of a methionine residue, which is influenced by local membrane composition. As a result, these states may impose context-dependent biases on the disposition of Ras' signaling domain, with possible implications for the accessibility of its effector binding surfaces. We investigate Ras' ability to nanocluster by fly-casting for patches of anionic lipids and find that while anionic lipids promote the intermolecular association of K-Ras4B membrane tethers, at short range this appears to be a passive process in which anionic lipids electrostatically screen these cationic peptides to mitigate their natural repulsion. Together with the sub-microsecond stability of interpeptide contacts, this result suggests that experimentally observed K-Ras4B nanoclustering is not driven by direct intermolecular contact of its membrane tethers.

High pressure NMR reveals conformational perturbations by disease-causing mutations in amyloid β-peptide

Here we present the high pressure NMR characterization of Aβ42 and two Aβ40 variants with Alzheimer-causing mutations E22G and D23N. While chemical shifts only identified localized changes at ambient pressure compared with Aβ40, high pressure NMR revealed a common site with heightened pressure sensitivity at Q15, K16 and L17 in all three variants, which correlates to higher β-propensity at central hydrophobic cluster (CHC) and faster aggregation.

Mechanistic insights into allosteric regulation of the A2A adenosine G protein-coupled receptor by physiological cations

Cations play key roles in regulating G-protein-coupled receptors (GPCRs), although their mechanisms are poorly understood. Here, 19F NMR is used to delineate the effects of cations on functional states of the adenosine A2A GPCR. While Na+ reinforces an inactive ensemble and a partial-agonist stabilized state, Ca2+ and Mg2+ shift the equilibrium toward active states. Positive allosteric effects of divalent cations are more pronounced with agonist and a G-protein-derived peptide. In cell membranes, divalent cations enhance both the affinity and fraction of the high affinity agonist-bound state. Molecular dynamics simulations suggest high concentrations of divalent cations bridge specific extracellular acidic residues, bringing TM5 and TM6 together at the extracellular surface and allosterically driving open the G-protein-binding cleft as shown by rigidity-transmission allostery theory. An understanding of cation allostery should enable the design of allosteric agents and enhance our understanding of GPCR regulation in the cellular milieu.

Equilibrium Denaturation and Preferential Interactions of an RNA Tetraloop with Urea

Urea is an important organic cosolute with implications in maintaining osmotic stress in cells and differentially stabilizing ensembles of folded biomolecules. We report an equilibrium study of urea-induced denaturation of a hyperstable RNA tetraloop through unbiased replica exchange molecular dynamics. We find that, in addition to destabilizing the folded state, urea smooths the RNA free energy landscape by destabilizing specific configurations, and forming favorable interactions with RNA nucleobases. A linear concentration-dependence of the free energy (m-value) is observed, in agreement with the results of other RNA hairpins and proteins. Additionally, analysis of the hydrogen-bonding and stacking interactions within RNA primarily show temperature-dependence, while interactions between RNA and urea primarily show concentration-dependence. Our findings provide valuable insight into the effects of urea on RNA folding and describe the thermodynamics of a basic RNA hairpin as a function of solution chemistry.

Can Specific Protein-Lipid Interactions Stabilize an Active State of the Beta 2 Adrenergic Receptor?

G-protein-coupled receptors are eukaryotic membrane proteins with broad biological and pharmacological relevance. Like all membrane-embedded proteins, their location and orientation are influenced by lipids, which can also impact protein function via specific interactions. Extensive simulations totaling 0.25 ms reveal a process in which phospholipids from the membrane's cytosolic leaflet enter the empty G-protein binding site of an activated β2 adrenergic receptor and form salt-bridge interactions that inhibit ionic lock formation and prolong active-state residency. Simulations of the receptor embedded in an anionic membrane show increased lipid binding, providing a molecular mechanism for the experimental observation that anionic lipids can enhance receptor activity. Conservation of the arginine component of the ionic lock among Rhodopsin-like G-protein-coupled receptors suggests that intracellular lipid ingression between receptor helices H6 and H7 may be a general mechanism for active-state stabilization.

Peptide Bond Isomerization in High-Temperature Simulations

Force fields for molecular simulation are generally optimized to model macromolecules such as proteins at ambient temperature and pressure. Nevertheless, elevated temperatures are frequently used to enhance conformational sampling, either during system setup or as a component of an advanced sampling technique such as temperature replica exchange. Because macromolecular force fields are now put upon to simulate temperatures and time scales that greatly exceed their original design specifications, it is appropriate to re-evaluate whether these force fields are up to the task. Here, we quantify the rates of peptide bond isomerization in high-temperature simulations of three octameric peptides and a small fast-folding protein. We show that peptide octamers with and without proline residues undergo cis/trans isomerization every 1-5 ns at 800 K with three classical atomistic force fields (AMBER99SB-ILDN, CHARMM22/CMAP, and OPLS-AA/L). On the low microsecond time scale, these force fields permit isomerization of nonprolyl peptide bonds at temperatures ≥500 K, and the CHARMM22/CMAP force field permits isomerization of prolyl peptide bonds ≥400 K. Moreover, the OPLS-AA/L force field allows chiral inversion about the Cα atom at 800 K. Finally, we show that temperature replica exchange permits cis peptide bonds developed at 540 K to subsequently migrate back to the 300 K ensemble, where cis peptide bonds are present in 2 ± 1% of the population of Trp-cage TC5b, including up to 4% of its folded state. Further work is required to assess the accuracy of cis/trans isomerization in the current generation of protein force fields.

Efficient Schmidt number scaling in dissipative particle dynamics

Dissipative particle dynamics is a widely used mesoscale technique for the simulation of hydrodynamics (as well as immersed particles) utilizing coarse-grained molecular dynamics. While the method is capable of describing any fluid, the typical choice of the friction coefficient γ and dissipative force cutoff rc yields an unacceptably low Schmidt number Sc for the simulation of liquid water at standard temperature and pressure. There are a variety of ways to raise Sc, such as increasing γ and rc, but the relative cost of modifying each parameter (and the concomitant impact on numerical accuracy) has heretofore remained undetermined. We perform a detailed search over the parameter space, identifying the optimal strategy for the efficient and accuracy-preserving scaling of Sc, using both numerical simulations and theoretical predictions. The composite results recommend a parameter choice that leads to a speed improvement of a factor of three versus previously utilized strategies.

Characterization of Aβ Monomers through the Convergence of Ensemble Properties among Simulations with Multiple Force Fields

Amyloid β (Aβ) monomers represent a base state in the pathways of aggregation that result in the fibrils and oligomers implicated in the pathogenesis of Alzheimer's disease (AD). The structural properties of these intrinsically disordered peptides remain unclear despite extensive experimental and computational investigations. Further, there are mutations within Aβ that change the way the peptide aggregates and are known to cause familial AD (FAD). Here, we analyze the ensembles of different isoforms (Aβ42 and Aβ40) and mutants (E22Δ, D23N, E22K, E22G, and A2T in Aβ40) of Aβ generated with all-atom replica exchange molecular dynamics (REMD) simulations on the μs/replica time scale. These were run using three different force field/water model combinations: OPLS-AA/L and TIP3P ("OPLS"), AMBER99sb-ILDN and TIP4P-Ew ("ILDN"), as well as CHARMM22* and TIP3SP ("CHARMM"). Despite fundamental changes in simulation parameters, we find that the resulting ensembles demonstrate a strong convergence in structural properties. In particular, antiparallel contacts between L17-A21 and A30-L34 are prevalent in ensembles of Aβ40, directly forming β sheets in the OPLS and ILDN combinations. A21-A30 commonly forms an interceding region that rarely interacts with the rest of the peptide. Further, Aβ42 contributes new β hairpin motifs involving V40-I41 in both OPLS and ILDN. However, the structural flexibility of the central region and the electrostatic interactions that characterize it are notably different between the different conditions. Further, for OPLS, each of the FAD mutations disrupts central bend character and increases the polymorphism of antiparallel contacts across the central region. However, the studied mutations in the ILDN set primarily encourage more global contacts involving the N-terminus and the central region, and promote the formation of new β topologies that may seed different aggregates involved in disease phenotypes. These differences aside, the large degree of agreement between simulation sets across multiple force fields provides a generalizable characterization of Aβ that is also consistent with experimental data and models.

Effects of truncating van der Waals interactions in lipid bilayer simulations

In membrane simulations, it is known that truncating electrostatic interactions results in artificial ordering of lipids at the truncation distance. However, less attention has been paid to the effect of truncating van der Waals (VDW) interactions. Since the VDW potential decays as r(-6), it is frequently neglected beyond a cutoff of around 1 nm. In some cases, analytical dispersion corrections appropriate for isotropic systems are applied to the pressure and the potential energy. In this work, we systematically study the effect of truncating VDW interactions at different cutoffs in 1,2-Dipalmitoyl-sn-glycero-3-phosphocholine bilayers with the Berger force field. We show that the area per lipid decreases systematically when the VDW cutoff (r(c)) increases. This dependence persists even when dispersion corrections are applied. Since the analytical form of the dispersion correction is only appropriate for isotropic systems, we suggest that a long VDW cutoff should be used in preference over a short VDW cutoff. To determine the appropriate cutoff, we simulate liquid pentadecane with the Berger parameters and find that r(c) ≥ 1.4 nm is sufficient to reproduce the density and the heat of vaporization of pentadecane. Bilayers simulated with r(c) ≥ 1.4 nm show an improved agreement with experiments in both the form factors and the deuterium order parameters. Finally, we report that the VDW cutoff has a significant impact on the lipid flip-flop energetics and an inappropriate short VDW cutoff results in a bilayer that is prone to form water defects across the bilayer.

Penetration of HIV-1 Tat47-57 into PC/PE Bilayers Assessed by MD Simulation and X-ray Scattering

The interactions of the basic, cell-penetrating region (Y47GRKKRRQRRR57) of the HIV-1 Tat protein with dioleoylphosphatidylcholine (DOPC) bilayers were previously assessed by comparing experimental X-ray diffuse scattering with atomistic molecular dynamics simulations. Here, we extend this investigation by evaluating the influence of phosphatidylethanolamine (PE) lipids. Using experimental bilayer form factors derivedfrom X-ray diffuse scattering data as a guide, our simulations indicate that Tat peptides localize close to the carbonyl-glycerol group in the headgroup region of bilayers composed of either DOPC or DOPC:DOPE (1:1) lipid. Our results also suggest that Tat peptides may more frequently insert into the hydrophobic core of bilayers composed of PC:PE (1:1) lipids than into bilayers composed entirely of PC lipids. PE lipids may facilitate peptide translocation across a lipid bilayer by stabilizing intermediate states in which hydrated peptides span the bilayer.

Impact of hydrodynamics on effective interactions in suspensions of active and passive matter

Passive particles exhibit unique properties when immersed in an active bath of self-propelling entities. In particular, an effective attraction can appear between particles that repel each other when in a passive solution. Here we numerically study the effect of hydrodynamics on an active-passive hybrid system, where we observe qualitative differences as compared to simulations with excluded volume effects alone. The results shed light on an existing discrepancy in pair lifetimes between simulation and experiment, due to the hydrodynamically enhanced stability of coupled passive particles.

Multisite ion model in concentrated solutions of divalent cations (MgCl2 and CaCl2): osmotic pressure calculations

Accurate force field parameters for ions are essential for meaningful simulation studies of proteins and nucleic acids. Currently accepted models of ions, especially for divalent ions, do not necessarily reproduce the right physiological behavior of Ca(2+) and Mg(2+) ions. Saxena and Sept (J. Chem. Theor. Comput. 2013, 9, 3538-3542) described a model, called the multisite-ion model, where instead of treating the ions as an isolated sphere, the charge was split into multiple sites with partial charge. This model provided accurate inner shell coordination of the ion with biomolecules and predicted better free energies for proteins and nucleic acids. Here, we expand and refine the multisite model to describe the behavior of divalent ions in concentrated MgCl2 and CaCl2 electrolyte solutions, eliminating the unusual ion-ion pairing and clustering of ions which occurred in the original model. We calibrate and improve the parameters of the multisite model by matching the osmotic pressure of concentrated solutions of MgCl2 to the experimental values and then use these parameters to test the behavior of CaCl2 solutions. We find that the concentrated solutions of both divalent ions exhibit the experimentally observed behavior with correct osmotic pressure, the presence of solvent separated ion pairs instead of direct ion pairs, and no aggregation of ions. The improved multisite model for (Mg(2+) and Ca(2+)) can be used in classical simulations of biomolecules at physiologically relevant salt concentrations.

Acceleration of Lateral Equilibration in Mixed Lipid Bilayers Using Replica Exchange with Solute Tempering

The lateral heterogeneity of cellular membranes plays an important role in many biological functions such as signaling and regulating membrane proteins. This heterogeneity can result from preferential interactions between membrane components or interactions with membrane proteins. One major difficulty in molecular dynamics simulations aimed at studying the membrane heterogeneity is that lipids diffuse slowly and collectively in bilayers, and therefore, it is difficult to reach equilibrium in lateral organization in bilayer mixtures. Here, we propose the use of the replica exchange with solute tempering (REST) approach to accelerate lateral relaxation in heterogeneous bilayers. REST is based on the replica exchange method but tempers only the solute, leaving the temperature of the solvent fixed. Since the number of replicas in REST scales approximately only with the degrees of freedom in the solute, REST enables us to enhance the configuration sampling of lipid bilayers with fewer replicas, in comparison with the temperature replica exchange molecular dynamics simulation (T-REMD) where the number of replicas scales with the degrees of freedom of the entire system. We apply the REST method to a cholesterol and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bilayer mixture and find that the lateral distribution functions of all molecular pair types converge much faster than in the standard MD simulation. The relative diffusion rate between molecules in REST is, on average, an order of magnitude faster than in the standard MD simulation. Although REST was initially proposed to study protein folding and its efficiency in protein folding is still under debate, we find a unique application of REST to accelerate lateral equilibration in mixed lipid membranes and suggest a promising way to probe membrane lateral heterogeneity through molecular dynamics simulation.

Folding and unfolding thermodynamics of the TC10b Trp-cage miniprotein

We examine the folding-unfolding of a variant of the Trp-cage, known as TC10b, and compare structural stability, dynamics, and thermodynamics with that of the TC5b variant, using replica exchange molecular dynamics (REMD). The TC10b variant was designed to have larger helical stability by the substitution of amino acids with greater alpha helical propensities in the N-terminal region. Experiments have shown TC10b to possess larger overall stability than TC5b. Simulations starting from unbiased, unfolded initial conditions are run for 1 μs per replica. The calculations show a higher melting temperature for TC10b than TC5b, and suggest a more ordered folded structure through the elimination of a substate found in the folded ensemble of TC5b. We model the difference in Gibbs free energy, ΔG(P,T), of folding using the bootstrap statistical method, which is used to calculate uncertainties associated with the thermodynamic parameters for both variants of the Trp-cage. We find that while the shape of the area for which the protein is stability folded is elliptical for TC5b, there is a degree of uncertainty associated with that of TC10b, with one model suggesting elliptical and another suggesting hyperbolic. This model suggests that at high pressures, TC5b can experience pressure denaturation, but TC10b may not.

Aβ monomers transiently sample oligomer and fibril-like configurations: ensemble characterization using a combined MD/NMR approach

Amyloid β (Aβ) peptides are a primary component of fibrils and oligomers implicated in the etiology of Alzheimer's disease (AD). However, the intrinsic flexibility of these peptides has frustrated efforts to investigate the secondary and tertiary structure of Aβ monomers, whose conformational landscapes directly contribute to the kinetics and thermodynamics of Aβ aggregation. In this work, de novo replica exchange molecular dynamics (REMD) simulations on the microseconds-per-replica timescale are used to characterize the structural ensembles of Aβ42, Aβ40, and M35-oxidized Aβ42, three physiologically relevant isoforms with substantially different aggregation properties. J-coupling data calculated from the REMD trajectories were compared to corresponding NMR-derived values acquired through two different pulse sequences, revealing that all simulations converge on the order of hundreds of nanoseconds-per-replica toward ensembles that yield good agreement with experiment. Though all three Aβ species adopt highly heterogeneous ensembles, these are considerably more structured compared to simulations on shorter timescales. Prominent in the C-terminus are antiparallel β-hairpins between L17-A21, A30-L36, and V39-I41, similar to oligomer and fibril intrapeptide models that expose these hydrophobic side chains to solvent and may serve as hotspots for self-association. Compared to reduced Aβ42, the absence of a second β-hairpin in Aβ40 and the sampling of alternate β topologies by M35-oxidized Aβ42 may explain the reduced aggregation rates of these forms. A persistent V24-K28 bend motif, observed in all three species, is stabilized by buried backbone to side-chain hydrogen bonds with D23 and a cross-region salt bridge between E22 and K28, highlighting the role of the familial AD-linked E22 and D23 residues in Aβ monomer folding. These characterizations help illustrate the conformational landscapes of Aβ monomers at atomic resolution and provide insight into the early stages of Aβ aggregation pathways.

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.

Influence of water-protein hydrogen bonding on the stability of Trp-cage miniprotein. A comparison between the TIP3P and TIP4P-Ew water models

We report extensive replica exchange molecular dynamics (REMD) simulations on the folding/unfolding equilibrium of Trp-cage miniprotein using the Amber ff99SB all atom forcefield and TIP3P and TIP4P-Ew explicit water solvent models. REMD simulation-lengths in the 500 ns to the microsecond regime per replica are required to adequately sample the folding/unfolding equilibrium. We observe that this equilibrium is significantly affected by the choice of the water model. Compared with experimental data, simulations using the TIP3P solvent describe the stability of the Trp-cage quite realistically, providing a melting point which is just a few Kelvins above the experimental transition temperature of 317 K. The TIP4P-Ew model shifts the equilibrium towards the unfolded state and lowers the free energy of unfolding by about 3 kJ mol(-1) at 280 K, demonstrating the need to fine-tune the protein-forcefield depending on the chosen water model. We report evidence that the main difference between the two water models is mostly due to the different solvation of polar groups of the peptide. The unfolded state of the Trp-cage is stabilized by an increasing number of hydrogen bonds, destabilizing the α-helical part of the molecule and opening the R-D salt bridge. By reweighting the strength of solvent-peptide hydrogen bonds by adding a hydrogen bond square well potential, we can fully recover the effect of the different water models and estimate the shift in population as due to a difference in hydrogen bond-strength of about 0.4 kJ mol(-1) per hydrogen bond.

Simulations of the confinement of ubiquitin in self-assembled reverse micelles

We describe the effects of confinement on the structure, hydration, and the internal dynamics of ubiquitin encapsulated in reverse micelles (RM). We performed molecular dynamics simulations of the encapsulation of ubiquitin into self-assembled protein/surfactant reverse micelles to study the positioning and interactions of the protein with the RM and found that ubiquitin binds to the RM interface at low salt concentrations. The same hydrophobic patch that is recognized by ubiquitin binding domains in vivo is found to make direct contact with the surfactant head groups, hydrophobic tails, and the iso-octane solvent. The fast backbone N-H relaxation dynamics show that the fluctuations of the protein encapsulated in the RM are reduced when compared to the protein in bulk. This reduction in fluctuations can be explained by the direct interactions of ubiquitin with the surfactant and by the reduced hydration environment within the RM. At high concentrations of excess salt, the protein does not bind strongly to the RM interface and the fast backbone dynamics are similar to that of the protein in bulk. Our simulations demonstrate that the confinement of protein can result in altered protein dynamics due to the interactions between the protein and the surfactant.

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.

Equilibrium study of protein denaturation by urea

Though urea is commonly used to denature proteins, the molecular mechanism of its denaturing ability is still a subject of considerable debate. Previous molecular dynamics simulation studies have sought to elucidate the mechanism of urea denaturation by focusing on the pathway of denaturation rather than examining the effect of urea on the folding/unfolding equilibrium, which is commonly measured in experiment. Here we report the reversible folding/unfolding equilibrium of Trp-cage miniprotein in the presence of urea, over a broad range of urea concentrations, using all-atom Replica exchange MD simulations. The simulations capture the experimentally observed linear dependence of unfolding free energy on urea concentration. We find that the denaturation is driven by favorable direct interaction of urea with the protein through both electrostatic and van der Waals forces and quantify their contribution. Though the magnitude of direct electrostatic interaction of urea is larger than van der Waals, the difference between unfolded and folded ensembles is dominated by the van der Waals interaction. We also find that hydrogen bonding of urea to the peptide backbone does not play a dominant role in denaturation. The unfolded ensemble sampled depends on urea concentration, with greater urea concentration favoring conformations with greater solvent exposure. The m-value is predicted to increase with temperature and more strongly so with pressure.

Computing the stability diagram of the Trp-cage miniprotein

We report molecular dynamics simulations of the equilibrium folding/unfolding thermodynamics of an all-atom model of the Trp-cage miniprotein in explicit solvent. Simulations are used to sample the folding/unfolding free energy difference and its derivatives along 2 isochores. We model the DeltaG(u)(P,T) landscape using the simulation data and propose a stability diagram model for Trp-cage. We find the proposed diagram to exhibit features similar to globular proteins with increasing hydrostatic pressure destabilizing the native fold. The observed energy differences DeltaE(u) are roughly linearly temperature-dependent and approach DeltaE(u) = 0 with decreasing temperature, suggesting that the system approached the region of cold denaturation. In the low-temperature denatured state, the native helical secondary structure elements are largely preserved, whereas the protein conformation changes to an "open-clamp" configuration. A tighter packing of water around nonpolar sites, accompanied by an increasing solvent-accessible surface area of the unfolded ensemble, seems to stabilize the unfolded state at elevated pressures.

Water penetration in the low and high pressure native states of ubiquitin

Theoretical studies on the solvation of methane molecules in water have shown that the effect of increased pressure is to stabilize solvent separated contacts relative to direct contacts. This suggests that high pressure stabilizes waters that have penetrated into a protein's core, indicating a mechanism for the high pressure denaturation of proteins. We test this theory on a folded protein by studying the penetration of water into the native state of ubiquitin at low and high pressures, using molecular dynamics. An ensemble of conformations sampled in the folded state of ubiquitin has been determined by NMR at two pressures below the protein's denaturation pressure, 30 atm and 3000 atm. We find that 1-5 more waters penetrate the high pressure conformations than the low pressure conformations. Low volume configurations of the system are favored at high pressures, but different components of the system may experience increases or decreases in their specific volumes. We find that penetrating waters have a higher volume per water than bulk waters, but that the volume per protein residue may be lowered by solvation. Furthermore, we find that penetration of the protein by water at high pressures is driven by the difference in the pressure dependence of the probability of cavity opening in the protein and pressure dependence of the probability of cavity opening in the bulk solvent. The volume changes associated with cavity opening and closing indicate that each penetrating water reduces the volume of the system by about 12 mL/mol. The experimental volume change going from the low pressure to the high pressure native state of ubiquitin is 24 mL/mol. Our results indicate that this volume change can be explained by penetration of the protein by two water molecules.

Folding time predictions from all-atom replica exchange simulations

We present an approach to predicting the folding time distribution from all-atom replica exchange simulations. This is accomplished by approximating the multidimensional folding process as stochastic reaction-coordinate dynamics for which effective drift velocities and diffusion coefficients are determined from the short-time replica exchange simulations. Our approach is applied to the folding of the second beta-hairpin of the B domain of protein G. The folding time prediction agrees quite well with experimental measurements. Therefore, we have in hand a fast numerical tool for calculating the folding kinetic properties from all-atom "first-principles" models.

Role of flexibility and polarity as determinants of the hydration of internal cavities and pockets in proteins

Molecular dynamics simulations of Staphylococcal nuclease and of 10 variants with internal polar or ionizable groups were performed to investigate systematically the molecular determinants of hydration of internal cavities and pockets in proteins. In contrast to apolar cavities in rigid carbon structures, such as nanotubes or buckeyballs, internal cavities in proteins that are large enough to house a few water molecules will most likely be dehydrated unless they contain a source of polarity. The water content in the protein interior can be modulated by the flexibility of protein elements that interact with water, which can impart positional disorder to water molecules, or bias the pattern of internal hydration that is stabilized. This might explain differences in the patterns of hydration observed in crystal structures obtained at cryogenic and room temperature conditions. The ability of molecular dynamics simulations to determine the most likely sites of water binding in internal pockets and cavities depends on its efficiency in sampling the hydration of internal sites and alternative protein and water conformations. This can be enhanced significantly by performing multiple molecular dynamics simulations as well as simulations started from different initial hydration states.

Replica exchange simulation of reversible folding/unfolding of the Trp-cage miniprotein in explicit solvent: On the structure and possible role of internal water

We simulate the folding/unfolding equilibrium of the 20-residue miniprotein Trp-cage. We use replica exchange molecular dynamics simulations of the AMBER94 atomic detail model of the protein explicitly solvated by water, starting from a completely unfolded configuration. We employ a total of 40 replicas, covering the temperature range between 280 and 538 K. Individual simulation lengths of 100 ns sum up to a total simulation time of about 4 micros. Without any bias, we observe the folding of the protein into the native state with an unfolding-transition temperature of about 440 K. The native state is characterized by a distribution of root mean square distances (RMSD) from the NMR data that peaks at 1.8A, and is as low as 0.4A. We show that equilibration times of about 40 ns are required to yield convergence. A folded configuration in the entire extended ensemble is found to have a lifetime of about 31 ns. In a clamp-like motion, the Trp-cage opens up during thermal denaturation. In line with fluorescence quenching experiments, the Trp-residue sidechain gets hydrated when the protein opens up, roughly doubling the number of water molecules in the first solvation shell. We find the helical propensity of the helical domain of Trp-cage rather well preserved even at very high temperatures. In the folded state, we can identify states with one and two buried internal water molecules interconnecting parts of the Trp-cage molecule by hydrogen bonds. The loss of hydrogen bonds of these buried water molecules in the folded state with increasing temperature is likely to destabilize the folded state at elevated temperatures.

Local structure formation in simulations of two small proteins

Massively parallel all-atom, explicit solvent molecular dynamics simulations were used to explore the formation and existence of local structure in two small alpha-helical proteins, the villin headpiece and the helical fragment B of protein A. We report on the existence of transient helices and combinations of helices in the unfolded ensemble, and on the order of formation of helices, which appears to largely agree with previous experimental results. Transient local structure is observed even in the absence of overall native structure. We also calculate sets of residue-residue pairs that are statistically predictive of the formation of given local structures in our simulations.

Molecular dynamics study of water penetration in staphylococcal nuclease

The ionization properties of Lys and Glu residues buried in the hydrophobic core of staphylococcal nuclease (SN) suggest that the interior of this protein behaves as a highly polarizable medium with an apparent dielectric constant near 10. This has been rationalized previously in terms of localized conformational relaxation concomitant with the ionization of the internal residue, and with contributions by internal water molecules. Paradoxically, the crystal structure of the SN V66E variant shows internal water molecules and the structure of the V66K variant does not. To assess the structural and dynamical character of interior water molecules in SN, a series of 10-ns-long molecular dynamics (MD) simulations was performed with wild-type SN, and with the V66E and V66K variants with Glu66 and Lys66 in the neutral form. Internal water molecules were identified based on their coordination state and characterized in terms of their residence times, average location, dipole moment fluctuations, hydrogen bonding interactions, and interaction energies. The locations of the water molecules that have residence times of several nanoseconds and display small mean-square displacements agree well with the locations of crystallographically observed water molecules. Additional, relatively disordered water molecules that are not observed crystallographically were found in internal hydrophobic locations. All of the interior water molecules that were analyzed in detail displayed a distribution of interaction energies with higher mean value and narrower width than a bulk water molecule. This underscores the importance of protein dynamics for hydration of the protein interior. Further analysis of the MD trajectories revealed that the fluctuations in the protein structure (especially the loop elements) can strongly influence protein hydration by changing the patterns or strengths of hydrogen bonding interactions between water molecules and the protein. To investigate the dynamical response of the protein to burial of charged groups in the protein interior, MD simulations were performed with Glu66 and Lys66 in the charged state. Overall, the MD simulations suggest that a conformational change rather than internal water molecules is the dominant determinant of the high apparent polarizability of the protein interior.

Helix-coil transition of alanine peptides in water: force field dependence on the folded and unfolded structures

The force fields used in classical modeling studies are semiempirical in nature and rely on their validation by comparison of simulations with experimental data. The all-atom replica-exchange molecular dynamics (REMD) methodology allows us to calculate the thermodynamics of folding/unfolding of peptides and small proteins, and provides a way of evaluating the reliability of force fields. We apply the REMD to obtain equilibrium folding/unfolding thermodynamics of a 21-residue peptide containing only alanine residues in explicit aqueous solution. The thermodynamics of this peptide is modeled with both the OPLS/AA/L and the A94/MOD force fields. We find that the helical content and the values for the helix propagation and nucleation parameters for this alanine peptide are consistent with measurements on similar peptides and with calculations using the modified AMBER force field (A94/MOD). The nature of conformations, both folded and unfolded, that contributes to the helix-coil transition profile, however, is quite different between these two force fields.

Atomic-Level Description of Amyloid β-Dimer Formation

All-atom simulations have been carried out on a monomer and dimer of the aggregation-prone fragment (16-22) of amyloid beta peptide, which is implicated in Alzheimer's disease. The replica exchange molecular dynamics method, which has been successfully applied to peptide folding, is utilized as a means to sample the configurational space with proper Boltzmann weighting so that the structural, motional, and thermodynamic description of self-assembly can be obtained. The free energy landscape showing the delicate balance between different monomer and dimer conformations is mapped along carefully chosen reaction coordinates. The canonical ensembles at 38 different temperatures are used to describe the thermodynamics and the relative stabilities of at least six different dimer conformations including that of parallel and antiparallel orientations. We also delineate the nature of the molecular forces that activate and stabilize these different dimer conformations as a function of temperature, especially as related to secondary structural propensity of monomer. We identify parallel loop dimer conformations that are stabilized due to specific interactions with water molecules.

Reversible temperature and pressure denaturation of a protein fragment: a replica exchange molecular dynamics simulation study

We determine the reversible folding-unfolding of the C-terminal (41-56) fragment of protein G as a function of density and temperature using replica exchange molecular dynamics simulations. We employ a total of 253 replicas, covering the temperature range between 320 and 515 K and the density range between 0.96 and 1.16 g cm(-3). Using the root mean square deviation from the folded structure as a quantitative measure, we are able to obtain the fraction of folded states, and can thus establish the free energy difference between the folded and the unfolded states of the protein fragment as a function of temperature and pressure. For the pressure denaturation the weakening of the hydrophobic interaction between the bulky side chains is found to be crucial at lower temperatures, leading to an apparent destabilization of the folded backbone structure at elevated pressures.

Role of backbone hydration and salt-bridge formation in stability of alpha-helix in solution

We test molecular level hypotheses for the high thermal stability of alpha-helical conformations of alanine-based peptides by performing detailed atomistic simulations of a 20-amino-acid peptide with explicit treatment of water. To assess the contribution of large side chains to alpha-helix stability through backbone desolvation and salt-bridge formation, we simulate the alanine-rich peptide, Ac-YAEAAKAAEAAKAAEAAKAF-Nme, referred to as the EK peptide, that has three pairs of "i, i + 3" glutamic acid(-) and lysine(+) substitutions. Efficient configurational sampling of the EK peptide over a wide temperature range enabled by the replica exchange molecular dynamics technique allows characterization of the stability of alpha-helix with respect to heat-induced unfolding. We find that near ambient temperatures, the EK peptide predominately samples alpha-helical configurations with 80% fractional helicity at 300 K. The helix melts over a broad range of temperatures with melting temperature, T(m), equal to 350 K, that is significantly higher than the T(m) of a 21-residue polyalanine peptide, A(21). Salt-bridges between oppositely charged Glu(-) and Lys(+) side chains can, in principle, provide thermal stability to alpha-helical conformers. For the specific EK peptide sequence, we observe infrequent formation of Glu-Lys salt-bridges (with approximately 10-20% probability) and therefore we conclude that salt-bridge formation does not contribute significantly to the EK peptide's helical stability. However, lysine side chains are found to shield specific "i, i + 4" backbone hydrogen bonds from water, indicating that large side-chain substituents can play an important role in stabilizing alpha-helical configurations of short peptides in aqueous solution through mediation of water access to backbone hydrogen bonds. These observations have implications on molecular engineering of peptides and biomolecules in the design of their thermostable variants where the shielding mechanism can act in concert with other factors such as salt-bridge formation, thereby increasing thermal stability considerably.

Nature of structural inhomogeneities on folding a helix and their influence on spectral measurements

Extensive conformational sampling and calculations of vibrational coupling provide a quantitative basis for the structurally inhomogeneous spectra of the amide unit in aqueous solutions containing folded and unfolded state distributions of helices. Replica exchange molecular dynamics simulations of the capped helical peptide, AA(AAKAA)(3)AAY, is carried out over a range of temperatures, where the system populates the folded and unfolded states. This sampling defines a set of ensembles that characterizes the conformational variability for configurations identified by their fraction of helical content. The effects of hydrogen bonding, both internal and external (with water), and the coupling between amide-I modes are computed as a function of temperature and helical content. End-to-end distance and coupling distributions are also computed. The solvent H-bonding, which is present at all temperatures, shifts the amide-I band toward lower frequency compared with the unsolvated band. Upon thermal denaturation of the peptide, the amide-I band shifts to higher frequency because the increase in solvent H-bonding fails to compensate for the loss in internal (helical) H-bonds. The loss of uniformity of the mode coupling along the helix at higher temperatures accounts for the well-known thermal broadening of the amide IR spectrum. The calculated inhomogeneities of segments of the peptide predict experimental properties of isotope-edited helices.

Folding a protein in a computer: an atomic description of the folding/unfolding of protein A

We study the folding mechanism of a three-helix bundle protein at atomic resolution, including effects of explicit water. Using replica exchange molecular dynamics we perform enough sampling over a wide range of temperatures to obtain the free energy, entropy, and enthalpy surfaces as a function of structural reaction coordinates. Simulations were started from different configurations covering the folded and unfolded states. Because many transitions between all minima at the free energy surface are observed, a quantitative determination of the free energy barriers and the ensemble of configurations associated with them is now possible. The kinetic bottlenecks for folding can be determined from the thermal ensembles of structures on the free energy barriers, provided the kinetically determined transition-state ensembles are similar to those determined from free energy barriers. A mechanism incorporating the interplay among backbone ordering, sidechain packing, and desolvation arises from these calculations. Large Phi values arise not only from native contacts, which mostly form at the transition state, but also from contacts already present in the unfolded state that are partially destroyed at the transition.

Simulation of the folding equilibrium of alpha-helical peptides: a comparison of the generalized Born approximation with explicit solvent

We compare simulations using the generalized Born/surface area (GB/SA) implicit solvent model with simulations using explicit solvent (transferable intermolecular potential 3 point, TIP3P) to test the GB/SA algorithm. We use the replica exchange molecular dynamics method to sample the conformational phase space of two alpha-helical peptides, A21 and the Fs, by using two different classical potentials and both water models. We find that when using GB/SA: (i) A21 is predicted to be more helical than the Fs peptide at all temperatures; (ii) the native structure of the Fs peptide is predicted to be a helical bundle instead of a single helix; and (iii) the persistence length and most probable end-to-end distance are too large in the unfolded state when compared against the explicit solvent simulations. We find that the potential of mean force in the phi(psi) plane is markedly different in the two solvents, making the two simulated peptides respond differently when the backbone torsions are perturbed. A fit of the temperature melting curves obtained in these simulations to a Lifson-Roig model finds that the GB/SA model has an unphysically large nucleation parameter, whereas the explicit solvent model produces values similar to experiment.

Peptide folding simulations

Developments in the design of small peptides that mimic proteins in complexity, recent advances in nanosecond time-resolved spectroscopy methods to study peptides and the development of modern, highly parallel simulation algorithms have come together to give us a detailed picture of peptide folding dynamics. Two newly implemented simulation techniques, parallel replica dynamics and replica exchange molecular dynamics, can now describe directly from simulations the kinetics and thermodynamics of peptide formation, respectively. Given these developments, the simulation community now has the tools to verify and validate simulation protocols and models (forcefields).

Interplay among tertiary contacts, secondary structure formation and side-chain packing in the protein folding mechanism: all-atom representation study of protein L

Experimental and theoretical results suggest that, since proteins are energetically minimally frustrated, the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble and on-pathway intermediate states in protein folding. Although the central role of native state topology in determining the folding mechanism is thought to be a quite general result-at least for small two-state folding proteins-there are remarkable exceptions. Recent experimental findings have shown that topology alone cannot always determine the folding mechanism, and demonstrated that the balance between topology and energetics is very delicate. This balance seems to be particularly critical in proteins with a highly symmetrical native structure, such as proteins L and G, which have similar native structure topology but fold by different mechanisms. Simplified, C(alpha)-atom only protein models have shown not be sufficient to differentiate these mechanisms. An all-atom Gō model provides a valuable intermediate model between structurally simplified protein representations and all-atom protein simulations with explicit/implicit solvent descriptions. We present here a detailed study of an all-atom Gō-like representation of protein L, in close comparison with the experimental results and with the results obtained from a simple C(alpha)-atom representation of the same protein. We also perform simulations for protein G, where we obtain a folding mechanism in which the protein symmetry is broken exactly in the opposite way to protein L as has been observed experimentally. A detailed analysis for protein L also shows that the role of specific residues is correctly and quantitatively reproduced by the all-atom Gō model over almost the entire protein.