The use of NMR chemical shifts to analyse the MD trajectories: simulation of bovine pancreatic trypsin inhibitor dynamics in water as a test case for solvent influences.

In this paper the NMR secondary chemical shifts, that are estimated from a set of 3D-structures, are compared with the observed ones to appraise the behaviour of a known x-ray diffraction structure (of the bovine pancreatic trypsin inhibitor protein) when various molecular dynamics are applied. The results of a 200 ps molecular dynamics under various conditions are analysed and different ways to modify the molecular dynamics are considered. With the purpose of avoiding the time-consuming explicit representation of the solvent (water) molecules, an attempt was made to understand the role of the solvent and to develop an implicit representation, which may be refined. A simulation of hydrophobic effects in an aqueous environment is also proposed which seems to provide a better approximation of the observed solution structure of the protein.     

Evaluation of a fast implicit solvent model for molecular dynamics simulations.

A solvation term based on the solvent accessible surface area (SASA) is combined with the CHARMM polar hydrogen force field for the efficient simulation of peptides and small proteins in aqueous solution. Only two atomic solvation parameters are used: one is negative for favoring the direct solvation of polar groups and the other positive for taking into account the hydrophobic effect on apolar groups. To approximate the water screening effects on the intrasolute electrostatic interactions, a distance-dependent dielectric function is used and ionic side chains are neutralized. The use of an analytical approximation of the SASA renders the model extremely efficient (i.e., only about 50% slower than in vacuo simulations). The limitations and range of applicability of the SASA model are assessed by simulations of proteins and structured peptides. For the latter, the present study and results reported elsewhere show that with the SASA model it is possible to sample a significant amount of folding/unfolding transitions, which permit the study of the thermodynamics and kinetics of folding at an atomic level of detail.     

RNA simulations: probing hairpin unfolding and the dynamics of a GNRA tetraloop

Simulations of an RNA hairpin containing a GNRA tetraloop were conducted to allow the characterization of its secondary structure formation and dynamics. Ten 10 ns trajectories of the folded hairpin 5'-GGGC[GCAA]GCCU-3' were generated using stochastic dynamics and the GB/SA implicit solvent model at 300 K. Overall, we find the stem to be a very stable subunit of this molecule, whereas multiple loop conformations and transitions between them were observed. These trajectories strongly suggest that extension of the C6 base away from the loop occurs cooperatively with an N-type-->S-type sugar pucker conversion in that residue and that similar pucker transitions are necessary to stabilize other looped-out bases. In addition, a short-lived conformer with an extended fourth loop residue (A8) lacking this stabilizing 2'-endo pucker mode was observed. Results of thermal perturbation at 400 K support this model of loop dynamics. Unfolding trajectories were produced using this same methodology at temperatures of 500 to 700 K. The observed unfolding events display three-state behavior kinetically (including native, globular, and unfolded populations) and, based on these observations, we propose a folding mechanism that consists of three distinct events: (i) collapse of the random unfolded structure and sampling of the globular state; (ii) passage into the folded region of configurational space as stem base-pairs form and gain helicity; and (iii) attainment of proper loop geometry and organization of loop pairing and stacking interactions. These results are considered in the context of current experimental knowledge of this and similar nucleic acid hairpins.     

Insights into conformation and dynamics of protein GB1 during folding and unfolding by NMR

Understanding protein stability requires characterization of structural determinants of the folded and unfolded states. Many proteins are capable of populating partially folded states under specific solution conditions. Occasionally, coexistence of the folded and an unfolded state under non- or mildly denaturing conditions can be observed by NMR, allowing us to structurally probe these states under identical conditions. Here we report on a destabilized mutant of the B1 domain of protein G (GB1) whose equilibrium unfolding was systematically investigated. Backbone amide residual dipolar couplings (RDCs), the tryptophan Nepsilon-H resonance and the amide nitrogen transverse relaxation rates (R2s) for varying pH values and different temperatures were measured. The backbone amide RDCs indicate that prior to complete unfolding, two melting hot spots are formed at the turn around T11, L12 and K13 and the N terminus of the helix at A24 and T25. The RDCs for the low pH, thermally unfolded state of GB1 are very small and do not indicate the presence of any native-like structure. Amide nitrogen transverse relaxation rates for GB1 in the folded state at different temperatures exhibit large contributions from exchange processes and the associated dynamics display considerable heterogeneity. Our data provide clear evidence for intermediate conformations and multi-state equilibrium un/folding for this GB1 variant.     

Structural dynamics and folding of β-lactoglobulin probed by heteronuclear NMR

Bovine β-lactoglobulin (βLG) has been one of the most extensively studied proteins in the history of protein science mainly because its abundance in cow's milk makes it readily available to researchers. However, compared to other textbook proteins, progress in the study of βLG has been slow because of obstacles such as a low reversibility from denaturation linked with thiol–disulfide exchange or monomer–dimer equilibrium preventing a detailed NMR analysis. Recently, the expression of various types of recombinant βLGs combined with heteronuclear NMR analysis has significantly improved understanding of the physico-chemical properties of βLG. In this review, we address several topics including pH-dependent structural dynamics, ligand binding, and the complex folding mechanism with non-native intermediates. These unique properties might be brought about by conformational frustration of the βLG structure, partly attributed to the relatively large molecular size of βLG. We expect studies with βLG to continue to reveal various important findings, difficult to obtain with small globular proteins, leading to a more comprehensive understanding of the conformation, dynamics and folding of proteins.     

Optimization of designed armadillo repeat proteins by molecular dynamics simulations and NMR spectroscopy

A multidisciplinary approach based on molecular dynamics (MD) simulations using homology models, NMR spectroscopy, and a variety of biophysical techniques was used to efficiently improve the thermodynamic stability of armadillo repeat proteins (ArmRPs). ArmRPs can form the basis of modular peptide recognition and the ArmRP version on which synthetic libraries are based must be as stable as possible. The 42-residue internal Arm repeats had been designed previously using a sequence-consensus method. Heteronuclear NMR revealed unfavorable interactions present at neutral but absent at high pH. Two lysines per repeat were involved in repulsive interactions, and stability was increased by mutating both to glutamine. Five point mutations in the capping repeats were suggested by the analysis of positional fluctuations and configurational entropy along multiple MD simulations. The most stabilizing single C-cap mutation Q240L was inferred from explicit solvent MD simulations, in which water penetrated the ArmRP. All mutants were characterized by temperature- and denaturant-unfolding studies and the improved mutants were established as monomeric species with cooperative folding and increased stability against heat and denaturant. Importantly, the mutations tested resulted in a cumulative decrease of flexibility of the folded state in silico and a cumulative increase of thermodynamic stability in vitro. The final construct has a melting temperature of about 85°C, 14.5° higher than the starting sequence. This work indicates that in silico studies in combination with heteronuclear NMR and other biophysical tools may provide a basis for successfully selecting mutations that rapidly improve biophysical properties of the target proteins.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Molecular dynamics characterisations of the Trp-cage folding mechanisms: in the absence and presence of water solvents

Protein folding is an important and yet challenging topic in current molecular biology. In this work, the folding dynamics and mechanisms of the Trp-cage mini-protein were studied with molecular dynamics simulations, in the absence and presence of water solvents. The important intermediates during the Trp-cage folding were determined by gradually decreasing the simulation temperature. The folding transition temperature was identified to be approximately 400 K, and the folding pathway was decomposed into six steps: U ? I ₁ ? I ₂ ? I ₃ ? I ₄ ? F ₁ ? F ₂, where U, I and F represent the unfolded, intermediate and folded states, respectively. The finding that the two helical subunits are successively formed is consistent with the experimental observations, and the Asp9/Arg16 salt bridge forms at the final stage and does not play a significant role during folding kinetics. The presence of water solvents induces hydrophobic collapse as the whole cage comparatively closes. Within aqueous solutions, the Trp-cage folding begins to contract into the meta-stable state, and by traversing the transition state it arrives at the native-like structure, which resembles the experimental structure closely.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Simulation and experiment conspire to reveal cryptic intermediates and a slide from the nucleation-condensation to framework mechanism of folding

There is a change from three-state to two-state kinetics of folding across the homeodomain superfamily of proteins as the mechanism slides from framework to nucleation-condensation. The tendency for framework folding in this family correlates with inherent helical propensity. The cellular myeloblastis protein (c-Myb) falls in the mechanistic transition region. An earlier, preliminary report of protein engineering experiments and molecular dynamics simulations (MD) showed that the folding mechanism for this protein has aspects of both the nucleation-condensation and framework models. In the more in-depth analysis of the MD trajectories presented here, we find that folding may be attributed to both of these mechanisms in different regions of the protein. The folding of the loop, middle helix, and turn is best described by nucleation-condensation, whereas folding of the N and C-terminal helices may be described by the framework model. Experimentally, c-Myb folds by apparent two-state kinetics, but the MD simulations predict that the kinetics hide a high-energy intermediate. We stabilized this hypothetical folding intermediate by deleting a residue (P174) in the loop between its second and third helices, and the mutant intermediate is long-lived in the simulations. Equilibrium and kinetic experiments demonstrate that folding of the DeltaP174 mutant is indeed three-state. The presence and shape of the intermediate observed in the simulations were confirmed by small angle X-ray scattering experiments.     

Principles of carbopeptoid folding: a molecular dynamics simulation study.

The conformational spaces of five oligomers of tetrahydrofuran-based carbopeptoids in chloroform and dimethyl sulfoxide were investigated through nine molecular dynamics simulations. Prompted by nuclear magnetic resonance experiments that indicated various stable folds for some but not all of these carbopeptoids, their folding behaviour was investigated as a function of stereochemistry, chain length and solvent. The conformational distributions of these molecules were analysed in terms of occurrence of hydrogen bonds, backbone torsional-angle distributions, conformational clustering and solute configurational entropy. While a cis-linkage across the tetrahydrofuran ring favours right-handed helical structures, a trans-linkage results in a larger conformational variability. Intra-solute hydrogen bonding is reduced with increasing chain length and with increasing solvent polarity. Solute configurational entropies confirm the picture obtained: they are smaller for cis- than for trans-linked peptides, for chloroform than for dimethyl sulfoxide as solvent and for shorter peptide chains. The simulations provide an atomic picture of molecular conformational variability that is consistent with the available experimental data.     

NMR and protein folding: equilibrium and stopped-flow studies.

NMR studies are now unraveling the structure of intermediates of protein folding using hydrogen-deuterium exchange methodologies. These studies provide information about the time dependence of formation of secondary structure. They require the ability to assign specific resonances in the NMR spectra to specific amide protons of a protein followed by experiments involving competition between folding and exchange reactions. Another approach is to use 19F-substituted amino acids to follow changes in side-chain environment upon folding. Current techniques of molecular biology allow assignments of 19F resonances to specific amino acids by site-directed mutagenesis. It is possible to follow changes and to analyze results from 19F spectra in real time using a stopped-flow device incorporated into the NMR spectrometer.     

Early intermediates in the folding of dihydrofolate reductase from Escherichia coli detected by hydrogen exchange and NMR.

The kinetic folding mechanism for Escherichia coli dihydrofolate reductase postulates two distinct types of transient intermediates. The first forms within 5 ms and has substantial secondary structure but little stability. The second is a set of four species that appear over the course of several hundred milliseconds and have secondary structure, specific tertiary structure, and significant stability (Jennings PA, Finn BE, Jones BE, Matthews CR, 1993, Biochemistry 32:3783-3789). Pulse labeling hydrogen exchange experiments were performed to determine the specific amide hydrogens in alpha-helices and beta-strands that become protected from exchange through the formation of stable hydrogen bonds during this time period. A significant degree of protection was observed for two subsets of the amide hydrogens within the dead time of this experiment (6 ms). The side chains of one subset form a continuous nonpolar strip linking six of the eight strands in the beta-sheet. The other subset corresponds to a nonpolar cluster on the opposite face of the sheet and links three of the strands and two alpha-helices. Taken together, these data demonstrate that the complex strand topology of this eight-stranded sheet can be formed correctly within 6 ms. Measurement of the protection factors at three different folding times (13 ms, 141 ms, and 500 ms) indicates that, of the 13 amide hydrogens displaying significant protection within 6 ms, 8 exhibit an increase in their protection factors from approximately 5 to approximately 50 over this time range; the remaining five exhibit protection factors > 100 at 13 ms. Only approximately half of the population of molecules form this set of stable hydrogen bonds. Thirteen additional hydrogens in the beta-sheet become protected from exchange as the set of native conformers appear, suggesting that the stabilization of this network reflects the global cooperativity of the folding reaction.     

Protein folding kinetics by combined use of rapid mixing techniques and NMR observation of individual amide protons

A method to be used for experimental studies of protein folding introduced by Schmid and Baldwin (J. Mol. Biol. 135: 199-215, 1979), which is based on the competition between amide hydrogen exchange and protein refolding, was extended by using rapid mixing techniques and 1H NMR to provide site-resolved kinetic information on the early phases of protein structure acquisition. In this method, a protonated solution of the unfolded protein is rapidly mixed with a deuterated buffer solution at conditions assuring protein refolding in the mixture. This simultaneously initiates the exchange of unprotected amide protons with solvent deuterium and the refolding of protein segments which can protect amide groups from further exchange. After variable reaction times the amide proton exchange is quenched while folding to the native form continues to completion. By using 1H NMR, the extent of exchange at individual amide sites is then measured in the refolded protein. Competition experiments at variable reaction times or variable pH indicate the time at which each amide group is protected in the refolding process. This technique was applied to the basic pancreatic trypsin inhibitor, for which sequence-specific assignments of the amide proton NMR lines had previously been obtained. For eight individual amide protons located in the beta-sheet and the C-terminal alpha-helix of this protein, apparent refolding rates in the range from 15 s-1 to 60 s-1 were observed. These rates are on the time scale of the fast folding phase observed with optical probes.     

Automated assignment of NMR chemical shifts using peak-particle dynamics simulation with the DYNASSIGN algorithm

A new algorithm, DYNASSIGN, for the automated assignment of NMR chemical shift resonances was developed in which expected cross peaks in multidimensional NMR spectra are represented by peak-particles and assignment restraints are translated into a potential energy function. Molecular dynamics simulation techniques are used to calculate a trajectory of the system of peak-particles subjected to the potential function in order to find energetically optimal configurations that correspond to correct assignments. Peak-particle dynamics-based simulated annealing was combined with the Hungarian algorithm for local optimization, and a residue-based score was introduced to distinguish between reliable assignments and “unassigned” resonances for which no reliable assignment can be established. The DYNASSIGN algorithm was implemented in the program CYANA and tested with data sets obtained from the experimental NMR data of nine small proteins. With a set of 10 commonly used NMR spectra, on average 82.5% of all backbone and side-chain ¹H, ¹³C and ¹⁵N resonances could be assigned with an average error rate of 3.5%.     

Hydrophobic folding units at protein-protein interfaces: implications to protein folding and to protein-protein association.

A hydrophobic folding unit cutting algorithm, originally developed for dissecting single-chain proteins, has been applied to a dataset of dissimilar two-chain protein-protein interfaces. Rather than consider each individual chain separately, the two-chain complex has been treated as a single chain. The two-chain parsing results presented in this work show hydrophobicity to be a critical attribute of two-state versus three-state protein-protein complexes. The hydrophobic folding units at the interfaces of two-state complexes suggest that the cooperative nature of the two-chain protein folding is the outcome of the hydrophobic effect, similar to its being the driving force in a single-chain folding. In analogy to the protein-folding process, the two-chain, two-state model complex may correspond to the formation of compact, hydrophobic nuclei. On the other hand, the three-state model complex involves binding of already folded monomers, similar to the association of the hydrophobic folding units within a single chain. The similarity between folding entities in protein cores and in two-state protein-protein interfaces, despite the absence of some chain connectivities in the latter, indicates that chain linkage does not necessarily affect the native conformation. This further substantiates the notion that tertiary, non-local interactions play a critical role in protein folding. These compact, hydrophobic, two-chain folding units, derived from structurally dissimilar protein-protein interfaces, provide a rich set of data useful in investigations of the role played by chain connectivity and by tertiary interactions in studies of binding and of folding. Since they are composed of non-contiguous pieces of protein backbones, they may also aid in defining folding nuclei.     

Parallel tempering simulations of HP-36

We report results from all-atom Monte Carlo simulations of the 36-residue villin headpiece subdomain HP-36. Protein-solvent interactions are approximated by an implicit solvent model. The parallel tempering is used to overcome the problem of slow convergence in low-temperature protein simulations. Our results show that this technique allows one to sample native-like structures of small proteins and points out the need for improved energy functions.     

Dynamics and cooperativity of Trp-cage folding

In this study, multiple independent molecular dynamics (MD) simulations on Trp-cage folding were performed at 300, 325 and 375 K using generalized Born (GB) implicit solvent model. The orientational movement of the side-chain of Trp6 to form a hydrophobic core with 3₁₀-helix was observed. The breaking/formation of a salt bridge between Asp9 and Arg16 was proposed to be the prerequisite for Trp-cage folding/refolding. Our results demonstrate that the cooperation between the salt bridge and the Trp6 orientation leads to a stable tertiary structure of Trp-cage. Analyses on backbone concerted motions at different temperatures indicate that interactions between Trp6 and 3₁₀-helix & Pro18 and between Pro12 and Pro17 & Pro18 are weakened at 375 K but strengthened at lower temperatures, suggesting that they could be the potential driving force of hydrophobic collapse.     

Extending the folding nucleus of ubiquitin with an independently folding beta-hairpin finger: hurdles to rapid folding arising from the stabilisation of local interactions

The N-terminal beta-hairpin sequence of ubiquitin has been implicated as a folding nucleation site. To extend and stabilise the ubiquitin folding nucleus, we have inserted an autonomously folding 14-residue peptide sequence beta4 which in isolation forms a highly populated beta-hairpin (>70%) stabilised by local interactions. NMR structural analysis of the ubiquitin mutant (Ubeta4) shows that the hairpin finger is fully structured and stabilises ubiquitin by approximately 8kJmol(-1). Protein engineering and kinetic (phi(F)-value) analysis of a series of Ubeta4 mutants shows that the hairpin extension of Ubeta4 is also significantly populated in the transition state (phi(F)-values >0.7) and has the effect of templating the formation of native contacts in the folding nucleus of ubiquitin. However, at low denaturant concentrations the chevron plot of Ubeta4 shows a small deviation from linearity (roll-over effect), indicative of the population of a compact collapsed state, which appears to arise from over-stabilisation of local interactions. Destabilising mutations within the native hairpin sequence and within the engineered hairpin extension, but not elsewhere, eliminate this non-linearity and restore apparent two-state behaviour. The pitfall to stabilising local interactions is to present hurdles to the rapid and efficient folding of small proteins down a smooth folding funnel by trapping partially folded or misfolded states that must unfold or rearrange before refolding.