Protonation/deprotonation effects on the stability of the Trp-cage miniprotein

The Trp-cage miniprotein is a 20 amino acid peptide that exhibits many of the properties of globular proteins. In this protein, the hydrophobic core is formed by a buried Trp side chain. The folded state is stabilized by an ion pair between aspartic acid and an arginine side chain. The effect of protonating the aspartic acid on the Trp-cage miniprotein folding/unfolding equilibrium is studied by explicit solvent molecular dynamics simulations of the protein in the charged and protonated Asp9 states. Unbiased Replica Exchange Molecular Dynamics (REMD) simulations, spanning a wide temperature range, are carried out to the microsecond time scale, using the AMBER99SB forcefield in explicit TIP3P water. The protein structural ensembles are studied in terms of various order parameters that differentiate the folded and unfolded states. We observe that in the folded state the root mean square distance (rmsd) from the backbone of the NMR structure shows two highly populated basins close to the native state with peaks at 0.06 nm and 0.16 nm, which are consistent with previous simulations using the same forcefield. The fraction of folded replicas shows a drastic decrease because of the absence of the salt bridge. However, significant populations of conformations with the arginine side chain exposed to the solvent, but within the folded basin, are found. This shows the possibility to reach the folded state without formation of the ion pair. We also characterize changes in the unfolded state. The equilibrium populations of the folded and unfolded states are used to characterize the thermodynamics of the system. We find that the change in free energy difference due to the protonation of the Asp amino acid is 3 kJ mol(-1) at 297 K, favoring the charged state, and resulting in ΔpK(1) = 0.5 units for Asp9. We also study the differences in the unfolded state ensembles for the two charge states and find significant changes at low temperature, where the protonated Asp side chain makes multiple hydrogen bonds to the protein backbone.     

Reversible folding simulation by hybrid Hamiltonian replica exchange

Reversible foldings of a beta-hairpin peptide, chignolin, by recently invented hybrid Hamiltonian replica exchange molecular dynamics simulations based on Poisson-Boltzmann model in explicit water are demonstrated. Initiated from extended structures the peptide folded and unfolded a couple of times in seven out of eight replica trajectories during 100 nanoseconds simulation. The folded states have the lowest all-atom root mean squared deviation of 1.3 A with respect to the NMR structures. At T=300 K the occurrence of folded states was converged to 62% during 80 ns simulation which agrees well with experimental data. Especially, a detailed structural evolution map was constructed based on 800,000 structural snapshots and from where a unique folding doorway emerges. Compared with 130 ns standard replica exchange simulation using 24 replicas on the same system, the hybrid Hamiltonian replica exchange molecular dynamics simulation presents consistent results.     

Exploration of the secondary structure specific differential solvation dynamics between the native and molten globule states of the protein HP-36

Recent experiments have shown that the time dependence of fluorescence Stokes shift of a chromophore is substantially different when the chromophore is located in a molten globule (MG) state and in the native state of the same protein. To understand the origin of this difference, particularly the role of water in the differential solvation of the protein in the native and the MG states, we have carried out fully atomistic molecular dynamics simulations with explicit water of a partially unfolded MG state of the protein HP-36 and compared the results with the solvation dynamics of the protein in the folded native state. It is observed that the polar solvation dynamics of the three helical segments of the protein is influenced in a nonuniform heterogeneous manner in the MG state. While the equilibrium solvation time correlation function for helix-3 has been found to relax faster in the MG state as compared to that in the native state, the decay of the corresponding function for the other two helices slows down in the MG state. A careful analysis shows that the origin of such heterogeneous relative solvation behavior lies in the differential location of the polar probe residues and their exposure to bulk solvent. We find a significant negative cross-correlation between the contribution (to the solvation energy of a tagged amino acid residue) of water and the other groups of the protein, indicating a competing role in solvation. The sensitivity of solvation dynamics to the secondary structure and the immediate environment can be used to discriminate the partially unfolded and folded states. These results therefore should be useful in explaining recent solvation dynamics experiments on native and MG states of proteins.     

Numerical Simulation of the Pressure Denaturation of a Helical β‐Peptide Heptamer Solvated in Methanol

The effect of elevated pressure on the conformational behavior of a β‐peptide heptamer ( 1 ) in MeOH solution was considered. The response of the peptide to elevated pressure was probed by means of molecular dynamics (MD) simulations, and described in atomic terms. The most‐striking features of the response are that the region of the ‘unfolded’ state of the peptide accessible at elevated pressure is narrow, and that thermal and pressure denaturation produce similar ‘unfolded’ states in the case of 1 .     

Folding of the 25 residue Abeta(12-36) peptide in TFE/water: temperature-dependent transition from a funneled free-energy landscape to a rugged one

The free-energy landscape of the Alzheimer beta-amyloid peptide Abeta(12-36) in a 40% (v/v) 2,2,2-trifluoroethanol (TFE)/water solution was determined by using multicanonical molecular dynamics simulations. Simulations using this enhanced conformational sampling technique were initiated from a random unfolded polypeptide conformation. Our simulations reliably folded the peptide to the experimental NMR structure, which consists of two linked helices. The shape of the free energy landscape for folding was found to be strongly dependent on temperature: Above 325 K, the overall shape was funnel-like, with the bottom of the funnel coinciding exactly with the NMR structure. Below 325 K, on the other hand, the landscape became increasingly rugged, with the emergence of new conformational clusters connected by low free-energy pathways. Finally, our simulations reveal that water and TFE solvate the polypeptide in different ways: The hydrogen bond formation between TFE and Abeta was enhanced with decreasing temperature, while that between water and Abeta was depressed.     

Insights into the dynamics of HIV-1 protease: a kinetic network model constructed from atomistic simulations

The conformational dynamics in the flaps of HIV-1 protease plays a crucial role in the mechanism of substrate binding. We develop a kinetic network model, constructed from detailed atomistic simulations, to determine the kinetic mechanisms of the conformational transitions in HIV-1 PR. To overcome the time scale limitation of conventional molecular dynamics (MD) simulations, our method combines replica exchange MD with transition path theory (TPT) to study the diversity and temperature dependence of the pathways connecting functionally important states of the protease. At low temperatures the large-scale flap opening is dominated by a small number of paths; at elevated temperatures the transition occurs through many structurally heterogeneous routes. The expanded conformation in the crystal structure 1TW7 is found to closely mimic a key intermediate in the flap-opening pathways at low temperature. We investigated the different transition mechanisms between the semi-open and closed forms. The calculated relaxation times reveal fast semi-open ? closed transitions, and infrequently the flaps fully open. The ligand binding rate predicted from this kinetic model increases by 38-fold from 285 to 309 K, which is in general agreement with experiments. To our knowledge, this is the first application of a network model constructed from atomistic simulations together with TPT to analyze conformational changes between different functional states of a natively folded protein.     

Slow dynamics in folded and unfolded states of an SH3 domain.

(15)N relaxation dispersion experiments were applied to the isolated N-terminal SH3 domain of the Drosophila protein drk (drkN SH3) to study microsecond to second time scale exchange processes. The drkN SH3 domain exists in equilibrium between folded (F(exch)) and unfolded (U(exch)) states under nondenaturing conditions in a ratio of 2:1 at 20 degrees C, with an average exchange rate constant, k(ex), of 2.2 s(-1) (slow exchange on the NMR chemical shift time scale). Consequently a discrete set of resonances is observed for each state in NMR spectra. Within the U(exch) ensemble there is a contiguous stretch of residues undergoing conformational exchange on a micros/ms time scale, likely due to local, non-native hydrophobic collapse. For these residues both the F(exch) <--> U(exch) conformational exchange process and the micros/ms exchange event within the U(exch) state contribute to the (15)N line width and can be analyzed using CPMG-based (15)N relaxation dispersion measurements. The contribution of both processes to the apparent relaxation rate can be deconvoluted numerically by combining the experimental (15)N relaxation dispersion data with results from an (15)N longitudinal relaxation experiment that accurately quantifies exchange rates in slow exchanging systems (Farrow, N. A.; Zhang, O.; Forman-Kay, J. D.; Kay, L. E. J. Biomol. NMR 1994, 4, 727-734). A simple, generally applicable analytical expression for the dependence of the effective transverse relaxation rate constant on the pulse spacing in CPMG experiments has been derived for a two-state exchange process in the slow exchange limit, which can be used to fit the experimental data on the global folding/unfolding transition. The results illustrate that relaxation dispersion experiments provide an extremely sensitive tool to probe conformational exchange processes in unfolded states and to obtain information on the free energy landscape of such systems.     

Unfolding the conformational behavior of peptide dendrimers: insights from molecular dynamics simulations

We present here the first comprehensive structural characterization of peptide dendrimers using molecular simulation methods. Multiple long molecular dynamics simulations are used to extensively sample the conformational preferences of five third-generation peptide dendrimers, including some known to bind aquacobalamine. We start by analyzing the compactness of the conformations thus sampled using their radius of gyration profiles. A more detailed analysis is then performed using dissimilarity measures, principal coordinate analysis, and free energy landscapes, with the aim of identifying groups of similar conformations. The results point to a high conformational flexibility of these molecules, with no clear "folded state", although two markedly distinct behaviors were found: one of the dendrimers displayed mostly compact conformations clustered into distinct basins (rough landscape), while the remaining dendrimers displayed mainly noncompact conformations with no significant clustering (downhill landscape). This study brings new insight into the conformational behavior of peptide dendrimers and may provide better routes for their functional design. In particular, we propose a yet unsynthesized peptide dendrimer that might exhibit enhanced ability to coordinate aquocobalamin.     

Measuring pK(a) values in protein folding transition state ensembles by NMR spectroscopy

Protein folding kinetic data have been obtained for the marginally stable N-terminal SH3 domain of the Drosophila protein drk as a function of pH in order to investigate the electrostatic properties of Asp8 in the folding transition state ensemble. The slow exchange between folded and unfolded forms of the protein gives rise to separate NMR resonances for both folded and unfolded states at equilibrium. As a result, kinetic data can be derived from magnetization transfer between these two states without the need for denaturants. Using the fact that ionization of Asp8 dominates the electrostatic behavior of the protein between pH 2 and 3, along with pKa values for titrating groups in both folded and unfolded states that have been determined in a previous study, values of 2.9 +/- 0.1 and 3.3 +/- 0.2 are obtained for the pKa of Asp8 in the transition state for the wild-type protein and for a His7Ala mutant, respectively. The data are consistent with the partial formation in the transition state ensemble of an Asp8 side chain carboxylate-a Lys21 backbone amide interaction that represents a highly conserved contact in folded SH3 domains.     

Probing electrostatic interactions and structural changes in highly charged protein polyanions by conformer-selective photoelectron spectroscopy

We have recorded the first conformer-selective photoelectron spectra of a protein polyanion in the gas-phase. Bovine cytochrome c protein was studied in 8 different negative charge states ranging from 5- to 12-. Electron binding energies were extracted for all charge states and used as a direct probe of intramolecular Coulomb repulsion. Comparison of experimental results with simulations shows that the experimental outcome can be reproduced with a simple electrostatic model. Energetics are consistent with a structural transition from a folded to an unfolded conformational state of the protein as the number of charges increases. Furthermore, the additional ion-mobility data show that the onset of unfolding can be assigned to charge state 6- where three conformers can be distinguished.     

Ultrafast Heme Dynamics of Ferric Cytochrome c in Different Environments: Electronic,Vibrational, and Conformational Relaxation

The excited‐state dynamics of ferric cytochrome c (Cyt c), an important electron‐transfer heme protein, in acidic to alkaline medium and in its unfolded form are investigated by using femtosecond pump–probe spectroscopy, exciting the heme and Tryptophan (Trp) to understand the electronic, vibrational, and conformational relaxation of the heme. At 390 nm excitation, the electronic relaxation of heme is found to be ≈150 fs at different pH values, increasing to 480 fs in the unfolded form. Multistep vibrational relaxation dynamics of the heme, including fast and slow processes, are observed at pH 7. However, in the unfolded form and at pH 2 and 11, fast phases of vibrational relaxation dominate, revealing the energy dissipation occurring through the covalent bond interaction between the heme and the nearest amino acids. A significant shortening of the excited‐state lifetime of Trp is observed at various pH values at 280 nm excitation due to resonance energy transfer to the heme. The longer time constant (25 ps) observed in the unfolded form is attributed to a complete global conformational relaxation of Cyt c.     

Effects of solute-solvent proton exchange on polypeptide chain dynamics: a constant-pH molecular dynamics study

A method for performing implicit-solvent molecular dynamics simulations at constant pH was applied to a pentapeptide acetyl-Ala-Asp-Ala-Lys-Ala-amide at pH 4. As a reference, molecular dynamics simulations were done for the same peptide with two variants of its fixed protonation patterns expected to dominate at pH 4, i.e., with a protonated and a deprotonated side chain of the Asp residue and the protonated Lys residue in both cases. The dynamic trajectories of the peptide were used to discuss the problem of the significance of the solute-solvent proton exchange phenomena for the dynamics and structural distributions of the polypeptide chain. The Asp-Lys distance was used as a probe of the overall molecular structure of the investigated pentapeptide. To characterize the dynamics, distributions of the "waiting" times for a transition from a "short" distance conformation to a "long" distance conformation were constructed, based on the generated molecular dynamics trajectories. We show that the relaxation time for the transitions, derived from the constant-pH simulations, is very close to the relaxation time characterizing a permanently protonated molecule, although the average protonation probability of the short-distance conformation is close to zero. However, the distribution of the Asp-Lys distances obtained from constant-pH simulations cannot be reproduced as a linear combination of the distributions resulting from the simulations with fixed protonation states.     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Towards a Quantitative Understanding of Protein Hydration and Volumetric Properties

Herein, we probe by pressure perturbation calorimetry (PPC) the coefficient of thermal expansion, the volumetric and the hydration properties of variants of a hyperstable variant of staphylococcal nuclease (SNase), Δ+PHS. The temperature‐dependent volumetric properties of the folded and unfolded states of the wild‐type protein are calculated with previously published data. The present PPC results are used to interpret the volume diagram and expansivity at a molecular level. We conclude that the expansivity of the unfolded state is, to a first approximation, temperature independent, while that of the folded state decreases with increasing temperature. Our data suggest that at low temperature the defining contribution to ΔV comes mainly from excluded volume differences and ΔV for unfolding is negative. In contrast, at high temperatures, differential solvation due to the increased exposed surface area of the unfolded state and, in particular, its larger thermal volume linked to the increased conformational dynamics of the unfolded state ensemble takes over and ΔV for unfolding eventually becomes positive.     

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.     

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.     

Estimation of protein folding rate from Monte Carlo simulations and entropy capacity

The problem of protein self-organization is one of the most important problems of molecular biology nowadays. Despite the recent success in the understanding of general principles of protein folding, details of this process are yet to be elucidated. Moreover, the prediction of protein folding rates has its own practical value due to the fact that aggregation directly depends on the rate of protein folding. The time of folding has been calculated for 67 proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native states using a Monte Carlo model where each residue is considered to be either folded as in the native state or completely disordered. The times of folding for 67 proteins which reach the native state within the limit of 10(8) Monte Carlo steps are in a good correlation with the experimentally measured folding rate at the mid-transition point (the correlation coefficient is -0.82). Theoretical consideration of a capillarity model for the process of protein folding demonstrates that the difference in the folding rate for proteins sharing more spherical and less spherical folds is the result of differences in the conformational entropy due to a larger surface of the boundary between folded and unfolded phases in the transition state for proteins with more spherical fold. The capillarity model allows us to predict the folding rate at the same level of correlation as by Monte Carlo simulations. The calculated model entropy capacity (conformational entropy per residue divided by the average contact energy per residue) for 67 proteins correlates by about 78% with the experimentally measured folding rate at the mid-transition point.