Constant-pH molecular dynamics with ionic strength effects: protonation-conformation coupling in decalysine

A new implementation of the stochastic titration method for constant-pH molecular dynamics is presented, which introduces ionic strength effects in the simulations. In addition, the new implementation uses a faster molecular dynamics algorithm and an improved treatment of protonation events and of their effect on force field parameters. This new methodology is applied to a decalysine peptide, yielding very good quantitative agreement with experiments, both in terms of titration and helix-coil transition. The results show a significant dependence on ionic strength, illustrating the importance of including this parameter in constant-pH molecular dynamics simulations. Overall, the method seems to properly capture the protonation-conformation coupling and its dependence on ionic strength.     

Molecular simulation with variable protonation states at constant pH

A new method is presented for performing molecular simulations at constant pH. The method is a Monte Carlo procedure where trial moves consist of relatively short molecular dynamics trajectories, using a time-dependent potential energy that interpolates between the old and new protonation states. Conformations and protonation states are sampled from the correct statistical ensemble independent of the trial-move trajectory length, which may be adjusted to optimize efficiency. Because moves are not instantaneous, the method does not require the use of a continuum solvation model. It should also be useful in describing buried titratable groups that are not directly exposed to solvent, but have strong interactions with neighboring hydrogen bond partners. The feasibility of the method is demonstrated for a simple test case: constant-pH simulations of acetic acid in aqueous solution with an explicit representation of water molecules.     

Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics

pH is an important parameter in condensed-phase systems, because it determines the protonation state of titratable groups and thus influences the structure, dynamics, and function of molecules in solution. In most force field simulation protocols, however, the protonation state of a system (rather than its pH) is kept fixed and cannot adapt to changes of the local environment. Here, we present a method, implemented within the MD package GROMACS, for constant pH molecular dynamics simulations in explicit solvent that is based on the λ-dynamics approach. In the latter, the dynamics of the titration coordinate λ, which interpolates between the protonated and deprotonated states, is driven by generalized forces between the protonated and deprotonated states. The hydration free energy, as a function of pH, is included to facilitate constant pH simulations. The protonation states of titratable groups are allowed to change dynamically during a simulation, thus reproducing average protonation probabilities at a certain pH. The accuracy of the method is tested against titration curves of single amino acids and a dipeptide in explicit solvent.     

Theoretical Evidence for Temperature-induced Proton Mobility in Isolated Lysine-rich Polyalanines

A multistate molecular mechanics method is introduced to model the possible competition between various protonation sites in gas-phase biomolecules with excess protons. The method relies on the Amber force field for each site and is calibrated against density-functional theory benchmark calculations at the 6-31+G(d,p) level. In its adiabatic version, where it has similarities with constant-pH algorithms, the model predicts that the small protonated Ala(4)-Lys peptide, unprotected at the N-terminus, changes protonation site above 400 K. In the larger [Ala(9)-Lys+H ](+) peptide, the proton remains at the lysine amine group in a favored charge/electric dipole conformation. In the three-state Ala(4)-Lys-Ala(4)-Lys peptide, the excess proton is found to be partially delocalized on the amine group of the first lysine and on the N-terminus. The statistical properties of the protonated peptides are found to significantly depend on the localized character of the proton. Finally, the model is extended by considering possible couplings between the protonation sites, in an empirical valence-bond version. Strong couplings can stabilize the peptides into unexpected proton-bound conformations over broad ranges of temperature.     

Multiple protonation equilibria in electrostatics of protein-protein binding

All proteins contain groups capable of exchanging protons with their environment. We present here an approach, based on a rigorous thermodynamic cycle and the partition functions for energy levels characterizing protonation states of the associating proteins and their complex, to compute the electrostatic pH-dependent contribution to the free energy of protein-protein binding. The computed electrostatic binding free energies include the pH of the solution as the variable of state, mutual "polarization" of associating proteins reflected as changes in the distribution of their protonation states upon binding and fluctuations between available protonation states. The only fixed property of both proteins is the conformation; the structure of the monomers is kept in the same conformation as they have in the complex structure. As a reference, we use the electrostatic binding free energies obtained from the traditional Poisson-Boltzmann model, computed for a single macromolecular conformation fixed in a given protonation state, appropriate for given solution conditions. The new approach was tested for 12 protein-protein complexes. It is shown that explicit inclusion of protonation degrees of freedom might lead to a substantially different estimation of the electrostatic contribution to the binding free energy than that based on the traditional Poisson-Boltzmann model. This has important implications for the balancing of different contributions to the energetics of protein-protein binding and other related problems, for example, the choice of protein models for Brownian dynamics simulations of their association. Our procedure can be generalized to include conformational degrees of freedom by combining it with molecular dynamics simulations at constant pH. Unfortunately, in practice, a prohibitive factor is an enormous requirement for computer time and power. However, there may be some hope for solving this problem by combining existing constant pH molecular dynamics algorithms with so-called accelerated molecular dynamics algorithms.     

A molecular dynamics study of Lys-Trp-Lys: structure and dynamics in solution following photoexcitation

We report studies of the structure and dynamics of a tripeptide Lys-Trp-Lys (KWK) in aqueous solution following photoexcitation by molecular dynamics simulations. For ground-state KWK, we observe three stable conformations with free energy differences of less than 5.2 kJ/mol. Each conformer is stabilized by a pi-cation interaction between one of three protonated amino groups and the indole moiety. For the excited state of tryptophan in KWK, the simulated molecular dynamics of the three isomers are similar, all in good agreement with recent femtosecond experiments (J. Phys. Chem. B 2005, 109, 16901). Specifically, we observe: (1) the fluorescence anisotropy is dominated by a single-exponential component and decays in approximately 130 ps, (2) the total dynamic Stokes shift reaches approximately 2700 cm(-1), and (3) the excited state relaxation dynamics occurs on several time scales ranging from femtoseconds to tens of picoseconds. The relaxation dynamics involve rapid initial response of neighboring water, followed by local motions of flexible peptide chains. These processes drive global restructuring of the tripeptide on a rather flat energy surface, inducing slower dynamics evident in both the water and protein contributions to the stabilization energy of the photoexcited chromophore. The water and protein dynamics are strongly correlated. On a still longer time scale, we observe isomerization of two excited state conformers to the other most stable one, an analogue for evolution of trajectories along the funnel on the rugged free energy landscape to the final "native" state. Our studies suggest new experiments to detect this unique dynamics.     

Molecular dynamics simulations of porphyrin-dendrimer systems: toward modeling electron transfer in solution

We have performed computational simulations of porphyrin-dendrimer systems--a cationic porphyrin electrostatically associated to a negatively charged dendrimer--using the method of classical molecular dynamics (MD) with an atomistic force field. Previous experimental studies have shown a strong quenching effect of the porphyrin fluorescence that was assigned to electron transfer (ET) from the dendrimer's tertiary amines (Paulo, P. M. R.; Costa, S. M. B. J. Phys. Chem. B 2005, 109, 13928). In the present contribution, we evaluate computationally the role of the porphyrin-dendrimer conformation in the development of a statistical distribution of ET rates through its dependence on the donor-acceptor distance. We started from simulations without explicit solvent to obtain trajectories of the donor-acceptor distance and the respective time-averaged distributions for two dendrimer sizes and different initial configurations of the porphyrin-dendrimer pair. By introducing explicit solvent (water) in our simulations, we were able to estimate the reorganization energy of the medium for the systems with the dendrimer of smaller size. The values obtained are in the range 0.6-1.5 eV and show a linear dependence with the inverse of the donor-acceptor distance, which can be explained by a two-phase dielectric continuum model taking into account the medium heterogeneity provided by the dendrimer organic core. Dielectric relaxation accompanying ET was evaluated from the simulations with explicit solvent showing fast decay times of some tens of femtoseconds and slow decay times in the range of hundreds of femtoseconds to a few picoseconds. The variations of the slow relaxation times reflect the heterogeneity of the dendrimer donor sites which add to the complexity of ET kinetics as inferred from the experimental fluorescence decays.     

Resonant infrared multiphoton dissociation spectroscopy of gas-phase protonated peptides. Experiments and Car-Parrinello dynamics at 300 K

The gas-phase structures of protonated peptides are studied by means of resonant infrared multiphoton dissociation spectroscopy (R-IRMPD) performed with a free electron laser. The peptide structures and protonation sites are obtained through comparison between experimental IR spectra and their prediction from quantum chemistry calculations. Two different analyses are conducted. It is first supposed that only well-defined conformations, sufficiently populated according to a Boltzmann distribution, contribute to the observed spectra. On the contrary, DFT-based Car-Parrinello molecular dynamics simulations show that at 300 K protonated peptides no longer possess well-defined structures, but rather dynamically explore the set of conformations considered in the first conventional approach.     

Reaction mechanism of soluble epoxide hydrolase: insights from molecular dynamics simulations

Molecular dynamics simulations have been performed to gain insights into the catalytic mechanism of the hydrolysis of epoxides to vicinal diols by soluble epoxide hydrolase (sEH). The binding of a substrate, 1S,2S-trans-methylstyrene oxide, was studied in two conformations in the active site of the enzyme. It was found that only one is likely to be found in the active enzyme. In the preferred conformation the phenyl group of the substrate is pi-sandwiched between two aromatic residues, Tyr381 and His523, whereas the other conformation is pi-stacked with only one aromatic residue, Trp334. Two simulations were carried out to 1 ns for each conformation to evaluate the protonation state of active site residue His523. It was found that a protonated histidine is essential for keeping the active site from being disrupted. Long time scale, 4 ns, molecular dynamics simulation was done for the structure with the most likely combination of binding conformation and protonation state of His523. Near Attack Conformers (NACs) are present 5.3% of the time and nucleophilic attack on either epoxide carbon atom, approximately 75% on C(1) and approximately 25% on C(2), is found. A maximum of one hydrogen bond between the epoxide oxygen and either of the active site tyrosines, Tyr465 and Tyr381, is present, in agreement with experimental mutagenesis results that reveal a slight loss in activity if one tyrosine is mutated and essential loss of all activity upon double mutation of the two tyrosines in question. It was found that a hydrogen bond from Tyr465 to the substrate oxygen is essential for controlling the regioselectivity of the reaction. Furthermore, a relationship between the presence of this hydrogen bond and the separation of reactants was found. Two groups of amino acid segments were identified each as moving collectively. Furthermore, an overall anti-correlation was found between the movements of these two individually collectively moving groups, made up by parts of the cap-region, including the two tyrosines, and the site of the catalytic triad, respectively. This overall anti-correlated collective domain motion is, perhaps, involved in the conversion of E.NAC to E.TS.     

Structure and dynamics of orientational defects in ice I

Orientational defects in hexagonal ice were investigated using molecular dynamics simulations. Energy relaxation during L- and D-defect migration was shown to be associated with improved alignment of water molecules along the local electric fields. Two new forms of defects, an "L+D complex," and a "5+7 defect," were characterized. These forms appear in ice trajectories close to the melting point, and in the course of L- and D-pair recombination process. Defect pair recombination was shown to be a complex process, involving collective H-bond changes in groups of molecules.     

Constant pH molecular dynamics in generalized Born implicit solvent

A new method is proposed for constant pH molecular dynamics (MD), employing generalized Born (GB) electrostatics. Protonation states are modeled with different charge sets, and titrating residues sample a Boltzmann distribution of protonation states as the simulation progresses, using Monte Carlo sampling based on GB-derived energies. The method is applied to four different crystal structures of hen egg-white lysozyme (HEWL). pK(a) predictions derived from the simulations have root-mean-square (RMS) error of 0.82 relative to experimental values. Similarity of results between the four crystal structures shows the method to be independent of starting crystal structure; this is in contrast to most electrostatics-only models. A strong correlation between conformation and protonation state is noted and quantitatively analyzed, emphasizing the importance of sampling protonation states in conjunction with dynamics.     

Conformational preference and potential templates of N-methylated cyclic pentaalanine peptides

Systematic N-methylation of all peptide bonds in the cyclic pentapeptide cyclo(-D-Ala-Ala(4)-) has been performed yielding 30 different N-methylated derivatives, of which only seven displayed a single conformation on the NMR time scale. The conformation of these differentially N-methylated peptides was recently reported by us (J. Am. Chem. Soc. 2006, 128, 15 164-15 172). Here we present the conformational characterization of nine additional N-methylated peptides from the previous library which are not homogeneous but exist as a mixture in which at least one conformation is preferred by over 80 %. The structures of these peptides are investigated employing various 2D-NMR techniques, distance geometry calculations and further refined by molecular dynamics simulations in explicit DMSO. The comparison of the conformation of these nine peptides and the seven conformationally homogeneous peptides allow us to draw conclusions regarding the influence of N-methylation on the peptide backbone of cyclic pentapeptide of the class cyclo(-D-Ala-Ala(4)-). Here we present the different conformational classes of the peptides arising from the definitive pattern of N-methylation which can eventually serve as templates for the design of bioactive peptides.     

Dielectric relaxation of aqueous solutions of hydrophilic versus amphiphilic peptides

We report on molecular dynamics simulations of the frequency-dependent dielectric relaxation spectra at room temperature for aqueous solutions of a hydrophilic peptide and an amphiphilic peptide at two concentrations. We find that only the high-concentration amphiphilic peptide solution exhibits an anomalous dielectric increment over that of pure water, while the hydrophilic peptide exhibits a significant dielectric decrement. The dielectric component analysis carried out by decomposing these peptide solutions into peptide, hydration layer, and outer layer(s) of water clearly shows the presence of a unique dipolar component with a relaxation time scale on the order of approximately 25 ps (compared to the bulk water time scale of approximately 11 ps) that originates from the interaction between the hydration layer water and the outer layer(s) of water. Results obtained from the dielectric component analysis further show the emergence of a distinct and much lower frequency relaxation process for the high-concentration amphiphilic peptide compared to the hydrophilic peptide due to strong peptide dipolar couplings to all constituents, accompanied by a slowing of the structural relaxation in all water layers, giving rise to time scales close to approximately 1 ns. We suggest that the molecular origin of the dielectric relaxation anomalies is due to frustration in the water network arising from the amphiphilic chemistry of the peptide that does not allow it to reorient on the picosecond time scale of bulk water motions. This explanation is consistent with the idea of the "slaving" of residue side chain motions to protein surface water, and furthermore offers the possibility that the anomalous dynamics observed from a number of spectroscopies arises at the interface of hydrophobic and hydrophilic domains on the protein surface.     

Use of molecular dynamics in the design and structure determination of a photoinducible beta-hairpin

The study presented here consists of three parts. In the first, the ability of a set of differently substituted diazobenzene-based linkers to act as photoswitchable beta-turn building blocks was assessed. A 12-residue peptide known to form beta-hairpins was taken as the basis for the modeling process. The central (beta-turn) residue pair was successively replaced by six symmetrically ((o,o), (m,m), or (p,p)) substituted (aminomethyl/carboxymethyl or aminoethyl/carboxyethyl) diazobenzene derivatives leading to a set of peptides with a photoswitchable backbone conformation. The folding behavior of each peptide was then investigated by performing molecular dynamics simulations in water (4 ns) and in methanol (10 ns) at room temperature. The simulations suggest that (o,o)- and (m,m)-substituted linkers with a single methylene spacer are significantly better suited to act as photoswitchable beta-turn building blocks than the other linkers examined in this study. The peptide containing the (m,m)-substituted linker was synthesized and characterized by NMR in its cis configuration. In the second part of this study, the structure of this peptide was refined using explicit-solvent simulations and NOE distance restraints, employing a variety of refinement protocols (instantaneous and time-averaged restraining as well as unrestrained simulations). We show that for this type of systems, even short simulations provide a significant improvement in our understanding of their structure if physically meaningful force fields are employed. In the third part, unrestrained explicit-solvent simulations starting from either the NMR model structure (75 ns) or a fully extended structure (25 ns) are shown to converge to a stable beta-hairpin. The resulting ensemble is in good agreement with experimental data, indicating successful structure prediction of the investigated hairpin by classical explicit-solvent molecular dynamics simulations.     

Helix formation in a pentapeptide: experiment and force-field dependent dynamics

We used a combined approach of experiment and simulation to determine the helical population and folding pathway of a small helix forming blocked pentapeptide, Ac-(Ala)(5)-NH(2). Experimental structural characterization of this blocked peptide was carried out with far UV circular dichroism spectroscopy, FTIR, and NMR measurements. These measurements confirm the presence of the α-helical state in a buffer solution. Direct molecular dynamics and replica-exchange simulations of the pentapeptide were performed using several popular force fields with explicit solvent. The simulations yielded statistically reliable estimates of helix populations, melting curves, folding, and nucleation times. The distributions of conformer populations are used to measure folding cooperativity. Finally, a statistical analysis of the sample of helix-coil transition paths was performed. The details of the calculated helix populations, folding kinetics and pathways vary with the employed force field. Interestingly, the helix populations, folding, and unfolding times obtained from most of the studied force fields are in qualitative agreement with each other and with available experimental data, with the deviations corresponding to several kcal/mol in energy at 300 K. Most of the force fields also predict qualitatively similar transition paths, with unfolding initiated at the C-terminus. Accuracy of potential energy parameters, rather than conformational sampling may be the limiting factor in current molecular simulations.     

Direct observations of conformational distributions of intrinsically disordered p53 peptides using UV Raman and explicit solvent simulations

We report the first experimental measurements of Ramachandran Ψ-angle distributions for intrinsically disordered peptides: the N-terminal peptide fragment of tumor suppressor p53 and its P27S mutant form. To provide atomically detailed views of the conformational distributions, we performed classical, explicit-solvent molecular dynamics simulations on the microsecond time scale. Upon binding its partner protein, MDM2, wild-type p53 peptide adopts an α-helical conformation. Mutation of Pro27 to serine results in the highest affinity yet observed for MDM2-binding of the p53 peptide. Both UV resonance Raman spectroscopy (UVRR) and simulations reveal that the P27S mutation decreases the extent of PPII helical content and increases the probability for conformations that are similar to the α-helical MDM2-bound conformation. In addition, UVRR measurements were performed on peptides that were isotopically labeled at the Leu26 residue preceding the Pro27 in order to determine the conformational distributions of Leu26 in the wild-type and mutant peptides. The UVRR and simulation results are in quantitative agreement in terms of the change in the population of non-PPII conformations involving Leu26 upon mutation of Pro27 to serine. Finally, our simulations reveal that the MDM2-bound conformation of the peptide is significantly populated in both the wild-type and mutant isolated peptide ensembles in their unbound states, suggesting that MDM2 binding of the p53 peptides may involve conformational selection.     

Alamethicin channels in a membrane: molecular dynamics simulations

Alamethicin (Alm) is a 20 residue peptide which forms a kinked alpha-helix in membrane and membrane-mimetic environments. Ion channels formed by intramembraneous aggregates of Alm are thought to be formed by bundles of approximately parallel Alm helices surrounding a central bilayer pore. Different channel conductance levels correspond to different numbers of helices per bundle, ranging from N = 5 to N > 8. Calculation of the predicted pKA values of the ring of Glu18 sidechains at the C-terminal mouth of the pore suggests that at neutral pH most or all of these sidechains will remain protonated. Nanosecond molecular dynamics (MD) simulations of N = 5, 6, 7 and 8 bundles of Alm helices in a POPC bilayer have been run, corresponding to a total simulation time of 4 ns. These simulations explore the stability and conformational dynamics of these helix bundle channels when embedded in a full phospholipid bilayer in an aqueous environment. The structural and dynamic properties of water in these model channels are examined. As in earlier in vacuo simulations (J. Breed, R. Sankararamakrishnan, I. D. Kerr and M. S. P. Sansom, Biophys. J., 1996, 70, 1643) the dipole moments of water molecules within the pores are aligned antiparallel to the helix dipoles. This helps to contribute to the stability of the helix bundles.