Conformational equilibria of valine studied by dynamics simulation.

The conformational probability distribution of a valine residue in the valine dipeptide and of the valine side chain in an alpha-helix, as well as the change in helix stability for replacing alanine with valine, has been calculated by molecular dynamics simulations of explicitly hydrated systems: dipeptide, tetrapeptide and 10-, 14- and 18-residue oligoalanine helices. All computed free-energy differences are means from at least eight separate slow-growth simulations, four in each direction and are reported with their root-mean-square deviations. Different values for the change in free energy of folding (delta delta G degrees) have been calculated with the use of forcefields having an all-atom and a central-atom representation of methyl groups, etc. The value obtained with the all-atom forcefield agrees well with new experimental values (3 kJ/mol = 0.7 kcal/mol). Furthermore, the most stable valine side-chain rotamer in the helix is different for these two representations. The most stable rotamer for the all atom conformation is the same one that predominates for valines in alpha-helices in proteins of known conformation. The lower conformational freedom of the valine side chain in the helix contributes 1 kJ/mol to the difference in stability computed with the all-atom potential; unfavorable interactions of the side chain with helix, even in the most stable conformation, further increase delta delta G degrees.     

Role of water on unfolding kinetics of helical peptides studied by molecular dynamics simulations

Molecular dynamics simulations have been carried out with four polypeptides, Ala13, Val(13), Ser13, and Ala4Gly5Ala4, in vacuo and with explicit hydration. The unfolding of the polypeptides, which are initially fully alpha-helix in conformation, has been monitored during trajectories of 0.3 ns at 350 K. A rank of Ala < Val < Ser < Gly is found in the order of increasing rate of unwinding. The unfolding of Ala13 and Val(13) is completed in hundreds of picoseconds, while that of Ser13 is about one order of magnitude faster. The helix content of the peptide containing glycine residues falls to zero within a few picoseconds. Ramachandran plots indicate quite distinct equilibrium distributions and time evolution of dihedral angles in water and in vacuum for each residue type. The unfolding of polyalanine and polyvaline helices is accelerated due to solvation. In contrast, polyserine is more stable in water compared to vacuum, because its side chains can form intramolecular hydrogen bonds with the backbone more readily in vacuum, which disrupts the helix. Distribution functions of the spatial and angular position of water molecules in the proximity of the polypeptide backbone polar groups reveal the stabilization of the coiled structures by hydration. The transition from helix to coil is characterized by the appearance of a new peak in the probability distribution at a specific location characteristic of hydrogen bond formation between water and backbone polar groups. No significant insertion of water molecules is observed at the precise onset of unwinding, while (i, i+3) hydrogen bond formation is frequently detected at the initiation of alpha-helix unwinding.     

Comparison of simulated and experimentally determined dynamics for a variant of the Lacl DNA-binding domain, Nlac-P.

Recent advances in the experimentally determined structures and dynamics of the domains within LacI provide a rare context for evaluating dynamics calculations. A 1500-ps trajectory was simulated for a variant of the LacI DNA-binding domain, which consists of the first three helices in LacI and the hinge helix of the homologous PurR. Order parameters derived from dynamics simulations are compared to those obtained for the LacI DNA-binding domain with 15N relaxation NMR spectroscopy (Slijper et al., 1997. Biochemistry. 36:249-254). The MD simulations suggest that the unstructured loop between helices II and III does not exist in a discrete state under the conditions of no salt and neutral pH, but occupies a continuum of states between the DNA-bound and free structures. Simulations also indicate that the unstructured region between helix III and the hinge helix is very mobile, rendering motions of the hinge helix essentially independent of the rest of the protein. Finally, the alpha-helical hydrogen bonds in the hinge helix are broken after 1250 ps, perhaps as a prelude to helix unfolding.     

Self‐guided Langevin dynamics study of regulatory interactions in NtrC

Multiple self‐guided Langevin dynamics (SGLD) simulations were performed to examine structural and dynamical properties of the receiver domain of nitrogen regulatory protein C (NtrC^r). SGLD and MD simulations of the phosphorylated active form structure suggest a mostly stable but broad structural ensemble of this protein. The finite difference Poisson–Boltzmann calculations of the pK_a values of the active site residues suggest an increase in the pK_a of His‐84 on phosphorylation of Asp‐54. In SGLD simulations of the phosphorylated active form with charged His‐84, the average position of the regulatory helix α4 is found closer to the starting structure than in simulations with the neutral His‐84. To model the transition pathway, the phosphate group was removed from the simulations. After 7 ns of simulations, the regulatory helix α4 was found approximately halfway between positions in the NMR structures of the active and inactive forms. Removal of the phosphate group stimulated loss of helix α4, suggesting that the pathway of conformational transition may involve partial unfolding mechanism. The study illustrates the potential utility of the SGLD method in studies of the coupling between ligand binding and conformational transitions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Modifying oligoalanine conformation by replacement of amide to ester linkage

Oligo(lactic acid) is an ester‐analogue of short oligoalanine sequence and adopts a rigid left‐handed helical structure. In this study, oligo(lactic acid) was incorporated into oligoalanine sequences and their conformations were studied by vibrational circular dichroism and electronic circular dichroism spectroscopy. The results suggested that oligo(lactic acid) moiety in these sequences maintains a left‐handed helix and increases the conformational propensity of the oligoalanine moiety to form a left‐handed polyproline type II‐like helix. The importance of the chirality of oligo(lactic acid) moiety for the oligoalanine conformation was also studied. The results obtained in this study should be useful in developing ester‐containing oligopeptides that function better than normal peptides.     

Residue specific resolution of protein folding dynamics using isotope-edited infrared temperature jump spectroscopy

A major difficulty in experimental studies of protein folding is the lack of nonperturbing, residue specific probes of folding. Here, we demonstrate the ability to resolve protein folding dynamics at the level of a single residue using 13C=18O isotope-edited infrared spectroscopy. A single 13C=18O isotopic label was incorporated into the backbone of the 36 residue, three-helix bundle villin headpiece subdomain (HP36). The label was placed in a solvent protected region of the second alpha-helix of the protein. The 13C=18O isotopic label shifted the carbonyl stretching frequency to 1572.1 cm-1 in the folded state, well removed from the 12C=16O band of the unlabeled protein backbone. The unique IR signature of the 13C=18O label was exploited to probe the equilibrium thermal unfolding transition using temperature-dependent FTIR spectroscopy. The folding/unfolding dynamics were monitored using temperature-jump (T-jump) IR spectroscopy. The equilibrium unfolding studies showed conformational changes suggestive of a loss of helical structure in helix 2 prior to the global unfolding of the protein. T-jump relaxation kinetics probing both the labeled site and the 12C=16O band were found to be biphasic with similar relaxation rates. The slow relaxation phase (approximately 2 x 10(5) s-1) corresponds to the global folding transition. The location of the label, a buried position in helix 2, provides an important probe of the origin of the fast relaxation phase (approximately 10(7) s-1). This phase has significant amplitude for the labeled position even though it is well protected from solvent in the folded structure. The fast phase likely represents a rapid pre-equilibrium that involves solvent penetration around the label and possible partial unfolding of helix 2 prior to the global unfolding transition. This work represents the first experimental study of ultrafast folding dynamics with residue specific resolution.     

Molecular dynamics simulation of transmembrane polypeptide orientational fluctuations

The orientation and motion of a model lysine-terminated transmembrane polypeptide were investigated by molecular dynamics simulation. Recent 2H NMR studies of synthetic polypeptides with deuterated alanine side chains suggest that such transmembrane polypeptides undergo fast, axially symmetric reorientation about the bilayer normal but have a preferred average azimuthal orientation about the helix axis. In this work, interactions that might contribute to this behavior were investigated in a simulated system consisting of 64 molecules of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and one alpha-helical polypeptide with the sequence acetyl-KK-(LA)11-KK-amide. In one simulation, initiated with the peptide oriented along the bilayer normal, the system was allowed to evolve for 8.5 ns at 1 atm of pressure and a temperature of 55 degrees C. A second simulation was initiated with the peptide orientation chosen to match a set of experimentally observed alanine methyl deuteron quadrupole splittings and allowed to proceed for 10 ns. Simulated alanine methyl group orientations were found to be inequivalent, a result that is consistent with 2H NMR observations of specifically labeled polypeptides in POPC bilayers. Helix tilt varied substantially over the durations of both simulations. In the first simulation, the peptide tended toward an orientation about the helix axis similar to that suggested by experiment. In the second simulation, orientation about the helix axis tended to return to this value after an excursion. These results provide some insight into how interactions at the bilayer surface can constrain reorientation about the helix axis while accommodating large changes in helix tilt.     

Cerebral aneurysm blood flow simulations are sensitive to basic solver settings

Computational modeling of peri-aneurysmal hemodynamics is typically carried out with commercial software without knowledge of the sensitivity of the model to variation in input values. For three aneurysm models, we carried out a formal sensitivity analysis and optimization strategy focused on variation in timestep duration and model residual error values and their impact on hemodynamic outputs. We examined the solution sensitivity to timestep sizes of 10⁻³ s, 10⁻⁴ s, and 10⁻⁵ s while using model residual error values of 10⁻⁴, 10⁻⁵, and 10⁻⁶ using ANSYS Fluent to observe compounding errors and to optimize solver settings for computational efficiency while preserving solution accuracy. Simulations were compared qualitatively and quantitatively against the most rigorous combination of timestep and residual parameters, 10⁻⁵ s and 10⁻⁶, respectively. A case using 10⁻⁴ s timesteps, with 10⁻⁵ residual errors proved to be a converged solution for all three models with mean velocity and WSS difference RMS errors less than <1% compared with baseline, and was computationally efficient with a simulation time of 62 h per cardiac cycle compared to 392 h for baseline for the model with the most complex flow simulation. The worst case of our analysis, using 10⁻³ s timesteps and 10⁻⁴ residual errors, was still able to predict the dominant vortex in the aneurysm, but its velocity and WSS RMS errors reached 20%. Even with an appealing simulation time of 11 h per cycle for the model with the most complex flow, the worst case analysis solution exhibited compounding errors from large timesteps and residual errors. To resolve time-dependent flow characteristics, CFD simulations of cerebral aneurysms require sufficiently small timestep size and residual error. Simulations with both insufficient timestep and residual resolution are vulnerable to compounding errors.     

Structure, dynamics, and elasticity of free 16s rRNA helix 44 studied by molecular dynamics simulations

Molecular dynamics (MD) simulations were employed to investigate the structure, dynamics, and local base-pair step deformability of the free 16S ribosomal helix 44 from Thermus thermophilus and of a canonical A-RNA double helix. While helix 44 is bent in the crystal structure of the small ribosomal subunit, the simulated helix 44 is intrinsically straight. It shows, however, substantial instantaneous bends that are isotropic. The spontaneous motions seen in simulations achieve large degrees of bending seen in the X-ray structure and would be entirely sufficient to allow the dynamics of the upper part of helix 44 evidenced by cryo-electron microscopic studies. Analysis of local base-pair step deformability reveals a patch of flexible steps in the upper part of helix 44 and in the area proximal to the bulge bases, suggesting that the upper part of helix 44 has enhanced flexibility. The simulations identify two conformational substates of the second bulge area (bottom part of the helix) with distinct base pairing. In agreement with nuclear magnetic resonance (NMR) and X-ray studies, a flipped out conformational substate of conserved 1492A is seen in the first bulge area. Molecular dynamics (MD) simulations reveal a number of reversible alpha-gamma backbone flips that correspond to transitions between two known A-RNA backbone families. The flipped substates do not cumulate along the trajectory and lead to a modest transient reduction of helical twist with no significant influence on the overall geometry of the duplexes. Despite their considerable flexibility, the simulated structures are very stable with no indication of substantial force field inaccuracies.     

Role of the C-terminal helix 9 in the stability and ligandin function of class alpha glutathione transferase A1-1

Helix 9 at the C-terminus of class alpha glutathione transferase (GST) polypeptides is a unique structural feature in the GST superfamily. It plays an important structural role in the catalytic cycle. Its contribution toward protein stability/folding as well as the binding of nonsubstrate ligands was investigated by protein engineering, conformational stability, enzyme activity, and ligand-binding methods. The helix9 sequence displays an unfavorable propensity toward helix formation, but tertiary interactions between the amphipathic helix and the GST seem to contribute sufficient stability to populate the helix on the surface of the protein. The helix's stability is enhanced further by the binding of ligands at the active site. The order of ligand-induced stabilization increases from H-site occupation, to G-site occupation, to the simultaneous occupation of H- and G-sites. Ligand-induced stabilization of helix9 reduces solvent accessible hydrophobic surface by facilitating firmer packing at the hydrophobic interface between helix and GST. This stabilized form exhibits enhanced affinity for the binding of nonsubstrate ligands to ligandin sites (i.e., noncatalytic binding sites). Although helix9 contributes very little toward the global stability of hGSTA1-1, its conformational dynamics have significant implications for the protein's equilibrium unfolding/refolding pathway and unfolding kinetics. Considering the high concentration of reduced glutathione in human cells (about 10 mM), the physiological form of hGSTA1-1 is most likely the thiol-complexed protein with a stabilized helix9. The C-terminus region (including helix9) of the class alpha polypeptide appears not to have been optimized for stability but rather for catalytic and ligandin function.     

Structure and dynamics of calcium-activated calmodulin in solution.

Two 4-ns molecular dynamics simulations of calcium loaded calmodulin in solution have been performed, using both standard nonbonded cutoffs and Ewald summation to treat electrostatic interactions. Our simulation results are generally consistent with solution experimental studies of calmodulin structure and dynamics, including NMR, cross-linking, fluorescence and x-ray scattering. The most interesting result of the molecular dynamics simulations is the detection of large-scale structural fluctuations of calmodulin in solution. The globular N- and C-terminal domains tend to move approximately like rigid bodies, with fluctuations of interdomain distances within a 7 A range and of interdomain angles by up to 60 deg. Essential dynamics analysis indicates that the three dominant types of motion involve bending of the central helix in two perpendicular planes and a twist in which the domains rotate in opposite directions around the central helix. In the more realistic Ewald trajectory the protein backbone remains mostly within a 2-3 A root-mean-square distance from the crystal structure, the secondary structure within the domains is conserved and middle part of the central helix becomes disordered. The central helix itself exhibits limited fluctuations, with its bend angle exploring the 0-50 degrees range and the end-to-end distance falling in 39-43 A. The results of the two simulations were similar in many respects. However, the cutoff trajectory exhibited a larger deviation from the crystal, loss of several helical hydrogen bonds in the N-terminal domain and lack of structural disorder in the central helix.     

Role of the helix capping in the stability of the mouse prion (180-213) segment: investigation through molecular dynamics simulations.

Molecular dynamics simulation of the 180-213 segment, forming the B and C helices in the mouse prion protein, and of three mutants, where the capping box residues or the hydrophobic staple motif residues were selectively mutated, have been carried out. The results indicate that the wild type segment is stable over all the trajectory, whilst the mutants display different degrees of destabilization. In detail mutation of Asp202 brings to a rapid unfolding of helix C likely because of the concomitant loss of a hydrogen bond and of a negative charge able to stabilize the dipole in the first turn of the helix. A lower destabilizing effect is observed upon mutation Thr199. On the other hand mutation of Phe198 and Val203, the hydrophobic staple residues, brings to an incorrect orientation of the first helix relative to the second one due to a weakening of the hydrophobic interaction. The results confirm the importance of the presence of both motifs for the structural integrity of the isolated fragment and suggest that these residues may have a main role in the structural transition observed in the inherited human prion diseases.     

Unfolding of alanine-based peptides using electron spin resonance distance measurements

We describe a scheme for tagging an alanine-based peptide with a Cu(II) and a nitroxide to measure unfolding transitions. The enhancement in longitudinal relaxation rate of the nitroxide due to the presence of Cu(II) was measured at physiological temperatures by pulsed electron spin resonance (ESR). The change in relaxation rate provided the average interspin distance between the Cu(II) and the nitroxide. Control experiments on a proline-based peptide verify the robustness of the method. The change in interspin distances with temperature for the alanine-based peptide is in accord with the change in helicity measured by circular dichroism. The data provide an opportunity to examine the unfolding process in polyalanine peptides. The distance in the folded state is in concordance with molecular dynamics. However, the ESR experiment measures an average distance of 17 A in the unfolded state, whereas molecular dynamics indicates a distance of 42 A if the unfolded geometry was a polyproline type II helix. Therefore, ESR demonstrates that the unfolded state of this alanine-based peptide is not an ideal extended polyproline type II helix.     

Molecular dynamics simulations of synthetic peptide folding

Because the time scale of protein folding is much greater than that of the widely used simulations of native structures, a detailed report of molecular dynamics simulations of folding has not been available. In this study, we Included the average solvent effect in the potential functions to simplify the calculation of the solvent effect and carried out long molecular dynamics simulations of the alanine-based synthetic peptides at 274 K. From either an extended or a randomly generated conformation, the simulations approached a helix-coil equilibrium in about 3 ns. The multiple minima problem did not prevent helix folding. The calculated helical ratio of Ac-AAQAAAAQAAAAQAAY-NH₂ was 47%, in good agreement with the circular dichroism measurement (about 50%). A helical segment with frayed ends was the most stable conformation, but the hydrophobic interaction favored the compact, distorted helix-turn-helix conformations. The transition between the two types of conformations occurred in a much larger time scale than helix propagation. The transient hydrogen bonds between the glutamine side chain and the backbone carbonyl group could reduce the free energy barrier of helix folding and unfolding. The substitution of a single alanine residue in the middle of the peptide with valine or glycine decreased the average helical ratio significantly, in agreement with experimental observations. © 1996 Wiley-Liss, Inc.     

Unfolding pathways of goat alpha-lactalbumin as revealed in multiple alignment of molecular dynamics trajectories

Molecular dynamics simulations of protein unfolding were performed at an elevated temperature for the authentic and recombinant forms of goat alpha-lactalbumin. Despite very similar three-dimensional structures, the two forms have significantly different unfolding rates due to an extra N-terminal methionine in the recombinant protein. To identify subtle differences between the two forms in the highly stochastic kinetics of unfolding, we classified the unfolding trajectories using the multiple alignment method based on the analogy between the biological sequences and the molecular dynamics trajectories. A dendrogram derived from the multiple trajectory alignment revealed a clear difference in the unfolding pathways of the authentic and recombinant proteins, i.e. the former reached the transition state in an all-or-none manner while the latter unfolded less cooperatively. It was also found in the classification that the two forms of the protein shared a common transition state structure, which was in excellent agreement with the transition state structure observed experimentally in the Phi-value analysis.     

Backbone relaxation coupled to the ionization of internal groups in proteins: a self-guided Langevin dynamics study

Pathways of structural relaxation triggered by ionization of internal groups in staphylococcal nuclease (SNase) were studied through multiple self-guided Langevin dynamics (SGLD) simulations. Circular dichroism, steady-state Trp fluorescence, and nuclear magnetic resonance spectroscopy have shown previously that variants of SNase with internal Glu, Asp, and Lys at positions 66 or 92, and Arg at position 66, exhibit local reorganization or global unfolding when the internal ionizable group is charged. Except for Arg-66, these internal ionizable groups have unusual pK_a values and are neutral at physiological pH. The structural trends observed in the simulations are in general agreement with experimental observations. The I92D variant, which unfolds globally upon ionization of Asp-92, in simulations often exhibits extensive hydration of the protein core, and sometimes also significant perturbations of the β-barrel. In the crystal structure of the V66R variant, the β1 strand from the β-barrel is domain-swapped; in the simulations, the β1 strand is sometimes partially released. The V66K variant, which in solutions shows reorganization of six residues at the C-terminus of helix α1 and perturbations in the β-barrel structure, exhibits fraying of three residues of helix α1 in one simulation, and perturbations and partial unfolding of three β-strands in a few other simulations. In sharp contrast, very small structural changes were observed in simulations of the wild-type protein. The simulations indicate that charging of internal groups frequently triggers penetration of water into the protein interior. The pK_a values of Asp-92 and Arg-66 calculated with continuum methods on SGLD-relaxed structures reached the normal values in most simulations. Detailed analysis of accuracy and performance of SGLD demonstrates that SGLD outperforms LD in sampling of alternative protein conformations without loss of the accuracy and level of detail characteristic of regular LD.     

Predicted unfolding order of the 13 alpha-helices in the catalytic domain of glucoamylase from Aspergillus awamori var. X100 by molecular dynamics simulations

The unfolding mechanism of the 13 alpha-helices in the catalytic domain of Aspergillus awamori var. X100 glucoamylase was investigated by 200 ps molecular dynamics simulations in explicit water with temperature jump technique. Rather than a simultaneous event, the unfolding of these 13 alpha-helices followed a random ordered mechanism as alpha8-->alpha1-->alpha11-->alpha7-->alpha10-->alpha3-->alpha12-->alpha13-->alpha4-->alpha5-->alpha9-->alpha6-->alpha2. No significant relationships were found between the unfolding order and the length and the hydrophobicity of the helix. alpha-Helix 8 located in the inner region of the catalytic domain was predicted to be the first helix to unfold, indicating that the destruction of the secondary structure motif was initiated from the inner region of the catalytic domain. The dynamic behavior of these alpha-helices induced by increased kinetic energy during the unfolding process is considered to be similar to the expansion and compression of a series of springs under the influence of mechanical stress.     

Brownian and essential dynamics studies of the HIV-1 integrase catalytic domain

The three-dimensional structure of the active site region of the enzyme HIV-1 integrase is not unambiguously known. This region includes a flexible peptide loop that cannot be well resolved in crystallographic determinations. Here we present two different computational approaches with different levels of resolution and on different time-scales to understand this flexibility and to analyze the dynamics of this part of the protein. We have used molecular dynamics simulations with an atomic model to simulate the region in a realistic and reliable way for 1 ns. It is found that parts of the loop wind up after 300 ps to extend an existing helix. This indicates that the helix is longer than in the earlier crystal structures that were used as basis for this study. Very recent crystal data confirms this finding, underlining the predictive value of accurate MD simulations. Essential dynamics analysis of the MD trajectory yields an anharmonic motion of this loop. We have supplemented the MD data with a much lower resolution Brownian dynamics simulation of 600 ns length. It provides ideas about the slow-motion dynamics of the loop. It is found that the loop explores a conformational space much larger than in the MD trajectory, leading to a "gating"-like motion with respect to the active site.     

Study of the stability and unfolding mechanism of BBA1 by molecular dynamics simulations at different temperatures.

BBA1 is a designed protein that has only 23 residues. It is the smallest protein without disulfide bridges that has a well-defined tertiary structure in solution. We have performed unfolding molecular dynamics simulations on BBA1 and some of its mutants at 300, 330, 360, and 400 K to study their kinetic stability as well as the unfolding mechanism of BBA1. It was shown that the unfolding simulations can provide insights into the forces that stabilize the protein. Packing, hydrophobic interactions, and a salt bridge between Asp12 and Lys16 were found to be important to the protein's stability. The unfolding of BBA1 goes through two major steps: (1) disruption of the hydrophobic core and (2) unfolding of the helix. The beta-hairpin remains stable in the unfolding because of the high stability of the type II' turn connecting the two beta-strands.