Conformational Jumps Research Articles

Accelerated Structural Prediction of Flexible Protein-Ligand Complexes: The SLICE Method.

Using existing and academically available software, we present a new method for the structural prediction of binding events containing flexible protein targets. SLICE (Selective Ligand-Induced Conformational Ensemble) combines opportunistic stochastic jumps of ligand position with standard molecular dynamics to model the induced-fit binding of ligands starting with unbound host coordinates. To induce the structural adaptations of the complex at the binding site, conformational jumps in ligand position are selected in SLICE from structures generated by a docking software. Multiple binding trajectories from the docking set are followed using molecular dynamics for a set time to relax the host structure and generate new host poses. A new configurational jump is made on the set of newly generated host poses. The process is then repeated. The method was implemented with AutoDock Vina as the docking method, Vina scores as the selection criterion, and Amber code for molecular dynamics and applied to several test systems. A system consisting of Chromobox protein homologue 8 (CBX8) and its small peptide ligand, H3K9Me3, for which the final (bound) configuration is known, is used for verifying SLICE in the present setup. The setup was also applied to several nonpeptide molecules on known difficult flexible targets exhibiting a large disparity between apo and holo host states. The SLICE simulations provide a promising approach to generate induced-fit configurations compared to existing long (microsecond) classical and accelerated dynamics approaches in all the test systems considered here. However, further optimization of SLICE parameters is required for replicating crystal structure coordinates for some systems. We discuss in the following pages the various SLICE parameters and how they can be optimized for the system at hand.

A Generative Angular Model of Protein Structure Evolution.

Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a generative, evolutionary model of protein structure and sequence that is valid on a local length scale. The model concerns the local dependencies between sequence and structure evolution in a pair of homologous proteins. The evolutionary trajectory between the two structures in the protein pair is treated as a random walk in dihedral angle space, which is modeled using a novel angular diffusion process on the two-dimensional torus. Coupling sequence and structure evolution in our model allows for modeling both “smooth” conformational changes and “catastrophic” conformational jumps, conditioned on the amino acid changes. The model has interpretable parameters and is comparatively more realistic than previous stochastic models, providing new insights into the relationship between sequence and structure evolution. For example, using the trained model we were able to identify an apparent sequence–structure evolutionary motif present in a large number of homologous protein pairs. The generative nature of our model enables us to evaluate its validity and its ability to simulate aspects of protein evolution conditioned on an amino acid sequence, a related amino acid sequence, a related structure or any combination thereof.

Single-Molecule Dynamics of Conformational Interchange in Calmodulin

The recognition and binding of target binding domains by calmodulin (CaM) require global protein conformational changes. We describe single-molecule measurements of conformational interchange in CaM. CaM labeled with a FRET pair (Alexa Fluor 488 and Texas Red) was trapped in lipid vesicles tethered to the surface of a cover slip. Conformational transitions were observed on the time scale of 2 to 11 ms. The probability of a transition to a compact conformation was significantly lower at low than at high Ca2+ concentration, revealing more frequent transitions to a compact conformational state for CaM with bound Ca2+. These results show that CaM undergoes functional conformational dynamics even in the absence of target enzyme. Conformational searching may permit CaM to readily adopt a binding geometry upon encountering a target binding domain.FRET trajectories were also analyzed by a novel iterative Bayesian propagator to determine the probability distribution of FRET efficiencies as a function of time. We show that this analysis outperforms conventional running averages to resolve conformational jumps and conformational distributions. The figure shows a CaM FRET efficiency probability distribution (color scale). The red line shows the running average. The time axis is in milliseconds.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Effect of the frequency of intramolecular motions on the NMR relaxation in liquid state temperature regime

Equations for the spectral densities of complex motion of a spin pair undergoing internal motion and isotropic/anisotropic overall rotation have been considered. The fluctuations of the interproton distances, caused by internal motion, have been taken into account in the theoretical equations. A method allowing a distinction between the isotropic and the anisotropic overall rotation of molecules has been proposed. The effect of the activation parameters of internal motions (known from the solid state study) on the measured T 1 relaxation of the 13C and 1H–1H cross-relaxation rates has been analysed for methyl-β-D-galactopyranoside in DMSO-d6 solution. The conformational trans-gauche jumps of the methylene group are not fast enough to affect the T 1 value of carbon C6 in the liquid state temperatures regime. Only the methyl group rotation is a very fast internal motion. This motion influences the carbon C7 relaxation and methyl protons–anomeric proton cross-relaxation. The values of interatomic distances between anomeric H(C1) and H(C5) as well as the three methyl protons H(C7) have been calculated from the cross-relaxation rates. The distance H(C1)–H(C7) fluctuates due to the rotation of methyl group. The application of the ‘model-free approach’ to study molecular dynamics in solutions is discussed.

NMR relaxation interference effects and internal dynamics in γ-cyclodextrin

Multiple-magnetic field (9.4, 14.1 and 21.1 T) measurements of 13C spin–lattice and spin–spin relaxation rates, the heteronuclear Overhauser enhancement and cross-correlated relaxation rates (CCRRs) in the methylene groups are reported for γ-cyclodextrin in water/dimethylsulfoxide solution at 323 and 343 K. The CCRRs are obtained from differences in the initial relaxation rates of the components of the CH 2 triplet in the 13C spectra. The relaxation data are analyzed using the Lipari–Szabo approach and a novel modification of the two-site jump model. According to the latter model, inclusion of the dipolar (CH,CH ′) cross-correlated longitudinal and transverse relaxation is important for estimating the rate of the conformational jumps in the hydroxymethyl group. Using the dynamic information from the jump model, we have also used the differences in the initial relaxation rates for the triplet components to estimate the anisotropy of the chemical shielding tensor.

How a Vicinal Layer of Solvent Modulates the Dynamics of Proteins

The dynamics of a folded protein is studied in water and glycerol at a series of temperatures below and above their respective dynamical transition. The system is modeled in two distinct states whereby the protein is decoupled from the bulk solvent at low temperatures, and communicates with it through a vicinal layer at physiological temperatures. A linear viscoelastic model elucidates the less-than-expected increase in the relaxation times observed in the backbone dynamics of the protein. The model further explains the increase in the flexibility of the protein once the transition takes place and the differences in the flexibility under the different solvent environments. Coupling between the vicinal layer and the protein fluctuations is necessary to interpret these observations. The vicinal layer is postulated to form once a threshold for the volumetric fluctuations in the protein to accommodate solvents of different sizes is reached. Compensation of entropic-energetic contributions from the protein-coupled vicinal layer quantifies the scaling of the dynamical transition temperatures in various solvents. The protein adapts different conformational routes for organizing the required coupling to a specific solvent, which is achieved by adjusting the amount of conformational jumps in the surface-group dihedrals.

Dynamics of the nitroxide side chain in spin-labeled proteins.

The dynamics of the tether linking methanethiosulfonate (MTSSL) spin probes to alpha-helices has been investigated with the purpose of rationalizing its effects on ESR line shapes. Torsional profiles for the chain bonds have been calculated ab initio, and steric interactions with the alpha-helix and the neighboring residues have been introduced at the excluded-volume level. As a consequence of the restrictions deriving from chain geometry and local constraints, a limited number of allowed conformers has been identified that undergo torsional oscillations and conformational jumps. Torsional fluctuations are described as damped oscillations, while transition rates between conformers are calculated according to the Langer multidimensional extension of the Kramers theory. The time scale and amplitude of the different motions are compared; the major role played by rotations of the outermost bonds of the side chain emerges, along with the effects of substituents in the pyrroline ring on the conformer distribution and dynamics. The extent and symmetry of magnetic tensor averaging produced by the side chain motions are estimated, the implications for the ESR spectra of spin-labeled proteins are discussed, and suggestions for the introduction of realistic features of the spin probe dynamics into the line shape simulation are presented.

Modeling the effects of structure and dynamics of the nitroxide side chain on the ESR spectra of spin-labeled proteins.

In the companion paper (J. Phys. Chem. B 2006, 110, jp0629487), a study of the conformational dynamics of methanethiosulfonate spin probes linked at a surface-exposed alpha-helix has been presented. Here, on the basis of this analysis, X-band ESR spectra of these spin labels are simulated within the framework of the Stochastic Liouville equation (SLE) methodology. Slow reorientations of the whole protein are superimposed on fast chain motions, which have been identified with conformational jumps and fluctuations in the minima of the chain torsional potential. Fast chain motions are introduced in the SLE for the protein reorientations through partially averaged magnetic tensors and relaxation times calculated according to the motional narrowing theory. The 72R1 and 72R2 mutants of T4 lysozyme, which bear the spin label at a solvent-exposed helix site, have been taken as test systems. For the side chain of the R2 spin label, only a few noninterconverting conformers are possible, whose mobility is limited to torsional fluctuations, yielding almost identical spectra, typical of slightly mobile nitroxides. In the case of R1, more complex spectra result from the simultaneous presence of constrained and mobile chain conformers, with relative weights that can depend on the local environment. The model provides an explanation for the experimentally observed dependence of the spectral line shapes on temperature, solvent, and pattern of substituents in the pyrroline ring. The relatively simple methodology presented here allows the introduction of realistic features of the spin probe dynamics into the simulation of ESR spectra of spin-labeled proteins; moreover, it provides suggestions for a proper account of such dynamics in more sophisticated approaches.

On the separation between torsion–vibration and conformational relaxation processes in the incoherent intermediate scattering function of polyethylene

Abstract We present a detailed study of the local dynamics of short polyethylene (PE) chains in a wide temperature range ( T =350, 450, 504 K) using molecular dynamics (MD) simulations based on a united atom model. Undercooled melt phases can be studied easily in simulations without any sign of crystallization in the sample. We focus on the interpretation of the incoherent intermediate scattering function in the range 0.375⩽ Q ⩽2.0 A −1 using a refined analysis of the time correlation functions in terms of a continuous linear combination of exponential decays weighted by a distribution of relaxation times (DRT). At 350 K, over the whole Q range investigated, the relaxation of the intermediate scattering function is due to a combination of a fast process occurring on the picosecond time scale and a slow process. The faster process is weakly Q - and T -dependent and is shown to originate from torsion–vibration motions. The DRT associated with the slow process, related to conformational jumps, changes quantitatively and qualitatively in the explored Q range and does not resemble a stretched exponential behaviour. The average global relaxation time related to the slow process evolves below Q =1 A −1 towards a Q −3.3 power law behaviour.

Chain dynamics and conformational transition in cis-polyisoprene: Comparison between melt and subglass state by molecular dynamics simulations

Molecular-dynamics simulations are performed to analyze the local chain dynamics of cis-1,4-polyisoprene at various temperatures. The volumetric glass transition was found at around 247 K. The torsional angle autocorrelation functions (TACF) for the three kinds of backbone chain and the orientation autocorrelation functions (OACF) for bond vectors in skeletal and side chain were analyzed both near the chain ends and in the middle of the chain. Various types of cooperative conformational jumps (and librations) were found in the melt chain. However, the cooperative counter-rotation at second-neighbor single bond pairs, HC–CH2 and CH2–C, became a major correlation as the temperature decreased to the subglass region. Even in the subglass chain at 173 K, more than 30% bond pairs showed cooperative counter-rotation at the second-neighbor (Group A) under the conditions in which about 60% of the bond pairs showed no conformational jump (Group B) during 20 ns molecular dynamics (MD) runs. The TACF decays for the torsions in Group A were highly different from those in Group B. In contrast, the OACF decays for the classified C–CH3 vectors next to Group A showed no difference from that next to Group B. These findings indicated that the cooperative transitions at the second-neighbor were only a short-range correlation on the single bond pairs without changing the reorientation of the two double bond planes next to the single bond pairs.

Local dynamics of isotactic and syndiotactic polypropylene in solution

The local dynamics of polypropylene (PP) in solution is studied by C13 NMR relaxation and by molecular dynamics (MD) simulation via the orientational autocorrelation function (OACF) of C-H bonds. The interpretation protocol of this function proposed by Dejean de la Bâtie, Lauprêtre and Monnerie (DLM) [R. Dejean de la Bâtie, F. Lauprêtre, and L. Monnerie, Macromolecules 21, 2045(1988)] is applied and tested on new NMR measurements of the various microstructures of polypropylene. This interpretation scheme of the OACF is supported by a detailed study employing simulated PP trajectories in an atomistic heat bath. MD simulations indicate that, quite generally, the correlation time for segmental motions, τ1, extracted from the DLM motional model is closely linked with the mean time between conformational jumps. Both experiments and simulations suggest a slightly higher mobility of meso sequences by comparison with racemic sequences. Our analysis of the microscopic aspects of the segmental dynamics and its manifestation in motional models allows us to trace the microscopic origin of the larger mobility of meso sequences.

Chain dynamics in the nematic melt of an aromatic liquid crystalline copolyester: A molecular dynamics simulation study

A molecular dynamics (MD) simulation study of chain dynamics and the relation to dipolar relaxation has been carried out on a 70/30 composition random copolymer of p-hydroxybenzoic acid and 2-hydroxy-6-naphthoic acid. The dynamics is analyzed in terms of the relatively flexible torsion at the ester oxygen-aromatic carbon bond. The effective torsional potential in the bulk that results from sampled torsional angle populations is found to differ from that of free chains in that the barriers are higher in bulk and the torsion connecting phenyl and naphthyl units has a higher barrier than that between pairs of phenyl units. Activation energies for conformational transitions are higher than those in the effective potentials. These effects indicate sensitivity to packing not found in simpler systems like polyethylene, and that frictional effects are operative. The distribution of transitions over individual bonds is found to be quite heterogeneous over the temperature range studied and is a signature for a vitrifying system. Conformational jumps were not found to be highly correlated, although some preference for next-neighbor events was indicated. Dipolar time autocorrelation functions were constructed separately for phenyl and naphthyl dipoles. The naphthyl units were found to relax more slowly than the phenyls. Comparison of MD relaxation times with experimental loss maxima indicates a degree of correspondence that lends credence to the assignment of the experimental β relaxation subglass process as associated with the naphthyl units and the γ subglass process with the phenyl units.

Chain Flexibility and 31P NMR Spin−Lattice Relaxation Measurements on Melts of Halogenated Poly(thionylphosphazenes)

The chain flexibility of halogenated poly(thionylphosphazenes) (PTPs) [(NSOX) (NPCl2)2]n (X = F, Cl) was investigated by measuring the 31 P spin−lattice relaxation times of PTP melts. T1 times were obtained at two different magnetic fields and at various temperatures above the glass transition of the polymers. The minimal T1 time occurred at lower temperatures for the fluorinated polymer than for the chlorinated polymer. This result is in agreement with trends in glass transition temperatures of these polymers and with ab initio molecular orbital calculations on the chain flexibility of model compounds of these polymers. The Hall−Helfand model for the dynamics of polymer chains was used to fit the experimental T1(T) curves. This model describes the motions of the polymer chains that lead to the longitudinal relaxation as correlated conformational jumps. T1 measurements at two different field strengths indicated that chemical shift anisotropy contributes significantly to the spin−lattice relaxation.

H and 13C NMR Study on Local Dynamics of Poly(vinyl alcohol) in Aqueous Solutions

To study the local dynamics of poly(vinyl alcohol) (PVA) in aqueous solutions, several relevant physical models for NMR spin−lattice relaxation in polymers have been tested for 13C spin−lattice relaxation times, T1C, nuclear Overhauser enhancement factor, η, determined at 100.6 MHz, and effective 1H spin−lattice relaxation times, T1eff, measured at 80, 300, and 400 MHz over a temperature range 5−87 °C. The fitting parameters of the models were obtained from the 13C NMR relaxation data, and the their validity was then tested by fitting the parameters to the 1H relaxation data. The autocorrelation function of Dejean de la Batie et al. (Macromolecules 1988, 21, 2045) provided the best fit to the data of the PVA−water system studied, showing that the local motion of the polymer could be interpreted by conformational jumps of the backbone and by a fast, anisotropic reorientation movement of the C−H bonds. An AX2 system was used successfully for the interpretation of the 1H relaxation data, indicating that dipolar interactions between the hydroxyl group and the protons of the polymer backbone are negligible. An energy barrier associated with the segmental motion of PVA was also estimated (13.4 kJ/mol).

Equilibrium and dynamic properties of polymethylene melts from molecular dynamics simulations. I. n-Tridecane

Employing an explicit atom (EA) model of polymethylene, we have carried out molecular dynamics simulations of n-tridecane (C13H28) melts at experimental densities to compute both equilibrium and dynamic properties. The calibrated EA model reproduces quite well the experimental results of pressure, x-ray diffraction patterns, and self-diffusion constants at different temperatures. A united atom (UA) model that reproduces the experimental pressures also yields good agreement with experimental x-ray diffraction patterns and self-diffusion data, and the calculated degree of intermolecular orientational correlation is in good agreement with predictions of the EA model. However, the UA model yields significantly more extended chain dimensions than a previously investigated model, and, most importantly, significantly enhanced local chain dynamics compared to the EA model, as monitored by the chain vector reorientation and local torsional dynamics. The EA model simulations yield C–H vector orientational correlation times associated with each carbon of n-tridecane, in excellent agreement with experimental values deduced from C13-NMR T1 spin–lattice relaxation times. The C–H vector reorientation was found to be closely related to conformational jumps. These jumps, whose rates closely follow torsional correlation times, appear to occur mostly as unconcerted individual transitions for these short chains.

Segmental dynamics of polymer melts

The various types of segmental motions occurring inside a polymer chain are presented and discussed as well as the most suitable expression for the orientational autocorrelation function (OACF) involved in spectroscopic techniques such as fluorescence anisotropy decay (FAD) and 13C NMR relaxation. FAD studies on anthracene labeled polybutadiene and 13C NMR on various low T g polymers show that the segmental dynamics of polymers can be described by considering: (1) conformational jumps leading to bond orientation diffusion along the chain sequence, and (2) additional librations at much higher frequencies, with an amplitude strongly dependent on the considered atomic group in a given chemical structure. The T-dependence of the correlation times associated to the conformational jumps proves that the segmental motions observed by these techniques are involved in the glass-rubber transition phenomenon. Further, the comparison of the results obtained on various polymers show that the polymers have similar segmental dynamics when they are at temperatures where their friction coefficients, determined from melt viscosity, are identical.

Molecular Dynamics in Ordered Structures: Computer Simulation and Experimental Results for Nylon 66 Crystals

A detailed comparison between molecular dynamics computer simulations and the experimental characterization of molecular motion through deuterium nuclear magnetic resonance (NMR) spectroscopic methods has been carried out for the crystalline phase of nylon 66 (polyhexamethyleneadipamide) at room temperature and just below the melting point. The computer simulations agree quantitatively with the experimental results at room temperature and qualitatively near the crystalline melting point. Both methods demonstrate that individual methylene groups within the crystals exhibit librational motion, which becomes very large in amplitude near the melting point, rather than undergoing discrete conformational jumps; furthermore, the hydrogen-bonded amides are relatively immobile at all temperatures below 230 degrees Celsius. The simulations are shown to be particularly useful for exaning the cooperativity of motion and for providing insight into structural-dynamical correlations. These aspects of the simulations are exemplified by the observation of concerted counterrotation of odd-numbered bonds within the methylene segments and the entropic stabilization of the crystal structure.

Chain mobility in solid polyelectrolyte complexes

Abstract2H NMR is used to study the mobility of the alkylene chain in solid poly[(dimethyliminio)‐alkylene]s (α,ω‐ionenes) complexed with poly(styrenesulfonate). In 10, 10‐ionene the alkylene chain motion was probed on samples selectively deuterated at the 1‐, 2‐, and 4‐position as well as in the methyl part of the quaternary ammonium groups. 2H NMR spectra show that all positions in the polymethylene chains are involved in conformational jumps between trans and gauche states. The mobility of the methylene units adjacent to charged centres was found to be significantly reduced compared with that of units in the inner part of the chain. The charged quaternary ammonium groups themselves, however, do not take part in trans‐gauche isomerization. An increase in mobility resulting from increasing the length of the alkylene chains between the charge centres was observed in 3,3‐, 6,6‐ and 10,10‐ionene complexes labelled in the 2‐position. The differences in chain dynamics were also detected via EPR line shapes of small spin probe molecules incorporated into the complexes.

Segmental dynamics during the thermal polymerization of styrene: a kinetic fluorescence anisotropy decay study

The segmental dynamics of anthracene-labelled polystyrene chains is studied during the thermal polymerization process of styrene by means of fluorescence anisotropy decay. The characteristic time of conformational jumps starts to increase drastically after a conversion rate of ca. 15 wt%, due to the direct steric interaction between different chains. The shape of the orientation autocorrelation function remains rather independent of the polymer concentration. It is well described by the process of ‘diffusive conformational jumps’. The corresponding ‘distribution of relaxation times’ is significantly narrower than the one observed in depolarized Rayleigh scattering, indicating that multimolecular interactions affect this latter technique significantly. The variation of the correlation times as a function of the concentration is in agreement with the free-volume models for concentrated solutions proposed by Fujita and Mashimo. However, the large difference between the concentration dependence of the conformational jump rate of the polymer chain and that of the reorientation time of styrene monomers rules out the idea of a single ‘local viscosity’ valid for all the species in the mixture.

ChemInform Abstract: MONTE CARLO SIMULATIONS OF THE RATE OF INTRAMOLECULAR END‐TO‐END CONTACT IN ALKANE CHAINS

We report Monte Carlo simulations of the dynamics of intramolecular contact in alkane chains and in end‐labeled alkane chains. The chain is confined to a diamond lattice except during conformational jumps. Rotational jumps around internal bonds provide the mechanism for change in the end‐to‐end separation but crankshaft‐like motions of the chain are also permitted. No adjustable parameters are used. End‐to‐end contact is found to obey first‐order kinetics, and the rate constants for contact decrease monotonically with chain lengths of from 10 to 20 atoms. Simulations for end‐labeled chains are compared with experimental measurements of intramolecular electron transfer and intramolecular fluorescence quenching.