Mechanical unfolding of segment-swapped protein G dimer: results from replica exchange molecular dynamics simulations

The protein G dimer (pdb code 1Q10) is a mutated dimeric form of the immunoglobulin-binding domain B1 of streptococcal protein G, in which the two monomeric units have swapped elements of their secondary structure. We have used replica exchange molecular dynamics simulations to study how this dimer responds to a mechanical force that pulls the N-terminus of one unit and the C-terminus of the other apart. We have further compared the mechanical response of the dimer to that of the protein G monomer. When the pulling force is low enough, the mechanical unfolding can be viewed as a thermally activated barrier crossing process. For each protein, we have computed the corresponding free energy barrier and its dependence on the pulling force. While the dimer is found to be less resistant to mechanical unfolding than its monomeric counterpart, the two proteins exhibit essentially the same mechanical unfolding mechanism involving separation of the terminal parallel strands. On the basis of our results, we speculate that the mechanical properties of natural adhesives, composites, fibers, and other materials may be optimized not only at a single molecule level but also at the mesoscopic level through the interactions among individual chains.     

Short time molecular dynamics simulations: Stressed polyethylene results

The multiple signal classification method (MUSIC) for frequency estimation is used to compute the spectrum (intensity versus frequency) for stressed polyethylene in a crystal from the time-dependent structure factor. In this article we demonstrate that MUSIC can accurately determine the frequencies for our model from very short time trajectories and can compute the frequency shifts for various stress perturbations. A preliminary study of the dynamical effects of stress on the fracture of a PE chain showed that at low stress the chain had an irregular period of the end-to-end distance (reaction coordinate) oscillation and at higher stress a periodic extension and contraction.     

Characterization of the stereochemical selectivity of beta-hairpin formation by molecular dynamics simulations

The stability of secondary structure motifs found in proteins is influenced by the choice of the configuration of the chiral centers present in the amino acid residues (i.e., D vs L). Experimental studies showed that the structural properties of the tetrapeptide (L)V(L)P(L)A(L)L (all-L) are drastically altered upon mutating the L-proline and the L-alanine by their d-enantiomers [J. Am. Chem. Soc. 1996, 118, 6975]. The all-L diastereomer is unstructured, experiencing little or no beta-hairpin formation, while the (L)V(D)P(D)A(L)L peptide exhibits a substantial population of beta-hairpin conformation. In this study, we perform molecular dynamics simulations to investigate the folding propensity of these two model peptides. The results confirm the experimental findings, namely, that the presence of d-amino acids in the loop region strongly induces beta-hairpin formation (a population increase from about 1.5% to 50% is observed). The major factor determining the different behavior is found to be the large difference in energy between the two diastereomers, approximately 22 kJ/mol, when they adopt a beta-hairpin structure. The higher energy observed for the all-L peptide is a consequence of none-ideal hydrogen bond formation and of steric repulsions. The results suggest that selective incorporation of D-amino acids in proteins can be used to enhance certain secondary structure elements. The kinetic behavior of the folding process observed in the simulations is also investigated. We find that the decay rate of the folded structure fits to a biexponential function, suggesting that the folding/unfolding process of a beta-hairpin is governed by two different mechanisms.     

Application of principal component analysis in protein unfolding: an all-atom molecular dynamics simulation study

We have performed molecular dynamics (MD) simulation of the thermal denaturation of one protein and one peptide-ubiquitin and melittin. To identify the correlation in dynamics among various secondary structural fragments and also the individual contribution of different residues towards thermal unfolding, principal component analysis method was applied in order to give a new insight to protein dynamics by analyzing the contribution of coefficients of principal components. The cross-correlation matrix obtained from MD simulation trajectory provided important information regarding the anisotropy of backbone dynamics that leads to unfolding. Unfolding of ubiquitin was found to be a three-state process, while that of melittin, though smaller and mostly helical, is more complicated.     

Temperature and pressure dependence of alanine dipeptide studied by multibaric-multithermal molecular dynamics simulations

We applied the multibaric-multithermal (MUBATH) molecular dynamics (MD) algorithm to an alanine dipeptide in explicit water. The MUBATH MD simulation covered a wide range of conformational space and sampled the states of PII, C5, alphaR, alphaP, alphaL, and C7(ax). On the other hand, the conventional isobaric-isothermal simulation was trapped in local-minimum free-energy states and sampled only a few of them. We calculated the partial molar enthalpy difference DeltaH and partial molar volume difference DeltaV among these states by the MUBATH simulation using the AMBER parm99 and AMBER parm96 force fields and two sets of initial conditions. We compared these results with those from Raman spectroscopy experiments. The Raman spectroscopy data of DeltaH for the C5 state against the PII state agreed with both MUBATH data with the AMBER parm96 and parm99 force fields. The partial molar enthalpy difference DeltaH for the alphaR state and the partial molar volume difference DeltaV for the C5 state by the Raman spectroscopy agreed with those for the AMBER parm96 force field. On the other hand, DeltaV for the alphaR state by the Raman spectroscopy was consistent with our AMBER-parm99 force-field result. All the experimental results fall between those of simulations using AMBER parm96 and parm99 force fields, suggesting that the ideal force-field parameters lie between those of AMBER parm96 and parm99.     

Folding mechanisms of individual beta-hairpins in a Go model of Pin1 WW domain by all-atom molecular dynamics simulations

This paper examines the folding mechanism of an individual beta-hairpin in the presence of other hairpins by using an off-lattice model of a small triple-stranded antiparallel beta-sheet protein, Pin1 WW domain. The turn zipper model and the hydrophobic collapse model originally developed for a single beta-hairpin in literature is confirmed to be useful in describing beta-hairpins in model Pin1 WW domain. We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second, but the formation process are significantly dependent on temperature. More specifically, beta1-beta2 hairpin folds via the turn zipper model at a low temperature and the hydrophobic collapse model at a high temperature, while the folding of beta2-beta3 hairpin follows the turn zipper model at both temperatures. The change in folding mechanisms is interpreted by the interplay between contact stability (enthalpy) and loop lengths (entropy), the effect of which is temperature dependent.     

Unbinding of nicotine from the acetylcholine binding protein: steered molecular dynamics simulations

The ligand binding/unbinding process is critical to our understanding of the pharmacology of both the nicotinic acetylcholine receptor (nAChR) and the acetylcholine binding protein (AChBP). Steered molecular dynamics simulations were performed to learn about the unbinding process of the full agonist nicotine. Three different pulling models were designed to investigate the possible binding/unbinding pathways: radial and tangent models, and also a mixed model. Of the three, the tangent pulling model finally failed to dissociate nicotine from the ligand binding pocket. The efficiency of the pulling force profiles was superior, and the opening of the C-loop was smaller in the mixed pulling model than that in the radial model. The most favorable pathway for the cholinergic agonist nicotine to enter or leave the binding pocket is through the principal binding side, following a curvilinear track. Noticeably, it has been seen that the unbinding of the nicotine is concomitant with a global rotation of the protein-ligand complex which could be caused by the interactions of the ligand with protein at the tangent direction.     

Phase behavior in model homopolymer/CO2 and surfactant/CO2 systems: discontinuous molecular dynamics simulations

Discontinuous molecular dynamics simulations are performed on surfactant (HmTn)/solvent systems modeled as a mixture of single-sphere solvent molecules and freely jointed surfactant chains composed of m slightly solvent-philic head spheres (H) and n solvent-philic tail spheres (T), all of the same size. We use a square-well potential to account for the head-head, head-solvent, tail-tail, and tail-solvent interactions and a hard-sphere potential for the head-tail and solvent-solvent interactions. We first simulate homopolymer/supercritical CO2 (scCO2) systems to establish the appropriate interaction parameters for a surfactant/scCO2 system. Next, we simulate surfactant/scCO2 systems and explore the effect of the surfactant volume fraction, packing fraction, and temperature on the phase behavior. The transition from the two-phase region to the one-phase region is located by monitoring the contrast structure factor of the equilibrated surfactant/scCO2 system, and the micelle to unimer transition is located by monitoring the aggregate size distribution of the equilibrated surfactant/scCO2 system. We find a two-phase region, a micelle phase, and a unimer phase with increasing packing fraction at fixed temperature or with increasing temperature at fixed packing fraction. The phase diagram for the surfactant/scCO2 system in the surfactant volume fraction-packing fraction plane and the density dependence of the critical micelle concentration are in qualitative agreement with experimental observations. The phase behavior of a surfactant/scCO2 system can be directly related to the solubilities of the corresponding homopolymers that serve as the head and tail blocks for the surfactant. The influence of surfactant structure (head and tail lengths) on the phase transitions is explored.     

A recent development in computational chemistry: chemical reactions from first principles molecular dynamics simulations

First-principles molecular dynamics simulations have recently been found an effective tool to study a large variety of chemical problems. Finite temperature simulations reveal unique information, including explicit dynamical effects and the evaluation of proper free energy differences. Moreover, dynamics simulations reveal information on the flexibility of molecular systems, and elucidate, often otherwise inaccessible, mechanistic details of chemical reactions. In addition this methodology allows the study of larger, periodic, systems, revealing computationally unique information which may be directly compared to experiments on realistic chemical systems. A variety of examples will be given, although most focus on the important field of catalysis.     

Parametric studies of interaction strengths in polymer/CO2 systems: discontinuous molecular dynamics simulations

Discontinuous molecular dynamics simulations are performed on homopolymer/solvent and surfactant/solvent systems. The homopolymer and surfactant molecules are modeled as freely jointed square-well chains. Solvent molecules are modeled as both hard spheres and square-well spheres. We explore how the various interaction parameters affect the types of phase behavior and micellization observed in the homopolymer/solvent and surfactant/solvent systems. Increasing the packing fraction of homopolymers in both hard-sphere solvents and square-well solvents increases the solvent's ability to dissolve homopolymers only when the segment-solvent interaction strength exceeds a critical value. Although only upper critical solution temperature (UCST) behavior is observed for homopolymers in hard-sphere solvents, both UCST and lower critical solution temperature (LCST) behavior are observed for homopolymers in square-well solvents, depending upon the interaction strengths and chain length. This indicates that it is necessary to account for the solvent-solvent attraction to model LCST behavior in supercritical CO2. Our simulation results on surfactants in hard-sphere solvents show that it is necessary to account for the interactions experienced by both the head and tail blocks in order to capture the essential features of surfactant/supercritical CO2 systems.     

Concentration enrichment of urea at cellulose surfaces: results from molecular dynamics simulations and NMR spectroscopy

A combined solid-state NMR and Molecular Dynamics simulation study of cellulose in urea aqueous solution and in pure water was conducted. It was found that the local concentration of urea is significantly enhanced at the cellulose/solution interface. There, urea molecules interact directly with the cellulose through both hydrogen bonds and favorable dispersion interactions, which seem to be the driving force behind the aggregation. The CP/MAS ¹³C spectra was affected by the presence of urea at high concentrations, most notably the signal at 83.4 ppm, which has previously been assigned to C4 atoms in cellulose chains located at surfaces parallel to the (110) crystallographic plane of the cellulose Iβ crystal. Also dynamic properties of the cellulose surfaces, probed by spin-lattice relaxation time ¹³CT ₁ measurements of C4 atoms, are affected by the addition of urea. Molecular Dynamics simulations reproduce the trends of the T ₁ measurements and lends new support to the assignment of signals from individual surfaces. That urea in solution is interacting directly with cellulose may have implications on our understanding of the mechanisms behind cellulose dissolution in alkali/urea aqueous solutions.     

AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling

We have developed an implicit solvent effective potential (AGBNP) that is suitable for molecular dynamics simulations and high-resolution modeling. It is based on a novel implementation of the pairwise descreening Generalized Born model for the electrostatic component and a new nonpolar hydration free energy estimator. The nonpolar term consists of an estimator for the solute-solvent van der Waals dispersion energy designed to mimic the continuum solvent solute-solvent van der Waals interaction energy, in addition to a surface area term corresponding to the work of cavity formation. AGBNP makes use of a new parameter-free algorithm to calculate the scaling coefficients used in the pairwise descreening scheme to take into account atomic overlaps. The same algorithm is also used to calculate atomic surface areas. We show that excellent agreement is achieved for the GB self-energies and surface areas in comparison to accurate, but much more expensive, numerical evaluations. The parameter-free approach used in AGBNP and the sensitivity of the AGBNP model with respect to large and small conformational changes makes the model suitable for high-resolution modeling of protein loops and receptor sites as well as high-resolution prediction of the structure and thermodynamics of protein-ligand complexes. We present illustrative results for these kinds of benchmarks. The model is fully analytical with first derivatives and is computationally efficient. It has been incorporated into the IMPACT molecular simulation program.     

Analytic first and second derivatives of the energy in the fragment molecular orbital method combined with molecular mechanics

Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional theory. The importance of the orbital response terms is demonstrated. The role of electrostatic embedding upon molecular vibrations is analyzed, comparing force field and quantum mechanical treatments for an ionic liquid and a solvated protein. The method is applied for 100 protein conformations sampled in molecular dynamics (MD) to take into account the complexity of a flexible protein structure in solution, and a good agreement with experimental data is obtained: Frequencies from an experimental infrared (IR) spectrum are reproduced within 17 cm⁻¹ .     

Dual function of the hydration layer around an antifreeze protein revealed by atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations are used to investigate the mechanism by which the antifreeze protein from the spruce budworm, Choristoneura fumiferana, binds to ice. Comparison of structural and dynamic properties of the water around the three faces of the triangular prism-shaped protein in aqueous solution reveals that at low temperature the water structure is ordered and the dynamics slowed down around the ice-binding face of the protein, with a disordering effect observed around the other two faces. These results suggest a dual role for the solvation water around the protein. The preconfigured solvation shell around the ice-binding face is involved in the initial recognition and binding of the antifreeze protein to ice by lowering the barrier for binding and consolidation of the protein:ice interaction surface. Thus, the antifreeze protein can bind to the molecularly rough ice surface by becoming actively involved in the formation of its own binding site. Also, the disruption of water structure around the rest of the protein helps prevent the adsorbed protein becoming covered by further ice growth.     

Estimating the temperature dependence of peptide folding entropies and free enthalpies from total energies in molecular dynamics simulations

The temperature dependence of thermodynamic quantities, such as heat capacity, entropy and free enthalpy, may be obtained by using well-known equations that relate these quantities to the enthalpy of the molecular system of interest at a range of temperatures. In turn, the enthalpy of a molecular system can be estimated from molecular dynamics simulations of an appropriate model. To demonstrate this, we have investigated the temperature dependence of the enthalpy, heat capacity, entropy and free enthalpy of a system that consists of a beta-heptapeptide in methanol and have used the statistical mechanics relationships to describe the thermodynamics of the folding/unfolding equilibrium of the peptide. The results illustrate the power of current molecular simulation force fields and techniques in establishing the link between thermodynamic quantities and conformational distributions.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

Probing the neutral graphene-ionic liquid interface: insights from molecular dynamics simulations

We study basic mechanisms of the interfacial layer formation at the neutral graphite monolayer (graphene)-ionic liquid (1,3-dimethylimidazolium chloride, [dmim][Cl]) interface by fully atomistic molecular dynamics simulations. We probe the interface area by a spherical probe varying the charge (-1e, 0, +1e) as well as the size of the probe (diameter 0.50 nm and 0.38 nm). The molecular modelling results suggest that: there is a significant enrichment of ionic liquid cations at the surface. This cationic layer attracts Cl(-) anions that leads to the formation of several distinct ionic liquid layers at the surface. There is strong asymmetry in cationic/anionic probe interactions with the graphene wall due to the preferential adsorption of the ionic liquid cations at the graphene surface. The high density of ionic liquid cations at the interface adds an additional high energy barrier for the cationic probe to come to the wall compared to the anionic probe. Qualitatively the results from probes with diameter 0.50 nm and 0.38 nm are similar although the smaller probe can approach closer to the wall. We discuss the simulation results in light of available experimental data on the interfacial structure in ionic liquids.     

Experimental resolution of early steps in protein folding: testing molecular dynamics simulations

Time-resolved Tyr fluorescence spectroscopy coupled with a laser-induced temperature-jump (T-jump) was employed to follow the folding relaxation dynamics of the B-domain of Staphylococcal protein A. The single Tyr is located in helix 1 (H1) and is a sensitive probe of the structure of this helix and the overall helical bundle structure. The results from this study were compared to those from a complementary infrared T-jump study on this protein [Vu, D. M.; Myers, J. K.; Oas, T. G.; Dyer, R. B. Biochemistry 2004, 43, 3582]. Both methods detect a microsecond process that follows the cooperative relaxation of the helical bundle core. However, a fast process (10-7 s) that follows the relaxation of the individual helices was observed only with the infrared probe. Thus, fast formation of H1 is not observed, but rather H1 forms in the microsecond phase, concomitantly with the docking to (and stabilization by) the other two helices to form the helical bundle structure. This observation validates the results of several previous molecular dynamics simulations that predict H1 formation only in the final assembly of the helix bundle.     

Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a gamma distribution or rational function approximation to its Laplace transform.     

A novel algorithm to model the influence of host lattice flexibility in molecular dynamics simulations: loading dependence of self-diffusion in carbon nanotubes

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.