Coarse-grained protein molecular dynamics simulations

A limiting factor in biological science is the time-scale gap between experimental and computational trajectories. At this point, all-atom explicit solvent molecular dynamics (MD) are clearly too expensive to explore long-range protein motions and extract accurate thermodynamics of proteins in isolated or multimeric forms. To reach the appropriate time scale, we must then resort to coarse graining. Here we couple the coarse-grained OPEP model, which has already been used with activated methods, to MD simulations. Two test cases are studied: the stability of three proteins around their experimental structures and the aggregation mechanisms of the Alzheimer's Abeta16-22 peptides. We find that coarse-grained isolated proteins are stable at room temperature within 50 ns time scale. Based on two 220 ns trajectories starting from disordered chains, we find that four Abeta16-22 peptides can form a three-stranded beta sheet. We also demonstrate that the reptation move of one chain over the others, first observed using the activation-relaxation technique, is a kinetically important mechanism during aggregation. These results show that MD-OPEP is a particularly appropriate tool to study qualitatively the dynamics of long biological processes and the thermodynamics of molecular assemblies.     

Accelerated molecular dynamics simulations of protein folding

Folding of four fast‐folding proteins, including chignolin, Trp‐cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred‐of‐microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2–2.1 Å of the native NMR or X‐ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second‐order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein‐folding studies. © 2015 Wiley Periodicals, Inc.     

Dynamic structures of phosphodiesterase-5 active site by combined molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Various quantum mechanical/molecular mechanical (QM/MM) geometry optimizations starting from an x-ray crystal structure and from the snapshot structures of constrained molecular dynamics (MD) simulations have been performed to characterize two dynamically stable active site structures of phosphodiesterase-5 (PDE5) in solution. The only difference between the two PDE5 structures exists in the catalytic, second bridging ligand (BL2) which is HO- or H2O. It has been shown that, whereas BL2 (i.e. HO-) in the PDE5(BL2 = HO-) structure can really bridge the two positively charged metal ions (Zn2+ and Mg2+), BL2 (i.e. H2O) in the PDE5(BL2 = H2O) structure can only coordinate Mg2+. It has been demonstrated that the results of the QM/MM geometry optimizations are remarkably affected by the solvent water molecules, the dynamics of the protein environment, and the electronic embedding charges of the MM region in the QM part of the QMM/MM calculation. The PDE5(BL2 = H2O) geometries optimized by using the QM/MM method in different ways show strong couplings between these important factors. It is interesting to note that the PDE5(BL2 = HO-) and PDE5(BL2 = H2O) geometries determined by the QM/MM calculations neglecting these three factors are all consistent with the corresponding geometries determined by the QM/MM calculations that account for all of these three factors. These results suggest the overall effects of these three important factors on the optimized geometries can roughly cancel out. However, the QM/MM calculations that only account for some of these factors could lead to considerably different geometries. These results might be useful also in guiding future QM/MM geometry optimizations on other enzymes.     

Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts

We test a coarse-grained model assigned based on united atom simulations of C50 polyethylene to seven chain lengths ranging from C76 to C300. The prior model accurately reproduced static and dynamic properties. For the dynamics, the coarse-grained time evolution was scaled by a constant value [t=alphatCG] predictable based on the difference in intermolecular interactions. In this contribution, we show that both static and dynamic observables have continued accuracy when using the C50 coarse-grained force field for chains representing up to 300 united atoms. Pair distribution functions for the longer chain systems are unaltered, and the chain dimensions present the expected N0.5 scaling. To assess dynamic properties, we compare diffusion coefficients to experimental values and united atom simulations, assign the entanglement length using various methods, examine the applicability of the Rouse model as a function of N, and compare tube diameters extracted using a primitive path analysis to experimental values. These results show that the coarse-grained model accurately reproduces dynamic properties over a range of chain lengths, including systems that are entangled.     

Dynamic mechanism for the autophosphorylation of CheA histidine kinase: molecular dynamics simulations

The two-component system (TCS) is an important signal transduction component for most bacteria. This signaling pathway is mediated by histidine kinases via autophosphorylation between P1 and P4 domains. Taking chemotaxis protein CheA as a model of TCS, the autophosphorylation mechanism of the TCS histidine kinases has been investigated in this study by using a computational approach integrated homology modeling, ligand-protein docking, protein-protein docking, and molecular dynamics (MD) simulations. Four nanosecond-scale MD simulations were performed on the free P4 domain, P4-ATP, P4-TNPATP, and P1-P4-ATP complexes, respectively. Upon its binding to the binding pocket of P4 with a folded conformation, ATP gradually extends to an open state with help from a water molecule. Meanwhile, ATP forms two hydrogen bonds with His413 and Lys494 at this state. Because of the lower energy of the folded conformations, ATP shrinks back to its folded conformations, leading to the rupture of the hydrogen bond between ATP and Lys494. Consequently, Lys494 moves away from the pocket entrance, resulting in an open of the ATP lid of P4. It is the open state of P4 that can bind tightly to P1, where the His45 of P1 occupies a favorable position for its autophosphorylation from ATP. This indicates that ATP is not only a phosphoryl group donor but also an activator for CheA phosphorylation. Accordingly, a mechanism of the autophosphorylation of CheA is proposed as that the ATP conformational switch triggers the opening of the ATP lid of P4, leading to P1 binding tightly, and subsequently autophosphorylation from ATP to P1.     

Cyan fluorescent protein: molecular dynamics, simulations, and electronic absorption spectrum

The dynamics and electronic absorption spectrum of enhanced cyan fluorescent protein (ECFP), a mutant of green fluorescent protein (GFP), have been studied by means of a 1 ns molecular dynamics (MD) simulation. The two X-ray conformations A' and B' of ECFP were considered. The chromophore was assumed to be neutral, and all titratable residues were taken in their standard protonation state at neutral pH. The protein was embedded in a box of water molecules (and counterions). The first result is that the two conformations A' and B' are found to be stable all along the simulation. Then, an analysis of the hydrogen-bond networks shows strong differences between the two conformations in the surroundings of the nitrogen atom of the indolic part of the chromophore. This is partly due to the imperfection in the beta barrel near the His148 residue, which allows the access of one solvent molecule inside the protein in conformation A'. Finally, quantum mechanical calculations of the electronic transition energies of the chromophore in the charge cloud of the protein and solvent water molecules were performed using the TDDFT method on 160 snapshots extracted every 5 ps of the MD trajectories. It is found that conformations A' and B' exhibit very similar spectra despite different H-bond networks involving the chromophore. This similarity is related to the weak charge transfer involved in the electronic transition and the weak electrostatic field created by ECFP near the chromophore, within the hypotheses made in the present simulation.     

Modern protein force fields behave comparably in molecular dynamics simulations

Several molecular dynamics simulations were performed on three proteins--bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and domain IIA of bacillus subtilis glucose permease--with each of the AMBER94, CHARMM22, and OPLS-AA force fields as implemented in CHARMM. Structural and dynamic properties such as solvent-accessible surface area, radius of gyration, deviation from their respective experimental structures, secondary structure, and backbone order parameters are obtained from each of the 2-ns simulations for the purpose of comparing the protein portions of these force fields. For one of the proteins, the interleukin-4 mutant, two independent simulations were performed using the CHARMM22 force field to gauge the sensitivity of some of these properties to the specific trajectory. In general, the force fields tested performed remarkably similarly with differences on the order of those found for the two independent trajectories of interleukin-4 with CHARMM22. When all three proteins are considered together, no force field showed any consistent trend in variations for most of the properties monitored in the study.     

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.     

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.     

Nuclear quantum effects at aqueous metal interfaces captured by molecular dynamics simulations

In this review, we summarize the recent development in modeling nuclear quantum effects at aqueous metal interfaces. First, we review the nuclear quantum effects on the water-metal interface at ultrahigh vacuum. Then, we illustrate the nuclear quantum effects at the potential of zero charge conditions. At last, we give some outlook for the perspective work in modeling the nuclear quantum effects at electrochemical interfaces and some practical simulation strategies.     

Dynamic properties of water around a protein-DNA complex from molecular dynamics simulations

Formation of protein-DNA complex is an important step in regulation of genes in living organisms. One important issue in this problem is the role played by water in mediating the protein-DNA interactions. In this work, we have carried out atomistic molecular dynamics simulations to explore the heterogeneous dynamics of water molecules present in different regions around a complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. It is demonstrated that such heterogeneous water motions around the complex are correlated with the relaxation time scales of hydrogen bonds formed by those water molecules with the protein and DNA. The calculations reveal the existence of a fraction of extraordinarily restricted water molecules forming a highly rigid thin layer in between the binding motifs of the protein and DNA. It is further proved that higher rigidity of water layers around the complex originates from more frequent reformations of broken water-water hydrogen bonds. Importantly, it is found that the formation of the complex affects the transverse and longitudinal degrees of freedom of surrounding water molecules in a nonuniform manner.     

Stability and migration of metal ions in G4-wires by molecular dynamics simulations

We present a molecular dynamics investigation of guanine quadruple helices based on classical force fields. We analyze the dependence of the helical conformation on various compositional factors, such as the length of the G4-wire, as well as the incorporation into the helix channel of alkali ions of different species and in different amounts. In compliance with previous indications, our results suggest that monovalent alkali cations assist the stability of the quadruplex arrangement against disruption on the few nanoseconds time scale in the order of increasing van der Waals radius. Whereas very short G4-wire fragments immediately unfold in the absence of coordinating metal ions or in the presence of tiny ions (e.g., Li+) in agreement with the experimental evidence that empty short guanine quadruplexes are not formed in any synthetic conditions, our simulations show that longer empty helices do not discompose. This finding supports the possibility of producing long G4-wires with different guanine-cation stoichiometries than those routinely known. The classical trajectories allow us to identify different stationary axial sites for the different metal species, which are confirmed by complementary quantum calculations.     

The influence of aqueous versus glassy solvents on protein dynamics: vibrational echo experiments and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo measurements are used to measure the vibrational dephasing of the CO stretching mode of carbonmonoxy-hemoglobin (HbCO), a myoglobin mutant (H64V), and a bacterial cytochrome c(552) mutant (Ht-M61A) in aqueous solution and trehalose glasses. The vibrational dephasing of the heme-bound CO is significantly slower for all three proteins embedded in trehalose glasses compared to that of aqueous protein solutions. All three proteins exhibit persistent but notably slower spectral diffusion when the protein surface is fixed by the glassy solvent. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to reveal that the structural dynamics, as sensed by the CO, of the three proteins in trehalose and aqueous solution are dominated by fast (tens of femtoseconds), motionally narrowed fluctuations. MD simulations of H64V in dynamic and "static" water are presented as models of the aqueous and glassy environments. FFCFs are calculated from the H64V simulations and qualitatively reproduce the important features of the experimentally extracted FFCFs. The suppression of long time scale (picoseconds to tens of picoseconds) frequency fluctuations (spectral diffusion) in the glassy solvent is the result of a damping of atomic displacements throughout the protein structure and is not limited to structural dynamics that occur only at the protein surface. The analysis provides evidence that some dynamics are coupled to the hydration shell of water, supporting the idea that the bioprotection offered by trehalose is due to its ability to immobilize the protein surface through a thin, constrained layer of water.     

Car‐parrinello molecular dynamics investigation of active surfaces and Ti catalytic sites in Ziegler‐Natta heterogeneous catalysis

A first principles molecular dynamics study of various active surfaces and Ti catalytic sites is presented. We first review some of our recent results about MgCl₂ lateral cuts acting as a support for Ti catalytic sites and inspect the structure and stability of the standard binuclear model. We find that catalytic adducts TiCl₄ and Ti₂Cl₆, which are the standard precursors of the active catalytic system, can bind more or less efficiently to the support according to the morphology of the active surfaces. Furthermore, the activation and polymerization phases are shown to be critical in determining whether or not a particular site is stable and suitable to carry out the polymerization process. We also address the problem of regioselectivity. Finally, we have attempted for the first time a first principles study of the role of a typical donor phthalate elucidating its binding properties on the different substrate cuts and its behavior as a poisoning agent for the Corradini mononuclear active site. These studies are very preliminary.     

Dynamic mechanism of fatty acid transport across cellular membranes through FadL: molecular dynamics simulations

FadL is an important member of the family of fatty acid transport proteins within membranes. In this study, 11 conventional molecular dynamics (CMD) and 25 steered molecular dynamics (SMD) simulations were performed to investigate the dynamic mechanism of transport of long-chain fatty acids (LCFAs) across FadL. The CMD simulations addressed the intrinsically dynamic behavior of FadL. Both the CMD and SMD simulations revealed that a fatty acid molecule can move diffusively to a high-affinity site (HAS) from a low-affinity site (LAS). During this process, the swing motion of the L3 segment and the hydrophobic interaction between the fatty acid and FadL could play important roles. Furthermore, 22 of the SMD simulations revealed that fatty acids can pass through the gap between the hatch domain and the transmembrane domain (TMD) by different pathways. SMD simulations identified nine possible pathways for dodecanoic acid (DA) threading the barrel of FadL. The binding free energy profiles between DA and FadL along the MD trajectories indicate that all of the possible pathways are energetically favorable for the transport of fatty acids; however, one pathway (path VI) might be the most probable pathway for DA transport. The reasonability and reliability of this study were further demonstrated by correlating the MD simulation results with the available mutagenesis results. On the basis of the simulations, a mechanism for the full-length transport process of DA from the extracellular side to the periplasmic space mediated by FadL is proposed.     

On simulations of complex interfaces: molecular dynamics simulations of stationary phases

Methodological considerations for molecular dynamics simulations of complex interfaces are presented in this article. A slab geometry is examined in the context of stationary phases where selectivity occurs predominantly in pores within silica beads. Specifically, we examine the Whelk-O1 interface with n-hexane/2-propanol, the TMA-(Pro)(2)-N(CH(3))-tether interface with n-hexane/2-propanol, and the C(18)H(37)Si interface with water/methanol. The following methodological issues are considered in detail: The assessment of solvent density within the confined region and excluded volume of the interface; the structural equilibration of surface-bound moieties; solvent equilibration for binary mixtures; surface size effects, and periodic boundary conditions; the treatment of electrostatic interactions; and the impact of pore size.     

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Phonostat: thermostatting phonons in molecular dynamics simulations

Thermostat algorithms in a molecular dynamics simulation maintain an average temperature of a system by regulating the atomic velocities rather than the internal degrees of freedom. Herein, we present a "phonostat" algorithm that can regulate the total energy in a given internal degree of freedom. In this algorithm, the modal energies are computed at each time step using a mode-tracking scheme and then the system is driven by an external driving force of desired frequency and amplitude. The rate and amount of energy exchange between the phonostat and the system is controlled by two distinct damping parameters. Two different schemes for controlling the external driving force amplitude are also presented. In order to test our algorithm, the method is applied initially to a simple anharmonic oscillator for which the role of various phonostat parameters can be carefully tested. We then apply the phonostat to a more realistic (10,0) carbon nanotube system and show how such an approach can be used to regulate energy of highly anharmonic modes.