Normal mode partitioning of Langevin dynamics for biomolecules

We propose a novel normal mode multiple time stepping Langevin dynamics integrator called NML. The aim is to approximate the kinetics or thermodynamics of a biomolecule by a reduced model based on a normal mode decomposition of the dynamical space. Our basis set uses the eigenvectors of a mass reweighted Hessian matrix calculated with a biomolecular force field. This particular choice has the advantage of an ordering according to the eigenvalues, which have a physical meaning of being the square of the mode frequency. Low frequency eigenvalues correspond to more collective motions, whereas the highest frequency eigenvalues are the limiting factor for the stability of the integrator. In NML, the higher frequency modes are overdamped and relaxed near their energy minimum while respecting the subspace of low frequency dynamical modes. Our numerical results confirm that both sampling and rates are conserved for an implicitly solvated alanine dipeptide model, with only 30% of the modes propagated, when compared to the full model. For implicitly solvated systems, NML gives a twofold improvement in efficiency over plain Langevin dynamics for sampling a small 22 atom (alanine dipeptide) model and in excess of an order of magnitude for sampling an 882 atom (bovine pancreatic trypsin inhibitor) model, with good scaling with system size subject to the number of modes propagated. NML has been implemented in the open source software PROTOMOL.     

An oscillating electric field with thermal noise increases the rotational diffusion and drives rotation in a dipole

Here we consider a dipole in a viscous medium under the influence of an oscillating electric field and thermal noise. Because of the very low Reynolds numbers involved in molecular processes, we considered overdamped Langevin dynamics. As a consequence the inertia term becomes negligible. We observed a great increase in the rotational diffusion and also net rotation for some values of the parameters.     

Magnetization of ferromagnetic clusters

The magnetization and deflection profiles of magnetic clusters in a Stern-Gerlach magnet are calculated for conditions under which the magnetic moment is fixed in the intrinsic frame of the cluster, and the clusters enter the magnetic field adiabatically. The predicted magnetization is monotonic as a function of the ratio of magnetic energy ₀ B to the rotational thermal energyk _BT. In low field the average magnetization is 2/3 of the Langevin function. The high-field moment approaches saturation asymptotically asB ^–1/2 instead of theB ^–1 dependence in the Langevin function     

First principles calculation of the thermodynamic properties of silicon clusters

The thermodynamic properties of Si clusters are calculated using first principles quantum methods combined with molecular dynamics for simulating the trajectories of clusters. A plane wave basis is used with ab initio pseudo potentials and the local density approximation for determining the electronic energies and forces. Langevin molecular dynamics simulates thermal contact with a constant temperature reservoir. Vibrational spectra, moments of inertia, anharmonic corrections, and free energies are predicted for Si₂ through Si₅. The translational contribution is based on the ideal gas limit. The rotation contribution is approximated using a classical rigid rotator. Vibrational modes are determined from the dynamical matrix in the harmonic approximation. Corrections due to anharmonicity and coupling between rotational and vibrational modes are fit from the molecular dynamics simulations. Received: 17 September 1997 / Accepted: 14 October 1997     

Hierarchical structure of the energy landscape of proteins revisited by time series analysis. II. Investigation of explicit solvent effects

Time series analysis tools are employed on the principal modes obtained from the C(alpha) trajectories from two independent molecular-dynamics simulations of alpha-amylase inhibitor (tendamistat). Fluctuations inside an energy minimum (intraminimum motions), transitions between minima (interminimum motions), and relaxations in different hierarchical energy levels are investigated and compared with those encountered in vacuum by using different sampling window sizes and intervals. The low-frequency low-indexed mode relationship, established in vacuum, is also encountered in water, which shows the reliability of the important dynamics information offered by principal components analysis in water. It has been shown that examining a short data collection period (100 ps) may result in a high population of overdamped modes, while some of the low-frequency oscillations (<10 cm(-1)) can be captured in water by using a longer data collection period (1200 ps). Simultaneous analysis of short and long sampling window sizes gives the following picture of the effect of water on protein dynamics. Water makes the protein lose its memory: future conformations are less dependent on previous conformations due to the lowering of energy barriers in hierarchical levels of the energy landscape. In short-time dynamics (<10 ps), damping factors extracted from time series model parameters are lowered. For tendamistat, the friction coefficient in the Langevin equation is found to be around 40-60 cm(-1) for the low-indexed modes, compatible with literature. The fact that water has increased the friction and that on the other hand has lubrication effect at first sight contradicts. However, this comes about because water enhances the transitions between minima and forces the protein to reduce its already inherent inability to maintain oscillations observed in vacuum. Some of the frequencies lower than 10 cm(-1) are found to be overdamped, while those higher than 20 cm(-1) are slightly increased. As for the long-time dynamics in water, it is found that random-walk motion is maintained for approximately 200 ps (about five times of that in vacuum) in the low-indexed modes, showing the lowering of energy barriers between the higher-level minima.     

The Equilibrium Structure of Methyl Fluoride

The equilibrium structure of CH₃F has been determined using new sets of accurate rotational constants that have been determined by taking into account all the interactions between the excited vibrational states. This experimental structure is in excellent agreement with the equilibrium geometry calculated at the CCSD(T) level of theory with the cc-pV(5, Q)Z basis set (including corrections for the core correlation and for the effect of diffuse functions on fluorine). Finally, the experimental and ab initio structures have been combined by a least-squares analysis. The results are , and L _e(HCH) = 110.2 (1)°, where the uncertainties shown in parentheses correspond to three standard deviations.     

Interaction of Carrier Protein with Potential Metallic Drug Candidate N-Glycoside ‘GATPT’: Validation by Multi-Spectroscopic and Molecular Docking Approaches

Lysozyme is often used as a model protein to study interaction with drug molecules and to understand biological processes which help in illuminating the therapeutic effectiveness of the drug. In the present work, in vitro interaction studies of 1-{(2-hydroxyethyl)amino}-2-amino-1,2-dideoxy-d-glucose triphenyl tin (IV) (GATPT) complex with lysozyme were carried out by employing various biophysical methods such as absorption, fluorescence, and circular dichroism (CD) spectroscopies. The experimental results revealed efficient binding affinity of GATPT with lysozyme with intrinsic binding (K_b) and binding constant (K) values in the order of 10⁵ M⁻¹. The number of binding sites and thermodynamic parameters ΔG, ΔH, and ΔS at four different temperatures were also calculated and the interaction of GATPT with lysozyme was found to be enthalpy and entropy driven. The CD spectra revealed alterations in the population of α–helical content within the secondary structure of lysozyme in presence of GATPT complex. The morphological analysis of the complex with lysozyme and lysozyme-DNA condensates was carried out by employing confocal and SEM studies. Furthermore, the molecular docking studies confirmed the interaction of GATPT within the larger hydrophobic pocket of the lysozyme via several non-covalent interactions.     

DNA vibrational coupling revealed with two-dimensional infrared spectroscopy: insight into why vibrational spectroscopy is sensitive to DNA structure

Two-dimensional infrared (2D IR) spectroscopy was used to study the carbonyl vibrational modes of guanine and cytosine bases in A- and B-form DNA. Located between 1600 and 1700 cm(-1), these modes are often used to monitor DNA secondary structure with traditional infrared spectroscopies such as FTIR, but traditional spectroscopies lack the necessary observables to unravel the coupling mechanisms that make these modes sensitive to secondary structure. By using 2D IR spectroscopy and electronic structure calculations on d(G(5)C(5)) and d(GC)(8) model nucleic acids, we find that hydrogen-bonded guanine/cytosine base pairs are primarily electrostatically coupled and that the coupling between these modes can be modeled with a transition dipole density approach. In comparison, electrostatics is insufficient to model stacked bases because of cooperative charge-sharing effects, but the coupling can be accurately calculated using a finite difference method. We find that the coupling is very strong for both hydrogen-bonded and stacked base geometries, creating vibrational modes that extend both across the base pairs and along the lengths of the helices. Our results provide a physical basis for understanding how strong coupling gives rise to the empirically established relationship between infrared spectroscopy and DNA/RNA secondary structure.     

Si~2Cl~6分子的内旋转能垒和振动基频的理论研究

用从头算方法HF/6-31G^*^*和密度函方法B3LYP/6-31G^*^*,对Si~2Cl~6分子的平衡几何构型进行优化,优化的结果与实验结果吻合得较好.并用上述两种不同的方法计算Si~2Cl~6分子的内旋转能垒,结果分别为8.786和6.694kJ/mol,其中DFT方法的计算结果与实验结果4.18kJ/mol吻合得较好.对Si~2Cl~6分子的振动基频进行计算.用HF/6-31G^*^*SQM力场所计算的频率理论值与实验值的平均误差为7.3cm^-^1,用B3LYP/6-31G^*^*未标度的力场所计算的频率理论值与实验值的平均误差为6.0cm^-^1.该密度泛函方法(B3LYP/~6-31G^*^*)的理论计算值比用HF/6-31G^*^*标度后的SQM力场计算的频率与实验值(除Si--Si键扭转振动基频之外的11条振动基频)吻合得更好.并给出了Si--Si键扭转振动基频的预测值。     

Long-time overdamped Langevin dynamics of molecular chains

We present a novel algorithm of constrained, overdamped dynamics to study the long-time properties of peptides, proteins, and related molecules. The constraints are applied to an all-atom model of the molecule by projecting out all components of the nonbonding interactions which tend to alter fixed bond lengths and angles. Because the overdamped dynamical equations are first order in time, the constraints are satisfied by inversion of a banded matrix at each timestep, which is computationally efficient. Thermal effects are included through a Langevin noise term in the equation of motion. Because high-frequency components of the motion have been eliminated, the timestep of the algorithm is determined by the nonbonding forces, which are two to three orders of magnitude weaker than the bonding forces. Using polyalanine as a test example, we demonstrate that trajectories simulating a microsecond of motion can be run about 10³ times faster than an equivalent molecular dynamics simulation. © 1994 by John Wiley & Sons, Inc.     

The (3000), (4000) and (5000) stretching overtone bands of silane—I. The effect of local-mode vibration on rotational constants

The (4000) stretching overtone band of SiH₄ has been observed near 8347 cm⁻¹. A symmetric top rotational structure, similar to that observed in the (3000) band of GeH₄: Q.-S. Zhu, B. A. Thrush and A. G. Robiette, Chem. Phys. Lett. 150, 181 (1988); Q.-S. Zhu and B. A. Thrush, J. Chem. Phys. 92, 2691 (1990) [1], and the (3000) and (5000) bands of SiH₄: Q.-S. Zhu, B.-S. Zhang, Y.-R. Ma and H.-B. Qian, Chem. Phys. Lett. 164, 596 (1989) [2], are clearly demonstrated. Three local-mode bands of SiH₄, (3000), (4000) and (5000) are analysed in the symmetric top model. A striking effect of local-mode vibration on rotational constants is observed and accounted for in a classical picture of vibrational localization.     

Collective dynamics of hydrated β-lactoglobulin by inelastic x-ray scattering

Inelastic x-ray scattering measurements of hydrated β-lactoglobulin (β-lg) were performed to investigate the collective dynamics of hydration water and hydrated protein on a picosecond time scale. Samples with different hydration levels h [=mass of water (g)/mass of protein (g)] of 0 (dry), 0.5, and 1.0 were measured at ambient temperature. The observed dynamical structure factor S(Q,ω)/S(Q) was analyzed by a model composed of a Lorentzian for the central peak and a damped harmonic oscillator (DHO) for the side peak. The dispersion relation between the excitation energy in the DHO model and the momentum transfer Q was obtained for the hydrated β-lg at both hydration levels, but no DHO excitation was found for the dry β-lg. The high-frequency sound velocity was similar to that previously observed in pure water. The ratio of the high-frequency sound velocity of hydrated β-lg to the adiabatic one of hydrated lysozyme (h=0.41) was estimated as ～1.6 for h=0.5. The value is significantly smaller than that (～2) of pure water that has the tetrahedral network structure. The present finding thus suggests that the tetrahedral network structure of water around the β-lg is partially disrupted by the perturbation from protein surface. These results are consistent with those reported from Brillouin neutron spectroscopy and molecular dynamics simulation studies of hydrated ribonuclease A.     

Langevin model of the temperature and hydration dependence of protein vibrational dynamics

The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.     

Theoretical investigation of the structure and vibrational spectra of carbamoyl azide

Molecular structure and vibrational frequencies of carbamoyl azide NH2CO-NNN have been investigated with ab initio and density functional theory (DFT) methods. The molecular geometries for all the possible conformers of the molecule were optimized using DFT-B3LYP, DFT-BLYP and MP2 applying the standard 6-311++G** basis set. From the calculations, the molecule was predicted to exist predominantly in cis conformation with the cis-trans rotational barrier of about 7.91-9.10 kcal/mol depending on the level of theory applied. The vibrational frequencies and the corresponding vibrational assignments of carbamoyl azide in Cs symmetry were examined theoretically and the calculated Infrared and Raman spectra of the molecule in the cis conformation were plotted. Observed frequencies for normal modes were compare with those calculated from normal mode coordinate analysis carried out on the basis of ab initio and DFT force fields using the standard 6-311++G** basis set of the theoretical optimized geometry. Theoretical IR intensities and Raman activities are reported.     

Photoexcitation of the blue light using FAD photoreceptor AppA results in ultrafast changes to the protein matrix

Photoexcitation of the flavin chromophore in the BLUF photosensor AppA results in a conformational change that leads to photosensor activation. This conformational change is mediated by a hydrogen-bonding network that surrounds the flavin, and photoexcitation is known to result in changes in the network that include a strengthening of hydrogen bonding to the flavin C4═O carbonyl group. Q63 is a key residue in the hydrogen-bonding network, and replacement of this residue with a glutamate results in a photoinactive mutant. While the ultrafast time-resolved infrared (TRIR) spectrum of Q63E AppA(BLUF) is characterized by flavin carbonyl modes at 1680 and 1650 cm(-1), which are similar in frequency to the analogous modes from the light activated state of the wild-type protein, a band is also observed in the TRIR spectrum at 1724 cm(-1) that is unambiguously assigned to the Q63E carboxylic acid based on U-(13)C labeling of the protein. Light absorption instantaneously (<100 fs) bleaches the 1724 cm(-1) band leading to a transient absorption at 1707 cm(-1). Because Q63E is not part of the isoalloxazine electronic transition, the shift in frequency must arise from a sub picosecond perturbation to the flavin binding pocket. The light-induced change in the frequency of the Q63E side chain is assigned to an increase in hydrogen-bond strength of 3 kcal mol(-1) caused by electronic reorganization of the isoalloxazine ring in the excited state, providing direct evidence that the protein matrix of AppA responds instantaneously to changes in the electronic structure of the chromophore and supporting a model for photoactivation of the wild-type protein that involves initial tautomerization of the Q63 side chain.     

3D Generalized langevin equation approach to gas–surface reactive scattering: model H+H→H2/Si(100)-(2×1)

Classical trajectory calculation has been performed for the H+H→H₂/Si(100)-(2×1) reaction by the 3D Generalized Langevin Equation (GLE) approach. The implementation of the 3D GLE approach to the H+H→H₂/Si(100)-(2×1) reaction is presented. Reaction probabilities are calculated for given surface temperatures and given collision energies. We also calculated vibrational and rotational distributions of product H₂ molecules from the reaction. About 80% of the product hydrogen molecules are in the ground vibrational state and the remaining 20% of the products are in the excited states. The rotational state shows non-Boltzmann distribution which can be seen in the direct collision process. Vibrational and Rotational distributions are strongly related to the impact parameter. The vibrational distribution is correlated with the x-component of the impact parameter and reflects the dimer nature of the silicon (2×1) surface. Details of the dynamics involving vibrational and rotational transitions are discussed.     

Effects of complex formation on vibrational circular dichroism spectra

The determination of absolute configurations of chiral compounds using VCD is performed by comparing measured vibrational circular dichroism (VCD) spectra with calculated spectra. The process is based on two facts: the two enantiomers have rotational strengths of opposite sign, and the absolute configuration of the molecule used in the calculation is known. However, calculations on isolated molecules very often predict VCD intensities of very different magnitude or even different signs compared to the spectra measured in solution. Therefore, we have carefully analyzed what type of changes are induced by complexation of a solvent molecule to a solute. In the theoretical example of benzoyl-benzoic acid (in a particular chiral conformation) hydrogen bonded to the achiral NH3, we distinguish six cases, ranging from no or very small changes in the rotational strengths of solute modes (case A) to changes of sign of rotational strengths (case B), changes in magnitude (case C), nonzero rotational strengths for modes of the achiral solvent ("transfer of chirality", case D), large frequency shifts accompanied by giant enhancements of the IR and VCD intensities of modes involved in hydrogen bonding (case E), and emergence of new peaks (case F). In this work, all of these situations will be discussed and their origin will be elucidated. On the basis of our analysis, we advocate that codes for VCD rotational strength calculation should output for each mode i the angle xi(i) between the electric and magnetic transition dipole moments because only "robust modes" with xi far from 90 degrees should be used for the determination of the absolute configuration.     

Force-constant computations in cartesian coordinates. Elimination of translational and rotational contributions

A projection method is described for elimination of spurious contributions to calculated cartesian force constants which give rise to non-zero frequencies for translational and rotational modes and which may cause errors in vibrational frequencies. Illustrative calculations for water monomer (in STO—3G) and water dimer (in 4–31G) are discussed. The preference for deuterium-bonded versus hydrogen-bonded isotopomeric water -dimer structures is demonstrated by calculations which satisfy the Teller—Redlich product rule provided that projected force constants are employed.