Coupling overall rotations with modal dynamics

 We consider a model for protein dynamics in which only certain collective, global motions are allowed. These directions are given by the slowest harmonics modes, as given in the reference frame of the protein. Furthermore, the latter is allowed to rotate and translate in response to interactions with other molecules. The model is obtained by projecting the (averaged) Newton equations onto this set of harmonic modes. We show that the subsequent homogenization of the time scales allows time steps one order of magnitude larger than the standard ones. This homogenization is also shown to be a necessary ingredient in order to get meaningful statistics of the trajectory. Received: 3 July 2000 / Accepted: 15 September 2000 / Published online: 21 December 2000     

Rotationally inelastic molecule–surface scattering: dynamical lie algebraic method

The rotationally inelastic molecule–surface scattering is analyzed using dynamical Lie algebraic method. We treat, by example, the simple model of the scattering of NO from a rigid, flat Ag(111) surface. The explicit expressions of transition probability and the probability current density are obtained. It is proved that dynamical Lie algebraic method can be useful for describing the scattering problems. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 500–510, 2000     

Molecular motion and relaxation studies of aliphatic polyureas by thermal windowing thermally stimulated depolarization current technique

Molecular motion and relaxation studies using a thermal windowing thermally stimulated depolarization current (TW‐TSDC) were performed for aliphatic polyureas 7 and 9. Global thermally stimulated depolarization current gave three characteristic major peaks corresponding to the α, β, and γ relaxation modes at 78.5, −44, and −136°C for polyurea 7 and at 80, −50, and −134°C for polyurea 9, respectively. The α relaxation is related to the large‐scale molecular motion due to micro‐Brownian motion of long‐range segments. This relaxation is significantly related to the glass‐transition temperature. The β relaxation is caused by the local thermal motion of long‐chain segments. The γ relaxation is caused by the limited local motion of hydrocarbon sections. Temperature dependence of relaxation times was expressed well using Vogel–Tammann–Fulcher (VTF) expression. 3‐D simulation of dielectric constants of dielectric strength and loss factor were performed in the frequency range from 10⁻⁶ to 10⁴ Hz and temperature range from −150 to 250°C, using the relaxation parameters obtained from the TW‐TSDC method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 88–94, 2000     

MBO(N)D: A multibody method for long‐time molecular dynamics simulations

A modeling approach that can significantly speed up the dynamics simulation of large molecular systems is presented herein. A multigranular modeling approach, whereby different parts of the molecule are modeled at different levels of detail, is enabled by substructuring. Substructuring the molecular system is accomplished by collecting groups of atoms into rigid or flexible bodies. Body flexibility is modeled by a truncated set of body‐based modes. This approach allows for the elimination of the high‐frequency harmonic motion while capturing the low‐frequency anharmonic motion of interest. This results in the use of larger integration step sizes, substantially reducing the computational time required for a given dynamic simulation. The method also includes the use of a multiple time scale (MTS) integration scheme. Speed increases of 5‐ to 30‐fold over atomistic simulations have been realized in various applications of the method. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 159–184, 2000     

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.     

Alkylation Effects on the Energy Transfer of Highly Vibrationally Excited Naphthalene

The energy transfer of highly vibrationally excited isomers of dimethylnaphthalene and 2‐ethylnaphthalene in collisions with krypton were investigated using crossed molecular beam/time‐of‐flight mass spectrometer/time‐sliced velocity map ion imaging techniques at a collision energy of approximately 300 cm^?1. Angular‐resolved energy‐transfer distribution functions were obtained directly from the images of inelastic scattering. The results show that alkyl‐substituted naphthalenes transfer more vibrational energy to translational energy than unsubstituted naphthalene. Alkylation enhances the V→T energy transfer in the range ?ΔE_d=?100～?1500 cm^?1 by approximately a factor of 2. However, the maximum values of V→T energy transfer for alkyl‐substituted naphthalenes are about 1500～2000 cm^?1, which is similar to that of naphthalene. The lack of rotation‐like wide‐angle motion of the aromatic ring and no enhancement in very large V→T energy transfer, like supercollisions, indicates that very large V→T energy transfer requires special vibrational motions. This transfer cannot be achieved by the low‐frequency vibrational motions of alkyl groups.     

Coherent Motion Reveals Non‐Ergodic Nature of Internal Conversion between Excited States

We found that specific nuclear motion along low‐frequency modes is effective in coupling electronic states and that this motion prevail in some small molecules. Thus, in direct contradiction to what is expected based on the standard models, the internal conversion process can proceed faster for smaller molecules. Specifically, we focus on the S₂→S₁ internal conversion in cyclobutanone, cyclopentanone, and cyclohexanone. By means of time‐resolved mass spectrometry and photoelectron spectroscopy the relative rate of this transition is determined to be 13:2:1. Remarkably, we observe coherent nuclear motion on the S₂ surface in a ring‐puckering mode and motion along this mode in combination with symmetry considerations allow for a consistent explanation of the observed relative time‐scales not afforded by only considering the density of vibrational states or other aspects of the standard models.     

Collective motion artifacts arising in long‐duration molecular dynamics simulations

We tested a variety of molecular dynamics simulation strategies in long‐duration (up to several nanoseconds) constant‐temperature simulations of liquid water under periodic boundary conditions. Such long durations are necessary to achieve adequate conformational sampling in simulations of membrane assemblies and other large biomolecular systems. Under a variety of circumstances, serious artifacts arise in the form of spurious collective behavior that becomes obvious only after the simulation has gone at least several hundred picoseconds. The potential energy of the system drops and the system changes from a liquid to an icy or glassy state. The underlying cause is accumulated center‐of‐mass motion of the system, coupled with velocity rescaling associated with constant‐temperature control. The velocity rescaling in the constant‐temperature algorithm reduces the thermal velocity as the net center‐of‐mass velocity grows, effectively causing the kinetic energy of the system to drain from thermal motions into coordinated motions. We found that the incidence and magnitude of the underlying artifactual motion leading to the spurious transition is mediated by: choice of method for computing electrostatic interactions; choice of ensemble; size of the simulation cell; SHAKE tolerance; frequency of nonbonded pairlist updating; and closeness of coupling to the temperature bath. The appearance of the spurious transition can be avoided by periodically subtracting net center‐of‐mass motion during the dynamics, or by improving the accuracy of the simulation by means of tightening SHAKE tolerance and updating nonbonded pairlists every timestep. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 121–131, 2000     

OPAL: A multiscale multicenter simulation package based on MPI‐2 protocol

By using MPI‐2 standard, we designed and implemented a new multiscale simulation architecture OPAL. It requires minimum modification to existing simulation code as maintaining the execution efficiency. The new architecture is capable of dynamical region identification, dynamical process spawning, and is grid‐computing friendly. We demonstrated its usage and power with a simple test case: NaCl dissociation in water. The code shows excellent linear scaling capability, and no obvious degradation is observed. The communication time used by OPAL is negligible compared with its execution time, proving its high efficiency. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Conductivity relaxation behavior of interpenetrating polymer network composites of polypyrrole and poly(styrene‐co‐butyl acrylate)

Conductivity relaxation spectra of interpenetrating network conducting composites of polypyrrole (PPy) and poly(styrene‐co‐butyl acrylate) (SBA) have been analysed on the basis of coupling model developed by Ngai. The macroscopic activation energy obtained from coupling model using the stretch exponent β compares favourably with the tunnel energy estimated from the overlapping large polaron tunnelling (OLPT) model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1193–1200, 2000     

Interpretation of the TSDC fractional polarization experiments on the α‐relaxation of polymers

We report on the interpretation of the thermally stimulated depolarization current (TSDC) experiments, with partial polarization methods, on the dielectric α‐relaxation. The results obtained on polyvinyl acetate are rationalized on the basis of the Boltzmann superposition principle in combination with a Kohlrausch–Williams–Watts (KWW) time decay of the polarization (with the β exponent essentially temperature independent and equal to the value determined by conventional dielectric methods at T_g). From this analysis of the global TSDC spectrum we found a complex temperature dependence of the KWW relaxation time, which is Arrhenius‐like at the lowest temperatures but crosses over to the Vogel–Fulcher behavior observed above T_g in the temperature range of the TSDC peak. On the basis of these results, we found the way of predicting the TSDC spectra measured after partial polarization procedures. We found that, the distribution of activation energies and compensation behavior deduced by following the standard way of analysis are associated to the assumption of an Arrhenius‐like temperature dependence of the α‐relaxation time in the temperature range explored by TSDC. Therefore we conclude that both the distribution of activation energies and compensation behavior obtained by following the standard way of analysis do not give a proper physical picture of the α‐relaxation of glassy polymers around the glass‐transition temperature. Our results also show that the partial polarization TSDC methods are not able to give insight about the actual existence or not of a distribution of relaxation times at the origin of the nonexponentiality of the α‐relaxation of polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2105–2113, 2000     

A Sharp Thermal Transition of Fast Aromatic‐Ring Dynamics in Ubiquitin

Aromatic amino acid side chains have a rich role within proteins and are often central to their structure and function. Suitable isotopic‐labelling strategies enable studies of sub‐nanosecond aromatic‐ring dynamics using solution NMR relaxation methods. Surprisingly, it was found that the three aromatic side chains in human ubiquitin show a sharp thermal dynamical transition at approximately 312 K. Hydrostatic pressure has little effect on the low‐temperature behavior, but somewhat decreases the amplitude of motion in the high‐temperature regime. Therefore, below the transition temperature, ring motion is largely librational. Above this temperature, a complete ring‐rotation process that is fully consistent with a continuous diffusion not requiring the transient creation of a large activated free volume occurs. Molecular dynamics simulations qualitatively corroborate this view and reinforce the notion that the dynamical character of the protein interior has much more liquid‐alkane‐like properties than previously appreciated.     

Fluorine Substitution Effects on Flexibility and Tunneling Pathways: The Rotational Spectrum of 2‐Fluorobenzylamine

The effect of ring fluorination on the structural and dynamical properties of the flexible model molecule 2‐fluorobenzylamine has been studied by rotational spectroscopy in free‐jet expansion and quantum chemical methods. The complete potential energy surface originating from the flexibility of the aminic side chain has been calculated at the B3LYP/6‐311++G** level of theory and the stable geometries were also characterized with MP2/6‐311++G**. The rotational spectra show the presence of two of the predicted four stable conformers: the global minimum (I), in which the side chain’s dihedral angle with the phenyl plane is almost perpendicular, is stabilized by an intramolecular hydrogen bond between the fluorine atom and one hydrogen of the aminic group; and a second conformer II (E_II?E_I≈5 kJ mol^?1) in which the dihedral angle is smaller and the amino group points towards the aromatic ortho hydrogen atom. This conformation is characterized by a tunneling motion between two equivalent positions of the amino group with respect to the phenyl plane, which splits the rotational transition. The ortho fluorination increases, with respect to benzylamine, the tunneling splitting of this motion by four orders of magnitude. The motion is analyzed with a one‐dimensional flexible model, which allows estimation of the energy barrier for the transition state as approximately 8.0 kJ mol^?1.     

Langevin dynamics of molecules with internal rigid fragments in the harmonic regime

An approximation scheme is developed to compute Brownian motion according to the Langevin equation for a molecular system moving in a harmonic force field (corresponding to a quadratic potential energy surface) and characterized by one or more rigid internal fragments. This scheme, which relies on elements of the rotation translation block (RTB) method for computing vibrational normal modes of large molecules developed by Sanejouand and co-workers [Biopolymers 34, 759 (1994); Proteins: Struct., Funct., Genet. 41, 1 (2000)], provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment. The number of dynamical degrees of freedom in the problem is thereby reduced, often dramatically. To illustrate the method, the relaxation kinetics of the small membrane-bound ion channel protein gramicidin-A, subjected to an externally imposed impulse, is computed. The results obtained from all-atom dynamics are compared to those obtained using the RTB-Langevin dynamics approximation (treating eight indole moieties as internal rigid fragments): good agreement between the two treatments is found.     

Exact quantum solutions of general driven time‐dependent quantum quadratic system

We studied the general time‐dependent linear and quadratic system via dynamical symmetries. In an algebraic framework, we obtained exact solutions of the evolution operators, propagators, and wave functions of the general time‐dependent linear and quadratic system. To illustrate our calculations, we discuss a few special cases, including a particle driven by a monochromatic electric field, and cases of oscillatory, linear, or monotonic with respect to the time of the quadratic system. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Thermophysical Characterization of Paraffin Wax Based on Mass-Accommodation Methods Applied to a Cylindrical Thermal Energy-Storage Unit

Two mass-accommodation methods are proposed to describe the melting of paraffin wax used as a phase-change material in a centrally heated annular region. The two methods are presented as models where volume changes produced during the phase transition are incorporated through total mass conservation. The mass of the phase-change material is imposed as a constant, which brings an additional equation of motion. Volume changes in a cylindrical unit are pictured in two different ways. On the one hand, volume changes in the radial direction are proposed through an equation of motion where the outer radius of the cylindrical unit is promoted as a dynamical variable of motion. On the other hand, volume changes along the axial symmetry axis of the cylindrical unit are proposed through an equation of motion, where the excess volume of liquid constitutes the dynamical variable. The energy–mass balance at the liquid–solid interface is obtained according to each method of conceiving volume changes. The resulting energy–mass balance at the interface constitutes an equation of motion for the radius of the region delimited by the liquid–solid interface. Subtle differences are found between the equations of motion for the interface. The differences are consistent with mass conservation and local mass balance at the interface. Stationary states for volume changes and the radius of the region delimited by the liquid–solid interface are obtained for each mass-accommodation method. We show that the relationship between these steady states is proportional to the relationship between liquid and solid densities when the system is close to the high melting regime. Experimental tests are performed in a vertical annular region occupied by a paraffin wax. The boundary conditions used in the experimental tests produce a thin liquid layer during a melting process. The experimental results are used to characterize the phase-change material through the proposed models in this work. Finally, the thermodynamic properties of the paraffin wax are estimated by minimizing the quadratic error between the temperature readings within the phase-change material and the temperature field predicted by the proposed model.     

Light‐induced Modulation of Protein Dynamics During the Photocycle of Bacteriorhodopsin†

Knowledge about the dynamical properties of a protein is of essential importance for understanding the structure–dynamics–function relationship at the atomic level. So far, however, the correlation between internal protein dynamics and functionality has only been studied indirectly in steady‐state experiments by variation of external parameters like temperature and hydration. In the present study we describe a novel type of (laser‐neutron) pump‐probe experiment, which combines in situ optical activation of the biological function of a membrane protein with a time‐dependent monitoring of the protein dynamics using quasielastic neutron scattering. As a first successful application we present data obtained selectively in the ground state and in the M‐intermediate of bacteriorhodopsin (BR). Temporary alterations in both localized reorientational protein motions and harmonic vibrational dynamics have been observed during the photocycle of BR. This observation is a direct proof for the functional significance of protein structural flexibility, which is correlated with the large‐scale structural changes in the protein structure occurring during the M‐intermediate. We anticipate that functionally important modulations of protein dynamics as observed here are of relevance for most other proteins exhibiting conformational transitions in the time course of functional operation.     

Quantum effects in light and heavy liquid water: A rigid-body centroid molecular dynamics study

The centroid molecular dynamics (CMD) method is applied to the study of liquid water in the context of the rigid-body approximation. This rigid-body CMD technique, which is significantly more efficient than the standard CMD method, is implemented on the TIP4P model for water and used to examine isotopic effects in the equilibrium and dynamical properties of liquid H(2)O and D(2)O. The results obtained with this approach compare remarkably well with those determined previously with path integrals simulations as well as those obtained from the standard CMD method employing flexible models. In addition, an examination of the impact of quantization on the rotational and librational motion of the water molecule is also reported.