Molecular modeling of the neurophysin I/oxytocin complex

Neurophysins I and II (NPI and NPII) act in the neurosecretory granules as carrier proteinsfor the neurophyseal hormones oxytocin (OT) and vasopressin (VP), respectively. The NPI/OTfunctional unit, believed to be an (NPI/OT)2 heterotetramer, was modeled using low-resolution structure information, viz. the C carbon atom coordinates of the homologousNPII/dipeptide complex (file 1BN2 in the Brookhaven Protein Databank) as a template. Itsall-atom representation was obtained using standard modeling tools available within theINSIGHT/Biopolymer modules supplied by Biosym Technologies Inc. A conformation of theNPI-bound OT, similar to that recently proposed in a transfer NOE experiment, was dockedinto the ligand-binding site by a superposition of its Cys1-Tyr2 fragment onto the equivalentportion of the dipeptide in the template. The starting complex for the initial refinements wasprepared by two alternative strategies, termed Model I and Model II, each ending with a100 ps molecular dynamics (MD) simulation in water using the AMBER 4.1 force field. The freehomodimer NPI2 was obtained by removal of the two OT subunits from their sites, followedby a similar structure refinement. The use of Model I, consisting of a constrained simulatedannealing, resulted in a structure remarkably similar to both the NPII/dipeptide complex anda recently published solid-state structure of the NPII/OT complex. Thus, Model I isrecommended as the method of choice for the preparation of the starting all-atom data forMD. The MD simulations indicate that, both in the homodimer and in the heterotetramer, the310-helices demonstrate an increased mobility relative to the remaining body of the protein.Also, the C-terminal domains in the NPI2 homodimer are more mobile than the N-terminalones. Finally, a distinct intermonomer interaction is identified, concentrated around its mostprominent, although not unique, contribution provided by an H-bond from Ser25O in one NPI unit to Glu81 O in the other unit. This interaction is present in the heterotetramer(NPI/OT)2 and absent or weak in the NPI2 homodimer. We speculate that this interaction,along with the increased mobility of the 310-helices and the carboxy domains, may contributeto the allosteric communication between ligand binding and NPI dimerization.     

Non-adiabatic molecular dynamics with quantum solvent effects

Three novel approaches extending quantum-classical non-adiabatic (NA) molecular dynamics (MD) to include quantum effects of solvent environments are described. In a standard NA-MD the solute subsystem is treated quantum mechanically, while the larger solvent part of a system is treated classically. The three novel approaches presented here are based on the Bohmian formulation of quantum mechanics, the stochastic Schrödinger equation for the evolution of open quantum systems and the quantized Hamilton dynamics generalization of classical mechanics. The approaches extend the standard NA-MD to incorporate the following quantum effects of the solvent. (1) Branching, i.e. the ability of solvent quantum wave packets to split and follow asymptotically diverging trajectories correlated with different quantum states of the solute. (2) Decoherence, i.e. loss of quantum interference within the solute subsystem induced by the diverging solvent trajectories. (3) Zero point energy that contributes to NA coupling and must be preserved during the energy exchange between solvent and solute degrees of freedom. The Bohmian quantum-classical mechanics, stochastic mean-field and quantized mean-field approximations incorporate the quantum solvent effects into the standard quantum-classical NA-MD in a straightforward and efficient way that can be easily applied to quantum dynamics of condensed phase chemical systems.     

Extending molecular dynamics time scales with milestoning: example of complex kinetics in a solvated peptide

A recently introduced computational algorithm to extend time scales of atomically detailed simulations is illustrated. The algorithm, milestoning, is based on partitioning the dynamics to a sequence of trajectories between "milestones" and constructing a non-Markovian model for the motion along a reaction coordinate. The kinetics of a conformational transition in a blocked alanine is computed and shown to be accurate, more efficient than straightforward molecular dynamics by a factor of about 9, and nonexponential. A general scaling argument predicts a linear speedup with the number of milestones for diffusive processes and an exponential speedup for transitions over barriers. The algorithm is also trivial to parallelize. As a side result, milestoning also produces the free energy profile along the reaction coordinate and is able to describe nonequilibrium motions along one (or a few) degrees of freedom.     

Quasi-Hamiltonian equations of motion for internal coordinate molecular dynamics of polymers

Conventional molecular dynamics simulations of macromolecules require long computational times because the most interesting motions are very slow compared to the fast oscillations of bond lengths and bond angles that limit the integration time step. Simulation of dynamics in the space of internal coordinates, that is, with bond lengths, bond angles, and torsions as independent variables, gives a theoretical possibility of eliminating all uninteresting fast degrees of freedom from the system. This article presents a new method for internal coordinate molecular dynamics simulations of macromolecules. Equations of motion are derived that are applicable to branched chain molecules with any number of internal degrees of freedom. Equations use the canonical variables and they are much simpler than existing analogs. In the numerical tests the internal coordinate dynamics are compared with the traditional Cartesian coordinate molecular dynamics in simulations of a 56 residue globular protein. For the first time it was possible to compare the two alternative methods on identical molecular models in conventional quality tests. It is shown that the traditional and internal coordinate dynamics require the same time step size for the same accuracy and that in the standard geometry approximation of amino acids, that is, with fixed bond lengths, bond angles, and rigid aromatic groups, the characteristic step size is 4 fs, which is 2 times higher than with fixed bond lengths only. The step size can be increased up to 11 fs when rotation of hydrogen atoms is suppressed. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1354–1364, 1997     

Electron-vibrational dynamics of photoexcited polyfluorenes

The highly polarizable pi-electron system of conjugated molecules forms the basis for their unique electronic and photophysical properties, which play an important role in numerous biological phenomena and make them important materials for technological applications. We present a theoretical investigation of the dynamics and relaxation of photoexcited states in conjugated polyfluorenes, which are promising materials for display applications. Our analysis shows that both fast (approximately 20 fs) and slow (approximately 1 ps) nuclear motions couple to the electronic degrees of freedom during the excited-state dynamics. Delocalized excitations dominate the absorption, whereas emission comes from localized (self-trapped) excitons. This localization is attributed to an inherent nonlinear coupling among vibronic degrees of freedom which leads to lattice and torsional distortions and results in specific signatures in spectroscopic observables. Computed vertical absorption and fluorescence frequencies as well as photoluminescence band shapes show good agreement with experiment. Finally, we demonstrate that dimerization such as spiro-linking does not affect the emission properties of molecules because the excitation becomes confined on a single chain of the composite molecule.     

利用基于直接动力学的轨线面跳跃方法处理非绝热过程

势能面交叉引起的非绝热过程广泛存在于光化学和光物理中。对这一过程进行描述是理论化学的重要挑战之一。非绝热过程涉及原子核与电子之间的耦合运动,因此量子化学的基本假设之一"玻恩-奥本海默"近似被打破,所以对其进行描述需要发展新的动力学理论方法。在这些方法中,Tully发展的最少轨线面跳跃方法凭借易于程序化、便于计算等优点已经发展成为处理非绝热问题的主要动力学方法之一。其中原子核以经典的方式在单一势能面上进行演化,电子以量子的方式沿着同一轨线进行演化。在整个演化过程中,非绝热跃迁通过轨线在不同势能面间的跃迁来描述,其中跳跃发生的几率与电子的演化有关。如果将该方法与从头算直接动力学相结合,可以在全原子水平上研究实际分子体系的非绝热动力学,给出其激发态寿命、非绝热动力学中分子的主要运动方式、反应通道以及分支比等重要信息。本文旨在讨论最少面跳跃直接动力学方法研究非绝热问题的一些进展,包括动力学基本理论,特别关注将最少面跳跃方法和直接动力学结合的数值实现细节,同时讨论该方法在研究实际体系当中的一些应用,并对轨线面跳跃方法下一步发展的一些方向进行合理的展望。     

The flying ice cube: Velocity rescaling in molecular dynamics leads to violation of energy equipartition

This article describes an unexpected phenomenon encountered during MD simulations: velocity rescaling using standard protocols can systematically change the proportion of total kinetic energy (KE) found in motions associated with the various degrees of freedom. Under these conditions, the simulation violates the principle of equipartition of energy, which requires a mean kinetic energy of RT/2 in each degree of freedom. A particularly pathological form of this problem occurs if one does not periodically remove the net translation of (and rotation about) the center of mass. In this case, almost all of the kinetic energy is converted into these two kinds of motion, producing a system with almost no kinetic energy associated with the internal degrees of freedom. We call this phenomenon “the flying ice cube.” We present a mathematical analysis of a simple diatomic system with two degrees of freedom, to document the origin of the problem. We then present examples from three kinds of MD simulations, one being an in vacuo simulation on a diatomic system, one involving a low resolution model of DNA in vacuo, and the third using a traditional all-atom DNA model with full solvation, periodic boundary conditions, and the particle mesh Ewald method for treating long-range electrostatics. Finally, we discuss methods for avoiding the problem. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 726–740, 1998     

Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Nonlinear reaction dynamics through a rank-one saddle is investigated for many-particle system with spatial rotation. Based on the recently developed theories of the phase space geometry in the saddle region, we present a theoretical framework to incorporate the spatial rotation which is dynamically coupled with the internal vibrational motions through centrifugal and Coriolis interactions. As an illustrative simple example, we apply it to isomerization reaction of HCN with some nonzero total angular momenta. It is found that no-return transition state (TS) and a set of impenetrable reaction boundaries to separate the "past" and "future" of trajectories can be identified analytically under rovibrational couplings. The three components of the angular momentum are found to have distinct effects on the migration of the "anchor" of the TS and the reaction boundaries through rovibrational couplings and anharmonicities in vibrational degrees of freedom. This method provides new insights in understanding the origin of a wide class of reactions with nonzero angular momentum.     

Nonadiabatic quantum dynamics of Br2 in solid Ar: A four-dimensional study of the B to C state predissociation

Quantum dynamics simulations are performed for a diatomics-in-molecules based model of Br₂ in solid Ar which incorporates four nuclear degrees of freedom and four electronic states. The nuclear motions comprise two large amplitude coordinates describing the Br₂ bond distance and an effective symmetry-preserving matrix mode. Two symmetry-lowering harmonic modes are added in the spirit of linear vibronic coupling theory. Initiating the dynamics on the B state by means of an ultrafast laser pulse, nonadiabatic transitions to the two degenerate C states are monitored and the effect of vibrational preexcitation in the electronic ground state is investigated.     

Sampling of slow diffusive conformational transitions with accelerated molecular dynamics

Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an accelerated molecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.     

Molecular dynamics with quantum transitions study of the vibrational relaxation of the HOD bend fundamental in liquid D2O

The molecular dynamics with quantum transitions method is used to study the vibrational relaxation of the HOD bend fundamental in liquid D(2)O. All of the vibrational bending degrees of freedom of the HOD and D(2)O molecules are described by quantum mechanics, while the remaining translational and rotational degrees of freedom are described classically. The effect of the coupling between the rotational and vibrational degrees of freedom of the deuterated water molecules is analyzed. A kinetic mechanism based on three steps is proposed in order to interpret the dynamics of the system. It is shown that intermolecular vibrational energy transfer plays an important role in the relaxation process and also that the transfer of energy into the rotational degrees of freedom is favored over the transfer of energy into the translational motions. The thermalization of the system after the relaxation is reached in a shorter time scale than that of the recovery of the hydrogen bond network. The relaxation and equilibration times obtained compare well with experimental and previous theoretical results.     

Simulating quantum dynamics in classical environments

Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum–classical systems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approximation. The dynamics of these composite systems are governed by a quantum–classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of trajectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many-body environments.     

Software news and updates. Carma: a molecular dynamics analysis program

A computer program has been developed to aid the analysis of molecular dynamics trajectories. The program is tuned for macromolecular large-scale problems and supports features such as removal of global translations-rotations of the solute, calculation of average distance maps and their corresponding standard deviations, calculation of the variance-covariance and cross-correlation matrices, and principal component analysis of trajectories with the added ability to create artificial trajectories based on selected eigenvectors. Limited graphics (trajectory viewing) capabilities are also available.     

A 45-ns molecular dynamics simulation of hemoglobin in water by vectorizing and parallelizing COSMOS90 on the earth simulator: dynamics of tertiary and quaternary structures

Molecular dynamics (MD) simulations of human adult hemoglobin (HbA) were carried out for 45 ns in water with all degrees of freedom including bond stretching and without any artificial constraints. To perform such large-scale simulations, one of the authors (M.S.) accelerated his own software COSMOS90 on the Earth Simulator by vectorization and parallelization. The dynamical features of HbA were investigated by evaluating root-mean-square deviations from the initial X-ray structure (an oxy T-state hemoglobin with PDB code: 1GZX) and root-mean-square fluctuations around the average structure from the simulation trajectories. The four subunits (alpha(1), alpha(2), beta(1), and beta(2)) of HbA maintained structures close to their respective X-ray structures during the simulations even though no constraints were applied to HbA in the simulations. Dimers alpha(1)beta(1) and alpha(2)beta(2) also maintained structures close to their respective X-ray structures while they moved relative to each other like two stacks of dumbbells. The distance between the two dimers (alpha(1)beta(1) and alpha(2)beta(2)) increased by 2 A (7.4%) in the initial 15 ns and stably fluctuated at the distance with the standard deviation 0.2 A. The relative orientation of the two dimers fluctuated between the initial X-ray angle -100 degrees and about -105 degrees with intervals of a few tens of nanoseconds.     

Improving efficiency of large time-scale molecular dynamics simulations of hydrogen-rich systems

A systematic analysis is performed on the effectiveness of removing degrees of freedom from hydrogen atoms and/or increasing hydrogen masses to increase the efficiency of molecular dynamics simulations of hydrogen-rich systems such as proteins in water. In proteins, high-frequency bond-angle vibrations involving hydrogen atoms limit the time step to 3 fs, which is already a factor of 1.5 beyond the commonly used time step of 2 fs. Removing these degrees of freedom from the system by constructing hydrogen atoms as dummy atoms, allows the time step to be increased to 7 fs, a factor of 3.5 compared with 2 fs. Additionally, a gain in simulation stability can be achieved by increasing the masses of hydrogen atoms with remaining degrees of freedom from 1 to 4 u. Increasing hydrogen mass without removing the high-frequency degrees of freedom allows the time step to be increased only to 4 fs, a factor of two, compared with 2 fs. The net gain in efficiency of sampling configurational space may be up to 15% lower than expected from the increase in time step due to the increase in viscosity and decrease in diffusion constant. In principle, introducing dummy atoms and increasing hydrogen mass do not influence thermodynamical properties of the system and dynamical properties are shown to be influenced only to a moderate degree. Comparing the maximum time step attainable with these methods (7 fs) to the time step of 2 fs that is routinely used in simulation, and taking into account the increase in viscosity and decrease in diffusion constant, we can say that a net gain in simulation efficiency of a factor of 3 to 3.5 can be achieved. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 786–798, 1999     

Conformational dynamics of polypeptides and proteins in the dihedral angle space and in the cartesian coordinate space: Normal mode analysis of deca-alanine

Effects of different treatments of the degrees of freedom of bond length stretching and bond angle bending in computational analysis of conformational dynamics of proteins and polypeptides are assessed. More specifically, the normal mode analysis of conformational dynamics of α-helix of deca-alanine has been carried out both in the dihedral angle space (DAS) and in the Cartesian coordinate space (CCS). Almost perfect one-to-one correspondence has been found between normal modes in the CCS with frequencies less than 128 cm^?1 and those in the DAS with frequencies less than 164 cm^?1. Patterns of atomic displacements in the corresponding modes are very similar. This indicates that the effects of fixing degrees of freedom of bond length stretching and bond angle bending on the very-low-frequency normal modes in the CCS with frequencies less than 128 cm^?1 are almost solely to increase the frequencies by about 20%. The conclusion indicates that the different treatment of these degree does not lead to qualitatively different results as long as low-frequency motions are concerned. Based on the results of calculation, mechanical property of the α-helix of deca-alanine is discussed.     

Representing and selecting vibrational angular momentum states for quasiclassical trajectory chemical dynamics simulations

Linear molecules with degenerate bending modes have states, which may be represented by the quantum numbers N and L. The former gives the total energy for these modes and the latter identifies their vibrational angular momentum jz. In this work, the classical mechanical analog of the N,L-quantum states is reviewed, and an algorithm is presented for selecting initial conditions for these states in quasiclassical trajectory chemical dynamics simulations. The algorithm is illustrated by choosing initial conditions for the N = 3 and L = 3 and 1 states of CO2. Applications of this algorithm are considered for initial conditions without and with zero-point energy (zpe) included in the vibrational angular momentum states and the C-O stretching modes. The O-atom motions in the x,y-plane are determined for these states from classical trajectories in Cartesian coordinates and are compared with the motion predicted by the normal-mode model. They are only in agreement for the N = L = 3 state without vibrational angular momentum zpe. For the remaining states, the Cartesian O-atom motions are considerably different from the elliptical motion predicted by the normal-mode model. This arises from bend-stretch coupling, including centrifugal distortion, in the Cartesian trajectories, which results in tubular instead of elliptical motion. Including zpe in the C-O stretch modes introduces considerable complexity into the O-atom motions for the vibrational angular momentum states. The short-time O-atom motions for these trajectories are highly irregular and do not appear to have any identifiable characteristics. However, the O-atom motions for trajectories integrated for substantially longer period of times acquire unique properties. With C-O stretch zpe included, the long-time O-atom motion becomes tubular for trajectories integrated to approximately 14 ps for the L = 3 states and to approximately 44 ps for the L = 1 states.