Molecular dynamics slow motions

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

When the friction coefficient is set to zero, HyperChem performs regular molecular dynamics, and one should use a time step that is appropriate for a molecular dynamics run. With larger values of the friction coefficient, larger time steps can be used. This is because the solution to the Langevin equation in effect separates the motions of the atoms into two time scales the short-time (fast) motions, like bond stretches, which are approximated, and longtime (slow) motions, such as torsional motions, which are accurately evaluated. As one increases the friction coefficient, the short-time motions become more approximate, and thus it is less important to have a small timestep. 

The most serious practical limitation of molecular dynamics comes from its slowness for a small (10-20 atom) system each second of computer time suffices to simulate about 1 picosecond of physical time, whereas one is often interested in simulating phenomena taking place on a much longer time scale. This problem is not merely a matter of existing computers being too slow— indeed, 1 to 10 picoseconds per second is about as fast as one can comfortably watch an animated display of molecular motion— rather it is a manifestation of a common paradox in molecular dynamics concealment of the desired information by mountains of irrelevant detail. ... 

Clarkson et al. investigated molecular dynamics of vanadyl-EDTA and DTPA complexes in sucrose solution or attached to PAMAM dendrimers by EPR [74,75]. The motion-sensitive EPR data of the dendrimeric system have been fitted to an anisotropic model which is described by an overall spherical rotation combined with a rotation around the axis of the arm branching out of the central core. The motions around the axis of the branch connecting the chelate to the central core were found to be very rapid, whereas the overall tumbling was slow. 

Another study used H T, T2 and 13C T, T p measurements to assess the molecular dynamics in dry and wet solid proteins bacterial RNAase, lysozyme and bovine serum albumin.115 All relaxation time data were analysed assuming three components for the molecular motion methyl group rotation and slow and fast oscillations of all atoms. An inhomogeneous distribution of correlation times was found for all samples, not surprisingly given the inhomogeneous nature of the samples. Interestingly, it was found that dehydration affected only the slow internal motions of the proteins and that the fast ones remained unaltered. 

At room temperature, these molecules occupy well-defined locations in their respective crystal lattices. However, they tumble freely and isotropically (equally in all directions) in place at their lattice positions. As a result, their solid phase NMR spectra show features highly reminiscent of liquids. We will see an illustration of this point shortly. Other molecules may reorient anisotropically (as in solid benzene). Polymer segmental motions in the melt may cause rapid reorientation about the chain axis but only relatively slow reorientation of the chain axes themselves. Large molecular aggregates in solution (such as surfactant micelles or protein complexes or nucleic acids) may appear to have solidlike spectra if their tumbling rates are sufficiently slow. There are numerous other instances in which our macroscopic motions of solid and liquid may be at odds with the molecular dynamics. Nuclear magnetic resonance is one of the foremost ways of investigating these situations. 

Similar to fluorescence depolarization and NMR, two limiting cases exist in which the molecular motion becomes too slow or too fast to further effect the ESR lineshape (Fig. 8) (35). At the fast motion limit, one can observe a narrow triplet centered around the average g value igxx + gyy + giz with a distance between lines of aiso = Axx- -Ayy- -A2,z)l3, where gu and Ajj are principal values of the g-tensor and the hyperflne splitting tensor A, respectively. At the slow motion limit, which is also referred to as the rigid limit, the spectrum (shown in Fig. 8) is a simple superposition of spectra for all possible spatial orientations of the nitroxide with no evidence of any motional effects. Between these limits, the analysis of the ESR lineshape and spectral simulations, which are based on the Stochastic Liouville Equation, provide ample information on lipid/protein dynamics and ordering in the membrane (36). 

Relaxation measurements require a considerable investment of syectrometer time and in some cases it may be possible to derive basic information about molecular dynamics from the structural ensemble alone. Although regions of disorder can reflect factors other than dynamics, a recent analysis (55) suggests that ill-defined regions in structural ensembles often do reflect slow, large-amplitude motions. Even if relaxation measurements are... 

Molecular dynamics simulations have shown that for isolated reactants rotational excitation contributes to the enhanced reactivity (cf. Fig. 5, Ref. 97). In the kinematic limit, initial reagent rotational excitation is needed for a finite orbital angular momentum of the relative motion of the products. This is intuitively clear for the H2 -f I2 —t 2 HI reaction, where there is a large change in the reduced mass. The rather slow separation of the heavy iodine atoms means that rotational excitation of HI is needed if the two product molecules are to separate. This is provided by the initial rotational excitation of the reactants. The extensive HI rotation is evident in Fig. 9 which depicts the bond distances of this four-center reaction on a fs time scale. 

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