Atomic fluctuations

They compared the PME method with equivalent simulations based on a 9 A residue-based cutoflF and found that for PME the averaged RMS deviations of the nonhydrogen atoms from the X-ray structure were considerably smaller than in the non-PME case. Also, the atomic fluctuations calculated from the PME dynamics simulation were in close agreement with those derived from the crystallographic temperature factors. In the case of DNA, which is highly charged, the application of PME electrostatics leads to more stable dynamics trajectories with geometries closer to experimental data [30]. A theoretical and numerical comparison of various particle mesh routines has been published by Desemo and Holm [31]. 

An important characteristic of biomolecular motion is that the different types of motion are interdependent and coupled to one another. For example, a large-scale dynamic transition cannot occur without involving several medium-scale motions, such as helix rearrangements. Medium-scale motions cannot occur without involving small-scale motions, such as side-chain movement. Finally, even side-chain motions cannot occur without the presence of the very fast atomic fluctuations, which can be viewed as the lubricant that enables the whole molecular construction to move. From the point of view of dynamic... 

Atomic fluctuation Temporal diffusion pathways onds (ps) (10 -10 s) less... 

T Ichiye, M Karplus. Collective motions m proteins A covariance analysis of atomic fluctuations m molecular dynamics and normal mode simulations. Proteins Stiaict Eunct Genet 11 205-217, 1991. 

In the procedure of X-ray refinement, the positions of the atoms and their fluctuations appear as parameters in the structure factor. These parameters are varied to match the experimentally determined strucmre factor. The term pertaining to the fluctuations is the Debye-Waller factor in which the atomic fluctuations are represented by the atomic distribution tensor ... 

Figure 2. Temperature dependence of mean square atomic fluctuations of the Z-DNA hexamer. (a) Mean square atomic fluctuations were calculated directly from the molecular dynamics trajectories.

In order to discuss the various techniques we must distinguish between diffusive and non-diffusive systems (J8). Diffusive systems, such as liquids, are characterized by the eventual diffusion of particles over all of the available space non-diffusive systems such as solids, glasses and macromolecules with a definite average structure are characterized by time independent average positions around which the atoms fluctuate. 

One can hence think of (normal-mode composition factor) ej = ejaSja as the fractional involvement of atom j in normal mode a.The dimensionless vector eja also specifies the direction of the motion of atom j in the ot-th normal mode. Interestingly, the mode composition factors are also related to the magnitude of the atomic fluctuations. In a stationary state ) of a harmonic system, the mean square deviation (msd) of atom j from its equilibrium position may be expressed as a sum over modes of nonzero frequency ... 

Stereodynamics of Cyclic Nitronates From general considerations and according to X-ray diffraction data (263a), molecules of hve-membered cyclic nitronates should adopt an envelope conformation with the C-5 atom deviating from the plane. This atom fluctuates together with its substituents (R4 and R5) (Scheme 3.83, process a). 

One result from the analysis of the MD simulation was the proposal of a new enzymic pathway for hydrolysis by lysozyme. We begin with a description of the alternative mechanism, and the basis on which it was proposed. The energetics of the individual GlcNAc units in the lysozyme cleft are then presented, followed by a graphical representation of the correlation between the atomic fluctuations of the substrate and those of the enzyme. Of particular interest is the fact that the binding interactions stabilize a bound state conformation for the two glycosides involved in hydrolysis that is optimum for catalysis by the alternative mechanism and which differs from the conformations of the other glycosides. These conformational features are described in the final two sections. 

Normalized cross-correlations in the atomic fluctuations between substrate and lysozyme atoms were calculated from... 

To provide an understanding of the importance of solvent mobility and the intrinsic protein energy surface, an MDS of proteins and surrounding solvent molecules at different temperatures has been performed. The simulation of myoglobin dynamics showed that solvent mobility is the dominant factor in determining protein atomic fluctuations above 180 K (Vitkup et ah, 2000). The drastic effects of water molecule dynamics on the intramolecular motion of RNase and xylase was demonstrated in recent computer simulation studies (Reat et al., 2000 Tarek et al, 2000). Extensive simulations were carried out to identify the time-scale of water attachment to lysozyme (Steprone et... 

The picosecond internal dynamics of myoglobin was explored by measuring inelastic neutron scattering by Smith et al. [25]. At low temperatures they found the dynamics to be harmonic while at higher temperatures a considerable quasielastic scattering was detected. Agreement between the experimentally observed spectra and that calculated from molecular dynamics simulations also showed evidence for restriction of the conformational space sampled at 80 K relative to 300 K. On the basis of these results it was concluded that the protein is trapped in local minima at low temperatures in accord with the multiple substate model suggested by low temperature flash photolysis experiments and previous molecular dynamics simulations. Comparison of atomic fluctuation data sets collected at both 325 K and 80 K confirms that the room temperature... 

A final interesting observation is the existence of a frequency scale, 3x10 see in Eq. (2-39). This is the frequency at which the electronic cloud around an atom fluctuates it is therefore the rate at which the spontaneous dipoles fluctuate. Since the electromagnetic field created by these dipoles propagates at the speed of light c = 3 x lO cm/sec, only a finite distance c/v 100 nm is traversed before the dipole has shifted. Since the dispersion interaction is only operative when these dipoles are correlated with each other, and this correlation is dismpted by the time lag between the fluctuation and the effect it produces a distance r away, the dispersion interaction actually falls off more steeply than r when molecules or surfaces become widely separated. This effect is called the retardation of the van der Waals force. The effective Hamaker constant is therefore distance dependent at separations greater than 5-10 nm or so. 

In an insightful chapter in his textbook T/ie Feynman Lectures in Physics which includes a description of the relation of physics to other sciences, Feynman pointed out the importance of motion in the function of proteins (Fig. 1.5a). Figure 1.5b is a more poetic description of the atomic fluctuations by my friend, the late Claude Poyart. However, the existence of... 

Given a potential energy function, one may use any of a variety of approaches to study enzymes and proteins, in general (Brooks et al. 1988). The most detailed information comes from molecular dynamics simulations, in which one solves Newton s equations of motion for all the atoms of the protein and the surrounding solvent. With currently available computers, one can simulate small proteins in solvent for periods of up to several nanoseconds. This is long enough to characterize the librations of small groups in the protein and to determine the dominant contribution to the atomic fluctuations. 

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