Dynamical fluctuations

The relative molecular dynamics fluctuations shown in Figure 7-17 can be compared with the crystallographic B-factors, which are also called temperature factors. The latter name, especially, indicates the information content of these factors they show how well defined within the X-ray structure the position of an atom is. Atoms with high temperature have an increased mobility. In principle, this is the same information as is provided by the molecular dynamics fluctuations. Using Eq. (48), the RMS fluctuation of an atom j can be converted into a B-factor... 

Rick S W and B J Berne 1996. Dynamical Fluctuating Charge Force Fields The Aqueous Solvation of Amides, Journal of the American Chemical Society 118 672-679. 

Rick S W, S J Stuart and B J Berne 1994. Dynamical Fluctuating Charge Force Fields Application to Liquid Water. Journal of Chemical Physics 101 6141-6156. 

It is important to note that in this method, the dynamic fluctuations associated with the QM subsystem are assumed to be independent of the fluctuations from the MM subsystem. Also, in this method we assume that the contributions of the fluctuations of the QM subsystem to the total free energy are the same along the reaction coordinate. We have recently addressed these approximations by developing a novel reaction path potential method where the dynamics of the system are sampled by employing an analytical expression of the combined QM/MM PES along the MEP [40],... 

Rick SW, Stuart SJ, Berne BJ (1994) Dynamical fluctuating charge force-fields - application to liquid water. J Chem Phys 101 (7) 6141—6156... 

Rick SW, Berne BJ (1996) Dynamical fluctuating charge force fields The aqueous solvation of amides. J Am Chem Soc 118(3) 672—679... 

Abstract The theoretical basis for the quantum time evolution of path integral centroid variables is described, as weU as the motivation for using these variables to study condensed phase quantum dynamics. The equihbrium centroid distribution is shown to be a well-defined distribution function in the canonical ensemble. A quantum mechanical quasi-density operator (QDO) can then be associated with each value of the distribution so that, upon the application of rigorous quantum mechanics, it can be used to provide an exact definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables can thus be defined and explored. Importantly, this perspective shows that the centroid constraint on the imaginary time paths introduces a non-stationarity in the equihbrium ensemble. This, in turn, can be proven to yield information on the correlations of spontaneous dynamical fluctuations. This exact formalism also leads to a derivation of Centroid Molecular Dynamics, as well as the basis for systematic improvements of that theory. 

Fig. 9. Schematic diagram showing the concentration fluctuations in gels, dynamic fluctuation (left), static inhomogeneity (center), and the superimposed fluctuations (right)...

It has been established that the volume phase transition of gels is an universal phenomenon [17]. Dynamic light scattering studies indicate that the dynamic fluctuations of the density correlation diverges in the vicinity of the volume phase transition point of the gel. It has also been shown that the time scale of the density fluctuations become slow in the vicinity of the volume phase transition... 

The temperature dependence of the dynamic fluctuations which contribute to the effective pore size may be estimated by means of mode coupling theory, which views a gel as consisting of N pores of diameter t, over which the density fluctuations are correlated [4, 20, 21]. 

In our discussion of the transition-state theory with static solvent effects, it was noticed that it is a mean field description where the effects of dynamical fluctuations in the solvent molecule positions and velocities were excluded. 

Most modern investigations of the effects of a solvent on the rate constant, where dynamical fluctuations are included, are based on a classical paper by Kramers from 1940 [1], His theory is based on the transition-state theory approach where we have identified the reaction coordinate as the normal mode of the activated complex that has an imaginary frequency. In ordinary transition-state theory, we assume that the motion in that coordinate is like a free translational motion with no recrossings. This... 

It has often been assumed that the second step, intracomplex ET, takes place within a static reactant complex. However, a number of cases have been observed in which the reactant complex is not static, but undergoes dynamic configurational fluctuations (defined as protein-protein orientations in the bound complex) [65] or conformational changes (defined as a tertiary structure of each protein) [40]. If the reaction is rate limited by dynamic fluctuation in configuration rather than by the... 

Castano JP, Kineman RD, Frawley LS (1994) Dynamic fluctuations in the secretory activity of individual lactotropes as demonstrated by a modified sequential plaque assay. Endocrinology 755 1747-1752. 

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