Path-distance frequency distribution

Figure 5.2. GRID positive MIF (a) and path—distance frequency distribution (b) for the methotrexate. Two nodes are used as an example their euclidean distance and minimum path are highlighted with green lines (a) and the point representing that node pair is indicated by P (b).

The frequency of path-distance pairs for a single molecule can be viewed by means of three-dimensional plots in which the frequency distribution (z axis) is reported versus distances [x axis) and the path-distance (y axis), see Fig. 5.2. Molecular shape peculiarities are condensed in the frequency distribution graph in which low path-distance values (path = distance), represented by points close to the distance axis of the plot in Fig. 5.2, characterize more planar surfaces, whereas high path-distance values (path > distance) characterize more wrinkled surfaces. 

These qualitative statements are due to a simple graphical analysis of the cavity frequency distribution plot compared in Fig. 5.8. However, each cavity can be inspected and compared in detail. For example, the peak indicated by the arrow in Fig. 5.8 for 3A4 corresponds to the path-distance pairs reported in red color in Fig. 5.8(d). They end up far away from the heme in a subpocket region generated by the residues Leu 211 and Tyr 307. This subpocket is not present in the other CYPs and can be involved in a selective recognition of the substrate molecule. 

VmaY = the frequency at which the band has a maximum fimax = the intensity of the absorption Ho = the applied magnetic field g = the spectroscopic splitting factor r = the distance between protons P = the angle between a line joining the protons and Hq S2 = the mean-square deviation of the field firom the center of the line Hq Mn = the mass of a neutron particle A = the wave length of a neutron beam V = the partiele velocity A (= X2 - xi) = changing path distance r = is the reflection coefficient T = the transmission coefficient of the beam splitter yl(v) = the fi quency distribution 1(D) and B(n) = orthogonal fimctions F y) = the fi-equency distribution N = number of points in a Fourier Transform 9 = a set of normal coordinates... 

Figure 9.5 Frequency distribution of LogDet distances among the main lineages of jawed vertebrates. Path lengths from the most recent common ancestor (MRCA) to sharks, the bichir, teleosts, the coelacanth, the lungfishes and tetrapods were calculated across the NJ tree recovered from the 28S rRNA gene data set.A faster evolutionary rate is observed for the lungfishes and the bichir.

From equation 5, it is apparent that each shell of scatterers will contribute a different frequency of oscillation to the overall EXAFS spectrum. A common method used to visualize these contributions is to calculate the Fourier transform (FT) of the EXAFS spectrum. The FT is a pseudoradial-distribution function of electron density around the absorber. Because of the phase shift [< ( )], all of the peaks in the FT are shifted, typically by ca. —0.4 A, from their true distances. The back-scattering amplitude, Debye-Waller factor, and mean free-path terms make it impossible to correlate the FT amplitude directly with coordination number. Finally, the limited k range of the data gives rise to so-called truncation ripples, which are spurious peaks appearing on the wings of the true peaks. For these reasons, FTs are never used for quantitative analysis of EXAFS spectra. They are useful, however, for visualizing the major components of an EXAFS spectrum. 

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