Distance-distribution measure

Nilakantan et described a similarity measure based also on the interatomic distances between all sets of three nonhydrogen atoms, using a bit-string representation of molecular shape. It is also possible to consider doublets or quadruplets of nonhydrogen atoms (the doublets give rise to similarity measures which are related to the distance-distribution measure described by Pepperrell and Willett see also Ref. 86). 

Given two molecules, A and B, the simplest measure that was tested by Pepperrell and Willett was the distance-distribution measure. Here, an N-element frequency distribution is generated for each molecule, in which the /th element contains the number of interatomic distances in that molecule that lie within the /th distance range (1 N). The resulting frequency... 

Figure 12. Potential energy contour plots for He + I Cl(B,v = 3) and the corresponding probability densities for the n = 0, 2, and 4 intermolecular vibrational levels, (a), (c), and (e) plotted as a function of intermolecular angle, 0 and distance, R. Modified with permission from Ref. 40. The I Cl(B,v = 2/) rotational product state distributions measured following excitation to n = 0, 2, and 4 within the He + I Cl(B,v = 3) potential are plotted as black squares in (b), (d), and (f), respectively. The populations are normalized so that their sum is unity. The l Cl(B,v = 2/) rotational product state distributions calculated by Gray and Wozny [101] for the vibrational predissociation of He I Cl(B,v = 3,n = 0,/ = 0) complexes are shown as open circles in panel (b). Modified with permission from Ref. [51].

From half width of the intensity distribution measured along the Debye ring of reflection derived from a distance between polymer chains obtained by X-ray diffraction, the practical standard value of parallelism degree in orientation was determined to be 0.92. 

Double-quantum coherence (DQC) was used to measure interspin distances in eight doubly labelled derivatives of T4 lysozyme.25 Distances between 20 and 47 A with distance distributions of 1.0 to 2.8 A were measured. For some variants two conformations were detected with distances that differed by 5 to 5.4 A. It was shown that a few measurements of large distances provided significant constraints on protein structure. 

The Na+/proline transporter of E. coli (PutP) is an integral membrane protein that is proposed to contain 13 transmembrane helices.85 Four-pulse DEER measurements found distances of 48,22, and 18 A for three doubly spin-labelled variants.The 48 A distance confirmed that those two labels were on opposite sides of the membrane. The large distance distribution widths that were observed in the pair functions reveal the substantial flexibility of the loop regions to which the spin labels were attached. 

Frequency-domain measurements of fluorescence energy transfer are used to determine the end-to-end distance distribution of donor-acceptor D-A) pairs linked by flexible alkyl chains. The length of the linker is varied from 11 to 2B atoms, and two different D-A pairs are used. In each case the D-A distributions are recovered from global analysis of measurements with different values for the FSrster distance, which are obtained by collislonal quenching of the donors. In all cases essentially the same distance distribution Is recovered from the frequency-domain data for each value of tha Ffirster distance. The experimentally recovered distance distributions are compared with those calculated from the RIS model. The experimentally recovered distance distributions for the largest chain molecules are In agreement with the predictions of the RIS model. However, the experimental and RIS distributions are distinct for the shorter D-A pairs. 

For the selected experimental examples discussed within the next two sections the conditions of a broad size and distance distribution of the surface structures are well supported by the real space analysis. Thus in the following experimental sections instead of the full measured 2d intensity, only one selected horizontal slice at constant qz (of the critical angle of the polymer under investigation) will be shown [20], From a comparison of the Figs. 2-4 it is obvious, that in addition to the full 2d intensity, the split Yoneda peak is visible in a single horizontal slice at constant qz as well. 

Beechem J.M. and Haas, E. (1989) Simultaneous determination of intramolecular distance distributions and conformational dynamics by global analysis of energy transfer measurements, Biophys. J. 55, 1225-1236. 

Raitsimring, A. (2000) 2+ pulse sequence as applied for distance and spatial distribution measurements of paramagnetic centers, In Berliner, L. J., Eaton, S. S., and Eaton, G. R. (eds.), (2000) Biological Magnetic Resonance, 19, Distance Measurements in biological Systems by EPR, Kluwer Academic/Plenum Publisher, N.Y., pp. 461-492. 

Amir D, Haas E. Estimation of intramolecular distance distributions in bovine pancreatic trypsin-inhibitor by site-specific la- 167. beling and nonradiative excitation energy-transfer measurements. Biochemistry 1987 26 2162-2175. 

Fig. 4.12. Pt/ceria catalysts made by colloidal lithography using suspensions of d = 107 nm polystyrene particles with three different NaCI concentrations, resulting in different surface coverages and interparticle separations. NN refers to the nearest neighbor distance, as measured by the main peak in the radial distribution function, gir), shown in the inset of each SEM picture (from [92])...

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