Surface topography index

The comparison of two given molecular surfaces on the basis of curvature can be done interactively by the use of two-dimensional texture maps, with color coding of the two canonical curvatures calculated for different selection distances along the x and y coordinate of the texture map. However, the information from the curvature profile can be further reduced by introducing a surface topography index STI as demonstrated by... 

Heiden and Brickmann. The surface topography index s may be defined on the basis of two global curvatures, c, and C2, as follows ... 

The segmentation of molecular surfaces can be carried out on the basis of different surface qualities.Here we shall focus on a segmentation with respect to topographical criteria. The shape analysis is based on the surface topography index (STI) described previously. Following Heiden and Brickmann, a six class linguistic variable... 

Figure 18 Molecular surfaces of the enzyme trypsin. The surfaces are color coded according to the surface topography index (left) and the hydrogen bonding ability (right). Left blue, bag green, saddle red, knob. Right blue, acceptor red, donor...

Prom the electron paramagnetic resonance (EPR) spectmm of the nitroxide side chain, four primary parameters are obtained 1) solvent accessibility, 2) mobility of the R1 side chain, 3) a polarity index for its immediate environment, and 4) the distance between R1 and another paramagnetic center in the protein. Solvent accessibility of the side chain is determined from the collision frequency of the nitroxide with paramagnetic reagents in solution. The mobility, polarity, and distances are deduced from the EPR spectral line shape. For regular secondary stmc-tures, accessibility, mobility, and polarity are periodic functions of sequence position. The period and the phase of the function reveal the type of secondary stmcture and its orientation within the protein, respectively (71, 74). In the case of membrane proteins, the topography of the secondary stmcture with respect to the membrane surface can also be described (75, 76). 

The index Df measures the topography of the surface. In smooth surfaces, Df approaches 2. For rough or convoluted surfaces, Df will exceed 2. Truly fractal objects will have a unique exponent, whereas local variations are expected in actual molecules.In the latter case, instead of a single fractal exponent we find a scalar field Df i), where r is a point on the surface. 

Figure 19 Segmentation of the Connolly surface of the pancreatic trypsin inhibitor (PTI). The domains are classified by topography descriptors as introduced by Heiden et al. Each domain is color coded according to a special index number of the domain ...

Fig. 9.31 (a) Intensity profile of SR SAXS reflections with the Lorentz correction red circle) observed for the powder X3 sample. The numbers given on the figure are the (hkO) indexes. In (b), most probable reconstitution of the electron density map for the X3 phase by the nine, reflections with the phase differences. The map indicates that the cylindrical rods packed into the hexagonal lattice are constructed of two concentric cylinders as illustrated in (c). The cylindrical association is also supported by AFM topography image of (d) observed on the surface of the fan-shaped domain in the X3 phase... 

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