3D Contour map

The 3D density contour maps for the Na+ ion distribution determined over the last 250 ns of simulation (Figure 14-8) show that the overall highest probability Na+ occupation sites were concentrated in the active site for both the reactant and activated precursor. This suggests that the HHR folds to form a strong local electronegative pocket that is able to attract and bind Mg2+ if present in solution, or recruit a high local concentrations of Na+ ions in the absence of Mg2+. 

Figure 14-8. The 3D density contour maps (yellow) of Na+ ion distributions derived from the activated precursor simulation. The hammerhead ribozyme is shown in blue with the active site in red. Only the high-density contour is shown here to indicate the electrostatic recruiting pocket formed in the active site...

Fig. 21. The product D-atom velocity-flux contour map, d

Fig. 11. HCCO product flux (velocity-angle) contour map from the 0(3P) + C2H2 reaction at Ec = 9.5kcalmol 1 (a). 3D perspective (b).

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

Fig. 26 Contour map (from 0.6 to 5 eA 3) of the cross section of the MEM charge density for Sm2.78C7o at ambient pressure (left) and at 2.5 GPa (right). The sections were obtained by cutting the 3D charge density maps by the plane of the C-Sm-C bonds, which is parallel to the (110) or (111 )ja planes...

Moreover, a final 3D-QSAR model vahdation was done using a prospective study with an external test set. The 82 compounds from the data set were used in a lead optimization project. A CoMFA model gave an (cross validated) value of 0.698 for four relevant PLS components and a conventional of 0.938 were obtained for those 82 compounds. The steric descriptors contributed 54% to the total variance, whereas the electrostatic field explained 46%. The CoMSIA model led to an (cross vahdated) value of 0.660 for five PLS components and a conventional of 0.933. The contributions for steric, electrostatic, and hydrophobic fields were 25, 44, and 31%. As a result, it was proved that the basic S4-directed substituents should be replaced against more hydrophobic building blocks to improve pharmacokinetic properties. The structural and chemical interpretation of CoMFA and CoMSIA contour maps directly pointed to those regions in the Factor Xa binding site, where steric, electronic, or hydrophobic effects play a dominant role in ligand-receptor interactions. 

The combination of the two methods in the 2D setup dramatically increases the resolution of the separation system and gives a clear picture of the complex nature of the sample mixture. A three-dimensional (3D) representation of the gradient HPLC-SEC separation is given in Figure 5 each trace represents a fraction transferred from HPLC into the SEC system and gives the result of the SEC analysis. The 3D view already indicates the complexity of the sample mixture. The point of view can be chosen deliberately in the software. Based on the 2D analysis, a contour map with 16 spots would be expected. Each spot would represent a component within the complex sample that is defined by a single composition and molar mass. The contour map should also reflect the (4 X 4)... 

The ELF is a scalar function of three variables, and in order to obtain more information from it, it is necessary to use a mathematical approach called differential topology analysis. This was first done by Silvi and Savin,11 and later on extended by them and co-workers.45,46 Unfortunately, one cannot visualize in a global way a three-dimensional function. Usually, one resorts to isosurfaces like the ones in Figure 1, or to contour maps. A three-dimensional function has a richer structure than a one-dimensional function, and their mathematical characterization introduces some new words which are necessary to understand in order to go further. It is the purpose of this section to explain this new terminology in a manner as simpler as possible. Let us begin with a one-dimensional (ID) example, a function f(x) like the one in Figure 3. The function has three maxima and two minima characterized by the sign of the second derivative. In three dimensions (3D) there are more possibilities, for there are nine second derivatives. Hence, one does not talk about maxima but about attractors. In ID, the attractors are points, in... 

Fig. 10. 3D plot and contour map for Vhccch in propane, calculated as a function of the dihedral angles ip, and ip3 by DFT/FPT at 30° intervals of the angles. 3D spline interpolations were used to create the graphs, which illustrate how the coupling constant changes sign, depending on the values of, i and, ... 

Fig. 2. Six-hump camel back function (a) contour map, (b) 3D topology...

The resulting field calculated as a 3D grid map with 0.5 A grid step size is contoured using an in-house algorithm to produce envelopes, whose location, shape, and volume are indicative of the ligand binding pockets. 

---