Grid-based approaches

Figure 7.1 Examples of automatically identified ligand-binding pockets with inhibitors bound. For pocket detection, a grid-based approach was used (Pocket-Picker). Dots represent surface cavities identified by PocketPicker, colored by buriedness . Solvent-accessible pocket surfaces are indicated by a mesh (left) or as hard surface (right). Darker shading of the grid dots indicates greater buriedness. a) Thrombin active site (PDB identifier 2cf8, 1.3 A resolution with a lactam inhibitor), b) co-crystal structure of Factor Xa (PDB entry lezq, 2.2 A resolution with inhibitor RPR128515). The automatically extracted pocket does not match with the surface-exposed parts of the actual inhibitor binding pocket. (Adapted from ref. 3.)...

SOM FA is a grid-based approach that does not use a probe to determine interaction energies. Instead, each grid point is assigned the shape or —> molecular electrostatic potential (MEP) value (a) shape is represented by binary values equal to 1 for points inside the van der Waals envelope and zero otherwise (b) electrostatic potential values at grid points are calculated from partial charges distributed across the atom centers [Robinson, Winn et al., 1999]. 

The Katchalski-Katzir method is a grid based approach to evaluate the shape complementarity between two proteins (see Figure 8.3). Consider two mol-... 

Numerical discretization methods pose an interesting consequence for fully numerical Dirac-Hartree-Fock calculations. These grid-based methods are designed to directly calculate only those radial functions on a given set of mesh points that occupy the Slater determinant. It is, however, not possible to directly obtain any excess radial functions that are needed to generate new CSFs as excitations from the Dirac-Hartree-Fock Slater determinant. Hence, one cannot directly start to improve the Dirac-Hartree-Fock results by methods which capture electron correlation effects based on excitations that start from a single Slater determinant as reference function. This is very different from basis-set expansion techniques to be discussed for molecules in the next chapter. The introduction of a one-particle basis set provides so-called virtual spinors automatically in a Dirac-Hartree-Fock-Roothaan calculation, which are not produced by the direct and fully numerical grid-based approaches. 

It should also be pointed out that the presence of the momentum operators in the ZORA Hamiltonian generates the small-component basis set. If a numerical integration scheme is employed, the small component must be tabulated on the grid as well as the large component. Thus, no matter whether a matrix approach or a grid-based approach is used, the small component is present either explicitly or implicitly. 

In Monte Carlo Localization, the space is digitized into some random samples (k). As discussed above, multi modal representation is used because of the global localization. Because of this reason, it requires less memory and is computationally more capable. Grid-based approaches were also used, but more memory was required because of 3-D figures (Oxford, 2012). 

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