The generation of the grid representation

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

Schematic of our strategy for generating and screening docked protein complexes.

Schematic of our strategy for generating and screening docked protein complexes.

static molecule static molecule discretise mobile molecule loop

Fourier transform

discretise

mobile grid

* -------

convolution

reverse transfrom

select best 3

--

Fourier transform stack finished loop pair potentails matrix biological information few predicted complexes score complexes

m Static grid

shifts (here 4,5)

m Convolved grids

Scoring shape complementarity using a grid-based scoring approach. The Figure illustrates the approach used in FTDOCK. The top two grids show the individual m Convolved grids

Scoring shape complementarity using a grid-based scoring approach. The Figure illustrates the approach used in FTDOCK. The top two grids show the individual m mobile grid Key

CH score 0, empty cell O score 1, surface of static, all of mobile Q score -15, core of static

no overlap

overlap of mobile with surface of static

" " overlap of mobile with core of static a ""

discretisation of the static and mobile molecules. The lower grid shows the convolved grids with the calculation of shape complementarity.

shifts (here 4,5)

ecules A and B. Let A be the larger of the two and taken to be the static molecule. B will be the smaller mobile component to be docked against A.

Each molecule is placed onto a 3-dimensional grid and the algorithm requires that both grids are the same dimension (N x N x N). The size of grid cell must be sufficiently small to model the atomic structure of the molecules. However the computational time increases as the cell size decreases. We currently use a value of 0.7 A that is sufficiently small that generally only one atom (excluding hydrogen) is in an individual cell. To evaluate the required N, for each protein the maximum distance from any atom to the geometric centroid is calculated (DMAXa and DMAXB). The value XN is calculated from:

N is set to the nearest integer to XN. For ease of computation in the Fourier method, N should be even and so if N is odd, the next highest even integer is used. The result of this calculation of N ensures that the mobile molecule can always be placed to touch the static molecule and there will remain grid cells at the boundary unoccupied by the protein.

The discretization is done with each molecule at the centre of each grid. The empty space not filled by the molecule is necessary for the algorithm. To perform the discretization, each grid cell within which an atomic position is found is turned 'on'. Grid cells whose centre is within 1.8 A of any atomic position are also turned 'on'. This value of 1.8 A is chosen to approximate an effective van der Waals radius for an atom combined with any hydrogen atoms that are bound to it. Thus the surface of the resulting grids will represent the atomic surface of the molecules.

Next, the larger static molecule (A) is assigned a surface thickness below its atomic surface in order to be able to calculate the quality of the fit. For algorithmic speed, this surfacing procedure is done to the static molecule, and accordingly it needs to be done only once by the program. The depth of this surface is 1.4 A, so that the surface is never more than two cells thick. After the surface has thereby been assigned, the core cells still cover all the actual atomic positions, but the van der Waals radius has been effectively removed, so allowing closer interactions between the two components of the complex. This representation of the surface provides a model for complex formation in which there is some side-chain rearrangement followed by side-chain interdigitation.

Continue reading here: Evaluation of shape complementarity

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