# Electrostatic effects

Both shape complementarity and electrostatic effects are important in the recognition process in protein complex formation. Accordingly a treatment of electrostatics was introduced into the Fourier correlation approach. The charge-charge interaction is evaluated from point charges of the mobile molecule B interacting with the potential from static molecule A. This choice results in having to perform the potential calculation only once (for the static molecule) whilst the charge calculation (see below) is performed for every rotation of the mobile molecule. In the above treatment of rigid body docking based on shape complementarity, it is possible to place two charges closer together than would be allowed by van der Waals packing. Since the potential energy of two interacting charges depends inversely on their separation, this would result in an artificially highly favorable or very unfavourable interaction. These artificial terms are prevented by the method now described to calculate the potential.

Charges (see Gabb et al. [12]) are assigned to the atoms of molecule A

and the electrostatic potential evaluated from

where m, n is the potential at node i, m, n (position i), qj is the charge on atom j, rij is the distance between i and j (with a minimum value of 2 A to avoid artificially large values of the potential) and e(rij) is a distance dependent dielectric function. The sigmoidal function of Hingerty et al. [72] is used:

This function was introduced for modelling the effective dielectric between atoms in proteins. The rationale for this function is that at close separation [rij < 6A) when there is no intervening water molecules, the effective dielectric is that of protein atoms and a value of 4 is appropriate. For separations of 8 A or more then the dielectric is dominated by the screening effect of the intervening water and the value for bulk water (80) is used. Between these two separations a linear interpolation is used. In FTDOCK, we do not use precise atomic positions, but still need to model the complex dielectric behavior of proteins in solvent and this function was used and found to perform well.

The potential fa m n is only assigned to nodes outside and on the surface region of molecule A. Inside the core of molecule A, fa m, n is zero. For the mobile molecule B, the charges on the charged atoms are distributed amongst the closest 8 grid cells, see Figure 8.5. Given the atomic position of the charged atom normalised onto the centre of the 8 neighbouring cells as (x, y, z), and the normalised centre of one of those closest 8 cells as

Schematic diagram of the approach to transfer an electronic charge to its nearest eight grid nodes.

Schematic diagram of the approach to transfer an electronic charge to its nearest eight grid nodes.

8.3 Methodology of a protein-protein docking strategy | 373 (X, Y, Z), then the charge given to that cell is

(qi,m,n/8) * (( + X)/X) * ((y + Y)/Y) * ((z + Z)/Z)

The electrostatic interaction ea,p, y for a shift of a, p, y is calculated from

Eq. (2) is analogous to Eq. (1) for shape complementarity and accordingly the Fourier correlation approach can be also used to speed up the calculation.

Continue reading here: Generation of putative complexes

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