Ideally, a user would like to graphically move the interacting molecules in real time on a workstation while computing the interaction energy. While the energy expression is straightforward to compute, the computation time increases as a square of the number of interacting atoms, making the process too slow for many molecular systems on most workstations.
As proposed by Langridge (Pattabiraman et al. 1985) an energy grid approximating the larger of the two molecules can be precomputed. Since the interaction energy can now be approximated by calculating the energy between the atom of the moving molecule and the appropriate grid points, the docking can be done in real time.
The construction of energy grids depends on the forcefield in use. This is explained in the following sections.
Making the assumption that a grid point lies reasonably close to an atom in the moving molecule, the quantity rij can be rewritten as rig (rig being the distance between the grid point and the atom in the non-moving molecule). Since rig is constant (the grid does not move in relation to the non-moving molecule), the values of the inner summations can be computed once and stored at each grid point.
where Ge (Pj), GA (Pj ) and GB (Pj ) represent the value at the grid points for the pre-computed electrostatic and van der Waals energies, Pj being the position of the atom in the moving molecule.
Nonbond Potential in CFF9X
The CFF (CFF91 and CFF) forcefield uses the nonbonded interaction potential
where Aij and Bij are parameters with units of kcal mol-1 angstrom9 and kcal mol-1 angstrom6 respectively and Rij is the distance between atoms i and j in A. A completely equivalent representation is:
where ij* is the potential well depth in kcal mol-1 and Rij* is the interatomic distance in angstroms at which the minimum occurs. The conversion between the two representations is straightforward:
Since CFF 9X uses the sixth-power combination rule:
The repulsive term cannot be factorized:
Thus, the following approximation is introduced:
This is actually the geometric combination rule used in CVFF and AMBER, except that the 12th power is replaced by the 9th power. Apparently, the approximation is exact for homogeneous atom pairs and the error is largest when the radii r differ most for the atom pair. Note that the dispersive term in the 9-6 potential can be factorized the same way as that in the 12-6 potential for CVFF and AMBER.
Nonbond Potential in AMBER
Since AMBER uses the 6-12 potential for vdw as CVFF, the vdw energy grids for AMBER can be created the same way as for CVFF. But for electrostatics, AMBER uses distance-dependent dielectric constant and therefore the in Eq. 8-7 needs to be set to rij, instead of 1 for CVFF and CFF9X. It should be noted that the 10-12 hydrogen bonding term in AMBER is neglected in constructing the energy grids.
The Docking module provides facilities for calculating the nonbond energy between two molecules using the methods described in the preceding theory section.
The number of atoms included in the calculation can be limited by specifying a monomer or residue based cutoff. Any monomer or residue having one or more atoms within the specified cutoff distances of the atom currently being evaluated is included in the calculation. A monomer or residue having no atoms within the specified cutoff distance of the current atom being evaluated is not included in the calculation.
The Grid pulldown is used to create and manipulate an energy grid for a given molecule. You may create and compute the energy grid, display and undisplay this grid, and write this grid to an output file that is readable by the commands in the Contour pulldown.
The Evaluate pulldown includes commands to allow examination of intermolecular energies. You may select which nonbond energy terms to use for calculations, and can set up single-point or continuous evaluations of these interactions.
The Intermolecular command allows you to examine or to monitor the total energy between two molecules. You can perform a single-point, or continuous evaluation of the energy. You can specify the cutoff value to be used when computing the energy, and indicate whether or not you are using the electrostatic or van der Waals energy parameters to compute the total energy. The maximum derivatives with the total energy values can be displayed.
The Docking_Grid pulldown is used to create and manipulate an energy grid for a given molecule. This pulldown contains the commands Create, Compute, and Display.
The Create Docking_Grid command allows you to define a 3D set of points that represents the net contribution of all atoms of a specified molecule at discrete points. The size of the set of points depends on the boundaries which are described as an enclosure plus a defined border space. The position of the discrete points is controlled with the Grid Step.
The Compute Docking_Grid command allows you to calculate the energy grid for the specified molecule. The grid must have been previously defined using the Create Docking_Grid command. The Van_der_Waals and Coulomb parameters allow you to modify which energies are calculated, while the Cut_off parameter allows you to control the radius of interaction.
The Display Docking_Grid command allows you to display the extents of the grid defined for the specified molecule. Grids are displayed automatically when they are first created to make redefinition of the extents clearer.
As of this release, most tutorials are now available online for use with the Pilot interface. To access the online tutorials for Docking, click the biplane or mortarboard icon in the Insight interface.