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8.3.1 PBE SETUP Command


     PBE SETUP repeat(pbe-setup-options) atom-selection
                           [SOLVent real]
                           [NWARN int]
                           [IONStr real]
                           [GRID real]
                           [SUBDivisions int]
                           [TEMPerature real]
     pbe-setup-options ::= [WATEr real]
                           [STERn real]
                           [XDIM int]
                           [YDIM int]
                           [ZDIM int]
                           [MARGin int]
                           [MINRadius real]
                           [EPSAve averaging-option]
                           [SMOOTH repeat(smooth-option) END]
     interior-options ::= repeat([INTErior real exposure-opts atom-selection END])
     exposure-opts ::= [ABSQ real] [EXPOsure real] [RESAve]
     charge-options ::= [UNIForm  ]
                                   [ZERO    ]
     boundary-options ::= BOUNdary [ADEBye  ]
                                   [SDEBye  ]
     charge-edit-options ::= repeat([CHARge edit-type real atom-selection END])
     edit-type ::= [SCALe]
     averaging-option ::= [HARMonic  ]
                        [TYPE type-option]
                        [WEIGht weight-option]
     smooth-options ::= [OFFGrid offgrid-option]
                        [RADIus real]
                        [POINts int]
                        [ALPHa real]
                     [NONE  ]
     type-option ::= [VOLUME]
                     [GRID  ]
     weight-option ::= [CONStant]
     offgrid-option ::= [SOLVent]
                        [EDGE   ]


The PBE SETUP command creates the pbe_info data structure, see PBE Data Structures, which stores the grids upon which the electrostatic potential is computed. The command has a large number of options and an atom-selection, see Atom Selection. The atom selection allows the user to select any portion of the system for the calculation. For example, if one is interested in the calculation of the binding energy of a complex, the atom selection can be used to select each component and then all the atoms for separate electrostatic calculations. The options are described in the following table.

Specifies the dielectric constant of the solvent in units of the vacuum dielectric. Thus, the vacuum dielectric would be 1, and the dielectric constant of water is around 78. The default is 78.
The INTERIOR option is used to specify the dielectric constant of the interior of the atom selection in the INTERIOR option. Any number of these options can be specified, and thus, it is possible to specify different dielectric constants for different parts of the system. It is possible to adjust the dielectric constant of exposed atoms to that of the solvent1. If the either option, ABSQ or EXPOSURE, is specified, then the exposure adjustment calculation will be done. Any atom whose exposure and charge meet the criteria will have the dielectric constant set to the solvent value as specified by the SOLVENT keyword. N.B. This option is highly experimentally and has not been proven useful in any system. The meaning of the keywords is given as follows:
The magnitude of the charge of the atom must be greater than or equal to this option in order for surface charge adjustment to be performed.
The relative molecular surface exposure of the atom for the adjustment is specified by this parameter. If the relative molecular surface exposure is less than EXPOSURE - 0.1, then the dielectric constant will be left alone. If the relative molecular surface exposure is greater than EXPOSURE + 0.1, then the dielectric constant will be set to the solvent value. Otherwise, it will be scaled harmonically between the interior value and solvent value.
The average relative molecular surface is calculated for all the atoms within a residue, and the exposure test above and the scaling is applied for the average.

The charging options, UNIFORM and TRILINEAR, along with the options SUBDIVISIONS and SPILL, control how the charge grid is set. With the TRILINEAR option, the charge of each atom is divided among the eight nearest points to the atom center. With the UNIFORM option, the charge of each atom is divided evenly among all the points within the van der Waals radii of the atom, except in the case where the number of such points is less than eight. In that case, trilinear interpolation is used. The option, NWARN, controls how many warning of this conversion are displayed.

The uniform charging option can be further improved using the SUBDIVISIONS and SPILL options. One problem with the use of grid based methods to represent molecular structure is the quantization of space. The same problem has arisen in the development of computer graphics using raster devices, and using the techniques of anti-aliasing, CONGEN can smooth the charge distribution of atoms. When the SUBDIVISIONS option is used, the space around each atom is subdivided into SUBDIVISION^3 virtual cubes, and the charge distribution is calculated over these virtual cubes, and then added onto the real cubes in the grid. If the SPILL option is turned on (recommended!), then charge can spill onto cubes outside the van der Waals radius of each atom. If SPILL is not specified, then the charge will not extend beyond the van der Waals radius.

The NWARN option specifies the maximum number of warning messages to be issued if an atom is too small for the uniform charging scheme to charge eight points. The default is 5.
The boundary-options are used to specify how the potential is set for the boundary of the grid. The ZERO option specifies that the boundary potential should be zero. The ADEBYE option specifies that the atomic Debye method should be used, see Introduction to Poisson-Boltzmann Electrostatics. This option is very slow. The SDEBYE options specifies that the system Debye method should be used. The keyword, PREVIOUS, is not implemented.
The IONSTR parameter is used to set the ionic strength. The units are in molarity. The default value is 0.0.
The GRID option sets the physical spacing between grid points. This is a critical parameter in the calculation of electrostatics using the Poisson-Boltzmann equation. The smaller the grid, the better the accuracy, but computation time scales as the grid size to the 4th power. The default value is 1.25 Angstroms.
The TEMPERATURE option is used to set the temperature for calculating the Debye-Huckel parameter, kappa. The default value is 300 K.
The radius of water in Angstroms is set using the WATER option. The radius of water is added to the van der Waals radii of all atoms and the dielectric constant of the midpoints of grid lines within this combined radius is set to the interior dielectric value for the atoms. Use of the WATER option causes the program to use the solvent accessible surface to define the interior. The default value is 0.0. Our current view is that this parameter should be left at 0.0 because ion solvation energies are calculated more accurately that way.
The thickness of the ion exclusion layer (Stern layer) is set to the STERN option. Within this distance of any atom, it is assumed that ion screening does not take place, and the Debye-Huckel parameter is set to zero. The default value is 2.0 Angstroms.
If the MARGIN option is non-negative, this option has no effect. Otherwise, when the CENTER option is specified, the center of grid is placed at the geometric center of the system. Otherwise, the center of grid is placed at the origin.
The XDIM option sets the number of grid points in the X direction.
The YDIM option sets the number of grid points in the Y direction.
The ZDIM option sets the number of grid points in the Z direction.
The MARGIN option sets the number of empty grid points surrounding the molecule. If set to a non-negative number, then CONGEN determines a rectangular box that will surround the molecule including the van der Waals radius, plus two grid spacings if the SPILL option is on. Then, the dimensions of the box will be increased in order to center this box within the grid with MARGIN grid points around all sides. When the MARGIN option is non-negative, the CENTER option has no effect.
The MINRADIUS keyword allows the user to specify the minimum radius for any atom placed on the grid. This keyword is important for potentials, such as AMBER94, see AMBER94PARM, which have several atoms with zero or small radius. Because the electrostatic self energy of a sphere is inversely proportional to the radius, such small atoms cause convergence problems. Therefore, one can set the minimum radius using the above option.
The REUSE option specifies that the current PBE SETUP command should update rather than initialize the pbe_info data structure. For the keyword options described here, the default values are taken from the current values rather than the values described in this documentation. The OLDGRID option is similar, except it maintains only the grid, but not the values within

These options are important for doing binding energy calculations. In order to cancel errors due to grid positioning, it is essential to first calculate the energy of the complex, and then, using the OLDGRID option, calculate the energies of the components by selecting the atoms of the components, but leaving the atoms and grids in the same spatial positions.

When this option is used, you should not specify any grid dimensions or the MARGIN option. If you do, and they are different than the actual values, then the REUSE or OLDGRID option will be turned off.

This option specifies that the interior of the molecule is defined by the molecular surface as computed by the GEPOL algorithm, see Atom Properties, for more information about GEPOL. The dielectric constant of points covered by the molecular surface but not atomic spheres is determined by the following scheme: GEPOL generates additional spheres which define the molecular surface. Each of these spheres derives from one or two previous spheres or atoms. The dielectric constant of each sphere is set to the average of its “parents”, where the average is determined by the EPSAVE keyword. Then, points covered by each of these spheres is averaged into the dielectric grid.
Whenever dielectric constants are combined, the EPSAVE controls how the averaging is performed. The averaging can either be ARITHMETIC (the "standard" mean) or HARMONIC (the reciprocal of the mean of the reciprocals). This option applies to averaging dielectric constants when atoms overlap in the grid, for dielectric smoothing, and for generating the dielectric constant for spheres generated by the molecular surface algorithm.
The charge-edit-options allows the user to modify the charges used for a calculation. Charges for the atoms in the atom-selection can be changed in one of three ways. The SET option specifies the charge explicitly. The SCALE option specifies a multiplicative scale factor to be applied to the current charges of the selected atoms. The SHIFT option specifies an additive term to be added to the current charges of the selected atoms.
The SMOOTH command “smooths” the dielectric grids. After the dielectric grids have been assigned internal and external values “smoothing” averages each point with the other points in its neighborhood to produce a dielectric grid with less abrupt changes in value. One hope of the process is to reduce the position dependence of the PBE electrostatic calculations. Its success in this endeavor is still a topic of research.

Several types of smoothing are supported. The smoothing TYPE can either be NONE, VOLUME, or GRID. Of course, no smoothing is done when NONE (the default) is specified. For VOLUME based smoothing the dielectric is averaged over a fixed volume in real space defined by the RADIUS keyword. For GRID based smoothing the dielectric is averaged over a set number of points specified by the POINTS keyword (9 and 15 point averaging are currently supported). In both case all three dielectric grids are averaged togeher. In 9-point averaging each point is averaged with the eight grid points from the other two grids which surround this point in space. In 15-point averaging the six nearest neighbors from the same grid are also included. (Note that volume smoothing with a radius just smaller (larger) than the grid spacing is equivalent to 9-point (15-point) averaging.)

Which ever TYPE is selected, The type of averaging is determined by the EPSAVE keyword above. The WEIGHTING can either be CONSTANT (all points in average counted equally), or GAUSSIAN weighted (points are weighted by exp(-alpha^2*r^2) where r is the distance from the central point in units of the grid dimension and alpha is specified by the ALPHA keyword).

For points at the edge of the grid the averaging extends to points beyond the grid. Using the OFFGRID keyword, these offgrid points can either be assumed to be SOLVENT or equal to the value at the nearest EDGE of the grid. (Note that the SOLVENT assumption will run faster.)


[1] This is suggested by a paper by T. Simonson and D. Perahia, “Internal and interfacial dielectric properties of cytochrome c from molecular dynamics in aqueous solution. Proc. Natl. Acad. Sci. USA 92, 1082-1086 (1995).