The PBEQ module allows the setting up and the numerical solution of the Poisson-Boltzmann equation on a discretized grid for a solute molecule.

Note

Problems should be reported to

- Benoit Roux at Benoit.Roux@med.cornell.edu, phone (212) 746-6018
- Wonpil Im at Wonpil.Im@cornell.edu
- Dmitrii Beglov at beglovd@moldyn.com

```
PBEQ enter the PBEQ module
END exit the PBEQ module
Subcommands:
SOLVe PB-theory-specifications
solver-specifications grid-specifications
iteration-specifications charge interpolation-spec.
boundary potential-spec. dielectric boundary-spec.
physical variable-spec. membrane-specifications
spherical droplet-spec. orthorhombic box-spec.
cylinder-specifications solvation force-spec.
atoms-selection
ITERate PB-theory-specifications solver-specifications
iteration-specifications
ENPB [INTE atoms-selection]
CAPAcitance
COUNTERION
WRITE property [[CARD] [write-range]] [UNIT integer]
READ [PHI] [PHIX] [FKAP] [MIJ] [UNIT integer]
COOR coordinate-manipulation-command
SCALar scalar-manipulation-command
PBAVerage [PHI] [ATOM atom-selection] [UPDATE] [units]
grid-specifications
HELP
RESET
PB-theory-specifications::= [NONLinear] [PARTlinear]
default : linear PB by default (no need to specify)
NONLin [.FALSE.] : non-linear PBEQ solver
PARTlin [.FALSE.] : partially linearized PBEQ solver
solver-specifications::=[OLDPB]
[OSOR] [UNDER] [[FMGR] [NCYC integer] [NPRE integer] [NPOS integer]]
default : SOR (Successive OverRelaxation) method for linearized PB
OLDPB [.FALSE.] : old PBEQ solver (used in c26a2)
OSOR [.FALSE.] : optimization of the over-relaxation parameter
UNDER [.FALSE.] : Under-relaxation for non-linear and partially linearized
PBEQ solvers with fixed LAMBda value
FMGR [.FALSE.] : full multigrid method
NCYC [100] : maximum number of cycles (in FMGR)
NPRE [2] : number of relaxation for PRE-smoothing (in FMGR)
NPOS [2] : number of relaxation for POST-smoothing (in FMGR)
grid-specifications::= [NCEL integer] [DCEL real]
[NCLX integer] [NCLY integer] [NCLZ integer]
[XBCEN real] [YBCEN real] [ZBCEN real]
NCEL [65] : number of grid point in 1D for a cubic
DCEL [0.1] : size of grid unit cell
NCLX [NCEL] : number of grid point in X for general parallelepiped
NCLY [NCEL] : number of grid point in Y for general parallelepiped
NCLZ [NCEL] : number of grid point in Z for general parallelepiped
XBCEN [0.0] : the center of a box in X
YBCEN [0.0] : the center of a box in Y
ZBCEN [0.0] : the center of a box in Z
iteration-specifications::=[MAXIter integer] [DEPS real]
[DOMEga real] [LAMBda real] [KEEPphi]
MAXIter [2000] : number of iterations
DEPS [0.000002] : parameter (tolerance) of convergence
DOMEga [1.0] : initial mixing factor
LAMBda [1.0] : initial mixing factor (LAMBda = DOMEga)
KEEPphi [.FALSE.] : Use the potential from previous calculation
as a initial guess for current calculation
charge interpolation-spec.::= [BSPLine]
default : the trilinear interpolation method
BSPLine [.FALSE.] : the Cardinal B-spline method is used?
boundary potential-specifications::= [ZERO] [INTBP] [FOCUS] [PBC] [NPBC]
[NIMGB integer]
default : use the Debye-Huckel approximation at each boundary point
use XY periodic boundary conditions in membrane
calculation
INTBP [.FALSE.] : INTerpolation of Boundary Potential is used?
ZERO [.FALSE.] : boundary potential is set to ZERO ?
(metallic conductor boundary conditions)
FOCUS [.FALSE.] : previous potential is used to set up boundary potential?
PBC [.FALSE.] : 3d periodic boundary condition
NPBC [.FALSE.] : supress XY periodic boundary conditions in membrane
calculations
NIMGB [0] : use the image atoms for boundary potential
in membrane calculation
(NIMGB=1 means the 8 nearest image cells)
(NIMGB=2 means the 24 nearest image cells, i.e.,
2 shells of images)
dielectric boundary-specifications::= [SMOOTH] [SWIN real] [REEN]
default : the vdW surface is used for the dielectric boundary
SMOOth [.FALSE.] : invoke smoothing dielectric boundary
SWIN [0.5] : solute-solvent dielectric boundary Smoothing WINdow
REEN [.FALSE.] : the molecular (contact+reentrant) surface is created
with WATRadius for the dielectric boundary
physical variable-specifications::= [EPSW real] [EPSP real]
[WATR real] [IONR real]
[CONC real] [TEMP real]
EPSW [80.0] : bulk solvent dielectric constant
EPSP [1.0] : protein interior dielectric constant
WATR [0.0] : solvent probe radius
IONR [0.0] : ion exclusion radius (Stern layer)
CONC [0.0] : salt concentration [moles/liter]
TEMP [300.0] : Temperature [K]
membrane-specifications:: [TMEMb real] [HTMEmb real] [ZMEMb real] [EPSM real]
[EPSH real] [VMEMB real]
TMEMB [0.0] : thickness of membrane (along Z)
HTMEMB [0.0] : thickness of headgroup region
ZMEMB [0.0] : membrane position (along Z)
EPSM [1.0] : membrane dielectric constant
EPSH [EPSM] : membrane headgroup dielectric constant (optional)
VMEMB [0.0] : potential difference across membrane (entered in [volts])
spherical droplet-spec.::= [DROPlet real] [EPSD real]
[XDROplet real] [YDROplet real] [ZDROplet real]
[DTOM] [DKAP]
DROPlet [0.0] : radius of spherical droplet
EPSD [1.0] : dielectric constant of spherical droplet
XDROp [0.0] : position of spherical droplet in X
YDROp [0.0] : position of spherical droplet in Y
ZDROp [0.0] : position of spherical droplet in Z
DTOM [.FALSE.] : the dielectric constant of the overlapped region
with membrane is set to EPSM ?
DKAP [.FALSE.] : the Debye-Huckel factor inside sphere is set to KAPPA ?
orthorhombic box-spec.::= [LXMAx real] [LYMAx real] [LZMAx real]
[LXMIn real] [LYMIn real] [LZMIn real]
[BTOM] [BKAP]
LXMAx [0.0] : maximum position of a box along X-axis
LYMAx [0.0] : maximum position of a box along Y-axis
LZMAx [0.0] : maximum position of a box along Z-axis
LXMIn [0.0] : minimum position of a box along X-axis
LYMIn [0.0] : minimum position of a box along Y-axis
LZMIn [0.0] : minimum position of a box along Z-axis
EPSB [1.0] : dielectric constant inside box
BTOM [.FALSE.] : the dielectric constant of the overlapped region
with membrane is set to EPSM ?
BKAP [.FALSE.] : the Debye-Huckel factor inside box is set to KAPPA?
cylinder-specifications::= [RCYLN real] [HCYLN real] [EPSC real]
[XCYLN real] [YCYLN real] [ZCYLN real]
[CTOM] [CKAP]
RCYLN [0.0] : radius of cylinder
HCYLN [0.0] : height of cylinder
EPSC [1.0] : dielectric constant inside cylinder
XCYLN [0.0] : position of cylinder in X
YCYLN [0.0] : position of cylinder in Y
ZCYLN [0.0] : position of cylinder in Z
CTOM [.FALSE.] : the dielectric constant of the overlapped region
with membrane is set to EPSM ?
CKAP [.FALSE.] : the Debye-Huckel factor inside cylinder is set to KAPPA?
solvation force-spec.::= [FORCE] [STEN real] [NPBEQ integer]
FORCe [.FALSE.] : invoke solvation force calculation
STEN [0.0] : surface tension coefficient (in kcal/mol/A^2)
NPBEQ [1] : the frequency for calculating solvation forces
during minimizations and MD simulations
write-range::= [XFIRST real] [YFIRST real] [ZFIRST real]
[XLAST real] [YLAST real] [ZLAST real]
property::= [[PHI] [KCAL] [VOLTS]] [[PHIX] [KCAL] [VOLTS]]
[FKAPPA2]
[CHRG]
[EPSX] [EPSY] [EPSZ]
[MIJ]
[TITLE]
PHI : electrostatic potential [ KCAL/MOL ] [ VOLTS ]
(default [UNIT CHARGE]/[ANGS])
PHIX : external static electrostatic Potential [ KCAL/MOL ] [ VOLTS ]
(default [UNIT CHARGE]/[ANGS])
FKAPPA2 : Debye screening factor
CHRG : charges on the lattice
EPSX : X sets of dielectric constant
EPSY : Y sets of dielectric constant
EPSZ : Z sets of dielectric constant
MIJ : MIJ matrix
TITLE : formatted title line
atoms-selection::= a selection of a group of atoms
```

SOLVE

Prepare grids and solve PB equation for the selected atoms and return the electrostatic free energy in ?enpb = (1/2)*Sum Q_i PHI_i over the lattice. The factor of 1/2 is there for the linear response free energy of charging. The atomic contributions are returned in WMAIN (destroying the radii).

Note

At the first stage of PBEQ or after “RESET”, WMAIN should be set to the atomic radii for the calculation. After a call to SOLVE the atomic radii are saved in a special array. The atomic contribution to the electrostatic free energy are returned in WMAIN (destroying the radii). To modify the value of the radii, the keyword RESET must be issued.

PB SOLVERs

(Reference: Klapper et al. Proteins 1, 47 (1986), A. Nicholls et al; J. Comput. Chem, 12(4),435-445 (1991))

Currently, PBEQ module supports various PB equation solvers. The default solver uses the SOR (Successive OverRelaxation) method for the linearized PB equation.

This is much faster than the old PBEQ solver which was used in c26a2. With OSOR keyword, the relaxation parameter will be optimized. This is especially useful when the system contains a salt concentration. Solvers for non-linear and partially linearized PB equations for 1:1 charge-paired salt are now available. Both use the SOR method as a default. In many cases, the direct use of both solvers may cause some convergence problems. So, it is the best way to use the potential from the linearized PB equation as a initial guess. Though, you may want to use the under-relaxation by adjusting the mixing factor (LAMBda). The partially linearized PB equation means that the linearized form of one of two exponential function is used like

phi > 0 --> exp(phi) = 1 + phi phi < 0 --> exp(-phi) = 1 - phi

Full multigrid (FMG) method is efficient for the uniform dielectric medium. When there is a discontinuity in the dielectric function, the method could be slower than the SOR method. You can improve the calculation speed using the smoothing dielectric boundary. Cubic grid should be used and number of grid points should be 2**(n+1) where n is a integer upto 9. Currently, FMG does not support MEMBRANE and PBC. (see ~chmtest/c28/pbeqtest5.inp and pbeqtest6.inp)

Grid The number of grid points in X, Y, and Z (NCEL,NCLX,NCLY,NCLZ) must be odd. Otherwise, the number of grid points will be increased by ONE without any WARNING message.

Iteration The maximum number of iterations (MAXIter) can be specified. The convergence parameters DEPS should not be modified. One could use the potential from previous calculation as a initial guess for current calculation using KEEPphi keyword. This is useful for the nonlinear (or partially linearized) PB equation. See also ITERate.

Charge Distribution Method The default is the trilinear method to distribute a charge over nearest 8 grid points. BSPLINE keyword will invoke the 3rd-order B-splines interpolation over nearest 27 grid points. B-splines method removes discontinuities in the reaction field forces.

Boundary Potential By default, boundary potential is calculated using the Debye-Huckel approximation for every boundary point. However, the computational time increases prohibitively as the number of grid points and of atoms in the system increases.

INTBP keyword uses the bilinear interpolation to construct boundary potential in a box with DCEL and (NCLx,NCLy,NCLz) from those in the same box with 2*DCEL and (NCLx/2+1,NCLy/2+1,NCLz/2+1). ZERO keyword sets boundary potential at the edge of the grid to zero. FOCUS keyword uses previously calculated potentials to set up boundary potential.

(Reference: M.K. Gilson et al; J. Comput. Chem. 9(4),327-335 (1987)) (see also an example below)

PBC keyword invokes the full 3d periodic boundary condition so that no boundary potential is calculated directly using the Debye-Huckel approximation.

(Reference: P.H. Hunenberger and J.A. McCammon JCP v.110(4) p.1856 (1999)) (alos, see ~chmtest/c28/pbeqtest4.inp)

NPBC keyword suppress XY periodic boundary conditions in membrane calculations.

Boundary potential of XY plane in membrane calculations can be constructed using the image atoms. When NIMGB=1, boundary potential includes the influence of the 8 nearest image cells.

Dielectric boundary SMOOTH and REEN change the attribute of the solute-solvent boundary. By default (NO SMOOTH), the boundary is defined by the van der Waals surface or the molecular surface (with WATR). SMOOTH keyword changes the boundary as a region having +/- SWIN (Smoothing WINdow) from the surface of the solute. Within the solute-solvent boundary, the dielectric constant and the Debye screening factor will be changed continuously from EPSP and zero to EPSW and the screening factor at bulk solvent.

REEN keyword with WATR creates the molecular (contact+reentrant) surface as the dielectric boundary.

Note

WATR without REEN just increases the atomic radii by it.

Various geometric objects PBEQ module supports three geometric objects with various options (see spherical droplet-, orthorhombic box-, and cylinder-spec. above) When using more than one geometry at the same time, the order of creating geometries is as follows: first is a droplet, second is a cylinder, and the last is a box.

Solvation force This keyword invokes the calculation of the solvation free energy and forces and must be followed by SMOOTH keyword. The solvation energy is taken as a sum of electrostatic and nonpolar solvation energy. The former is calculated from the PB equation and the latter by using the surface tension coefficient (STEN) that relates free energy with surface area. Note that the calculated surface is approximately the van der Waals surface. If membrane is considered, the surface of the membrane is also approximately included. The corresponding forces are also calculated and will be used in minimizations and MD simulations where NPBEQ can be used to specify the frequency for calculating the solvation forces. Note that SWIN must be equal or greater to DCEL to get correct solvation free energy and forces.

(Reference: W. Im, D. Beglov and B. Roux Continuum Solvation Model: computation of electrostatic forces from numerical solutions to the PB equation, Comput. Phys. Commun. 109,1-17 (1998))

Note

To print out the force of each atom, PRNLEV should be greater than 6.

ITERATE Pursue the iteration on the grid. SOLVE must have been called first. The main difference with the keyword KEEPphi (see above) is that the physical specifications (e.g., dielectric interface, membrane, etc...) must remain the same with ITERate. However, it is possible to change from linear to non-linear PB using ITERate. (see pbeqtest5.inp)

ENPB Compute the electrostatic PB energy Sum Q_i PHI_i over the lattice. Notice that the electrostatic energy is twice as much as the electrostatic free energy (see above). The value of the electrostatic energy is passed through the substitution parameter enpb. With INTE keyword, you can specify the atoms of interest.

CAPACITANCE Compute the capacitance based on the net induced charge in the double layer. The induced charge beyond the limits of the box are estimated based on the analytical solution to a planar membrane.

COUNTERION Compute the counter-ion (1:1 salt) distribution along Z-axis.

WRITE The WRITE command is used to write out the grid properties. By default, a binary file of the property will be written for the whole grid. The keyword CARD implies that a formatted output will be produced. In that case, the spatial range can be specified for the output. By default, the electrostatic potential PHI is given in [UNIT CHARGE]/[ANGS]. If specified, the PHI can be given in [VOLTS] or in [KCAL/MOL].

READ The READ command is used to read the electrostatic potential PHI or PHIX in [UNIT CHARGE]/[ANGS], Debye screening factor FKAPPA2, and the generalized reaction field MIJ matrix written in a binary file.

RESET Resets all assignments of the PBEQ module and free the HEAP array. Destroys all lists and grids. By default, the grids and arrays remain assigned when exiting and re-entering the PBEQ module. This is to allow multiple call to PBEQ without having to free the HEAP and other arrays if they are going to be used again. The RESET keyword must be used to re-assign new values for the atomic radii.

Miscellaneous command manipulations

*Miscellaneous Commands*are supported within the PBEQ module, allowing opening and closing of files, streaming of files, label assignments (e.g., LABEL), and repeated loops (e.g., GOTO), parameter substitutions (e.g., @1,@2, etc...) control (e.g., IF 1 eq 10.0 GOTO LOOP) and CALC (e.g., CALC energy = ?enpb).Note

TIMER 2 gives the times of various components in PBEQ module; the grid parameter preparation (subroutine MAYER), iterative solution (subroutine PBEQ1), and, force calculation (subroutine RFORCE and BFORCE).

COORMAN and SCALAR commands

*The Coordinate Manipulation Commands*and*SCALar : commands to manipulate scalar atom properties*are supported within the PBEQ module, allowing the easy manipulation of charges, radii, rotation and translations of molecules, etc...A set of “ATOMIC BORN RADII” Atomic radii derived from solvent electrostatic charge distribution may be used. (test/data/radius.str) These radii were tested with free energy perturbation with explicit solvent.

(Reference: M. Nina, D. Beglov and B. Roux. Atomic Radii for Continuum Electrostatics Calculations based on Molecular Dynamics Free Energy Simulations. J. Phys. Chem. 101(26),5239-5248,1997).

Note

A typo for residue HSD was present in the original set of radii. Check with M. Nina for new updated file.

To get the set of appropriate radii when using SWIN, the commands are as follows;

STREAM RADIUS.STR SCALAR WMAIN ADD {SWIN} SCALAR WMAIN MULT {FACTOR} SCALAR WMAIN SET 0.0 SELE TYPE H* END

The factor has a linear relationship with SWIN.

SWIN

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

FACTOR

0.979

0.965

0.952

0.939

0.927

0.914

0.901

0.888

0.875

0.861

(FACTOR = -0.1296 x SWIN + 0.9914 (a least-square fit))

PBAVerage subcommand

This subcommand allows for the averaging of the (precalculated) electrostatic potential (PHI values) over specified regions of the grid. The region is specified as a rectangular box, with or without an atom selection. The units may be specified as KCAL (kcal/mol), VOLT (volts), or not at all, in which case the default units (charge/angs) are used. The calculated average may be assigned to a CHARMM parameter through the symbol ?AVPH. The PBAV PHI subcommand does not calculate the PHI values themselves; hence the electro- static potential should have already been calculated before this subcommand is given.

The following calculates the average PHI value over a rectangular-box region of the grid:

PBAV PHI KCAL xfirst [real] xlast [real] - yfirst [real] ylast [real] - zfirst [real] zlast [real]

The grid limits must be specified the first time the PBAV PHI subcommand is invoked. For subsequent invocations, the command will use the stored limits unless the limits are respecified.

The following calculates the average PHI values over the grid points that are both within the grid limits and within the van der Waals radii of the selected atoms:

PBAV PHI KCAL UPDAte xfirst [real] xlast [real] - yfirst [real] ylast [real] - zfirst [real] zlast [real] - ATOM SELE [selection] END

The UPDAte keyword updates the atom-based grid, so that when the PBAV PHI ATOM subcommand is given for the first time, the UPDATE keyword must be used and an atom selection given. For subsequent invocations, the atom selection (for defining the set of atoms over which the calculation is to be done) and the UPDATE command (for updating the grid, based on the position of the selected atoms) are optional. If UPDATE is specified but the atom selection (or grid limits) are not, the algorithm will use the atom selection (or grid limits) that were last specified. If the PBAV PHI subcommand has not been previously given, the grid limits must be specified.

GSBP is a boundary potential for simulating a reduced system while
incorporating implicitly the dominant electrostatic forces of the surrounding
atoms. It has been developed in the same spirit as the SBOUND and the SSBP,
see *sbound* and *ssbp*.

The current implementation of the method is described in W. IM, S. Berneche, and B. Roux. J. Chem. Phys. (2000, in preparation). Briefly, the system is partitioned in two regions: an inner region of interest and an outer region. The inner region includes all atom explicitly.

GSBP represents the electrostatic forces from the outer region as the sum of two components. One is the static external field (PHIX) which arises from the charge distribution in the outer region (taking into consideration the solvent as a featureless dielectric medium). The second contribution is the reaction field which is created by the charge distribution inside the inner region considering the whole molecular configuration and the dielectric solvent. In the GSBP, the reaction field is calculated through a generalized multipolar expansion of the instantaneous charge density in the inner system coupled with a generalized reaction field matrix MIJ.

The numerical implementation of the GSBP can be divided into two parts; SETUP and UPDATE parts. In the SETUP part, the static external field and the MIJ matrix are calculated once and stored before a simulation. The SETUP part mostly uses the PBEQ module. In UPDATE part, the energy and forces are updated using the stored external field and the MIJ matrix in each step of the molecular dynamics.

GSBP Syntax GSBP is a subcommand inside PBEQ module like SOLVe and uses all options (except solvation force-spec.) in SOLVe.

GSBP decomposition-spec. inner region-specifications basis functions-spec. large box-specifications cavity potential-spec. all options in SOLVE decomposition-spec.::= [GTOT] [G_oo] [G_io] [G_ii] GTOT [.FALSE.] : total electrostatic solvation free energy G_oo [.FALSE.] : electrostatic solvation free energy in outer region G_io [.FALSE.] : electrostatic free energy due to the interactions between inner and outer regions G_ii [.FALSE.] : electrostatic solvation free energy in inner region inner region-specifications:: [ [RECTbox] [XMAX real] [YMAX real] [YMAX real] [XMIN real] [YMIN real] [YMIN real] ] [ [SPHEre] [SRDIst real] [RRXCen real] [RRYCen real] [RRZCen real] ] RECTbox [.FALSE.] : rectangular (box) inner region XMAX [0.0] : maximum position of inner region along X-axis YMAX [0.0] : maximum position of inner region along Y-axis ZMAX [0.0] : maximum position of inner region along Z-axis XMIN [0.0] : minimum position of inner region along X-axis YMIN [0.0] : minimum position of inner region along Y-axis ZMIN [0.0] : minimum position of inner region along Z-axis SPHEre [.FALSE.] : spherical inner region SRDIst [0.0] : radius of spherical inner region RRXCen [0.0] : X position of spherical inner region RRYCen [0.0] : Y position of spherical inner region RRZCen [0.0] : Z position of spherical inner region basis function-spec.:: [ [XNPOl integer] [YNPOl integer] [ZNPOl integer] ] [NMPOl integer] [MAXNpol integer] [NLISt integer] [NOSOrt] [CGSCal real] XNPOl [0] : number of Legendre polynomials in X direction YNPOl [0] : number of Legendre polynomials in Y direction ZNPOl [0] : number of Legendre polynomials in Z direction NMPOl [0] : number of multipoles with spherical harmonics MAXNpol [NTPOL] : maximum number of basis functions which are used in the energy and forces calculations NLISt [1] : updating frequency for the ordered list of basis functions during molecular dynamics NOSOrt [.FALSE.] : surpress the ordering of basis functions CGSCale [1.0] : charge scaling factor for the monopole basis function large box-specifications:: [LBOX] [LDCEl real] [LNCEl integer] [FOCUS] [LXBCen real] [LYBCen real] [LZBCen real] LBOX [.FALSE.] : invoke large box calculation (see below) LDCEL [4*DCEL] : grid spacing of large box LNCEL [33] : number of grid point in 1D for a cubic large box : this should be smaller than or equal to NCEL LXBCEN [0.0] : the center of a large box in X LYBCEN [0.0] : the center of a large box in Y LZBCEN [0.0] : the center of a large box in Z FOCUS [.FALSE.] : use the potential from a large box calculation for the boundary potential in finer calculation cavity potential spec ::= CAVI atom-selection [DRDI real] [DRCA real]

Free energy decomposition The total electrostatic solvation energy is decomposed into G_oo, G_io, and G_ii. All decomposition calculations are performed using the PB solver. With G_io keyword we can calculate the static external field and save it using WRITE PHIX. G_ii gives the exact reaction field energy with which we can compare the basis-set reaction field energy.

Inner region & Basis functions Currently, GSBP supports two shapes for the inner regions: an orthorhombic rectangular box and a sphere. For the rectangular box, Legendre polynomials are used as a basis-set. The number of function along each cartesian axis can be specified using XNPOL, YNPOL, and ZNPOL. The resulting total number of basis functions (NTPOL) is XNPOL*YNPOL*ZNPOL. For the spherical inner region, spherical harmonics are used. The number of electric multipoles is specified as NMPOL, and the resulting total number of basis functions (NTPOL) is NMPOL*NMPOL (e.g., with NMPOL = 2 one is including the reaction field for the monopole and dipole of the inner system).

The calculation of the MIJ matrix can be done in a single job but can also be restarted. This is convenient since one does not always know how many basis functions would yield accurate results. For example, one could calculate the MIJ matrix with NMPOL=11 spherical harmonics. After comparing the result with exact PB reaction field, one may decide to increase the number of multipoles in NMPOL. This procedure is illustrated in the test case gsbptest1.inp. The list of basis functions can be ordered and sorted such that the number of multipole basis function used for the energy and force (MAXNpol) calculations is reduced.

The focussing method with a large initial box and interpolating boundary condition (INTBP) is a necessary procedure for computing the MIJ matrix because the charge distribution corresponding to a given basis function involves a large number of lattice point charges. All grid points inside the inner region contain a partial charge assigned by a basis function. Therefore, it would take a long time to set the boundary potential directly. In practice, the charges density from a basis function are interpolated onto a large (coarse) grid to reduce the number of grid-point charges which increase the computational cost of setting up the boundary conditions. In this case, the focussing method is much more useful because the boundary potential can be obtained from the coarse grid calculation.

Cavity Potential The GSBP cavity potential is a restrictive potential that keeps water molecules from escaping the simulation region. Usually it is applied only on the oxygen atom of the water molecules. The DRDI option specifies the offset where the restrictive potential is placed from the dielectric boundary for the spherical geometry. The DRCA option gives the offset of the quartic potential (same form as the one in MMFP module) for the orthorhombic geometry.

This examples are meant to be a partial guide in setting up an input file for PBEQ. There are two test files, pbeqtest1.inp, pbeqtest2.inp, pbeqtest3.inp, and pbeqtest7.inp.

This example shows how to perform two PB calculations, one for a surrounding dielectric of 80 (water) and one for a surrounding of 1.0 (vacuum). The difference between the two energies then corresponds to the electrostatic contribution to the solvation free energy. The salt concentration was zero in this calculation.

```
PBEQ
scalar wmain = radius
SOLVE epsw 80.0 conc 0.0 ncel 30 dcel 0.4
set ener80 = ?ENPB
SOLVE epsw 1.0
set ener1 = ?ENPB
CALC total = @ener80 - @ener1
RESET
END
```

This example shows how to use a set of atomic Born radii with a smoothing window.

```
set sw 0.4
set factor 0.939
PBEQ
stream radius.str
scalar wmain add @sw
scalar wmain mult @factor
scalar wmain set 0.0 sele type H* end
scalar wmain show
SOLVE epsw 80.0 ncel 100 dcel 0.3 -
smooth swin @sw force sten 0.03 npbeq 1
RESET !! If you consider a minimization or dynamics with PB forces,
!! don't use RESET here.
END
```

This example shows how to set up a membrane potential and how to get the electrostatic contribution to the solvation free energy in the membrane environment. Note that a non-zero concentration is required for a sensible system with a membrane potential.

```
PBEQ
scalar wmain = radius
SOLVE epsw 80.0 ncel 150 dcel 0.5 conc 0.150 -
Tmemb 25.0 Zmemb 0.0 epsm 2.0 vmemb 0.100
set ener80 = ?ENPB
SOLVE epsw 1.0 conc 0.000 -
Tmemb 25.0 Zmemb 0.0 epsm 1.0 vmemb 0.000
set ener1 = ?ENPB
CALC total = @ener80 - @ener1
RESET
END
```

This example shows how to set up boundary potentials using FOCUS keyword, how to read the saved potential, and how to calculate the electrostatic contribution to the solvation free energy using FOCUS.

```
PBEQ
scalar wmain = radius
SOLVE epsw 1.0 ncel 60 dcel 0.4
open write file unit 40 name phi.dat
write phi unit 40
SOLVE epsw 1.0 dcel 0.2 focus ! boundary potentials from DCEL 0.4 potentials
! NOTE: YOU CAN CHANGE NCEL IN THE FOCUSSED SYSTEM AS FOLLOWS;
! SOLVE epsw 1.0 ncel 80 dcel 0.2 focus
SOLVE epsw 1.0 dcel 0.1 focus ! boundary potentials from DCEL 0.2 potentials
open read file unit 41 name phi.dat
read phi unit 41
SOLVE epsw 1.0 dcel 0.1 focus ! boundary potentials from DCEL 0.4 potentials
RESET
END
PBEQ
scalar wmain = radius
SOLVE epsw 80.0 ncel 60 dcel 0.4
set ener81 = ?ENPB
SOLVE epsw 80.0 dcel 0.2 focus
set ener82 = ?ENPB
SOLVE epsw 80.0 dcel 0.1 focus
set ener83 = ?ENPB
SOLVE epsw 80.0 dcel 0.05 focus
set ener84 = ?ENPB
SOLVE epsw 1.0 dcel 0.4
set ener11 = ?ENPB
SOLVE epsw 1.0 dcel 0.2 focus
set ener12 = ?ENPB
SOLVE epsw 1.0 dcel 0.1 focus
set ener13 = ?ENPB
SOLVE epsw 1.0 dcel 0.05 focus
set ener14 = ?ENPB
calc total = @ener81 - @ener11
calc total = @ener82 - @ener12
calc total = @ener83 - @ener13
calc total = @ener84 - @ener14
SOLVE epsw 80.0 ncel 120 dcel 0.2
set ener80 = ?ENPB
SOLVE epsw 1.0
set ener1 = ?ENPB
calc total = @ener80 - @ener1
RESET
END
```

This example shows pKa Poisson-Bolztmann calculations which deals with explicit charge distribution on the ionizable site. (see also ~chmtest/c28/pbeqtest7.inp)

```
! set residue for pKa calculation and the patch for the ionizable sidechain
set segid = syst
set resid = 2
set patch = GLUP
!Miscelaneous variables
set Dcel = 0.5 ! initial value for the mesh size in the finite-difference
set Ncel = 65 ! maximum number of grid points
set EpsP = 1.0 ! dielectric constant for the protein interior
set EpsW = 80.0 ! solvent dielectric constant
set Conc = 0.0 ! salt concentration
set Focus = Yes
!Note that the resid must be set before streaming into this file
scalar wcomp = charge
patch @patch @Segid @resid setup
hbuild !build any missing hydrogens
scalar wcomp store 1
scalar charge store 2
define SITE select .bygroup. ( resid @resid ) show end
define REST select .not. site end
! Charges of the unprotonated state
scalar wmain recall 1
scalar wmain show
scalar wmain stat select SITE end
! Charges of the protonated state
scalar wmain recall 2
scalar wmain show
scalar wmain stat select SITE end
! Estimate the grid dimensions
format (f15.5)
coor orient norotate
coor stat select all end
calc DcelX = ( ?Xmax - ?Xmin ) / @Ncel
calc DcelY = ( ?Ymax - ?Ymin ) / @Ncel
calc DcelZ = ( ?Zmax - ?Zmin ) / @Ncel
if @DcelX gt @Dcel set Dcel = @DcelX
if @DcelY gt @Dcel set Dcel = @DcelY
if @DcelZ gt @Dcel set Dcel = @DcelZ
coor stat select SITE end
set Xcen = ?xave
set Ycen = ?yave
set Zcen = ?zave
PBEQ
stream @0radii.str
scalar charge recall 2 ! Protonated charge distribution
SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW
if Focus eq yes -
SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -
XBcen @Xcen YBcen @Ycen ZBcen @Zcen
set EnerPs = ?enpb ! Protonated side chain in structure
SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW select SITE end
if Focus eq yes -
SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -
XBcen @Xcen YBcen @Ycen ZBcen @Zcen select SITE end
set EnerPi = ?enpb ! Protonated side chain isolated
scalar charge recall 1 ! Unprotonated charge distribution
SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW
if Focus eq yes -
SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -
XBcen @Xcen YBcen @Ycen ZBcen @Zcen
set EnerUs = ?enpb ! Unprotonated side chain in structure
SOLVE ncel @Ncel Dcel @Dcel EpsP @epsP EpsW @EpsW select SITE end
if Focus eq yes
SOLVE ncel @Ncel Dcel 0.25 EpsP @EpsP EpsW @EpsW focus -
XBcen @Xcen YBcen @Ycen ZBcen @Zcen select SITE end
set EnerUi = ?enpb ! Unprotonated side chain isolated
calc Energy = ( @EnerPs - @EnerUs ) - ( @EnerPi - @EnerUi )
calc pKa = -@Energy/( ?KBLZ * 300.0 ) * log10(exp(1)) != log10(exp(-@Energy/(?KBLZ*300)))
END
```