Note

**Questions and comments regarding GBSW should be directed to**

- Wonpil Im (wonpil@ku.edu)
- Charles L. Brooks, III (brooks@scripps.edu)

**References for GBSW:**

- W. Im, M.S. Lee, and C.L. Brooks III “Generalized Born Model with a Simple Smoothing Function.” J. Comput. Chem. 24:1691-1702 (2003).
- W. Im, M. Feig, and C.L. Brooks III “An Implicit Membrane Generalized Born Theory for the Study of Structure, Stability, and Interactions of Membrane Proteins.” Biophys. J. 85:2900-2918 (2003).
- W. Im, J. Chen, and C.L. Brooks III “Application of a rotationally invariant procedure to a Generalized Born Model” in preparation (2005).

The GBSW module provides the (electrostatic + nonpolar) solvation energy and forces. A Generalized Born method is used for the electrostatic part and the solvent-exposed surface ares for the nonpolar part with a phenomenological surface tension coefficient. Based on volume integration schemes used in the GBMV module [M.S. Lee, F.R. Salabury, Jr., and C.L. Brooks III, J. Chem. Phys., 116, 10606 (2002)], we have recast the calculation of the self-electrostatic solvation energy to utilize a simple smoothing function at the dielectric boundary. The GBSW model is formulated in this manner to provide consistency with the Poisson-Boltzmann (PB) theory previously developed to yield numerically-stable electrostatic solvation forces based on finite-difference methods [W. Im, D. Beglov, and B. Roux, Comp. Phys. Comm., 111, 59 (1998)]. However, it is also possible to mimic the PB results with the molecular surface by reparametrizing two adjustable parameters, a_0 to modulate the Coulomb field term and a_1 to include a correction term beyond Coulomb field.

The GBSW module takes the influence of biological membranes into account. Consistent with continuum Poisson-Boltzmann (PB) electrostatics, the membrane is approximated as an solvent-inaccessible infinite planar low-dielectric slab. The membrane GB model closely reproduces the PB electrostatic solvation energy profile across the membrane.

The GBSW module works with the IMAGE facility. The GBSW calculations are about 4 times slower than the corresponding vacuum calculations. Using the simple smoothing function makes the present GB model roughly 2-3 times faster than the GBMV module.

The backbone phi/psi cross-term (CMAP) and the atomic input radii were recently re-optimized specifically for GBSW implicit solvent, to balance the solvation and intramolecular interactions and to reproduce experimental conformational equilibria of a range of peptides. See Examples for detailed description of the optimal settings (Ref: Chen, Im and Brooks, JACS, 2006).

```
GBSW [SW real] [AA0 real] [AA1 real] [MOLSURF] [GBENER] [ROTINV] -
[NANG integer] [NRAD integer] [RMAX real] [DGP real] [RBUFFER real] -
[EPSP real] [EPSW real] [CONC real] [TEMP real] [SGAMMA real] -
[TMEMB real] [MSW real] -
[IGBFRQ integer]
GBSW RESET ! reset GBSW
```

SW | [0.3] | half of smoothing length in Ang. (default value is changed to 0.2 when MOLSURF is issued.) |

AA0 | [aa0(sw)] | coefficient for the Coulomb Field Approximation term |

AA1 | [aa1(sw)] | coefficient for the correction term (optimized default values for aa0(sw) and aa1(sw) are given below) |

MOLSURF | [FALSE] | approximation to PB with molecular surface |

GBENER | [FALSE] | calculate and print the solvation energy (No cutoff is used for GB electrostatic solvation energy.) |

ROTINV | [FALSE] | rotationally invariant numerical quadrature procedure |

NANG | [38] | number of angular integration points |

NRAD | [0] | number of radial integration points (default value means the use of optimized 24 radial integration points) |

RMAX | [20.0] | maximum distance for radial integration in Ang. |

DGP | [1.5] | grid spacing for lookup table in Ang. |

RBUFFER | [0.0] | buffer length for lookup table in Ang. |

EPSP | [1.0] | dielectric constant of both protein and reference state |

EPSW | [80.0] | solvent dielectric constant |

CONC | [0.0] | salt concentration in M |

TEMP | [300.0] | temperature in K (only necessary with CONC) |

SGAMMA | [0.0] | nonpolar surface tension coefficients in kcal/(molxA^2) |

TMEMB | [0.0] | thickness of low-dielectric membrane slab centered at Z=0 (in Ang.) |

MSW | [sw] | half of membrane switching length in Ang. |

IGBFRQ | [1] | updating frequency of effective Born radii |

Volume Integration

The GBSW module uses the numerical quadrature method for the volume integration. The integration points and weights for the radial component are generated by the Gaussian-Legendre quadrature those for the angular component by the Lebedev quadrature. The default values for the integration (NANG, NRAD, and RMAX) should be appropriate for most cases. However, one can specify NANG, NRAD, and RMAX independently. Note that NANG should be one of 26, 38, or 50.

A grid-based lookup table is used to increase the efficiency of the integration. Keywords DGP and RBUFFER are related with the lookup table. The current default value should be optimal for most case. However, one can check the efficiency and optimize those by performing short MD runs.

Choice of SW In prinicple, one can choose any SW. However, it should be noted that GBSW calculations take more time as SW increases. As default, SW=0.3 is recommended for the smooth boundary and SW=0.2 for the molecular surface. The optimized coefficients a_0 and a_1 are shown below for each SW. Those coefficients were obtained by minimizing the error between GB and PB self-electrostatic solvation energies.

default A_0 and A_1 for the smoothed dielectric boundary

SW

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

A_0

-0.0811

-0.1481

-0.1801

-0.1680

-0.1542

-0.1731

-0.2279

-0.3064

-0.3943

-0.4820

A_1

1.6000

1.7292

1.8174

1.8560

1.8864

1.9453

2.0359

2.1472

2.2645

2.3801

default A_0 and A_1 for the molecular surface

SW

0.1

0.2

0.3

A_0

1.2642

1.2045

1.1177

A_1

0.0593

0.1866

0.3406

Physical Parameters

It should be noted that a_0 and a_1 were optimized with EPSP=1.0 and EPSW=80.0. Therefore, one should be careful when other values for EPSP and EPSW are used. In other words, the electrostatic solvation contribution may not be optimal. The influence of salt is taken into account based on the formalism of [J. Srinivasan, M.W. Trevathan, P. Beroza, and D.A. Case, Theor. Chem. Acc., 101, 426-434 (1999)].

The nonpolar solvation contribution is considered only when non-zero SGAMMA is issued. Note that the dimension is kcal/(molxA^2), and 0.01 to 0.04 might be suitable for SGAMMA.

Low-dielectric slab for membrane

The influence of membrane hydrophobic core as the low dielectric medium is approximately captured in the GBSW module (see reference 2 for details). Note that the membrane switching function is applied in the following region;

- Z > 0 : Tmemb/2.0 - MSW to Tmemb/2.0 + MSW
- Z < 0 : -Tmemb/2.0 + MSW to -Tmemb/2.0 - MSW

The examples below illustrate some of the uses of the GBSW module. (See also c30test/gbsw.inp)

There are two requirements for running GBSW;

- “SWITCH” should be chosen in NBOND specifications.
- WMAIN should be filled with a proper set of radii. It is recommended to use the optimized PB radii (~charmm/test/data/radius.str) for the GBSW module.

Note

A self-consistent GBSW force field is optimal for peptide and protein simulations (as of 2005). For this, WMAIN should be filled with a new set of radii (“radius_gbsw.str”). In addition, a special CMAP should be used for optimal treatment of peptide backbone (“par_all22_prot_gbsw.inp”). Both files locate in ~charmm/toppar/gbsw/. (see Example 5 for illustration).

For optimal performance in folding simulations, the following GBSW command-line options should be used with the self-consistent GBSW force field:

GBSW sgamma 0.005 nang 50

```
!To perform a single-point energy calculation with infinite cutoffs:
prnlev 0
stream radius.str
prnlev 5
scalar wmain statistics select .not. type H* end
define check select (.not type H* ) .and. ( prop wmain .eq. 0.0 ) show end
if ?nsel ne 0 stop !some heavy atom have a zero radius
GBSW sw 0.3 sgamma 0.03 dgp 1.5 GBenergy
```

```
!To perform a minimization or dynamics with cutoffs
prnlev 0
stream radius.str
prnlev 5
scalar wmain statistics select .not. type H* end
define check select (.not type H* ) .and. ( prop wmain .eq. 0.0 ) show end
if ?nsel ne 0 stop !some heavy atom have a zero radius
GBSW sw 0.3 sgamma 0.03 dgp 1.5 GBenergy
NBOND atom switch cdie vdw vswitch -
ctonnb 16 ctofnb 16 cutnb 20
ENERGY
(minimization or dynamics)
```

```
!To perform a minimization or dynamics with images
(image definition)
NBOND atom switch cdie vdw vswitch -
ctonnb 20 ctofnb 20 cutnb 24 cutim 24 ! should be before GBSW
prnlev 0
stream radius.str
prnlev 5
scalar wmain statistics select .not. type H* end
define check select (.not type H* ) .and. ( prop wmain .eq. 0.0 ) show end
if ?nsel ne 0 stop !some heavy atom have a zero radius
GBSW sw 0.3 sgamma 0.03 dgp 1.5 GBenergy
ENERGY
(minimization or dynamics)
```

```
!To perform a minimization or dynamics with membrane
prnlev 0
stream radius.str
prnlev 5
scalar wmain statistics select .not. type H* end
define check select (.not type H* ) .and. ( prop wmain .eq. 0.0 ) show end
if ?nsel ne 0 stop !some heavy atom have a zero radius
GBSW sw 0.3 sgamma 0.03 dgp 1.5 tmemb 35.0 msw 2.5
NBOND atom switch cdie vdw vswitch -
ctonnb 16 ctofnb 16 cutnb 20
ENERGY
(minimization or dynamics)
```

```
!To setup for using the self-consistent GBSW force field
! read in the CMAP topology file (standard)
open read card unit 10 name @toppar/top_all22_prot_cmap.inp
read rtf card unit 10
close unit 10
!read in the parameter file that contains GBSW specific CMAP
open read card unit 10 name @topar/par_all22_prot_gbsw.inp
read para card unit 10
close unit 10
...
! read in the new input radii
prnlev 0
stream @toppar/radius_gbsw.str
prnlev 5
! verify that all heavy atoms have non-zero radii
scalar wmain statistics select .not. type H* end
define check select (.not type H* ) .and. ( prop wmain .eq. 0.0 ) show end
if ?nsel ne 0 goto diehard !some heavy atom have a zero radius
! ativate GBSW energy term
gbsw sgamma 0.005 nang 50
nbond atom switch cdie vdw vswitch -
ctonnb 16 ctofnb 16 cutnb 20
energy
...
(minimization and/or dynamics)
```