Nonpolar grid-based calculations
Parameters for a grid-based nonpolar solvation calculation.
Objects can be initialized with dictionary/JSON/YAML data with the following keys:
calculate energy
: seecalculate_energy()
calculate forces
: seecalculate_forces()
displacement
: finite difference displacement for force calculationgrid spacings
: grid spacings for integral calculation; seegrid_spacings()
molecule
: alias string for molecule to use in calculation; seemolecule()
pressure
: solvent hard sphere pressure; seepressure()
solvent density
: seesolvent_density()
solvent radius
: seesolvent_radius()
surface density
: density of points to use for surface integrals; seesurface_density()
surface method
: method used to calculate the solvent-solute interface; seesurface_method()
surface tension
: seesurface_tension()
temperature
: seetemperature()
APBS apolar calculations follow the very generic framework described in Wagoner JA, Baker NA. Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion and volume terms. Proc Natl Acad Sci USA, 103, 8331-8336, 2006. doi:10.1073/pnas.0600118103.
Nonpolar solvation potentials of mean force (energies) are calculated according to:
and mean nonpolar solvation forces are calculated according to:
In these equations, \(\gamma\) is the repulsive (hard sphere) solvent
surface tension (see surface_tension()
), A is the
conformation-dependent solute surface area (see solvent_radius()
and
surface_method()
), p is the repulsive (hard sphere) solvent
pressure (see pressure()
), V is the conformation-dependent solute
volume (see solvent_radius()
and surface_method()
),
\(\rho\) (see solvent_density()
keywords) is the bulk solvent
density, and the integral involves the attractive portion (defined in a
Weeks-Chandler-Andersen sense) of the Lennard-Jones interactions between
the solute and the solvent integrated over the region of the problem domain
outside the solute volume V. Lennard-Jones parameters are taken from APBS
parameter files as read in through an APBS input file READ statement (see
Data loading input file section (required)).
Note
The above expressions can easily be reduced to simpler apolar solvation formalisms by setting one or more of the coefficients to zero through the keywords.
Warning
All APOLAR calculations require a parameter file which contains Lennard-Jones radius and well-depth parameters for all the atoms in the solute PDB. This parameter file must also contain radius and well-depth parameters for water (specifically: residue “WAT” and atom “OW”). Complete parameter files for protein and nucleic acid parameters are not currently available; we prefer geometric flow calculations (coupled polar and apolar components) rather than this model.