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: see calculate_energy()

  • calculate forces: see calculate_forces()

  • displacement: finite difference displacement for force calculation

  • grid spacings: grid spacings for integral calculation; see grid_spacings()

  • molecule: alias string for molecule to use in calculation; see molecule()

  • pressure: solvent hard sphere pressure; see pressure()

  • solvent density: see solvent_density()

  • solvent radius: see solvent_radius()

  • surface density: density of points to use for surface integrals; see surface_density()

  • surface method: method used to calculate the solvent-solute interface; see surface_method()

  • surface tension: see surface_tension()

  • temperature: see temperature()

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:

\[{W}^{(\mathrm{np})}(x) = \gamma A(x) + pV(x) + \bar \rho \sum^N_{i=1} \int _{\Omega} u_i^{(\mathrm{att})} (x_i, y) \theta (x,y) \, \mathrm{d}y\]

and mean nonpolar solvation forces are calculated according to:

\[\mathbf{F}_i^{(\mathrm{np})}(x) = -\gamma \frac{\partial A (x)}{\partial x_i} - p \int _{\Gamma _i (x)} \frac{y-x_i}{\lVert y - x_i \rVert} \, \mathrm{d}y - \bar \rho \sum _{i=1}^N \int _{\Omega} \frac{\partial u_i^{(\mathrm{att})}(x_i,y)}{\partial x_i} \theta (x,y) \, \mathrm{d}y\]

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.