One of the canonical examples for polar solvation is the Born ion: a nonpolarizable sphere with a single charge at its center surrounded by an aqueous medium. In the absence of external ions, the polar solvation energy for this system is given by
where q is the ion charge, a is the ion radius, and the two ε variables denote the internal and external (solution) dielectric constants. This model assumes zero ionic strength.
We can setup a PQR file for the Born ion for use with APBS with the contents:
We're interested in performing two APBS calculations for the charging free energies in homogeneous and heterogeneous dielectric coefficients. We'll assume the internal dielectric coefficient is 1 (e.g., a vacuum) and the external dielectric coefficient is 78.54 (e.g., water). for these settings, the polar Born ion solvation energy expression has the form
where z is the ion charge in electrons and R is the ion size in Å.
This solvation energy calculation can be setup in APBS with the following input file:
Note that the Born example above can be easily generalized to other polar solvation energy calculations. For example, ions could be added to the solv ELEC, dielectric constants could be modified, surface definitions could be changed (in both ELEC sections!), or more complicated molecules could be examined. Many of the examples included with APBS (e.g.,
Note that, as molecules get larger, it is important to examine the sensitivity of the calculated polar solvation energies with respect to grid spacings and dimensions.