Some methods are based on solutions to the Poisson–Boltzmann equation (PBE), often referred to as FDPB-based methods (FDPB stands for "finite difference Poisson–Boltzmann"). The PBE is a modification of Poisson's equation that incorporates a description of the effect of solvent ions on the electrostatic field around a molecule.
The [http://newbiophysics.cs.vt.edu/H++/ H++ web server], the [https://web.archive.org/web/20070728080556/http://enzyme.ucd.ie/pKD pKD webserver], [https://gunnerlab.github.io/Stable-MCCE/ MCCE2], [http://agknapp.chemie.fu-berlin.de/karlsberg Karlsberg+], [https://www.itqb.unl.pt/labs/molecular-simulation/in-house-software/ PETIT] and [https://rtullmann.de/parts/gmct-gcem.html GMCT] use the FDPB method to compute pK values of amino acid side chains.
FDPB-based methods calculate the change in the pK value of an amino acid side chain when that side chain is moved from a hypothetical fully solvated state to its position in the protein. To perform such a calculation, one needs theoretical methods that can calculate the effect of the protein interior on a pK value, and knowledge of the pKa values of amino acid side chains in their fully solvated states.