Table 1.
Existing numerical methods and corresponding solvers for solving PBE
| Program name | charge | Program available for download | URL | description |
|---|---|---|---|---|
| Finite Difference | ||||
| PBSA (AMBER) | Part of Amber package | yes | http://ambermd.org | FD scheme offering numerous algorithms to deliver the solution; polarizable force field |
| DELPHI | No charge for academia | yes | http://compbio.clemson.edu/DelPhi.php | FD scheme with the Gauss-Seidel iteration technique |
| MEAD | No charge | yes | http://hospital.stjude.org/mead_filerequest/request.html | FD algorithm; includes modeling of a membrane as a low dielectric slab, possibly with a water-filled channel through a protein in the membrane |
| MIBPB | No charge | yes | http://www.math.msu.edu/~wei/MIBPB | High order discretization scheme close to the molecule-solvent interface; Dirichletto Neumann mapping method |
| PBEQ | Part of Charmm package | yes | http://www.charmmgui.org/?doc=input/pbeqsolver | Calculates electrostatic potential and solvation energy, in both aqueous solvent and membrane environments. |
| UHBD | No charge | yes | http://proiects.hits.org/mcm/projects/afwb2002/uhbd.html | Capable of solving the linear and nonlinear Poisson-Boltzmann equation using a finite-difference method; performing Brownian dynamics simulations of the association of two molecules and of the internal dynamics of a protein. |
| ZAP | commercial | yes | http://www.eyesopen.com/zaptk | Very fast algorithm with Gaussian representation of the dielectric constant |
| Finite element | ||||
| APBS | No charge | yes | www.poissonboltzmann.org/apbs | An adaptive finite element Poisson–Boltzmann solver |
| NA | NA | no | NA | Numerical solution of the Poisson–Boltzmann equation using tetrahedral finite-element meshes |
| NA | NA | no | NA | FEM using Newton-Krylov iterations |
| NA | NA | no | NA | A mortar FEM Poisson–Boltzmann solver |
| NA | NA | no | NA | A first-order system least-squares FEM for the PBE |
| Boundary element | ||||
| AFMPB | NA | yes | http://cpc.cs.qub.ac.uk/summaries/AEGB v1 0.html | An adaptive fast multipole Poisson–Boltzmann solver |
| FTWARE | NA | yes | http://cvcweb.ices.utexas.edu/software | Derivative boundary formulation of the problem; A smooth approximation of the molecular surface. |
| FFTSVD | NA | no | NA | multiscale algorithm and FFT method |
| FPB | commercial | no | http://continuum-dynamics.com/lib-pro-fpb.html | A hybrid approach for solving the nonlinear Poisson–Boltzmann equation |