pbam-auto¶
PB-AM is an analytical solution to the linearized Poisson-Boltzmann equation for multiple spherical objects of arbitrary charge distribution in an ionic solution. More details on the method are available in Lotan, Head-Gordon (2006). The physical calculations are uses to perform various actions on a system of molecules such as calculation of energies, forces, torques, electrostatic potentials, and Brownian dynamics schemes. This fast method coarse-grains all molecules of the system into single spheres large enough to contain all molecule atoms.
The current implementation of PB-AM in APBS includes:
- Calculation of energies, forces and torques
- Calculation of electrostatic potentials
- Brownian dynamics simulations
Keywords for this calculation type include:
Background information¶
PB-AM is an analytical solution to the linearized Poisson-Boltzmann equation for multiple spherical objects of arbitrary charge distribution in an ionic solution. The solution can be reduced to a simple system of equations as follows:
Where \(A^{(i)}\) represents the effective multipole expansion of the charge distributions of molecule \(i\). \(E^{(i)}\) is the free charge distribution of molecule \(i\). \(\Gamma\) is a dielectric boundary-crossing operator, \(\Delta\) is a cavity polarization operator, \(T\) an operator that transforms the multipole expansion to a local coordinate frame. \(A^{(i)}\) is solved for through an iterative SCF method.
From the above formulation, computation of the interaction energy \(\Omega^{(i)}\) for molecule \(i\), is given as follows:
where \(\langle M, N \rangle\) denotes the inner product. Forces can be obtained from