pbam-auto

Todo

This command has not yet been ported to the new APBS syntax (see YAML- and JSON-format input files).

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.

Todo

If there’s only one mode to PBAM, let’s call it pbam instead of pbam-auto. Documented in https://github.com/Electrostatics/apbs/issues/498

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:

ELEC pbam-auto keywords:

• 3dmap
• diff
• dx
• grid2d
• gridpts
• mol
• ntraj
• pbc
• pdie
• randorient
• runname
• runtype
• salt
• sdie
• temp
• term
• termcombine
• units
• xyz

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:

\[A = \Gamma \cdot (\Delta \cdot T \cdot A + E)\]

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:

\[\Omega^{(i)}=\frac{1}{\epsilon_s} \left \langle \sum_{j \ne i}^N T \cdot A^{(j)} , A^{(i)} \right \rangle\]

where \(\langle M, N \rangle\) denotes the inner product. Forces can be obtained from

\[\textbf{F}^{(i)} = \nabla_i \Omega^{(i)}=\frac{1}{\epsilon_s} \left[ \langle \nabla_i \,T \cdot A^{(i)} , A^{(i)} \rangle + \langle T \cdot A^{(i)} , \nabla_i \, A^{(i)} \rangle \right]\]