# Re: AMBER: Solute-solvent boundary in pbsa

From: Ray Luo <rluo.uci.edu>
Date: Tue, 24 May 2005 22:54:50 -0700

Hi Jenk,

To discuss properties of dielectric in electrostatic field, it is very
useful to use the concept of induced surface charge. Suppose there are M
atomic charges, Q_1, ..., Q_M. After solving Poisson's equation, the
electrostatic potential distribution around these charges can be obtained.

Inversely, we can recover these charges according to Gauss' Law:

\nabla E = 4 \pi \rho,

where E is electrostatic field and \rho is charge density. Note that
\rho is non-zero apparently at atomic centers because we put charges
there. However, \rho is non-zero also at the dielectric boundary. This
is due to the discontinuity of E when there is a discontinuity of
dielectric constant at the boundary. E is very easy to obtain given
electrostatic potential according to the finite-difference method. So it
is straightforward to obtain \rho at the dielectric boundary.

Now suppose there are N included surface charges, q_1, ..., q_N at the
boundary. An interesting finding is that the reaction field energy is
equal to

1/2 \sum_{i=1, M} \sum_{j=1, N} Q_i q_j

This is equivalent to

1/2 \sum{{i=1, M} Q_i \phi_i^{reac}

where \phi_i^{reac} is reaction field potential at atomic charge Q_i.
The latter equation is used in Lu and Luo, JCP. The equivalence of the
two relations can be proven based on Poisson's equation and Green's
Theorem, or just divergence theorem.

The induced surface charge approach is more intuitive but slower. We are
replacing the nonuniform dielectric media by induced boundary charges.
So electrostatic interactions between solute and solvent can be
described by pairwise interactions between atomic solute charges and
induced boundary solvent charges.

All the best,
Ray

Cenk Andac wrote:

>Dear Prof. Luo,
>
>I do not have any versions of Delphi. Would you
>possibly provide me with an equation for electrostatic
>potential at the solute-solvent boundary that
>is coded in pbsa for single-point Poisson computations
>at zero salt concentrations?
>
>Best regards,
>
>Jenk
>
>
>

--
====================================================
Ray Luo, Ph.D.
Department of Molecular Biology and Biochemistry
University of California, Irvine, CA 92697-3900
Office: (949)824-9528         Lab: (949)824-9562
Fax: (949)824-8551          e-mail: rluo.uci.edu