# Re: [AMBER] The Calculate Formula of Ionic strength in MM_PBSA/GBSA

From: Wesley Michael Botello-Smith <wmsmith.uci.edu>
Date: Mon, 9 Jul 2018 09:45:13 -0700

In the case of linear solutions to the poisson boltzmann-equation, the
ionic strength term is most easily conceptualized as a perturbation of the
diagonal elements of the matrix representation of the discretization of the
differential equations being solved numerically.

For the non-linear case, the mathematics is indeed a bit too complex to be
easily represented in an email.

As for a previous question on whether or not to include protein
contribution: In PBSA this depends on your choice of boundary conditions
(see manual for appropriate flag to control this). For linear PBSA, you
have 3 choices: Zero potential boundary, Free Boundary, and Periodic
Boundary.

1) The first is probably the least helpful to you, but in essence, zero
potential boundary (also called Dirichlet boundaries in some cases) would
be akin to placing the system inside a small cavity within an infinite
conductor. Conceptually, you could think of it like carving out a nanometer
scale cube (or rectangular prism) inside a non-reactive metal block and
In this case, the protein would quite certainly be contributing and would
represent something akin to a single molecule experiment. In some sense,
the boundaries of the system act like electrostatic 'mirrors' so the
protein essentially sees its inverse charge image right at the boundary. So
this case is where the effects of the protein's charge distribution are
most pronounced

dilution setup that Dr. Case mentioned earlier. In that case, there is
really no need to accommodate the protein's charge contribution since its
concentration is effectively zero. This is the case where the effects of
the protein's net charge is least pronounced.

3) Periodic boundary conditions, this is essentially equivalent to periodic
boundary conditions used in PME. Conceptually represents a bulk solution
with a fixed (and likely relatively high) concentration of the protein. The
protein will 'see' an infinite lattice of copies of itself whose spacing is
equal to the grid box lengths along each dimension. Thus, depending on the
size of your system, it may indeed be important to accommodate a protein's
net charge if it is relatively high. So this case falls somewhere between
case one and case 2.

So long story short, if you use zero potential conditions, you most likely
would want to account for the proteins net charge... however, this setup is
rarely used outside of method validation purposes.
For periodic boundary conditions, you may or may not need to consider the
protein's net charge. This depends on how strongly charged your protein is,
and how much padding you leave between it and the boundaries of the
simulation region (again you can look up the settings for this in the
since the setup is essentially modeling an infinite dilution.

On Mon, Jul 9, 2018 at 5:44 AM, David A Case <david.case.rutgers.edu> wrote:

> On Mon, Jul 09, 2018, 龚乾坤 wrote:
> >
> > Here,I have a question about MM_PBSA/GBSA.When I calculate the Ionic
> > strength (parameter ISTRNG --
> >
> > Ionic strength (in mM) for the Poisson-Boltzmann solvent in MM_PBSA ),
> > which formula should I use ?
>
> Please consult the wikipedia article on "Ionic Strength" (or textbooks,
> etc.) Math is kind of hard to represent in an email.
>
> >
> > And what is the formula's unit ?
>
> mM, as you quote above.
>
> ....dac
>
>
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Received on Mon Jul 09 2018 - 10:00:03 PDT
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