# AMBER Archive (2004)Subject: Re: AMBER: Sander klambda question

From: David A. Case (case_at_scripps.edu)
Date: Wed May 05 2004 - 18:43:44 CDT

On Wed, May 05, 2004, Linda Prengaman wrote:

> I'm working on a thermodynamic integration project using Sander, and
> I'm not quiet sure I understand conceptually why the klambda value
> should be set to 4 when atoms are disappearing during the perturbation
> process. Could someone please enlighten me? I understand
> mathematically this value keeps the integral finite as lambda
> approaches 1, but beyond that I'm at a loss.
>

It sounds like you already understand the situation, and there is nothing
"conceptually" that goes much beyond what you wrote: in order to evaluate the
integral numerically, it is easiest to have a smooth integrand that is finite
everywhere. Setting klambda to 4 (or even to 5 or 6) is one simple way to
accomplish this.

Don't be afraid to just play with things. For example, try a simulation
with klambda=1, looking especially at the behavior at lambda = 0.90,
0.95, 0.99, 0.999, etc. You will see that the value of <dV/dlambda> gets very
large and negative, and that the uncertainties also get very large. Then
try a simulation with klambda=4, and look at the behavior in the same
region of lambda (from 0.9 to 0.99).

A brief but very clear discussion of this is given by Tom Simonson:

%A T. Simonson
%T Free energy calculations
%B Computational Biochemistry and Biophysics
%E O. Becker
%E A.D. MacKerell
%E B. Roux
%E M. Watanabe
%I Marcel Dekker
%C New York
%D 2001
%P 169-197

This review contains references to the original literature where these points
are treated in greater depth. A nice (if quite detailed) example of
annihilation is given here:

%A M.R. Shirts
%A J.W. Pitera
%A W.C. Swope
%A V.S. Pande
%T Extremely precise free energy calculations of amino acid side chain
analogs: Comparison of common molecular mechanics force fields for proteins
%J J. Chem. Phys.
%V 119
%P 5740-5761
%D 2003

(see. esp. Eq. 8 and Figure 2). These authors use a somewhat more complicated
lambda dependence (which may accelerate convergence of their estimates of
the required MD averages), but the basic simulations are very similar to those
you can carry out in sander. (When things larger than a methyl group are
disappearing, I have found it advantageous to use klambda=5 or 6, but this is
a matter of efficiency of sampling, not of the final result that one obtains.)

...hope this helps....dac

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David A. Case                     |  e-mail:      case_at_scripps.edu
Dept. of Molecular Biology, TPC15 |  fax:          +1-858-784-8896
The Scripps Research Institute    |  phone:        +1-858-784-9768