# AMBER: Statistical uncertainty estimation in Thermodynamic integration calculation..

From: cgji <cgji.itcc.nju.edu.cn>
Date: Mon, 24 Sep 2007 21:13:36 +0800

Dear Amber users,

Recently I tried to use molecular dynamics free energy simulations (MDFE) to compute proton pka
shifts as described in amber tutorial (http://amber.scripps.edu/tutorials/advanced/tutorial6/index.htm).

This tutorial reproduces the calculation of the pKa value of the ASP residue in the protein thioredoxin as described in the following paper:
Simonson, T., Carlsson, J., Case, D.A., "Proton Binding to Proteins: pKa Calculations with Explicit and Implicit Solvent Models", JACS 2004, 126, pp4167-4180.
In table 1 of the article ,they showed us expilicit solvent MDFE results for Thioredoxin ASP26 .

Part of this table was listed bellow ,

-----------------------------------
AMBER
-----------------------------------
ASP26

lamba=0.11270 -3.1(12.0)
lamba=0.50000 -64.5(4.6)
lamba=0.88279 -131.4(7.8)

Delta G -66.0(3.9)

Delta,Delta G 9.1 (4.1)
-------------------------------------

12.0 ,4.6 and 7.8 in parentheses was statistical uncertainty for the three
seperated trajectory .
My question is :
1.how can I estimate statistical uncertainty from each seperated trajectory ?
in their article , they said "for the derivatives , it is estimated as twice the standard derivation of block averages ,each trajectory being divided into four blocks." , however , i can't understand it clearly .
2. How can I use these data from seperated trajectory to construct statistical uncertainty (3.9) for
Delta G ?
I tried to calculate it as follows

sqrt ( (12.0*0.27777)**2+(4.6*0.44444)**2+(7.8*0.27777) **2)
but I can't get 3.9 .

I appreciate it very much for your help......

Yours sincerely,
Changge Ji
2007-09-24

cgji

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Received on Mon Sep 24 2007 - 17:45:26 PDT
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