AMBER Archive (2007)

Subject: AMBER: Free Energy Calculations

From: Mike Wykes (wykesm_at_averell.umh.ac.be)
Date: Wed Dec 12 2007 - 12:08:20 CST

Dear AMBER users

I apologise for the lengthy email, I am new to Amber and would be very
grateful of your advice.

I am studying a molecule (234 atoms) consisting of two perylene bisimide
(PBI) chromophoric units bridged via a calix[4]arene spacer unit. Due to
the flexibility of the calixarene, two different pinched cone
conformations of the calix[4]arene unit can exist, one conformation
showing a pi stacked sandwich arrangement of the PBI units (the "closed"
conformation) and the second revealing a non-stacked conformation with
the chromophores pointing away from each other (the "open"
conformation). Absorption spectra of solutions have shown the
equilibrium between the two conformations to be dependent upon the
polarity of the solvent.

I would like to model the system to see if I can replicate the
dependence of equilibrium upon solvent polarity.

Before becoming an Amber user, I modelled the system using Tinker and
the MM3 polarisable force field. Running MD in vacuum showed that the
open form readily converted to the closed form, the closed form being
lower in total PE by 15 kcal/mol. This difference is attributed mainly
to larger VDW interaction between the two chromophores in the closed
form. Upon the addition of explicit solvent molecules, transitions
between the open and closed forms were no longer observed. I tried
running separate open and closed MD simulations in order to extract a
difference in total PE, but it was like looking for a needle in a hay
stack. Any small difference was dwarfed by solvent-solvent interactions
and so the signal to noise ratio is very low. I also tried looking at
only solute-solvent interactions, but this suffered from the same
problem of being very noisy.

Then I read about thermodynamic integration and umbrella sampling and
the capability of Amber to perform such calculations. From what I have
read in the Amber archive, manual and tutorials, umbrella sampling seems
to be the recommended method for changes in conformation, allowing one
to calculate the free energy profile along a reaction coordinate. The
problem seems to be defining a suitable reaction coordinate. In the
molecule I am studying the change in conformation is complex, with
changes in many dihedral angles.

My question is what you think will happen if I approximate the reaction
coordinate as the distance between the end of each chromophore, so that
I can sample from large distance (open) to a small distance (closed).
Since the reaction path followed may not be the real one, I will not be
able to extract information about the activation energy or rate
constants. All I want for the moment however is to find out which
conformer is more stable. Will I be able to extract the change in energy
between the open and closed forms simply by subtracting the values at
the two local minima either side of the activation hill of the free
energy profile along the reaction coordinate?

Another idea I had was to compute the free energy of solvation for each
conformer separately using thermodynamic integration. I could then
calculate the difference in free energy between open and closed and see
how it varied depending on the solvent.
I thought I may have to constrain the molecule to prevent it converting
to the other conformer during in the necessary md simulation, but so far
in vacuum MD and MD in chloroform (AMBER GAFF parameters by Antechamber,
CM2 charges from divcon) inter-conversion of the two conformations has
not occurred (5ns md) and hence treating open and closed forms
separately should be not problem. My only concern is that making a 234
atom molecule 'disappear' by removing the VDW terms may result in
non-converging dV/dL integral. In the manual it states "We have found
that setting klambda = 6 with disappearing groups as large as tryptophan
works well." My molecule is 10 times larger, so I am not sure if the
integral will remain finite.

Your comments on either approach or ideas for alternative approaches
would be most appreciated.

Many thanks

Mike
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