Crown Tutorial

Related material, not necessary to understanding the tutorial:

 Dang LX.
     Mechanism and thermodynamics of ion selectivity 
	in aqueous solutions of 18-crown-6 ether -
	a molecular dynamics study.
     Journal of the American Chemical Society, 1995 Jul 5 V117 N26:6954-6960.
 Billeter M, Howard AE, Kuntz ID, Kollman PA.
     A new technique to calculate low-energy conformations of
	cyclic molecules utilizing the ellipsoid algorithm
	and molecular dynamics: application to 18-crown-6.
     Journal of the American Chemical Society, 1988, Dec 7 V110 N25:8385-8391.

 Ross WS and Hardin CC.
     Ion-Induced Stabilization of the G-DNA Quadruplex: 
        Free Energy Perturbation Studies.
     Journal of the American Chemical Society, 1994, V116, 6070-.

Overview

• Leap:
  • Build residue template
  • Load pdb of whole molecule
  • Add complexed ion
  • Add perturbation to ion
  • Save 'parm' files for dynamics & perturbation
• Sander:
  • Run dynamics to equilibrate
• Gibbs:
  • Run perturbation forward/back
  • Run some plain dynamics in the perturbed state
  • Optionally vary parameters
• Carnal:
  • Analyze trajectories

Leap

  Build residue template
	(if this was done in a previous session, 
		> loadoff cra.lib
	to reload)

  Load pdb of whole molecule:

	> crown = loadpdb cr6.pdb
	> edit crown

  Close the open bond and add complexed ion:

	

  Hold down the two right buttons and push forward/back to zoom in/out.
  The middle button alone rotates, the right button translates, and
  the spacebar recenters the molecule.

	  - select 'Draw' mode and connect the carbons
	  - Unit / Import / Na+
	  - select 'Select' mode, select the ion, and 
	  - select 'Move' mode and move the ion to the center of the ring
		(use middle button to rotate everything)

  Add perturbation to ion:

	  - ion is still selected, so 'Edit / Edit selected atoms'
	  - fill in the 'PERTURB/PERT' parameters as shown

		


  Save system in leap format for future reference:

	> saveoff crown built.lib

  Save 'parm' files for dynamics & perturbation:

	> saveamberparm crown crowni.top crowni.crd
	> saveamberparmpert crown crownip.top crownip.crd

Sander

  Equilibrate the system:

	% sander -O \
		-i md0.in \
		-p crowni.top \
		-c crowni.crd \
		-o md0.out \
		-x md0.crd \
		-r md0.rst

  The protocol is very simple because this is a conformationally
  limited system in vacuum.

Gibbs

  Run perturbation forward/back:

	% gibbs -O \
		-i gib10.in \
		-p crownip.top \
		-c md0.rst \
		-o gib10.out \
		-r gib10.rst

	% gibbs -O \
		-i gib01.in \
		-p crownip.top \
		-c gib10.rst \
		-o gib01.out \
		-r gib01.rst 

  Run some dynamics in the K+ state to compare trajectories:

	% gibbs -O \
		-i gib0.in \
		-p crownip.top \
		-c gib10.rst \
		-o gib0.out \
		-x gib0.crd \
		-r gib0.rst

Carnal

  Analyze trajectories:

	% carnal -O -i carnal_na.in > carnal_na.out
	% carnal -O -i carnal_k.in > carnal_k.out

  We compare the 'stiffness' of the crown in both cases by
  measuring the backbone torsions. The statistics for these
  measurements are printed to the .out files. Since torsions
  can vary over 0..+-360, 'circular statistics'** are used. The
  's' parameter corresponds to the standard deviation, and
  it turns out that 's' is more for Na+ than K+, indicating
  less flexibility with the larger ion.

  **  Batschelet, Edward.  Circular statistics  in  Biology  (1981)
      Academic  Press  Inc.,  New York, NY. This method is used for
      averaging angles that can encompass a full 360  degrees.  For
      motivation, think of what the average of 0 and 359 degrees or
      0 and 180 degrees would be. The 'averages' from  this  method
      are  in  the range [-180..180], so e.g. a single value of 183
      would result in a statistical  'average'  of  -177.   Another
      reference  for  circular  statistics  mentioned on the net as
      being easier to find: Fisher, N. I.  Statistical Analysis  of
      Circular Data (1993) Cambridge University Press, New York.