Calculating PMF from a constant velocity SMD simulation!

From: Gungor Ozer (gungor.ozer_at_gmail.com)
Date: Sat Apr 05 2008 - 19:10:06 CDT

Dear all,
I've done a series of constant velocity SMD simulations and now trying to
compute the average PMF of these trajectories. As far as I get from the two
Schulten papers ("Calculating potentials of mean force from steered
molecular dynamics simulations" in JCP & "Free energy calculation from
steered molecular dynamics simulations using Jarzynski's equality") and from
the manuals this is done;

1) by first calculating the work => integrate f*v*dt over time elapsed.
2) then by applying the Jarzynski's equality.

My questions:

1) Since any SMD simulation is not perfect, and not exactly following a
constant velocity path, shouldn't we use f*dx in eq.1 with dx being the
exact displacement of the steered particle?
2) f in eq 1 is a vector, how are we supposed to integrate a vector*scalar?

and a different question.

3) I am using TCL script to calculate force vector:

"
 set ff [expr $k*($nx*($r0x-$rx)+$ny*($r0y-$ry)+$nz*($r0z-$rz) +
$time*$velocity)]
 set fx [expr $ff*$nx]
 set fy [expr $ff*$ny]
 set fz [expr $ff*$nz]
"

ff being the force derived from the potential given U = 1/2k [ vt - (r-r0)*n
] where r is the current position, r0 is the initial position and n is the
direction vector.

Does my TCL script seem to calculate correct amount of work?

Any help to any of the questions will be much appreciated.

Regards,

Gungor Ozer
Georgia Tech

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