amber tutorials
crown tutorial
crown equilibration

Crown Demo - Equipartition

When running in vacuum, without collisions from solvent molecules, one can imagine that a topologically simple system such as the crown molecule might become stuck in one mode of movement and not sample its phase space effectively. (The presence of a bound ion may alleviate this situation somewhat when the ion is small and binding is loose, by providing collisions unconstrained by bonding. When the ion is large and binding is tight, the issue might become moot if the crown molecule cannot move much anyway.)

Velocity reassignment is one technique that may help to better explore the phase space. Here we explore its effects on the backbone torsions of the crown molecule without the complexed ion and with Na+ and K+ ions. Four regimes are tried: using no velocity rescaling; and reassigning velocities every 100, 1,000, and 10,000 steps. First, a gross measure of the conformational range is examined, the average flexibility of the backbone torsion angles:

Average 's' values for backbone torsions (indicating amount of torsional variation)

               ------- velocity reassignment -------
               none    100_steps  1k_steps  10k_steps

crown_plain    30.6      21.3      33.8      33.5
crown_na       32.3      11.1      12.6      21.0
crown_k        20.0      18.2      18.2      13.7

From this table, we can see that velocity reassignment actually seems to reduce the phase space explored by the crown/ion complex. 100 steps (50 fs) is clearly too short an interval for velocity reassignment in any case; evidently the molecule cannot move very far before the velocities are reassigned, and the reassignments on average tend to cancel.

The reduction in flexibility in the velocity-reassigned crown_na case is perplexing. A look at the final coordinates for each of the runs in the table above suggests a reason:

crown_na final coordinates

(order as in table, above)
how this picture was made

Apparently, the crown/Na+ complex takes some time to work itself into a "folded" conformation which is more flexible, as in the leftmost image with no velocity reassignment; only in the rightmost (reassignment at 10k steps) does it approach this configuration.

Demo by Bill Ross.