Hi Rob,
thank you, your comments helped a lot.
From the Refmac5 paper I did not get the fact that d is set to d_current
after each step. In that case you are right, jelly-body corresponds rather to
DEN with gamma=1 than to gamma=0.
And of course, a very important difference is, as you said, the fact that
jelly-body is applied only to the second derivative.
However, I would like to clarify this one point you made:
For gamma=1 the DEN potential can follow anywhere, the entire conformational
space is accessible and dij(t+1) depends only on Dij(t) and dij(t).
The update formula is (again, for gamma=1):
dij(t+1) = (1-kappa)*dij(t) + kappa * Dij(t+1)
Dij(t) : distance between atom i and j and time t.
dij_ref : distance between atom i and j in the reference structure.
dij(t) : equilibrium distance of restraint between atom i and j at time t.
The parameter kappa just defines how quickly dij(t) changes,
i.e. kappa=1 sets dij(t+1)= Dij(t+1) at each time step.
The parameter kappa is usually set to 0.1, which means the restraints
slowly follow the atomic coordinates. But, again, the starting (or reference)
model is completely forgotten and never used after the first iteration.
This also means that the position of the minima of the target function
are not changed by the DEN (gamma=1) restraints. It could just take longer
to get there as the restraints need to be dragged along.
For gamma<1, the situation is different, there are additional forces toward
the reference (could be the starting) model, in which case dij(t+1) additionally
depends on dij_ref. This also changes the position of the minima of the target
function. It is therefore usually useful to run a final minimization without
restraints to test whether the refinement reached a stable minimum of the
target function.
From the user perspective, I think the main difference is that DEN is designed
to be used in simulated annealing MD refinement, whereas jelly-body is designed
to be used in minimization (and cannot be used for MD refinement as there are
no second derivatives).
Cheers,
Gunnar
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