With Keren, we ran into problem caused the fact that em restraints go to 1 as they are increasingly violated while hard sphere restraints go to larger numbers (and are dependent on the number of particles). The result was that the em restraint would get more or less ignored by the optimizer  unless a large scaling factor was added to EM. This experience raises an important question: Do we want a convention about how restraint scores behave as they are increasingly violated?<div>
<br></div><div>A convention could be something like:</div><div>- all satisfiable restraints (ones whose optimal is at 0) should have scores that go as x^2 (or just as x) per atom where x is the displacement is angstroms from a satisfying conformation.</div>
<div>- a restraint score can stop increasing at a value where there is no longer any signal.</div><div><br></div><div>Obviously, one could only very roughly approximate this in practice, but a rough approximation might be good enough to get many of the benifits</div>
<div><br></div><div>Advantages:</div><div>- You have a natural starting point for weight values between the various restraints. Variations from this are directly upweighting or downweighting data relative to them having equal importance.</div>
<div>- The relative importance of restraints does not depend on how far from optimal you are</div><div>- The relative importance of restraints does not depend on how many particles they are restraining</div><div>- The importance of various terms won&#39;t depend on the scale of the representation</div>
<div><br></div><div>Feasibility:</div><div>- core restraints such as Diameter and stuff would require using a per-particle scaling factor (to incorporate the number of atoms). Excluded volume is approximately correct too given such a scaling (at least if the model isn&#39;t too messed up)</div>
<div>- EM would require adding a term to penalize things for escaping far from the map as well as some experiments on how things break down under random displacements of various amounts (and rescaling of cross correlation accordingly) and scaling by the number of particles. Such could easily be added as a wrapper around a CC based restraint. And understanding of those issues seems important anyway.</div>
<div>- others?</div>