[RASMB] Time to equilibrium calculator

[Borries Demeler]

> However, I agree with Arthur in that such estimates are only a starting
> point.  In my experience they are not very useful other than giving you a
> lower limit for the time it might take.  

I would like to address this point:

In my experience the predictions made by UltraScan are reliable in the
great majority of cases (> 90%) we have measured. This alone is a big
time saver - we start the run on Thursday night and over the weekend we
get all speeds, without user intervention. From a practical standpoint
this makes simulation very worthwhile.

> As you all know, there are two
> inherent assumptions: 1) We should know the s-value, i.e. the shape of the
> molecules.  In particular with proteins that are naturally unfolded, have
> large unstructured domains, or are heavily glycosylated, the hydrodynamic
> friction can be much higher, and the time to equilibrium I believe should
> directly scale with that. (That could make a potential error in estimated
> equilibrium time of perhaps 30%?)  We've had one of those largely

Yes, that is a good point. I failed to mention that I try to err on the
side of caution by always modeling the equilibrium run as a prolate
ellipsoid with an axial ratio of ~ 20, and simulating for the inner
channel, where the force is the smallest. While this may be overkill,
it turns out to be a time saver anyway, since the longest time is used in
the first equilibration speed, successive speeds equilibrate much faster
and simulating this with the successive speed option is where the real
time savings come from. Of course, there will always be exceptions and
they will have to be treated differently.

> equilibrate. Lateron I realized that the frictional ratio from velocity
> was about f/f0 = 2.  2) In the presence of interactions that are slow,

I usually do velocity expts. *before* the equilibrium experiment precisely
to have this and other additional information available that are useful in
the design of an equilibrium experiment. For example, a veloc. expt. may
tell me that the predominant species is a dimer-tetramer, rather than
a monomer-dimer, which would change the design considerably.

> common, but apparently not extremely unusual, either.  Also, of course,
> the buffer viscosity may be a big factor, for cases where glycerol can't
> be avoided.  Therefore, I tend to accommodate for a great deal longer
> equilibrium time, while scanning in 6 h intervals, and using MATCH to look
> how the pairwise differences between scans (relative to the last scan)
> slowly level off and reach a constant value.

..which is why UltraScan considers the viscosity and density of the buffer
in the simulation. It would be nice to have the ability to automatically 
analyze scans 6 hrs. apart and then be able to send a signal to the XLA
to change to the next speed, but the Beckman software doesn't work
this way.

> Another concern relevant to this topic is that we found the profiles CLOSE
> TO equilibrium frequently already look nicely exponential, and can also be
> modeled reasonably well with a combination of equilibrium exponentials
> (unfortunately not entirely correct ones).

This is also a very important point. The only thing that helps here
is fitting a lot of different speeds and loading concentrations in
different channels. If the experiment contains scans that are not at
equilibrium, then you will find that you can fit the majority of the 
scans to a simple model, except those scans that are not at equilibrium,
which will stick out like a sore thumb. Invariably, I find that these
scans come from the inner channel when using a 6-channel centerpiece,
and most often they are from the first speed. Regardless, the 6-hour
repeat scan proves valuable to determine if equilibrium has been
reached.

Best, -Borries