Why is running an equilibrium experiment a bad idea?
At the end of any velocity experiment the sample reaches transport
equilibrium. At this point, neither sedimentation nor diffusion will
contribute to a net flow, since their transports cancel out. That
means there is no change in concentration anymore, and the radial
profile remains constant with time. The concentration gradient
that establishes itself if you wait long enough in your velocity
experiment follows an exponential function, for more information
please visit
this link.
It turns out there is remarkably low information content in equilibrium
experiments. For example, in an experiment where the monomer-dimer
equilibrium Kd is measured, sedimentation velocity experiments can achieve
~25 fold lower 95% confidence intervals than sedimentation equilibrium
experiments on the Kd value. Furthermore, anisotropy information for
the monomer and dimer is available, as well as kinetic information,
at least for slowly equilibrating systems which react on the time scale
of the sedimentation transport. For more information please review
Demeler B, Brookes E,
Wang R, Schirf V, Kim CA. Characterization of Reversible Associations
by Sedimentation Velocity with UltraScan. Macromol. Biosci. Macromol
Biosci. 2010 Jul 7;10(7):775-82.PMID: 20486142.
The reason for the low confidence in the results from sedimentation
equilibrium experiments is grounded in the small amount of data available,
as well as the fact that the problem is mathematically ill-conditioned.
In an equilibrium experiment, each solute gives rise to a different
exponential distribution, but only the weight average of all solutes are
visible in the final distribution. So if there is any heterogeneity in the sample,
the analysis is tasked with deconvolution (correctly!) multiple exponentials,
which in their sum all look like another exponential! In a velocity experiment,
different boundaries have different sedimentation speeds and are therefore
more easily distinguished, but in an equilibrium experiment they all flow
into one single scan.
What's worse is that in a velocity experiment you can globally fit hundreds of scans,
where each scan looks different (has different information), using whole boundary modeling. In an equilibrium
experiment, you have to wait until equilibrium is established, and then you look
only at the
last scan!! Taking multiple scans doesn't help much, as they all
look the same. So, that's a single dataset instead of hundreds.
It gets worse: Since it typically takes a lot of time to equilibrate sedimentation
with diffusion transport, especially for slow diffusing solutes, experimentalist
take another shortcut. They reduce the column length to about 3 mm to get to the
equilibrium point more quickly. That of course reduces the number of datapoints
that can be collected to about 1/4th of a single velocity scan. Actually, it is
less than that, because the dynamic range of the detector is limited by the
total absorbance (if using absorbance optics) to about 1.2 OD for most wavelengths
or below, and a certain steepness, before the gradient is so steep it acts as
a lens and diffracts the light so the recorded radial position is not where
it is recorded, falsifying results further, and of course, reducing the useful
number of datapoints as well. So now we have about 1/5th or 1/6th of the data
measured in a single velocity scan. To help themselves with the low data point
count and low information content, experimentalists started using multiple speeds
and fitting them globally (something that can of course also be done in
velocity experiments). The problem with that is that it further lengthens the
experiment, giving the protein more time to degrade or aggregate. One could
just run slower to avoid steep gradients, but then there is no information
content left in the data and one could almost fit it to a straight line with the
same confidence.
This brings up the next problem: Since an equilibrium experiment requires
a balance of sedimentation and diffusion to occur before the models are valid,
one needs to wait until this gradient is established. But the gradient at the
bottom of the cell gets to be quite large, so the concentration at the bottom
may be so high, that the protein tends to aggregate and simply drop out of solution
once the gradient is a certain height. At this point, conservation of mass
is no longer satisfied, and the overall concentration keeps reducing and reducing,
while the equilibrium gradient is constantly trying to re-establish itself.
This process continues until everything is pretty much aggregated and equilibrium
is actually never reached (but still attempted to be fitted in lots of
publications that basically show useless results). For the same reason,
equilibrium analysis sucks when it comes to the detection of aggregates or
contaminants. They will either not be seen at all or simply distort the "expected"
model. Not good.
But wait, there are more problems: Since there is no time-variant information
in a single scan, time-invariant noise cannot be determined. That means one
must collect absorbance instead of intensity data to at least extract some of
the time invariant noise, though this leaves scratches and dirt on cell windows
as a time-invariant noise contribution that cannot be removed. And of course the
dreaded increase in stochastic noise by a factor of ~1.4 resulting from the
subtraction of the reference scan doesn't help.
Are equilibrium experiments totally useless? No, you can still choose to run
until equilibrium is reached and include the last scan in your global fit
of the velocity data, although it won't make much of a difference. So why is
the literature full of equilibrium experiments? I guess the reason is that
it is simple to fit an exponential. You don't even need a computer to do that.
No finite element solutions of the Lamm equation are needed, no large computers
for high-resolution fitting are needed. The price that is paid when running
equilibrium experiments is loss and lack of information, lack of precision,
long instrument times, and basically useless results when compared to velocity
experiments.
Summary:
Sedimentation equilibrium experiments are basically useless unless they are used
in analytical buoyant density mode, in which case different questions are asked
than in a velocity experiment and they can actually provide very useful
experimental data (see:
Matthew Meselson and Franklin W. Stahl. THE REPLICATION OF DNA IN ESCHERICHIA COLI.
Proc Natl Acad Sci U S A. 1958 Jul 15; 44(7): 671–682). Design your experiments
as velocity experiments with this information in mind and make the most out
of your expensive samples and instrument.
