Why is running an equilibrium experiment a bad idea?
At the end of any sedimentation velocity (SV) 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.
Sedimentation quilibrium (SE) experiments gained a lot of favor
because a) they are easy to analyze by linearizing a simple
exponential, and b) because they provide access to kD values of
self-associating oligomerizations. However, 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, SV experiments can achieve ~25 fold improvement
in the confidence intervals compared to SE experiments for 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 SE experiments is
grounded in the small amount of data available, as well as the fact that
the problem is mathematically ill-conditioned. In an SE 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
correctly deconvoluting multiple exponentials, which in their sum all
look like another exponential! In a SV experiment, different boundaries
have different sedimentation speeds and are therefore more easily
distinguished, but in an SE experiment they all flow into one single scan.
What's worse is that in a SV 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 even
more 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 SV 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 SE 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
drops 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 SE 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 SE 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 SE experiments is loss and lack of information,
lack of precision, long instrument times, and basically useless results
when compared to velocity experiments.
Summary:
SE experiments are basically useless unless they are used
in analytical buoyant density mode, in which case different questions are asked
than in a SV 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 SV experiments with this information in mind and make the most out
of your expensive samples and instrument.
