[RASMB] non-ideality in velocity [was: interference optics]

John Philo jphilo at mailway.com
Mon Apr 7 13:41:08 PDT 2008


Arthur,
 
I was referring to non-ideality in general, not to ks values or any specific
model or parameterization to try to deal with it. Yes, of course, at high
concentrations you can still assign a sedimentation coefficient to at least
the main component, and using ks is an approach to handling the
concentration dependence that has a long history. My remarks were really
more addressed to the biotech crowd, where people would like to quantify low
levels of aggregates in samples at concentrations even much higher than 10
mg/mL, which I view as pretty problematic.
 
But with respect to Johnston-Ogston effects in multi-component solutions,
could you be more specific about which theory for two-component systems you
are talking about, and give us references? As I recall the Fujita book
discusses some work by Trautman and co-workers in the early 1950's. Since it
sounds like you are up on the quantitative aspects, if its not a lot of
trouble could you give us a ballpark estimate of the error in estimating
dimer content due to J-O say for a solution at 10 mg/mL total protein
concentration that is 20% dimer?
 
Also, are you aware of any texts or reviews covering these J-O effect things
in the last 10-20 years? The reality is that the older literature is very
hard for many people to access.
 
John

  _____  

From: Arthur Rowe [mailto:arthur.rowe at nottingham.ac.uk] 
Sent: Monday, April 07, 2008 4:55 AM
To: jphilo at mailway.com; farisaka at bio.titech.ac.jp; rasmb at server1.bbri.org
Subject: Re: [RASMB] interference optics



Hi Fumio/John (and everybody)

Just one or two points about working at high concentrations using
interference optics. Mostly things which (as John says) are to be found in
the archives:

1. The 'Wiener skewing' issue - and the level of c-gradient you can cope
with

There is actually no limit on the the gradient in refraction which you can
cope with, provided that
(i) the fringes are not so close together that they cannot be resolved
(ii) the Rayleigh optics are accurately focussed on the two-thirds plane of
the cell.

The first of these two conditions is quite restricting - but clearly there
is no danger of getting misleading output, as the data acquisition will
simply fail.

The second condition is more troublesome, and it needs a little
understanding of the basic principles of Rayleigh interference optics to
sort out what it might mean. So - here goes.

To start off, we tend to assume that there exists a simple, linear
relationship between the change in optical path length (delta-S) arising
from a given, solute caused increment in refraction (n-n(0)). i.e.

   delta-S = a(n-n(0))        where a is the length of the solution /solvent
traversed within the cell

Alas, as Svensson (1954) showed, it is not that simple. The full equation is

   delta-S = a(n-n(0))  + [ O(2) term ]   +  {a^3(dn/dr)^2(2 - 3r)}/6n(0)

where 0<r<1 defines the plane of focus used, as a fraction of the distance
between front and back planes of the solution/solvent column. Clearly, if
the optics are focussed such that r = 2/3 (i.e. on the 'two-thirds plane)
then the simple equation, rather analogous to Beer's Law in absorption
optics, holds. 

Well - except for that O(2) term. Which becomes zero IF YOU FOCUS ON THE
MID-PLANE OF THE CELL. Alas. But all that term does if non-zero is to cause
the fringes to fuzz a bit, to an extent that one can live with. 

Conclusion: if one is using conventional 12 mm cells, and the optics are
focussed on the two-thirds plane, then all you need to do is to keep the
speed down to the level where the fringes are not so bunched that you cannot
resolve them. Which (in very hand-waving terms) tends in our experience to
mean SV up to a few mg/ml, SE up to a few tens of mg/ml.

But what if you use 3 mm path length cells instead of 12 mm? Ignoring (for
the moment) the effects of change in optical path length arising from
substituting 9 mm of vacuum for 9 mm of aqueous solution, we note that if we
leave the optics un-touched (focussed on the two-thirds plane, i.e. 2 mm
beyond mid-plane), then the r-term to go into the Svensson equation is
un-defined, the plane of focus now being 1 mm beyond the 'lower' window
face! Perhaps this may not matter too much. After all, by lowering a by a
factor of 4, the ratio of the (error-causing) O(3) term to the O(1) term is
lowered by 4^2, i.e 16-fold. But it would be nice if someone could do the
optical physics necessary for a complete reassurance on the issues raised.

2. What you can do with data from high concentration solutions?

As John says, there is a current problem with any full and rigorous analysis
of SV of a (say) 10 mg/ml protein solution. But - getting an 'operational'
s(c)-value is simple enough, as any lack of theoretical rigour in fitting*
is counter-balanced by the self-sharpening effect, which actually makes it
quite difficult to get an equivocal value. And, in the absence of
significant charge effects at least, there is simple theory to define the
hydrodynamic ks term (John - is that a typo of yours? Unlike the
c-dependence of diffusion, you do not need to add on a 'thermodynamic'
term). The analytical equation for c-dependence is simple enough - see my
chapter in the 1992 Book - and it agrees exactly for spheres with the
rigorous numerical solution from the fluid dynamics people - "The
sedimentation rate of disordered suspensions"  Brady, John F.; Durlofsky,
Louis J. Physics of Fluids 1988 31 717-727. The use of the analytical
equation has various uses, e..g. it enables one to sort out reversible
monomer-dimer equilibria in the presence of ks effects, see e.g. Patel et
al( 2007) Weak Self-Association in a Carbohydrate System  Biophysical
Journal 93 741-749.

Quite true, of course, that Johnston-Ogston effects can complicate life for
finding the % composition of mixtures of several components, but the
calculation of the necessary correction for simple 2-component mixtures is
straightforward enough - and the correction often trivially small unless the
s values are rather close together. And as the J-R theory has found
application in the great wide world outside of the AUC, surely someone has
ways of correcting for the effect in n-component mixtures?

*nice point as to which approach is the best to use

Best wishes to all

Arthur




--
*******************************************************
Arthur J Rowe
Professor of Biomolecular Technology
NCMH Business Centre
University of Nottingham
School of Biosciences
Sutton Bonington
Leicestershire LE12 5RD   UK

Tel:        +44 (0)115 951 6156
           +44 (0)116 271 4502
Fax:        +44 (0)115 951 6157
email:      arthur.rowe at nottingham.ac.uk
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*******************************************************






Fumio,

There is a limit on the maximum gradient that can be measured (fringes/mm)
due to Weiner (? spelling) skewing, and you are exceeding that limit.  As
Ariel said you should switch to 3 mm centerpieces, and then at some point to
get to higher concentrations you would have to drop the rotor speed too to
broaden the boundaries. If you look through the old RASMB postings you will
find a number of excellent posts from others about Weiner skewing and proper
optical alignment to minimize distortion of strong gradients.

But probably the more important question is what are you going to be able to
do with such data even if you collect it? Remember, in velocity there is
hydrodynamic non-ideality as well as thermodynamic non-ideality, so the
non-ideality effects will kill you at much lower concentrations than in
equilibrium. To my knowledge the only model available to analyze a velocity
experiment at 10 mg/mL is a single non-ideal species. At high concentrations
you cannot even correctly measure the fractions of different components
(e.g. aggregates) in a multi-component mixture due to the Johnston-Ogston
effect. 

John 

-----Original Message-----
From: rasmb-bounces at rasmb.bbri.org [mailto:rasmb-bounces at rasmb.bbri.org] On
Behalf Of Fumio Arisaka
Sent: Saturday, April 05, 2008 4:20 AM
To: rasmb at server1.bbri.org
Subject: [RASMB] [Fwd: interference optics]

Dear RASMBers,

This concerns measurement of high concentrations of IgG with interference
optics. I have not much experience with IF, but have started to use it for
the necessity to measure high concentration samples. Concentrations less
than 5 mg/mL had no problem.
Attached jpg file is to show the problem at 10mg/mL. Somehow, the boudaries
tend to go horizontally before reaching the plateau.

I thought this was due to the misalignment of optics or something, because
the fringe pattern is not so good as I expect, but the BeckmanCoulter person
who came to fix it could not make it better.

I would like to know what is the common highest concentration that you could
measure by IF. As I understand one could measure SE at higher concentrations
than 100 mg/mL, but when the boundary gets too steep in SV measurement, the
fringes get too much squeezed to count precisely.

Any comments and advice are highly appreciated.

Best wishes, Fumio





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