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<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2>Arthur,</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2>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.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2>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?</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2>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.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=257495018-07042008><FONT face=Arial
color=#0000ff size=2>John</FONT></SPAN></DIV><BR>
<DIV class=OutlookMessageHeader lang=en-us dir=ltr align=left>
<HR tabIndex=-1>
<FONT face=Tahoma size=2><B>From:</B> Arthur Rowe
[mailto:arthur.rowe@nottingham.ac.uk] <BR><B>Sent:</B> Monday, April 07, 2008
4:55 AM<BR><B>To:</B> jphilo@mailway.com; farisaka@bio.titech.ac.jp;
rasmb@server1.bbri.org<BR><B>Subject:</B> Re: [RASMB] interference
optics<BR></FONT><BR></DIV>
<DIV></DIV>
<BLOCKQUOTE><FONT color=#800000>Hi Fumio/John (and everybody)<BR><BR>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:<BR><BR><B>1. The 'Wiener skewing' issue - and the level of
c-gradient you can cope with<BR></B><BR>There is actually no limit on the the
gradient in refraction which you can cope with, provided that<BR>(i) the
fringes are not so close together that they cannot be resolved<BR>(ii) the
Rayleigh optics are accurately focussed on the two-thirds plane of the
cell.<BR><BR>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.<BR><BR>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.<BR><BR>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.<BR><BR> delta-S = a(n-n(0))
where a is the length of the
solution /solvent traversed within the cell<BR><BR>Alas, as Svensson (1954)
showed, it is not that simple. The full equation
is<BR><BR> delta-S = a(n-n(0)) + [ O(2) term ]
+ {a^3(dn/dr)^2(2 - 3r)}/6n(0)<BR><BR>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.
<BR><BR>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.
<BR><BR>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.<BR><BR>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.<BR><B><BR>2. What you can do with
data from high concentration solutions?<BR></B><BR>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 <U>et al</U>( 2007)
Weak Self-Association in a Carbohydrate System Biophysical Journal 93
741-749.<BR><BR>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?<BR><BR><FONT size=2>*nice point as to which approach is the best to
use<BR></FONT><BR>Best wishes to
all<BR><BR>Arthur<BR><BR><BR></FONT></BLOCKQUOTE><FONT
color=#800000>--<BR>*******************************************************<BR>Arthur
J Rowe<BR>Professor of Biomolecular Technology<BR>NCMH Business
Centre<BR>University of Nottingham<BR>School of Biosciences<BR>Sutton
Bonington<BR>Leicestershire LE12 5RD UK<BR><BR>Tel:
+44 (0)115 951
6156<BR> +44
(0)116 271 4502<BR>Fax: +44 (0)115 951
6157<BR>email:
arthur.rowe@nottingham.ac.uk<BR>Web:
www.nottingham.ac.uk/ncmh/business<BR>*******************************************************<BR></FONT><BR><FONT
color=#800000><BR><BR></FONT>
<BLOCKQUOTE><BR><FONT size=2>Fumio,<BR><BR>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.<BR><BR>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.</FONT> <BR><BR><FONT
size=2>John</FONT> <BR><BR><FONT size=2>-----Original Message-----<BR>From:
rasmb-bounces@rasmb.bbri.org [mailto:rasmb-bounces@rasmb.bbri.org] On Behalf
Of Fumio Arisaka<BR>Sent: Saturday, April 05, 2008 4:20 AM<BR>To:
rasmb@server1.bbri.org<BR>Subject: [RASMB] [Fwd: interference
optics]<BR><BR>Dear RASMBers,<BR><BR>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.<BR>Attached jpg file is to show the problem at 10mg/mL. Somehow, the
boudaries tend to go horizontally before reaching the plateau.<BR><BR>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.<BR><BR>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.<BR><BR>Any comments and advice are highly
appreciated.<BR><BR>Best wishes,
Fumio<BR><BR><BR><BR><BR></FONT><BR><TT>_______________________________________________<BR>RASMB
mailing
list<BR>RASMB@rasmb.bbri.org<BR>http://rasmb.bbri.org/mailman/listinfo/rasmb<BR><BR></TT></BLOCKQUOTE><TT><BR></TT><BR>
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