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<TITLE>Re: [RASMB] interference optics</TITLE>
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<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>
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Arthur J Rowe<BR>
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</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>
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