[RASMB] peak in sedimentation velocity scans at high protein conc.

Mon Oct 31 07:27:45 PST 2005

Greetings, everyone

Yes, there continues to be a problem associated with the (obsolescent)
algorithm used in the XL-I for tracking fringe displacements via phase
determination. The trouble with determining the absolute phase of a
sinusoidal function is that the precision is given by the derivative of the
function - and hence, twice per cycle, goes to zero!

There have long been excellent alternative algorithms available - fringe
analysis has been (and is) a major topic of research in the engineering
community, people who want to follow how the engine housing shakes when you
open the throttle, and all that. Good algorithms are not compute-intensive,
and really do need to be applied. Harding & Rowe (1988) gives one such
algorithm, it looks pretty elderly now I guess . . . . but way out modern as
compared to the DeRosier approach used in the XL-I. See also the paper by
Rowe, Wynne-Jones, Thomas & Harding (1989).

It is indeed absolutely vital - as Tom says - that the optics be focussed on
the mid-plane of the cell, to avoid 3rd order artifacts (Svensson 1954
equation - Optica Acta, 1, 25). In doing this one sacrifices a bit of
sharpness of the fringes (via 2nd order effects), but we can live with that.
If the focus is on the mid-point of the cell (not far away, especially in a
3 mm c'piece cell) then errors pile up when fringe steepness exceeds 38
fringes/mm (at a precision of ±0.01 fringe) - see Lloyd 1974.

So - we need (1) proper focussing of the optics in the hardware; (2) a
modern fringe detection algorithm in the software.

Not really rocket science, I suggest.

Arthur

Arthur J Rowe & Stephen E Harding (1988)
Automatic data capture and analysis of Rayleigh fringe displacements in
analytical ultracentrifugation
Optics and Lasers in Engineering, 8(2) 83-96)

A J Rowe, S.Wynne-Jones, D Thomas & S E Harding (1989)
Analysis of solute concentration and concentration derivative distributions
by means of frameshift Fourier and other algorithms applied to Rayleigh
interferometric and Fresnel fringe patterns
Fringe Pattern Analysis, Graeme T Reid, Editor, Proc SPIE 1163 138-148

Peter H Lloyd (1974) Optical Methods in Ultracentrifugation, Electrophoresis
& Diffusion pp 87-88

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Arthur J Rowe
Professor of Biomolecular Technology
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University of Nottingham
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Hi-
The transformation from phase to fringe displacement does limit changes
in the fringe displacement to +/- 0.5 fringe. At one time the software
would let you increase this value (say to 0.9 fringe), but the same
sorts of issues would arise. There are particular problems that arise
when the phase is at the 0 - 2pi boundary and a steep gradient is
present, when there are defects in the image and at the menisci. Other
algorithms have been used- with the faster computers available now,
these should be revisited. Keep in mind that the gradients where the
interference system fails are steeper than where schlieren effects
become significant absorbance data. Thus, the interference optics are
more accurate for high concentration (and steep concentration gradient)
systems. We are starting work on the next generation of interference
optics, so now is a good time to review the algorithms. We estimate that
these new optics will be ~100x more precise and ~2x more sensitive than
the current optics.

As long as we are on the subject,  the accuracy of the fringe
displacement measurements (and the absorbance system) depends on having
the optics focused properly. The optics must be focused at the 2/3 plane
(i.e. 2/3 of the distance through the sample, going from the source
towards the detector). Focusing above this point (i.e. at the midpoint
of the cell) leads to the fringe displacement being exaggerated in steep
gradients... from the standpoint of data analysis, it would appear that
there is a weak self-association for a single ideal component. If the
optics are focused below this point (i.e. at the 3/4 point) leads to a
suppression of the fringe diplacement in regions with high concentration
gradients, and analysis of the data will overestimate nonideality.

There is an excellent discussion of the accuracy of the interference
optics in David Yphantis's 1964 paper: D. A. Yphantis. Equilibrium
Ultracentrifugation of Dilute Solutions. Biochemistry 3:297-317, 1964.
Note that it is the third order effects that cause significant problems,
not the second order problems.
Best wishes to all-
Tom

Peter Schuck wrote:

>
> Hi Everybody,
>
> I agree with everything said, but since there seems to be a developing
> general interest in this topic, I'd like to add one observation we
> made repeatedly with the interference optics.
>
> First - and this is certainly not new - one can easily visualize the
> lensing effect of the boundary. I am attaching a powerpoint slide
> showing the camera image from a run with several mg/ml thyroglobulin
> at 50000 rpm. There's an obvious lack of light intensity in the
> boundary when using the 12 mm centerpiece, which is absent from the
> image of the 3 mm centerpiece in the same run, as John mentioned. The
> lack of light intensity is what causes the artificial peaks in the
> absorbance scans.    [sorry, version with the attachment bounced back
> awaiting approval ]
>
> But the interesting point is that one can frequently still acquire
> fringe shift data through the boundary - in fact even through the one
> shown in the picture. They do not exhibit an artificial peak, but they
> have different problems. At very high gradients, the scans seem to
> 'skip' fringes, i.e. the algorithm to assign fringe shifts from
> neighboring points fails and instead of an increase in fringe shift
> from one radial point to the next, one may see even a slight decrease
> from one point to the next (I suspect the XLI software simply can't
> deal with more than 0.5 fringes shift for neighboring radial points).
> As Jack mentioned, we've seen this a lot also in CsCl gradients, and
> at this occasion I've built into SEDFIT some limited capability to
> repair this problem afterwards in software (with an algorithm assuming
> that the boundary and its derivatives are monotonic). However, there
> also seems to be a range of boundary steepness that is already
> producing peaks in absorbance, but not yet exhibiting the fringe
> 'skipping' in interference optics. Of course, the fringe profiles from
> these steep gradients can still be questioned with regard to their
> faithful representation of the concentration gradient, which I doubt.
>
> However, the absence of the artificial peak at least allows us to load
> the data and conveniently determine an empirical s-value from the
> midpoint. Assuming that the distortion of the boundary shape is not
> modifying the integral over the boundary in a time-dependent way, one
> might even be able to get a fairly good precision on the
> weight-average s.
>
> Best,
> Peter
>
>
>
>
>> X-SBRS: 5.5
>> X-BrightmailFiltered: true
>> X-Brightmail-Tracker: AAAAAA==
>> Date: Fri, 28 Oct 2005 08:59:27 -0400
>> From: Peter Schuck <pschuck at helix.nih.gov>
>> User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716)
>> X-Accept-Language: en-us, en
>> To: Norbert.Muecke at dkfz-heidelberg.de
>> Subject: Re: [RASMB] peak in sedimentation velocity scans at high
>> protein
>>  conc.
>> X-Sanitizer: murus Advosys mail filter
>>
>> Hi Norbert,
>> this is Wiener skewing from refraction of light within the boundary.
>> If you use interference optics, you should not observe this. Also,
>> you can probably minimize it by running slower rotor speed and not
>> generating as steep gradients. Peter
>>
>>
>> Norbert Muecke wrote:
>>
>>> Hi,
>>> I have done some velocity runs at high protein conc. (up to 6g/l).
>>> A new peak within the boundary could be observed.
>>> I have attached the scans of three different concentrations.
>>> Absorbance was measured at 284nm.
>>> Any idea of how to explain that phenomena would be appreciated.
>>>
>>> Best regards
>>> Norbert
>>>
>>>
>>> Division Biophysics of Macromolecules, B040
>>> German Cancer Research Center (DKFZ), TP3
>>> Im Neuenheimer Feld 580
>>> D-69120 Heidelberg, Germany
>>>
>>>
>>>
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