[RASMB] MW calculation question

Leech, AP andrew.leech at york.ac.uk
Wed Aug 14 11:14:13 PDT 2013 

Dear all,

My inference from John's information, is that this material is composed
of unimers which are themselves generated by a polymerisation process.
I would expect this to generate a distribution of MWs, of which the
NMR determined average is 27900; these then assemble into micelles with
an aggregation number of 40, I suppose an average also. Although the
polydispersity is small, it is not 1.000, so there is a distribution
of MWs and hence of sizes. The SLS does not seem to have been done by
a fractionation method (SECMALLS), so that has not had an opportunity
to demonstrate heterogeneity.

So on centrifuging this material, I would expect to see a distribution
of s values. The question is whether the distribution is wide enough to
be interpreted as boundary spreading by diffusion, in an analysis whose
model presupposes a single homogeneous molecular species (as one might
expect of a protein).

I guess that given some assumptions about the s <-> Mw relation for
things of appropriate shape, it would be possible to model the sed
coeff distribution resulting from the supposed Mw distribution.

At this point I'll let the polymer chemists shoot me down.

Andrew

On 13/08/2013 20:45, John Sumida wrote:
> Dear Tom, RASMB.
>
> The PDI value determined by GPD Mw/Mn was 1.06.  Thus at this level they appear to be mono-disperse.
>
> The second virial coefficient (A2) determined by SLS was 1.34E-4.  Other diblock copolymers with BMA cores reported in the literature range from 1 to 3E-4, so the value determined seems reasonable and does not appear to suggest any strong pairwise interactions consistent, I think, with the concentration independent behavior of the s-value in the centrifuge.
>
> The Debye plot of light scattering intensity as function of polymer concentration was completely linear. Thus, once again and please correct me if mistaken, I think this says that at this level this material seems mono-disperse.
>
> The Aggregation number determined was 40.  The unimer mass, determined by NMR, is 27,900 Daltons.
>
> Best regards
> John Sumida
> Analytical Biopharmacy Core
> University of Washington.
>
> -----Original Message-----
> From: Laue, Thomas [mailto:Tom.Laue at unh.edu]
> Sent: Tuesday, August 13, 2013 12:25 PM
> To: John Sumida; 'Leech, AP'
> Cc: rasmb at rasmb.org
> Subject: RE: [RASMB] MW calculation question
>
> Hi-
> How was the the sample heterogeneity handled? The SLS will give roughly a z-average value of A2. Did the DLS reveal the heterogeneity observed in AUC?
> Best to all-
> Tom
> ________________________________________
> From: rasmb-bounces at list.rasmb.org [rasmb-bounces at list.rasmb.org] on behalf of John Sumida [jpsumida at u.washington.edu]
> Sent: Tuesday, August 13, 2013 2:42 PM
> To: 'Leech, AP'
> Cc: rasmb at rasmb.org
> Subject: Re: [RASMB] MW calculation question
>
> Dear RASMB,
>
> I am providing more information regarding the DLS measurements.  These measurements were performed by our collaborators and as there has been some interested expressed in knowing what the diffusion value was determined to be will post that once that information is shared with me.
>
> DLS was performed to determine particle mean diameter and by SLS to evaluate particle molecular weight using a Malvern Zetasizer Nano equipped with a 5 mW He-Ne laser operating at 633 nm (Worcestershire, UK) for both techniques.
>
> DLS measurements were performed in 1X DPBS at 200 µg/mL with mean diameters reported as the number average ± peak half-width.
>
> Prior to SLS measurements, the micelle solutions were dialyzed against 1X DPBS using a Slide-A-Lyzer® MINI Dialysis Device with a 3.5K MWCO (Thermo Scientific, Rockford, IL).
>
> Serial dilutions of these solutions (0.5 – 0.1 mg/mL) were manually injected into a refractometer (Wyatt Optilab-rEX, Dernbach, Germany) to determine a dn/dc value for each diblock copolymer micelle.
>
> Micelle molecular weight (Mw) and second virial coefficient (A2) were determined from a Debye plot generated by SLS measurements at a constant scattering angle of 173° using the Rayleigh equation: KC/Rθ = (1/Mw + 2A2C), in which C was varied from 1 – 0.125 mg/mL, K is an optical constant, and Rθ is the Rayleigh ratio of the scattered to incident light intensity.
>
> The parameter K can be represented by the following relationship: K = 4π2n02(dn/dc)2/NAλ4, in which n0 is the refractive index of the solvent, NA is Avogadro’s number, and λ is the wavelength of the light source.
>
>
> Best regards,
> John Sumida
> Analytical Biopharmacy Core
> University of Washington.
>
> -----Original Message-----
> From: rasmb-bounces at list.rasmb.org [mailto:rasmb-bounces at list.rasmb.org] On Behalf Of Leech, AP
> Sent: Tuesday, August 13, 2013 11:28 AM
> Cc: rasmb at rasmb.org
> Subject: Re: [RASMB] MW calculation question
>
> Hello all,
>
> Further to John P. and Walter's comments, it would be interesting to know how the DLS and SLS measurements were done and what, if any, degree of inhomogeneity was apparent in them.
>
> Andrew
>
> On 13/08/2013 18:04, John Philo wrote:
>> John S., I agree with Walter Stafford that heterogeneity is causing
>> the single-species fit to underestimate the mass, but I don't think
>> there is any reason to think the primary cause is heterogeneity of
>> monomer mass or conformation. You said yourself that the /c(s)/
>> analysis gives one major peak that is only 80% of the total area. If
>> the sample is only 80% pure, why would you expect a single-species fit to give the correct MW?
>> If /c(s)/ is giving one narrow main peak then it is not its ability to
>> emulate multiple overlapping species that is primarily improving the
>> fit quality relative to a single-species fit, it is the addition of
>> the 20% of minor species (presumably with significantly different
>> sedimentation coefficients).
>> The strength of whole-boundary analysis is that it fits all the scans,
>> but that means that to get good results it must account for all
>> species that are present, whether or not they are things you are interested in!
>> That is, a weakness of whole boundary analysis is that it isn't
>> particularly easy to exclude impurities, aggregates, fragments or
>> other 'junk' from the data analysis, and your results simply
>> demonstrate that problem. This is a case where a quick and simple
>> /g(s*) /analysis via the dc/dt approach, and then fitting only the
>> main peak of that distribution (excluding the junk at high and low
>> sedimentation
>> coefficients) would probably correctly identify the MW of your 80%
>> major species (but always the best precision should come from whole
>> boundary analysis).
>> Further, fundamentally your question is an apples vs. oranges
>> comparison. You say you want to compare the two different analysis
>> programs, but you are trying to compare two fundamentally different
>> fitting models. You can easily do a single-species fit in SEDFIT and
>> then compare that to the one from SEDANAL (and I'm sure the results
>> will be similar).
>> John P.
>>
>> ----------------------------------------------------------------------
>> --
>> *From:* rasmb-bounces at list.rasmb.org
>> [mailto:rasmb-bounces at list.rasmb.org] *On Behalf Of *Walter Stafford
>> *Sent:* Monday, August 12, 2013 6:30 PM
>> *To:* John Sumida
>> *Cc:* <rasmb at rasmb.org>
>> *Subject:* Re: [RASMB] MW calculaiton question
>>
>> I think this was already answered. I think your sample is heterogeneous.
>> Small variations on composition (I.e molar mass heterogeneity) will
>> cause peak broadening that will appear as diffusion. If you include
>> enough data in the fit. It should be apparent in the residuals. C(s)
>> will add enough components to account for the heterogeneity (albeit
>> with the same f/fo) and should give better residuals. Sedanal will not
>> because fitting to a single species (I. E, the wrong model) should not
>> give as good of a fit. The heterogeneity will cause Sedanal to return
>> a value that is too large and therefore, a molar mass that is too small.
>>
>> Walter Stafford
>> wstafford3 at walterstafford.com <mailto:wstafford3 at walterstafford.com>
>>
>>
>> On Aug 12, 2013, at 20:57, "John Sumida" <jpsumida at u.washington.edu
>> <mailto:jpsumida at u.washington.edu>> wrote:
>>
>>> Dear RASMB,
>>>
>>> The following was posted on the SEDFIT user list and it has been
>>> suggested that I also post this message to the RASMB list.  Thus I am
>>> reposting my question to RASMB and am including some edits and
>>> additional information for clarity and correctness.
>>>
>>> Objective
>>>
>>> I am trying to reconcile results obtained using two different
>>> approaches, SEDANAL and SEDFIT.
>>>
>>> Observations
>>>
>>> In SEDFIT, analysis of sed velocity FDS data returns an s20w of 8.5s
>>> and MW=1.3 MDa for the major peak, comprising >80% of the total
>>> loading concentration, determined in a c(s) fit.  Please note after
>>> checking with our collaborators this value is consistent with the MW
>>> returned from DLS and static light scattering experiments.  Thus the
>>> SEDFIT result is consistent with the DLS and static light scattering
>>> data which estimate a MW of 1.1 MDa.
>>>
>>> In SEDANAL, the simplest model necessary to fit the data well was a
>>> single species model.  Using this model, analysis of the same
>>> data-set returns an s20w of 8.8s, similar to the value calculated in
>>> SEDFIT, but a MW of 655 kDa is calculated.
>>>
>>> My question:
>>>
>>> Why does the value of the MW returned for SEDANAL and SEDFIT differ
>>> by a factor of ~2 when the s20w in each case are similar (8.5s versus
>>> 8.8s).  My purpose here is that I believe the apparent difference
>>> being returned from these parallel analyses is saying something
>>> fundamentally important about the behavior of these materials in
>>> buffer and our assumptions thereof.
>>>
>>> Background.
>>>
>>> <!--[if !supportLists]-->1.<!--[endif]-->Rotor speed was 30 krpm,
>>> vbar=0.917 (measured), solution density = 1.00506 g/cm3 (measured),
>>> and viscosity =0.0100281 Poise (measured).  Temperature = 20oC.
>>>
>>> <!--[if !supportLists]-->2.<!--[endif]-->The material being studies
>>> is a polymer micelle with a CMC of 14 micrograms/ml.
>>>
>>> <!--[if !supportLists]-->3.<!--[endif]-->The polymer was run over a
>>> series of concentrations ranging from 0.2 mgs/ml to 1.00 mgs/ml.
>>>
>>> <!--[if !supportLists]-->a.<!--[endif]-->Thus under the conditions of
>>> the experiment I am at least 14 times the CMC at the lowest concentration.
>>>
>>> <!--[if !supportLists]-->4.<!--[endif]-->A major peak is observed in
>>> the initial c(s) distribution comprising >80% of the total loading
>>> and the position of this peak (7.7 s-exp; s20w=8.5) does not shift
>>> with concentration.
>>>
>>> <!--[if !supportLists]-->5.<!--[endif]-->From the analysis of raw SV
>>> data, SEDANAL returns an experimental sedimentation coefficient of
>>> 7.9s and a calculated s20w of 8.8s.
>>>
>>> <!--[if !supportLists]-->6.<!--[endif]-->A global analysis in SEDPHAT
>>> was performed over the entire concentration range, transforming the
>>> initial c(s) distribution into a set of 8 discrete species.
>>>
>>> <!--[if !supportLists]-->a.<!--[endif]-->Four of these 8 species
>>> survived a critical chi square analysis suggesting that these four
>>> species were important in retaining the quality of the fit.
>>>
>>> <!--[if !supportLists]-->b.<!--[endif]-->Of these four discrete
>>> species, three were grouped beneath the major peak observed in the
>>> initial c(s) analysis.
>>>
>>> <!--[if !supportLists]-->c.<!--[endif]-->The calculated weight
>>> averaged s20w for these three species was 8.1s.
>>>
>>> <!--[if !supportLists]-->d.<!--[endif]-->The  s20w values were
>>> checked and confirmed with a manual calculation, SEDNTERP verstion
>>> 1.09, as well as the calculate “s(20,w) from s(xp) in SEDFIT.
>>>
>>> <!--[if !supportLists]-->7.<!--[endif]-->Using the ratio of s/D in
>>> the Svedberg equation and values for diffusion estimated by assuming
>>> 655 kDA, (the MW returned in SEDANAL), I calculate a MW of 655 kDa.
>>> Thus I believe that the value for diffusion being estimated in
>>> SEDANAL is consistent with the 655 kDA molecular weight.
>>>
>>> <!--[if !supportLists]-->a.<!--[endif]-->Estimates of the diffusion
>>> coefficient in SEDFIT and SEDNTERP (and thus presumable also from
>>> SEDANAL) are not very different.
>>>
>>> <!--[if !supportLists]-->b.<!--[endif]-->The diffusion coefficient
>>> estimate in SEDFIT is 3.19E-7 cm2/sec and the value calculated in
>>> SEDNTERP 3.67E-7 cm2/sec (Teller approximation).
>>>
>>> <!--[if !supportLists]-->8.<!--[endif]-->Using the calculate M(s)
>>> function in SEDFIT and providing the experimental sedimentation
>>> coefficient noted above I need to input an ff0<1 (0.8967) in order to
>>> arrive at the 655kDA MW returned by SEDANAL.
>>>
>>> <!--[if !supportLists]-->a.<!--[endif]-->I understand that this is
>>> nonsensical as ff0 cannot be less than 1.
>>>
>>> <!--[if !supportLists]-->b.<!--[endif]-->Notably SEDNTERP version
>>> 1.09 also calculates a frictional ratio<1; namely SEDNTERP calculate
>>> ffp=0.9449.
>>>
>>> <!--[if !supportLists]-->c.<!--[endif]-->The c(s) analysis in SEDFIT
>>> returns an ff0=1.47.
>>>
>>> Thus to summarize:
>>>
>>> <!--[if !supportLists]-->1.<!--[endif]-->Relatively similar s20w
>>> values are determined in both SEDFIT and SEDANAL for the same data-set.
>>>
>>> <!--[if !supportLists]-->a.<!--[endif]-->8.5s from SEDFIT
>>>
>>> <!--[if !supportLists]-->b.<!--[endif]-->8.8s from SEDANAL
>>>
>>> <!--[if !supportLists]-->2.<!--[endif]-->SEDFIT calculates a MW
>>> almost exactly 2 times the value of the MW returned by SEDANAL for the same s20w.
>>>
>>> <!--[if !supportLists]-->3.<!--[endif]-->The estimates of diffusion
>>> in both programs are quite similar
>>>
>>> <!--[if !supportLists]-->4.<!--[endif]-->The frictional ratio ff0 in
>>> the SEDFIT analysis is 1.47 whereas the calculated ffp in SEDNTERP
>>> based on the observe MW in SEDANAL is <1.
>>>
>>> <!--[if !supportLists]-->5.<!--[endif]-->The frictional ratio
>>> calculated in SEDNTERP, assuming the MW=1.3 MDa, is 1.54
>>>
>>> <!--[if !supportLists]-->6.<!--[endif]-->There does appear to be
>>> heterogeneity in the major peak observed in the c(s) analysis.
>>>
>>> Thank you in advance for your comments and suggestions.  I apologize
>>> for the length of this post, but in fairness, I am attempting to
>>> provide information that would enable an informed response.
>>>
>>> Best regards
>>>
>>> John Sumida
>>>
>>> University of Washington
>>>
>>> Analytical Biopharmacy Core
>>>
>>> _______________________________________________
>>> RASMB mailing list
>>> RASMB at list.rasmb.org <mailto:RASMB at list.rasmb.org>
>>> http://list.rasmb.org/listinfo.cgi/rasmb-rasmb.org
>>
>>
>> _______________________________________________
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>> RASMB at list.rasmb.org
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>>
>
> --
> Dr Andrew Leech                   *  Laboratory Head
> Technology Facility               *  Molecular Interactions Laboratory
> Department of Biology (Area 15)   *  Tel   : +44 (0)1904 328723
> University of York                *  Fax   : +44 (0)1904 328804
> Wentworth Way,  York  YO10 5DD    *  Email : andrew.leech at york.ac.uk
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-- 
Dr Andrew Leech                   *  Laboratory Head
Technology Facility               *  Molecular Interactions Laboratory
Department of Biology (Area 15)   *  Tel   : +44 (0)1904 328723
University of York                *  Fax   : +44 (0)1904 328804
Wentworth Way,  York  YO10 5DD    *  Email : andrew.leech at york.ac.uk
EMAIL DISCLAIMER: http://www.york.ac.uk/docs/disclaimer/email.htm

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