[BioC] Combining data from scans at different intensities

[Henrik Bengtsson]

Hi.

On 2/13/07, John Fowler <fowlerj at science.oregonstate.edu> wrote:
> Hello,
>
> I would like to use data extracted from images scanned at 3 different
> intensities in our GenePix scanner.  There are a couple of papers
> that I could find (Lyng et al 04, Piepho et al 06) that describe
> methods to combine these data and thus help deal with problems of
> saturation and signals across the dynamic range of the scanner.
>
> I looked for a way to do this in bioconductor, and found a post from
> Dr. Henrik Bengtsson, indicating that this was possible using the
> aroma.light package in bioconductor.  However, he indicated that this
> should be done with data from scans in which the laser intensity =was
> not changed=.
>
> Unfortunately, my scans used two different laser intensities.

So, what was your settings for the three scans?  If two scans have the
same laser setting, how does the third scan differ?  Different PMT
settings?

>
> Does this invalidate using aroma.light for this purpose?  Is there
> any other Bioconductor package that could deal with my (apparently
> incorrectly obtained) data?

What we observed from scanning at different sensitivity (=PMT) levels
was that the scanner adds an offset to the signals and that this
offset is independent of the PMT setting.  We also observed that this
offset is more or less constant across arrays (also roughly between
channels), indicating that the offset is added either in the PMT
(photomultiplier type) or more likely in the analogue-to-digital
electronics just after the PMT.  We observed this in both of the
scanners investigated, Axon GenePix 4000A and Agilent G2505A.

The multiscan calibration model is applied to each channel separately.
Let c={R,G} be the two channels, and let e_c be the offset in channel
c.  Say you do multiple scans k=1,...,K.  Then y_{c,i}^(k) denotes the
probe signal in channel c for probe i and scan k.  Let the unknown
amount of hybridized sequence in this probe is denoted by x_{c,i},
which is independent of scan k. To be really precise here, x_{c,i} is
the amount of light emitted from probe i entering the PMT.  We
proposed the model:

 y_{c,i}^(k) = a_c^(k) + b_c^(k)*x_{c,i} + eps_{c,i}^(k)
                \approx e_c + b_c^(k)*x_{c,i} + eps_{c,i}^(k)  (*)

where eps_{c,i}^(k) is zero-mean noise.  By do multiscan at various
*PMT settings*, we can  identify e_c and all of the b_c^(k). Even
better, we get a good estimate of x_{c,i}, the amount of light
entering the PMT tube, so in the end of the day we control for effects
in the PMT and the electronics afterwards.  We strongly believe this
is a good model for those effects.

Now, if you adjust the laser power, you effectively adjust the amount
of light being emitted from each probe too, that is, you can no longer
assume x_{c,i} being constant, but you have x_{c,i}^{m} where
m=1,...,M is the different *laser levels*.  You may provide a similar
model to (*) for laser-adjusted scans, e.g.

 x_{c,i}^(m) \approx d_c + g_c^(m)*z_{c,i} + xi_{c,i}^(m)  (**)

where now z_{c,i} is the amount of labels on the hybridized target on
probe i ,and x_{c,i}^(m) is the amount of light emitted by this probe
at laser level m.  One open question is if "laser offset" d_c is
constant or if it depends on m too.

Now, if (**) is true, when combining (*) and (**), which are both so
called _affine_ functions, you will get another affine function:

 y_{c,i}^(k) = e_c + b_c^(k)*(d_c + g_c^(m)*z_{c,i} + xi_{c,i}^(m)) +
eps_{c,i}^(k)
                = e_c + d_c*b_c^(k) + h_c^(k,m)*z_{c,i} + nu_{c,i}^(k,m)  (***)

where nu_{c,i}^(k,m) is confounded noise.  Compare Models (***) and
(*).  If d_c = 0, then (*) and (***) are similar, and you can use (*)
for your data.  If d_c != 0, then d_c*b_c^(k) must be estimated too.

The Y <- calibrateMultiscan(X) in aroma.light applies to Model (*).
There is no implementation for Model (***) when d_c != 0, but I would
say give it a try.

If you want to, I can have a look at your multiscan data for a typical
array.  If so, we'll have to figure out a way to transfer three GPR
files.

Best

Henrik



>
> many thanks!
> John
>
> --
> John Fowler                             Associate Professor
> Botany and Plant Pathology (BPP) Dept.
> 2082 Cordley Hall                        Phone: (541) 737-5307
> Oregon State University                  FAX: (541) 737-3573
> Corvallis, OR  97331-2902  USA           Email: fowlerj at science.oregonstate.edu
>         [[alternative HTML version deleted]]
>
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