Python Programming for Biology: Bioinformatics and Beyond

Figure 16.3 (Plate 4).  The results of various array comparison procedures. Shown

from left to right are: the product of red and green channels, displayed as yellow, to

illustrate the coincidence between channels; the G-test scores of red × log

2

(red/green),

which is designed to show where the values in the two channels are different and of

significant value; hierarchical clustering to produce shuffled rows and columns in the test

data, which here shows that there are replicates for each row.

As another example, next we find the logarithm (here in base 2) of the ratio of the red

and green channels. Combining two-channel red and green microarray data in this way is

commonplace  (for  example,  when  making  ‘MA’  plots).  To  achieve  this  we  first  define  a

small helper function log2Ratio which will accept two input data arrays and give back the

combined,  comparison  array,  noting  that  we  take  a  copy  of  the  original  data  and  add  a

small amount to each array, to ensure that we do not divide by zeros or take logarithms of

zero:

from numpy import log2

def log2Ratio(data1, data2):

data1 = array(data1) + 1e-3

data2 = array(data2) + 1e-3

return log2(data1/data2)

We can use this function to combine the red and green channels (index 0 and 1), placing

the result in the blue channel (index 2).

rgArray = loadArrayImage(imgFile, 'TwoChannel', 18, 17)

rgArray.combineChannels(0, 1, combFunc=log2Ratio, replace=2)

The result can be visualised by selecting only the blue channel, here making a greyscale

image.

rgArray.makeImage(20, channels=(2,2,2)).show()

A further alternative to show differences between the two channel intensities is to use

logarithms  to  calculate  x*log(x/y),  where  x  and  y  are  two  colour  channels,  which  is  a

convenient way of showing the information content

5

of one distribution over another and

which  is  used  in  the  G-test  (see

Chapter  22

).  Similar  to  the  previous  example  red  and

green channel arrays are both shifted away from zero by a small amount, so that zeros do

not occur in the division that will follow.

---

from numpy import log2

def gScore(data1, data2):

data1 = array(data1) + 1e-3

data2 = array(data2) + 1e-3

return data1 * log2(data1/data2)

This  can  be  tested  as  before,  though  we  normalise  the  values  so  the  logarithms  are

scaled into the same range as the other channels:

rgArray = loadArrayImage(imgFile, 'TwoChannel', 18, 17)

rgArray.combineChannels(0, 1, combFunc=gScore, replace=2)

rgArray.normaliseMax(perChannel=True)

rgArray.makeImage(20, channels=(2,2,2)).show()

With  values  calculated  in  this  way  we  can  perform  significance  tests,  as  described  in

Chapter 22

, given that the random expectation is that values will be chi-square distributed.

Here  the  comparative  term  has  been  calculated  from  the  perspective  of  the  red  channel,

but we could also do it for green (i.e. green * log(green/red)).