[BioC] 2x2 factorial loop without common reference (pool)

[francois fauteux]

Hi;

We are doing an experiment with agilent 44K (3 biological reps,
complete dye-swap):

a - control
b - treatment 1
c - treatment 2
d - treatment 1 + treatment 2

and I would like to output evidence of the interaction between two
treatments and effect on gene expression.

24 chips:

SlideNumber	Cy3	Cy5
1	a1	b1
2	a2	b2
3	a3	b3
4	b1	a1
5	b2	a2
6	b3	a3
7	a1	c1
8	a2	c2
9	a3	c3
10	c1	a1
11	c2	a2
12	c3	a3
13	b1	d1
14	b2	d2
15	b3	d3
16	d1	b1
17	d2	b2
18	d3	b3
19	c1	d1
20	c2	d2
21	c3	d3
22	d1	c1
23	d2	c2
24	d3	c3

I've done several tests with limma to isolate significant results in
the following:
1- a vs b;
2- a vs c;
3- b bs d;
4- c vs d;

with this "targets.txt":

SlideNumber	Cy3	Cy5
1	a	b
2	a	b
3	a	b
4	b	a
5	b	a
6	b	a
7	a	c
8	a	c
9	a	c
10	c	a
11	c	a
12	c	a
13	b	d
14	b	d
15	b	d
16	d	b
17	d	b
18	d	b
19	c	d
20	c	d
21	c	d
22	d	c
23	d	c
24	d	c

First option:

> f <- paste(targets$Cy3, targets$Cy5, sep = ".")
> f <- factor(f, levels = c("a.b", "b.a", "a.c", "c.a", "b.d", "d.a", "c.d", "d.a"))
> design1 <- model.matrix(~0 + f)

> design
   a.b b.a a.c c.a b.d d.b c.d d.c
1    1   0   0   0    0    0    0    0
2    1   0   0   0    0    0    0    0
3    1   0   0   0    0    0    0    0
4    0   1   0   0    0    0    0    0
5    0   1   0   0    0    0    0    0
6    0   1   0   0    0    0    0    0
7    0   0   1   0    0    0    0    0
8    0   0   1   0    0    0    0    0
9    0   0   1   0    0    0    0    0
10   0   0   0   1    0    0    0    0
11   0   0   0   1    0    0    0    0
12   0   0   0   1    0    0    0    0
13   0   0   0   0    1    0    0    0
14   0   0   0   0    1    0    0    0
15   0   0   0   0    1    0    0    0
16   0   0   0   0    0    1    0    0
17   0   0   0   0    0    1    0    0
18   0   0   0   0    0    1    0    0
19   0   0   0   0    0    0    1    0
20   0   0   0   0    0    0    1    0
21   0   0   0   0    0    0    1    0
22   0   0   0   0    0    0    0    1
23   0   0   0   0    0    0    0    1
24   0   0   0   0    0    0    0    1

This gives significant results for each one of the "levels" but does
not take into account the dye-swap (i.e "a.b" and "b.a" are considered
independent).

Other tested option is:
> design2 <- modelMatrix(targets,ref="a")

> design
      p  s sp
ab1   0  1  0
ab2   0  1  0
ab3   0  1  0
ba1   0 -1  0
ba2   0 -1  0
ba3   0 -1  0
ac1   1  0  0
ac2   1  0  0
ac3   1  0  0
ca1  -1  0  0
ca2  -1  0  0
ca3  -1  0  0
bd1  0 -1  1
bd2  0 -1  1
bd3  0 -1  1
db1  0  1 -1
db2  0  1 -1
db3  0  1 -1
cd1 -1  0  1
cd2 -1  0  1
cd3 -1  0  1
dc1  1  0 -1
dc2  1  0 -1
dc3  1  0 -1

This gives results for "b" effect, "c" effect, and "d" effect.
However, I could'nt get results for the 4 comparisons of interest
(even though the matrix is coherent).

Questions:

1 - What would be the best option (design and operations) to get to
contrasts of interest considering that the experiment has a 4
treatments in a factorial design without common reference  (a vs b, a
vs c, b vs d, c vs d) and taking into account the dye-effect;

2- Is this method (4 contrasts) the best one considering that
treatment "d" is a combination of treatments "b" and "c" (factorial
type design). How could one directly get to identify genes
differentially expressed due to the interaction between treatment "b"
and treatment "c" (i.e effect of "d" over "b" and "c").

In Limma Users Guide and elsewhere on this forum, I could not find a
clear description of how this type of analysis should be performed,
even though it is a simple design (i.e 2X2 factorial without a common
reference - two color arrays - complete dye swap).

Thanks for your time, best regards.

François Fauteux
Étudiant à la maîtrise en biologie végétale
Centre de recherche en horticulture
Université Laval
francois.fauteux at gmail.com