[BioC] Problem with limma for two-color factorial design - Coefficients not estimable

[Stephen Turner]

Hello. This is my first time posting to the mailing list - usually
I've been able to find answers in the archives here or elsewhere, but
I have a problem that I haven't been able to solve, so here goes.

I have microarray data I downloaded from Array Express using the
ArrayExpress function in the ArrayExpress package. I managed to
convert the NChannelSet object into an RGList object that I can use in
limma using a tip I found in the archives
(https://stat.ethz.ch/pipermail/bioconductor/2009-September/029705.html).
After some bg subtraction and normalization, I have an MAList object
with 32 arrays (red and green) by 34,944 probes.

The experiment consists of two cell types (WT or KO), by 4 treatments
(control, CD70, CD80, CD70+CD80), at four different time points (2, 4,
8, 14 hours), with a dye-swap. I'm mostly interested in genes that are
differentially expressed when WT cells are hit with CD70+CD80 versus
CD80 alone.

I'm trying to create a targets file so I can use modelMatrix to create
my design matrix. But I have a multifactorial design using a two color
dye-swap design, and I'm not sure how to specify this in the targets
file. The limma manual has information about factorial designs, but no
examples for two-color experiments. I have the following factors:

1: Celltype: WT or KO
2: Treatment: control (x), CD70, CD80, or CD70+CD80 (CD7080).
3: Timepoints: 2, 4, 8, and 14 hours.

I tried collapsing all of factors and levels into a single string in
my targets file:

> targets
       array          Cy3            Cy5
1  array3329    WT.CD70.2         WT.x.2
2  array2675  KO.CD7080.8    WT.CD7080.8
3  array2242  WT.CD7080.2    KO.CD7080.2
4  array3328       WT.x.2      WT.CD70.2
5  array3310       WT.x.8      WT.CD70.8
6  array2246  KO.CD7080.2    WT.CD7080.2
7  array3337  WT.CD7080.4      WT.CD80.4
8  array3323 WT.CD7080.14     WT.CD80.14
9  array2673    KO.CD70.8      WT.CD70.8
10 array1938 WT.CD7080.14   KO.CD7080.14
11 array2240    WT.CD70.2      KO.CD70.2
12 array3336    WT.CD80.4    WT.CD7080.4
13 array3322   WT.CD80.14 WT.CD7080.14.2
14 array2674  WT.CD7080.8    KO.CD7080.8
15 array3321   WT.CD70.14        WT.x.14
16 array2241    KO.CD70.2      WT.CD70.2
17 array2597  KO.CD7080.4    WT.CD7080.4
18 array3313  WT.CD7080.8      WT.CD80.8
19 array1939 KO.CD7080.14 WT.CD7080.14.2
20 array3335    WT.CD70.4         WT.x.4
21 array2672    WT.CD70.8      KO.CD70.8
22 array3320      WT.x.14     WT.CD70.14
23 array3334       WT.x.4      WT.CD70.4
24 array3311    WT.CD70.8         WT.x.8
25 array3331  WT.CD7080.2      WT.CD80.2
26 array1941   KO.CD70.14   WT.CD70.14.2
27 array2588    WT.CD70.4      KO.CD70.4
28 array2596  WT.CD7080.4    KO.CD7080.4
29 array3330    WT.CD80.2    WT.CD7080.2
30 array3312    WT.CD80.8    WT.CD7080.8
31 array1940 WT.CD70.14.2     KO.CD70.14
32 array2593    KO.CD70.4      WT.CD70.4

I then created a design matrix, where the reference group is WT cells,
untreated, 2-hour timepoint.

design <- modelMatrix(targets, ref="WT.x.2")

This creates a 32x25 design matrix, but when I fit the model, I get a
"Coefficients not estimable" error/warning:

> fit <- lmFit(d, design)
Coefficients not estimable: WT.CD70.14.2 WT.CD80.14 WT.CD80.2
WT.CD80.4 WT.CD80.8 WT.x.14 WT.x.4 WT.x.8
Warning message:
Partial NA coefficients for 34944 probe(s)

Any help with how I can specify this multifactorial time-course design
in a two-channel dye-swap experiment would be greatly appreciated. As
I said, I'm most interested in the conditions on arrays 8-9, 13-14,
19, 26, and 30-31, where I'm looking at WT cells treated with CD70 and
CD80 versus CD80 alone.

Thanks in advance for any help!