[BioC] Experimental Design Question(s)

[Nathan.Watson-Haigh at csiro.au]

I'm trying to understand and analyse a microarray experiment performed by someone else, and I've been reading about experimental design in some books and have a few questions.

The experiment involves groups of animals assigned to one of 3 time points (measured as the number of days since treatment) and administered with either A or B treatment. 2 out 3 tissue samples are taken from the groups at their designated time point. This is basically to identify expression differences over a time course in response to one of the two treatments. In addition a control group is used which received neither A or B treatment and sampled at a single time point.

Am I correct in thinking I have an incomplete fractional factorial design since each group only has 2 of 3 possible tissue samples taken and it makes no sense to have control groups for ever time point and a control can not be treated with either A or B? E.g. as mentioned at the bottom of this page:
http://www.socialresearchmethods.net/kb/expfact2.php

I was thinking of the below as a possible design. '-' no group possible as it's a control group

Tissue 1:
     days since treatment
      0    3    7    21
C     8    -    -    -
A     -    4    4    4
B     -    4    4    4

Tissue 2:
     days since treatment
      0    3    7    21
C     4    -    -    -
A     -    4    4    4
B     -    0    0    0

Tissue 3:
     days since treatment
      0    3    7    21
C     4    -    -    -
A     -    0    0    0
B     -    4    4    4

I'm wondering how best to approach the analysis in limma such that the following can be answered:
1) Identify genes that change in expression over the days since treatment.
2) Genes that show tissue specific responses
3) Genes that show the same response over tissues - I don't think this can be done since all three tissue samples were not taken for both treatments, only Tissue 1 was taken for both treatments.
4) Find genes in Tissue 1 that respond to both treatments.

I think I'm getting confused with parameterising the experiment into an appropriate design matrix. Should I parameterise it using 3 factors (treatment, days since treatment and tissue) with 3 (control, A and B), 4 (0, 3, 7 and 21) and 3 (1, 2 and 3) levels respectively:
Treatment: Control, A and B
Days since treatment: 0, 3, 7 and 21
Tissue: 1, 2 and 3

Since it's only possible to have days since treatment for non-control groups, how do I best approach the analysis? Should I normalise the expression levels to that of the corresponding controls for that tissue and then proceed with the analysis using a fractional factorial design:
Tissue 1:
     days since treatment
      3    7    21
A     4    4    4
B     4    4    4

Tissue 2:
     days since treatment
      3    7    21
A     4    4    4
B     0    0    0

Tissue 3:
     days since treatment
      3    7    21
A     0    0    0
B     4    4    4


Thanks for any input!
Nathan

-------------------------------------------------------------
Dr. Nathan S. Watson-Haigh
OCE Post Doctoral Fellow
CSIRO Livestock Industries
J M Rendel Laboratory
Rockhampton
QLD 4701                              Tel: +61 (0)7 4923 8121
Australia                             Fax: +61 (0)7 4923 8222