[BioC] Loop design - biological, technical replication and contrasts

[Maciej Jończyk]

Dear list Members.

I'd like to ask for advice.

I have 2x2 factorial experiment conducted in a loop-design (two-colour
data).
There are two maize lines (dh7, dl3) and two temperature treatments
(cold=c and control=k).
Following hybridizations were conducted : dh_c vs dh_k; dh_k vs dl_k;
dl_k vs dl_c; dl_c vs dh_c (forming a square on a diagram)
and two (diagonal on a diagram), namely: dl_k vs dh_c and dh_k vs dl_c.
I have four biological replications of this design, including dye-swap
(i.e. two hyb. cy3-cy5 and two cy5-cy3).
In each biological replication I have also three technical replications
of each RNA source
(i.e. in dh_c vs dh_k; dl_c vs dh_c and dl_k vs dh_c, sample dh_c is
from the same RNA pool).

I don't know how analyse it in limma. I want to get following contrasts:
dh_c vs dh_k; dh_k vs dl_k; dl_k vs dl_c; dl_c vs dh_c and include
effect of temperature,
maize line and interaction.

My targets frame is:

   SlideNumber                   FileName     Cy3     Cy5
1           93  c_093_DH_K_vs_DH_CHex.gpr dh7_k_1 dh7_c_1
2          104  c_104_DH_CH_vs_DH_Kex.gpr dh7_c_2 dh7_k_2
3          116    c_116_DHK_vs_DHCHex.gpr dh7_k_3 dh7_c_3
4           16   c_016_DH_C_vs_DH_Kex.gpr dh7_c_4 dh7_k_4
5           94   c_094_DH_K_vs_DL_Kex.gpr dh7_k_1 dl3_k_1
6          105   c_105_DL_K_vs_DH_Kex.gpr dl3_k_2 dh7_k_2
7          117     c_117_DHK_vs_DLKex.gpr dh7_k_3 dl3_k_3
8          139   c_139_DL_K_vs_DH_Kex.gpr dl3_k_4 dh7_k_4
9           92  c_092_DL_CH_vs_DL_Kex.gpr dl3_c_1 dl3_k_1
10         106  c_106_DL_K_vs_DL_CHex.gpr dl3_k_2 dl3_c_2
11         118    c_118_DLCH_vs_DLKex.gpr dl3_c_3 dl3_k_3
12          23   c_023_DL_K_vs_DL_Cex.gpr dl3_k_4 dl3_c_4
13          95 c_095_DL_CH_vs_DH_CHex.gpr dl3_c_1 dh7_c_1
14         107 c_107_DH_CH_vs_DL_CHex.gpr dh7_c_2 dl3_c_2
15         119   c_119_DLCH_vs_DHCHex.gpr dl3_c_3 dh7_c_3
16         136   c_136_DH_C_vs_DL_Cex.gpr dh7_c_4 dl3_c_4
17         101  c_101_DL_K_vs_DH_CHex.gpr dl3_k_1 dh7_c_1
18         103  c_103_DH_CH_vs_DL_Kex.gpr dh7_c_2 dl3_k_2
19         121    c_121_DLK_vs_DHCHex.gpr dl3_k_3 dh7_c_3
20          15   c_015_DH_C_vs_DL_Kex.gpr dh7_c_4 dl3_k_4
21         100  c_100_DH_K_vs_DL_CHex.gpr dh7_k_1 dl3_c_1
22         102  c_102_DL_CH_vs_DH_Kex.gpr dl3_c_2 dh7_k_2
23         120    c_120_DHK_vs_DLCHex.gpr dh7_k_3 dl3_c_3
24         140   c_140_DL_C_vs_DH_Kex.gpr dl3_c_4 dh7_k_4

In "Cy3" and "Cy5" columns last number denotes biological replication.

I've read in limma documentation, that this desing can be analysed using
single channel analysis.
So I created following contrast matrix:

FileName			dye	dhc	dhk	dlc
c_093_DH_K_vs_DH_CHex.gpr	1	-1	1	0
c_104_DH_CH_vs_DH_Kex.gpr	1	1	-1	0
c_116_DHK_vs_DHCHex.gpr		1	-1	1	0
c_016_DH_C_vs_DH_Kex.gpr	1	1	-1	0
c_094_DH_K_vs_DL_Kex.gpr	1	0	1	0
c_105_DL_K_vs_DH_Kex.gpr	1	0	-1	0
c_117_DHK_vs_DLKex.gpr		1	0	1	0
c_139_DL_K_vs_DH_Kex.gpr	1	0	-1	0
c_092_DL_CH_vs_DL_Kex.gpr	1	0	0	1
c_106_DL_K_vs_DL_CHex.gpr	1	0	0	-1
c_118_DLCH_vs_DLKex.gpr		1	0	0	1
c_023_DL_K_vs_DL_Cex.gpr	1	0	0	-1
c_095_DL_CH_vs_DH_CHex.gpr	1	-1	0	1
c_107_DH_CH_vs_DL_CHex.gpr	1	1	0	-1
c_119_DLCH_vs_DHCHex.gpr	1	-1	0	1
c_136_DH_C_vs_DL_Cex.gpr	1	1	0	-1
c_101_DL_K_vs_DH_CHex.gpr	1	-1	0	0
c_103_DH_CH_vs_DL_Kex.gpr	1	1	0	0
c_121_DLK_vs_DHCHex.gpr		1	-1	0	0
c_015_DH_C_vs_DL_Kex.gpr	1	1	0	0
c_100_DH_K_vs_DL_CHex.gpr	1	0	1	-1
c_102_DL_CH_vs_DH_Kex.gpr	1	0	-1	1
c_120_DHK_vs_DLCHex.gpr		1	0	1	-1
c_140_DL_C_vs_DH_Kex.gpr	1	0	-1	1

As a reference sample I choosen "dlk", I've included also dye effect.
Now, I don't know how can I include information about technical
replication.
I assume that if I don't do it, it will be treated as biological
replication.
I read about command "duplicateCorrelation" is it the right one to deal
with these problem?

I also have problem in contrasts definition.
Is it simply dhc-dhk, dhk-dlk, dlk-dlc, dlc-dhc
and for main effect (maize line): (dhc+dhk-dlc-dlk)/4;
for effect of temperature (dhc+dlc-dhk-dlk)/4
and for interaction (dhc-dlc)-(dhk-dlk)?

Thank You in advance for help.
Yours sincerely

Maciej Jończyk
Department of Plant Molecular Ecophysiology
Institute of Plant Experimental Biology
Faculty of Biology, University of Warsaw
02-096 Warszawa, Miecznikowa 1



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