Towards a temporal modeling of the genetic network controlling systemic acquired resistance in Arabidopsis thaliana

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Publisher’s version / Version de l'éditeur:

2010 IEEE Symposium on Computational Intelligence in Bioinformatics and

Computational Biology (CIBCB), pp. 1-8, 2010-05-05

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Towards a temporal modeling of the genetic network controlling

systemic acquired resistance in Arabidopsis thaliana

Tchagang, Alain; Shearer, Heather; Phan, Sieu; Famili, Fazel; Fobert, Pierre;

Pan, Youlian

https://publications-cnrc.canada.ca/fra/droits

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https://nrc-publications.canada.ca/eng/view/object/?id=0a781464-afcc-445b-8641-add274937326 https://publications-cnrc.canada.ca/fra/voir/objet/?id=0a781464-afcc-445b-8641-add274937326

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—We studied defense mechanism of the

subjected to Salicylic Acid (SA) treatment for 0, 1, and 8 hours using a broader application of the frequent itemset approach. Four genotypes of the plant were used in this study, Columbia wild type, mutant , double mutant and triple mutant . We defined the major patterns of transcription regulation governing pathogen defense mechanism, thereby creating a model of the Systemic Acquired Resistance (SAR) at three time points. The temporal model describes the relationships among the regulators and defines groups of genes that are subject to similar regulation. The results obtained offered a first glimpse into the temporal pattern of the gene network controlling SAR in plant. We found that most of the genes that responded to SA challenge are in fact dependent on one or more of the NPR1 and TGA transcription factors tested in this study.

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& # * Arabidopsis ' )*,+A 3

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Towards a Temporal Modeling of the Genetic Network Controlling

Systemic Acquired Resistance in

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" Eq. 1a)% Eq. 1b)

                    = % % 6 % * % % % 6 % * % % 6 % 6 6 % 6 * % 6 % * % * 6 % * * % * M N a m N a N a N a M n a m n a n a n a M a m a a a M a m a a a A * S = {G, C} *( & G = {g(1), g(2), …, g(n), …, g(N)} ! & ! " " C = {c(1), c(2), …, c(m), …, c(M)} ! " % % ! " " a(n,m) ! " " Eq. 1a " ' ! nth %

mth a(n,:) = [a(n,1) a(n,2) … a(n,m) … a(n,M)]

1 J M ' " ' ! g(n)

M a(:,m) = [a(1,m) a(2,m) … a(n,m) …

a(N,m)]T N J 1 ' "

' ! N c(m) mth

B. Gene Expression Data

" & (

!! " Arabidopsis ! 660*1

( ( & $ % npr1% (

tga1 tga4, tga2 tga5 tga6 &

& salicylic acid ! 1% *% 0 %

( ! C % & & 6.*@ & ! " ' F 8 ! % ( & $ ( 8 6 ! " ' ' & $ ' F C " " ( $*% 1% * ! ' δ% & $ % % $ ' ( & $ ' & % ! 6

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≤

δ%

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tga1 tga4% tga2 tga5 tga6

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5- 9 I 3= & ? " ! ! all 1 ( A. Matrix Decomposition ! ! ! " C " " ! ' $*% 1% * ( D1, D0, D1 ? D = 1D1 + 0D0 + 1D1 2 " %             +             +             − =             − − − − = 1 1 1 * * 1 * 1 1 1 1 1 * 1 * 1 1 1 * 1 * * 1 * 1 1 * 1 * 1 1 1 1 1 1 * 1 * * * 1 * * * 1 * 1 1 * 1 * D 6 ! ! ; % ! % & ' ! & ( & % ( ! 2 2 " % D1 * ! & 2 ' ! 2 % D0 * & % 2 ' !! 2 % D1 * % 2 ' & ! % & & D1% D0% D1 % % & ' ' ! 2 NB. & ! 2 ! &

B. All 1 Submatrices Identification

! ! ! all 1 ( ! D1% D0% D1 all 1 ( " Bk = )bij+ ( " ! D1% D0% D1 & * 2 ! ( " & 8 & ! ! ( % ' N$( $M 1%* $ "% ! ( ! *L

& M ; largest & ( "

9 % 8 ! % & all 1 ( " ( all 1 ( ' ( & (H ( ! % ( ! ! all 1 ( ! ( " & ( NP$ & ! ( ( ' )6,+ 9 % & 8 '

! ! & & ! & "

( ! ! ( Eq. 3 uk .* r(n,:) = uk @ N OL & ! & ' 2 " % )1 * *+ O)* 1 *+ K )1 1 *+ & & "

npr1, tga1 tga4, tga2 tga5 tga6% U &

uk ! & ' / K 231

& ' ? U K B)1 1 *+A )1 * 1+A ) 1 * *+A )*1 1+A )* 1 *+A )*

* 1+A )* * *+D ! uk # *% 3 6 3 G 3 6 3 , 3 . ' 2 " uk = )* 1 1+ ! ! ( # * D1% & ( # * D1 ! & # * !! D0 uk K )* * *+ ! ! ( & % ( ! 2 # *% 3 6 3 G 3 6 3 , 3 . D1 D1 ' % ! ! ! 2 # *% 3 6 3 G 3 6 3 , 3 . D0 r(n,:) & ! D1% D0% D1 5 % U ! (

Eq. 2 ' ! ( % i.e. & !

D1% D0% D1% ( ( !

all 1 ( " Bk = )bij+ 2 " % ! & " ! ( ' Eq. 2 % uk = )* 1 *+ &

* G &

* @% (

2 ! % * G * @ !

all 1 ( " & ( '

& * & G ' ! Eq. 3 ( ' ? )* 1 *+ .* r(1,:) = )* 1 *+ )* 1 *+ .* r(4,:) = )* 1 *+% & r(1,:) r(4,:) * G & ! " ' ( ! & ! ! all 1 ( Bk = )bij+ ! D1% D0% D1 ! ! ( U " ( ! all 1 ( ( ! ( "% & / % ' & & ( ( % uk ! U ( ( ! ( ! 1 2M1 M ( % & M ( ! ! ( "

&( 8 ! brute force %

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C. Algorithms Algorithms 1 Algorithm 2 ! " ! ! all 1 ( ' & ' ! all 1 ( " ( ' ? Bk = [bij]% ( ! ? Bk = {Ik, Jk}% & IK ( ! IK

⊆

G % JK ( ! JK

⊆

C % & i

∈

Ik j

∈

Jk k = 1 K% & K " ( ! all 1 ( ( ! ( "? K = 2M1 L% N% M ( ! % & % ! D ' .

1) Algorithm 1: matrix decomposition.

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ : $ D = C " " $ α = [ 1 0 1+ ! ' : $ D1, D0, and D1 = ( & % % & ' , [N,M] = (D);

D1 = zeros(N,M); D0 =zeros(N,M); D1 = zeros(N,M);

n = 1 N m = 1 M D(n,m) == 1 D1(n,m) = 1 D(n,m) == 0 D0(n,m) = 1 D(n,m) == 1 D1(n,m) = 1 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

2) Algorithm 2: All 1 submatrices identification.

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ :

$ D1, D0, and D1 (from Algorithm 1)

$ U = {uk} = ! ( $ C = [c(1) c(2) … c(m) … c(M)] = ! $ G = [g(1) g(2) … g(n) …g(N)]T = ! : $ I = ! all 1 ( $ J = ! all 1 ( Z(:,:,1) = D1; Z(:,:,2) = D0; Z(:,:,3) = D1; [N,M,L] = (Z); I = []; J = []; l = 1 L k = 1 K J{k,l} =C( (b(k) == 1); n = to U(k,:). .* Z(n,:,l) == U(k,:) I{k,l} = [I{k};g(n)]; ! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ D. Complexity Analysis F " ! " ( (NJM) ! all 1 ( ! O((NJM+N+P+PJM) JLJ 2M1)) ( & ! P 2M 1)NJM ( % N % P PLJ 2M 1) 9 % 2M1 " ( ! all 1 ( P ( ! ( Eq. 3 ' ! " ! ( ! P O(NJMJLJ2M) I K @

& & ' ! &

% & 5 K @ "

& ( PO(2613J3J3J 231))=164619 &

% & 5 ( ' % " " 2M & & ! all 1 ( ( ' ? M = 5 25 = 32A M = 7 27 = 128A M = 10 210 = 1024A M = 20 220 = 1048576 Q - I ( ' ( % & ( ! &

A. Potential Transcription Factor Gene Interactions

Fig. 113 & ( ! ( # *% 3 * 3 G% 3 6 3 , 3 . ' !! " ? 1 % * % 0 % ' ( & 2 " % 1 % ,@/ ,01 & ( # * ' 1 R* R0 & ( ! / & 7 ! ! # * !! ! ( # * !! ( ! & ( # * ! ! # * & ! ! 8 !! ! # *% ( ! ( 3 * 3 G ( ! ! % & " & * 2 * # * (

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2 6 3 * 3 G ( 2 @ 3 6 3 , 3 . ( ( ! 3 6 3 , 3 . ! # * ( & # * ( ! ( # * ( 3 6 3 , 3 . 3 * 3 G % ( ! & ( 3 6 3 , 3 . ! 1 * 0 F % ! 1 * ! % ( & ! & ' ( & ! ( ' ! 2 !! ( ' ' ! ' ( ' !! ! !! ! !

B. Similarities and Differences between Transcription Factors

Fig. 417 & ! ( & !

2 !! ? 1 % * % 0 % ' ( & 2 G # * 3 * 3 G ( 2 , # * 3 6 3 , 3 . ( 2 . 3 * 3 G 3 6 3 , 3 . ( 2 / # *% 3 * 3 G% 3 6 3 , 3 . (

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( ! & ( # * 3 * 3 G 2 % ( ! ! % & " * % & ( ( ! ! ! ( ! & ( # * 3 6 3 , 3 . 2 % ! ! % & ( ( ! ! ! I 8 3 * 3 G% ( ! ! ! ( 3 * 3 6 3 6 3 , 3 . ( ! ! % & " & * 2 % ( ! & ( ! 2 # *% 3 6 3 G 3 6 3 , 3 . ( ! ! % & " * % ( ! ! ! 9 % % ( & ! & ' ( & ! ( ! 2 !!

C. Time Varying Transcriptional Network Model

( ( ' % & ( &

! & 8 ! Arabidopsis

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%

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( ' " ' % ▼ ! 8 & % ▼ % ▲ & % ? ( ! 1 ! " % *6* *6, & ' ( ( ! 2 2 % * @@@ */0 & % ' % ( ( ! 2 % & 0 6** *,0 & % ' % ( ( ! 2 ( ! # * ! 3 * 3 G 3 6 3 , 3 . 1 ; 0 % ' & ( ! # * ( 3 * 3 G 3 6 3 , 3 .% ' & ! # * " ( & & ( ! 1 0 ! Fig. 11 # * 3 * 3 G 3 6 3 , 3 . *,0 6** 6@G 6,/ 667 60@ .@1 ,*1 ,6G /1* /6. 0G0 7*, **07 2 *1 & 8 0 # * 3 * 3 G 3 6 3 , 3 . */@ @@@ @61 ,,* 6.6 G6G //1 000 @1. ,*0 .16 0/0 /1/ 007 2 7 & 8 * # * 3 * 3 G 3 6 3 , 3 . *6, *6* 6/, 606 66, 61/ /*G .6, 6*/ 66@ ,0G .17 ,01 ,@/ 2 0 & 8 1

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Fig. 117 & ! & ' ( &

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