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DON'T PUT A COMMENT ! -- Inferring Gene Regulation Networks From Microarray Expression Data :: ----- this is a comment ---------------------------------------------------- Gene Regulation Networks§Deduce patterns of gene regulation from measured expression data. :: --- Inference Techniques Boolean networks Mutual information Linear networks Neural Networks Review and taxonomy: Wessels et al. :: --- Boolean networks Ideker et al. Represent gene levels and stimuli as on or off Very simple biological model, simple computational approach Boolean formula True 1, False 0, and, or, not 1 and 0 = 0 1 and 1 = 1 1 or 0 = 1 1 or 1 = 1 not 0 = 1, not 1 = 0 Boolean network A set of nodes, edges, and boolean formulas See Ideker Figure 1 !iboolean.png :: --- Expression Matrix For a set of genes and a set of perturbation experiments construct an expression matrix as in Figure 2 !iematrix.png :: --- Inference Procedures From the expression matrix, the Predictor generates (possibly several) network hypothesis The Chooser selects a new perturbation experiment, that would best discriminate between available hypotheses. :: --- Predictor Look at all pairs of experiments where a given gene differs except where it is forced (-, +). Build a multiset of all other genes that also changed between those rows. Construct the hitting set, the smallest set of elements such that there is a member of each subset. Generate the boolean functions by inspection of the members of the hitting set. :: -- The Predictor in action x0 - no changes x1 - no changes x2 - row pairs, set (0,1) {x0, x3} (0,2) {x1} (1,4) {x0} (2,4) {x1, x3} hitting set Smin = {x0, x1} x3 - see paper :: --- Generating the boolean functions The truth table for x2 can be generated by looking at the values seen for the members of Smin !itruth.png The '*' represents an unknown value (x0 and x1 are never 0 in the same experiment) :: --- Mutual information Reveal (Liang et al) Find combinations of genes that account for a change in state Can be extended to more than two states Slightly more realistic model, well-studied computational approach :: --- Shannon Entropy !ishannon.png X(i) = 0 1 1 1 1 1 1 0 0 0 Y(j) = 0 0 0 1 1 0 0 1 1 1 H(X) = - 4/10 log 4/10 - 6/10 log 6/10 = 0.97 H(Y) = - 5/10 log 5/20 - 5/10 log 5/10 = 1 :: --- Combined Entropy !icombined.png For each possible pair of i,j count the occurence in X,Y X 0111111000 Y 0001100111 !ifreq.png H(X,Y) = - 3/10 log 3/10 - 2/10 log 2/10 - 1/10 log 1/10 - 4/10 log 4/10 = 1.85 :: --- Mutual Information Also called rate of transmission M(X,Y) = H(X) + H(Y) - H(X,Y) M(X,Y) = 0.97 + 1 - 1.85 = 0.12 Can be generalized M(X,{A,B,C,...,N}) :: --- REVEAL Expression Model See Figure 1 !ireveal1.png :: --- Expression table Letters (columns) represent genes each row is a separate condition input and output are two time points A and A' are the same gene at two time points :: --- REVEAL For each output gene G' and each subset of input genes S if M(G',S)/H(G') = 1 then S determines G' From each link, the boolean function can be inferred by inspection :: --- Inferring the B' Rule See Figure 5 !ireveal5.png :: --- Linear networks D'Haeseleer, Wen, Fuhrman, Somogyi Expression level is a linear combination of input levels Expression levels are real numbers :: --- Nonlinear networks S Kim et al (Genomics) Nonlinear perceptrons (neural networks) Expression is an arbitrary function of inputs (thresholding) Expression levels are -1, 0, or 1 :: --- Training a perceptron See Smith (online) !ilinear.gif :: --- References Pacific Symposium on Biocomputing !hhttp://psb.stanford.edu/psb-online/ A Comparison of Genetic Network Models, L.F.A. Wessels, E.P. Van Someren, and M.J.T. Reinders; Pacific Symposium on Biocomputing 6:508-519 (2001). Discovery of Regulatory Interactions Through Perturbation: Inference and Experimental Design, T.E. Ideker, V. Thorsson, and R.M. Karp; Pacific Symposium on Biocomputing 5:302-313 (2000). Linear Modeling of mRNA Expression Levels During CNS Development and Injury, P. D'haeseleer, X. Wen, S. Fuhrman, and R. Somogyi; Pacific Symposium on Biocomputing 4:41-52 (1999). REVEAL, A General Reverse Engineering Algorithm for Inference of GeneticNetwork Architectures, S. Liang, S. Fuhrman and R. Somogyi; Pacific Symposium on Biocomputing 3:18-29 (1998). Kim S, Dougherty ER, Bittner ML, Chen Y, Sivakumar K, Meltzer P, Trent JM., General nonlinear framework for the analysis of gene interaction via multivariate expression arrays. J Biomed Opt. 2000 Oct;5(4):411-24. Kim S, Dougherty ER, Chen Y, Sivakumar K, Meltzer P, Trent JM, Bittner M. Multivariate measurement of gene expression relationships. Genomics. 2000 Jul 15;67(2):201-9. An Introduction to Neural Networks, Dr. Leslie Smith, Centre for Cognitive and Computational Neuroscience, Department of Computing and Mathematics, University of Stirling. !hhttp://www.cs.stir.ac.uk/~lss/NNIntro/InvSlides.html