Reverse Engineering of Regulatory Networks Ka-Lok Ng Department of Bioinformatics Asia University

Contents Introduction – Gene regulatory network (GRN) The steady-state approach - time-series model

Introduction – Gene regulatory network (GRN) One gene can affect the expression of another gene by binding of the gene product of one gene to the promoter region of another gene > 2 genes, we refer to the regulatory network as the regulatory interactions between the genes Given a larger number measurements of the expression levels of a number of genes, we should be able to model or reverse engineer the regulatory network that controls their expression level. 2 approaches  the time-series and steady-state approaches

The time-series approach Expression level of a gene at a certain time point x j (t) can be modeled as some function of the expression levels of all other genes at all previous time points x i (t-1), where i may or may not equal j, if i = j that means self regulate where r i,j is a weight factor representing how gene i affects gene j, that is, i  j (activate) or i -| j (inhibit), positively or negatively Problem ! Many more genes > number of time points Suppose there are g genes  g 2 possible connections among them (for instance, g = 4  16 possibilities, including self-regulation) There are g(g+1)/2 possible interactions It is called one has a dimensionality problem A possible solution is cluster the genes that have similar behavior into gene clusters

The time-series approach Example At t =0, gene c is induced, at t = 1,2,3,4 we follow the expression level of gene c and three other genes, a, b and d Deduce a GRN from the time-series data (5 time points). gene c ↑, but genes (a, b, d) ↓ gene c represses gene a ? Gene\time a00 b000 c01111 d0000 a b c d -1, 0, 1  inhibit, no interaction, activate

The time-series approach Gene\time01234 a00 b000 c01111 d genes  16 possible regulation relations Consider the system of equation governing the regulation of gene a 4 equations, 4 unknowns r i,j = -1, 0, 1  inhibit, no interaction, activate

The time-series approach Gene\time01234 a00 b000 c01111 d0000

The time-series approach Gene\time01234 a00 B000 C01111 d0000

The time-series approach Gene\time01234 a00 B000 C01111 d0000 gene\gene abcd a + b + c -+ d Interaction matrix between four genes

Reference Knudsen S. (2002). A biologist’s guide to analysis of data microarray data. J. Wiley