### A Reconstruction Algorithm from Expression Data for Sparse Noninteracting Gene Networks

Ilaria Mogno^{1}, Lorenzo Farina^{2}, Salvatore Monaco

^{1}mogno@dis.uniroma1.it, DIS, Universita di Roma La Sapienza; ^{2}lorenzo.farina@uniroma1.it, DIS, Universita di Roma La Sapienza

Reconstructing gene networks from expression data is one of the most challenging problems recently arising in Molecular Biology. Anyway, once a mathematical formulation is obtained, the problem of reconstructing a network from experimental data is a standard issue in the Systems and Control Theory; we therefore propose a methodology, which, given expression data coming from microarray experiments, allows us to reverse engineer and to deduce some information about the gene network topology and structure. Assuming some common biological knowledge, we consider the simplest significant model: we assume gene networks dynamics to be generated by a LTI system (continuous-time, linear, time invariant, finite dimensional system). This simple, but far from trivial case, is used to generate artificial data for the reconstructing algorithm (thus allowing us to evaluate algorithm performance). Moreover, we deal with the problem of reconstructing gene networks in the typical practical situation in which the number of available data is largely insufficient to uniquely determine the network. In order to try to remove this ambiguity, we will exploit some additional biologically relevant a priori assumptions, such as sparseness (each gene interacts with only a small percentage of all the genes in the entire genome). We will also refer to non interacting gene networks, i.e. we will assume that the overall gene network is composed of smaller subnetworks, such that the genes involved in more than one of such subnetworks is a very small percentage of the total number of genes. Moreover, any source of noise is neglected, thus allowing us to concentrate only on the basic problem of reconstructing "large" networks with a "small" amount of available data. Finally, algorithm performance is tested on artificial data.