Finding the Minimal Gene Regulatory Function in the Presence of Undefined Transitional States Using a Genetic Algorithm Rocio Chavez-Alvarez, Arturo Chavoya ⋆ , and Cuauhtemoc Lopez-Martin Department of Information Systems, Universidad de Guadalajara, Periferico Norte 799-L308, Zapopan, Jal., Mexico 45100 {rociochavezmx,achavoya,cuauhtemoc}@cucea.udg.mx http://www.cucea.udg.mx Abstract. After the sequencing of whole genomes and the identification of the genes contained in them, one of the main challenges remaining is to understand the mechanisms that regulate the expression of genes within the genome in order to gain knowledge about structural, biochem- ical, physiological and behavioral characteristics of organisms. Some of these mechanisms are controlled by so-called Genetic Regulatory Net- works (GRNs). Boolean networks can help model biological GRNs. In this paper, a genetic algorithm is used to make inferences in Boolean networks, in combination with the Quine-McCluskey algorithm, when not all the output states of the genes have been determined. This lack of information could be treated as “don’t care” states. Genetic algorithms are useful in multi-objective optimization problems, such as minimiza- tion of Gene Regulatory Functions, where it is important not only to have the smallest quantity of disjunctions, but also the smallest quantity of genes involved in the regulation. Keywords: Genetic regulatory networks, Boolean networks, Don’t care states, Genetic algorithm, Quine-McCluskey algorithm. 1 Introduction In order to discover the mechanisms that regulate gene expression in Genetic Regulatory Networks (GRNs), it is necessary to know how genes are intercon- nected and the kind of influence they have on each other. In GRNs, genes can be translated into proteins through messenger RNA (mRNA) molecules. These proteins can activate or inhibit the expression of other genes by binding to reg- ulatory regions present near the genes [1]. This means that the expression of regulated genes can be detected by the existence or the absence of the mRNA produced by regulatory genes. This mRNA can be quantified by oligonucleotide microarray chips. These chips are able to generate large amounts of data stored in databases containing the quantities of mRNA strands that are being pro- duced simultaneously by thousands of genes [2]. An example of these databases ⋆ Corresponding author. M.A. Lones et al. (Eds.): IPCAT 2012, LNCS 7223, pp. 238–249, 2012. c  Springer-Verlag Berlin Heidelberg 2012