BioSystems 94 (2008) 95–101 Contents lists available at ScienceDirect BioSystems journal homepage: www.elsevier.com/locate/biosystems A cell pattern generation model based on an extended artificial regulatory network Arturo Chavoya a,c,∗ , Yves Duthen b,c a Universidad de Guadalajara, Periférico Norte 799, Zapopan, Jal., CP 45000, Mexico b Université de Toulouse 1, 1 Place Anatole France, 31000 Toulouse, France c Institut de Recherche en Informatique de Toulouse (IRIT), VORTEX Team, 118 Route de Narbonne, 31062 Toulouse, France article info Article history: Received 7 May 2007 Received in revised form 30 October 2007 Accepted 23 May 2008 Keywords: Cell pattern Artificial regulatory network Genetic algorithms French flag problem Cellular automata abstract Cell pattern generation has a fundamental role in both artificial and natural development. This paper presents results from a model in which a genetic algorithm (GA) was used to evolve an artificial regula- tory network (ARN) to produce predefined 2D cell patterns through the selective activation and inhibition of genes. The ARN used in this work is an extension of a model previously used to create simple geo- metrical patterns. The GA worked by evolving the gene regulatory network that was used to control cell reproduction, which took place in a testbed based on cellular automata (CA). After the final chromosomes were produced, a single cell in the middle of the CA lattice was allowed to replicate controlled by the ARN found by the GA, until the desired cell pattern was formed. The model was applied to the problem of generating a French flag pattern. © 2008 Elsevier Ireland Ltd. All rights reserved. 1. Introduction Computational Development is a relatively new sub-field of Evolutionary Computation that studies artificial models of cel- lular growth, with the objective of understanding how complex structures and patterns can emerge from a small group of initial undifferentiated cells (Kumar and Bentley, 2003). In biological sys- tems, development is a fascinating and very complex process that involves following an extremely intricate program coded in the organism’s genome. One of the crucial stages in the development of an organism is that of pattern formation, where the fundamental body plans of the individual are delineated. It is now evident that gene regulatory networks play a central role in the development and metabolism of living organisms (Davidson, 2006). Furthermore, it has been found in recent years that the different cell patterns created during the development of an organism are mainly due to the selective acti- vation and inhibition of very specific regulatory genes. Artificial regulatory networks (ARNs) are computer models whose objective is to mimic to some extent the gene regulatory networks found in nature. ARNs have previously been used to study ∗ Corresponding author at: Universidad de Guadalajara, Periférico Norte 799, Zapopan, Jal., Mexico CP 45000, Mexico. E-mail addresses: achavoya@cucea.udg.mx (A. Chavoya), yves.duthen@univ-tlse1.fr (Y. Duthen). differential gene expression either as a computational paradigm or to solve particular problems (Eggenberger, 1997; Reil, 1999; Banzhaf, 2003; Kuo and Banzhaf, 2004; Stewart et al., 2005; Flann et al., 2005). On the other hand, evolutionary computation tech- niques have been extensively used in the past in a wide range of applications, and in particular they have previously been used to evolve ARNs to perform specific tasks (Bongard, 2002; Kuo et al., 2004). In this paper we describe results on the use of a genetic algo- rithm (GA) to evolve an ARN in order to create predefined 2D patterns by means of the selective activation and inhibition of genes. The ARN used in this work is an extension of the model devel- oped by Banzhaf (2003). We decided to extend the model because in previous work we ran into limits in the number of regulatory genes that could be reliably synchronized under the conditions essayed (Chavoya and Duthen, 2007). In order to test the functionality of the ARN found by the GA, we applied the chromosomes represent- ing the ARN to a cellular growth model that we have successfully used in the past to develop simple 2D and 3D geometrical shapes (Chavoya and Duthen, 2006b). The paper starts with a section describing the French flag prob- lem with a brief description of models that have used it as a test case. The next section describes the cellular growth testbed devel- oped to evaluate the evolved ARNs, followed by a section presenting the ARN model and how it was implemented. The following section describes the GA used and how it was applied to evolve the ARN. Results are presented next, followed by a section of conclusions. 0303-2647/$ – see front matter © 2008 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2008.05.015