Universal and simple operations for gene assembly in ciliates Andrzej Ehrenfeucht * Ion Petre † David M. Prescott ‡ Grzegorz Rozenberg §* Abstract The way that ciliates transform genes from their micronuclear to the macronuclear form is very interesting (and unique), also from a computational point of view. In this paper, we describe the model of gene assembly in ciliates presented in [2], [3], and [4]. Moreover, we prove that the set of three operations underlying this model is universal, in the sense that it suffices for gene assembly from any micronuclear pattern. We also prove that the set of simple versions of these operations is not universal – this fact is interesting from the experimental point of view. 1 Introduction DNA computing, initiated by L. Adleman in [1], is a fast growing interdisciplinary research area (see, e.g., [7]). The research in this area includes both DNA computing in vitro and DNA computing in vivo. Within the area of DNA computing in vivo, one investigates (the use of) living cells as computational agents. To this aim, one studies the computational aspects of DNA processing in living cells. A series of papers by L. Landweber and L. Kari (see, e.g., [5] and [6]) has brought to the attention of DNA computing community the computational power of DNA processing taking place in ciliates. Ciliates are a very ancient group of organisms (their origin is estimated at about 2 × 10 9 years ago). It is a very rich group which comprises about 10000 genetically different organisms. A very interesting feature of ciliates is the nuclear dualism. A ciliate contains two kinds of nuclei: a germline nucleus (micronucleus) that is used in cell mating, and a somatic nucleus (macronucleus) that provides RNA transcripts to operate the cell. The DNA in the micronucleus is hundreds of kilobase pairs long with genes occurring individually or in groups dispersed along the DNA molecule, separated by long stretches of spacer DNA. The DNA molecules in the macronucleus are gene-size, on average about 2000 base-pairs long. As a matter of fact, a macronucleus results from a micronucleus, through an intricate transformation process. This process turns out to be fascinating (see, e.g, [8] and [9]), also from the computational point of view. In this paper, we present a model of this process, described in [2], [3], and [4]. We also prove that the set of three operations underlying this model is universal, in the sense that it suffices for gene assembly from any micronuclear pattern. Moreover, we prove that the set of simple versions of these operations is not * University of Colorado, Department of Computer Science, Boulder CO 80309-0347 USA, email:andrzej@cs.colorado.edu † Turku Centre for Computer Science and Department of Mathematics, University of Turku, FIN 20520, Finland, email:ipetre@cs.utu.fi ‡ University of Colorado, Department of Molecular, Cellular and Developmental Biology, Boulder CO 80309-0347 USA, email:prescotd@spot.colorado.edu § Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands, email:rozenber@liacs.nl 1