Two models for gene assembly in ciliates Tero Harju 1,3 , Ion Petre 2,3 , and Grzegorz Rozenberg 4 1 Department of Mathematics, University of Turku Turku 20014 Finland harju@utu.fi 2 Department of Computer Science, ˚ Abo Akademi University Turku 20520 Finland ipetre@abo.fi 3 Turku Centre for Computer Science Turku 20520 Finland 4 Leiden Institute for Advanced Computer Science, Leiden University Niels Bohrweg 1, 2333 CA Leiden, the Netherlands, and Department of Computer Science, University of Colorado at Boulder Boulder, Co 80309-0347, USA rozenber@liacs.nl Abstract. Two models for gene assembly in ciliates have been proposed and investigated in the last few years. The DNA manipulations postu- lated in the two models are very different: one model is intramolecular – a single DNA molecule is involved here, folding on itself according to various patterns, while the other is intermolecular – two DNA molecules may be involved here, hybridizing with each other. Consequently, the assembly strategies predicted by the two models are completely differ- ent. Interestingly however, the final result of the assembly (including the assembled gene) is always the same. We compare in this paper the two models for gene assembly, formalizing both in terms of pointer reductions. We also discuss invariants and universality results for both models. 1 Introduction Ciliates are unicellular eukaryotic organisms, see, e.g. [23]. This is an ancient group of organisms, estimated to have originated around two billion years ago. It is also a very diverse group – some 8000 species are currently known and many others are likely to exist. Their diversity can be appreciated by comparing their genomic sequences: some ciliate types differ genetically more than humans differ from fruit flies! Two characteristics unify ciliates as a single group: the possession of hairlike cilia used for motility and food capture, and the presence of two kinds of functionally different nuclei in the same cell, a micronucleus and a macronucleus, see [15], [24], [25]; the latter feature is unique to ciliates. The macronucleus is the “household” nucleus – all RNA transcripts are produced in the macronucleus. The micronucleus is a germline nucleus and has no known function in the growth or in the division of the cell. The micronucleus is activated only in the process of sexual reproduction, where at some stage the micronuclear 1