# Complex Systems and Computing

– Molecular Computing

Molecular computing is based on aspects of recombination in molecular biology. Modelling of recombination processes is part of DNA computing which is a novel area at the crossroad of mathematics, computer science and molecular biology. Mathematical problems in DNA based computing were initiated by Tom Head in automata theory (1987) when he introduced the splicing systems as a model for genetic recombination. This problem area was made more widely known by Leonard Adleman (1994) using a more computationally oriented approach.

Our research team has concentrated mostly in combinatorial modelling of biologically motivated operations. The main problem proposed by T. Head on the regularity of splicing systems was solved positively by T. Harju and K. Culik (U. South Carolina) in 1991:

- K. Culik, T. Harju. Splicing semigroups of dominoes and DNA. Discrete Applied Mathematics 31, 261-277, 1991.

This result is often mentioned as one of the pioneering studies in DNA computing. Together with research teams in Abo Akademi University (I. Petre), U. Leiden (G. Rozenberg) and U. Colorado at Boulder (A. Ehrenfeucht, D.M. Prescott), we have worked on modelling molecular recombination operations using combinatorial and computational tools. These operations are motivated by the acrobatic genetic reassembly processes that happen in unicellular organisms called Stichotrichs ciliates. The reassembling process transforms a defragmented and shuffled inactive micronuclear genome to a functional macronuclear genome of the expressible genes. The mathematical tools for this modelling process include permutations, strings and graphs. The following book is devoted to this topic:

- A. Ehrenfeucht, T. Harju, I. Petre D. Prescott and G. Rozenberg. "Computation in Living Cells". (Springer-Verlag, 2004)

See also, Computational Biomodelling Laboratory.