Soft Comput (2005) 9: 761–768 DOI 10.1007/s00500-004-0441-0 ORIGINAL PAPER Giuditta Franco · Vincenzo Manca An algorithmic analysis of DNA structure Published online: 28 June 2005 © Springer-Verlag 2005 Abstract Bilinearity, complementarity and antiparallelism of the double stranded DNA structure are proved, in a general and abstract setting, as requirements of an efficient duplica- tion algorithm for ‘mobile strings’. Keywords DNA structure · Strings · Duplication Algorithms · DNA Computing · Molecular Computing 1 Introduction DNA molecules have a structure that satisfies three basic principles: (1) they are constituted of two strings; (2) each symbol of the first string corresponds to its ‘complementary’ in the second string; (3) these strings have opposite directions [3]. These three principles are usually referred as: bilinear- ity, complementarity and antiparallelism. In this paper we show that they depend on a ‘deep’ logic that is dictated by the informational and computational aspects of duplication algorithms. In other words, if one wants to design an efficient duplication system for strings (finite sequences of symbols) represented as mobile polymers (floating in a fluid environ- ment), then one needs symbol molecules asymmetric with respect to the three space directions [2] and arranged accord- ing to the three principles mentioned above. This abstract and information-based logic underlying DNA structure seems to be paradigmatic in suggesting a general perspective of investigation, where computational aspects of- fer research inspirations both to biology and to computer sci- ence [1, 5]. G. Franco · V. Manca (B ) Dipartimento di Informatica, Universit` a di Verona, Strada Le Grazie, 15, 37134 Verona, Italia Tel.: +39-045-8027981 Fax: +39-045-8027068 E-mail: franco@sci.univr.it, vincenzo.manca@univr.it Present address: V. Manca Dipartimento di Informatica, Ca’Vignal 2, Strada Le Grazie 15, 37134 Verona, Italia The present investigation seems to be connected in a natu- ral way with P systems area [6]. In fact, floating strings, com- partments and multisets are basic ingredients in the analysis here developed, and, in the context of P systems, duplica- tion algorithms are important in solving NP-complete prob- lems [6]. Moreover, a deep connection between string duplication and membrane duplication seems to be implicit in the pro- cess on which nature replication is based (e.g. in the mitosis process a somatic cell is replicated by means of the DNA string duplication inside the nucleus). 2 String duplication algorithms In the following we refer to [7] for basic notions and notations of Formal Language Theory. Given a string α we consider the problem of duplicat- ing it and distinguish three different methods based on: (1) transposition, (2) dissolution, (3) pairing. 2.1 Duplication by transposition (TDA) With the TDA (transposition duplication algorithm) the lin- ear structure is preserved and each symbol is equipped with a ‘shadow’ copy near it; after that, shadows are moved all together to one side of the structure by keeping their rela- tive positions, so that a shadow copy of the whole original string is obtained whence a copy of the original string can be recovered. This algorithm can be easily represented by the following set of replacing rules, where {a,b} is the (terminal) alphabet of the string α that has to be duplicated, i, j ∈{a,b} and the other symbols are auxiliary (nonterminal) symbols. 1. α → SαS ′ 2. Si → X i Y i S 3. SiS ′ → X i ′ Y i ′ 4. Y i X j → X j Y i