In this paper we propose a universal rewriting system whose computational steps closely resemble the manner in which nature computes double stranded DNA molecules. The basic data structure is given by a couple of strings paired by a complementarity relation (such as the Watson–Crick one), and the rewriting rules have a biotechnological implementation as DNA computing standard procedures. The antiparallel orientation of the formal strings laying on the double structure is taken into consideration, as in [G. Franco, V. Manca, An algorithmic analysis of DNA structure, Soft Computing–A Fusion of Foundations, Methodologies and Applications 9 (10) (2005) 761–768] it was shown to be essential for some informational and computational aspects underlying the DNA autoduplication process. The universality of such a system has been proved and the biotechnological details of a possible implementation have been outlined. Moreover, the membrane system which turned out to be the natural context to describe our system in [G. Franco, M. Margenstern, Computing by Floating Strings, in: N. Busi, C. Zandron (Eds.), Proceedings of the First Workshop on Membrane Computing and Biologically Inspired Process Calculi (MeCBIC 2006), July 9, S. Servolo, Venice, Italy, in: ENTCS, vol. 171(issue 2), July 2007, pp. 95–104] has been proposed here in more technical detail, and the announced extension work has been developed.