DNA Computing Based on Splicing: The Existence of Universal Computers

Abstract.

We prove that splicing systems with finite components and certain controls on their work are computationally complete (they can simulate any Turing Machine); moreover, there are universal splicing systems (systems with all components fixed which can simulate any given splicing system, when an encoding of the particular system is added—as a program—to the universal system).

Splicing systems are based on the splicing operation which is a model for DNA recombination. Informally, a prefix of a word is catenated to a suffix of another word, thus yielding a (possibly) new word. Cutting occurs at specific sites which correspond to specific sequences in DNA strands as they can be recognized by restriction enzymes.

When no additional control is assumed, splicing systems with finitely many starting words (axioms) and finitely many splicing rules are known to characterize only regular languages (those recognized by finite automata ). However, when a splicing rule is allowed to be used

(1)\hskip .5em only in the presence of certain symbols (``catalyst'') or

(2)\hskip .5em only in the absence of certain symbols (``inhibitors''),

then we can characterize the recursively enumerable languages (recognized by Turing Machines ); the same result is obtained when counting the number of copies of (some of) the words used. From the proofs, we also infer the existence of universal (hence programmable) splicing systems.