Engineering bacteria to solve the Burnt Pancake Problem

<p>Abstract</p> <p>Background</p> <p>We investigated the possibility of executing DNA-based computation in living cells by engineering <it>Escherichia coli </it>to address a classic mathematical puzzle called the Burnt Pancake Problem (BPP). The BPP is solved by sorting a stack of distinct objects (pancakes) into proper order and orientation using the minimum number of manipulations. Each manipulation reverses the order and orientation of one or more adjacent objects in the stack. We have designed a system that uses site-specific DNA recombination to mediate inversions of genetic elements that represent pancakes within plasmid DNA.</p> <p>Results</p> <p>Inversions (or "flips") of the DNA fragment pancakes are driven by the <it>Salmonella typhimurium </it>Hin/<it>hix </it>DNA recombinase system that we reconstituted as a collection of modular genetic elements for use in <it>E. coli</it>. Our system sorts DNA segments by inversions to produce different permutations of a promoter and a tetracycline resistance coding region; <it>E. coli </it>cells become antibiotic resistant when the segments are properly sorted. Hin recombinase can mediate all possible inversion operations on adjacent flippable DNA fragments. Mathematical modeling predicts that the system reaches equilibrium after very few flips, where equal numbers of permutations are randomly sorted and unsorted. Semiquantitative PCR analysis of <it>in vivo </it>flipping suggests that inversion products accumulate on a time scale of hours or days rather than minutes.</p> <p>Conclusion</p> <p>The Hin/<it>hix </it>system is a proof-of-concept demonstration of <it>in vivo </it>computation with the potential to be scaled up to accommodate larger and more challenging problems. Hin/<it>hix </it>may provide a flexible new tool for manipulating transgenic DNA <it>in vivo</it>.</p