Davidson Missouri W/Solving the HPP in vivo

In 1994 Adleman developed a system to solve the Hamiltonian Path problem using DNA in vitro. We have implemented a bacterial system to solve Hamiltonian Path problems in vivo.

Overview

Our bacterial computer works by taking advantage of the Hin Recombinase protein and HixC sites to perform a "flipping" operation. By strategically placing HixC sites on a plasmid, along with reporter genes, we can simulate paths on a graph through flipping.

The Hin Recombinase/HixC System Revisited

Salmonella typhimurium is a bacterium which moves using flagella. Depending on its environment, it expresses different sets of surface proteins on its flagella. It is able to change this expression through the use of Hin Recombinase and Hix sites. The Hin Recombinase enzyme catalyzes the inversion of DNA that lies between a pair of Hix sites. By flipping DNA segments between Hix sites S. typhimurium can express alternate flagellar surface proteins.

Flipping Pancakes

In the 2006 iGEM competition, Davidson and Missouri Western used the Hix Recombinase/HixC to model a mathematical problem, called the Pancake Flipping problem. The problem is the following: given a stack of pancakes which are burnt on one side and golden on the other, and two spatulas, what is the minimum number of flips required to sort the stack by pancake size and with all burnt sides facing downwards?

The Hamiltonian Path Problem

Using the same flipping mechanism, we are trying to develop a bacterial computer which solves a new type of mathematical problem. Given a graph, a starting point, and an endpoint, is there a Hamiltonian path?

What is it?

A Hamiltonian Path is a trip through a graph which visits each node exactly once. A graph may have multiple Hamiltonian Paths, only one, or even none.