After graduating from Boston University, I had the opportunity to participate in the International Genetically Engineered Machines (iGEM) competition on the BU-Wellesley team under the guidance of Professor Doug Densmore. For this project, our group developed a suite of software tools that take synthetic biologists through the entire design process, from researching different genes to automating assembly protocols on a liquid handling robot. I co-presented this work at the regional jamboree, and at the World Jamboree we received the 2011 Best Software Tool Award.

One of the focuses of this project was to develop fully permutable plasmids, called permutons, using a class of recombinases known as invertases, which invert the region of DNA between sequence specific recognition sites. For my contribution to this project, I developed two different methods of placing these recognition sites around *n* DNA components such that all *n!* permutations of these components can be achieved by applying the correct sequence of invertases. For each method, I developed two algorithms: a design algorithm that places the invertase sites relative to the DNA components and a key generating algorithm that takes in a specific permutation and returns the series of invertases, i.e. the invertase key, required to achieve that permutation. Below is an example illustrating the layout of a three-component permuton as it achieves the permutation 3-2-1, starting from the original permutation 1-2-3. The three DNA components are represented by their respective numbers and the pairs of invertase sites are depicted as rightwards and leftwards facing triangles connected to one another.

This particular type of permuton achieves any single permutation in under 2n-1 inversions but suffers from an invertase site complexity of O(n^{3}). Interestingly, the second type of permuton design achieves any single permutation in under 3n-3 inversions and has a site complexity of O(n^{2}), demonstrating the tradeoff between permuton complexity and key length. To try out these algorithms, visit http://permuton.synbiotools.org. To learn more about this software, plese refer to our supplementary material.

Bhatia S., LaBoda, C., Yanez V., Haddock T., and Densmore, D. (2016). Permutation Machines. *ACS Synthetic Biology*. 5:827-834.