Student: Andrew Parent
Advisor: Jo Ellis-Monaghan
Work supported by CURM, Spring 2010
Design Optimization for DNA Nanostructures Part II: Symmetries in the Octet Truss
Research Summary: Over the course of this year myself and five other students studied a variety of
aspects of DNA nanostructures in order to attempt to find every structure that could be built from them
and come up with strategies to solve how they would self assemble into these various structures.
Thomas Dickerson and myself sought to find every tile (building block used to assemble these
structures) in its lexicographically minimal form. We approached this by first analyzing the symmetry
groups represented in the octet truss so that we could have various strategies for eliminating duplicate
tiles. We then studied the angular isomorphisms between arm-angle pairs to use as a criteria for
grouping tiles under their lexicographically minimal representatives. On top of this we studied
rotational symmetries in order to completely group the tiles. We then wrote a program which
implemented our research based upon the ideas we came up with in our development stage. After
completing the program we performed a self check researched by the students in previous semesters
called the orbits and stabilizers theorem to prove that our results were in fact correct.
Activities: This project was a continuation of research done by students in previous semesters. Our first
goal was to catch the new researchers, myself being one, up to date with what the project was about
and what research they had already conducted. The previous researchers presented there current
presentation to the new researchers and we read the papers the previous research group wrote.
Our next task was to get caught up on graph theory and combinatorics, two of the major
mathematical subjects we used in our research. We used a textbook by Alan Tucker and every week
read a new chapter and did some exercises relating to the topics. At the end of the week we all
exchanged exercises and corrected them.
Having a sufficient background in combinatorics we then expanded to our respective projects.
We developed various methods to find our Lexiographically minimal representative tiles using Zome
tools to analyze angle-arm pairings and rotational symmetries. They turned out to be very helpful tools
for visualizing our tile structures rotating into each other and allowed us to actually take our ideas and
put them into program form because we had such a strong visualization from the models. We also used
them in demonstrating how we labeled tiles and rotational axes in our presentation to help others
visualize what exactly we were discussing.
We then took our ideas and translated them into a program in the Java language applying
various combinatorical, graph theory and coding strategies to optimize the programs efficiency while
accomplishing our goals. We also coded in our self check along with our code to find the Lexicographical
minimal tiles in order to ensure that what we performed was in fact 100% correct.
Outcomes: Having solved our problems we formalized our work into a paper and presentation with our
code as an appendix to the paper. We travelled to various locations presenting the findings of our
research. We created a powerpoint for our presentations purposes and along with the aforementioned
Zome tools we created a strong visualization for those who came as to what we actually had
accomplished. We had two presentation locations HRUMC undergraduate mathematics conference at
Keene State College in New Hampshire and CURM at BYU in Utah where in general our work was well
received. We will be finishing up our work with a poster which we will be presenting at Saint Michael’s
College’s Undergraduate Research Symposium.
Impact: This research project was a very positive experience for me, it allowed me to apply my
computer science knowledge to a brand new area and gave me a new perspective on just how useful
the field is. In addition it made you learn to make use of time management since as a student one has
to balance a full class schedule on top of research work on the side with a relatively heavy load for time
and effort. I learned how to more effectively budget time in a group setting and work as a team to
accomplish a number of goals. There are a number of positives however having successfully
accomplished a project which when we had no concept of the scope of when we set out is fantastically
rewarding and has been very enjoyable.