Self-Assembly of Three-Arm Junctions in DNA Strands Sebastian Perusset, Ivan Lucatero, Anahita Mirtabatabaei, Francesco Bullo Department of Mechanical Engineering, UCSB Contact: perusset@umail.ucsb.edu, anaheata@gmail.com , bullo@engineering.ucsb.edu Introduction Simulink Attempt Simulink is a toolbox within Matlab that incorporates physics to defined bodies. Simulink is useful for creating objects such as pendulums and circuits, but its lack of collision detection was problematic for our project. Our code became overcomplicated with too many sensors and actuators. There was far too much redundancy required in Simulink to create a self assembly simulation with hundreds of particles. Matlab Editor Simulation Assumptions made in the experiment: 1. Equal reaction rates 2. All of the reactions are irreversible Assumptions that we added: 1. The velocity of the particles are constant. 2. The concentration of the catalyst is proportional to the amount of collisions between “A” particles that results in the formation of pairs. The aim of our project was to simulate and study the catalytic self assembly of three-arm junctions in DNA strands. We created a simulation with variable parameters that depicts the actual experiment as accurately as possible. We then used our simulation to gather data and compare it to experimental data gathered by Peng Yin. Self-Assembly The process by which individual parts spontaneously rearrange into a desired structure. Motivations: Simulations of biological processes Robotics Aerospace Self assembly occurs in many biological and chemical reactions. It is now beginning to find its way into robotics through programming. By studying localized programming as well as the process of self-assembly researchers can get closer to creating self-assembling robots. Catalytic Formation of Three-Arm Branched Junctions of DNA Strands No Collisions 1 2 4 3 Simulink Flowchart: 6 Bodies Results and Conclusions Experimental Results: Matlab Editor Simulation Methods In order to begin creating our simulation we had to establish a graph grammar to distinguish single monomers from pairs and junctions. Analogous Simulation Results: Graph Grammar: All single particles will be given the Label “A” Once two “A” particles attach they will both be given the label “B” When a “B” particle attaches to an “A” particle, the three are now labeled “C” Metastable Monomers Initiator (catalyst) Three-Arm DNA Junction Similarities: Differences: Upward slope Amount of junctions Catalyst increases reaction rates Beginning slopes Lines converge to similar value Time-frame Once the particles are in groups of threes, they no longer change labels because they are in their completed state. They stay together, labeled as “C,” until the end of the simulation. Advantages of Matlab: Easier to achieve collision detection. The use of loops allows for less redundancy than Simulink Easy to access information Runs simulations faster, allowing for a better time complexity Project Goals Create a simulation for the catalytic formation of three-arm junctions of DNA strands. Use our simulation to measure reaction rates and time complexities using variance in the amount of catalyst and initial amount of monomers. We wish to adjust our simulation so that our graphs resemble the adjacent graphs that were created experimentally Basis of how our simulation works: Pattern of threes No correlation between time and number of particles given less than thirty particles. Share their labels Particles Collide Bounce apart Bind together Run through conditional algorithm References Yin, Peng. “Programming Biomolecular Self-Assembly Pathways. Nature . 17 January, 2008 Paolo Di Prodi, Picollo Particle Simulator, 3 November, 2010 Klavins, Eric. “Programmable Self-Assembly.” IEEE Control Systems Magazine. August 2007 Future Directions Simulate more complex Self-Assembly Make Simulation more user friendly Run tests with more particles