1. Self-Assembly of Three-Arm Junctions in DNA Strands
Sebastian Perusset, Ivan Lucatero, Anahita Mirtabatabaei, Francesco Bullo
Department of Mechanical Engineering, UCSB
Contact: ,
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