1. 1. A Monte-Carlo Simulation on Self- binding Polymers Tianchu(Alex) Liang Lawrence University Advisor: Professor Jef Wagner http://upload.wikimedia.org/wikipedia/commons/a/a4/Pre-mRNA- 1ysv-tubes.png
2. 2. What is a polymer? Large molecule, or macromolecule. Repeated subunits, monomers. http://injectionmoldingonline.com/Molding101/Polymers.aspx
3. 3. Why are we interested? Ubiquitous in life: Synthetic: rubber, plastic, etc. Biological: DNA, RNA, proteins, etc. Physical properties: Size Persistence Length Motion Self-binding(RNA, protein) http://upload.wikimedia.org/wikipedia/commons/a/a4/ Pre-mRNA-1ysv-tubes.png
4. 4. Polymer Physics Investigate physical properties Simulation: Linking Interaction Excluded Volume Interaction Bonding Interaction A B
5. 5. Intuition on Interactions: Linking Interaction: 1 2 Exclusion Volume Interaction: 1 22 H-Bond Interaction: 21
6. 6. Behavior Over Time: Time Time Radius of Gyration:
7. 7. My Simulation Realistic chain: Link Interaction, Exclusion Interaction, H-Bond. Quantify avg(Rg) Visualize-3D Behavioral Difference Time
8. 8. How To Implement? Molecular Dynamics? Force Equation of MotionNO! Lack of Computing Power/Patience Monte-Carlo Simulation with a Coarse-Grained model Simplified Structure Reduced (Microscopic)Degrees of Freedom Thermal (Energy) Equilibrium
9. 9. Movement of A Monomer A B Ct=t_i A Change in Energy: Linking Interaction Exclusion Volume Interaction H-Bond Interaction
10. 10. Average of Rg & Monte-Carlo Method A, a quantity in a thermal system:
11. 11. Implementation A B C A t=t_i Random Movement Generator Energy Evaluator Stay put Move to new position
12. 12. Quantitative Results
13. 13. Visualization Only Linking Interaction Linking Interaction & Exclusion Volume Interaction Linking Interaction & Exclusion Volume Interaction & H- Bond Interaction
14. 14. Conclusion The simulation is functional: Produced sensible data for visualization Did not deliver good calculation for the average radius of gyration. Future Work: Further tuning of parameters in the program Take away: Computers are awesome Simulating complicated system: efficient, informative, fun!
15. 15. Acknowledgements Project Advisor: Professor Jef Wagner Lawrence University