1. Stochastic Simulation of thymic Selection
Joshua Mannheimer
PH 492
February 27, 2013

2. Outline of Topics Auto-immunity and the Thymus
Selection: Positive and Negative
The Random Walk
The Problem

3. The Thymus

4. Thymus Anatomy Two Parts: Medulla Cortex
Human Max 35 g (puberty) Min 5g (~70 years old)

5. Auto-Immunity Cells chop protein fragments display on surface
T-cell scans surface if it finds foreign protein illicit immune response
Sometimes T-cell recognizes self protein and illicit immune response.

6. Selection
Each T-Cell has specific receptor (TCR) to bind to specific antigen
Antigen  Protein Sequence ~ 10 Amino Acids 2010
Selection is process where (TCR) matching self-peptides are “weeded” out.
Two processes: Positive and Negative

7. Selection Positive Negative In cortex
Must interact with antigen presenting cell to move on
No reaction after certain amount of time cell death
Positively Selected T-cells move to medulla.
If interacts strongly with antigen  death
No reaction after ~ 4vdays becomes mature

8. Random Walk Series Random steps  Markov Process
Distance from origin is proportional to t1/2
Several Types i.e. Normal, Levy, continuous time ….

9. Examples of Random Walks
Bees foraging patterns have been observed to show RW behavior.
Some evidence suggests that animals alter foraging patterns with levy walk
Levy walks and random walks have been used to make financial models and predictions .
Simplified model for Brownian motion.
Used describe thermal movements of polymers
Used to study population dynamics.

10. First Passage Problem Drunkard in Mine Field
Approximated by Rosenstock

11. Examining the Problem
The existence of the event is dependent on more than just contact with a site.
Due to timed nature of selection there is a trade of between “thoroughness” and sites visited.
Net result: for small peptide expression thymic selection is very “leaky”
Question: do experimental observations show that this process has been optimized?

12. Acknowledgements
I would like to thank Dr. Ashok Prasad for giving me the opportunity and resources to work on this project.
The flying spaghetti monster

13. To be Continued……..
Experimental Results and Discussion!