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

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

The Thymus

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

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.

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

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

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

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.

First Passage Problem Drunkard in Mine Field Approximated by Rosenstock

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?

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

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