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Stochastic Simulation of thymic Selection

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

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Stochastic Simulation of thymic Selection

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  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!

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