Movement of Flagellated Bacteria Graduate Student Group Project PCMI 2005 Evelyn Dittmer Free University Berlin Hannah McKenzie University of Alberta Andrea Weiße Free University Berlin

IAS/PCMI Summer School 2005 Overview Setting up a Model Simulating Chemotaxis Spatially fixed chemotactic substance Moving chemotactic substance Improving Movement Outlook IAS/PCMI Summer School 2005

IAS/PCMI Summer School 2005 Setting up a Model What do we know? Markov Jump Process Run Tumble “Run”-Phase: Bacterium moves forward “Tumble”-Phase: Bacterium moves “in a highly erratic manner”  new direction Assuming constant speed, position at end of run-phase is determined by realization of run-time Simplification: assuming straight run, but actually slightly curved Angle distribution HMM: explain Explain realization process: Draw tumbling time Draw gamma Draw running time Compute position by assuming constant speed  Hidden Markov Model with deterministic observable in “Run”-State IAS/PCMI Summer School 2005

Realizations of Random Walk Small time intervalls? IAS/PCMI Summer School 2005

Simulating Chemotaxis Effect of chemotactic substance: Bacterium measures gradient of substance via memory Mechanism: longer run time by methylization of signal proteins (slow) Realization in Model: Measure gradient directly after tumbling Change average run time immediately IAS/PCMI Summer School 2005

IAS/PCMI Summer School 2005 Biased Walk IAS/PCMI Summer School 2005

IAS/PCMI Summer School 2005 Moving Attractant Attractant slow Attractant fast Speed Run Time 5x faster 10x smaller Speed Run Time 50x faster 10x smaller IAS/PCMI Summer School 2005

Can we improve Movement? Uniform and positive competing at different time steps Standard always worst Different measure of succes: time until specific attractant concentration is achieved horizontal line in plot  no change in rank of success of different models Standard Positive Uniform IAS/PCMI Summer School 2005

IAS/PCMI Summer School 2005 Outlook Optimality Analysis: Optimal distribution for angle? Biased? Optimal run time adaptation? Speed adaptation? Analysis of Attractant speed: At which speed ratio does bacterium loose attractant? Curved run Of course: Comparison with real Data IAS/PCMI Summer School 2005