1. 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

2. 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

3. 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

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

5. 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

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

7. 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

8. 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

9. 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