Exact results for optimal phenotypic switching rates

1. Exact results for optimal phenotypic switching rates A Jamie Wood, Bernadett Gaal, Jon Pitchford

2. Phenotypic switching

3. Phenotypic switching

4. Importance May be very relevant to infection, the cull is the antibiotic, regrowth of nasty phenotype still occurs. NOT a mutation. When to switch? When not to switch? How has switching evolved? What is optimal switching?

5. Previous Work ...environment that periodically fluctuates between two states Ishii et al. 1989 ...optimal rate of switching is approximately equal to the rate of environmental change. Lachmann and Jablonka, 1996 Thattai and van Oudenaarden, 2004 Kussell and Leibler, 2005 ...what about when environments are different? Reluga 2005 Salathé et al. 2009

6. Problem setup... Periodic environments, “A” and “B”. We can think of one of the environments as a period of antimicrobial treatment

7. Problem setup, in maths Long term max growthrate: where

8. The Solution... where and Gaal, Pitchford, Wood. Genetics Vol. 184, 1113

9. Some definitions Universal switching rate Fitness of fitter types is the same Differing fitness penalties in the two different environments Time spent in environment A Time spent in environment B Gaal, Pitchford, Wood. Genetics Vol. 184, 1113

10. Key result – not switching is good Gaal, Pitchford, Wood. Genetics Vol. 184, 1113

11. Key result – discontinuous change Max Max Max Gaal, Pitchford, Wood. Genetics Vol. 184, 1113

12. More exotic outcomes Allowing time periods to also vary Gaal, Pitchford, Wood. Genetics Vol. 184, 1113

13. A few other ideas Mathematical framework is well established – can we move to more interesting examples for biology? Fitness? Is switching directly or indirectly affecting fitness? Spatial position in a biofilm for instance. What implications do these results have for evolution of switching?

14. Thanks to: Bernadett Gaal Jon Pitchford Marjan van der Woude