Stripe formation In an expanding bacterial colony with d ensity-suppressed motility

1. Stripe formation In an expanding bacterial colony with density-suppressed motility discovery of novel mechanisms and function Phenotype (structure and spatiotemporal dynamics) Traditional biological research (painstaking) Synthetic biology Molecular mechanisms (players and their interactions) Lei-Han Tang Beijing Computational Science Research Center and Hong Kong Baptist U genetics biochemistry The5th KIAS Conference on Statistical Physics: Nonequilibrium Statistical Physics of Complex Systems 3-6 July 2012, Seoul, Korea

2. The Team HKU UCSD: Terry Hwa Marburg: Peter Lenz Xiongfei Fu(physics) Chenli Liu(Biochem) Dr Jiandong Huang(Biochem) HKBU Xuefei Li Lei-Han Tang C. Liu et al, Science 334, 238 (2011); X. Fu et al., Phys Rev Lett108, 198102 (2012)

3. fruit fly embryo dicty Periodic stripe patterns in biology snake

4. Morphogenesis in biology: two competing scenarios • Morphogen gradient (Wolpert 1969) • Positional information laid out externally • Cells respond passively (gene expression and movement) • Reaction-diffusion (Turing 1952) • Pattern formation autonomous • Typically involve mutual signaling and movement Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation, S Kondo and T Miura, Science329, 1616 (2010)

5. Cells have complex physiology and behavior Components characterization challenging in the native context Growth Sensing/Signaling Movement Differentiation All play a role in the observed pattern at the population level Synthetic molecular circuit inserted into well-characterized cells (E. coli)

6. Experiment

7. Swimming bacteria (Howard Berg)

8. cheZ needed for running Extended run along attractant gradient =>chemotaxis Bacterial motility 1.0: Run-and-tumble motion CheY-P low ~10 body length in 1 sec CheY-P high

9. Couple cell density to cell motility High density Low density cheZ expression normal cheZ expression suppressed

10. Genetic Circuits AHL Quorum sensing module LuxR AHL cI LuxI PluxI CI luxI luxR Plac/ara-1 CheZ cheZ Pλ(R-O12) Motility control module

11. Experiments done at HKU Seeded at plate center at t = 0 min WT control 200 min 300 min 400 min 600 min 500 min engr strain 300 min 700 min 900 min 1100 min 1400 min • Colony size expands three times slower • Nearly perfect rings at fixed positions once formed!

12. Phase diagram Simulation Experiments at different aTc (cI inducer) concentrations Increase basal cI expression=> decrease cheZ expression=> reduction of overall bacterial motility many rings => few rings => no ring

13. Qualitative and quantitative issues • How patterns form? • Anything new in this pattern formation process? • Robustness?

14. How patterns form Initial low cell density, motile population Growth => high density region => Immotile zone Expansion of immotile region via growth and aggregation Appearance of a depletion zone Same story repeats itself? Sequential stripe formation

15. Modeling and analysis

16. Traveling wave solution ρ Exponential front ρs c x Front propagation in bacteria growth Fisher/Keller-Segel: Logistic growth + diffusion No stripes!

17. AHL (repressor) Nutrient Growth equations for engineered bacteria 3-component model Bacteria (activator) nutrient-limited growth AHL-dependent motility

18. Sequential stripe formation from numerical solution of the equations front propagation aggregationbehind the front propagating frontunperturbed Band formation

19. Analytic solution: 2-component model μ(h) Non-motile motile 0 Kh-ε Kh h random walk immotile low density/AHL high density/AHL Bacteria Growth rate AHL Degradation rate

20. Solution of the rho-eqn in two regions Solution of the h-eqn using Green’s fn Cell depletion zone Motile front Steady travelling wave solution (no stripes) Moving frame, z = x - ct • Solution strategy • Identify dimensionless parameters • Exact solution in the linear case • Perturbative treatment for growth with saturation Stability limit

21. “Phase Diagram” from the stability limit Characteristic lengths Cell density profile AHL diffusion Stability boundary: Lh/Lρ≈ 0.3-0.5

22. Key parameters governing the stability of the solution • AHL profile follows the cell density profile most of the time. • In the depletion zone, AHL profile is smoothened compared to the cell density profile. The degree of smoothening determines if AHL density can exceed threshold value in the motile zone. • If the latter occurs, nucleation of high density/immotile band takes place periodically=> formation of stripes Bacteria profile AHL profile

23. Discussion

24. The mathematics of biological pattern formation

25. Debate:cells are much more complex than small molecules => Deciphering necessary ingredients in the native context challenging Resort to synthetic biology (E. coli) Minimal ingredients: cell growth, movement, signaling, all well characterized Defined interaction: motility inhibited by cell density (aggregation) Formation of sequential periodic stripes on semi-solid agar Genetically tunable Stripe formation in open geometry (new physics) Theoretical analysis deepens understanding of the experimental system in various parameter regimes

26. Open issues Period of stripes analysis of the immotile band formation in the motile zone Robustness of the pattern formation scheme Residual chemotaxis Inhomogeneous cell population Cell-based modeling Sharpness of the zones Multiscale treatment (cell => population)

27. This work Population: pattern formation 5mm Life is complex! New problems for statistical physicists Biology goes quantitative Close collaboration key to success Cell: reaction-diffusion dynamics Biological game: precise control of pattern through molecular circuits 5mm

28. Acknowledgements: The RGC of the HKSAR Collaborative Research Grant HKU1/CRF/10 HKBU Strategic Development Fund

29. Thank you for your attention!

30. S Kondo and T Miura, Science 329, 1616 (2010) Turing patterns The Chemical Basis of Morphogenesis A. M. Turing Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences237, 37-72 (1952) Ingredients: two diffusing species, one activating, one repressing • Pattern formation (concentration modulation) requires • Slow diffusion of the active species (short-range positive feedback) • Fast diffusion of the repressive species (long-range negative feedback) control circuit (reaction)