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Active Walker Model for Bacterial Colonies: Pattern Formation and Growth Competition

Active Walker Model for Bacterial Colonies: Pattern Formation and Growth Competition. Shane Stafford Yan Li. Introduction:. Bacterial colonies exhibit complex growth patterns on starvation conditions Experimental facts:

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Active Walker Model for Bacterial Colonies: Pattern Formation and Growth Competition

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  1. Active Walker Model for Bacterial Colonies:Pattern Formation and Growth Competition Shane Stafford Yan Li

  2. Introduction: • Bacterial colonies exhibit complex growth patterns on starvation conditions • Experimental facts: • The growth pattern and fractal dimension depend on both the nutrient concentration and roughness of the agar substrate • Bacteria perform a random walk like movement on the substrate, within a well-defined envelope (lubrication layer) • Under extreme adverse living conditions, patterns become dense again by chemo tactic signaling (not dealt with in our simulations) E Ben-Jacob et al, Nature,368, (47)1994,

  3. Simulation overview: • Model: Active Walker Model (AWM) • Variables: • Nutrient concentration P • Surface roughness Nc • Number of inoculation points • Results: • Patterns under different growth conditions (single colony) • Growth radius Rg, ,Rmax • Fractal dimension d • Patterns of two bacterial colonies

  4. Algorithm: active walker model • Walkers • Each walker is a bacteria cluster (103 –104 individual bacterium) and is characterized by its location (xi, yi) and internal energy wi • Perform off-lattice random walk of step size d[0,dmax] at an angle [0,2] generated by two random numbers • loses energy at a fixed metabolism rate e • consumes nutrient at a fixed rate cr or the maximum amount available • divides at threshold wi= tr,, becomes stationary when wi=0 • Threshold collision time Ncroughness of substrate • Nc is changed from 2 to 10 in our simulation

  5. Landscape: • The landscape is the nutrient (pepton) concentrationc(r,t) on lattice • At each time step, the landscape is updated by solving the diffuision equation locally: • Boundary conditions are needed to realistically represent the system • Initial nutrient concentration P is varied from high (supporting 10 walkers on a lattice site) to low (supporting 1 walker on a site only) • Scaling: • Parameters scaling is important for simulation to reproduce the phenomena in real life in both the correct time and space scales • Diffusivity of nutrient, step size of walkers, lattice size, time step

  6. Sample parameter input_____________________ //general parameters size = 200 initWalkers = 20 totalSteps = 2000 diffusionSteps = 1 seed = 5 peptoneConc = 20. lambda = 1.44 //lambda is D * dt / dx**2 (unitless)  //walker parameters reproThresh = 1.0 inactThresh = 0.0 maxUptake = 0.2 metabolism = 0.0667 maxJump = 0.4 initEnergy = 0.33 reproEnergy = 0.30 envelHits = 6 //Nc

  7. Algorithm: fractal dimension • Dimension of fractal structures • Between regularity and total randomness: self-similarity • Box counting method • Divide the pattern into  grid and count N, the minimal number of blocks to cover the pattern. • Mass distribution method • Up limit of R is the gyration radius defined as • Problem: high concentration at the center bias the dimension towards high values

  8. Results: patterns 200*200 lattice, run time=2000 steps, ten runs per set of parameters • One inoculation points at the center (100,100) (a) Fixed surface roughness Nc=6 and vary the initial nutrient concentration P=1.0, 3.0, 5.0, 7.0 and 9.0

  9. P=9.0 P=7.0 P=1.0 P=5.0 P=5.0 Nc=6

  10. Results: • 200*200 lattice, run time=2000 steps, ten runs per set of parameters • One inoculation point at the center (100,100) • (a) Fixed surface roughness Nc=6 and vary the initial nutrient concentration P=9.0, 7.0, 5.0, 3.0 and 1.0 • (b) )Fixed initial nutrient concentration P=2.0 and vary surface roughness Nc=2,4,6,8 and10

  11. Nc=2 Nc=4 Nc=10 Nc=6 Nc=8 P=2.0

  12. Results: growth radius Fixed surface roughness Nc=6

  13. Fixed initial concentration level P=2.0

  14. Results: fractal dimension Fixed surface roughness Nc=6

  15. Fixed initial concentration level P=2.0

  16. Conclusion: • The growth radius Rg and Rmax decrease when the nutrient level is lowered or the surface becomes harder, consistent with the observation from experiments • (2) The structure becomes more ramified as the nutrient level decrease, as expected. • (3) The change of fractal dimension is less obvious in the case when the surface roughness is varied. • Possible reason: the range of surface hardness is not large enough • Need a faster algorithm to generate same size of patterns under extreme hard surface.

  17. Competition between two colonies 1    Nc=6, p=5.0; Inoculation points (40,100) and (160,100), d=80

  18. 2.    Nc=6, p=5.0; Inoculation points (75,100) and (125,100), d=50

  19. Bacterial Capacitors I am happy with what I have e- e- e- e- e- e- e- e- e- e- e- e- e- e- Invader, Run!! Drive for food e- e- e- e- e- e- e- e- e- e- e- e- e- e- Drive for food

  20. Further investigation • High level interaction? • Bacterial colonies interact not only locally, but also indirectly via marks left on the agar surface and chemical (chemo tactic) signaling. Patterns become dense at extreme low food level. • Two landscapes: nutrient concentration and chemical concentration • Inactive walkers generate a communicating field to attract active ones • More realistic parameters • Variable metabolism rate and consumption rate • Need to obtain more insight into the physics in the growth process • Speed up the code! • Optimization of template instantiation and random number mapping • Better diffusion solver

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