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Aggregation Patterns in Stressed Bacteria (PRL Vol. 75, Number 9) Lev Tsiming and Herbert Levine, Igor Aranson, Eshel Ben-Jacob, Inon Cohen and Ofer Shochet & William N. Reynolds Presented by: Hudson Borja da Rocha
1
Introduction
! Study of the formation of spot patterns in bacterial colonies
! Bacteria are subjected to oxidative stress
! Turing instability
! Reproduction of patterns by the model
Previous studies
! Spot and stripe patterns in bacterial growth
! Berg and Budrene in e. coli bacteria
! Highly oxidized nutrients from respiratory by-products
! Similar structures have been seen in Salmonella typhimurium and Bacillus subtilis
Berg and Budrene’s experiment
Model
⇢
x
⇢ = D⇢r2⇢+G(⇢, n)� ⌫cr.(⇢rc)� I[w]⇢,
⇢n = I[w]⇢,
n = Dnr2n� ↵⇢n,
w = Dwr2w + ↵w⇢n� (�w + �⇢)w,
c = Dcr2c+ T [w, c]� �cc.
Model
! Implicite fonctions
G =
r⇢pn
n+ n0� g⇢3
I[w] = �⇥(nc � nth)
T [w, c] = gcsgn[⇥(w � w0)⇥(c� c0) +⇥(w � w1)]
Simulations
! Lattice 128x128
! Fast Fourier transform for linear parts
! Finite differences for non-linear terms
! The instability is generated by the chemotactic term
! Importance of waste dynamics is discussed
Simulations
! Fist approximation
! Absence of threshold for chemo attractant emission
! Not in accord to Berg and Budrene’s experiments
Simulation
Conclusion
! “Interplay of front propagation and a Turing-type instability can lead to spot patterns similar to those observed in bacterial aggregation”
! “Turning on” process of chemo attractant is of critical importance in giving rise to the observed colonies
! Good description without complex hierarchy of biological mechanisms