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