Discrete and Continuum Multiscale Behaviour in Bacterial Communication - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 306

AIP

AgrB AgrC

AgrD

AgrA

mRNA

agrBDCA genes associated with the

quorum−sensing−induced phenotype

Fig. 1 Schematic representation of the agr system. Arrows illustrate the positive feedback loop.
AgrB and AgrC are transmembrane proteins, while AgrD is anchored to the cell membrane

differential equation) model can be found in [ 7 ] and the simplifications which have
been made to arrive at the model in this chapter can be identified from [ 9 ]. For
conciseness, these details are omitted here. While we provide only the nondi-
mensional model, the full dimensional model is easily extrapolated from this and,
again, details can be found in [ 7 ]. The spatially structured model we consider is
accordingly given by:

o M i

os ¼ 1

vP i M i þ 1 ;

ð 26 Þ

o A i

os ¼ k ð M i A i Þ gA i R i þ lgA P ;

ð 27 Þ

o B i
os ¼ a ð M i B i Þ;

ð 28 Þ

o S i
os ¼ k ð B i S i Þ k s T i S i ;

ð 29 Þ

o T i
os ¼ k ð B i T i Þ;

ð 30 Þ

o a i

os ¼ 1

kb/
g

T i S i 1

bR i a i þ 1 bcR i k a a i þ D ð a i þ 1 2a i þ a i 1 Þ

; ð 31 Þ

2 h 2

o R i

os ¼ k ð B i R i Þ g / R i a i þ gc / R i ;

ð 32 Þ