Discrete and Continuum Multiscale Behaviour in Bacterial Communication - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 311

Fig. 4 Time dependent solutions when k ¼ 25 (these correspond with the steady state plots in
Fig. 3 ), identical initial conditions for each are employed (n ¼ 19 central compartments begin in
an active state) and with various diffusion rates: a D ¼ 4 10 5 , b D ¼ 8 : 12 10 5 ,
c D ¼ 8 : 2 10 5 and d D ¼ 8 : 4 10 4 . Moving through the plots, it is easy to see the effect
of increasing the diffusion rate: more and more outside compartments are drawn into the up-
regulated state by the central (initially active) compartments
In Fig. 4 some complementary time-dependent solutions are given for each
value of D employed in Fig. 3 . The time taken for the cells to evolve to their
steady state varies significantly with diffusion rate and initial conditions.
4.5 k ¼ 40: Faster Protein Degradation Requires Greater Signal
Accumulation for Quorum to be Attained
An alternative scenario is that protein degradation, compared to other reactions
within the cell, is sufficiently high that the quorum-sensing machinery must work
much harder to make one or more cells active, making the down-regulated state in
some sense more stable than the active one (i.e. the converse case to that described
in Sect. 4.4 ); enhancing protein degradation could provide a mechanism for pre-
venting virulence, so scenarios such as that described here are of interest in ana-
lysing possible treatments for bacterial infections. Again, a number (n) of central
compartments is chosen to begin in an active state, but this time the cells are more
likely to be drawn into an inactive state by loss of signal molecules to neigh-
bouring inactive cells.