Suppose autoinducer
diffuses across the cell membrane, and
that the local volume fraction of cells is
. Then,
![\begin{displaymath}
(1-\rho)({dE\over dt}+k_EE) = \delta (A-E).
\end{displaymath}](img28.gif) |
(9) |
![\begin{displaymath}
{\frac {dA}{dt}} = -k_{RA}R A +k_PP+k_2L-k_AA
-{\delta\over \rho}(A-E).
\end{displaymath}](img29.gif) |
(10) |
Question: Does this system exhibit quorum sensing?
Take everything but
and
to be in steady state:
where
and
.
Figure:
Nullclines
and
with three different
values of
, shown for parameter values
.
![\begin{figure}
\epsfxsize =4in
\centerline {\epsffile{twodss.ps}}\end{figure}](img37.gif) |
Jim Keener
2000-09-06