A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules
Figure 3
Polarity is repressed below a critical total density of signaling molecules.
(A) Illustration shows stability of equilibrium values for cytosolic densities, and
, for varying
when
. Red: stable root; black unstable root. (B) Shown is equilibrium membrane fraction
of signaling molecules on the membrane
for various cell densities and different values of
. Cytosolic buffering occurs when
is nearly zero. (C) The probability,
, that the: cytosol contains exactly
molecules is shown for different total molecule numbers,
, scanned between 0 and
. Steady state probabilities of molecule numbers in the cytosol are computed from stochastic master equation (Protocol S1). Inset: zoom-in of transition region showing bimodality of probability distribution.