Cooperative response and clustering: Consequences of membrane-mediated interactions among mechanosensitive channels

Mechanosensitive channels are ion channels which act as cells' safety valves, opening when the osmotic pressure becomes too high and making cells avoid damage by releasing ions. They are found on the cellular membrane of a large number of organisms. They interact with each other by means of deformations they induce in the membrane. We show that collective dynamics arising from the interchannel interactions lead to first- and second-order phase transitions in the fraction of open channels in equilibrium relating to the formation of channel clusters. We show that this results in a considerable delay of the response of cells to osmotic shocks, and to an extreme cell-to-cell stochastic variations in their response times, despite the large numbers of channels present in each cell. We discuss how our results are relevant for E. coli.

Figure 1

Diagram representing the lattice model. Channels interact with nearest neighbors with energies ${\varepsilon }_{oo}$, ${\varepsilon }_{cc}$, and ${\varepsilon }_{oc}$, depending on the states of the interacting channels.

Figure 2

Fraction of open channels in the system, $P_o$ (a), and fraction of channels that belong to the cluster, $f$ (b), as functions of the membrane tension $\tau$, for different values of $\rho$. Here ${\varepsilon }_{oo}=-15.0k_{B}T$, ${\varepsilon }_{cc}=-5.0k_{B}T$, and ${\varepsilon }_{oc}=10.0k_{B}T$.

Figure 3

(a) Average fraction of open channels as a function of simulated time, for different values of $\tau$. Black squares represent the same system without interaction between channels. Real time is shown in parentheses on the $x$ axis. (b) Number of samples with a given fraction of open channels, for three different transients, for the interacting case with $\tau =3.0k_{b}T/{\mathrm{nm}}^2$. The parameters are ${\lambda }_D/{\lambda }_G=0.02$, $L=400$, $\rho =0.002$, ${\varepsilon }_{oo}=-15.0k_{B}T$, ${\varepsilon }_{cc}=-5.0k_{B}T$, and ${\varepsilon }_{oc}=10.0k_{B}T$. For each set of parameters, 500 samples were considered, and error bars correspond to one standard deviation.