Correlated phenotypic transitions to competence in bacterial colonies

Genetic competence is a phenotypic state of a bacterial cell in which it is capable of importing DNA, presumably to improve survival under stress. Motivated by several colony-level known responses, we present a model for the influence of quorum sensing on the transition to competence of B. Subtilis. Coupling to the external signal creates an effective inhibitory mechanism, which results in anticorrelation between the cycles of adjacent cells. We show that this is consistent with recent experimental measurements and propose measurement methods to verify the role of quorum-sensing signals.

Figure 1

(Color online) (a) Schematic representation of the competence circuit in B. Subtilis. Solid lines represent direct interaction; dashed lines represent indirect interaction. (b) Time development of a colony of cells. Color code represents the ComK level, from low ComK level (vegetative state, black) to high ComK level (competent state, white). Adjacent cells rarely become competent simultaneously, due to effective mutual inhibition.

Figure 2

(Color online) Phase planes diagram for the ComK-ComS system [Eqs. (1, 2)]. Null clines are presented for ComK (blue, thick dark) and ComS (green, thick gray), and the system fixed points. (a) The excitable system, obtained from Eqs. (1, 2) with the parameters $a=0.004$, $b_K=0.08$, $b_S=0.8$, $k_0=0.2$, and $k_1=0.222$. The noise rms amplitude is 3.5 and $\Delta t=0.01$. The fixed points are (from left to right) a stable point, a saddle point, and an unstable point. A characteristic trajectory is presented (thin black line) for a single cell, starting from the vegetative state (low ComK). (b) The monostable system, for Eq. (3) and $Q=0.9$, $b_s=0.6$, $c_s=0.2$, and ${\delta }_Q=1$, $D_Q=1$ [other parameters as in (a)]. The only fixed point refers to the vegetative state.

Figure 3

(Color online) (a) Correlation between ComK values of adjacent cells as a function of diffusivity. The mutual inhibition, as identified by negative correlation, vanishes for small diffusivities as well as for large diffusivities. (b) Cumulative histograms of differences between excursion times, of the entire colony (solid line) and adjacent cells (markers).

Figure 4

(Color online) A striped colony of cells simulation results. The cell state is represented by color code, from vegetative (white) to competent (black). (a) For $D=1$, the stripe pattern is unstable and the cells return to their vegetative state. (b) For $D=2$, the stripe pattern is stable. (c) The steady-state profile of $Q\left(x\right)$, analytic solution (solid line) and simulation results (asterisks).