Figure 1.
Simplified scheme of a genetic network in the frame of one cell.
Mutually repressing genes u and v form a toggle switch. Membrane diffusion of an autoinducer molecule, denoted as w, provides intercell coupling.
Figure 2.
Time series for different number of cells with fixed noise intensity (σa2 = 0.002).
The dynamics of u is plotted for different cells in different colors. From top to bottom, and from left to right: N = 2, 10, 30, 50, 500, 1000. The parameters are chosen so that cells are in the bistable regime: α1 = 2, α2 = 4, α3 = 2, α4 = 1, β = γ = 3, η = 1, ε = 0.01, d = 0.03 and de = 1.
Figure 3.
Top: population growth leads to restoration of bistability hidden by noise.
The cell cycle duration is T = 100. The concentration ui of the corresponding cell (from N = 2 to 128) is color-coded (see color bar on the right). Bottom left: average number of jumps per cell versus population size. Bottom left: fraction of cells that perform at least one jump between two states versus population size. Parameters are α1 = 2, α2 = 4, α3 = 2, α4 = 1, ε = 0.01, d = 0.03, de = 1 and σa2 = 0.002.
Figure 4.
Effect of noise on a population of N = 256 coupled cells in the oscillation death regime.
The concentration ui is shown in color code according to the scale of Fig. 3. Time runs horizontally from left to right, while the different cells are plotted along the vertical axis, each cell represented by a horizontal line. Simulations were started with random initial conditions, and after a transient of around 900 time units (in which the oscillations are highly synchronous), two stable clusters emerge. At time t = 1800 noise is switched on with intensity σa2 = 0.4, and this leads to jumps between clusters. Parameters are α1 = 3, α2 = 5, α3 = 1, α4 = 4, ε = 0.05, d = 1 and de = 30.
Figure 5.
Top: population growth leads to restoration of bistability (in the form of oscillation death).
The cell cycle duration is here T = 100. The concentration ui of each cell (from N = 8 to 256) is represented in color code (see color bar on Fig. 3). Bottom left: average number of jumps per cell versus population size. Bottom left: coefficient of variation of the interval between jumps versus noise intensity. Parameters are: α1 = 3, α2 = 5, α3 = 1, α4 = 4, β = γ = η = 2, ε = 0.05, d = 0.3 and de = 1.