Figure - PMC

Skip to main content

View full-text article in PMC

. Author manuscript; available in PMC: 2017 Jul 13.

Published in final edited form as: Quant Biol. 2017 Mar 30;5(1):55–66. doi: 10.1007/s40484-017-0100-y

Two-strain population toggle with equal growth rates. (a) The equilibrium $x_{1}^{*}$ as a function of population ratio r. The dashed and solid lines correspond to unstable and stable equilibria, respectively. (b) Two trajectories of Eq. (1) approaching one of the two stable equilibria marked by ( ) and ( ) based on the initial conditions. The third, unstable equilibrium is denoted by ( ). The gray dashed line shows the separatrix between the two basins of attraction of the stable equilibria. The parameters are chosen as β₁ = β₂ = 0.023 min⁻¹ corresponding to E. coli's cell cycle of approximately 30 minutes, α = 10 min⁻¹, θ = 500, N = 200, and n = 2. The simulations are carried out for constant population ratio r = 0.4 and initial conditions (x₁(0), x₂(0)) = (100, 200) proteins per cell and (x₁(0), x₂(0)) = (300, 100) proteins per cell.

Inline graphic — Two-strain population toggle with equal growth rates. (a) The equilibrium $x_{1}^{*}$ as a function of population ratio r. The dashed and solid lines correspond to unstable and stable equilibria, respectively. (b) Two trajectories of Eq. (1) approaching one of the two stable equilibria marked by ( ) and ( ) based on the initial conditions. The third, unstable equilibrium is denoted by ( ). The gray dashed line shows the separatrix between the two basins of attraction of the stable equilibria. The parameters are chosen as β₁ = β₂ = 0.023 min⁻¹ corresponding to E. coli's cell cycle of approximately 30 minutes, α = 10 min⁻¹, θ = 500, N = 200, and n = 2. The simulations are carried out for constant population ratio r = 0.4 and initial conditions (x₁(0), x₂(0)) = (100, 200) proteins per cell and (x₁(0), x₂(0)) = (300, 100) proteins per cell.