Fast Evaluation of Fluctuations in Biochemical Networks With the Linear Noise Approximation

Properties of a system with coupled exit flow (two-component system, equation 17). (A) The average concentrations (Y-axis) of X molecules for an increasing rate of X synthesis (k₁, X-axis). Lines correspond to LNA and circles to estimates from Gillespie simulations. The synthesis rate of Y molecules is k₂ = 10^-6 M/sec, and the association rate constant is k₅ = 10⁶ M/sec. These parameters are also used in B-D. (B) The Fano-factor for X molecules, δX²/X, as given by LNA (lines) and Gillespie simulation (circles). (C) Gillespie simulation of the variation of the number of X and Y molecules (Y-axis) over time (X-axis) for balanced synthesis (i.e., k₁ = k₂ = 10^-6 M/sec). (D) The modified Fano-factor, σ²_w/ΩX₁, at the point of balanced synthesis (Y-axis) for different values of the decay rate (X-axis) as given by LNA (lines) and Gillespie simulation (circles).