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

LNA combined with elimination of fast variables (four-component system, equation 22). The stationary marginal distribution for the number of B molecules, P(B), has been estimated by three different methods: (1) by Gillespie simulation (gray line), which converges toward the correct solution; (2) direct application of LNA (solid black line), which approximates the distribution with a normal distribution; and (3) LNA combined with elimination of fast variables (dashed black line). Parameters: Ω = 10^-15l; k₁ = 200 sec^-1; k₂ = 1.67 × 10⁵ M-1 sec^-1; k₃ = 10,000 sec^-1; k₄ = 100 sec^-1; k₅ = 1.67 × 10⁵ M^-1 sec^-1; k₆ = 1000 sec^-1; k₇ = 1.67 × 10⁶ M^-1 sec^-1; e_A^tot = 83 nM;e_B^tot = 167 nM.