Figure 1.

Nucleated polymerisation in the presence of seed material. The thick dashed lines are the exact solution to the rate equations Equation (9); the thin solid lines are calculated from numerical simulations of the master equation Equation (1). The dotted lines are the initial gradients dM/dt|_t=0 = M(0) + 2k₊m(0)P(0)t; a lag-phase exists when the initial gradient is not the maximal gradient. The numbers accompanying each curve are k₀/λ; Equation (14) predicts that a lag-phase only exists when this ratio is less than unity. (a): Nucleated polymerisation in the presence of an increasing quantity of seed material of a fixed average length (5000 monomers per seed) added at the beginning of the reaction. The seed concentrations given as a fraction of the total concentration of monomer present are right to left): 0, 0.01, 0.04, 0.1, 0.2, 0.5; (b): Nucleated polymerisation in the presence of a fixed quantity (1% of total monomer in the system) of seed material of varying average length. The average number of monomer per seed are (right to left): N/A (unseeded), 5000, 1000, 500, 200, 50. The other parameters for both panels are: m_tot = 10 μM, n_c = 3, k_nm _tot^n_c−1 = 1 · 10⁻⁹ s⁻¹, k₊ = 1 · 10⁵ M⁻¹ s⁻¹.