Robustness of DNA Repair through Collective Rate Control
Figure 3
Analytical model of the formation of a catalytic multi-protein complex on DNA.
(A) Sequential (above) and random (below) assembly schemes for a complex of three components (A, B and C); x0 denotes the empty assembly site (e.g., a DNA lesion), xA the assembly site with component A bound etc. The complete complex (xABC) catalyses a reaction (e.g., lesion repair) with rate r. The repair process consists of several such assembly-reaction modules (cf. Fig. 1). (B) The mean reaction time τ given by Eq. (2) depends on the number of assembling protein components N and on the assembly mechanism. Parameters: apparent on-rates k equal to off-rates (k = l = 1 min−1), ρ = 10 s−1 (C) In the case of reversible assembly (k = l = 1 min−1, N = 9, random mechanism), the formation of the reaction product follows exponential kinetics (solid red line, fitted perfectly by a mono-exponential time course with time constant τ). Irreversible assembly (l = 0) follows a sigmoidal time course (dashed red line, N = 9, random mechanism, on-rate k = 0.037 min−1 chosen to get the same time constant). The results for a sequential assembly mechanisms are qualitatively similar.