Figure 3.

Cartoon of the coarse-grained model. (a) A typical time trace of the receptor state n(t) of the original system. (b) Time trace of the coarse-grained model. (Top-left cartoon; red) a successful and an unsuccessful binding trajectory; (blue) a trajectory in which a ligand molecule undergoes a number of rounds of receptor dissociation and rebinding before it escapes into the bulk. The key observation is that the time a molecule spends near the receptor is very short on the timescale at which molecules arrive from the bulk. This makes it possible to integrate out the receptor rebindings and the unsuccessful arrivals of molecules from the bulk, giving the two-state model of Eq. 19. Fig. S1 in the Supporting Material quantifies the timescale separation. To see this figure in color, go online.