Fig. 8.

Impact of relative bound and unbound state lifetimes on the distribution of N_b+d. (A,B) Simulated intensity versus time traces for probes with equal (τ_bound = τ_unbound = 20 s) and very different (τ_bound = 2 s, τ_unbound = 38 s) lifetimes in the bound and unbound states. (C) N_b+d distributions for 2,000 simulated intensity versus time traces with τ_bound = τ_unbound = 20 s (blue curve) or τ_bound = 2 s, τ_unbound = 38 s (orange curve). The distribution becomes broader if τ_bound ≠ τ_unbound due to strong temporal correlation between binding and dissociation events. (D) Standard deviation in the N_b+d values of 2,000 simulated intensity versus time traces as a function of average N_b+d value, which increases with increasing observation time. When τ_bound = τ_unbound (blue circles), σ(N_b+d) increases as $\sqrt{\langle N_{b+d}\rangle }$ (gray dashed line), consistent with expectations for a Poisson process. However, when τ_bound ≠ τ_unbound (orange squares), σ(N_b+d) increases more rapidly due to temporal correlation of binding and dissociation events. In the limit where either τ_bound or τ_unbound is infinitesimal, σ(N_b+d) increases as $\sqrt{2\langle N_{b+d}\rangle }$ (black dashed line) – consistent with N_b+d/2 being Poisson-distributed.