Lifetime analysis of classical and hybrid states for complex 1 and complex 2. (*A*) Dwell time histograms for the classical and hybrid states of complex 2 are shown at two different [Mg^{2+}], 3.5 mM and 15 mM. All histograms are fitted with a double exponential function, *A*_{1} × exp (−*t*/*τ*_{1}) + *A*_{2} × exp (−t/*τ*_{2}), and fitted curves are shown in black. The decay profile of the hybrid state is similar between the two [Mg^{2+}]s, whereas the average lifetime of the classical state becomes significantly longer at [Mg^{2+}] = 15 mM. (*B*) Apparent kinetics of the classical and hybrid states at five different [Mg^{2+}]s is shown as two-dimensional scatter plots. All dwell-time histograms have two decay components, and each decay component is summarized by its lifetime along the *x* axis and its fractional frequency of occurrence along the *y* axis. The lifetimes (*τ*_{1}, *τ*_{2}) and fractional frequencies of occurrence (*F*_{1}, *F*_{2}) were obtained from the fitting parameters as explained in the main text. The error bars represent standard errors for the fitting parameters, which are computed from the variation of the fitting parameters across five different bootstrap data sets. [Mg^{2+}] is specified by the same color scheme as in . (*C*) Monte Carlo simulation of apparent lifetimes as a result of Cy5 photophysics. Blinking and recovery rates of Cy5 were experimentally determined as a function of laser intensity. The intensity used throughout our experiments is defined to be 1. The unit of time is 0.025 s, which is our integration time. As an example, when the real lifetimes of the classical and hybrid states are taken to be 1.0 s and 0.05 s, the apparent lifetimes will be 0.6 s and 0.05 s at intensity = 1 according to this simulation. Therefore, the lifetimes we extracted, especially the ones for slow decay components, are likely to be shorter than the real values.

## PubMed Commons