= Binding-plus-opening first-passage time
{title2=$\mathbb E[T]=(a+b+c)/(ac)$}
Consider unbound U, bound closed C and open O in a <continuous-time Markov chain>, with rates $U\to C=a$, $C\to U=b$, $C\to O=c$, and O absorbing over the observation interval. The mean first-opening times satisfy $T_U=1/a+T_C$ and $T_C=1/(b+c)+bT_U/(b+c)$, hence $T_U=(a+b+c)/(ac)$. Repeated unsuccessful binding attempts make this different from $1/c$. A <FRET> trace that cannot distinguish U from C does not by itself identify the individual binding and opening rates.
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