(A) If fluorescence profiles are approximated by step functions (left), correlation functions are piecewise linear (right). Autocorrelations decrease linearly and reach 0 at a delay equal to the persistence time of the red and green signals. Cross-correlation shows four angles, each reflecting the delay between a rise or fall in the red signal and a rise or fall in the green signal. (B) This can be generalized to the case where fluorescence signals rise as ramps (spanning the width of each cassette). In this case, the sharp angles described above become smooth when one or two of the fluorescence transitions they involve is a ramp. (C) If the red fall precedes the green rise (i.e., splicing precedes transcription of MS2 cassette), crosscorrelation at τ = 0 is null because the two signals never overlap. If the red signal falls while the green signal is up (i.e., splicing occurs after the MS2 cassette but before release), crosscorrelation at τ = 0 is non-null and is increasing with the same slope on either side of the y-axis. Finally, if both signal fall at the same time (i.e., splicing succeeds or coincides with transcript release), the crosscorrelation shows a break of slope at τ = 0, with a positive slope for τ < 0 and a null slope for τ > 0. (D) The correlation functions originating from a heterogeneous (stochastic) population of transcripts is simply the average of the correlation functions for each transcript. Hence, all the pre-release splicing events contribute a positive slope on either site of the y-axis, while all the post-release splicing events only contribute a positive slope on the left side of the axis. The resulting crosscorrelation displays a change of slope that directly reflects the fraction of pre- and post-release splicing events.