Precision of Readout at the hunchback Gene: Analyzing Short Transcription Time Traces in Living Fly Embryos
Fig 3
The autocorrelation prediction and autocorrelation based inference analysis performed on short trace simulated data for models of various complexity and positioning of the MS2 probe.
A cartoon of the construct with the MS2 cassette placed (A) after the gene (3’) and (B) before the gene (5’). Examples of the autocorrelation function’s analytical predictions compared to ones calculated from simulated traces (according to the Gillespie simulations described in SI Section G) show perfect agreement for 3’ MS2 insertions assuming a two state (telegraph) model, three state model and gamma function bursty model (C), as well as for the 3’ and 5’ constructs in the two state model (D). (E) Comparison between prediction and simulation for the cross-correlation between the signal coming from two different colored fluorescent probes positioned at the 3’ and 5’ ends. (F) The inference procedure for the two state model correctly finds the parameters of transcription initiation in a wide parameter range. The inference range grows with trace length and the number of nuclei. Error bars shown only for T = 240s, N = 50 nuclei (blue line) and T = 600s, N = 200 nuclei (red line) for clarity of presentation. Parameters for the simulations and predictions are, (C) for the two state model kon = 0.005 s−1, koff = 0.01 s−1, sampling time dt = 6 s, T = 360 s and number of cells M = 20000, the same parameters for the three state cycle model with koff = 0.01 s−1, k1 = 0.01 s−1 and k2 = 0.02 s−1, the same parameters for the Γ model with koff = 0.005 s−1 and α = 2 and β = 0.01 s−1; (D) kon = 0.02 s−1, koff = 0.01 s−1, sampling time dt = 6 s, T = 600 s and number of cells M = 20000; (E) kon = 0.01 s−1, koff = 0.01 s−1, dt = 6 s, T = 480 s and M = 20000. The 5’ construct is modeled as by adding a 3000bp non-MS2 binding sequence to the 3′ end of the MS2-binding cassette. (F) Pon = 0.1.