Slow nucleosome dynamics set the transcriptional speed limit and induce RNA polymerase II traffic jams and bursts
Fig 3
Deriving and validating the mean and variance of first passage time equations.
(A) A state transition diagram utilized to calculate the mean (Ee) and variance (Ve) of first passage time to enter a nucleosome. Each arrow is labeled with the rate constant for the transition between the neighboring states. (B) Log-log plot of simulated mean first passage time (Eq 22) against the predicted analytical expression for mean first passage time. The black line represents the theoretical prediction. The dashed red line represents the Bare DNA limit obtained by simulations with hc = 0. (C) Log-log plot of simulated variance of first passage time against the predicted analytical expression for VFPT (Eq 26) with the Bare DNA limit represented by the dashed red line. (D) Plot of index of dispersion of the waiting time to enter a nucleosome De = Ve/Ee against the resting state binding probability of the nucleosomes (). hc is set to be 0.001 (blue), 0.01 (green), 0.1 (orange), and 1 (red). ho was adjusted to achieve γ∈{0.002, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 0.99}. Solid lines indicate the theoretical prediction given by Eq 27. (E) Log-log plot of the analytical expression for the index of dispersion of the waiting time to enter a nucleosome De (Eq 27, analytical) as a function of the expected waiting time for nucleosome opening (1/ho). The dashed black line shows the index of dispersion in the limit of ho→0.