Figure 1.

Transitions in the kinetic model. (A) The forward and backward reactions are shown on the left and right, respectively. The left depicts the enzyme-induced modification, $U\to M$, at the i^th nucleosome. The right sketches the removal of the mark, $M\to U$, from the j^th nucleosome. Modifications to unmarked (U) nucleosomes and removal of marks from the M-type nucleosomes are shown by arrows. Important mediators relevant to the spreading processes are shown in color: the nucleation site (NS) is in green, and U (M) nucleosomes are shown in yellow (red). Some or all elementary transitions are considered simultaneously, representing four separate spreading mechanisms (see Fig. S1). The forward reaction occurs if an unmarked nucleosome i has a neighbor nucleosome in the modified state with a probability $P_{1D}^{+}\left(i\right)$ (orange arrow) or with a probability $P_{3D}^{+}\left(i\right)$ if it is in the spatial vicinity of an NS/modified nucleosome (purple arrow). The backward reaction can always proceed with a probability P_N(j), indicated by a black dashed arrow. The $M\to U$ reaction may also depend on the presence of other unmarked nucleosomes. In such cases, neighbor nucleosomes might induce the $M\to U$ transition in nucleosome j with a probability $P_{1D}^{-}\left(j\right)$ (cyan arrow), while U nucleosomes in the spatial vicinity of j may induce the reverse reaction with probability, $P_{3D}^{-}\left(j\right)$ (magenta arrow). (B) Asymmetric spreading from the NS (green) and non-NS sites (red). The forward rate for the non-NS sites is scaled by a factor of α compared with that for the NS site. Typically, we use $\alpha \ll 1$ in this study, which means that the ability of spreading of a non-NS site is much smaller than that of the NS site. To see this figure in color, go online.