(a) Nucleosome (cyan boxes) dynamics have three kinetics events: nucleosome binding, dissociation, and sliding. (b) In the PHO5 promoter region, transcription activators (green boxes) can associate or dissociate with certain kinetic rates at specific-sites (UAS1 and UAS2). Regulatory elements, such as UAS1, UAS2, and the TATA are indicated. The arrow at the origin (0) indicates the start of the gene. The DNA is color-coded according to the nucleosome affinity given by the total potential energy. (c) When one transcription activator is bound at the j^th site, it modifies the potential energy by adding (remodeling potential giving rise to localised nucleosome removal) as shown here. (d) When two transcription activators are simultaneously bound at UAS1 and UAS2 (where the separation d < k), the potential has the form shown here. The width of is taken as b = 150 bp and the slope (tanθ) is varied such that the height is given by h = btanθ.

(a) The competition between nucleosomes (filled circles) and Pho4p (filled triangles) proteins gives rise to different promoter states. At the top, we show a typical PHO5 promoter region with “T” representing the TATA box, the two empty triangles representing the two Pho4p binding sites (UAS1 and UAS2) and the three vertical line segments representing reference locations for −1 (right), −2 (middle) and −3 (left) nucleosomes. When there are no Pho4p bound (both the triangles are empty), we can define eight different arrangements of nucleosomes (leftmost column) as done by Brown et al.. These eight states are also depicted in the rightmost column without explicitly showing the binding sites of Pho4p (labelled as “implicit states”). The dark green (filled) triangles represent bound Pho4p proteins. When the presence/absence of 3 nucleosomes and 2 Pho4p proteins are explicitly accounted for, we can define 24 different states (see the shaded region labelled as “explicit states”). Among these 24 states, there are eight states where at least one Pho4p is bound and the TATA site is exposed. We define these states as “active” (A_i) states. The rest are “inactive” states (I). (b) The dynamics of nucleosomes and Pho4p make the promoter switch between active and inactive states with some effective equilibrium constant which will depend on the protein binding rate (r_onp) and local chromatin remodeling parameter (h). Promoter at the active state can produce mRNA (m) at the rate ε and the mRNA can decay at the rate δ.

(a) Nucleosome occupancies for various amounts of basal ATPase activity designated as V_eff. The cyan curve is for V_eff = −7 k_BT with no sequence effects. Other curves are with sequence effects for V_eff = −10, −7, −4 and 0 k_BT values (top to bottom). The Pho4p binding sites, UAS1 and UAS2, and the TATA box are indicated by grey strips. (b) Promoter-state distribution: In the X-axis, the eight implicit promoter states are depicted schematically as boxes with nucleosomes as dots—the top dot is nucleosome N − 1 and the bottom dot is nucleosome N − 3. The Y-axis gives the probability of finding these states. CRB1 (circles) and CRB2 (squares) are experimentally measured probabilities of these promoter states when the PHO5 gene is repressed or inactive, as reported by Brown et al. (for details, see text). The experimental findings are compared with our simulation results obtained under the same conditions as in (a). The inset indicates the average number of nucleosomes for various V_eff values. The region −8 < V_eff < −4 is shaded (grey) to indicate nucleosome density of ≈75% to 90%.

(a) Promoter-state distributions of the eight states as described in . Pho4p binding is introduced with small binding rates, r_onp ≈ 0.001–0.1 × k₀s⁻¹ as well as with high binding rate, r_onp = 10 × k₀s⁻¹. In the legends, r_onp are expressed in units of k₀ per second. (b,c) are the corresponding mRNA distributions and nucleosome occupancies, respectively. In (b), grey-shade is provided to indicate the fraction of the cells that are in the OFF state. All simulations were performed for V_eff = −7k_BT and LRA, h = 0k_BT.

(a) Promoter-state distribution for selected Pho4p binding rate, r_onp ≈ 0.3–0.6 × k₀s⁻¹, that are the best fit with the experimental data, CRBact (triangles). CRBact data points were obtained from transcriptionally active PHO4 pho80Δ cells where Pho80p has lost its phosphorylation activity. (b,c) are the corresponding mRNA distributions and nucleosome occupancies. In (b), grey-shade denotes the percentage of OFF cells, otherwise ON cells. Green curve in (c) is the occupancy in the repressed state. The data presented here are for V_eff = −7k_BT and LRA, h = 21k_BT.

(a) Phase plot of Fano factor, , as a function of activator binding rate, r_onp, and LRA, h. The color gradient on the right represents the value of F. (b) mRNA distributions: OFF-like long-tail (red), long-tail (green-square), bimodal (green-circle), and Poisson (blue). (c) Plot of Fano factor as a function of mRNA abundance, 〈m〉, for different values of h in the unit of k_BT. Each point in the plot is obtained by keeping h constant and varying the protein binding rate, r_onp. The data points were fitted using analytic functional form of Fano factor derived for a two-state random telegraph model: , where k_off is the transition rate constant from active to inactive state. Here k_off = 0.001 s⁻¹. All the simulations were conducted with V_eff = −7 k_BT.