Thermodynamics of Intragenic Nucleosome Ordering

The nucleosome ordering observed in vivo along yeast genes is described by a thermodynamical model of nonuniform fluid of 1D hard rods confined by two excluding energy barriers at gene extremities. For interbarrier distances $\mathcal{L}\lesssim 1.5\mathrm{kbp}$, nucleosomes equilibrate into a crystal-like configuration with a nucleosome repeat length (NRL) $\mathcal{L}/n\sim 165\mathrm{bp}$, where $n$ is the number of regularly positioned nucleosomes. We also observe “bistable” genes with a fuzzy chromatin resulting from a statistical mixing of two crystal states, one with an expanded chromatin (NRL $\sim \mathcal{L}/n$) and the other with a compact one (NRL $\sim \mathcal{L}/(n+1)$). By means of single nucleosome switching, bistable genes may drastically alter their expression level as suggested by their higher transcriptional plasticity. These results enlighten the role of the intragenic chromatin on gene expression regulation.

Figure 1

Average (4554 yeast genes) in vivo (red, grey line) [3] and theoretical (blue, black line) nucleosome occupancy (${log}_2$) profiles, and mean theoretical energy profile (blue, dashed line) plotted around (a) the TSS and (b) the TTS. (c) and (d): same as in (a) and (b) but with individual profiles aligned on the first flanking nucleosome ($+1$) downstream the TSS and ($-1$) upstream the TTS. The dotted line corresponds to the theoretical nucleosome occupancy profile obtained when imposing an artificial excluding energy barrier at TSS and/or TTS when not predicted by the sequence (see text). (e) and (f): same as in (c) and (d) for the average in vitro (red, grey line) [4] and the theoretical low density nucleosome occupancy profile (blue, black line) and energy profile (blue, dashed line). The solid bars (white bars) histograms correspond to experimental (theoretical) distance between TSS and $+1$ nucleosome (a) and between TTS and $-1$ nucleosome (b). The model parameters are (a)–(d) $\delta E=⟨(E-⟨E⟩{)}^2{⟩}^{1/2}=2\mathrm{kT}$, $\tilde{\mu }=-1.3\mathrm{kT}$ (blue, black line), $\delta E=0.75\mathrm{kT}$, $\tilde{\mu }=1.5\mathrm{kT}$ (blue, black dotted line) and (e)–(f) $\delta E=2\mathrm{kT}$, $\tilde{\mu }=-6\mathrm{kT}$. $\tilde{\mu }=\mu -⟨E⟩$ has been adjusted so that the mean in vivo (a)–(d) and in vitro (e)–(f) nucleosome densities are correctly reproduced.

Figure 2

(a) Nucleosome occupancy (${log}_2$) profile along the yeast chromosome II genome: in vivo [3] (top red curve), in vitro [4] (bottom red curve), theoretical profiles for $\delta E=2\mathrm{kT}$, $\tilde{\mu }=-2\mathrm{kT}$ (top blue curve) and $\tilde{\mu }=-6.7\mathrm{kT}$ (bottom blue curve). (b) Same as in (a) for chromosome XII. In (a) and (b) are indicated the positions of TSS (red dots), TTS (red circles) and of TF binding sites (black triangles).

Figure 3

(a) 2D map of local minima (red) of the experimental in vivo nucleosome occupancy profile at yeast genes [3]; genes are ordered vertically by the distance $L$ between the $+1$ and $-1$ nucleosomes. Insets: mean experimental (red) and one individual theoretical (blue) nucleosome occupancy profiles for crystal genes harboring 5 nucleosomes (right, top), 6 nucleosomes (right, bottom) and the bi-stable genes with $5/6$ nucleosomes. (b) Zoom on the first 2000 genes in (a); on the top of the experimental data (red) are superimposed the predictions of our physical modeling (blue); horizontal grey-shaded bands correspond to some bi-stable $L$ domains. Same model parameters as in Figs. 1a, 1b, 1c, 1d.

Figure 4

Theoretical probability of nucleosome occupancy at each point of a box bordered by two infinite walls mimicking excluding barriers at gene extremities: (a) box large enough to shelter $n=5$ nucleosomes (black); (b) larger box where the two $n=5$ and 6 configurations (grey) are possible; the weighted average of these crystal-like profiles yields a fuzzy-looking profile (black); (c) larger box where 6 nucleosomes can be inserted (black). (d) Probability of crystal configurations with a fixed number $n$ of nucleosomes vs. the box size. Vertical dashed lines correspond to the interbarrier distances used in (a), (b) and (c) respectively. (e) NRL dependency on the box size: thin black dotted lines correspond to a fixed number $n$ of nucleosomes and the thick black dotted lines to the NRL at a fixed nucleosome density ($\sim 85\%$); grey dots correspond to individual crystal gene values. Vertical grey-shaded bands correspond to the experimental bi-stable $\mathcal{L}$-domains. (f) Average transcription rate [20] (black) and transcriptional plasticity (square ${log}_2$ expression ratio) [17] (grey) from various microarray experiments [21]. (g) Proportion of bi-stable genes.