Nucleosome-mediated cooperativity between transcription factors

The Model of Nucleosome-Mediated Cooperativity.

We consider interactions of TFs with a stable nucleosome, containing an array of n TFBSs within its DNA footprint (147 bps) (Fig. 1). This region of DNA can be in one of two states: the nucleosome (N) state and the open (O) state, in which histones are absent from the region. While histones limit access of other proteins to nucleosomal DNA, the nucleosome is highly dynamic, with DNA unwrapping and wrapping at a high rate, thus making nucleosomal DNA at least partially accessible to TFs (28, 29). TFBSs can be occupied by TFs in either the N or O state leading to 2n states labeled N_i and O_i (i = 0,1,…n), where i is the number of occupied sites. The equilibrium between the N and O states in the absence of bound TFs is characterized by the constant L = [N₀]/[O₀], where L≫1 for a stable nucleosome. The affinity of TFs for the sites depends on the state, with binding constants K_N and K_O (K_O ≪ K_N due to higher affinity in the open state). Suppression of TF binding to nucleosomal DNA is reflected by the free energy cost of DNA unwrapping required to accommodate one more TF (30) and is taken into account by parameter c ≡ K_O/K_N ≪ 1.

For simplicity of presentation, we assume all TFBSs to have the same affinity and experience the same suppression by the nucleosome. More complicated models that drop these assumptions and consider partial unwrapping are considered in SI Text but yield similar results.

TFs can be activated by different mechanisms: increased intranuclear concentration of a TF (e.g., by facilitating its nuclear localization or inhibiting degradation) or elevated TF affinity for its cognate sites (e.g., through a conformational change upon a modification or binding to a ligand). Both factors are taken into account by a dimensionless parameter α = [P]/K_O, where [P] is the intranuclear concentration of the activated TF. In equilibrium, the system is fully determined by three dimensionless parameters: c, L, and α (Fig. 1). We study equilibrium properties, assuming that rapid exchange of TFs and histones leads to fast equilibration.

Cooperative Binding and Nucleosomal Occupancy.

The two quantities of primary biological interest are TF occupancy per site (Y) and the occupancy by the nucleosome (Y_N). Using statistical mechanics, and analogy to the MWC model, we obtain expressions for these quantities (see SI Text):

[1]

[2]

Fig. 2A presents TF and nucleosome occupancies as a function of TF concentration, computed using parameters inferred from experiments with α = 0–10, L ≈ 10³, c ≈ 10^-2 (see Materials and Methods). Strikingly, nucleosome-mediated cooperativity results in a sharp transition with a twofold increase in TF concentration leading to a more than eightfold increase in the occupancy. The nucleosome occupancy also changes cooperatively, dropping from about 65% to less than 10% due to a twofold change in TF concentration.

Complex cis-regulatory elements of higher eukaryotes may require several activating TFs (or several copies of the same TF) to be bound for initiation of gene expression (4, 31). To take this into account, we calculate another quantity, the probability of having at least k TF bound, P_k, as a measure of occupancy, which also shows a significant cooperativity (Fig. 2B and SI Text).

Importantly, as in the case of hemoglobin, the cooperativity stems from suppression of TF binding at low TF concentration (Fig. 2A, dotted vs. solid green lines). This behavior is distinct from cooperative binding enhanced by attractive protein–protein interactions. Cooperative suppression of TF binding by nucleosomes, however, could be advantageous in multicellular eukaryotes that contain an overwhelming number of spurious binding sites in their genomes (12, 27).

Surprisingly, our model suggests that nucleosome destabilization should have opposite effects on cooperativity and on TF binding. Factors that destabilize nucleosomes, [e.g., histone modification, poly(dA:dT), etc.] facilitate TF binding but make this binding less cooperative. Similarly, factors that stabilize nucleosomes suppress binding at a low TF concentration, making binding more cooperative. In Discussion, we review recent genomics findings that reveal signatures of nucleosome stabilization in human regulatory regions (26).

Analogy to Hemoglobin.

Strikingly, the system of TFs and a nucleosome is identical to the scheme of cooperativity in hemoglobin described by the classical MWC model (20) (see Fig. 1 C and D). Table S1 summarizes equivalent parameters and analogous phenomena between the two systems. The MWC model considers the equilibrium between two states of hemoglobin: the R state, which has a higher affinity for O₂, and the low-affinity T state. In the absence of the O₂, hemoglobin is mostly in the T state. Binding of O₂ shifts the equilibrium toward the R state, making binding of successive oxygen molecules more likely and thus cooperative (Fig. 1D). The R and T states of hemoglobin correspond to the O and N states of the nucleosomal DNA, and the binding of O₂ to hemoglobin domains corresponds to the binding of TFs to individual sites (Fig. 1 C and D and Table S1).

The analogy to the MWC model allows us to reveal features of the nucleosome–TF system that are essential for cooperativity (Table S1). The MWC system has a strong cooperativity as long as L is sufficiently large (L > 100) and c is sufficiently small (c < 0.1), i.e., the nucleosome is stable (in the absence of TFs) and significantly attenuates TF binding. These requirements are consistent with estimated parameters (see Materials and Methods), as well as with high stability (32, 33) and slow exchange (34, 35) of nucleosomes in regions depleted in TFBSs. In vitro studies of TF binding to nucleosomal DNA demonstrate the required attenuation of TF binding (36).

The Bohr Effect and Chromatin Modification.

We also use the analogy to hemoglobin to examine implications of sequence-specific nucleosome positioning, histone modifications, and other processes involved in gene regulation. These effects can be considered as allosteric heterotropic regulation of the nucleosome–TF system, analogous to heterotropic effectors of hemoglobin. A prototypical heterotropic allosteric regulation of hemoglobin is the Bohr effect: Lowering the pH decreases the affinity to oxygen, thus providing more oxygen to actively working muscles. The basis of the Bohr effect is the higher affinity of hydrogen ions to the T state. Thus, low pH stabilizes the T state, shifting the equilibrium away from the high-affinity R state. Other allosteric effectors of hemoglobin (e.g., DPG) act in a similar way: Binding hemoglobin in one state affects the R-T equilibrium and thus changes the affinity of hemoglobin to oxygen.

While heterotropic effectors of hemoglobin affect equilibrium between R and T states, effectors of the nucleosomes–TF system such as histone modifications and histone-binding proteins influence nucleosome stability, thus altering the balance between N and O states. Fig. 2C shows the manifestation of the Bohr effect in the TF-nucleosome system: Small changes in nucleosomal affinity (from L to L^′) due to histone modifications can shift the balance in TF-nucleosome competition toward or away from the nucleosome. For example, a modification that reduces nucleosome stability by about ΔG = 1 kcal/mol (ΔG = k_BT log(L/L^′)) can lead to an 80% drop in nucleosome occupancy (Fig. 2C, Inset) and a concurrent rise of the TF occupancy (Fig. 2C). Similarly, nucleosome-positioning sequences have a similar effect: They alter nucleosome stability, thus shifting the occupancy curve. Competition between the nucleosome and TFs leads to amplification of the nucleosome-positioning sequence signal, i.e., small changes in histone affinity translate into significant changes in nucleosome occupancy (Fig. 2C, Inset).

Similarly, small changes in TF concentration can significantly reduce nucleosomal occupancy (Fig. 2A and Fig. S3C) in TFBS-rich regions. For example, activation of a tissue-specific TF can lead to selectively reduced chromatization and increased accessibility of tissue-specific regulatory regions (Fig. 3). This is in agreement with a recent genome-scale mapping of DNase I hypersensitive sites (DHS), which found that several loci exhibit tissue-specific DHS profile (37). Note that this mechanism of passive nucleosome eviction does not rely on recruitment of chromatin modification machinery, which may play a role in further destabilizing nucleosomes and expanding nucleosome-free regions.

Critical Size of the TFBS Cluster.

Nucleosome-induced cooperativity, however, has some properties without counterparts in hemoglobin. For example, the number and the affinity of binding sites are constant in hemoglobin but vary in cis-regulatory regions. Fig. 2D presents nucleosomal occupancy as a function of the number, n, of TFBSs. As the number of TFBSs exceeds a certain critical value n_c, nucleosomal occupancy drops sharply, manifesting another allosteric effect in the system. Our calculations show that the critical number of TFBSs is given by n_c ≈ log(L)/ log(1 + α), yielding a narrow range n_c = 3–6 that is not very sensitive to model parameters (see SI Text). This range of TFBSs per nucleosomal footprint is consistent with the recent characterization of Drosophila enhancers (1, 3) that contain about 20 TFBSs per 0.7–1 Kb (i.e., 4–6 sites per nucleosome) (2). Similarly, the cis-regulatory system of endo16 in sea urchins has about 50 sites localized within 2.3 Kb and grouped into seven clusters of five to 10 sites (4). Such passive eviction of nucleosomes could explain widespread depletion and rapid exchange of nucleosomes in TFBS-rich regions (33, 34, 38–40).

This cluster size is consistent with our recent information-theoretical estimates (27) of the minimal significant TFBS cluster. Nucleosomes-mediated cooperativity can suppress binding to widespread spurious sites that are unlikely to cluster, while providing binding to clusters of sites. An example on Fig. 3 demonstrates that clusters of five high-affinity (or eight low-affinity TFBSs) become occupied and nucleosome-free, while isolated sites remain unoccupied by TFs.

Our approach allows one to consider the contributions of low-affinity sites (9, 41) and mixtures of sites of different TFs (see SI Text). Fig. 3 illustrates how arrays of low-affinity and high-affinity sites in nucleosomal DNA respond differently to increasing levels of TFs.

Approach.

We use a statistical mechanics approach to derive occupancy and other equilibrium properties of the system presented in Fig. 1 (see SI Text). The advantage of our approach is that it allows generalization for more complex cases considered in SI Text.

Estimation of Parameters from Experimental Data.

To estimate α, we take into account TF binding to both specific and nonspecific DNA, with binding constants K and K^NS, respectively. Due to competition between specific and nonspecific DNA the occupancy of a single site is y = [P]/([P] + K(1 + [DNA]/K^NS)) = α/1 + α, where α ≡ [P]/K^eff, effective binding constant defined as K^eff = K(1 + [DNA]/K^NS) ≈ K[DNA]/K^NS, and [DNA] is the concentration of TF-accessible nonspecific DNA. The dissociation constant of most eukaryotic TFs is in the range of K ≈ 1–10 nM, while known nonspecific binding constants are K^NS ≈ 1–10 μM (63, 64). Using the length of genomic DNA and the measured copy number of TFs ([P] ≈ 500–5,000 in yeast and [P] ≈ 10⁴–10⁵ protein copies per nucleus in multicellular eukaryotes) (65) (BioNumbers database, http://bionumbers.hms.harvard.edu/) with the assumption of 90% chromatinization, we obtain the range of α ≈ 0.5–5.

We estimate L using in vivo nucleosome equilibrium occupancy f = [N]/([N] + [O]), yielding L = f/(1 - f). Although for stable nucleosomes, occupancy is very close to 1, the fraction of DNA covered by nucleosomes provides a lower bound for f and has a range of 0.9–0.99 (66), yielding L > 10–100. This constitutes a lower bound for f and L, because most nucleosome-free regions are maintained by competition with TFs or active chromatin modification.

Parameter c of the model reflects suppression of TF binding by a nucleosome while in the N state. Acting through steric hindrance, such suppression is not permanent and nucleosomal DNA becomes transiently exposed for TF binding (Fig. 1B) (36, 67). This suppression is equivalent to the experimentally measured equilibrium constant of site exposure, which depends on the location of the site with respect to the center of the nucleosome and has the range c = 2·10^-2–10^-5. Detailed treatment of partially unwrapped states (see SI Text) shows that they can be aggregated into a single N state.

Obtained estimated values of parameters are sufficient to provide nucleosome-mediated cooperativity. The mechanism of cooperativity is very robust, requiring only L≫1 and c ≪ 1 for the onset of cooperativity (Fig. S1).