Nonspecific bridging-induced attraction drives clustering of DNA-binding proteins and genome organization

Abstract

Molecular dynamics simulations are used to model proteins that diffuse to DNA, bind, and dissociate; in the absence of any explicit interaction between proteins, or between templates, binding spontaneously induces local DNA compaction and protein aggregation. Small bivalent proteins form into rows [as on binding of the bacterial histone-like nucleoid-structuring protein (H-NS)], large proteins into quasi-spherical aggregates (as on nanoparticle binding), and cylinders with eight binding sites (representing octameric nucleosomal cores) into irregularly folded clusters (like those seen in nucleosomal strings). Binding of RNA polymerase II and a transcription factor (NFκB) to the appropriate sites on four human chromosomes generates protein clusters analogous to transcription factories, multiscale loops, and intrachromosomal contacts that mimic those found in vivo. We suggest that this emergent behavior of clustering is driven by an entropic bridging-induced attraction that minimizes bending and looping penalties in the template.

Keywords: Brownian dynamics; chromatin looping; nucleosome; polymer physics.

Fig. 1.

Small proteins bind to DNA and form rows. MD simulations involving one string of blue beads (2.5 nm diameter) representing 36.75 kbp of DNA (persistence length, 50 nm; volume fraction, 0.26%; the radius of gyration of the unconfined polymer is ∼456 nm) (18) interacting with 400 DNA-binding proteins (2.5-nm-diameter red spheres; volume fraction, 0.02%) in a cube (250 × 250 × 250 nm). The interaction energy and range (protein bead center to DNA bead center) were 4.12 k_BT and 3.25 nm, respectively; times shown in all figures are in simulation units (here equivalent to 70 ns/unit, assuming a viscosity of 1 cP). (A–D) Snapshots taken at different times. In D, only proteins are shown (Inset: magnified region with proteins and DNA). As proteins bind, they form into rows, locally folding DNA. (E) Both the fraction of beads in clusters and average cluster size increase with time (two bound proteins are in a cluster if center-to-center distance is <3.5 nm).

Fig. 2.

Large proteins form quasi-spherical clusters on binding to DNA. MD simulations involving one string of blue beads (2.5 nm diameter) representing 73.53 kbp of DNA (persistence length, 50 nm; volume fraction, 0.16%; the radius of gyration of the unconfined polymer is ∼645 nm) (18) interacting (12.4 k_BT,;range, 10 nm from center of protein bead to DNA bead) with 100 DNA-binding proteins (red spheres, 12.5 nm diameter; volume fraction 0.2% equivalent to 3.15 μM) in a cube (375 × 375 × 375 nm). (A and B) Two views (with/without DNA) of one structure after 30,000 simulation units; many complexes cluster. (Inset) Example of DNA wrapping reminiscent of that around a nucleosome core from a simulation involving exactly the same parameters but only one protein; such structures are rarely seen with many proteins. (C) The fraction of beads in clusters increases with time only if there is an attraction (two proteins are in one cluster if center-to-center distance is <17.5 nm).

Fig. 3.

Binding of nucleosome cores generates disordered chromatin fibers. MD simulations involving one string of blue beads (2.5 nm diameter) representing 36.76 kbp of DNA (persistence length, 50 nm; volume fraction, 0.02%; the radius of gyration of the unconfined polymer is ∼456 nm) (18) interacting (energy, 4.31 k_BT; range, 3.5 nm from center of DNA bead to center of DNA-binding patch) with 100 nucleosomal cores (volume fraction 0.006%) in a cube (750 × 750 × 750 nm). Each core is represented by four planar (red) spheres each bearing two (green) binding sites. (A and B) Two views (with/without DNA) of one structure after 1.5 × 10⁵ simulation units (one unit corresponds to 35 ns, assuming a viscosity of 1 cP); many cores cluster. (C–E) Three views (with/without DNA or cores) of one cluster in A shown from a different viewpoint; DNA is folded around cores much as in nucleosomes. (F) Both the fraction of beads in clusters and average cluster size increase with time (two bound cores form one cluster if center-to-center distance of each core is <17.5 nm).

Fig. 4.

Clustering of 20-nm complexes on binding to euchromatin. MD simulations involving one string of blue beads (20 nm diameter; 2 kbp of DNA) representing 10 Mbp euchromatin (persistence length, 60 nm; the radius of gyration of the unconfined polymer is ∼1.4 μm) interacting (4.12 k_BT; range, 26 nm from DNA center to polymerase center) with 100 complexes containing RNA polymerases and transcription factors (red beads, 20 nm diameter) in a cube (2 × 2 × 2 μm). (A and B) Two views (with/without DNA) of one structure after 30,000 simulation units (one unit corresponds to 0.36 ms, assuming a nucleoplasmic viscosity of 10 cP); complexes cluster. (Insets) High-power views of one cluster. (C) Both the fraction of beads in clusters and average cluster size increase with time (two complexes form one cluster if center-to-center distance is <28 nm; using this stringent threshold, the fraction in clusters only reaches ∼0.6, despite all but three red beads appearing to be in clusters in B).

Fig. 5.

Clustering of NFκB and RNA polymerase II bound to human chromosomes 5, 8, 14, and 17. MD simulations involving four strings of beads (diameter 30 nm) representing human chromosomes 5 (red), 8 (blue), 14 (green), and 17 (yellow) modeled as polymers of appropriate length (persistence length, 90 nm; volume fraction, 10%) in a cube (3 × 3 × 3 µm). Radii of gyration of unconfined chromosomes 5, 8, 14, and 17 are ∼7.4, ∼6.6, ∼5.6, and ∼4.9 µm, respectively, so polymers are in the semidilute to concentrated regime (18). The cube also contained 5,000 NFκB complexes (green 9-nm spheres) plus 5,000 RNA polymerases (red 18-nm spheres) that bind to cognate sites on the chromosomes. As a result, there are four types of beads: nonbinding, able to bind just NFκB or just the polymerase, and able to bind both. Binding data for p65 (a subunit of NFκB) and the polymerase were obtained by ChIP-seq using HUVECs 30 min after stimulation with TNFα. For polymer:polymerase interactions, the interaction energy was set to 15.95 k_BT and the range (between centers of DNA and protein beads) to 43.2 nm; for polymer:p65 interactions, corresponding values were 13.52 k_BT and 36 nm. (A) Browser views of the 5′ region of SAMD4A showing binding sites for the polymerase and p65 (fold enrichment indicated). The cartoon below the map indicates how binding of just NFκB to each 3-kbp segment is modeled; only the indicated 3 of 14 beads (at the SAMD4A promoter) possess a surrounding attractive zone (pink) and can bind NFκB. (B) A snapshot taken after 100,000 simulation units (equivalent to ∼120 s, assuming a viscosity of 10 cP). (C) Magnification of Inset in B without chromosomes to highlight protein clustering. (D) Both the fraction of beads in clusters and average cluster size increase with time (two polymerases or two NFκB complexes form one cluster if center-to-center distance is <36 nm). (E) Contacts (marked as a cross and defined as center-to-center distance <90 nm) within and between the four chromosomes; the four remain segregated in territories to form more intra- than interchromosomal contacts (indicated by the high concentration of crosses in blue boxes). (F) Simulations and ChIA-PET yield similar contacts. Data on contacts made by every 3-kbp region within SAMD4A were obtained from the simulation (contact defined as two monomers lying within 90 nm) or ChIA-PET (using data from ref. ; contact defined as number of paired reads with no base pair mismatch in the SAMD4A tag and up to two mismatches in the paired tag). The contact number (coarse-grained into 15-kbp bins) detected by the two methods falls in much the same way with distance from the transcription start site (TSS).

Fig. 6.

The bridging-induced attraction. Each panel illustrates part of a long polymer and some DNA-binding proteins (green spheres surrounded by attractive zones). (A) When proteins bind, the mobility of black monomers is restricted (reducing their entropy); the gray flanking monomers also lose some entropy, and more distant ones progressively less (not indicated). (B) The two structures contain the same number of monomers and proteins, but the one on the right will be more stable as it contains one less loop and fewer gray monomers. (C) Once one bridge forms, monomers on each side of the bridge are likely to be positioned in a way favoring binding of a second bridge. This binding does not exact the full entropic cost, as much of that cost was paid when the first bridge formed. With stiff polymers like naked DNA, this probably drives the formation of rows of bound proteins (Fig. 1; Fig. S5). (D) Once two bridges connect two DNA segments, the resulting high local concentration creates a collisional cross section likely to sieve out any protein that diffuses by. (E) When the left-hand bridge dissociates, rebinding nearby is promoted by the high local DNA concentration. After several steps of dissociation/rebinding, or sliding, the resulting zipping together gives the structure on the right, which is the most stable (with four fewer gray monomers than the other two structures).