Supercoils Stabilize a “DNA Corset” Condensate with Torsion-Dependent Hysteretic Compaction

Abstract

Biomolecular condensates formed through phase separation are critical physical mechanisms for organizing membraneless compartments in eukaryotic cells. To achieve precise spatiotemporal control of biochemical reactions, cells must effectively regulate condensate size. The microscopic mechanism underlying these regulation processes, on the other hand, remains largely elusive. We herein explicitly incorporate DNA torsional flexibility into a coarse-grained DNA–protein “Bridging-Induced Phase Separation” model, enabling the direct simulation and visualization of how DNA supercoiling regulates the condensate structure and size. DNA supercoiling generates a compact “DNA corset” condensate with a dense DNA–protein core encircled by plectonemic loops that laminate the surface. Increasing supercoiling compacts the condensate, whereas torsional relaxation restores its size through entropy-driven expansion. For short DNA, this transition is fully reversible, whereas longer chains exhibit hysteresis in which compaction and relaxation follow distinct pathways and thresholds. Supercoiling, therefore, functions as a topological switch that couples twist-to-writhe conversion with condensate mechanics. These findings link DNA supercoiling to the dynamic control of chromatin condensates and provide a physical framework for the topology-based condensate design.

Introduction

Biomolecular condensatesdynamic subcellular assemblies formed by phase separation of proteins, nucleic acids, and other macromoleculesgovern critical biological processes, including transcription, , three-dimensional genome organization, − DNA damage repair, , immune response, , and cellular signaling. , Importantly, condensate functions are often tightly coupled to their physical sizes: in metabolic regulation, for instance, enzyme colocalization within condensates enhances substrate channeling but only within an optimal size window; in the nucleus, aberrant size increments of nucleoli, Cajal bodies, and nuclear speckles often correlate with the pathological states. − For example, persistent nucleolar hypertrophy not only signifies hyperactivated ribosome production but also associates with oncogenesis and Hutchinson–Gilford progeria syndrome. , The mechanisms driving size changes (such as the formation of excessively enlarged condensates) and their pathological significance, on the other hand, remain largely elusive.

Cells maintain condensate size homeostasis via multiscale control mechanisms. At the molecular scale, condensates emerge via phase separation driven by a variety of short-range interactions among biomacromolecules, including electrostatic forces, dipole–dipole interactions, π–π stacking, cation−π interactions, hydrophobic interactions, and hydrogen bonding. − The strength and nature of these interactions directly determine the condensate assembly and size distribution. For example, long-range electrostatic repulsion mediated by charge asymmetry can effectively inhibit coarsening, enabling the equilibrium coexistence of numerous droplets with comparable sizes. , At the mesoscopic scale, condensates reside in a complex intracellular environment characterized by viscoelasticity, molecular crowding, and the pervasive presence of biopolymeric networks such as chromatin and the cytoskeleton. By modulation of the physicochemical properties of the surrounding medium, cells can influence condensate dynamics. For instance, the elastic stresses generated by chromatin or cytoskeletal networks can suppress coarsening, thereby stabilizing the coexistence of multiple condensates. −

Focusing on chromosomal phase separation, cells package megabase-length DNA into micrometer-scale condensates that participate in diverse nuclear functions such as nonmembranous organelle formation, heterochromatin assembly, and transcriptional hub organization. Biomolecules undergoing phase separation constitute an extremely heterogeneous polymer composed of tens of thousands of distinct combinations of DNA sequences and DNA-binding proteins. Recent studies on cohesin complexes and the H-NS protein, for instance, have demonstrated that highly heterogeneous DNA can co-condense with bridging protein complexes. − Elucidating the mechanisms that regulate the size of chromosomal condensates requires not only accounting for the influence of their mesoscopic environment but also incorporating the contributions of protein–DNA interactions. Two mechanistic paradigms have been proposed for protein–DNA condensation: , bridging-induced phase separation, in which multivalent protein–DNA interactions nucleate condensates by looping distant DNA segments; and self-association-induced phase separation, driven by multivalent protein–protein interactions that scaffold DNA–protein clusters. Bridging-induced phase separation critically depends on DNA-binding affinity and halts upon full chromatin decoration, whereas SIPS growth is governed by the competition between Ostwald ripening and droplet diffusion.

When DNA is subject to enzymatic regulation by RNA polymerases and topoisomerases, a considerable extent of supercoiling is introduced; − for example, transcriptional condensates contain RNA polymerase. Previous studies have begun to explore how DNA superhelicity influences DNA–protein condensates. For example, ParB (a CTP-hydrolase partition protein B) forms condensates with DNA, and experiments have shown that supercoiled DNA enhances ParB–DNA condensation (initiating condensates at lower ParB concentrations than on relaxed DNA) with the resulting ParB clusters absorbing the DNA’s supercoiling writhe. Similarly, the nucleoid-associated protein H-NS oligomerizes and bridges separate DNA segments to compact the bacterial chromosome (a bridged condensate akin to phase separation); Structural Maintenance of Chromosomes (SMC) complex binding and DNA looping are stimulated by supercoiled DNA, and condensin preferentially binds near the tips of supercoiled plectonemes. Upon loop extrusion, condensin collects nearby plectonemes into a single supercoiled loop that is highly stable. Notably, none of these studies explicitly address whether or not DNA supercoiling affects the size or internal structure of the condensates formed. The precise mechanisms by which supercoiling regulates condensate size remain unclear.

The present study explicitly incorporates DNA torsional flexibility into a coarse-grained DNA–protein bridging-induced phase separation model and then carried out the molecular dynamics simulations to examine the influence of DNA supercoiling on condensate size and architecture. Our study reveals that supercoiling leads to a “DNA corset” condensate structure, which has a dense core of tightly packed DNA and associated proteins, surrounded by the plectonemic DNA loops that wrap around and snugly laminate (rather than jutting outward) the condensate’s surface. As the superhelical density increases, the exponent α in the scaling relation R _g ∼ N ^α between the condensate radius of gyration R _g and the DNA chain length N decreases from 0.45 (close to ideal-chain behavior) to 1/3 (consistent with polymer collapse in a poor solvent). Notably, this condensate is dynamically reversible (see Figure a): relaxing the torsion allows entropy-driven expansion back toward an open state. For short DNA chains, this reversibility is complete, while for longer DNAs, hysteresis is observed in this transition, meaning that the pathway and thresholds for compaction versus relaxation differ. This suggests that the structure can act as a topological “switch” with a memory of its prior state. Collectively, these findings provide new insights into how supercoiling regulates the spatial organization of protein–DNA condensates, an important facet of chromosome organization and gene regulation.

1.

(a) Protein bridging-induced DNA phase separation and structural evolution of the condensate modulated by supercoiling density. Inset: schematic illustrations of free, binding, and bridge proteins, as well as the setup of angle and torsional potentials in the adjacent DNA units (details in the Methods Section) (b) No supercoiling: Proteins (large cyan spheres, with two red DNA-binding sites) are randomly and uniformly distributed around the DNA (blue semiflexible polymer chain) in a random coil conformation. Phase separation is induced via protein bridging, leading to condensate formation. (c) Apply supercoiling: Starting from the equilibrated condensate configuration in (b), the DNA supercoiling density σ_↑ is gradually increased. (d) Release supercoiling: Starting from the final state at σ_↑ = 0.05, the supercoiling density progressively decreased, showing system snapshots at the corresponding σ_↓ values. Insets in b, c, d show DNA conformations corresponding to each state after the removal of proteins from the condensate, revealing the formation of plectonemes promoted by supercoiling. In the snapshots, the red DNA segments denote plectonemes. The DNA chain in these simulations consists of N = 2000 beads.

Results and Discussion

We employed a bead–spring model to construct circular DNA polymers subject to both bending and torsional loads and introduced patch particles to regulate the supercoiling density. The torsional deformation of DNA is generated by a symmetric harmonic potential that imposes no energetic preference for the handedness of supercoiling. Consequently, the formation of positive and negative supercoils follows identical rules and incurs the same energetic costs. Accordingly, we define DNA supercoiling density σ as a nonnegative quantity that denotes only the magnitude of the superhelical density and does not encode its sign. Proteins were represented using a rigid stacker–spacer model, in which the “stacker” denotes the central core that preserves the spatial configuration through steric repulsion, while the two terminal “spacers” serve as DNA-binding sites that establish specific attractive interactions with DNA, thereby enabling bridging and condensate formation. Detailed model parameters and simulation settings are provided in the Methods Section and Supporting Information.

Ten independent simulations were carried out, in each of which, the protein-mediated regulation of condensate size has three stages (Figure a): Stage 1­(σ = 0.0): no supercoiling, condensation induced by only bridging-induced phase separation; Stage 2­(σ_↑): incremental increase in σ by 0.005. After each increment, the system is fully relaxed until the target supercoiling density of σ_↑ = 0.05 (in cells, the typical magnitude of σ is about 0.05 ∼ 0.06) is reached; Stage 3 (σ_↓): the supercoiling density is then decreased in the same increments, each followed by the same relaxation period, until it is fully released (σ_↓ = 0.0).

2.

Time evolutions of physical quantities along a single simulation trajectory: (a) Two vertical dashed black lines divide the simulation into three sequential stages: no supercoiling, the supercoiling-imposition stage, and the supercoiling release stage. (b–e) Evolution of various physical quantities as a function of supercoiling across different stages: (b) potential energy U, (c) radius of gyration R _g, (d) asphericity A, and (e) the DNA–protein binding ratio R, where green, orange, and gray curves denote the fractions of proteins in the bridging, binding, and free states, respectively. (f) R _g at different values of σ. The blue and green triangles indicate the R _g values measured during the supercoiling-accumulation and supercoiling-removal stages, respectively. The data shown correspond to DNA with N = 2000 beads (∼14.7 kbp); the results for other DNA lengths are provided in Supporting Information (Figure S2).

In the bridging-induced phase separation model employed herein, proteins can adopt one of the three states: bridge (both binding sites are bound to DNA), binding (only one site is bound), or free (neither site is bound; Figure a).

During condensation, a “free” protein binds to the DNA with one of its DNA-binding sites and becomes a “binding” protein (Figure b). Its unoccupied binding site might bind to another unit of the DNA distant along the sequence but spatially proximal, and the protein adopts a “bridge” state. In Stage 1, “free” proteins rapidly adsorb onto DNA and transit into the “binding” and “bridge” states (Figures b–d and e), both “binding” and “bridge” proteins can form the nucleation centers of the complex, leading to small, locally formed DNA–protein condensates, which later coarsen into a larger, single condensate (Figure b). Binding-state proteins, which are adsorbed to DNA via only one terminus, are predominantly distributed on the surface of the condensate. Condensate formation is associated with a reduction in R _g and a corresponding decrease in the system energy U resulting from protein–DNA bridging. As the system enters Stage 2, the DNA twisting induced by supercoiling gradually reduces the R _g value (Figure c). In Stage 3, the release of supercoiling increases R _g (Figure ). To quantitatively characterize the shape of the condensate, we compute the asphericity

$$A=({({\lambda }_1-{\lambda }_2)}^2+{({\lambda }_2-{\lambda }_3)}^2+{({\lambda }_3-{\lambda }_1)}^2)/2{({\lambda }_1+{\lambda }_2+{\lambda }_3)}^2$$

where λ₁, λ₂, and λ₃ are the eigenvalues of the gyration tensor defined as

$$S_{\mathit{ij}}=\frac{1}{N}\sum _{n=1}^N(x_{n,i}-x_{\mathrm{cm},i})(x_{n,j}-x_{\mathrm{cm},j})$$

Here, x _cm,i and x _n,i denote the condensate center of mass and the coordinate of the nth bead, respectively. A provides a quantitative measure of the condensate’s deviation from a perfect sphere, with A = 0 corresponding to an ideal spherical shape. Thus, a decreasing trend in A indicates that the condensate gradually adopts a more spherical morphology during condensation (Figure d).

During stage 2, an increase in σ_↑ induces the accumulation of torsional stress in the DNA. When the applied torque exceeds a critical threshold, a fraction of the twist is relieved by conversion into spatial writhe. This twist-to-writhe conversion reduces the system’s total free energy and promotes the formation of plectonemes (inset of Figure ). Each plectoneme represents a localized three-dimensional intertwining of the chain, which appears as a distinct peak in the local writhe function W _r defined along the contour coordinate C

$$W_r=\frac{1}{4\pi }{\iint }_C\frac{(\mathrm{d}{\mathit{r}}_2\times \mathrm{d}{\mathit{r}}_1){\mathit{r}}_{12}}{{\mathit{r}}_{12}^3}$$

where r ₁ and r ₂ are the points passing along the DNA sequence C, r ₁₂ = r ₂ – r ₁, and r ₁₂ = | r ₁₂|. Further computational details can be found in the Supporting Information. As shown in Figure a, when adjacent DNA fragments cross and form plectonemic structures, the particles within these structures exhibit a higher writhe value (W _r). To quantify this, we evaluated the local writhe for each bead by employing a sliding window of suitable length, thereby generating the value of W _r(s) along the chain. The local maxima are subsequently identified using a peak-detection algorithm (see Supporting Information). To suppress spurious contributions arising from thermal noise, only peaks exceeding an amplitude threshold (chosen as W _r > 0.7) are retained. The number of such qualified peaks is then taken as the total number of plectonemes in the system.

3.

(a) Adjacent DNA segments exhibit higher writhe when crossing to form plectonemic structures, whereas the resulting hairpin structures exhibit lower writhe. The writhe values of DNA beads at various positions during the supercoiling process (b) and supercoil release process (c). Each peak corresponds to a plectoneme, and beads with W _r > 0.7 (gray dashed line) are classified as having formed plectonemes. In the snapshots, the red segments represent the tips of the plectonemes, characterized by a higher W _r. For clarity, proteins are omitted in the snapshots. (d) Number of plectonemes present in the condensates at different supercoiling levels. Solid upward-pointing triangles connected by solid lines represent the supercoiling process, while hollow downward-pointing triangles connected by dashed lines represent the supercoil release process. Different DNA lengths are indicated by distinct colors.

We calculated the W _r values of DNA in condensates at supercoiling densities of σ = 0.0, σ_↑ = 0.02, and σ_↑ = 0.05. Figure b,c demonstrates that each peak with W _r > 0.7 corresponds to a plectoneme structure, and the number of peaks reflects the number of plectonemes formed within the condensate, which increases with σ_↑ increment (Figure d).

The formation of plectonemes leads to substantial changes in the internal density of condensates. To quantify this effect, we defined the local density n _i of each DNA bead i as the number of neighboring beads within a spherical region of radius R _c = 5σ _b centered on bead i. The overall condensate density was then characterized by the average value of ⟨n⟩ for all n _i . Our results reveal that as the superhelical density increases, the inner density of the condensate rises correspondingly, whereas during supercoil release in stage 3, the average density gradually decreases (Figure c). To investigate the origin of the observed density changes, we examined the distribution of local densities n _i at different supercoiling densities. At low values of σ_↑ or σ_↓, the n _i distribution is unimodal, with its peak located at a low density. As σ increases, the distribution evolves from unimodal to bimodal, with a new peak emerging in the high-density region (Figure d,e). We fitted the distribution with a bimodal probability density function $p(n_i)=\mathcal{wN}(n_i;{\mu }_1,{\sigma }_1)+(1-w)\mathcal{N}(n_i;{\mu }_2,{\sigma }_2)$ , where w is the weight of the low-density peak, and $\mathcal{N}(n_i;\mu ,\sigma )$ denotes the Gaussian probability density function $\mathcal{N}(n_i;\mu ,\sigma )=\frac{1}{\sqrt{2\pi }\sigma }\exp [-\frac{{(n_i-\mu )}^2}{2{\sigma }^2}]$ . Here μ₁, σ₁ and μ₂, σ₂ are the mean and standard deviation of the low- and high-density peaks, respectively. We quantified the influence of supercoiling on n _i by employing p ₂ = p(μ₂), which represents the position of the high-density peak. As shown in the inset of Figure e, p ₂ increases with the supercoiling density and decreases during supercoiling release, mirroring the behavior of the mean density ⟨n⟩ (Figure c). Furthermore, the high-density regions within the condensates spatially coincide with DNA segments covered by plectoneme structures (Figure g), indicating that supercoiling-induced plectoneme formation is the direct cause of local densification. Meanwhile, compared with the condensates formed in stage 1, the torque generated during the imposition of supercoiling compacts the condensate, strengthening the steric/repulsive interaction between DNA and spacer segments, thereby driving proteins to become enriched at the condensate core (Figure f). This mechanism drives the initially loose condensates formed in stage 1 toward progressively more compact states, thereby substantially reducing the overall condensate size.

4.

(a) Relationship between the average distance of surface plectonemes from the condensate center, R _p, and R _g. (b) Variation in the ratio R _p/R _g with N and σ. Insets: (left) for clarity, only surface-localized plectonemes are shown, with red markers indicating the cross-linking sites between surface-bound proteins and plectonemes; (right) schematic illustration of cross-linking between surface-bound proteins and plectonemes. (c) Average number density ⟨n⟩ of DNA at different σ values. (d) and (e) show the distributions of n _i for different values of σ_↑ and σ_↓, respectively. The inset in panel (e) illustrates the evolution of the peak p ₂ of the high-density peak as a function of σ. (f) The distance distribution between the protein and the center of mass of the condensate in the relaxed state (σ = 0), and at σ_↑ = 0.05 and σ_↓ = 0, the distribution corresponds to DNA of length N = 1600. (g) Conformations of a DNA chain of length N = 2000 at different supercoiling densities. Orange beads indicate regions with a higher local density n _i , while gray beads correspond to a lower local density.

We calculated the average distance R _p between the center of mass of plectonemes and the condensate center of mass under different superhelical densities and DNA lengths, and compared it with the condensate size R _g. The results show that, across different DNA lengths N and superhelical densities σ, R _p falls within the range from R _g(N, σ) to R _g(N, σ) + 5σ_b, indicating that the plectoneme center of mass is typically located within the shell extending from R _g to approximately 1.2R _g. In other words, plectonemes generally reside within about 5σ_b from the condensate surface (Figure a,b). In the left inset of Figure b, we hid the DNA and proteins inside a typical condensate configuration to display only the surface plectonemes and their associated binding sites. Each plectoneme is cross-linked to the surface by at least one binding protein. The right inset schematically illustrates how plectonemes can extend along the condensate surface: outward (radial) growth of these structures would oppose a reduction in the condensate’s R _g, whereas lateral (tangential) extension along the surface does not increase the condensate radius. The “binding” proteins on the surface cross-link with the plectonemes, limiting their growth to the surface region. This narrow spatial confinement indicates that the plectonemes do not protrude radially outward. Such protrusion would push their mass center far beyond R _g + 5σ_b and stretch the surface-bound bridging proteins, incurring a substantial energy cost. Therefore, the increase in plectonemes leads to compaction of the internal structure of the condensate, resulting in a significant reduction in size.

We further calculated the scaling relationship between R _g and N for DNA lengths longer than 3 kbp under varying σ_↑ values, i.e., R _g ∼ N ^α. For DNA shorter than 3 kbp, it is difficult for proteins to induce bending via bridging mechanisms (details of the discussion provided in the Supporting Material). As shown in Figure a,b, the size of the condensates increases with increasing DNA length. At relaxation (σ = 0), the scaling exponent α = 0.43, which is consistent with the experimental measurement α = 0.45 for the cohesion complex on DNA in vitro. As supercoiling increases, the DNA adopts increasingly saturated plectonemic structures (Figure d), and the scaling exponent gradually decreases to α ≈ 1/3, which is close to the exponent α = 1/3 of a collapsed polymer in a poor solvent (inset of Figures b and c). This indicates a transition in the condensation mechanism from “winding-induced” to “dense-packing-induced” compaction. Thus, increasing σ_↑ not only modulates the condensate size over a broad range but also reshapes its internal physical state and mechanical properties.

5.

(a) Relative radius of gyration of DNA condensates, R _g(σ_↑)/R _g(σ = 0), as a function of superhelical density σ_↑, for different DNA lengths N (1200, 1600, 2000, 2400). (b) Log–log scaling of the radius of gyration R _g with DNA length l (kbp) at different superhelical densities, R _g ∼ l ^α. Inset: Scaling exponent α extracted from the log–log fits at each superhelical density. (c, d) Similar to (a) and (b) but corresponding to the supercoiling release process. The dashed line in (d) indicates the radius of gyration of the condensates formed by relaxed DNA, serving as a reference. Data for the other chain lengths are provided in the Supporting Information. Each data point represents the mean and standard deviation obtained from 10 independent simulation trajectories.

Our study, therefore, reveals that supercoiling induces a “DNA corset” condensate structure with a dense core of tightly packed DNA and associated proteins (which tend to stay closer to the core regime), surrounded by the plectonemic DNA loops that wrap around and snugly laminate (rather than jutting outward) the condensate’s surface. This enables the regulation of condensate size over a broad range (Figures a and S3). Given the presence of molecular crowding in the cellular environment, such a regulatory mechanism may be further amplified under physiological conditions.

During stage 3, the release of supercoiling density leads to the disappearance of plectonemic structures (Figures , and S5). Once supercoiling is fully relaxed, the system no longer sustains a net torque to maintain the writhe. Thermodynamically, the relaxed state generally has a higher conformational entropy S _conf, and the entropic contribution −TS _conf to the free energy favors the restoration of the condensate size. Consistently, the recovery ratio R _g(σ_↓)/R _g(σ = 0) increases as the superhelical density decreases (Figure c).

Protein bridging strongly influences this recovery. When proteins link DNA segments, particularly those formerly intertwined through plectonemes, each bridge constrains the relative degrees of freedom between the segments. In the absence of bridging, segments could relax their entanglements via sliding; however, bridging suppresses this motion, thereby limiting topological relaxation and reducing entropy. More critically, bridging raises the local energy barriers in the configurational space. Transformations that would otherwise be reversible now require the cooperative unbinding of multiple bridges. Thus, even after torque removal, the bridges can stabilize the intertwined states. Bridging and entanglement reinforce each other, amplifying the energy barriers; relaxation requires both the rupture of bridges and the disentanglement of knots, leading to an exponential increase in the time scale. Assuming that bridges are formed uniformly along the DNA, their number increases approximately linearly with the chain length, as does their contribution to the energy barrier. By contrast, entanglement complexity increases more steeply, often superlinearly, because longer chains allow more extensive winding and knotting. Together, these effects cause the barrier to increase sharply with DNA length, suppressing recovery and producing stronger irreversibility in longer chains. Consequently, condensates formed by short DNA exhibit nearly reversible size changes upon supercoiling and relaxation, whereas those formed by long DNA exhibit pronounced hysteresis (Figures c, and f).

In Figure , the hysteresis observed between the supercoiling and relaxation pathways does not originate from large instantaneous structural differences between stages 2 and 3. Instead, it reflects a path-dependent kinetic trapping mechanism associated with protein-mediated bridging under topological constraints. While visible plectonemic structures largely disappear upon supercoil release, residual entanglements and long-lived protein bridges formed during the supercoiled state can persist and act as latent constraints in configurational space. These constraints do not necessarily manifest as pronounced snapshot-level differences, but they significantly impede complete relaxation over long time scales. As a result, hysteresis becomes evident only upon comparison of the fully relaxed states reached along different paths, particularly for sufficiently long DNA chains. To quantify this effect, we compared the condensate sizes after complete supercoiling release (σ_↓ = 0, end of stage 3) with those in stage 1 across DNAs of varying lengths and superhelical densities (Figure d). The deviation between the relaxed condensate size and the initial no-supercoiling size increases with DNA length. Thus, although the relaxed state is thermodynamically favored, large kinetic barriers prevent the system from fully recovering its original size within experimental time scales, giving rise to irreversibility and hysteresis.

We emphasize that the present model describes supercoiled naked DNA and does not explicitly account for the nucleosome organization or higher-order chromatin structure. Consequently, the proposed “DNA corset” mechanism, in its most direct form, is expected to be most relevant for systems with absent or low nucleosome density, such as prokaryotic chromosomes, plasmids, and topologically constrained in vitro DNA. ,, In these contexts, DNA mechanics are dominated by the intrinsic bending and torsional stiffness of naked DNA, and protein-mediated bridging can stabilize supercoiled conformations and promote condensation. In eukaryotic chromatin, however, nucleosome assembly fundamentally alters torsional mechanics by buffering the linking number through conformational changes of nucleosomes and by modifying twist–writhe partitioning, effectively reducing torsional stiffness. Under such conditions, protein-mediated condensation is likely to involve chromatin fibers or nucleosome arrays rather than bundles of naked DNA supercoils, and the “DNA corset” mechanism may be reshaped or attenuated. Nevertheless, related physical principles may still be operative in specific chromatin contexts, such as within locally constrained domains or genomic regions of low or dynamic nucleosome occupancy, where DNA mechanics more closely resemble those of the naked DNA. Explicitly incorporating nucleosomes and chromatin hierarchy into the model, therefore, represents an important direction for future work, which will be necessary to assess the quantitative relevance of the mechanism in eukaryotic systems.

This laminated shell confers mechanical and regulatory advantages. It is possible that, as an elastic girdle, the DNA corset can reinforce the boundary, distributing external forces around the circumference and buffering torsional shocks, stabilizing droplet size and shape against coalescence or fragmentation. At the same time, the tangential orientation can leave segments on the surface selectively accessible, enabling a leaky regulatory interface: DNA sites on surface loops can still engage with polymerases, transcription factors, or remodelers in the nucleoplasm, while sequences sequestered in the core remain refractory. Additionally, the observed hysteresis can supply memory and thresholding, preventing spurious toggling under weak fluctuations but allowing decisive switching when the torsional inputs cross critical values.

These physical principles suggest a torsion-tuned chromatin domain with broad biological implications. Supercoiling naturally partitions genomes into topological domains; a supercoil-driven condensate would represent a topologically insulated case in which a region is compacted into a self-contained phase whose plectonemic shell acts as a built-in barrier. This architecture provides a physical substrate for stable repression and epigenetic memory: once overwound and trapped in a corset-like state, a locus remains silent until topoisomerases and remodelers actively drain the stored twist to overcome the reopening barrier. It also rationalizes sharp domain boundaries, as plectonemic shells can couple with architectural elements (e.g., loop-extrusion boundaries) to barricade condensed domains from neighboring euchromatin. In this view, DNA mechanics might complement histone marks and protein multivalency to establish and maintain silent territories.

Conclusions

Our simulations herein establish that DNA supercoiling can act as a topological and mechanical switch that drives condensate compaction by producing a unique “DNA corset” architecture: a tightly bridged DNA–protein core encircled by plectonemic loops that laminate the condensate surface. Increasing the torsional strain progressively compacts the condensate, while relaxing the twist allows for entropy-driven re-expansion. Notably, short DNA supports fully reversible size changes, whereas longer DNA exhibits pronounced hysteresis. In the latter case, compaction and relaxation follow distinct pathways, providing built-in topological memory and a thresholding mechanism. These findings offer mechanistic insights linking DNA topology to condensate mechanics, with direct implications for chromatin biology. By tuning supercoiling, cells could modulate chromatin domain compaction and buffer torsional stress, potentially influencing transcriptional regulation through the structural insulation of genomic regions. Overall, our results highlight a fundamental principle: DNA is not a passive scaffold but an elastic, twistable element contributing to robust and reversible control of the structure and size of condensates.

Methods

Our two-component model system consists of a torsionally semiflexible circular DNA polymer , and DNA-binding proteins. , DNA is represented as a chain of N beads, each with a diameter of σ_b = 2.5 nm, corresponding to approximately 7.35 base pairs (bp). Adjacent beads are connected by finitely extensible springs and interact via purely repulsive Lennard-Jones (LJ) potentials to prevent chain self-crossing. The bending stiffness of the DNA is modeled using the Kratky–Porod potential, with a DNA persistence length of l _p = 20σ_b = 50 nm. To incorporate torsional flexibility and supercoiling, we adopt a method from previous studies in which each bead is associated with three auxiliary patch particles. , These patches define two dihedral angles between adjacent backbone beads, thereby constraining their relative rotation angle ψ to an equilibrium value of ψ₀. The torsional interaction is modeled as a harmonic potential with stiffness k _t = 50 and σ_b = 125 nm, corresponding to the torsional persistence length of DNA. To incorporate DNA supercoiling into a coarse-grained framework, we introduce effective dihedral angle and torsional potentials that enforce a prescribed linking number along the polymer. While this strategy is necessarily phenomenological, it is designed to capture the net mechanical consequences of torsional stress that arise from well-established biological and experimental sources. In vivo, DNA supercoiling is continuously generated and regulated by active processes such as transcription, which produces torsional stress via the twin-domain mechanism, topoisomerase activity that modulates DNA topology, , and loop extrusion by SMC-family proteins, which can impose local torsional constraints during dynamic loop growth. Rather than explicitly modeling these microscopic processes, our approach represents their cumulative effect through an effective torsional constraint, allowing us to systematically investigate how supercoiling influences DNA conformations and protein-mediated bridging under fixed topology. In addition, similar torsional stresses can be generated under in vitro conditions when DNA molecules are rotationally constrained and subjected to perturbations such as intercalating agents, which locally unwind the helix and induce compensatory supercoiling. , The torsional and dihedral potentials employed here, therefore, provide a coarse-grained representation of torsional stress that is directly relevant to both intracellular and controlled experimental settings. Each bead and its associated patch particle form a rigid body that defines a local reference frame along the DNA backbone. The patch particles themselves do not participate in any other interactions and serve solely to impose a torsional structure. To ensure the alignment of each bead’s local frame with the DNA backbone, we apply a stiff harmonic potential that constrains the tilt angle θ = π, enforcing collinearity with the local tangent. The system also includes 0.04N DNA-binding proteins, each modeled as a rigid “stacker–spacer” structure with two DNA-binding domains (see Figure ). Each protein consists of a central body with a diameter of 10σ_b, flanked on both sides by two DNA-binding patches with a diameter of σ_b. To mimic the bridging interaction between proteins and DNA, these binding sites interact attractively with DNA beads via Morse potential, while the central body interacts with DNA purely through excluded volume.

The imposed dihedral angle ψ₀ determines the thermodynamically preferred helical pitch of the torsional chain, given by p = 2π/ψ₀, which in turn sets the preferred linking number as Lk = N/p. The superhelical density is defined as σ = Lk/N = 1/p, and it can be tuned by adjusting ψ₀. For circular DNA, the interconversion between local twist (T _w) and global writhe (W _r) must obey the White–Fuller–Călugăreanu (WFC) theorem, Lk = T _w + W _r, which ensures conservation of the total linking number Lk, and hence of the supercoiling density σ. In our model, the supercoiling is symmetric with respect to its handedness; therefore, we report σ without a sign. This coarse-graining choice is justified because the physical asymmetries between the positive and negative supercoils arise primarily from double-helix level features, such as groove geometry, twist-bend coupling, and sequence-dependent anisotropies, which are intentionally averaged out in our mesoscale representation. At length scales relevant to plectoneme formation and protein-induced clustering (tens to hundreds of nanometers), the mechanical response of DNA is governed mainly by the magnitude of the imposed superhelical strain rather than its handedness. Therefore, treating positive and negative supercoiling as energetically equivalent does not affect the mesoscopic behaviors that our model aims to capture. To facilitate a controlled and unambiguous treatment of DNA supercoiling, we employed a circular DNA topology as an idealized coarse-grained setup in which the linking number is strictly conserved. We emphasize that this choice is primarily motivated by technical and conceptual considerations rather than by the intent to reproduce the full complexity of chromatin architecture in eukaryotic cells. While most eukaryotic chromosomes are globally linear, circular, or effectively closed DNA configurations, they arise in several specific biological and experimental contexts and, more generally, serve as a useful limiting case for studying torsionally constrained polymers. In particular, prokaryotic genomes and plasmids are naturally circular, and linear DNA molecules subjected to strong end constraints in vitro can exhibit topological behavior equivalent to that of closed loops. , In addition, within eukaryotic nuclei, chromatin is partitioned into finite domains whose boundaries may restrict rotational relaxation over intermediate time scales, giving rise to locally confined torsional stress. From this perspective, the circular DNA model should be viewed as a simplified representation of a torsionally constrained DNA or chromatin segment, intended to isolate generic physical mechanisms such as the coupling between DNA torsion and protein-mediated bridging, rather than to provide a quantitative description of any specific in vivo system.

We perform molecular dynamics simulations in the NVT ensemble under periodic boundary conditions to investigate the system’s dynamical properties. All simulations are carried out using the LAMMPS package with a Langevin thermostat. The time step is set to dt = 0.005τ_B, where ${\tau }_{\mathrm{B}}={\sigma }_{\mathrm{b}}\sqrt{m/ϵ}$ is the time unit, and m = 1 is the mass of all beads. Due to the semiflexible nature of DNA, its fragment length must exceed approximately 3 kilobases (kbp) for proteins to induce phase separation via bridging. Compared to the dispersed state without bridging, this aggregated state is thermodynamically more favorable (theoretical derivations based on energy and entropy are detailed in Supporting Material S3). Therefore, in the simulations, we selected DNA molecules longer than 3.2 kbp, corresponding to a coarse-grained bead count of N > 400 for each DNA molecule. See Supporting Information for simulation details.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.6c00013.

• Detailed simulation parameters; DNA length dependence of BIPS; method for quantifying plectonemes; and associated data on the supercoiling-mediated compression and hysteresis phenomena of DNA–protein condensates (PDF)

X.W.: conceptualization, data curation, formal analysis, methodology, validation, visualization, writingoriginal draft; B.W.: formal analysis, writingoriginal draft; W.Z.: conceptualization, project administration, resources, writingreview and editing. CRediT: Xuefeng Wei conceptualization, data curation, investigation, methodology, visualization, writing - original draft, writing - review & editing; Biao Wan formal analysis; Wei Zhuang conceptualization, project administration, resources, writing - review & editing.

The authors declare no competing financial interest.