Anharmonic Torsional Stiffness of DNA Revealed under Small External Torques

DNA supercoiling plays an important role in a variety of cellular processes. The torsional stress related with supercoiling may be also involved in gene regulation through the local structure and dynamics of the double helix. To check this possibility steady torsional stress was applied to DNA in the course of all-atom molecular dynamics simulations. It is found that small static untwisting significantly reduces the torsional persistence length ($l_t$) of GC-alternating DNA. For the AT-alternating sequence a smaller effect of the opposite sign is observed. As a result, the measured $l_t$ values are similar under zero stress, but diverge with untwisting. The effect is traced to sequence-specific asymmetry of local torsional fluctuations, and it should be small in long random DNA due to compensation. In contrast, the stiffness of special short sequences can vary significantly, which gives a simple possibility of gene regulation via probabilities of strong fluctuations. These results have important implications for the role of local DNA twisting in complexes with transcription factors.

💡 Research Summary

The authors investigate how small static torques influence the torsional stiffness of DNA at the atomic level, addressing a long‑standing question about the physical basis of supercoiling‑mediated gene regulation. Using all‑atom molecular dynamics (MD) simulations, they studied two 14‑base‑pair duplexes: an AT‑alternating (d(AT)₇) and a GC‑alternating (d(GC)₇) sequence. For each duplex, nine independent 16‑ns trajectories were generated under fixed torques ranging from –20 to +20 pN·nm, providing a total simulation time of roughly 3 µs. The simulations employed the AMBER98 force field, TIP3P water, and explicit Na⁺ ions to neutralize the system.

The key observable is the overall winding angle Φ of the central 12 bp segment. From the time‑averaged ⟨Φ⟩ and its variance Δ²Φ, the torsional persistence length lₜ is calculated via lₜ = L/(k_BT·Δ²Φ). In the harmonic (linear) elasticity picture, lₜ should be independent of applied torque, and ⟨Φ⟩ should vary linearly with torque according to Φ_τ – Φ₀ = τL/(k_BT lₜ).

Results show that both sequences obey linear ⟨Φ⟩‑versus‑torque behavior up to about ±10 pN·nm, confirming a harmonic response in that range. However, beyond this limit the GC‑alternating duplex displays pronounced anharmonicity: at +20 pN·nm the extracted lₜ increases by roughly 30 % relative to its zero‑torque value, whereas the AT‑alternating duplex shows only a slight, opposite‑signed trend. Probability distributions P(Φ) remain Gaussian for the 12‑bp segment, but the underlying single‑step twist fluctuations are strongly non‑Gaussian and skewed. GpC and CpG steps in the GC‑rich fragment exhibit left‑skewed distributions, meaning the right‑hand side of the free‑energy profile is steeper. Consequently, an untwisting torque pushes the system toward the flatter side, reducing lₜ; an overwinding torque does the opposite, increasing lₜ. In the AT‑rich fragment, opposing skewnesses of TpA and ApT steps largely cancel, yielding an almost constant lₜ.

The authors argue that such sequence‑specific anharmonicity can be biologically significant for short DNA motifs (10–20 bp) that often serve as spacers between transcription‑factor binding sites. Even a modest untwisting of 1–2 %—the magnitude typical of physiological supercoiling—can change the probability of large twist excursions by several‑fold, potentially switching transcription factor binding on or off. In long, random DNA the opposite skewnesses of many steps average out, explaining why bulk measurements report a relatively constant torsional persistence length (~90 nm).

Overall, the study demonstrates that DNA torsional stiffness is not a fixed material constant but a torque‑dependent, sequence‑specific property. This insight provides a plausible physical mechanism whereby supercoiling can fine‑tune gene expression: by locally altering the stiffness of specific short motifs, the cell can modulate the likelihood of strong twist fluctuations required for the assembly of transcription complexes. The work also highlights the need for further simulations and experiments at longer timescales and in protein‑DNA complexes to fully elucidate the role of torsional anharmonicity in vivo.