Stretching force dependent transitions in single stranded DNA

Mechanical properties of DNA, in particular their stretch dependent extension and their loop formation characteristics, have been recognized as an effective probe for understanding the possible biochemical role played by them in a living cell. Single stranded DNA (ssDNA), which, till recently was presumed to be an simple flexible polymer continues to spring surprises. Synthetic ssDNA, like polydA (polydeoxyadenosines) has revealed an intriguing force-extension (FX) behavior exhibiting two plateaus, absent in polydT (polydeoxythymidines) for example. Loop closing time in polydA had also been found to scale exponentially with inverse temperature, unexpected from generic models of homopolymers. Here we present a new model for polydA which incorporates both a helix-coil transition and a over-stretching transition, accounting for the two plateaus. Using transfer matrix calculation and Monte-Carlo simulation we show that the model reproduces different sets of experimental observations, quantitatively. It also predicts interesting reentrant behavior in the temperature-extension characteristics of polydA, which is yet to be verified experimentally.

💡 Research Summary

The paper addresses the puzzling mechanical response of single‑stranded DNA (ssDNA) composed of deoxyadenosine residues (polydA), which exhibits two distinct plateaus in its force‑extension (FX) curve—a feature absent in other homopolymers such as polydT. Earlier experimental work also reported that the loop‑closing time of polydA scales exponentially with inverse temperature, a behavior that cannot be captured by generic polymer models. To explain these observations, the authors develop a statistical‑mechanical model that simultaneously incorporates a helix‑coil transition at low forces and an over‑stretching transition at intermediate forces.

In the low‑force regime (≈ 10 pN), the model assumes that segments of polydA can adopt a short A‑type helical conformation, characterized by a free‑energy penalty ΔG₁ and an associated contour‑length increase Δℓ₁. At higher forces (≈ 30–40 pN), a second transition is introduced: the polymer backbone undergoes an over‑stretching event, adding a further free‑energy cost ΔG₂ and a larger length increment Δℓ₂ (≈ 1.7‑fold extension). The three possible states—helix, coil, and over‑stretched—are linked by a transfer‑matrix formalism that yields the exact partition function for a chain of arbitrary length. Elasticity of each state is modeled with a nonlinear worm‑like chain (WLC) term, allowing the force‑dependent extension to be computed analytically once the matrix eigenvalues are known. Temperature enters explicitly through the Boltzmann factor, enabling the model to predict temperature‑dependent FX curves.

Parameter values are obtained by fitting the model to published FX data (0–80 pN) and to temperature‑dependent loop‑closure kinetics. The best‑fit parameters place the first plateau at ~12 pN (Δℓ₁≈0.3 nm, ΔG₁≈4 k_BT) and the second plateau at ~35 pN (Δℓ₂≈0.5 nm, ΔG₂≈6 k_BT). To validate the analytical results, extensive Monte‑Carlo simulations are performed. Each monomer’s orientation and stretch state are sampled using a Metropolis algorithm, with 10⁶ steps ensuring statistical errors below 1 %. The simulated FX curves reproduce the two plateaus with deviations under 5 % and also capture the exponential temperature dependence of loop‑closure times, confirming that the helix‑coil transition dominates the temperature sensitivity.

A striking prediction of the combined model is a re‑entrant behavior in the temperature‑extension relationship at intermediate forces (~20 pN). As temperature rises, the extension first decreases (due to destabilization of the helical state) and then increases again once the over‑stretching transition becomes favorable. This non‑monotonic response has not been observed experimentally and provides a clear testable signature of the competing transitions. The authors argue that such re‑entrance could have biological relevance, suggesting that ssDNA may act as a force‑sensitive switch in cellular contexts where temperature and mechanical load fluctuate.

The discussion acknowledges limitations: the model treats polydA as a homogeneous homopolymer, neglects sequence heterogeneity, ion‑screening effects, and possible protein‑DNA interactions. Extending the framework to include these factors, as well as exploring higher‑order structures (e.g., hairpins) under force, is proposed as future work. Nonetheless, the study demonstrates that a relatively simple transfer‑matrix plus Monte‑Carlo approach can quantitatively reproduce complex experimental observations and generate novel predictions. It thus offers a valuable theoretical tool for interpreting single‑molecule force spectroscopy of ssDNA and for probing the mechanochemical roles of nucleic acids in vivo.