Dynamical modelling of molecular constructions and setups for DNA unzipping

We present a dynamical model of DNA mechanical unzipping under the action of a force. The model includes the motion of the fork in the sequence-dependent landscape, the trap(s) acting on the bead(s), and the polymeric components of the molecular construction (unzipped single strands of DNA, and linkers). Different setups are considered to test the model, and the outcome of the simulations is compared to simpler dynamical models existing in the literature where polymers are assumed to be at equilibrium.

💡 Research Summary

The paper presents a comprehensive dynamical model for DNA mechanical unzipping under an applied force, explicitly incorporating the motion of the unzipping fork, the dynamics of the beads trapped in optical or magnetic tweezers, and the polymeric behavior of the opened single‑stranded DNA (ssDNA) and any linker segments. Starting from the thermodynamics of the system, the authors define the sequence‑dependent free‑energy landscape using base‑pair stacking energies g₀(bᵢ,bᵢ₊₁) obtained from MFOLD, and they calculate the work required to stretch the newly opened ssDNA, g_ss(f), via a modified freely‑jointed chain (FJC) model that includes elastic stretching (γ_ss = 800 pN·nm). For double‑stranded DNA linkers they employ an extensible worm‑like chain (WLC) model with parameters L = 0.34 nm, A = 48 nm, and γ_ds = 1000 pN.

The mechanical construction considered consists of two optical traps (or a single magnetic trap) characterized by spring constants k₁ and k₂, a dsDNA handle of length N_ds, and two ssDNA strands whose length grows as the fork opens (N₀^{ss}+n, where n is the number of opened base pairs). The total free energy of the system is written as a sum of trap potentials, polymer elastic energies, and the sequence free energy G(n;B). By applying a saddle‑point approximation the authors derive force‑balance equations: k₁·x₁ = w′_ds = w′_ss = k₂·(X−x₄) = \bar f, together with a condition linking the base‑pair binding energy to the work of stretching ssDNA, g₀ = g_ss(\bar f). These relations allow the calculation of the effective stiffness k_eff of the whole assembly, which decreases as more base pairs open because the ssDNA contribution (k_m^{ss} / (N₀^{ss}+n)) becomes dominant.

Two experimental protocols are simulated: fixed‑force (constant f) and fixed‑extension (constant trap separation X). In the fixed‑force case, the fork behaves as a particle in a tilted periodic potential; near the critical force f_c ≈ 15.9 pN the free‑energy minima at n ≈ 0 and n ≈ 50 are separated by a barrier of ~12 k_BT, leading to observable hopping between closed and partially opened states. Small changes in force dramatically alter hopping rates, reproducing stick‑slip dynamics reported in earlier studies. In the fixed‑extension scenario, the trap stiffness controls force fluctuations: softer traps reduce force noise, making the hopping rates converge to the fixed‑force values. The authors also quantify thermal fluctuations of the polymers, showing that relative extensions and forces scale as 1/√n, and provide explicit tables of fluctuation amplitudes for both ssDNA and dsDNA at 15 pN and 16.7 °C.

By comparing their full non‑equilibrium model with earlier approaches that assumed instantaneous polymer equilibration, the authors demonstrate that neglecting polymer dynamics can lead to significant errors in predicted force–time traces, especially when the experimental bandwidth is on the order of 10 kHz and spatial resolution reaches 0.1 nm. Their framework thus offers a realistic tool for designing and interpreting single‑molecule unzipping experiments, guiding the choice of trap stiffness, linker lengths, and data acquisition rates. Moreover, the model is readily extensible to more complex situations such as protein‑DNA interactions, transcription‑complex dynamics, or nanopore‑based sequencing, where the interplay of mechanical forces and polymer fluctuations is crucial.