Free Energy and Dynamics of Annihilation of Topological Defects in Nanoconfined DNA

Abstract

Topological defects in DNA strands, such as hairpin folds, can prevent their correct reading in nanofluidic sequencing and mapping methods. An understanding of the dynamics of these defects could be used to prevent or compensate for them in design. We employ coarse-grained modeling tools to study the thermodynamics and mechanics of defect relaxation within the classic Odijk and back-folded Odijk confinement regimes. Two types of defects are analyzed: single fold (or hairpin) and a double fold (also called S-loop). In the absence of excluded-volume effects, the time for hairpin unfolding is found to scale as the DNA contour length L to the third power. The unfolding time is derived from the free-energy landscape via Monte Carlo models, and it is corroborated by Brownian dynamic simulations. Chain self-interaction and the entropy difference between the folded and unfolded region of the chain drive defect removal. The entropic force f determined from the slope of free-energy curves matches the theoretical scaling D –5/3 expected for the Odijk regime. For a 45 nm channel, the estimated value of the force, divided by the friction per unit length, f/ξ ≈ 0.75 μm2/s, is in remarkable agreement with the published experimental value of f/ξ ≈ 1 μm2/s. Thermodynamic analyses were employed to study the tendency of an S-loop defect to external or internal annihilation. The free-energy curves reveal that two oppositely oriented hairpins tend to merge into a single loop when they approach each other. This mechanism is more favorable for longer DNA chains, as the diffusive length for external annihilation increases. Our analyses show that calculating the mean first-passage time from the free-energy curve is a reliable alternative to Brownian dynamics when the quasi-equilibrium assumption is valid.