Scaling theory of DNA confined in nanochannels and nanoslits

A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits. It is argued that there are several regimes in between the de Gennes and Odijk limits introduced long ago. The DNA chain folds back on itself giving rise to a global persistence length which may be very large owing to entropic deflection. Moreover, there is an orientational excluded-volume effect between the DNA segments imposed solely by the nanoconfinement. These two effects cause the chain statistics to be intricate leading to nontrivial power laws for the chain extension in the intermediate regimes. It is stressed that DNA confinement within nanochannels differs from that in nanoslits because the respective orientational excluded-volume effects are not the same.

💡 Research Summary

The paper presents a comprehensive scaling analysis of long DNA molecules confined within nano‑scale geometries—specifically nanochannels (rectangular cross‑section) and nanoslits (planar confinement). Building on the classic de Gennes “blob” regime for weak confinement and the Odijk regime for strong confinement, the authors demonstrate that a multitude of intermediate regimes exist between these two limits. The key insight is that confinement induces two coupled effects that dramatically alter the polymer’s effective stiffness and its configurational statistics.

First, entropic deflection from the walls generates a “global persistence length” (often denoted Lp*), which can be orders of magnitude larger than the intrinsic persistence length ℓp of DNA. When the channel or slit dimension D is comparable to or smaller than ℓp, the polymer repeatedly collides with the walls, each collision re‑orienting the chain but also straightening it over distances much larger than ℓp. This results in an effective stiffening that scales with D and ℓp in a non‑trivial way.

Second, the confinement imposes an orientational excluded‑volume interaction. In a nanochannel the DNA is restricted in two transverse directions, so successive segments cannot freely rotate relative to each other; this creates a strong orientational “crowding” that further suppresses bending fluctuations. In a nanoslit only one transverse direction is confined, so the orientational excluded‑volume effect is weaker. The authors quantify this difference by introducing distinct scaling exponents for channels versus slits.

By combining these two mechanisms, the authors derive a hierarchy of scaling laws for the average extension ⟨X⟩ of the DNA along the longitudinal axis of the confinement. In the de Gennes regime (D ≫ ℓp) the familiar blob picture holds, ⟨X⟩ ∝ L (D/ℓp)‑1/3. In the Odijk regime (D ≪ ℓp) the classic Odijk result, ⟨X⟩ ≈ L