Extended de Gennes Regime of DNA Confined in a Nanochannel

Abstract

Scaling regimes for polymers confined to tubular channels are well established when the channel cross-sectional dimension is either very small (Odjik regime) or large (classic de Gennes regime) relative to the polymer Kuhn length. However, experiments of confined polymers using DNA as a model system are usually located in the intermediate region between these two regimes. In the literature, controversy exists regarding the existence of the extended de Gennes regime in this intermediate region. Here we use simulations and theory to reconcile conflicting theories and confirm the existence of extended de Gennes regime. We show that prior work did not support the notion of this regime because of the use of a wrong confinement free energy. In a broad sense, the extended de Gennes regime corresponds to the situation when excluded volume interaction is weaker than thermal energy. Such a situation also occurs in many other cases, such as semidilute polymer solutions and polymers under tension. This work should benefit the practical applications of nanochannels to stretch DNA, such as deepening the understanding of the relationship between the chain extension and channel size and providing the scaling behaviors of recoiling force for DNA at the entrance of nanochannels.

Nanoconfined Circular and Linear DNA: Equilibrium Conformations and Unfolding Kinetics

“…[28][29][30] In this regime, an asymptotically exact theory for the equilibrium statistics of a linear polymer predicts that the mean and variance of the extension are given by [31] ! "# = 1.18…”

Wall depletion length of a channel-confined polymer

“…The models developed for channel-confined polymers make scaling law predictions for the confinement free energy, F , the average size of the confined chain, X , and the variance about that size, δX 2 , for a neutral polymer confined by hard walls [29][30][31][39][40][41]. In some cases, the prefactors for the scaling laws are known exactly [41][42][43].…”

Mixed confinement regimes during equilibrium confinement spectroscopy of DNA

“…8,9 As the channel size increases further, the chain is able to backfold and enters a poorly understood "transition" regime. Provided the chain is sufficiently long, 6, 10-12 numerous simulations of confined wormlike chains indicate that (i) the average chain extension scales 10,[12][13][14][15] like X ∼ D −1 and (ii) this regime ends when D ≈ 2l p , with l p being the persistence length of the chain. 6,12,15 As the channel size increases even further, the chain enters into a so-called "extended de Gennes" regime 12 where the chain consists of sausage-like, anisometric blobs.…”

“…Provided the chain is sufficiently long, 6, 10-12 numerous simulations of confined wormlike chains indicate that (i) the average chain extension scales 10,[12][13][14][15] like X ∼ D −1 and (ii) this regime ends when D ≈ 2l p , with l p being the persistence length of the chain. 6,12,15 As the channel size increases even further, the chain enters into a so-called "extended de Gennes" regime 12 where the chain consists of sausage-like, anisometric blobs. 6,16 At the largest values of D, the weak confinement results in the classical de Gennes regime, 3 where the chain consists of isometric blobs.…”

“…The latter scaling is based on a Flory exponent ν = 3/5; the more accurate estimate X ∼ D (ν − 1)/ν ∼ D −0.7015 is in excellent agreement with simulation data for long chains in the extended de Gennes and de Gennes regimes. [12][13][14][15]17 It is important to recognize that, while the extension of the confined chain is the simplest observable metric and quite relevant for genomic applications of confined DNA, [18][19][20][21][22][23][24] this single thermodynamic variable is likely insufficient to resolve many of the open questions surrounding different regimes. Rather, we require measurements of both the average chain extension and its variance, the latter being related to the effective spring constant of the chain.…”