Free energy and extension of a semiflexible polymer in cylindrical confining geometries

Yang, Yingzi; Burkhardt, Theodore W.; Gompper, Gerhard

doi:10.1103/physreve.76.011804

Cited by 117 publications

(179 citation statements)

References 25 publications

(46 reference statements)

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“…To examine in more detail the extended de Gennes regime, we plot the difference between the confinement free energy of a real chain and an ideal chain in Figure 3c because in the extended de Gennes regime eq 1 can be converted to 32 The crossover between the transition regime and the extended/classic de Gennes regime is estimated as D t = 2L k . The estimated statistical errors are less than symbol sizes.…”

Section: Resultsmentioning

confidence: 99%

Extended de Gennes Regime of DNA Confined in a Nanochannel

2014

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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.

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Section: Resultsmentioning

confidence: 99%

Extended de Gennes Regime of DNA Confined in a Nanochannel

2014

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“…Although there are challenges in using DNA beyond those discussed here, for example the inability to tune the system so that different confinement regimes span multiple decades in channel size [39,74], DNA remains the most convenient model system for studying confined polymers. While it may ultimately prove challenging to use DNA to test the existing models down to the prefactors for the scaling laws [23,25,[41][42][43], there is no better experimental system to directly visualize the effects of confinement at the single molecule level and investigate the universal properties of confined polymers at the scaling level.…”

Section: Discussionmentioning

confidence: 99%

“…In some cases, the prefactors for the scaling laws are known exactly [41][42][43]. These thermodynamic quantities depend on the contour length L of the polymer, its persistence length l p , the effective width w of the polymer backbone, and the channel size D. The persistence length and effective width of DNA, which are affected by the relative amount of screening of electrostatics by the ionic environment, can be obtained from polyelectrolyte theory [44][45][46][47], albeit with some uncertainty arising from the effect of the intercalating dye [48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Wall depletion length of a channel-confined polymer

Cheong

Dorfman

2017

Phys. Rev. E

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Numerous experiments have taken advantage of DNA as a model system to test theories for a channel-confined polymer. A tacit assumption in analyzing these data is the existence of a well defined depletion length characterizing DNA-wall interactions such that the experimental system (a polyelectrolyte in a channel with charged walls) can be mapped to the theoretical model (a neutral polymer with hard walls). We test this assumption using pruned-enriched Rosenbluth method (PERM) simulations of a DNA-like semiflexible polymer confined in a tube. The polymer-wall interactions are modeled by augmenting a hard wall interaction with an exponentially decaying, repulsive soft potential. The free energy, mean span, and variance in the mean span obtained in the presence of a soft wall potential are compared to equivalent simulations in the absence of the soft wall potential to determine the depletion length. We find that the mean span and variance about the mean span have the same depletion length for all soft potentials we tested. In contrast, the depletion length for the confinement free energy approaches that for the mean span only when depletion length no longer depends on channel size. The results have implications for the interpretation of DNA confinement experiments under low ionic strengths. * dorfman@umn.edu

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“…From a theoretical perspective, the Odijk regime for nanochannel confinement is very well established. 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.…”

Section: Introductionmentioning

confidence: 99%

Mixed confinement regimes during equilibrium confinement spectroscopy of DNA

Gupta

Sheats²,

Muralidhar

et al. 2014

The Journal of Chemical Physics

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We have used a combination of fluorescence microscopy experiments and Pruned Enriched Rosenbluth Method simulations of a discrete wormlike chain model to measure the mean extension and the variance in the mean extension of λ-DNA in 100 nm deep nanochannels with widths ranging from 100 nm to 1000 nm in discrete 100 nm steps. The mean extension is only weakly affected by the channel aspect ratio. In contrast, the fluctuations of the chain extension qualitatively differ between rectangular channels and square channels with the same cross-sectional area, owing to the "mixing" of different confinement regimes in the rectangular channels. The agreement between experiment and simulation is very good, using the extension due to intercalation as the only adjustable parameter.

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Free energy and extension of a semiflexible polymer in cylindrical confining geometries

Abstract: We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D< Show more

Cited by 117 publications

References 25 publications

Extended de Gennes Regime of DNA Confined in a Nanochannel

Extended de Gennes Regime of DNA Confined in a Nanochannel

Wall depletion length of a channel-confined polymer

Mixed confinement regimes during equilibrium confinement spectroscopy of DNA

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