Free Energy of a Folded Semiflexible Polymer Confined to a Nanochannel of Various Geometries

Abstract

Monte Carlo simulations are used to study the conformational properties of a folded semiflexible polymer confined to a long channel. We measure the variation in the conformational free energy with respect to the end-to-end distance of the polymer, and from these functions we extract the free energy of the hairpin fold, as well as the entropic force arising from interactions between the portions of the polymer that overlap along the channel. We consider the scaling of the free energies with respect to varying the persistence length of the polymer, as well as the channel dimensions for confinement in cylindrical, rectangular and triangular channels. We focus on polymer behaviour in both the classic Odijk and backfolded Odijk regimes. We find the scaling of the entropic force to be close to that predicted from a scaling argument that treats interactions between deflection segments at the second virial level. In addition, the measured hairpin fold free energy is consistent with that obtained directly from a recent theoretical calculation for cylindrical channels. It is also consistent with values determined from measurements of the global persistence length of a polymer in the backfolded Odijk regime in recent simulation studies.

Polymer translocation into cavities: Effects of confinement geometry, crowding, and bending rigidity on the free energy

“…We have previously used this procedure to measure free-energy functions in other simulation studies of polymer translocation 40,41,63 as well in studies of polymer segregation under cylindrical confinement 64,65 and polymer folding in long nanochannels. 66,67 To implement the SCH method, we carry out many independent simulations, each of which employs a unique "window potential" of a chosen functional form. The form of this potential is given by:…”

“…This is due to the effect of entropic depletion, in which the monomer density is significantly reduced in sharp corners of confined spaces. 67,70,71 This effect tends to be especially strong in triangular cavities, which have the sharpest angles, and is absent for the case of cylindrical confinement. Such monomer depletion in these regions leads to an effective cross-sectional area that is less than the actual area accessible to the monomer centers.…”

“…To explain the origin of the linear regions and the variation of the slope with the number of hairpins, we use a theoretical approach that we previously employed to explain backfolding of semiflexible polymers in infinitely long channels. 66,67 This model relies on the Odijk regime condition that P ≫ D, which is marginally satisfied for κ=15 and D=4. In the case of L=∞ there is no backfolding and thus no overlap of the polymer along the tube.…”

Limitations of the equivalent neutral polymer assumption for theories describing nanochannel-confined DNA

“…DNA in channel confinement stretches out from its coiled structure in free solution [1] to a significant fraction of its contour length, and exhibits a rich variety of confinement regimes [2][3][4]. Theories developed over the past decade have described semiflexible polymers in weak confinement where the polymer still has a locally coiled blob structure [2,[5][6][7][8][9][10][11][12][13][14][15][16][17], moderate confinement characterized by occasional hairpins in the polymer backbone [16][17][18][19][20][21][22][23][24][25][26], and strong confinement where the polymer is stretched to a significant fraction of its contour length [17,[27][28][29]. The fractional extension realized in confinement depends on the DNA stiffness, the extent of segmental excluded volume, and the size of the confining channel.…”

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

“…The statistical behaviors of semiflexible polymers confined in nano-and micro-tubes are fundamental problems in polymer physics and have been investigated both experimentally and theoretically for decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. A thorough understanding of these problems is very important in the development of various application techniques that exploit the effects of confinement and stretching on polymers, including genome mapping [15,16], DNA sorting [17], and DNA denaturation mapping [18,19], etc.…”