The effect of internal and global modes on the radial distribution function of confined semiflexible polymers

Abstract

The constraints imposed by nano-and microscale confinement on the conformational degrees of freedom of thermally fluctuating biopolymers are utilized in contemporary nano-devices to specifically elongate and manipulate single chains. A thorough theoretical understanding and quantification of the statistical conformations of confined polymer chains is thus a central concern in polymer physics. We present an analytical calculation of the radial distribution function of harmonically confined semiflexible polymers in the weakly bending limit. Special emphasis has been put on a proper treatment of global modes, i.e. the possibility of the chain to perform global movements within the channel. We show that the effect of these global modes significantly impacts the chain statistics in cases of weak and intermediate confinement. Comparing our analytical model to numerical data from Monte Carlo simulations we find excellent agreement over a broad range of parameters.PACS numbers: 87.15.ad,82.35.Lr,36.20.Ey Understanding the statistical properties of biopolymers on the single molecule level has been one major objective of polymer research over the past decades. While our theoretical knowledge about semiflexible chain molecules in free space is developed to a fairly sophisticated level, a steadily growing theoretical interest in the mechanical properties of semiflexible polymer solutions [1][2][3][4][5], and networks [6][7][8][9][10][11], as well as the impetus from nano-technological applications [12,13] On the theoretical side, questions related to thermodynamic properties and the end-to-end distance statistics of polymers in confining geometries have largely been addressed by means of computer simulations [19][20][21][22]. A recent contribution to analytically capture the radial distribution function (RDF) [23] of semiflexible chains in cylindrical confinements was based on the physical idea that the polymer's transverse fluctuations are effectively suppressed along the contour, if the confining channel is sufficiently narrow. In order to facilitate calculations, this approach then employed torqued ends boundary conditions [24] within a channel-fixed reference frame [29], assuming that the particular choice of boundary conditions is of minor importance for the determination of the chain's end-to-end distance statistics. While feasible in a strong confinement regime, where the polymer almost perfectly aligns with the symmetry axis of the channel, the chain statistics predicted by this approach is at variance with our results from Monte Carlo simulations for intermediate and weak confinement strengths.In this letter we go beyond this strong confinement approximation and provide a thorough analysis of the endto-end distance statistics of semiflexible chains, trapped in cylindrically symmetric confinements, based on analytical and numerical methods. Special attention is paid to the role of global chain movements, which is technically captured by means of a careful choice of boundary conditions. As a central result we wil...

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

“…Semiflexible polymers confined in narrow channels have found abiding interests recently, both in experiments, [1][2][3][4][5][6][7][8][9][10][11][12][13][14] analytical theory, [15][16][17][18][19][20][21][22][23][24][25] and in computer simulations. [26][27][28][29][30][31][32][33][34][35][36][37][38][39] From the application side, this problem is of great interest for the detection of single DNA molecules, separating them by size, and to develop tools for their sequence analysis.…”

DNA conformation in nanochannels: Monte Carlo simulation studies using a primitive DNA model

“…1 This scaling theory has been further extended to regimes where the intrinsic stiffness of a polymer is comparable to the confinement dimensions by Odijk and others. [2][3][4][5][6][7] However, the verification of the theories through realistic systems has not been possible until recent advances in highly sophisticated nanofabrication and single molecule detection. [8][9][10] The primary focus of these recent studies is on understanding the structural and dynamic behavior of DNA in nanochannels or nanoslits, since they potentiate a novel high-throughput and high-resolution genome analysis platform.…”

Harmonically Confined, Semiflexible Polymer in a Channel: Response to a Stretching Force and Spatial Distribution of the Endpoints

“…The result is given in Eqs. (6), (13)- (16), and (19). We have checked with Mathematica that it does indeed satisfy the Fokker-Planck equation (17) with initial condition (18).…”

“…The properties of a semi-flexible polymer in cylindrical channels, but without the longitudinal stretching force, have been studied by simulations [10][11][12][13][14][15][16][17] and calculated theoretically [16][17][18][19] with the channel replaced by a parabolic confining potential. The dynamical evolution of the confined polymer under sudden changes of a longitudinal stretching force or relaxation of the confinement is studied in Ref.…”