Nanoscale and microscale confinement of biopolymers naturally occurs in cells and has been recently achieved in artificial structures designed for nanotechnological applications. Here, we present an extensive theoretical investigation of the conformations and shape of a biopolymer with varying stiffness confined to a narrow channel. Combining scaling arguments, analytical calculations, and Monte Carlo simulations, we identify various scaling regimes where master curves quantify the functional dependence of the polymer conformations on the chain stiffness and strength of confinement. DOI: 10.1103/PhysRevE.75.050902 PACS number͑s͒: 87.16.Ac, 36.20.Ey, 82.35.Lr, 87.16.Ka What is the effect of confinement on the shape of a biopolymer? With recent advances in visualizing and manipulating macromolecules on ever shrinking length scales, an answer to this question has gained increasing importance. In the crowded environment of a cell the conformations of cytoskeletal filaments are highly constrained by other neighboring macromolecules. This confinement largely alters the viscoelastic response of entangled biopolymer solutions ͓1,2͔. There is growing interest in manufacturing nanostructures such as nanopores ͓3͔ and nanochannels ͓4,5͔ for investigating and manipulating DNA with improved technologies aiming toward smaller and smaller structures. Hence an improved understanding of the effect of confinement on biopolymer conformations has potential implications for the design of nanoscale devices in biotechnological applications. Similarly, microfluidic devices have been used to explore confinement effects on actin filaments and DNA ͓6,7͔. What makes the confinement of biopolymers both a challenging and interesting problem is that biopolymers, unlike their synthetic counterparts, are generally stiff on a length scale much larger than their monomer size. The persistence length ᐉ p , the scale below which bending energy dominates over thermal fluctuations, is approximately 50 nm for DNA ͓8͔ and 16 m for F-actin ͓9͔. Depending on whether the contour length L is smaller or larger than the persistence length we may distinguish between stiff and flexible chains.For cellular systems as well as for nanoscale devices, biopolymers are confined on length scales comparable with their persistence length ᐉ p such that the polymer's intrinsic bending stiffness plays a decisive role for its conformations. For simplicity, consider a cylindrical tube of diameter d. Upon balancing the bending stiffness of a chain with thermal energy, Odijk ͓10͔ has identified a length L d measuring the typical distance between successive deflections of the chain, Fig. 1. This suggests to use the number of collisions c = L / L d per filament length L as a natural dimensionless parameter to measure the strength of confinement and = L / ᐉ p to measure the flexibility of a polymer. The physics in the strong confinement regime ͑c 1͒ is genuinely different from the regime where the radius of gyration R G of a long flexible chain ͑with L ᐉ p ͒ becomes comparable...

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...

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