Effects of Strong Confinement on Semiflexible Polymers

Many biomolecules can be effectively modeled as semiflexible polymers (e.g., DNA, actin, and microtubules) facilitating the need to understand, develop, and compare polymer models to biological and experimental processes. Spatial confinement effects have been utilized to map and sequence DNA, with numerous clinical applications. DNA nanochannel mapping experiments seek to study large scale structural variation in the genome while nanopore sequencing allows for single molecule resolution of isolated subsegments of DNA. Spatially confined semiflexible polymers exhibit markedly different conformational properties compared to a polymer in bulk due to the entropic depletion induced by the confining walls. The nature of these effects depends strongly on the geometry to which the polymer is confined as well as its inherent stiffness. In this work, we will review modern DNA confinement experiments, including DNA mapping and sequencing, and the semiflexible polymer models which apply to them. We will expand upon the current understanding of confinement effects on semiflexible polymers by utilizing Weakly Bending Rod (WBR) and Weakly Fluctuating Rod (WFR), Mean Field (MF), and telegraph models, comparing the results to Metropolis Monte Carlo (MC) and Telegraph simulations of wormlike chains (WLCs). We detail the correlations of WLC's in confinement and use the MF model to infer statistical properties relevant in DNA slit experiments. A hairpin detection algorithm is detailed to distinctly identify the effects of hairpin backfolding, where a fold is formed along the confining axis in a channel, on WLC's in linear and curved confinement. We determine that curvature increases the probability of hairpin formation in strongly confined WLC's an effect which would be directly applicable to Convex Lens induced Confinement (CLiC) and mapping experiments. We show that this is not an effective decrease in the confinement strength but rather a direct consequence of the curved channel geometry.