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We compute the free energy of confinement F for a wormlike chain (WLC), with persistence length lp, that is confined to the surface of a cylinder of radius R under an external tension f using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of lp, the Odijk deflection length (ld = (R2lp)1/3), and the Pincus length (lf = kBT/f, with kBT being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at f = 0, with F ∼ Ll−1/3p R−2/3. For moderate values of f, the Odijk scaling is discernible only when lp   R for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes. 

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed state to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find that the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show that the theory is highly sensitive to fluctuations in length in two dimensions and the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts.