Abstract Biopolymers, like chromatin, are often confined in small volumes. Confinement has a great effect on polymer conformations, including polymer entanglement. Polymer chains and other filamentous structures can be represented by polygonal curves in three-space. In this manuscript, we examine the topological complexity of polygonal chains in three-space and in confinement as a function of their length. We model polygonal chains by equilateral random walks in three-space and by uniform random walks (URWs) in confinement. For the topological characterization, we use the second Vassiliev measure. This is an integer topological invariant for polygons and a continuous functions over the real numbers, as a function of the chain coordinates for open polygonal chains. For URWs in confined space, we prove that the average value of the Vassiliev measure in the space of configurations increases as O ( n 2 ) with the length of the walks or polygons. We verify this result numerically and our numerical results also show that the mean value of the second Vassiliev measure of equilateral random walks in three-space increases as O ( n ). These results reveal the rate at which knotting of open curves and not simply entanglement are affected by confinement.
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Scaling regimes for wormlike chains confined to cylindrical surfaces under tension
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.
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- Award ID(s):
- 2019745
- PAR ID:
- 10512510
- Publisher / Repository:
- The European Physical Journal E
- Date Published:
- Journal Name:
- The European Physical Journal E
- Volume:
- 47
- Issue:
- 1
- ISSN:
- 1292-8941
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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