Force and Fluctuations in Polymer Ensembles
Waters, James T
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The focus of this work is on developing mechanical models for studying polymer chains under different constraints and confining geometries. This will have application to biological processes, where the bending and looping of DNA molecules plays an important role in transcriptional regulation, replication, repair, and packaging, but by using a general model, we produce results which may prove relevant for a range of polymeric problems. We use a combination of statistical mechanical and classical mechanical methods to construct a distribution of forces within the canonical ensemble. This provides us with a mechanical explanation for entropic forces that favor breakage of loops or detachment of polymers from a surface. We find a distribution of forces that is asymmetric and non-Gaussian, implying that the average force is not the most probable force, and that large outliers may appear more frequently than a normal distribution would predict.