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28 March 2024
 
  » arxiv » cond-mat/0501171

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A Formulation of the Worm Like Chain Model Appropriate to Double-Strand DNA Subject to Spatial Constraints
C. Bouchiat ;
Date 9 Dec 2004
Subject Soft Condensed Matter; Statistical Mechanics; Biomolecules | cond-mat.soft cond-mat.stat-mech q-bio.BM
AffiliationLPT Ecole Normale Superieure Paris
AbstractIn absence of supercoiling, the Worm Like Chain (WLC) model provides a good description of the dsDNA entropic elasticity within a wide range of force. Since the elastic-energy linear density of the WLC model is proportional to the square of the molecular chain curvature, a natural dynamical variable is the unitary tangent vector, but this choice leads to unbearable complications in the implementation of spatial constraints via a one-monomer potential. To circumvent this difficulty the first obvious step is to use the monomer coordinate as a dynamical variable. If it were used as the sole dynamical variable, second-order derivatives relative to the chain arc length would creep in the elastic energy. This can be avoided by introducing an auxiliary vector variable. Using standard path integration techniques, we obtain the Hamiltonian for the spatially constrained Worm Like Chain (SCWLC), where both the monomer coordinate and the unitary tangent vector appear as independent variables. The final version of the SCWLC model is a "transfer-matrix" iterative formulation, numerically quite efficient and leading to a suggestive interpretation in terms of a Markovian random walk. To test the potentialities of the SCWLC model, we have studied two configurations of a single dsDNA molecule confined between two parallel plates.
Source arXiv, cond-mat/0501171
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