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Conformational Statistics of Dna and Diffusion Equations on The Euclidean Group

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Mathematics of DNA Structure, Function and Interactions

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 150))

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Abstract

Semi-flexible (or wormlike) polymer chains such as DNA possess bending and torsional stiffness. Given a semi-flexible polymer structure that is subjected to Brownian motion forcing, the distribution of relative positions and orientations visited by the distal end of the chain relative to its proximal end provides important information about the molecule that can be linked to experimental observations. This probability density of end-to-end position and orientation can be obtained by solving a Fokker-Planck equation that describes a diffusion process on the Euclidean motion group. In this paper, methods for solving this diffusion equation are reviewed. The techniques presented are valid for chains of up to several persistence lengths in open environments, where the effects of excluded volume can be neglected.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Johns Hopkins University, 21218, Baltimore, MD, USA

    Gregory S. Chirikjian

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  1. Gregory S. Chirikjian
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Correspondence to Gregory S. Chirikjian .

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Editors and Affiliations

  1. Dept. Pharmacology & Genome Center, University of California, Davis, E. Health Sciences Drive 451, Davis, 95616, USA

    Craig John Benham

  2. Dept. Chemistry & Biochemistry, Georgia Institute of Technology, Atlanta, 30332-0400, USA

    Stephen Harvey

  3. Dept. Chemistry & Chemical Biology, Rutgers State University of New Jersey, Taylor Rd. 610, Piscataway, 08854-8087, USA

    Wilma K. Olson

  4. Dept. Mathematics, Florida State University, Tallahassee, 32306-4510, USA

    De Witt Sumners

  5. Dept. Mathematics, University of Pittsburgh, Thackeray Hall 301, Pittsburgh, 15260, USA

    David Swigon

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Chirikjian, G.S. (2009). Conformational Statistics of Dna and Diffusion Equations on The Euclidean Group. In: Benham, C., Harvey, S., Olson, W., Sumners, D., Swigon, D. (eds) Mathematics of DNA Structure, Function and Interactions. The IMA Volumes in Mathematics and its Applications, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0670-0_3

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