# The Mathematics of DNA Sturcture, Mechanics, and Dynamics

## Abstract

A brief review is given of the main concepts, ideas, and results in the fields of DNA topology, elasticity, mechanics and statistical mechanics. Discussion in- cludes the notions of the linking number, writhe, and twist of closed DNA, elastic rod models, sequence-dependent base-pair level models, statistical models such as helical worm-like chain and freely jointed chain, and dynamical simulation procedures. Experimental methods that lead to the development of the models and the implications of the models are also discussed. Emphasis is placed on illustrating the breadth of approaches and the latest developments in the field, rather than the depth and completeness of exposition.

## Key words

DNA topology elasticity mechanics statistical mechanics stretching## Preview

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## Notes

### Acknowledgments

The author wishes to express his thanks to Zuzana Swigonova for careful proofreading of the manuscript and numerous suggestions. Much of this work was written during a stimulating one semester visit at the Institute for Mathematics and its Applications, University of Minnesota. Support by A.P. Sloan Fellowship and NSF grant DMS-05-16646 is also acknowledged.

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