maths document

May 12th, 2015
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THE MATHEMATICS OF DNA STRUCTURE,MECHANICS, AND DYNAMICSDAVID SWIGONAbstract. A brief review is given of the main concepts, ideas, and results in thefields of DNA topology, elasticity, mechanics and statistical mechanics. Discussion includes the notions of the linking number, writhe, and twist of closed DNA, elastic rodmodels, sequence-dependent base-pair level models, statistical models such as helicalworm-like chain and freely jointed chain, and dynamical simulation procedures. Experimental methods that lead to the development of the models and the implications of themodels are also discussed. Emphasis is placed on illustrating the breadth of approachesand the latest developments in the field, rather than the depth and completeness ofexposition.Key words. DNA topology, elasticity, mechanics, statistical mechanics, stretching.1. Introduction. The discovery of DNA structure 55 years agomarked the beginning of a process that has transformed the foundationsof biology and medicine, and accelerated the development of new fields,such as molecular biology or genetic engineering. Today, we know muchabout DNA, its properties, and function. We can determine the structure of short DNA fragments with picometer precision, find majority ofthe genes encoded in DNA, and we can manipulate, stretch and twist individual DNA molecules. We can utilize our knowledge of gene regulatoryapparatus encoded in DNA to produce new microorganisms with unexpected properties. Yet, there

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