By Louis H. Kauffman (auth.), Jill P. Mesirov, Klaus Schulten, De Witt Sumners (eds.)
This IMA quantity in arithmetic and its functions MATHEMATICAL ways TO BIOMOLECULAR constitution AND DYNAMICS is likely one of the volumes according to the court cases of the 1994 IMA Sum mer software on "Molecular Biology" and contains Weeks three and four of the four-week software. Weeks 1 and a couple of seemed as quantity eighty one: Genetic Mapping and DNA Sequencing. We thank Jill P. Mesirov, Klaus Schulten, and De Witt Sumners for organizing Weeks three and four of the workshop and for modifying the complaints. We additionally take this chance to thank the nationwide Institutes of wellbeing and fitness (NIH) (National heart for Human Genome Research), the nationwide technological know-how beginning (NSF) (Biological Instrumen tation and Resources), and the dep. of strength (DOE), whose fi nancial help made the summer time application attainable. A vner Friedman Robert Gulliver v PREFACE The progressive growth in molecular biology in the final 30 years opens how to complete figuring out of the molecular constructions and mech anisms of residing organisms. Interdisciplinary study in arithmetic and molecular biology is pushed through ever starting to be experimental, theoretical and computational strength. The mathematical sciences accompany and help a lot of the growth completed via test and computation in addition to offer perception into geometric and topological homes of biomolecular constitution and methods. This quantity contains a consultant pattern of the papers offered over the last weeks of the month-long Institute for arithmetic and Its functions summer time 1994 software in Molecular Biology.
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Extra resources for Mathematical Approaches to Biomolecular Structure and Dynamics
Delbruck, Mathematical Problems in the Biological Sciences, AMS, Providence, RI, 1962 p. 55. V. V. D. V. Anshelevich, The knot probability in statistical mechanics of polymer chains, Sov. JETP 39 (1974), 1059-1063. J. W. Wiegel, On the topology of a polymer ring, Proc. Roy. Soc. A 403 (1986), 269-284. W. G. Whittington, Knots in self-avoiding walks, J. Phys. A: Math. Gen. 21 (1988),1689-1694.  N. Pippenger, Knots in random walks, Disc. AppI. Math. 25 (1989),273-278. E. W. G. Whittington, Entanglement complexity of graphs in Z3, Math.
If one is interested in the numerical values of properties such as the knot probability or the writhe at modest values of n the only useful approach seems to be a Monte Carlo method. 3), or the exponent determining the behaviour of the absolute value of the writhe. The idea of a Monte Carlo approach is to generate a random sample of polygons, and determine (for instance) what fraction of the sample is knotted. The difficulty is to generate a random sample in a reasonable amount of computer time.
Unfortunately the results do not resolve the question of the possible lattice dependence of a. All that can be said is that the 95% confidence intervals have substantial overlap. DNA and RNA are polyelectrolytes and their conformational properties are sensitive to the ionic strength of the solution in which they are dissolved. In particular, there is direct experimental evidence [3,4] that the knot probability in circular DNA increases as the ionic strength of the solution increases. The charges are screened by the presence of the supporting electrolyte and the inter-charge repulsion is thus reduced.