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Solving tangle equations arising in a DNA recombination model

Published online by Cambridge University Press:  01 January 1999

C. ERNST  and
D. W. SUMNERS
C. ERNST
Affiliation:
Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, U.S.A.
D. W. SUMNERS
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, U.S.A.
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Abstract

In the tangle model for DNA site-specific recombination, one is required to solve simultaneous equations for unknown tangles which are summands of observed DNA knots and links. For 0[les ]i[les ]3, given fixed 4-plats Ki where the set {K1, K2, K3} contains at least two distinct 4-plats, let O and R denote unknown 2-string tangles such that {O, R} are the variables in the system of four tangle equations N(O+iR)=Ki, where N is the numerator construction, and nR denotes the tangle sum of n copies of R. Then there is at most one simultaneous solution {O, R} and this solution must be of the form R an integral tangle and O either a rational tangle or the sum of two rational tangles. In addition, if there exists a solution, then at least one of the 4-plats is chiral. We exhibit an algorithm for solving simultaneous tangle equations of this form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 1 , January 1999 , pp. 23 - 36
Copyright
The Cambridge Philosophical Society 1999

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