UWEE Tech Report Series

Algebraic Systems Representation of DNA Sequence-Structure Relationships


Mary E. Karpen, Howard Jay Chizeck, Stephen D. Hawley

sequence dependent structure, DNA, algebraic systems theory


The Calladine-Dickerson rules predict variations in the three- dimensional structure of a DNA helix from its base-pair sequence. A new approach to modeling these DNA sequence/structure relationships is to represent them as an algebraic system. This requires the extension of algebraic systems theory to a new class of sequential systems, called group homatons. The base-pair sequence serves as the input to a group homaton, which sequentially processes the base- pairs according to an abstracted version of the Calladine-Dickerson rules. The output is a set of four structure parameters, at each base-pair location along the helix. This representation also provides a means of inverting the Calladine-Dickerson rules, determining the base-pair sequence from a specified sequence of structure variations. Both the inverse operation and the forward system are easily implementable on a microcomputer. The inverse system has potential use as a tool in designing sequences of DNA with desired structures. This technique is sufficiently general to allow future expansion to more complex models.

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