Algebraic systems representation of DNA sequence-structure
relationships
Mary E. Karpen Howard J. Chizeck Stephen D. Hawley
Department of Chemistry
Grand Valley State University
Allendale MI, 49401
Department of Electrical Engineering
University of Washington
Seattle WA, 98195-2500
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UW
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Electrical
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October 2003
Department of Electrical Engineering
University of Washington
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Algebraic systems representation of DNA sequence-structure
relationships
0
Mary E. Karpen
Howard J. Chizeck
Stephen D. Hawley
1
1
0
Department of Chemistry
Grand Valley State University
Allendale MI, 49401
1 Department of Electrical Engineering
University of Washington
Seattle WA, 98195-2500
University of Washington, Dept. of EE, UWEETR-2003-0022
October 2003
Abstract
The Calladine-Dickerson rules predict variations in the three-dimensional structure of a DNA helix from its basepair 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 homatons1 . 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.
1 This
report based upon the M.S. thesis work of Mary Karpen, Case Western Reserve University, 1986
1
Calladine and Dickerson developed their rules for predicting
DNA structure from the limited crystal data available at the time.
Since then many more sequences have been crystallized and their
structures determined to high resolution. Analysis of the crystal
structures has shown that Calladine and Dickerson correctly
identified tetranucleotide subsequences as the necessary context
to determine structure at the central base-step, for most cases.
Analysis has also shown that the four parameters Calladine and
Dickerson modeled are statistically dependent on other structural
parameters (Packer, 1998). The values of the base-step translations
shift and slide largely determines the structure of a base-step of
DNA.
The next task then is to develop a model of these base-step
translations and evaluate its accuracy. In a future work it will be
shown that the algebraic systems model presented here can be extended
to take the four Watson-Crick bases as inputs. And furthermore, with
the data now available from the Nucleic Acids Database the new
algebraic systems model can be parameterized to predict shift and
slide.
Packer, M.J. & Hunter, C.A. (1998) J Mol. Biol. 280, 407-420.