Proceedings of Symposia in Applied Mathematics
Volume 45, 1992
Evolution of DNA Topology:
Implications for Its Biological Roles
NICHOLAS R. COZZARELU
1. Scope of the Article
I shall write about DNA topology in this article in a way that I have not done
before, but in the manner in which I often teach the topic. I shall provide a
"teleological" interpretation of DNA topology: i.e., why and how the topological
structure of DNA evolved. All biologists are fascinated by evolutionary explanations
because they seek to answer the fundamental question: Why are we the way we are?
Evolutionary explanations are also heuristic in that they often provide the hunch that
is behind the stated rationale for an experiment. Despite this, teleological arguments
are sometimes viewed as unscientific and thus are rarely written down. It is extremely
difficult to determine how something evolved, let alone why, especially for something
so basic to life as the genetic material. The reader is forewarned that most of what I
shall write is unproven. I do, however, invite the reader to share in these secret
pleasures of biologists.
2. Topological properties of DNA
A schematic representation of a small section of double-stranded DNA
(deoxyribonucleic acid) is shown in Fig. 1. The DNA is depicted as a helically
twisted ladder. The uprights are polymers of the sugar, deoxyribose, esterified to
phosphoric acid and represent the backbones of the molecule. The rungs are pairs of
four specific organic bases. It is the sequence of the bases that encodes the genetic
information in DNA. A single strand of DNA consists of one backbone plus the
adjacent bases. The two strands of DNA come apart during the duplication of genetic
material by breakage of the weak bonds between the base pairs. Each single strand
thus acts as a template for the synthesis of the other (complementary) strand. DNA is
called a nucleic acid because it is found in the compartment of the cell called a nucleus
1991 Mathematics Subject Classification: Primary 92C40.57M25.
The research on which this summary is based was supported by grants from the
National Institutes of Health and the National Science Foundation.
This paper is in final form and no version of it will be submitted for publication
elsewhere.
© 1992 American Mathematical Society
0160-7634/92 $1.00 + $.25 per page
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http://dx.doi.org/10.1090/psapm/045/1196713 http://dx.doi.org/10.1090/psapm/045/1196713
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