Topology in Biology

For most of its life cycle the bacteriophage called Phi-X-174 has the curious property that its DNA is circular, i.e. has its ends joined, and is single stranded. During reproduction however it is double-stranded (and presumably still circular) giving it the classical "double helix" shape, which raises the following question.

Is it topologically equivalent to a cylinder or a Moebius band?

Since DNA has 5 base pairs for every 180 degree twist and Phi-X-174 has 5375 base pairs it has 1075 twists (prior to the join) which is an odd number of half-turns and so it is equivalent to a Moebius band.

This is a perfect example of a mathematician making inferences in a field of study about which he has almost no knowledge. As a result the statements are almost surely false ... none-the-less see Topology in biology for marginally more detail.

Ralph Buchholz

17 May 2003

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