The DNA Double Helix

a mathematical approach

to the physical structure

Abhranil Das

08MS34

IISER Kolkata (Freshman 2009)

The Double Helix is Skewed

The strands of the DNA double helix are not diametrically opposite.So, the distance between them at any cross-section is not equal to, but

less than the diameter of the helices.

The Helices in Equations

The parametric coordinates of the helices, with

time as a parameter, are:

(β > α)

A Turn of the Helix

For each helix, θ increases by 2π with each turn.

The pitch is given by:

Finding the Grooves

For a given θ, in the first helix,

Similarly, for the second helix,

Finding the Grooves

For minor groove, we need the difference in z between the first θ (n=1) of the two.

Finding the Grooves

For major groove, we need the difference in z between the first θ (n=1) of strand 1, and second θ (n=2) of strand 2.

Sum of the Grooves

Minor Groove + Major Groove =

= pitch, as derived before.

Phase Difference Between the Strands

Using Our Result

Thank You