1) The DNA double helix structure has two helical strands that are skewed and not directly opposite each other, resulting in a distance between the strands at any cross-section that is less than the diameter of the helices. 2) The structure of the two helical strands can be defined mathematically using parametric coordinates, where the angle θ increases by 2π with each turn of the helix. 3) The pitch of the helix, or vertical rise of one complete turn, can be calculated using the parametric coordinates and angles of the two helical strands.

1. The DNA Double Helix a mathematical approach to the physical structure Abhranil Das 08MS34 IISER Kolkata (Freshman 2009)

2. The Double Helix is Skewed

3. 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.

4. The Helices in Equations The parametric coordinates of the helices, with time as a parameter, are: ( β > α )

5. A Turn of the Helix For each helix, θ increases by 2 π with each turn. The pitch is given by:

6. Finding the Grooves For a given θ , in the first helix, Similarly, for the second helix,

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

8. 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.

9. Sum of the Grooves Minor Groove + Major Groove = = pitch, as derived before.

10. Phase Difference Between the Strands

11. Using Our Result

12. Thank You