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# The DNA Double Helix

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A mathematical approach to the physical structure.

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### The DNA Double Helix

1. 1. The DNA Double Helix a mathematical approach to the physical structure Abhranil Das 08MS34 IISER Kolkata (Freshman 2009)
2. 2. The Double Helix is Skewed
3. 3. <ul><li>The strands of the DNA double helix are not diametrically opposite. </li></ul><ul><li>So, the distance between them at any cross-section is not equal to, but less than the diameter of the helices. </li></ul>
4. 4. The Helices in Equations <ul><li>The parametric coordinates of the helices, with </li></ul><ul><li>time as a parameter, are: </li></ul><ul><li> </li></ul><ul><li>( β > α ) </li></ul>
5. 5. A Turn of the Helix <ul><li>For each helix, θ increases by 2 π with each turn. </li></ul><ul><li>The pitch is given by: </li></ul>
6. 6. Finding the Grooves <ul><li>For a given θ , in the first helix, </li></ul><ul><li>Similarly, for the second helix, </li></ul>
7. 7. Finding the Grooves <ul><li>For minor groove, we need the difference in z between the first θ (n=1) of the two. </li></ul>
8. 8. Finding the Grooves <ul><li>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. </li></ul>
9. 9. Sum of the Grooves <ul><li>Minor Groove + Major Groove = </li></ul><ul><li>= pitch, as derived before. </li></ul>
10. 10. Phase Difference Between the Strands
11. 11. Using Our Result
12. 12. <ul><li>Thank You </li></ul>