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So I know that the major/minor groove arise from the offset pairing of the two strands in the helix. All my textbook tells me is that "pitch causes the off-set pairing of DNA and this gives rise to the major and minor grooves."

I'm not too sure what this is saying. What exactly is pitch and how does it give rise to the grooves?

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Pitch is not a great word for this, as its meaning is ambiguous. It's hard to find a universal nomenclature for DNA geometry, but see the "Base pair geometry" section of this wikipedia page. The relevant property is what they call "opening".

From the biochemistry textbook by Berg:

enter image description here

To explain in words, if the glycosidic bonds (which attach the nucleic base to the sugar in the backbone) stuck straight out at 90 angles on both sides, then the grooves in double-stranded DNA would be symmetrical. Because the glycosidic bonds are at an angle (relative to the interface between the AT or GC pairs), one of the "faces" of the base pair is larger than the other.

Words and flat pictures, however, will never really give you a good intuitive sense of what's going on with the 3D structure of the grooves. A good modeling kit will be of great help to you.

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  • $\begingroup$ Would it be correct to claim that this is because the nucleobases they're attached to wouldn't base-pair properly (and would likely experience clashes) if they weren't? For instance, in the image in your answer, if the sugar-phosphate backbones were to be diametrically opposite to one another, then, the atoms on the major groove side would clash (i.e., physically encroach upon one another), while the atoms on the minor groove side would be too far away to establish a hydrogen-bond. $\endgroup$
    – Dunois
    Commented Jul 16, 2020 at 13:33

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