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##### RNA structures (DSSR) / Circular DNA parameters
« on: October 30, 2020, 01:27:01 pm »
Dear Dr. Xiang-Jun Lu,

Thank you for developing (and maintaining) this collection of beautiful and practical DNA geometry software!

For my project I want to generate circular DNA (plasmids) of various sizes.
Based on the book chapter of Calladine et al. (see source below) I found a way to determine the base roll angle for each base pair.

For example, we can determine the curvature of each helical turn to make a circle consisting of 100 bp as follows:

- assume 10 bp per turn
- assume helix angle of 36 degrees

First determine number of turns: 10
Determine the angle each turn has to make: 36 degrees
For a smooth transition per base step fit this angle to cosine:

First we need to determine the amplitude to account for +/- direction of helix
amplitude = 36 / (10*0.5)

Then each roll angle can be determined as follows:
for bp_i in range[0:100]:
roll_angle = amplitude*(cos(helix_angle)*bp_i))

which gives you periodic values of:
[7.2, 5.825, 2.225, -2.225, -5.825, -7.2, -5.825, -2.225,  2.225, 5.825, ....]

Of course this (could) work for an arbitrary length of sequences.
So may plan was to use these roll angle parameters to make circular DNA.

As a starting point I just used for each bp a twist and rise value of 36 and 3.34 respectively (since I want B-DNA) together with the periodic roll angle values and all other parameters black (zero). See attachement for parameter file.

When I visualize the structure with the rebuilder at the webserver (http://web.x3dna.org/custom/option) the result is very close to perfect, see image in attachement. However, the ring is not perfectly planar (although I want to have the geometry completely planar such that I can easily define the connections of the beginning and end in the pdb later on).

I very much hope that with your years of DNA geometry experience you could provide some insight on how to make the ring perfectly planar. I am probably overlooking something obvious... So apologies in advance if the question is unclear!

Thank you for reading my message and stay safe!

Best,
Thor

PS
Eventually I want to make this to work for arbitrary length of sequences, however, conceptually I couldn't think of a smart way to deal with the decimal numbers arising in the total number of "complete" turns. I guess one should start to introduce varying helix twists such that the outer ends properly meet?

Source: Calladine, C.R., Drew, H.R., Luisi, B.F. & Travers, A.A. Understanding DNA: theMolecule and How It WorksChapter 4 (Elsevier Academic Press, San Diego, CA,2004).

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Created and maintained by Dr. Xiang-Jun Lu [律祥俊] (xiangjun@x3dna.org)
The Bussemaker Laboratory at the Department of Biological Sciences, Columbia University.