cgDNA+min, an adaptation of cgDNAmin

This webpage serves as supplementary material for :

This thesis provides an adaptation of R. Manning's cgDNAmin software to suppport cgDNA+ coordinates and periodic closure DNA minicircles. The adaptation relies mainly on the following existing work:

Original (NCC) cgDNAmin is adapted in two different ways. We first add a new type of minicircle closure: the periodic closure (PC) using Glowacki's construction. Then we adapted the energy minimization procedure to work with cgDNA+ coordinates with both non-continuous (NCC) and periodic (PC) closure assumptions.

We provide the results for four different variants of the original cgDNAmin energy minimization:
 - Non-continuous closure, cgDNA energy:NCC cgDNAmin,
 - Periodic closure, cgDNA energy:PC cgDNAmin,
 - Non-continuous closure, cgDNA+ energy:NCC cgDNA+min,
 - Periodic closure, cgDNA+ energy:PC cgDNA+min.

We present our results for five different sequences:
- Kahn & Crothers: Crothers, D. M. et al. “DNA bending, flexibility, and helical repeat by cyclization kinetics”.
In: Methods in Enzymology 212 (1992), pp. 3–29.
- Poly A 158 bp,
- Pyne et al. 251 bp: Pyne et al. "Base-pair resolution analysis of the effect of supercoiling on DNA flexibility and major groove recognition by triplex-forming oligonucleotides".
In: Nature communications 12.1 (2021), pp. 1053–1053.
- Pyne et al. 339 bp,
- Widom 601: Coultier, T. and Widom, J. "Spontaneous Sharp Bending of Double-Stranded DNA".
In: Molecular cell 14.3 (2004), pp. 255-362.

For each sequence, we present the results for four chosen initial guesses that are shown in a bifurcation diagram. We then present the 3D views and the 2D coordinates plots of the results of the different energy minimization procedures. For each configuration/solution, we provide:
- the Link, i.e. the number of twists of the intertwined backbones,
- the smallest eigenvalue of the Hessian matrix at the solution,
- the molecule energy, Equation (2) in my thesis (♦): \[U(w; S,\mathcal{P}) = \frac{1}{2}(w-\mu)^T K (w-\mu)\] \(w\) is the coordinates of the configuration, \(\mu(S,\mathcal{P})\) is the groundstate and \(K(S,\mathcal{P})\) is the stiffness matrix. \(S\) is the sequence and \(P\) the parameter set.
We also provide MATLAB .fig files for all shown figures and .mat files containing the raw data of our results.

The full sequences an all results can be found through the links on the left.

The MATLAB scripts can be found on the separate sub-page.

Excel table containing the energy, link and five smallest eigenvalues for all computed configurations: Eigenvalues_Results-cgDNAmin.xlsx.
We note the negative eigenvalues in different cases. Further analysis of the results should be done to verify the stability of the solutions.