Sensitivity of cgDNA+min to computational parameters

This webpage serves as supplementary material for :

This semester project relies mainly on the following existing work:

This master semester project provides further analysis on Beaud's master thesis on cgDNA+min. Since the bBDNA software used in Beaud's thesis takes time to understand its employment, the aim of the study is to find a way to construct an initial minicircle configuration for the energy minimization step without the use of bBDNA software.

We want to prove numerically the hypothesis that "given the periodic ground-state of a specific sequence, if we change its inter variables, while intras and phosphate are left as they are, we can find a good initial guess for the energy optimization", and for doing that we take advantage of Beaud's Matlab scripts. In order to see if it holds we decided to consider two different initial guesses for the energy optimization:

  1. configuration obtained with the bBDNA software (will be called bBDNA);
  2. configuration in which the intra and phosphate coordinates are the same as the periodic ground-state, while the inter coordinates are the ones of the configuration obtained with the bBDNA software (will be called bBDNA with gd-intras).
We tested the energy minimization with these two configurations as starting point, because we want to compare the two numerically optimal results and analyze if they converge to the same optimum.

For the minimization step we used fminunc Matlab function, applying both the Trust region and Quasi-Newton methods, depending on the sequence. These two methods aim to minimize locally a quadratic model: $$ m_k(x_k+t)=f(x_k)+\langle\nabla f(x_k),t \rangle +\frac{1}{2} \langle t ,H(x_k)t \rangle $$

In particular we analized four 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.
- 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 run the minimization for the two initial guesses and evaluate the absolute difference between the two obtained optimal configurations, the energies, the eigenvalues and the Hessian condition numbers. The full sequences and all results can be found through the links on the left.

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

Further analysis of the results should be done to verify the stability of the solutions.