February – March 2020
Elisa De Llano
Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna
Dr. Luca Tubiana
Statistical and Biological Physics Group, University of Trento
Aim of the mission
The aim of this STSM was to computationally characterize the equilibrium mechanical properties of a planar network of rings inspired by the kinetoplast DNA. The kinetoplast DNA (kDNA) is the mitochondrial DNA of trypanosomatids and is formed by thousands of dsDNA mini-rings interlocked with one another and with a few dozens of maxi-rings. In the case of interest here, that of T. Bruceii, this genome forms a planar roughly hexagonal network of around 1,000 dsDNA minirings. With computational models we aim to study the effects that different parameters of the network, such as its size and topological properties (linking sign), have on the overall structure of the network.
Summary of the results
We model an ideal kDNA as an hexagonal network, in which each ring is linked to three others. In previous work we used infinitely thin rigid rings and we ran several Monte Carlo simulations with various network sizes. In this STSM we expanded this model introducing excluded volumes and semi-flexible rings to model dsDNA at high salt concentration. We represented the rings as closed chains of beads. The interaction between beads of different rings was modeled with a WCA potential. The bead size was adjusted to avoid the rings from altering the underlying topology. Semi-flexible rings were modeled introducing a FENE interaction between consecutive beads of the same ring (a bead-spring model). We performed molecular dynamics simulations for systems of 225 rings using LAMMPs.
The results of the simulations showed an amount of bending and torsion in the systems that we hadn’t observed in the Monte Carlo simulations. We tested the following hypothesis with more simulations:
- Whether increasing the number of beads, and thus effectively reducing the thickness of the rings,would approach the results to those of the Monte Carlo simulations.
- Whether the torsion could be due to introducing friction in the system, which was not previously present in the Monte Carlo simulations.
- Whether the semi-flexible model showed results significantly different from the rigid model.
Furthermore, we observed that the torsion could be related to a chiral property in the system. Two rings can be simply interlocked in two ways which are enantiomers. As a consequence, some chirality can be present in our networks too. In fact, considering +1 and -1 links, we found that most links in our network were +1, which we believe is, together with the steric hindrance, the reason behind the observed torsion. In order to analyse the data of the simulations we had to abstract the global structure of the network. Given the amount of particles in the system (between 31,500 and 126,000) we simplified further the network model. Because of the underlying hexagonal topology, the systems can be represented by triangular meshes formed by joining the centers of the hexagons. This has the benefits of highlighting the global structure, removing loosely connected rings at the boundary and reducing the amount of data that needs to be analyzed. On these meshes, we defined observables such as the network area, the bending, or the torsion, with respect to the triangular mesh. The triangular mesh was recreated for every step of the trajectories, and since the torsion depends on the reference frame, all trajectories were aligned to the initial system.
The main results obtained were:
- We defined the observables which describe the global structural properties of the network.
- We wrote a C++/python framework for the analysis and visualization of configurations.
- We performed simulations varying several parameters, from which it appears that the torsion observed is a robust property of the system, likely ascribable to the excluded volume of the rings.