Orientation of DNA Minicircles Balances Density and Topological Complexity in Kinetoplast DNA

Abstract

Kinetoplast DNA (kDNA), a unique mitochondrial structure common to trypanosomatid parasites, contains thousands of DNA minicircles that are densely packed and can be topologically linked into a chain mail-like network. Experimental data indicate that every minicircle in the network is, on average, singly linked to three other minicircles (i.e., has mean valence 3) before replication and to six minicircles in the late stages of replication. The biophysical factors that determine the topology of the network and its changes during the cell cycle remain unknown. Using a mathematical modeling approach, we previously showed that volume confinement alone can drive the formation of the network and that it induces a linear relationship between mean valence and minicircle density. Our modeling also predicted a minicircle valence two orders of magnitude greater than that observed in kDNA. To determine the factors that contribute to this discrepancy we systematically analyzed the relationship between the topological properties of the network (i.e., minicircle density and mean valence) and its biophysical properties such as DNA bending, electrostatic repulsion, and minicircle relative position and orientation. Significantly, our results showed that most of the discrepancy between the theoretical and experimental observations can be accounted for by the orientation of the minicircles with volume exclusion due to electrostatic interactions and DNA bending playing smaller roles. Our results are in agreement with the three dimensional kDNA organization model, initially proposed by Delain and Riou, in which minicircles are oriented almost perpendicular to the horizontal plane of the kDNA disk. We suggest that while minicircle confinement drives the formation of kDNA networks, it is minicircle orientation that regulates the topological complexity of the network.

Fig 1. Hopf Links and Models proposed to analyze the topological properties of the minicircle network.

A: A Hopf link; B: A grid of minicircles whose orientation has been biased. Volume effects are not considered and minicircle thickness is shown to help trace the trajectory of each minicircle; C: A grid of minicircles represented by freely jointed closed chains to study the effects of DNA bending; D: A grid of minicircles, represented by octagonal polygons, to study the effects of volume exclusion due to electrostatic interactions.

Fig 2. Estimation of the mean minicircle valence as a function of the minicircle density for biologically significant radii.

The sample size for each data point is 10⁵ and the sizes of the error bars are less than the sizes of the plotted data points.

Fig 3. Relationship between the linking probability (LP) of rigid (Geo Circ) and freely jointed minicircles (ERP) with volume exclusion.

Fig 4. Estimated average saturation density for various restriction angles.

Each data point in the figures is based on samples of sample size 1000 and minicircle grids of dimension 1000 × 1000. The 95% standard error bars are less than.0005 in all cases.