Single-Molecule Structure and Topology of Kinetoplast DNA Networks

Open Access

Single-Molecule Structure and Topology of Kinetoplast DNA Networks

Pinyao He, Allard J. Katan, Luca Tubiana, Cees Dekker, and Davide Michieletto

Phys. Rev. X 13, 021010 – Published 19 April 2023

Abstract

Kinetoplast DNA (kDNA) is a two-dimensional Olympic-ring-like network of mutually linked DNA minicircles found in certain parasites called trypanosomes. Understanding the self-assembly and replication of this structure are not only major open questions in biology but can also inform the design of synthetic topological materials. Here, we report the first high-resolution, single-molecule study of kDNA network topology using AFM and steered molecular dynamics simulations. We map out the DNA density within the network and the distribution of linking number and valence of the minicircles. We also characterize the DNA hubs that surround the network and show that they cause a buckling transition akin to that of a 2D elastic thermal sheet in the bulk. Intriguingly, we observe a broad distribution of density and valence of the minicircles, indicating heterogeneous network structure and individualism of different kDNA structures. Finally, we estimate the 2D Young modulus of the network to be orders of magnitude smaller than that of other 2D materials. Our findings explain outstanding questions in the field and offer single-molecule insights into the properties of a unique topological material.

Received 2 September 2022
Revised 10 December 2022
Accepted 27 February 2023

DOI:https://doi.org/10.1103/PhysRevX.13.021010

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Mechanical & acoustical properties Polymer conformation & topology

Biological materials Gels Topological materials

Atomic force microscopy Molecular dynamics

Polymers & Soft MatterPhysics of Living SystemsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Pinyao He ^1,2, Allard J. Katan ¹, Luca Tubiana ^3,4,5, Cees Dekker¹, and Davide Michieletto ^6,7,*

¹Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, Netherlands
²Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, School of Mechanical Engineering, Southeast University, Nanjing 211189, China
³Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
⁴INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
⁵Faculty of Physics, University of Vienna, 1090 Vienna, Austria
⁶School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
⁷MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom

^*Corresponding author. davide.michieletto@ed.ac.uk

Popular Summary

Trypanosomes are unique single-cell parasites: Their mitochondrial genome is made of thousands of DNA minicircles interlinked to form a giant 2D Olympic-ring-like network, known as a “kinetoplast DNA” (kDNA). This type of DNA organization is seen nowhere else in nature, and several questions on its evolution, self-assembly, and replication are far from answered. In this work, we combine high-resolution atomic force microscopy, quantitative image analysis, and molecular dynamics simulations to characterize the structure and topology of kDNAs at single-molecule resolution.

We show that the minicircles’ valence (the number of DNA rings linked to any one ring) has a broad distribution, with a mean around 3. We argue that the valence is controlled in vivo to drive the formation of a connected structure that preserves the integrity of the genome during replication yet avoids redundant constraints and a “topologically frustrated” rigid network. Our simulations explain that kDNAs undergo a buckling transition when extracted from the parasite, akin to the buckling of thermal elastic sheets. Finally, we estimate the bending rigidity and Young’s moduli of kDNAs to be thousands of times smaller than lipid vesicles. This ultrasoft nature of kDNAs may motivate the design of synthetic 2D interlocking ring networks, perhaps made of synthetic polycatenanes or DNA plasmids.

Our work sheds light on the structure and topology of a fascinating and topologically complex self-assembled genome at the single molecule scale and could inspire the creation of ultrasoft topological materials.

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Vol. 13, Iss. 2 — April - June 2023

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Images

Figure 1
(a) AFM images of kDNA from C. fasciculata. The scale bar is $2 μ m$ , and the yellow color scale ranges from 0 (black) to 3.5 nm height (white). (b),(c) Enlargements of the rim and cap, respectively. (d) Sketch of the network of minicircles from (b) where we color code the minicircles forming the rim in red. (e) Simplified sketch where we schematically show that the network is formed by linked rings. This is not a one-to-one representation of (d). (f) Box plot of minicircle density in the cap and the rim of the network (obtained from selected regions and averaged across three kDNA networks). The rim density is computed by taking a circular region of radius $r = 100 nm$ (about the size of a minicircle; see below) centered at the hubs. (g) Box plots of the density of minicircles as a function of the distance from the center.
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Figure 2
(a) Examples of single rings used to compute the perimeter and radius of gyration of single minicircles. The scale bar is 500 nm. (b),(c) Enlargements of minicircles with supercoiledlike (b) and open (c) conformations. Scale bars are 250 nm. (d) Size of the minicircles, computed as the radius of gyration of the AFM traces, $R_{g}$ , and the square root of the area, $A^{1 / 2}$ . We find a mean $R_{g} = 101.3 \pm 10.8 nm$ , in line with Ref. [29] reporting $R_{g} = 109 nm$ for 2.6-kb-long plasmids, and mean $A^{1 / 2} = 154.4 \pm 22.5 nm$ .
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Figure 3
(a),(b) Enlarged portions of kDNA showing hubs at the periphery. Scale bars are 500 nm. (c) Distribution of distances between nearest hubs. The dashed vertical line represents the diameter of a minicircle if pulled taut, i.e., $1 / 2 \times 2500 bp \times 0.34 nm / bp = 425 nm$ . (d) Distribution of a number of overlapping minicircles in the cap and in the hubs.
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Figure 4
(a) An in silico kDNA with hexagonal structure of rings. The border is highlighted in red. (b) Enlarged portion of (a) showing the hexagonal lattice linkages. See Supplemental Material [30] for details on how the network is built. (c) Absolute value of the sum of the mean curvature of the triangular mesh, $| Σ |$ , calculated by joining the center of mass of the rings and plotted as a function of the constriction $c = R_{g, \max} / R_{g, rim}$ . In these simulations, $R_{g, rim}$ is user defined and steered using a harmonic potential. The plot shows an abrupt buckling transition. Different symbols correspond to different network topologies chosen by random linking of neighboring rings while preserving the hexagonal structure. (d) Snapshots of the network at four different values of constriction $c$ .
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Figure 5
(a) Morphological segmentation of the AFM image show in Fig. 1. The scale bar is $1 μ m$ . (b) An enlarged region showing side by side the AFM picture and in (c) the result of morphological segmentation. (d) Probability density function (PDF) of mesh size. The inset shows a log-linear plot of the same PDF, with an exponential decay reported as a guide for the eye. (e) Average pore size as a function of the radial distance from the center of the network.
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Figure 6
(a) Figure showing a kDNA image (the scale bar is $2 μ m$ ) and an enlarged $1 μ m^{2}$ region with the corresponding thresholded image (black and white). (b) Starting configuration of the AFM steered MD: 90 rings are placed randomly in a quasi-two-dimensional simulation box. Phantom beads (yellow, orange, and red in the figure) are static and act as Gaussian attracting basins. (c) At the end of the MD simulation, we obtain ensembles of conformations that capture the correct length and size of minicircles, display no ambiguous crossings with other rings. and are compatible with the underlying AFM image. (d) Snapshot of the resulting network after having removed the slab confinement. (e) Distributions of $R_{g}$ of the minicircles from AFM (picked from outside the kDNA) and of the simulated ones (both from the center and periphery). (f) Network representation of (d), where each node is a minicircle and an edge between nodes represents that they are linked. Our simulated networks typically have all the nodes in one large connected component. (g) Distribution of valence, showing that the central minicircles are on average more connected than the peripheral ones. (h) Distribution of linking number, showing that the most linked pairs are singly linked, and about 10% of them are doubly linked.
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