Ionic Effects on the Equilibrium Conformation of Catenated DNA Networks

Kinetoplast DNA: a polymer physicist's topological Olympic dream

All life forms are miraculous, but some are more inexplicable than others. Trypanosomes are by far one of the most puzzling organisms on Earth: their mitochondrial genome, also called kinetoplast DNA (kDNA) forms an Olympic-ring-like network of interlinked DNA circles, challenging conventional paradigms in both biology and physics. In this review, I will discuss kDNA from the astonished perspective of a polymer physicist and tell a story of how a single sub-cellular structure from a blood-dwelling parasite is inspiring generations of polymer chemists and physicists to create new catenated materials.

Chirality effects in molecular chainmail

Motivated by the observation of positive Gaussian curvature in kinetoplast DNA networks, we consider the effect of linking chirality in square lattice molecular chainmail networks using Langevin dynamics simulations and constrained gradient optimization. Linking chirality here refers to ordering of over-under versus under-over linkages between a loop and its neighbors. We consider fully alternating linking, maximally non-alternating, and partially non-alternating linking chiralities. We find that in simulations of polymer chainmail networks, the linking chirality dictates the sign of the Gaussian curvature of the final state of the chainmail membranes. Alternating networks have positive Gaussian curvature, similar to what is observed in kinetoplast DNA networks. Maximally non-alternating networks form isotropic membranes with negative Gaussian curvature. Partially non-alternating networks form flat diamond-shaped sheets which undergo a thermal folding transition when sufficiently large, similar to the crumpling transition in tethered membranes. We further investigate this topology-curvature relationship on geometric grounds by considering the tightest possible configurations and the constraints that must be satisfied to achieve them.

Nanopore translocation of topologically linked DNA catenanes

The electrical signal associated with a biopolymer translocating through a nanoscale pore depends on the size, topology, and configuration of each molecule. Building upon recent interest in using solid-state nanopores for studying the topology of knotted and supercoiled DNA, we present experimental observations of topologically linked catenanes translocating through a solid-state nanopore. Using restriction enzymes, linked circular molecules were isolated from the mitochondrial DNA of Crithidia fasciculata, a structure known as a kinetoplast that comprises thousands of topologically interlocked minicircles. Digested kinetoplasts produce a spectrum of catenane topologies, which are identified from their nanopore translocation signals by spikes in the blockade current associated with the topological linkages. We attribute the different patterns of the measured electrical signals to 2-catenanes, linear and triangular 3-catenanes, and several types of 4- and 5-catenanes as well as more complex structures. Measurements of the translocation time of signals consistent with 2- and 3-catenanes suggest that topological friction between the linkages and the pore slows the translocation time of these structures, as predicted in recent simulations.

Flatness and intrinsic curvature of linked-ring membranes

Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from catenated DNA rings. Inspired by these studies, we use Monte Carlo simulations to examine the behavior of two-dimensional networks ("membranes") of linked rings. For simplicity, we consider only identical rings that are circular and rigid and that form networks with a regular linking structure. We find that the scaling of the eigenvalues of the shape tensor with membrane size are consistent with the behavior of the flat phase observed in self-avoiding covalent membranes. Increasing ring thickness tends to swell the membrane. Remarkably, unlike covalent membranes, the linked-ring membranes tend to form concave structures with an intrinsic curvature of entropic origin associated with local excluded-volume interactions. The degree of concavity increases with increasing ring thickness and is also affected by the type of linking network. The relevance of the properties of linked-ring model membranes to those observed in kinetoplasts is discussed.

Phase Transition of Catenated DNA Networks in Poly(ethylene glycol) Solutions

Conformational phase transitions of macromolecules are an important class of problems in fundamental polymer physics. While the conformational phase transitions of linear DNA have been extensively studied, this feature of topologically complex DNA remains unexplored. We report herein the polymer-and-salt-induced (Ψ) phase transition of 2D catenated DNA networks, called kinetoplasts, using single-molecule fluorescence microscopy. We observe that kinetoplasts can undergo a reversible transition from the flat phase to the collapsed phase in the presence of NaCl as a function of the crowding agent poly(ethylene glycol). The nature of this phase transition is tunable through varying ionic strengths. For linear DNA, the coexistence of coil and globule phases was attributed to a first order phase transition associated with a double well potential in the transition regime. Kinetoplasts, however, navigate from the flat to the collapsed phase by passing through an intermediate regime, characterized by the coexistence of a multipopulation with varying shapes and sizes. Conformations of individual molecules in the multipopulation are long-lived, which suggests a rugged energy landscape.

Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement

A kinetoplast is a planar network of catenated DNA rings with topology that resembles that of chain mail armor. In this work, we use single-molecule experiments to probe the conformation of kinetoplasts confined to slits. We find that the in-plane size of kinetoplasts increases with degree of confinement, akin to the slitlike confinement of linear DNA. The change in kinetoplast size with channel height is consistent with the scaling prediction from a Flory-type approach for a 2D polymer. With an increase in extent of confinement, the kinetoplasts appear to unfold and take on more uniform circular shapes, in contrast to the broad range of conformations observed for kinetoplasts in bulk.