Human bloodsucking parasite in service of materials science

Trypanosoma is a genus of single-cell eukaryote organisms—parasites living in the bloodstream (or sometimes inside cells) of humans or other mammals and causing a number of serious diseases (such as Leishmaniasis, African trypanosomiasis [sleeping sickness], American trypanosomiasis [Chagas disease], and others). In most cases, they are transmitted by blood-feeding invertebrates, such as flies or mosquitos. They are also called kinetoplastids, because their major distinguishing feature is a subcellular structure known as the kinetoplast—their form of mitochondrial DNA. Truly surprising at first glance, the kinetoplast is a sort of a chainmail composed of thousands of concatenated DNA rings. While a lot is known about kinetoplasts’ biology, Klotz et al. (1) in PNAS offer a fresh view, abstracting from kinetoplast biological function and considering it as a peculiar material.

Mitochondrial DNA of Kinetoplastids Is an Olympic Polymer Gel

Kinetoplasts were known to biologists a long time ago, but their structure came to light only starting around 1970 (see, e.g., review in ref. 2 and references therein). Interestingly, several related developments happened at about the same time. Perhaps unbeknown to one another, Vinograd and Hudson (3) observed a simple DNA catenane in human HeLa cell mitochondria; Sauvage and coworkers (4) invented protocols for chemical synthesis of molecular catenanes; and de Gennes (5), thinking of possible polymer gel structures, came up with the idea of the so-called olympic gel—a macroscopic network of concatenated ring polymers (ref. 5, section 5.1.2). The kinetoplast is actually just like an olympic gel, but more subtle. It consists of covalently closed (but, surprisingly, not supercoiled) DNA rings of 2 distinct types, minicircles and maxicircles. There are typically up to 10,000 minicircles, each about 0.5 to 3 kbp, and a few dozen maxicircles, each about 20 to 50 kbp. To place these numbers in context, persistence length of dsDNA is about 50 nm, or 150 bp, so maxicircles are very flexible, while minicircles are borderline; shorter ones are only a few persistence lengths and pretty rigid, while longer ones are more flexible. Although electron micrographs of isolated kinetoplasts seem to reveal a planar structure, experiments with topoisomerase II indicate that DNA rings are interlocked in a peculiar way: Minicircles are concatenated, each linked with 3 others on average; maxicircles are also linked to one another; and maxicircles are threaded through the minicircle network. Thus, although planar in appearance, kinetoplasts comprise 2 interpenetrating olympic gels.

How kinetoplast DNA performs its genetic function is nothing short of amazing. Functional mRNA is produced from the transcripts of maxicircles through the process of massive editing (involving up to 50% of all residues!) that is controlled by minicircle-encoded guide RNAs, explaining the large repertoire of minicircle sequences. Replication of the kinetoplast is also remarkable, although much less seems to be known about it, especially about maxicircles, while each minicircle is known to replicate once, and only once, every generation (2).

Topology, Geometry, and Mechanics of Kinetoplasts

Turning closer to the physics view, first of all, the idea of DNA-based materials is of course not new and has several implementations, for instance, based on DNA-covered colloids or DNA origami (6, 7) (see ref. 8 for review). Perhaps a superficial, but interesting observation is that DNA origami usually self-assembles with participation of long “scaffold” DNA strands and much shorter “staple” strands—clearly reminiscent of maxi- and minicircles in a kinetoplast. The difference, however, is also striking, as the kinetoplast appears to be held together by purely topological interactions of concatenation between rings.

The topological interactions effect in polymeric systems is well known, leading to very slow reptation-like relaxation processes in a concentrated system of linear or branched polymers (5, 9). However, as far as ring polymers are concerned, mostly the case of unconcatenated (and unknotted) rings was studied (reviewed in ref. 10). In particular, from the rheology standpoint, Kapnistos et al. (11) demonstrated that concentrated systems of unconcatenated rings exhibit a self-similar, power-law stress relaxation, with no “entanglement plateau” characteristic of the usual linear polymers. Concatenated rings are much less understood (12, 13), neither in terms of their statics nor in terms of their dynamics.

For instance, the simplest system of concatenated rings would be the so-called poly[n]catenane—a linear chain of $n$ pairwise interlocked rings, each of some $m$ monomers. Such an object, isolated in a dilute solution, would seem to be a pedestrian subject for a standard exercise in statistical physics of polymers. Nevertheless, even the most elementary question, what the gyration radius $〈R_g^2〉$ of poly[n]catenane is, and how it scales with $n$ and with $m$, is not understood (13). Only for a single unknotted ring is it known that the gyration radius scales as $〈R_g^2〉\sim m^{2\nu }$, with $\nu \approx 0.588$ standard Flory metric exponent, and this scaling is valid due to topological reasons even for an infinitely thin ring polymer with no appreciable excluded volume (see, e.g., the review in ref. 10).

Computer simulation of the many rings system was undertaken in refs. 14 and 15, with the explicit goal of shedding light on kinetoplasts. In particular, Michieletto et al. (15) show that a set of phantom (i.e., freely passing through one another) semiflexible polymeric loops confined in a box at an appropriate density forms a percolating cluster. Taking loops phantom mimics the idea that the kinetoplast forms in the medium with an abundance of topoisomerase II which may later be withdrawn, freezing the topology. Based on their simulations, Michieletto et al. (15) then argue that the kinetoplast has a degree of concatenation right at the percolation threshold.

When Klotz et al. (1) observed an individual kinetoplast in a dilute solution, it did appear like a cup-shaped curved surface (see images in ref. 1), and Klotz et al. think of it as a 2-dimensional polymer. This is consistent with the claim based on the electron microscopy data that kinetoplasts appear “planar,” but it is unclear how this relates to the claim of a percolation threshold. In fact, this question may deserve closer attention: What is the intrinsic fractal dimension of a kinetoplast? Moreover, even the definition of a fractal dimension for a topologically linked object such as a kinetoplast is less than obvious. Indeed, for a covalently connected (tethered) network, an intrinsic fractal dimension is called a spectral dimension, and it is independent on the embedding of the network in the surrounding 3D Euclidean space (16, 17). For a system of topologically concatenated rings, it is generally impossible to determine which ring is concatenated with which other ring, as is clear from the example of Borromean rings where no 2 rings are concatenated, but all 3 together are linked. Concatenation is generally not a pairwise property—unlike a covalent bond. Therefore, to make real progress in understanding kinetoplasts as materials this aspect will have to be clarified.

Why Is the Study Important for Materials Science?

The most exciting discovery of Klotz et al. (1) is the fact that the positive Gaussian curvature, cup-like shape of a kinetoplast is actually its equilibrium property. It follows from the experiment where Klotz et al. (1) were able to deform the kinetoplast by force, by pulling it into a capillary, and then they observed how the kinetoplast relaxed back to its original shape upon exiting from the capillary and thus releasing the stress. This of course makes kinetoplasts very similar to the regular polymers, where conformational entropy and thermal fluctuations of shapes are the signature property. Some years ago, theorists made significant progress understanding thermal fluctuations of tethered surfaces (16, 18) or even generalized polymers of arbitrary fractal structure (17). The most general result there is that a polymer fractal with intrinsic fractal dimension $d_{\mathrm{i}\mathrm{n}}$ in a good solvent in space of dimension $d_{\mathrm{o}\mathrm{u}\mathrm{t}}$ adopts a shape with fractal dimension $d=d_{\mathrm{i}\mathrm{n}}\frac{d_{\mathrm{o}\mathrm{u}\mathrm{t}}+2}{d_{\mathrm{i}\mathrm{n}}+2}$. This prediction was never tested experimentally, and this is, therefore, a second challenge, along with understanding the fractal dimension $d_{\mathrm{i}\mathrm{n}}$ (assuming that it somehow can be reasonably defined).

While a lot is known about kinetoplasts’ biology, Klotz et al. in PNAS offer a fresh view, abstracting from kinetoplast biological function and considering it as a peculiar material.

Furthermore, since the kinetoplast is an equilibrium-shaped object, we should be able to control its shape by varying solvent conditions: A solvent does not have to be good! In particular, it should be very sensitive to ionic conditions and especially to the presence of multivalent counterions (such as spermine or spermidine), which are known to cause DNA condensation and overcharging.

Closely related to the question of intrinsic fractal dimension of the kinetoplast is a more general question of its intrinsic geometry. Why does it look like a cup, and why does it have a positive Gaussian curvature? In a familiar case of clothes design, a tailor operates with intrinsically flat fabric and uses pleats to make desirable shapes: makes cuts and removes wedges to produce, say, a ski hat (surface with positive Gaussian curvature) or makes cuts and inserts wedges to produce, say, a widening skirt (Godet skirt, surface with negative Gaussian curvature). A similar mechanism controls also the shapes of plant leaves (19). Furthermore, conversely, if a crystal is placed on a curved 2D surface, it acquires peculiar defects similar to tailor-made pleats (20). Presumably something similar must also exist in a kinetoplast: If we think of rings along the rim of a cup-shaped kinetoplast as a poly[n]catenane, the number $n$ must be such that rim circumference is less than $2\pi r$, where $r$ is the radius counted along the surface of the cup; this inequality would make it bend to form a shape of a cup.

If we want to follow Klotz et al. (1) and to think of the kinetoplast as a non–one-dimensional polymer, then perhaps we may want to ask whether we can make a system of rings with the rim length greater than $2\pi r$, producing a surface with negative Gaussian curvature (Lobachevskii plane)—something more similar to a lettuce leaf. Can we negotiate with kinetoplastids to convince them to make such a material for us? This seems like another challenge worth the effort.

Further thinking about kinetoplast-based materials would require going beyond a single-molecule picture. How do different kinetoplasts interact, and how do they undergo an Onsager nematic transition? Do, for instance, kinetoplasts with positive and negative Gaussian curvature mix or phase separate? To conclude, it does look to me like Klotz et al. (1) have unearthed a rich treasure trove.