Equilibrium Structure and Deformation Response of 2D Kinetoplast Sheets

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BIOPHYSICS AND SEE COMMENTARY COMPUTATIONAL BIOLOGY roughly floral appearance and a diameter near 5 µm. There is a region of excess intensity around the edge of the kinetoplasts, likely corresponding to the thick fibril seen in SEM studies (32). While there is qualitative variation in their wrinkled outline, they have good monodispersity with respect to size. A small subpopulation of kinetoplasts has been doubled in size by the cell’s replication mechanism (33), an example of which is circled in Fig. 1B. Examining kinetoplasts in three dimensions using confocal microscopy (Fig. 1C) reveals that, despite their 2D topology, the networks have significant curvature and have a hemispherical shape not dissimilar to a jellyfish bell, with significant wrinkling and a lip at their opening. More quantitative data about the 3-dimensional structure of kinetoplasts are seen in Fig. 2. Fig. 2A shows two projections of a kinetoplast: one projecting the “cup” onto the image plane and viewed from the top, and the other viewed from the side. To characterize the dimensions of the kinetoplast, we compute Fig. 1. (A) Schematic diagram of a kinetoplast, a curved sheet-like structure the gyration tensor in three dimensions from confocal data and made of thousands of connected rings of DNA. (B) Fluorescence microscopy find its principal eigenvalues, corresponding to the length of the image of a population of C. fasciculata kinetoplasts in solution. The dashed three perpendicular axes. The shape can be simply described circle indicates a larger kinetoplast that has undergone replication. (Scale as a wrinkled bowl with an elliptical cross-section, where the bar: 10 µm.) (C) Confocal image of a single kinetoplast displayed at 4 angles, with a wrinkled hemispherical appearance. (Scale bar: 2 µm.) smallest axis corresponds to the depth of the bowl and the second and third correspond to the minor and major diameters of the opening, respectively. This is confirmed by examining by is believed that the rings are contained in a catenated network eye kinetoplasts with principal eigenvectors that are close to the in order to ensure that dividing cells have all of the neces- orthogonal axes of the pixel grid and the confocal z stack. His- sary minicircles (27). Outside the realm of parasitology, limited tograms of all three axes are seen in Fig. 2B, where notable mathematical investigation into kinetoplasts has focused on their outliers in the major axis data represent kinetoplasts that have network topology (28, 29), but to the authors’ knowledge, there has been no investigation of their material properties. The addition and removal of linked DNA in a network are facilitated by topoisomerases, a family of enzymes that can change the topology of DNA, are vitally important for cell division, and are adversely expressed in certain cancers (24). Assays for ascertaining the presence and function of topoisomerase are necessary for biomedical research, and such assays require a DNA substrate that has a highly mutable topology. Kinetoplasts from Crithidia fasciculata, a parasite that infects mosquitoes, are commercially available from multiple companies for this purpose. The field of single-DNA polymer physics was made possible in part due to the commercial availability of viral DNA, and it is fortuitous that we as physicists and engineers can study kinetoplast DNA without the need to culture parasites and mosquitoes or to synthesize molecules. Here, we report on the equilibrium properties and deformation response of individual Crithidia kinetoplasts in solution (30). We observe that, in good solvent conditions, the kinetoplasts appear as an extended hemispherical sheet, which can undergo small-scale thermal fluctuations with a subsecond timescale. Principal component analysis (PCA) is used to show that, while the ensemble average shape of a kinetoplast can be approximated by a hemisphere with a diameter of ∼5 µm, each kinetoplast appears to have a unique conformation, presumably related to subtle differences in topology. We further show that kinetoplasts behave like elastic sheets, which can reversibly fold and unfold in microfluidic deformation assays. Results and Discussion Kinetoplasts have primarily been imaged within cells or flattened onto surfaces for scanning electron microscopy (SEM) (26) or atomic force microscopy (AFM) (31). In the cell, they appear as a tight disk, and they appear as a flat ellipsoid on surfaces. We Fig. 2. (A) Projection of a confocal kinetoplast image onto the xy and xz report on the qualitative appearance of kinetoplasts in solution, planes showing the in-plane major and minor axes and the out-of-plane where we can image many of them at population scales (in con- transverse axis as determined from the eigenvectors of the 3 × 3 intensity- trast to SEM and AFM imaging) and can observe their dynamics weighted gyration tensor. (B) Histograms of the three principal axes for a at equilibrium. A population of fluorescently stained Crithidia population of 31 kinetoplasts imaged with confocal microscopy. The major kinetoplasts can be seen in Fig. 1B. In projection, they have a axis outliers (hatched) are a small subpopulation of replicated networks.

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BIOPHYSICS AND SEE COMMENTARY COMPUTATIONAL BIOLOGY form a repeating “rosette” pattern. The relationship between the fibril, the curvature of the network, and its overall connectivity is not fully known, nor is the causative relationship between the geometric shape of the fibril and the overall structure of the kinetoplast. It has been estimated based on restriction enzyme digestion that the topology of a kinetoplast network is that of a honeycomb lattice, with each loop connected to 3 others (36). A more recent study has estimated a spectrum of topologies but still is based around regular lattice structures (29). Another computational study suggests that the connectivity is such that the network is barely percolated (28). Our observations of the diversity of apparent shapes and their long time-stable nature suggest to us that there is a broad spectrum of network connectivities that varies significantly from one kinetoplast to the next. We posit that the lattice picture is overly simplistic and that the role of the edge fibril has been underestimated in determining the apparent shape of the network. The observation of kinetoplast network “individualism” suggests biophysical analyses to ascertain the underlying topology. While their shape does not significantly evolve over time, they undergo dynamic fluctuations at short timescales. For a linear polymer, the dominant timescale is that of conformational decorrelation, which is equivalent to the timescale over which a polymer diffuses a distance equivalent to its radius of gyration, as well as its stretch-relaxation timescale (37). For a 2D kinetoplast, these timescales are not necessarily equivalent, and the fixed topology restricts the conformational space. Over short periods of time, the kinetoplasts are observed to undergo small shape fluctuations (Movie S1). The kinetoplasts are observed to undergo translational and rotational diffusion, albeit slowly, taking several minutes to diffuse their own diameter or rotate completely. To quantify the dynamics of the kinetoplasts, we study the in- plane anisotropy, , defined as the ratio between the minor and major axes. We calculate the autocorrelation function A(∆t) of the kinetoplast’s anisotropy:

T−∆t 1 X A(∆t) = ((t) − ¯)((t + ∆t) − ¯), [1] σ2T t=1

where is measured over T camera frames, ¯ is the average 2 Fig. 4. (A) The anisotropy (ratio of minor and major planar axes) of a value over a given time series, and σ is the sample variance. kinetoplast over time, with representative images of a local minimum and An example time series of the anisotropy is seen in Fig. 4A, maximum. (B) Time autocorrelation function kinetoplast anisotropy show- and an ensemble of autocorrelation functions and their mean is ing the average curve over a population of kinetoplasts, each observed seen in Fig. 4B, with data recorded at 50 frames per second. The for 100 s at 50 frames per second. The autocorrelation function for each autocorrelation function of an individual kinetoplast anisotropy molecule is shown in gray. Inset shows the same data on a semilogarithmic is very quickly decaying at short timescales and has a longer- axis over a longer time. The short timescale is 0.216 ± 0.004 s (SE), and the time tail. The population-averaged fast timescale was found to be long timescale is 6.5 ± 0.1 s (SE). 0.216 ± 0.004 s (SE), comparable with that of the much smaller linear λ-DNA (48 kbp compared with ∼12 Mbp of a kinetoplast). (41–43). We examined the deformation response of kinetoplasts The longer-time tail has an ensemble-averaged characteristic under weak confinement using microfluidic constrictions with a timescale of 6.5 ± 0.1 s (SE), although this may vary between minimum width of 3.8 µm and a funnel-like entry that increases kinetoplasts (Fig. 4B) and is the result of microfluidic con- hyperbolically to a maximum width of 200 µm over a distance finement and out-of-plane effects. The kinetoplasts are weakly of 80 µm. The width of the channel, w, as a function of dis- confined in the microfluidic channels, which orient the kine- tance from where the constriction begins, x, can be described toplasts in the same plane and suppress out-of-plane rotation 310 µm2 without significantly deforming them. Small-amplitude partial as w(x) = x+1.55 µm . A bright-field image of the channel can be out-of-plane rotations increase the apparent correlation time found in SI Appendix. Channels are 2 µm in depth (45). As the of the kinetoplast’s shape fluctuations, and interactions of the kinetoplasts approach the constriction, they are typically rotated kinetoplast edge with the wall can lead to isolated changes in by the funnel walls such that their major axis is aligned with the the anisotropy. A discussion of these effects can be found in SI channel and are confined along their minor and transverse axes. Appendix. Because most kinetoplasts have a minor axis greater than 3.8 µm, Microfluidic and nanofluidic confinements are often used to they fold or crumple to adapt to the constraints of the confine- investigate the mechanical response of soft objects and single ment and elongate along the channel axis. As the kinetoplasts polymers through experiments, such as the nanochannel con- leave the confining channel, they expand elastically back to their finement assay (38–40) and the microfluidic constriction assay original equilibrium conformation.

124 | www.pnas.org/cgi/doi/10.1073/pnas.1911088116 Klotz et al. 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BIOPHYSICS AND SEE COMMENTARY COMPUTATIONAL BIOLOGY had not been appreciated, and our images and analysis sug- Microfluidic channels were made by pouring polydimethylsiloxane pre- gest an increased role for the outer fibril in determining overall polymer onto a master silicon wafer containing features patterned in SU8 network structure, topology, and curvature. Our preliminary using photolithography. After annealing at 65 ◦C overnight, the cured investigations into the deformation response of kinetoplasts sug- PDMS was removed from the master wafer and cut into individual chips; gest future investigations of kinetoplasts in complex flow to then, holes were poked in each reservoir. The PDMS chips were cleaned by sonicating them in ethanol solution for 20 min and storing them overnight complement rheology studies of graphene oxide (55), and their in TBE buffer to prevent permeation-driven flow. For experiments, chips 5-µm size makes them well suited for more detailed studies of were removed from the buffer, cleaned with water, dried, and placed onto microfluidic and nanofluidic confinement (13). Much like the a clean glass slide soaked previously in NaOH. DNA-containing buffer was first experiments with linear DNA that opened the door to a pipetted into the reservoir hole of each device; then, platinum wires con- new field of single-polymer physics, we hope that kinetoplasts nected to a voltage supply were inserted. The voltage was activated to can serve a similar role for 2D systems. move the DNA into the field of interest within the device and stopped for imaging. Materials and Methods Kinetoplasts were imaged using a Zeiss Axiovert microscope with a 63× oil immersion lens (numerical aperture = 1.4), illuminated using a kinetoplasts were obtained from TopoGEN Inc. They were C. fasciculata filtered light-emitting diode (ThorLabs), and recorded by a Photometrics stained using the same protocol used to stain viral genomic DNA with 95B Prime CMOS camera interfaced with a computer using Micro-Manager a 8:1 base pair:dye ratio. In short, a solution was prepared consisting of (56). Images were analyzed using home-built MATLAB scripts. The 2 pri- 87.9% (vol/vol) 0.5× Tris-boric acid-ethylenediaminetetraacetic acid (TBE), mary functions of the software were to calculate the gyration tensor and 4% (vol/vol) beta-mercaptoethanol, 1.3% (vol/vol) YOYO-1 fluorescent dye its eigenvectors and eigenvalues and to detect the edges and perform at 10 µM, and 6.8% (vol/vol) kinetoplast DNA that had been diluted from PCs analysis based on a population of detected edges. Both procedures stock to 10 µg/mL such that the stained solution contains 0.1 µg of DNA per are described in greater detail in SI Appendix, and the code is available 150-µL sample. While the kinetoplast DNA stains within seconds, standard on request. procedure allows at least an hour of incubation to ensure uniform staining. Raw data in the form of microscopy videos in .tif format are avail- The kinetoplast solution was either imaged under a microscope slide or in able on the Harvard Dataverse public repository located at https://doi.org/ a 2-µm-high microfluidic channel, in which case 0.1% polyvinylpyrrolidone 10.7910/DVN/I4TWFV. Processed data used for the preparation of figures are (10 kDa) solution was added to the buffer to prevent sticking and electroos- in Dataset S1. mosis. While the diffusion of kinetoplasts is slow (taking several minutes to translate their own diameter), glycerol was added to the solution (77% ACKNOWLEDGMENTS. This project was funded by NSF Grant CBET-1602406. vol/vol) to viscosify it and immobilize the kinetoplasts for confocal imag- B.W.S. is funded by the Agency for Science, Technology and Research, Singa- ing, which was performed with a DeltaVision Elite Widefield Deconvolution pore. We thank Dr. Wendy Salmon of the W. M. Keck Facility for Biological microscope. Imaging at the Whitehead Institute.

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