Molecular motor-driven filament transport across three-dimensional, polymeric micro-junctions

Molecular motor-driven filament systems have been extensively explored for biomedical and nanotechnological applications such as lab-on-chip molecular detection or network-based biocomputation. In these applications, filament transport conventionally occurs in two dimensions (2D), often guided along open, topographically and/or chemically structured channels which are coated by molecular motors. However, at crossing points of different channels the filament direction is less well determined and, though crucial to many applications, reliable guiding across the junction can often not be guaranteed. We here present a three-dimensional (3D) approach that eliminates the possibility for filaments to take wrong turns at junctions by spatially separating the channels crossing each other. Specifically, 3D junctions with tunnels and overpasses were manufactured on glass substrates by two-photon polymerization, a 3D fabrication technology where a tightly focused, femtosecond-pulsed laser is scanned in a layer-to-layer fashion across a photo-polymerizable inorganic–organic hybrid polymer (ORMOCER®) with µm resolution. Solidification of the polymer was confined to the focal volume, enabling the manufacturing of arbitrary 3D microstructures according to computer-aided design data. Successful realization of the 3D junction design was verified by optical and electron microscopy. Most importantly, we demonstrated the reliable transport of filaments, namely microtubules propelled by kinesin-1 motors, across these 3D junctions without junction errors. Our results open up new possibilities for 3D functional elements in biomolecular transport systems, in particular their implementation in biocomputational networks.


Introduction
Filament transport driven by surface-attached biomolecular motors has been widely explored for various biomedical and nanotechnological applications [1][2][3][4][5][6]. Biomolecular motor proteins such as kinesins or myosins provide self-driven and directional transport of corresponding cytoskeletal filaments, i.e. microtubules and actin filaments, respectively. Using the energy derived from ATP hydrolysis, such filament transport can be orders of magnitude faster than passive diffusion [7]. Moreover, motor-driven filaments can carry cargo or detect different antigens if they have been specifically modified beforehand [8][9][10][11][12][13]. Most commonly, filament transport is spatially controlled by microscale networks, in which guiding channels and directional rectifiers are etched into planar surfaces [5,14,15]. Despite these topographical surface structures, actual transportation occurs in two dimensions (2D), conventionally on the channel floor.
A recently reported application of molecular motor-driven filament transport is space-encoded network-based biocomputation [16]. Within this application, motor-driven filaments solve combinatorial problems by exploring all allowed paths in a 2D physical network. The filaments pass a number of different junctions along their paths through the network. A key requirement for biocomputation is a negligible error rate [17] at so-called pass junctions. These junctions are channel crossings where filaments are required to move in a straight direction along the same channel; i.e. they are not allowed to take turns into the crossing channel. However, intrinsic design limitations in the 2D junction geometry are prone to increase the total error rate when up-scaling the physical networks for biocomputation. Therefore, it is imperative to explore novel design approaches where, ideally, the crossing channels are completely separated from one another. Here, we demonstrate molecular motor-driven filament transport within two separate crossing channels of 3D polymeric micro-junctions on planar glass substrates without junction errors. Beyond their application in network-based biocomputation, the here presented 3D junctions, can also be implemented into other advanced devices based on motor-driven filament transport, for example, in sensor or lab-on-a-chip systems with channel crossings.

Results
For manufacturing biocompatible 3D-junctions with sufficient structure resolution we chose two-photon polymerization (2PP). 2PP, an inherently 3D micropatterning technology, is well-established in the academic domain, allows feature sizes down to less than 100 nm [18,19], and has recently been applied in microoptics [20,21], microfluidics [22][23][24], micromechanics [25,26], tissue engineering and drug delivery [27][28][29]. The 2PP manufacturing process is carried out similarly to 3D printing in a layer-to-layer fashion. The light of a tightly focused femtosecond laser (typically wavelengths around 780-800 nm or 515 nm [30,31]) is usually not absorbed by the photopolymerizable resin. However, if the light intensity within the focal volume is sufficiently high to trigger two-photon absorption, resin solidification is induced, similarly to conventional UV-lithography. Scanning the focal volume across the resin followed by washing with solvent to remove the unexposed resin lead to the desired 3D microstructures. In order to test filament transport across 3D junctions the layout was designed to guide the filaments from different directions toward a 3D junction ( figure 1(a)). Walls structured the surface into two pairs of a closed and an open reservoir, each connected by a channel. When crossing each other in the center of the layout, the two channels were spatially separated by a tunnel and an overpass. After designing this 3D junction using a computer-aided design software, the 3D data were translated into positioning and laser control commands, represented as contour and filling vectors (supplementary figure 1) (https://stacks.iop.org/NJP/23/125002/ mmedia). The design parameters (figure 1(b)) were not only selected for successfully realizing the 3D junctions but also for achieving reliable filament transport.
In our work, we applied microtubules as filaments (with a diameter of 25 nm, an average length of 5 to 10 μm and a persistence length of about 1 mm) which are propelled about 20 nm above the surface by kinesin-1 motor proteins [32]. For optimal performance of kinesin-1 driven motility, surface properties such as hydrophilicity and roughness are decisive parameters [33,34]. In addition, the materials used need to be non-toxic to the biological system. With respect to microtubule transport across 3D junctions, the interaction of the employed material with the biological system is crucial, as the structures are intended to act as surface substrates and physical guiding barriers. Thus, the 3D junctions were realized using The laser power as well as the Z-offset of the initial layer relative to the substrate was varied in X-and Y-direction, respectively. Increasing negative values of dZ mean that the 3D junction will protrude from the substrate. In addition to the 7 × 5 array of 3D junctions, identifier marks labeled '1a' to '7e' were inserted to associate the processing parameters to individual 3D junctions during fluorescence microscopic imaging. inorganic-organic hybrid polymers (ORMOCER ® s) that show good mechanical and thermal stability (glass-like properties). ORMOCER ® s are composed of inorganic oxidic structures, that can be cross-linked photochemically by organic groups, and represent a well-known resin class for 2PP microfabrication [21,31,35]. Varying the selection of precursors and adjusting the synthesis conditions modifies the physical and chemical properties of the material and allows a wide range of applications [36][37][38]. In our experiments we tested two different ORMOCER ® material systems: a standard system, labeled OC-I, based on methacrylates as polymerizable moieties and an acrylic system, OC-V, that has been used for microoptical applications in the past [39][40][41]. In initial tests, both materials revealed smooth kinesin-1 driven transport of microtubules on patterned ORMOCER ® s as well as on the surrounding glass surface. Microtubules were guided along the structure walls and did not get stuck. Thus, both ORMOCER ® s were compatible for the experiments on 3D junctions.
Because fabrication of the 3D junctions was very sensitive to the processing conditions and the detected position of the ORMOCER ® -substrate-interface did not exactly match the Z-position of the focal spot, an array of 3D junctions was created with varying processing parameters on each sample (figure 2(a)). Specifically, the laser power was varied in X-direction whereas the position of the initial layer relative to the substrate ('Z-offset', dZ) was varied in Y-direction. Laser scanning microscopy images of the fabricated 3D junctions show that the structures 'fade away' with decreasing laser power (figure 2(b)). We attribute this finding to the fact that decreased polymerization rates at lower laser powers led to smaller line widths and poorer crosslinking causing a lack of mechanical stability. The corresponding height profiles confirm that the 3D junctions tend to protrude more out from the substrate with increasing negative values of dZ. Figure 2(c) depicts a closer view on the topography of a 3D junction fabricated with a laser power of 2.25 mW and a Z-offset of −1.5 μm. When imaged by fluorescence microscopy, we found that the 3D junctions exhibited strong autofluorescence. In particular, the optical ORMOCER ® OC-V was autofluorescent across the entire wavelength range of visible light, whereas the standard ORMOCER ® OC-I only showed autofluorescence when excited by blue and green light, but not by red light. Therefore, only OC-I was used for motility experiments: blue or green light was applied to locate the 3D junctions, while red light was used to record the filament motility. Importantly, fluorescent imaging allowed us to check if the 3D junctions contained continuous (i.e. open) or blocked tunnels (figure 2(d)). Open tunnels could be identified for at least three 3D junctions on each sample, mainly located in rows d and (dZ = −1,5 or −2 μm). Additionally, we examined a number of 3D junctions with open tunnels by scanning electron microscopy (SEM) (figure 3). The channel walls, as well as the overpass floors and rims, were clearly formed by ORMOCER ® and had smooth surfaces. For some 3D junctions a small step between the channel floor and the start of the ramp leading to the overpass was observed (figures 3(a) and (b)). The entrance of the tunnel could also be identified but this was no proof for its continuity. Therefore, we used focused ion beam (FIB) milling to obtain a cross-section of the 3D junction. FIB sections were prepared with the help of a field emission-SEM/FIB apparatus equipped with a Kleindiek MM3A micromanipulator and a platinum gas injection system. When a 3D junction (after platinum coating) was cut parallel to the tunnel and perpendicular to the overpass direction a continuous tunnel with an average height of about 600 nm was revealed (figures 3(c)-(e)). When comparing the measured structure dimensions with the design, we found the rim height and width of the overpass matching within the fabrication accuracy, while the floor thickness and thus the tunnel height differed significantly. This was likely due to the elongation of thin structures in the Z direction as a consequence of the extended voxel length in that direction. Thus, polymerization occurs a few hundred nanometers outside the bounding box in the design.
In order to investigate the performance of the 3D junctions for biomolecular transport using the kinesin-microtubule system the samples were assembled into flow channels and a casein solution was applied for 5 min. Subsequently, the casein solution was exchanged for a kinesin-1 solution and the motor proteins were allowed to bind out of solution onto the casein-coated surface. Finally, an ATP-containing motility solution with Atto 647-labeled microtubules was introduced. Transport of the microtubules across four to seven different 3D junctions (with and without open tunnels) of a sample ( figure 4(a)) was imaged for 2 to 3 h, ensuring that the viability of the assay lasted at least that long. Microtubules were propelled smoothly across the whole surface of the sample and their otherwise random movement was for the most part guided by the ORMOCER ® walls. Occasionally, individual microtubules crossed the walls, but this did not impair the performance of the 3D junction. In fact, the walls were mainly designed to direct microtubules into the channels toward the 3D junction. In the future, the junction elements can be implemented into optimized, chemically selective network structures. For each 3D junction that had already revealed an open tunnel during previous optical inspection by fluorescence microscopy, movement of the labeled microtubules through the 5 μm long tunnels was actually observed. We also detected overpass events on the majority of 3D junctions. Importantly, for about half of the investigated 3D junctions with an open tunnel we observed both, microtubules moving through the tunnel as well as across the overpass. Examples of these events are illustrated in figures 4(b) and (c).
The average velocities of microtubules moving through tunnels or across overpasses of the 3D junctions were both similar and in the same range as those moving on the surrounding areas (table 1). When evaluating the performance of all 3D junctions for which tunnel and overpass events were observed, we followed every filament moving in a channel either toward the tunnel or toward the overpass. Thereby, we found that none of them ended up in the wrong reservoir. Thus, most importantly, the 3D junction showed zero junction errors. However, not all microtubules always reached the opposing reservoir. 87% of the microtubules moving from one reservoir toward the tunnel reached the connected reservoir. In contrast, only 39% of the microtubules moving toward the overpass arrived at the connected reservoir (table 1). The majority of microtubules which did not make it across the overpass detached from the surface when moving the ramp downward toward the connected reservoir. This likely happened due to the stiffness of the microtubules: Motor molecules interacting with the rear end of the microtubule continue to propel it forward whereas the fluctuating leading tip of the microtubule is hardly able to attach to the motors on the downward ramp due to the increasing distance between motors and filaments [42]. In some 3D junctions microtubules turned around inside the channel just before entering the ramp to the overpass. This behavior was probably observed when there was a physical step at the transition between the glass surface and the ORMOCER ® ramp of the overpass (see figure 3(b)). Compared to the performance of 2D pass-junctions, where 0.2%-0.4% of microtubules took a wrong path [16], the actual error-free performance of the 3D junctions is a major improvement. Admittedly, these error rates do not include any loss of filaments due to detachment or sticking. However, while these events will obviously affect the overall performance of an application, they importantly do not result in functional errors, such as errors in the calculation of network-encoded mathematical problems.

Conclusions
In conclusion, 3D micro-junctions suitable for advanced biomolecular transport devices, such as biocomputational networks, were designed and realized by 2PP of ORMOCER ® , an organically modified hybrid material. The 3D junctions spatially separated two perpendicularly oriented channels in the form of an overpass and a tunnel. Both structural elements were verified by optical and electron microscopical imaging and showed a high structure fidelity. In experiments with kinesin-1 driven microtubules, the compatibility of the applied ORMOCER ® structures with the biological system was verified and the guiding of microtubules across the overpasses and through the about 5 μm long tunnels was demonstrated. While the motion through the tunnel element of the 3D junctions was highly reliable, the design of the overpasses may profit from further optimization. One promising alteration to increase the overpass efficiency could be to cover the overpasses. This would prevent microtubule detachment when moving down the ramp by directing them back toward the motor proteins on the floors of the overpasses. Confined, tunnel-like transport has earlier been demonstrated for microtubules moving through coverslip-sealed submicron channels [32] and actin filaments moving through hollow nanowires [43]. However, our work is, to our knowledge, the first demonstration of simultaneous, spatially overlapping 2D molecular motor-driven filament transport along guiding structures separated in the third dimension. Importantly, the presented error-free junctions constitute a major advancement for the implementation in network designs of future upscaled biocomputing devices [16]. Furthermore, our approach of patterning surfaces with hybrid polymer structures including 3D elements is expected to open up new possibilities also in biomolecular transport applications like lab-on-a-chip devices.
In many nanotechnological applications with molecular motors as well as in network-based biocomputation, actin filaments propelled by myosin motors are explored extensively in parallel to the microtubule-kinesin system because each of the two systems has its own advantages [6]. Thus, the successful application of ORMOCER ® 3D junctions for actin-myosin would further enhance their potential. However, due to specific surface chemistry requirements for reliable actin motility (especially with respect to the hydrophobicity), the applied ORMOCER ® material and possible surface treatments (e.g. oxygen plasma ashing, silanization) will have to be chosen and optimized separately. Besides 3D junction designs supporting motility on both, the ORMOCER ® and the substrate surface, as presented in this work, designs that allow motility only on the ORMOCER ® might be worth exploring for the actin-myosin system in future efforts.

Materials and methods
2PP patterning instrumentation. 3D junction design was accomplished with the CAD-program Autodesk Inventor Professional 2020. The computer-aided manufacturing process was carried out in proprietary software (SliceLas (from Lightfab) running in Rhinoceros 3D (from Mc Neel)). A custom-built 2PP patterning setup [44][45][46] consisting of a femtosecond laser oscillator (amplitude systems, t-pulse 200), which is frequency doubled to 515 nm and is operating at 10.1 MHz repetition rate and 350 fs pulse duration, was used to fabricate 3D junctions. The positioning of the focal spot in 3D space was performed by a galvoscanner (XY-direction) and a 300 μm travel piezostage (Z-direction) that included the mount for the focusing optics (both part of a writing head developed by Lightfab GmbH, Aachen-Germany). In order to allow stitching for 3D junctions exceeding the field of view of the focusing optics or for large area positioning, the scanner and the sample were mounted to high-precision linear stages (Aerotech ABL in XY-direction and Aerotech ATS in Z-Direction). We used a 100x, NA = 1.4 microscope lens (Zeiss Plan-Apochromat) to focus the incoming beam into the resin.
2PP patterning of ORMOCER ® . A small amount of ORMOCER ® resin including 2 wt.% photoinitiator Irgacure 369 [46,47] was applied by drop casting onto a glass coverslip. In the next step, an automated interface recognition procedure ('autofocus') was carried out to locate the exact position of the first layer on the glass substrate prior to the exposure. The glass-ORMOCER ® -interface on the backside of the coverslip represented the best focusing conditions for the employed microscope lens (according to the design of the manufacturer). Thus, the 3D junctions were fabricated in a 'hanging' fashion and light for the exposure of the (n + 1)th layer had to penetrate the nth exposed layer. Within the array of 3D junctions on each sample, the laser power was varied in X-direction from P = 3.25 mW to 1.75 mW in −0.25 mW increments (7 steps) and the position of the initial layer relative to the substrate ('Z-Offset', dZ) was varied slightly in the Y-direction from 0 μm to −2.0 μm in increments of −0.5 μm (5 steps) to ensure optimal alignment of the channel floor with the ramp at the beginning of the overpass. The positioning velocity was set to 5 mm s −1 for all 3D junctions. Additional parameters regarding the exposure are given in table 2 and were chosen in a way that the resulting photon flux ensures sufficient crosslinking of the ORMOCER ® resin. Finally, after fabrication, all samples were developed for 20 min using a 1:1 solution of isopropanol and methyl-isobutyl-ketone followed by rinsing with pure isopropanol. Characterization of 3D junctions. The topography of the 3D junction and preliminary optical characterization (figures 2(a)-(c)) were carried out with a laser scanning microscope (Keyence VK-X210). SEM characterization (figures 3(a) and (b)) was performed on a scanning electron microscope from JEOL (JSM 7800F) using the lower electron detector. For the field emission-SEM/FIB and electron backscatter imaging experiments we applied a cross-beam scanning electron microscope from Zeiss (AURIGA ® -CrossBeam workstation) equipped with a Kleindiek MM3A micromanipulator and a platinum gas injection system. First, we extracted pieces (few mm 2 ) from the glass-substrate, which contained the ORMOCER ® -samples. Then, a platinum layer was deposited on top of the sample to reduce charging. A 10 × 10 × 10 μm 3 cubic shaped part of the sample was removed using Ga + ion milling with a current and voltage of 50 pA and 30 kV, respectively. Subsequently an Inlens-EsB detector was used to reveal the different materials (Pt, ORMOCER ® ) in the region of interest (figures 3(c) and (d)). For detailed images the sample was tilted by 36 • .
Preparation of flow channels. Glass coverslips (22 × 22 mm 2 or 24 × 60 mm 2 , Menzel-Gläser) were cleaned by sonication in Mucasol/water (1:20; v = v) for 15 min followed by rinsing in deionized water for 2 min. Further, coverslips were sonicated in ethanol/water (1:1; v = v) for 10 min, rinsed in deionized water for 2 min, rinsed in MilliQ-water for 2 min and finally dried using a nitrogen airflow. The kinesin-1 gliding motility experiments were performed in 3 mm-wide flow-channels consisting of a cleaned glass coverslip, an ORMOCER ® sample and two stripes of parafilm as spacers.
Kinesin-1 gliding motility experiments. All solutions were prepared in Brinkley Reassembly Buffer 80 mM (BRB80; adjusted to pH = 6.9 with KOH) that was composed of 80 mM 1,4-piperazinediethanesulfonic acid (PIPES), 1 mM EGTA and 1 mM MgCl 2 . Microtubules were polymerized from 4 mg ml −1 porcine brain tubulin [48], labeled with Atto647, in BRB80 with 5 mM MgCl 2 , 1 mM GTP, 5% dimethyl sulfoxide (DMSO) at 37 • C for 30 min. The microtubules were stabilized and diluted 60-fold in BRB80 containing 10 μM Taxol. Full-length Drosophila melanogaster kinesin-1 molecules were used as motor proteins that were expressed in insect cells and purified as described earlier [49]. A solution containing casein (0.5 mg ml −1 ) was perfused into the flow-cell and allowed to adsorb to the surface for 5 min. This solution was exchanged for a 10 μg ml −1 kinesin-1 solution in BRB80 with 0.2 mg ml −1 casein, 1 mM ATP as well as 10 mM dithiothreitol and incubated for 5 min. A BRB80 solution containing containing microtubules (33 nM polymerized tubulin), 10 μM Taxol, 1 mM ATP, 40 mM D-glucose, 55 μg ml −1 glucose oxidase, 11 mg ml −1 catalase and 10 mM dithiothreitol was added to the flow-cell. After the ORMOCER ® 3D junctions had been localized, image acquisition was started.
Imaging of gliding motility assays and data analysis. Image acquisition was performed using an inverted fluorescence microscope Zeiss Axiovert 200M (Zeiss, Germany) with a 40x air objective Plan-Apochromat NA = 0.95 (Zeiss, Germany). For excitation a LED lamp SOLA SE (Lumencor) was applied. The data were recorded with an electron multiplying charge-coupled device (EMCCD) camera (iXon + EMCCD, DU-897E, Andor) having a pixel size of 16 μm. If not stated differently, images were acquired every 2 s with an exposure time of 100 ms using MetaMorph (Molecular Devices, LLC., USA). The data was analyzed using Fiji. Each microtubule moving toward and leaving a junction was followed frame by frame in a time-lapse movie. Thereby their number was counted. Then the path of each microtubule crossing the junction was manually tracked, the length of the path was measured and divided by the time between the first and the last frame of the track. Finally, the obtained velocities of individual microtubules were averaged.