Design and fabrication of networks for bacterial computing

Non-deterministic polynomial (NP-) complete problems, whose number of possible solutions grows exponentially with the number of variables, require by necessity massively parallel computation. Because sequential computers, such as solid state-based ones, can solve only small instances of these problems within a reasonable time frame, parallel computation using motile biological agents in nano- and micro-scale networks has been proposed as an alternative computational paradigm. Previous work demonstrated that protein molecular motors-driven cytoskeletal filaments are able to solve a small instance of an NP complete problem, i.e. the subset sum problem, embedded in a network. Autonomously moving bacteria are interesting alternatives to these motor driven filaments for solving such problems, because they are easier to operate with, and have the possible advantage of biological cell division. Before scaling up to large computational networks, bacterial motility behaviour in various geometrical structures has to be characterised, the stochastic traffic splitting in the junctions of computation devices has to be optimized, and the computational error rates have to be minimized. In this work, test structures and junctions have been designed, fabricated, tested, and optimized, leading to specific design rules and fabrication flowcharts, resulting in correctly functioning bio-computation networks.


Introduction
Combinatorial mathematical problems, including nondeterministic polynomial-time (NP-) complete problems, have a number of possible solutions that increases exponentially with the problem size, which, in turn, makes them intractable for conventional sequentially operating electronic computers [1][2][3][4][5]. Next to DNA computing, which requires impractically large amounts of DNA when scaling up [6][7][8][9], and quantum computing, which appears to be limited in scale by de-coherence and by the small number of qubits that can be integrated [10], massively parallel computation employing motile biological agents in networks has been proposed to solve such problems [11]. This computational paradigm comprises several stages. First, the mathematical problem to be solved must be formalized in a graph, which is subsequently translated in the design of a network that physically encodes this mathematical problem. Next, the fabricated network is exposed to the random, parallel exploration by large numbers of motile biological entities, preferably small-sized, to increase the density of computation per volume, and rapid, to increase the speed of computation. The solutions of the problem can be then derived from the end points and trajectories of the agents in the network.
Previously, one of the classical NP-complete problems, i.e. the subset sum problem (SSP), was encoded into a graphical, modular, planar network comprising logical operational gates, i.e. 'split junctions' and 'pass junctions' [12]. Pass junctions consist of orthogonal crossings aiming to enforce the unperturbed directional passage of the intersecting pathways, whereas in the split junctions this crossing is additionally equipped with two Y-shaped bifurcations to enable the unbiased changing of traffic direction. A small SSP instance was embedded in a nanofabricated planar device, which was explored in a parallel fashion by a large number of cytoskeletal filaments, i.e. actin filaments, or microtubules. The motility of the computing agents was provided by protein molecular motors, i.e. myosin, or kinesin, respectively, which were attached to the bottom (and lateral walls) of the network channels, and which were in contact with an ATP-rich solution above the channels [12].
Autonomously moving bacteria are interesting alternatives to the motor-driven filaments for exploring such channel devices, especially if cell division during exploration could be employed to increase the number of agents in a diverging network [13,14], while preferably keeping the agent density constant during operation [14]. E. coli HCB437, a prokaryotic bacterial species, genetically engineered to have smooth swimming ability and impaired sensory receptors [15][16][17][18], is the agent of choice in the present study aiming to explore alternative designs of the SSP 'computer'. The E. coli cell is approximately 1 μm wide and 2 μm long, and its effective total length, i.e. cell plus propelling peritrichous flagella, is approximately 4-5 μm. E. coli is also known to be motile even in channels only 30% wider than its own diameter [19].
Although the widths and depths of the channels required to accommodate bacteria are typically larger than 1 μm, here nanometre-capable electron beam lithography was chosen in the network fabrication flowchart, against sub-micrometre-capable optical lithography, for the following reasons: (i) in prototyping and optimization studies like the one performed here, electron beam lithography is much more flexible and cost-effective, because one-time usage of expensive optical lithography masks is circumvented; (ii) we wanted to be able to explore sharp features (with a radius of curvature ideally up to 100 times smaller than the channel width) for optimizing pass junctions and bacterial traps (see below); (iii) some cell types, much larger than bacteria, are known to explore their surroundings by using focal adhesion points, and are able to detect/resolve/discriminate nano-scale details in their surroundings, and respond accordingly [20,21]. Consequently, nano-scale fabrication accuracy was considered essential, even for micro-scale features [22,23]. As will be discussed below, high aspect ratios of channel profiles proved to be critical, requiring the usage of reactive ion etching to obtain anisotropic etch profiles (in the casting master features). Another important fabrication condition in this study is that the networks should be fabricated in optically transparent materials, in order to be able to monitor the bacterial behaviour by optical microscopy.
Before designing, constructing, and scaling up the actual computation networks for this bacterial computational agent species, the geometries of the logical junctions must be optimized to achieve the lowest possible error rates, leading to bacteria-specific design rules. This study is necessary as the behaviour of bacteria in micro-confined environments is not fully understood to a level where ab initio designs can be proposed [13,23]. Consequently, the goals of the present work were: (i) to describe the optimised fabrication of such bacterial computing devices; (ii) to study the behaviour of bacteria in different geometrical structures, e.g. wave-shaped channels, sharp-edged zig-zag lines, arrow profiles, etc; (iii) to establish design rules for bio-computation networks; and (iv) to optimize the design of the logic junctions to be employed in future scaled-up bacterial-based network computers.

Materials and methods
The above considerations resulted in the following four-stages fabrication flowchart, presented schematically in figure 1:

Fabrication of a monolithic casting master in silicon
(i) A 500 nm thick SiO 2 layer was deposited on a 100 mm ('4 inch') silicon wafer by plasma enhanced chemical vapour deposition at 300 • C; (ii) hexamethyldisilazane (HMDS) was spin-coated on the wafer at 2000 rpm, which was subsequently baked on a hotplate at 200 • C for 2 min; (iii) a 200 nm thick layer of a negative tone electron beam resist (NEB22, from Sumitomo Corp.) was spin-coated on the wafer, which was subsequently pre-baked on a backing plate in an oven at 110 • C for 2 min; (iv) electron beam exposure of graphic design system (GDS II) patterns was performed on a VISTEC/Raith electron beam pattern generator EBPG-5200 system, at 100 kV, with a 17 μC cm −2 dose; for coarse patterns the exposure parameters were: 100 nm beam step size, 150 nm spot size (52 nm defocus) and 148 nA beam current, while for fine patterns these were: 25 nm beam step size, 40 nm spot size (8 nm defocus) and 7 nA beam current;  (vii) the wafer was spun dry at 2000 rpm; (viii) SiO 2 reactive ion etch (RIE) was performed in a pre-conditioned AMS 100 I-speeder Bosch system, using a 20 sccm C 4 F 8 /100 sccm He/10 sccm CH 4 flow, with RF 1 = 2500 W, RF 2 = 300 W, 100% pumping, with the operational parameters of the SH position source: 120 mm, chuck temperature 0 • C, and etch time 3 min 10 s; (ix) 2 μm deep Si-RIE was performed in an ICP chlorine system, with 9 sccm Cl 2 , 1 sccm O 2 , 7 μbar, RF power 100 W, chuck temperature 65 • C, and etch time 15 min 18 s; alternatively 5 μm deep Si RIE was performed in an AMS cryo-etcher system with chuck temperature −120 • C, RF 1 = 1100 W, LF generator pulsed (40 W 10 ms/0 W 90 ms),100% pumping, using one cycle of 26 sccm O 2 /200 sccm SF 6 flow, power 13 s ON + 5 min OFF (cooldown), and six cycles of 28 sccm O 2 /200 sccm SF 6 flow, power 15 s ON + 5 min OFF (cooldown); (x) the NEB22 residue was removed in an RIE system with 20 sccm O 2 at 30 μbar, with 50 W RF power 1 min and 30 s etch time; (xi) the SiO 2 residue was removed in a buffered HF solution (1:7) for 2 min and 30 s, followed by demineralized water rinse for 5 min, and spin drying at 3000 rpm; and finally (xii) the inspection of the fabricated structures was performed by scanning electron microscopy (SEM).

Casting of a PDMS replica from the monolithic Si master, dicing and release
(i) A small amount (0.5-1 ml) of chlorotrimethylsilane in a small glass vessel, was placed together with the silicon wafer in a vacuum chamber. After pump down, the vessel was opened to let silanization take place under the vapours for ∼2 h; (ii) Sylgard 184 kit (polydimethylsiloxane (PDMS)) was mixed in 10:1 ratio (monomer:crosslinker) and stirred ∼3 min; (iii) the PDMS mixture was poured over the master structure (all in a petri dish) and put in a vacuum chamber to remove air bubbles (∼2 h); (iv) the petri dish (master covered with PDMS) was either placed in the oven overnight at 60 • C or kept under room temperature during 2-3 d for curing: (v) the chip was cut around the structure and slowly peeled off from the master (the master was then usually covered with a new PDMS mixture to keep it free from contamination (following steps (ii)-(v)).

Sealing the replica with an oxygen permeable PDMS cover
(i) The PDMS cast (structure face up) was put, together with a PDMS coated glass coverslip, in a plasma cleaner (Harrick Plasma, PDC-32G), pumped down and exposed to the plasma 30 s-45 s; (ii) under vacuum, the cast was attached to the coverslip and plasma treated during 30 s for sealing; (iii) after the chip had been sealed, a small drop of phosphate-buffered saline medium was placed around the chip (in vacuo) to assure the medium wetted all structures (at least 5-10 min). The chip was stored in a wet chamber filled with growth medium like luria-bertani medium and refrigerated for future use.

Loading
Because of its motility characteristics, E. coli HCB437 was chosen to test the designs of the bio-computation networks [17,18]. The E. coli cells were transformed to constitutively express the plasmid pMF440mChe (Addgene Plasmid #62 550). Plasmid pMF440mChe was isolated from the E. coli DH5α using Qiagen plasmid prep kits (plasmid supplied in transformed E. coli DH5α). These isolated plasmids were transformed into the chemically competent cells of E. coli HCB437 following a transformation protocol [24]. The bacteria were positively selected using ampicillin (final concentration-100 μg ml −1 ) to maintain the plasmid and expressed constitutively in the further sub-culturing.
The top edge of the cover-slip-sealed microfluidic device was submerged in a ∼50 to 100 μl bacteria-containing solution. Bacteria enter through the edge openings in the loading zone and navigate towards the entry funnel shown below in figure 7. Since the device is entirely operated by the autonomous motility of bacteria, no external force is applied to the device to let the bacteria enter the network.

Detection
The bacterial culture was examined for red fluorescence using an OlympusIX83 fluorescence microscope with mChe filter. E. coli HCB437 transformed with green fluorescent protein (GFP) was also employed, using the plasmid pBAD-EGFP (Addgene plasmid #54 762). Since the tracked signals consisted of grayscale eight-bit images with bright fluorescent spots, both the green and the red fluorescence proteins could be employed here. All images were acquired at either 20 X or 10 X UPLANO objectives with image acquisition performed for 3-5 min. The image acquisition was performed using the Metamorph Advanced Olympus software with an exposure time of 250 ms for each frame (4 fps). The acquired images were post-processed using ImageJ FIJI freeware [25]. The bacterial behaviour was monitored and analysed using ImageJ tracking software with trackmate and MtrackJ plugins [25], and by compilation of fluorescence micrographs.  Figure 2 presents various test structures on a 2 μm deep master wafer, obtained by silicon etching in a chlorine ICP system. After casting PDMS replicas and performing the first experiments with E. coli, it was concluded that supporting pillars in large open areas, e.g. the loading zones, and deeper channels (i.e. ∼5 μm) were necessary to prevent 'roof collapse' due to cohesive forces in the sealing step [22]. However, the prolonged etching time needed to achieve this depth on the master wafer resulted into a systematic deposition of particles, which could not be removed. As an alternative, cryo-etching of Si in a fluorine type of chemistry was tested. While the particle deposition problem was addressed, the releasing of the PDMS cast from the master was very difficult. Beyond 2 μm depth, an undercutting emerged ( figure 3(a)), which appeared to block the release from the master after PDMS casting (similar to 'dovetail joints'). The Si etch rate was observed to increase in time, as soon as the undercutting started. These etching-related phenomena could be understood from RIE mechanistic considerations [26]. In previous work on RIE of transition metals, using a Luxtron fluoroptic thermometer, it was shown that plasma etching-generated heat is able to raise the temperature on the wafer surface far above the pre-set cooling (water) temperature of the electrode [27]. Apparently, a constant ion-bombardment-induced anisotropic etch rate competed with an increasing thermally activated (isotropic) etching. In order to solve this problem, instead of changing the etch recipe, the system was allowed to cool down repeatedly: in order to minimize undercutting, while maintaining sufficient etch depth, the RIE procedure was performed in seven short cycles with sufficient cool down time (5 min) in between. This 'cool switching' procedure resulted in the desired profile (figures 3(b)-(d)) with only minor undulations, which did not hamper PDMS cast release.   figure 4(B) suggests that the sharp zig-zag lines are detrimental to the maintenance of bacterial motility in confined spaces, as these geometries induce corner preferences and clogging, shown as saturated spots at the corners of the arrows and the zig-zag lines. Despite being detrimental to the preservation of motility, which is essential for the operation of logical junctions, this preference of E. coli for accumulation in corners and fissures, while avoiding sharp features (angle > 270 • ), was exploited in other operational instances, e.g. in rectifiers and for trapping bacteria that made errors during computation (described further). In the arrow-shaped rectifiers the bacteria easily move into the direction of the arrow (funnel with angle < 90 • ), whereas in the opposite direction they need to move between two sharp edges.

Bacterial motility
Individual bacterial movement was monitored and analysed ( figure 4(C)). Subsequently, these individual trajectories, presented as fluorescence micrographs, were aggregated to produce an image of the collective motility behaviour in each test structure (figures 4(B) and (D)). The analysis of the trajectories visualised in figure 4(C) suggest that the design of the split-and the pass junctions translate in the desired bacterial behaviour: (i) in a pass junction the agents cross over along their initial direction (blue-yellow traffic crossing point); and (ii) in a split junction the agents are randomly redistributed between the two forward paths (red-yellow and blue-green traffic split points).
A more detailed inspection of figure 4(D) indicates that the bacteria prefer to move along the edges between the bottom and the walls instead of centred on the axis of the channels, but the individual bacteria can still cross over randomly to the other edge; the random turning left or right at split junctions is still preserved, and the sharp edges at the (pass) crossings prevent the occurrence of wrong turn bends for the 4 to 5 μm long bacteria with flagella. Figure 5 and table 1 present an analysis of the reliability of the junctions as a function of channel width and height, for various junction geometries. The main conclusions that can be drawn from these results are as follows: (i) for E. coli, 2 μm wide channels translate in a considerably better performance than 4 μm wide channels; (ii) smooth structures translate in a considerably better performance than the sharp-cornered structures composed of straight-line pieces at 4 μm channel width; (iii) however, at 2 μm channel width no significant difference is apparent.

Junction performance and design rules
A more detailed discussion is required to consider the movement of bacteria in the volume of the channel, as opposed to just planar projections of trajectories ( figure 6(A)). Indeed, the optimum width and depths of the channel highly depend, in the first instance, on the dimensions of the computational agent being used. As noted before, the dimensions of E. coli are, approximately, 1 μm for width of the cell, 2 μm for its length, and 4-5 μm for the effective total length of the bacterium, that is, including its propelling peritrichous flagella. These dimensions suggest that, for E. coli, a 2 μm channel width is a good choice to prevent U-turn movements. E. coli is motile already in channels only 30% wider than its own diameter [19], on the other hand, in order to be effective in avoiding errors, especially in pass junctions, the channel width should not be much larger than twice the agent width.
The channel depth, however, should be more than 2 μm to account for the difficulties related to fabrication of PDMS structures, i.e. roof collapse due to cohesive forces in the sealing step, but not more than 4-5 μm to prevent 'tumbling-over' of bacteria, i.e. vertical switching to the opposite direction (see Table 1. Comparison of agent traffic behaviour in combined pass-and split-junctions, as a function of channel width and height, and for the various junction geometries shown above. The numbers of wrongly turning agents are shown in comparison with the total numbers of agents, and the percentage of correct passes. 'L' stands for junctions build from straight line pieces; 'C' stands for junctions build from smoothly curved line pieces, and the number attached shows the split junction angle.  figure 6(A)). These initial considerations based solely on channel and bacterial dimensions, should be augmented with considerations regarding the actual observed motility behaviour of the computational agent. In this context, it was observed in our experiments here that E coli swims preferentially along the edges between the walls and the bottom (or the roof) of the confining structure and may even accumulate (clog) in corners [22].  4(B)) and in the SEM image ( figure 6(D)).
The analysis of all the results for various designs of the logic junctions resulted in a set of design rules, as shown schematically in figure 6: (a) To prevent turning around of the bacteria and, subsequently, moving in the opposite direction, which is equivalent to 'un-computing' (and can even result in erroneous traffic when turning twice or more), the channel width has to be smaller than the effective bacterial length. (b) To prevent tumbling-over and moving in the opposite direction, the channel height also has to be smaller than the effective bacterial length. (c) Furthermore, it was observed that bacteria avoid sharp features, but prefer to move along the edges and into corners and fissures (figures 6(B)-(D)). With increasingly higher densities of bacteria, e.g. by slow movement, possibly coupled with cell division, this behaviour can easily lead to clogging of the network channels. Consequently, designs with sharp corners should be avoided, unless a deliberate trap is needed.
Exploiting these design rules, a network of the small instance SSP{2, 5, 9}, with channel widths of 2 μm and depths of 5 μm was fabricated. This device contains junctions with 60 • (split-) and 90 • (pass) junction angles. The graphic design system (GDS II) pattern is presented in figure 7(A). E. coli bacteria exploring the network are presented in figures 7(B) and (C). The GDS design was used in the e-beam lithography step in the fabrication process (figure 1). The fabricated bio-computing devices were then exposed to exploration by E. coli entering the network through the entry funnel (figure 7(B) (i)) and leaving the network through the (half) heart-shaped rectifiers (figure 7(C) (iv) and figure 7(B) (vi)), following the feedback loop (figure 7(C) (v)) into the loading zone. In principle, the rectifier channels and feedback loop can be replaced by 'exit trap' squares. Bacteria that make a wrong turn, i.e. do not obey the traffic logic rules embedded in the junctions, can be diverted to the 'dirt'-or 'ghost' lanes ( figure 7(B) (iii)), and then into square traps ( figure 7(B) (ii)). In figure 7(B), the white spots represent the bacteria in the network. It can be noticed that, in the square traps the fluorescence grayscale spots are accumulated in the corners, in accordance with the corner preference. Figures 7(B) and (C) are only snapshots of the bacteria in action, but the successful operation was recorded as a video, and the post-image processing analysis is presented in supplementary information (https://stacks.iop.org/NJP/23/085009/mmedia) movie 1. A dynamic bar chart corresponding to the evaluation of bacteria that explored solutions is also presented in the same supplementary information movie-1. The dynamic bar chart shows the number of agents that passed a specific exit, divided by the total number of agents that reached the exits. Note that the correct solutions for this SSP{2, 5, 9} network, i.e. 0, 2, 5, 7, 9, 11, 14 and 16 can indeed be discriminated in the bar chart against erroneous output.
In this paper the emphasis was on design (rules) and fabrication issues. In a forthcoming paper it will be shown that E. coli HCB437 bacteria successfully explored several networks, larger than the one shown in figure 7; those networks have also been fabricated according to the design rules presented here.

Conclusions
We have designed, successfully fabricated, and optimised the geometry of biocomputation networks, probing the motility behaviour of E. coli HCB437 bacteria. The optimum fabrication protocols were established, based on the use of electron beam lithography and RIE etching for creating casting masters with the correct lateral and vertical profiles of the computing network, subsequently replicated in PDMS-made bacterial 'computers', and successfully explored by E. coli HCB437. Specific to our interest, we have optimized the design rules for guiding bacterial traffic in computation networks. While the methodology presented here was developed for E. coli HCB437-specific computation, it can be equally well applied to the design optimisation of bio-computation networks for other species, as well as for other types of devices, e.g. for studying soil microbiology, water purification, and single-cell genomics, to name a few.