Large-Scale Cardiac Muscle Cell-Based Coupled Oscillator Network for Vertex Coloring Problem

Overall, this study describes a new type of oscillator, one made of beating heart cells, for more ef ﬁ cient processing of computationally hard problems compared to the heuristic Boolean-based algorithm in large-scale networks. Although there are limitations in terms of frequency and processing speed compared to CMOS-based oscillators, advantages in energy consumption and ease of fabrication and potential to extend this system to massively parallel 3D structures by leveraging the ever-growing ﬁ eld of biofabrication make heart muscle-based oscillators a promising new platform for collective computing applications.


Introduction
Modern computing is based on the Von Neumann architecture, characterized by clear separation of memory from processing units. Data moves between these two units constantly, inevitably leading to latency, bandwidth bottleneck, and higher energy consumption. In addition, in most of the mainstream computing devices, information is carried by a sequence of voltage level-based signals in conventional complementary metal-oxide-semiconductor (CMOS) transistors, leading to a poor representation of signals and the waste of information carried by the timing of signals. [1] These inefficiencies in processing become apparent when dealing with large amounts of data or solving computationally hard problems, such as combinatorial optimization problems. The vertex coloring problem, defined as the challenge of assigning the minimum number of colors (labels) to the vertices of a graph such that no two adjacent vertices have the same color, is an archetypal combinatorial optimization problem. This problem belongs to the nondeterministic polynomial time (NP)-hard computational complexity class of problems, which exhibit an exponential increase in the search space with problem size. Subsequently, this typically implies an exponential requirement in computing resources (memory, time). This motivates the need for an alternative computing model that can potentially provide a more energy-efficient and scalable pathway for solving such problems. Inspired by the biological observations in neurons, [2] the coupled oscillator system has been reported to provide a new computational platform to address combinatorial optimization problems. [3,4] The problems are reformulated as energy minimization problems and encoded in the parameters of oscillator systems, [5] such as the initial phases, frequencies, or interconnection patterns of the oscillators. As time passes, the energy of the oscillator systems will reduce to a minimum, and the steady-state oscillations represent the computation result of the encoded problems.
Different types of physical hardware have been used to implement the oscillator system, including relaxation oscillators based on phase transition, [6] spin-torque oscillators (STOs), [7] microand nanomechanical systems (MEMS) oscillators, [8] and CMOS circuitry. [9] Coupled oscillators can also be observed in various processes, [10] such as the rhythmic activity in heart cells, neural oscillations, and electrochemical reactions. [11] In our previous study, [12] we demonstrated the potential of cardiac muscle cells as an oscillatory building block to implement bio-oscillator systems using a simple four-node network as a proof of concept. Although the cardiac cell-based bio-oscillators have limitations in frequency, the most significant advantage of bio-oscillators is the extremely low energy consumption compared to other electrical or magnetic oscillators. For example, human hearts, each with over 2-3 billion cardiomyocyte cells, consume only about 6 watts [13] to sustain oscillations and perform highly complex metabolic activities. Another advantage is the high scalability of the bio-oscillator network due to the effectiveness in cell interconnection and 3D biofabrication.
In this article, we present experimental demonstrations of several multinode cardiac cell-based bio-oscillator networks, from small to medium to large scales, for solving vertex coloring problems. Using a simple cell patterning approach to control the localization and dimension of cardiac cell clusters and the connection pathways within them ( Figure 1A,B), we mapped the graph of a multinode coloring problem onto a bio-oscillator network, such that each vertex (or node) of the graph is represented by a bio-oscillator, a cardiac cell cluster composed of neonatal rat cardiomyocytes (rCMs), and fibroblasts (rCFs) ( Figure 1C). Any two nodes connected by an edge in the graph are coupled in the bio-oscillator system by a pure rCF bridge ( Figure 1D). The rCF bridges enable the bidirectional connection between the separated bio-oscillators, driving the system to be coupled at a steady state. In this steady state, the coupled bio-oscillators exhibit a unique phase ordering which encodes an approximate solution to the coloring problem. In order to record the coupling dynamics of the system with a large number of bio-oscillators, we used a bright-field video-based methodology to extract the frequency and phase information, which only showed a five-degree error compared with electrical recording. We mapped several graphs with different scales (9-node, 21-node, 29-node, and 44-node) using the bio-oscillator networks. For small-scale networks (i.e., 9-node), the bio-oscillator network finds the optimal solution instances natively, while for larger networks, a postprocessing scheme that uses the bio-oscillator solution as a starting point improved the solution of the bio-oscillator network. We benchmarked the bio-oscillator networks with a digital approach (Johnson algorithm) and showed comparable accuracy in large Figure 1. The schematic of cardiac muscle cell-based bio-oscillator network for vertex coloring problem. A) Fabrication process of a simplified two-node bio-oscillator network. The PDMS blocker and substrate are manually aligned as an assembly, followed by seeding with neonatal rCMs and rCFs. After the removal of the blocker, rCFs proliferate and fill in the empty bridge, coupling the two bio-oscillators. B) The bright-field image of a 64-node bio-oscillator network. C) The schematic of bio-oscillator to solve the vertex coloring problem. Following the arrow flow: a 64-node representative graph; a mapped 64-node bio-oscillator network; synchronization dynamics obtained from the bio-oscillators; the unique phase ordering exhibited in the synchronization dynamics which encodes an approximate solution to the coloring problem. D) The schematic of a simplified two-node bio-oscillator network. The biooscillators, cardiac cell clusters composed of rCMs and rCFs, and the pure rCFs bridge represent the vertices (or nodes) and the edge of the graph, respectively. E) The immunostaining results of the 64-node bio-oscillator network.
www.advancedsciencenews.com www.advintellsyst.com graph instances in a much slower scale rate with processing time.
We also compared the energy consumption of the cardiac cell-based and CMOS oscillators, showing that bio-oscillators consume less energy in computing but take a longer computation time.

Cell Patterning with PDMS Substrates and Blockers
In the cardiac cell-based bio-oscillator system, every two biooscillator pairs, cardiac cell clusters composed of neonatal rat cardiac cells, are connected by an rCF bridge. rCMs are electrically active cells which can spontaneously generate electrical signals and beat at a stable pace when coupled. On the other hand, rCFs are support cells that produce connective tissue in hearts. The rCFs are unable to beat but provide pathways for electrical signal propagation and therefore, couple the adjacent cardiac cell clusters. Previously, we have studied coupling dynamics and the utilization of this dynamic for solving a simple four-node vertex coloring problem using cardiac muscle cell clusters that are simply divided by PDMS strips. [12] In this study, in order to construct a large-scale (i.e. 64 nodes) bio-oscillator network to achieve computationally relevant scale of oscillators and connections, we scaled up a very controlled cell patterning approach [14] to precisely control the cluster size and localization of the bio-oscillator nodes (rCMs) and the connections/bridges between these nodes (rCFs). The PDMS substrate defines the node and bridge sections from the surroundings by the concaved patterns corresponding to the graph. The PDMS blocker is composed of two layers: protruding blockers at the bottom to avoid the rCMs presence in the bridge sections by obstructing the initial cell attachment and the top layer with openings to allow for fibronectin absorption and cell attachment in the node sections. After seeding the isolated rat cardiac cells (a mixture of rCMs and rCFs), and the removal of blockers, the cardiac cells are solely attached to the node sections constructing the individual bio-oscillators. The rCMs were unable to proliferate, while rCFs would proliferate and fill in the empty bridge sections, hence coupling the biooscillators ( Figure S1, Video S1,S2, Supporting Information). Immunofluorescence staining results were used to observe cell distribution and rCF growth on the PDMS substrate ( Figure 1E). The Troponin T (green) can be seen clearly in the node sections, but no Troponin T signals in the bridges, verifying that the PDMS blockers successfully obstructed the initial CM attachment. The vimentin (red) is a fibroblast marker, which can be observed in both sections of bridges and nodes, and the former indicated fibroblast growth in the bridges. The immunostaining results verified that our cell micropatterning method is successful in constructing the bio-oscillator network with corresponding patterns to the original graph ( Figure S2, Supporting Information).

Video-Based Phase Extraction Methodology
To monitor the spatial and temporal synchronization dynamics of a large number of coupled bio-oscillators, we used bright-field imaging to obtain the frequency and phase information. Figure 3 summarizes the methodology used to extract the phase of a pair of bio-oscillators coupled with a 300 μm rCF bridge. Figure 3A,B shows the beating dynamics extracted using bright-field microscopy video analysis. By taking the fast Fourier transform (FFT) of those waveforms, we can demonstrate that the two oscillators are synchronized, as shown in Figure 2C, in which each gray line corresponds to the FFT of one oscillator. By imposing a normalized amplitude and the synchronization frequency extracted from the Fourier analysis, we fit a sinusoid by performing a least-squares fitting to calculate the phase differences between oscillators. At the bottom of Figure 3D, we show the fitting between the sinusoids and the experimental data. Considering www.advancedsciencenews.com www.advintellsyst.com the low sampling frequency of recording optical videos (33 Hz) compared to the field potential (FP) recording using microelectrode arrays (MEAs) (thousands of Hz), we validate our videobased phase extraction methodology by extracting, for the same two sections, at the same time, the phase difference of the pair of oscillators using MEA recording and video analysis. The phase extracted from the waveforms of FPs was 107; meanwhile, the phase extracted from the optical videos was 112 with an error of only 5 indicating that the video analysis is precise enough to calculate the phase information ( Figure 3E).

Measurement of the Network Dynamics in Multinode Network
To demonstrate the scalability of bio-oscillator networks, we constructed several different sizes of bio-oscillator networks, from small to medium to large scales and measured their synchronization dynamics to experimentally obtain corresponding solutions. Since the biological system has a natural trend to reach the energy minimum state and cardiac cells can spontaneously realize oscillatory action without external electrical inputs, cardiac cell-based bio-oscillator networks provide an easy-tofabricate, scalable, and low-energy-consumption solution to construct the building blocks for oscillator-based computing. Figure 3 shows four configurations of graphs ( Figure 3A: 9-node graph simulated in the previous paper, [12] Figure 3F: 21-node Halin graph, Figure 3J,N: randomly generated 29-node and 44-node graphs) along with their colored solutions using experimental data from bio-oscillator networks. Figure 3B shows the bright-field image of the 9-node network. Each node is a circle with a diameter of 800 μm. The nodes are connected by 300 μm of rCF bridges. The larger bio-oscillator networks have the same node and bridge dimension. The overall dimension of the largest network (44-node graph) reaches 0.2 cm 2 . In order to obtain the phase ordering of medium and large scales of bio-oscillator networks, we successively recorded the entire network using brightfield imaging with overlapped nodes between every field of view and extracted the beating waveforms separately. The steady-state sequence of the overlapped nodes, that is, the phase differences among the overlapped nodes in two successive fields of view, were constant, and the identical synchronization frequencies imply that we can combine the phase information of the separate four tile images that were required to capture the entire network into a phase ordering of all nodes ( Figure S3, Supporting Information). Using the video-based methodology, we extracted the temporal waveforms and synchronization frequencies of the bio-oscillator networks ( Figure 3C,G,K,O). The overlapped peaks demonstrate that all nodes were synchronized at these frequencies. By fitting sinusoids to the temporal waveforms, we calculate the phase orderings of the bio-oscillator networks which can be partitioned into independent sets using a simple polynomial time operation, which compares the phase sequence to the adjacency matrix of the graph to identify the partition between two sets ( Figure 3D,H,L,P). Assigning a color to each set can approximate the colored solution of a vertex coloring problem. Notably, in the bio-oscillator network with the small scale (i.e., 9-node graph), we obtained an optimal three-color solution ( Figure 3E) which is consistent with the simulated results from our previously published computational model. [12] In the larger www.advancedsciencenews.com www.advintellsyst.com networks (21, 29, and 44 N), we obtained suboptimal solutions with 6, 7, and 8 colors, respectively. This is not unexpected since the oscillating systems tend to get trapped in the local minima of the high-dimensional phase space. To address this, we developed a postprocessing scheme to improve the suboptimal solutions in the large-scale bio-oscillator networks.

Postprocessing Scheme to Improve Solutions
In order to develop a postprocessing algorithm to improve the experimental outcomes, we used the bio-oscillator-based computational framework to perform simulations to further scale the bio-oscillator network up to 128 nodes [12] and evaluated these graph instances from the DIMACs dataset ( Figure 4A). [15] While the bio-oscillator networks produced optimal (or very close to optimal) solutions in small graphs, it was observed that the deviation of the measured solution from the optimal solution increases with the size of the graph. This trend is consistent with our experimental results. We therefore developed a polynomial time postprocessing scheme [12] that uses the oscillator solution as a starting point. Figure 4A shows the corresponding improvement in solution produced by the postprocessing algorithm for the representative graph instances. We also compared our biooscillator-based approach with the Johnson (heuristic) algorithm for graph coloring. [16] It can be observed that while the standalone bio-oscillator solution degrades more than the solution produced by the Johnson algorithm in larger graphs, the hybrid approach (with postprocessing) improves the solution to be comparable to the Johnson algorithm. Moreover, it can be observed that the time-to-solution for the heuristic Johnson algorithm scales much more steeply than the oscillator approach with or without the postprocessing, implying that the oscillator-based computational model has a performance advantage at larger nodes even with the addition of a postprocessing scheme ( Figure 4B).

Benchmarking of Coupled Bio-Oscillator Networks to Conventional Computing Platform
Furthermore, we benchmarked the energy and latency for graph coloring using coupled bio-oscillators and conventional CMOS oscillators. The maximum energy consumption in a single cardiac oscillator was calculated by the ratio of the single cardiac oscillator to the surface area of a culture well multiplied by all the energy provided by the culture medium, assuming all energy materials are consumed. The details are described in Supporting Information. Subsequently, we extrapolated to estimate energy consumption in larger systems. For the CMOS approach, experimentally measured energy values from prior work [3] were used for smaller system size networks and subsequently projected for larger systems. Delays for both approaches were measured using SPICE circuit simulation of the respective networks. Figure 4C shows the comparison of energy consumption of the cardiac cellbased bio-oscillator and CMOS oscillators for networks with different sizes. It can be observed that cardiac cells consume less energy in computing the graph coloring solution which can lead to significant energy saving in larger networks. The lower oscillating frequency of the cardiac cells, however, results in a longer computation time ( Figure 4D).

Discussion
Combinatorial optimization problems involve finding the "best" object from a finite set of objects which satisfies all constraints. The "best" (i.e., solution quality) is evaluated by an objective function which maps each object to a function value, and the goal is to find the object with the optimal objective function value. For example, the vertex coloring problem is a classic combinatorial optimization problem with the goal of finding the minimum number of colors needed to color a given graph. Such problems have broad applications in real world, including artificial intelligence, resource allocation, and scheduling. However, most of these problems belong to the class of NP-hard problems implying that even the best algorithm ends up searching the whole solution space for certain problem instances. Consequently, using conventional computing framework to solve such problems results in an exponential increase in computing resources (memory, time) as the problem size increases. One alternative computing system for such problems is coupled oscillator systems. In this approach, combinatorial optimization problems are reformulated as an energy minimization problem that can be implemented by the coupled oscillator network. [1]  www.advancedsciencenews.com www.advintellsyst.com The optimization problem is mapped into the parameters of the oscillator network, such as initial frequency or the interconnection pattern of the oscillator network. As time passes, the oscillators interconnect with each other (i.e., synchronization), driving the oscillator network toward an energy minimum state. In this state, the phase and frequency pattern of the oscillator network represent the results of optimization problem. The best solution is found at the global minimum, where the energy of the oscillator network is the lowest. There are many types of hardware that can be used to implement the elementary oscillators in the oscillator network, such as STO, [17] CMOS oscillator, [18,19] relaxation oscillator based on phase transitions, [20] and superconducting oscillator. [21,22] On the other hand, inspired by the massive information processing in living systems, using biological components to build unconventional computing platforms has recently received great attention. [23] Most studies focus on engineering the DNA, gene, or proteins to create data storage [24][25][26] or logic units. [27][28][29] Only a few studies aim to solve the computing problems using biocomputing systems. [30,31] For example, several DNA computing systems have been proposed to solve NP-hard problems, such as vertex coloring problem [32] or capacitated vehicle routing problem, [33] but most of these systems are based on simulations and have not been applied to reality. [34] Our work advances the biocomputing field by providing the experimental demonstration of a new cell-scale paradigm constructed with living cardiac muscle cells to exploit the intrinsic energy minimization tendencies for solving computationally hard problems. Biological systems have a natural ability to minimize their own energy to reach a ground state, which finds a natural analog to problems such as optimization. Based on this ability, we developed different scales of coupled cardiac muscle cell-based bio-oscillator networks for solving a prototypical optimization problem, for example, the vertex coloring problem. The rCMs in the cardiac cells can spontaneously generate oscillatory electrical signals and synchronize to a steady frequency when coupled, while rCFs enable the electrical coupling by providing pathways for ion fluxes through their heterocellular gap junctions. [35] In order to solve the vertex coloring problem, the problem is initially mapped onto the bio-oscillator network following the rules that each graph vertex and edge are represented by a cardiac cellbased bio-oscillator and rCF bridge, respectively. As the biooscillators are coupled, the bio-oscillator network naturally searches for the energy minimum state through the mutual interaction via the rCF bridges. The final steady state of the bio-oscillator network exhibits ordered phase differences which can be used to approximate the solution of the minimum vertex coloring problem.
In our previous study, [12] we have demonstrated the potential of living cardiac cells as oscillatory building blocks to implement the coupled bio-oscillator systems using a simple four-node network as a proof of concept. The previous four-node network was constructed on an MEA substrate using a cross-shape PDMS blocker to separate the rCM clusters, resulting in difficulty in scaling up. In this study, we aim to extend the bio-oscillator system to achieve computationally relevant scale of oscillators and connections. For this, we developed a cell patterning approach to both control the localization of the bio-oscillators nodes (i.e., CMs) and the connections/bridges between these nodes (i.e., CFs) in large scale. Unlike the random connections in the four-node network, the proposed cell patterning approach utilizes the concave patterns in PDMS substrates and the proliferation of rCFs to generate aligned rCF connections in a spatially controlled fashion. We also developed a video-based methodology using simple microscopy imaging to monitor the spatial and temporal synchronization dynamics of large-scale coupled bio-oscillators. Compared to the MEA substrate which only records the electrical signals from 2D culture, using imaging as a read-out strategy provides more flexible detection in future 3D cultures as well as decreases the manufacturing costs.
The computing in the coupled oscillator system is performed by the coupling of oscillators, as interconnections among the oscillators alter the phases and frequencies of the oscillators, and finally drives the network toward the energy-minimum state. In our previous paper, [12,14] we demonstrated that rCF bridges can successfully couple two bio-oscillators with distinct phase differences and provide an RC-type coupling through biooscillators. We also showed that the coupling strength can be controlled by the length of rCF bridge. For a higher length, the propagation of electrical signals through the rCF bridge takes a longer time, leading to a bigger phase difference. From the perspective of the electrical nature of coupling, the resistance increases for a higher length; therefore, the capacitive coupling dominates which tends to "push" phases out of each other, leading to a bigger phase difference. On the contrary, the conductance increases in a smaller length which tends to "pull" phases closer to each other, leading to a smaller phase difference. The combined "push-and-pull" effect in the coupled biooscillator network gives special properties to the phase ordering in the steady synchronization state which can be used to approximate the solution of a vertex coloring problem. [6] Herein, both experimental and simulated results show that the bio-oscillator network generates a suboptimal solution in large graphs, while the solution obtained from the small graph (9-node) is optimal. The reason for this is that as the graph scales, the bio-oscillator network in the high-dimensional phase space may settle to a local energy minima which is close to the global minima, [36] leading to the sub-optimal solutions. Therefore, we developed a postprocessing approach that iteratively expands the largest set to diminish the colors needed for the graph. The results in Figure 4a reveal that this hybrid approach (biooscillator network with post-processing) takes practically the same time compared to the computing time of bio-oscillator network, but meanwhile it significantly improves the solution to be optimal or near optimal even in large-scale networks. As shown in Figure 4b, the computing time scales slower as the size of graph increases for the bio-oscillator networks, even with postprocessing, indicating that bio-oscillators may have a significant performance advantage in large scale.
Compared to other physical implementations of coupled oscillator-based computing platforms, the most significant advantage of the cell-based bio-oscillator network is the ultralow energy requirement, making it a new and promising platform for oscillator-based computing. As shown in Figure 4c, the energy consumption of CMOS oscillators scales exponentially when the graph size increases, while the energy consumption of bio-oscillators scales much slower. In addition, the energy www.advancedsciencenews.com www.advintellsyst.com consumption of a bio-oscillator network in Figure 4 is the maximum energy consumption as we assumed that all energy resources (i.e., L-glutamine) provided by medium were consumed by cells, implying that the actual energy would be even less. Another significant advantage of bio-oscillator networks is in their scalability, as large-scale data processing is becoming important considering the current complexity of computational tasks. In this article, we experimentally demonstrated the scalability of bio-oscillators by fabricating different large-scale networks up to 64 nodes showing a great scalability in the larger realm of oscillator devices that have been explored for collective computing. Furthermore, using the simulations, we also evaluated the possibility of scaling the bio-oscillator network in larger graphs (>120-oscillator network). Other oscillator systems, STOs [17] or phase-transition oscillators [20] so far, have been used to construct corresponding networks of up to only nine and eight oscillators, respectively. The CMOS-based oscillator network can achieve hundreds or even thousands of oscillators in a single chip [18,19] due to the mature CMOS integration and miniaturization technology. But we are optimistic that with the rapid development of tissue engineering and microfabrication technology, such a large network of cell-based bio-oscillators would be feasible in the future. Another requirement for scalability is the easy and controllable connectivity within oscillators. We have previously shown the relation between coupling strength and rCF bridge length. [12] By controlling the cardiac cell patterning and the bridge length, we can engineer the interconnections between the bio-oscillators, that is, which oscillators are coupled and with which strength. In addition, combining some 3D fabrication methods, such as 3D bioprinting which can construct complex biological structures using multiple cell types, one can achieve 3D connectivity with self-forming patterns of cells which is hard to achieve in CMOS oscillators.
Although bio-oscillators are composed of biological components, both cardiac muscle cells and the cardiac fibroblasts are electrically responsive and as such could easily be interfaced with electronic circuits. For example, using the electrodes underneath the beating cardiac cell clusters, one can record the electrical outputs of beating cells [14] or introduce electrical stimulation to adjust the beating frequency [37] or to enhance the synchronization. [38] Furthermore, the usage of biological components enables the interface of bio-oscillators with living tissue through direct gap junctions or other paracrine signaling, which may broaden the application of bio-oscillators in areas of biological engineering and medicine. In other types of oscillators, the most straightforward coupling mechanism is to use the existing physics of the oscillator state variables, such as mechanical coupling in MEMS oscillators [39] and magnetic coupling [40] or spin waves in STOs, [17] which have significant limitations in available coupling configurations. Even though the nonelectrical oscillators can also exploit electrical coupling, [8,41,42] the transduction efficacy from other state variables to electrical signals is extremely low leading to high energy consumption. [1] One thing to note is that the frequency of the bio-oscillators (0.5-2 Hz) is much lower than other oscillators (up to GHz), such as superconducting oscillators, spin-torque oscillators, or CMOS oscillators. As illustrated in Figure 4D, the low frequency will inevitably cause longer computation times compared to other types of oscillators as each cycle takes longer time during evolution. The computation time of bio-oscillator systems is limited by the speed of the electrical signal propagation through the gap junctions between rCF and rCM. The conduction speed could be modified using tissue engineering methods, such as controlling the orientation of the cells forming the bio-oscillators or by incorporating conductive materials that are able to enhance synchronization. [38,43] Applying electrical stimulation can also pace the bio-oscillators to a faster frequency. [44] Although such approaches would increase the computing speed of cell-based bio-oscillator networks, considering the speed of biological processes, the computation time of the bio-oscillators is unable to match the CMOS oscillators.
Another potential concern of bio-oscillators is the stability of the cardiac cell beating during the computing procedure. In our previous experiments, [12] we have measured the extracellular electrical potential of rCMs in two bio-oscillators for long periods of time (up to 40 h) to track the frequency and monitor cell activity in long term, showing that the frequencies and phases of the bio-oscillators remain stable for long time (more than 10 h) after synchronization. Moreover, we improved the stability by optimizing the rCF bridge length. We considered different rCF lengths and selected 300 μm as the standard bridge length because of the distinct phase differences compared to other shorter lengths, as well as the better synchronization stability compared to 400 μm, even though it generated a more district phase difference. The rCF length longer than 400 μm resulted in unsynchronized clusters. The stability of the bio-oscillator system would also be affected by the operation environment. Most oscillators do not have temperature requirements and can be implemented at room temperature. The optimal temperature for bio-oscillators is 37°C as cardiac cells have the best efficiency for biochemical reaction at this temperature. In order to maintain the cell viability, the monitoring videos in this project were taken in a microscope incubation chamber which enables control of the temperature and CO 2 conditions during the monitoring procedure. However, the temperature requirement for bio-oscillators is not strict. Despite decreases in amplitude and duration, the relative contributions of calcium transport systems during the relaxation are not greatly affected at lower temperature. [45] Therefore, we can expect that cardiac muscle cells can still keep active even at room temperature. When compared to the superconducting oscillators that require cryogenic temperature to reduce resistance, the temperature requirement (37°C) of biooscillators is easy to achieve and consumes much less energy. Compared to the CMOS technology which has well-established manufacturability, low batch-to-batch variation, broad temperature range, as well as long service lifetime (usually over years), bio-oscillator systems may have limitations in terms of operation environment and batch-to-batch variation (i.e., the synchronized frequency may vary from experiment to experiment). However, the ultimate goal of the bio-oscillator network is not to replace the existing CMOS devices, but to complement them for applications that would require high degree of energy efficiency. Furthermore, bio-oscillator networks, that have the ability to interface both the living materials and traditional electronic devices, would have the added benefit of easily interface with living tissues in several applications such as human-machine interfaces or heart pacemakers.
Overall, this study describes a new type of oscillator, one made of beating heart cells, for more efficient processing of computationally hard problems compared to the heuristic Boolean-based algorithm in large-scale networks. Although there are limitations in terms of frequency and processing speed compared to CMOS-based oscillators, advantages in energy consumption and ease of fabrication and potential to extend this system to massively parallel 3D structures by leveraging the ever-growing field of biofabrication make heart muscle-based oscillators a promising new platform for collective computing applications.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.