The study of collective cellular behaviors, such as cell sorting during embryonic development, is governed by both biochemical signals and mechanical regulation, notably the differential adhesion hypothesis (DAH). While computational models such as the Cellular Potts and Vertex models have helped explain DAH, they lack biological plausibility due to oversimplified assumptions. Conversely, in vitro experiments offer authenticity but suffer from poor parameter controllability, biological noise, and high costs.
To bridge this gap, this paper introduces the MorphoSystem, an interdisciplinary platform integrating robot swarms, cell collectives, and computational simulations. This triadic framework enables precise, controllable, and reproducible investigation of mechanical principles underlying self-organization.
Biological, Computational, and Robotic Platforms
This study employed three complementary approaches to investigate collective cell sorting, which were biological experiments, computational simulations, and robot swarm experiments.
For biological experiments, two human cell lines were used, namely, human embryonic kidney (HEK) 293 and human gastric carcinoma (HGC)-27 gastric cancer cells. Both were cultured in standard medium at 37 degrees celsius (°C) with 5% carbon dioxide (CO2).
To visualize cell-cell adhesion proteins, immunostaining was performed using an antibody targeting E-cadherin, followed by fluorescence microscopy. Circular microstructures were fabricated on glass substrates using three-dimensional printing via two-photon polymerization.
For cell sorting assays, cells were labeled with fluorescent dyes, mixed in equal proportions, and seeded into the microstructured dishes. Time-lapse imaging captured the sorting process every 15 minutes over 24 hours using confocal microscopy.
For computational simulations, the team used CompuCell3D software, which implements the Glazier-Graner-Hogeweg model. This approach defines an effective energy function that accounts for cell-substrate adhesion, cell-cell adhesion, volume constraints, and surface-area constraints. The model simulates cell migration by repeatedly attempting energy-minimizing state changes.
For robot swarm experiments, custom-designed robots (63 millimeters (mm) diameter, 60 grams (g) weight) were built with magnetic shells to simulate cellular adhesion. Different magnet sizes provided controllable adhesion strengths. A dynamic model was established considering driving forces, inter-robot magnetic interactions, resistive forces, and random noise.
Robot motion followed alternating linear-circular trajectories, and velocity-position updates were calculated using equations of motion. This robotic platform enabled precise manipulation of adhesion parameters, offering a controllable testbed for validating findings from biological and computational studies.
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Validating Differential Adhesion Across Disciplines
The study experimentally validated that differences in intercellular adhesion drive cell sorting, consistent with the DAH. Using HGC-27 cells (weak adhesion, low E-cadherin) and HEK 293 cells (strong adhesion, high E-cadherin), the team observed that after 10 hours of co-culture, weak-adhesion cells completely surrounded strong-adhesion cells, forming a segregated structure.
Computational simulations using CompuCell3D confirmed these findings. When the adhesion energy of weak cells was increased (meaning weaker actual adhesion), sorting time lengthened from 150,000 to 330,000 Monte Carlo steps, and complete sorting shifted to incomplete sorting. Both experiments and simulations showed that the number of cell clusters decreased rapidly while the largest cluster size increased, with distinct crossover points observed.
The researchers then developed a robot swarm platform with programmable magnetic adhesion to test the hypothesis in a physical system. Robots with different adhesion strengths self-organized into sorting patterns that mirrored both biological and computational results. As weak-adhesion robot force increased, sorting time rose from 7.5 to 18 minutes, and complete sorting became incomplete. Both circular and hexagonal robot shapes successfully achieved sorting under the same adhesion condition.
However, unlike cell simulations, robot swarms did not exhibit crossover phenomena in clustering curves, suggesting fundamental differences between discrete robotic systems and continuous cellular tissues. Robot swarms operate under physical interaction laws, whereas cell simulations minimize computational energy functions, highlighting limitations of energy-based models in representing real physical mechanisms.
Toward a Unified Framework for Collective Behavior
This study presented MorphoSystem, a triadic platform integrating cell biology, computational simulation, and robot swarms to investigate adhesion-driven collective behaviors. Across all platforms, the DAH was validated. While robot swarms cannot fully replicate cellular complexity, they serve as controllable physical models that bridge the authenticity of biological experiments and the efficiency of simulations. Notably, sorting dynamics proved scale-invariant across vastly different timescales.
Future improvements include multimodal robotic stimuli and adaptive connections. MorphoSystem offers a powerful, quantitative tool for exploring mechanical principles in development, cancer metastasis, and swarm robotics.
Journal Reference
Pan, M., Long, M., Liu, L., & Yang, Y. (2026). Exploring the physical principles of cell collective behaviors using robot swarms. Biomimetic Intelligence and Robotics, 100335. DOI:10.1016/j.birob.2026.100335, https://www.sciencedirect.com/science/article/pii/S266737972600063X
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