Optimal Control of Collective Electrotaxis in Epithelial Monolayers.

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.

Quantifying cell cycle regulation by tissue crowding.

The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do not fully understand how cell proliferation regulation impacts cell migration phenomena. Here, we present a minimal continuum model of cell migration with cell cycle dynamics, which includes density-dependent effects and hence can account for cell proliferation regulation. By combining minimal mathematical modeling, Bayesian inference, and recent experimental data, we quantify the impact of tissue crowding across different cell cycle stages in epithelial tissue expansion experiments. Our model suggests that cells sense local density and adapt cell cycle progression in response, during G1 and the combined S/G2/M phases, providing an explicit relationship between each cell-cycle-stage duration and local tissue density, which is consistent with several experimental observations. Finally, we compare our mathematical model's predictions to different experiments studying cell cycle regulation and present a quantitative analysis on the impact of density-dependent regulation on cell migration patterns. Our work presents a systematic approach for investigating and analyzing cell cycle data, providing mechanistic insights into how individual cells regulate proliferation, based on population-based experimental measurements.

Bioelectric stimulation controls tissue shape and size.

Epithelial tissues sheath organs and electro-mechanically regulate ion and water transport to regulate development, homeostasis, and hydrostatic organ pressure. Here, we demonstrate how external electrical stimulation allows us to control these processes in living tissues. Specifically, we electrically stimulate hollow, 3D kidneyoids and gut organoids and find that physiological-strength electrical stimulation of ∼ 5 - 10 V/cm powerfully inflates hollow tissues; a process we call electro-inflation. Electro-inflation is mediated by increased ion flux through ion channels/transporters and triggers subsequent osmotic water flow into the lumen, generating hydrostatic pressure that competes against cytoskeletal tension. Our computational studies suggest that electro-inflation is strongly driven by field-induced ion crowding on the outer surface of the tissue. Electrically stimulated tissues also break symmetry in 3D resulting from electrotaxis and affecting tissue shape. The ability of electrical cues to regulate tissue size and shape emphasizes the role and importance of the electrical micro-environment for living tissues.

Spatial heterogeneity in collective electrotaxis: continuum modelling and applications to optimal control.

Collective electrotaxis is a phenomenon that occurs when a cellular collective, for example an epithelial monolayer, is subjected to an electric field. Biologically, it is well known that the velocity of migration during the collective electrotaxis of large epithelia exhibits significant spatial heterogeneity. In this work, we demonstrate that the heterogeneity of velocities in the electrotaxing epithelium can be accounted for by a continuum model of cue competition in different tissue regions. Having established a working model of competing migratory cues in the migrating epithelium, we develop and validate a reaction-convection-diffusion model that describes the movement of an epithelial monolayer as it undergoes electrotaxis. We use the model to predict how tissue size and geometry affect the collective migration of MDCK monolayers, and to propose several ways in which electric fields can be designed such that they give rise to a desired spatial pattern of collective migration. We conclude with two examples that demonstrate practical applications of the method in designing bespoke stimulation protocols.

Parameter identifiability and model selection for partial differential equation models of cell invasion.

When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide ranges of unseen scenarios, as well as for understanding the underlying mechanisms. In this work, we use a profile-likelihood approach to investigate parameter identifiability for four extensions of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) model, given experimental data from a cell invasion assay. We show that more complicated models tend to be less identifiable, with parameter estimates being more sensitive to subtle differences in experimental procedures, and that they require more data to be practically identifiable. As a result, we suggest that parameter identifiability should be considered alongside goodness-of-fit and model complexity as criteria for model selection.

Optimal control of collective electrotaxis in epithelial monolayers.

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.

E-cadherin biomaterials reprogram collective cell migration and cell cycling by forcing homeostatic conditions.

Cells attach to the world through either cell-extracellular matrix adhesion or cell-cell adhesion, and traditional biomaterials imitate the matrix for integrin-based adhesion. However, materials incorporating cadherin proteins that mimic cell-cell adhesion offer an alternative to program cell behavior and integrate into living tissues. We investigated how cadherin substrates affect collective cell migration and cell cycling in epithelia. Our approach involved biomaterials with matrix proteins on one-half and E-cadherin proteins on the other, forming a "Janus" interface across which we grew a single sheet of cells. Tissue regions over the matrix side exhibited normal collective dynamics, but an abrupt behavior shift occurred across the Janus boundary onto the E-cadherin side, where cells attached to the substrate via E-cadherin adhesions, resulting in stalled migration and slowing of the cell cycle. E-cadherin surfaces disrupted long-range mechanical coordination and nearly doubled the length of the G0/G1 phase of the cell cycle, linked to the lack of integrin focal adhesions on the E-cadherin surface.

E-cadherin biointerfaces reprogram collective cell migration and cell cycling by forcing homeostatic conditions.

Cells attach to the world around them in two ways-cell:extracellular-matrix adhesion and cell:cell adhesion-and conventional biomaterials are made to resemble the matrix to encourage integrin-based cell adhesion. However, interest is growing for cell-mimetic interfaces that mimic cell-cell interactions using cadherin proteins, as this offers a new way to program cell behavior and design synthetic implants and objects that can integrate directly into living tissues. Here, we explore how these cadherin-based materials affect collective cell behaviors, focusing specifically on collective migration and cell cycle regulation in cm-scale epithelia. We built culture substrates where half of the culture area was functionalized with matrix proteins and the contiguous half was functionalized with E-cadherin proteins, and we grew large epithelia across this 'Janus' interface. Parts of the tissues in contact with the matrix side of the Janus interface exhibited normal collective dynamics, but an abrupt shift in behaviors happened immediately across the Janus boundary onto the E-cadherin side, where cells formed hybrid E-cadherin junctions with the substrate, migration effectively froze in place, and cell-cycling significantly decreased. E-cadherin materials suppressed long-range mechanical correlations in the tissue and mechanical information reflected off the substrate interface. These effects could not be explained by conventional density, shape index, or contact inhibition explanations. E-cadherin surfaces nearly doubled the length of the G0/G1 phase of the cell cycle, which we ultimately connected to the exclusion of matrix focal adhesions induced by the E-cadherin culture surface.

Quantifying tissue growth, shape and collision via continuum models and Bayesian inference.

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues and organs coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach combining data from recent experiments, mathematical modelling and Bayesian parameter inference, to describe the self-assembly of multiple epithelial sheets by growth and collision. We use two simple and well-studied continuum models, where cells move either randomly or following population pressure gradients. After suitable calibration, both models prove to be practically identifiable, and can reproduce the main features of single tissue expansions. However, our findings reveal that whenever tissue-tissue interactions become relevant, the random motion assumption can lead to unrealistic behaviour. Under this setting, a model accounting for population pressure from different cell populations is more appropriate and shows a better agreement with experimental measurements. Finally, we discuss how tissue shape and pressure affect multi-tissue collisions. Our work thus provides a systematic approach to quantify and predict complex tissue configurations with applications in the design of tissue composites and more generally in tissue engineering.

Self-assembly of tessellated tissue sheets by expansion and collision.

Tissues do not exist in isolation-they interact with other tissues within and across organs. While cell-cell interactions have been intensely investigated, less is known about tissue-tissue interactions. Here, we studied collisions between monolayer tissues with different geometries, cell densities, and cell types. First, we determine rules for tissue shape changes during binary collisions and describe complex cell migration at tri-tissue boundaries. Next, we propose that genetically identical tissues displace each other based on pressure gradients, which are directly linked to gradients in cell density. We present a physical model of tissue interactions that allows us to estimate the bulk modulus of the tissues from collision dynamics. Finally, we introduce TissEllate, a design tool for self-assembling complex tessellations from arrays of many tissues, and we use cell sheet engineering techniques to transfer these composite tissues like cellular films. Overall, our work provides insight into the mechanics of tissue collisions, harnessing them to engineer tissue composites as designable living materials.

PVP1-The People's Ventilator Project: A fully open, low-cost, pressure-controlled ventilator research platform compatible with adult and pediatric uses.

Mechanical ventilators are safety-critical devices that help patients breathe, commonly found in hospital intensive care units (ICUs)-yet, the high costs and proprietary nature of commercial ventilators inhibit their use as an educational and research platform. We present a fully open ventilator device-The People's Ventilator: PVP1-with complete hardware and software documentation including detailed build instructions and a DIY cost of $1,700 USD. We validate PVP1 against both key performance criteria specified in the U.S. Food and Drug Administration's Emergency Use Authorization for Ventilators, and in a pediatric context against a state-of-the-art commercial ventilator. Notably, PVP1 performs well over a wide range of test conditions and performance stability is demonstrated for a minimum of 75,000 breath cycles over three days with an adult mechanical test lung. As an open project, PVP1 can enable future educational, academic, and clinical developments in the ventilator space.

Learning the rules of collective cell migration using deep attention networks.

Collective, coordinated cellular motions underpin key processes in all multicellular organisms, yet it has been difficult to simultaneously express the 'rules' behind these motions in clear, interpretable forms that effectively capture high-dimensional cell-cell interaction dynamics in a manner that is intuitive to the researcher. Here we apply deep attention networks to analyze several canonical living tissues systems and present the underlying collective migration rules for each tissue type using only cell migration trajectory data. We use these networks to learn the behaviors of key tissue types with distinct collective behaviors-epithelial, endothelial, and metastatic breast cancer cells-and show how the results complement traditional biophysical approaches. In particular, we present attention maps indicating the relative influence of neighboring cells to the learned turning decisions of a 'focal cell'-the primary cell of interest in a collective setting. Colloquially, we refer to this learned relative influence as 'attention', as it serves as a proxy for the physical parameters modifying the focal cell's future motion as a function of each neighbor cell. These attention networks reveal distinct patterns of influence and attention unique to each model tissue. Endothelial cells exhibit tightly focused attention on their immediate forward-most neighbors, while cells in more expansile epithelial tissues are more broadly influenced by neighbors in a relatively large forward sector. Attention maps of ensembles of more mesenchymal, metastatic cells reveal completely symmetric attention patterns, indicating the lack of any particular coordination or direction of interest. Moreover, we show how attention networks are capable of detecting and learning how these rules change based on biophysical context, such as location within the tissue and cellular crowding. That these results require only cellular trajectories and no modeling assumptions highlights the potential of attention networks for providing further biological insights into complex cellular systems.

Short-term bioelectric stimulation of collective cell migration in tissues reprograms long-term supracellular dynamics.

The ability to program collective cell migration can allow us to control critical multicellular processes in development, regenerative medicine, and invasive disease. However, while various technologies exist to make individual cells migrate, translating these tools to control myriad, collectively interacting cells within a single tissue poses many challenges. For instance, do cells within the same tissue interpret a global migration 'command' differently based on where they are in the tissue? Similarly, since no stimulus is permanent, what are the long-term effects of transient commands on collective cell dynamics? We investigate these questions by bioelectrically programming large epithelial tissues to globally migrate 'rightward' via electrotaxis. Tissues clearly developed distinct rear, middle, side, and front responses to a single global migration stimulus. Furthermore, at no point poststimulation did tissues return to their prestimulation behavior, instead equilibrating to a 3rd, new migratory state. These unique dynamics suggested that programmed migration resets tissue mechanical state, which was confirmed by transient chemical disruption of cell-cell junctions, analysis of strain wave propagation patterns, and quantification of cellular crowd dynamics. Overall, this work demonstrates how externally driving the collective migration of a tissue can reprogram baseline cell-cell interactions and collective dynamics, even well beyond the end of the global migratory cue, and emphasizes the importance of considering the supracellular context of tissues and other collectives when attempting to program crowd behaviors.

Correction to: An Easy-to-Fabricate Cell Stretcher Reveals Density-Dependent Mechanical Regulation of Collective Cell Movements in Epithelia.

[This corrects the article DOI: 10.1007/s12195-021-000689-6.].

An Easy-to-Fabricate Cell Stretcher Reveals Density-Dependent Mechanical Regulation of Collective Cell Movements in Epithelia.

INTRODUCTION: Mechanical forces regulate many facets of cell and tissue biology. Studying the effects of forces on cells requires real-time observations of single- and multi-cell dynamics in tissue models during controlled external mechanical input. Many of the existing devices used to conduct these studies are costly and complicated to fabricate, which reduces the availability of these devices to many laboratories. METHODS: We show how to fabricate a simple, low-cost, uniaxial stretching device, with readily available materials and instruments that is compatible with high-resolution time-lapse microscopy of adherent cell monolayers. In addition, we show how to construct a pressure controller that induces a repeatable degree of stretch in monolayers, as well as a custom MATLAB code to quantify individual cell strains. RESULTS: As an application note using this device, we show that uniaxial stretch slows down cellular movements in a mammalian epithelial monolayer in a cell density-dependent manner. We demonstrate that the effect on cell movement involves the relocalization of myosin downstream of Rho-associated protein kinase (ROCK). CONCLUSIONS: This mechanical device provides a platform for broader involvement of engineers and biologists in this important area of cell and tissue biology. We used this device to demonstrate the mechanical regulation of collective cell movements in epithelia. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s12195-021-00689-6.

Tardigrades exhibit robust interlimb coordination across walking speeds and terrains.

Tardigrades must negotiate heterogeneous, fluctuating environments and accordingly utilize locomotive strategies capable of dealing with variable terrain. We analyze the kinematics and interleg coordination of freely walking tardigrades (species: Hypsibius exemplaris). We find that tardigrade walking replicates several key features of walking in insects despite disparities in size, skeleton, and habitat. To test the effect of environmental changes on tardigrade locomotor control circuits we measure kinematics and interleg coordination during walking on two substrates of different stiffnesses. We find that the phase offset between contralateral leg pairs is flexible, while ipsilateral coordination is preserved across environmental conditions. This mirrors similar results in insects and crustaceans. We propose that these functional similarities in walking coordination between tardigrades and arthropods is either due to a generalized locomotor control circuit common to panarthropods or to independent convergence onto an optimal strategy for robust multilegged control in small animals with simple circuitry. Our results highlight the value of tardigrades as a comparative system toward understanding the mechanisms-neural and/or mechanical-underlying coordination in panarthropod locomotion.

Come together: On-chip bioelectric wound closure.

There is a growing interest in bioelectric wound treatment and electrotaxis, the process by which cells detect an electric field and orient their migration along its direction, has emerged as a potential cornerstone of the endogenous wound healing response. Despite recognition of the importance of electrotaxis in wound healing, no experimental demonstration to date has shown that the actual closing of a wound can be accelerated solely by the electrotaxis response itself, and in vivo systems are too complex to resolve cell migration from other healing stages such as proliferation and inflammation. This uncertainty has led to a lack of standardization between stimulation methods, model systems, and electrode technology required for device development. In this paper, we present a 'healing-on-chip' approach that is a standardized, low-cost, model for investigating electrically accelerated wound healing. Our device provides a biomimetic convergent field geometry that more closely resembles actual wound fields. We validate this device by using electrical stimulation to close a 1.5 mm gap between two large (30 mm2) layers of primary skin keratinocyte to completely heal the gap twice as quickly as in an unstimulated tissue. This demonstration proves that convergent electrotaxis is both possible and can accelerate healing and offers an accessible 'healing-on-a-chip' platform to explore future bioelectric interfaces.

Overriding native cell coordination enhances external programming of collective cell migration.

As collective cell migration is essential in biological processes spanning development, healing, and cancer progression, methods to externally program cell migration are of great value. However, problems can arise if the external commands compete with strong, preexisting collective behaviors in the tissue or system. We investigate this problem by applying a potent external migratory cue-electrical stimulation and electrotaxis-to primary mouse skin monolayers where we can tune cell-cell adhesion strength to modulate endogenous collectivity. Monolayers with high cell-cell adhesion showed strong natural coordination and resisted electrotactic control, with this conflict actively damaging the leading edge of the tissue. However, reducing preexisting coordination in the tissue by specifically inhibiting E-cadherin-dependent cell-cell adhesion, either by disrupting the formation of cell-cell junctions with E-cadherin-specific antibodies or rapidly dismantling E-cadherin junctions with calcium chelators, significantly improved controllability. Finally, we applied this paradigm of weakening existing coordination to improve control and demonstrate accelerated wound closure in vitro. These results are in keeping with those from diverse, noncellular systems and confirm that endogenous collectivity should be considered as a key quantitative design variable when optimizing external control of collective migration.

Corrigendum to "The Kaleidoscope Model of Integrative Healthcare as a collaborative paradigm for cardiology and chiropractic: a call to action" [Integr Med Res 2018; 7(1): 1-8].

[This corrects the article DOI: 10.1016/j.imr.2018.01.009.].