Mathematical model of collective cell migrations based on cell polarity

Cell-center-based model for simulating three-dimensional monolayer tissue deformation

The shape of the epithelial monolayer can be depicted as a curved tissue in three-dimensional (3D) space, where individual cells are tightly adhered to one another. The 3D morphogenesis of these tissues is governed by cell dynamics, and a variety of mathematical modeling and simulation studies have been conducted to investigate this process. One promising approach is the cell-center model, which can account for the discreteness of cells. The cell nucleus, which is considered to correspond to the cell center, can be observed experimentally. However, there has been a shortage of cell-center models specifically tailored for simulating 3D monolayer tissue deformation. In this study, we developed a mathematical model based on the cell-center model to simulate 3D monolayer tissue deformation. Our model was confirmed by simulating the in-plane deformation, out-of-plane deformation, and invagination due to apical constriction.

A machine learning based model accurately predicts cellular response to electric fields in multiple cell types

Many cell types migrate in response to naturally generated electric fields. Furthermore, it has been suggested that the external application of an electric field may be used to intervene in and optimize natural processes such as wound healing. Precise cell guidance suitable for such optimization may rely on predictive models of cell migration, which do not generalize. Here, we present a machine learning model that can forecast directedness of cell migration given a timeseries of previous directedness and electric field values. This model is trained using time series galvanotaxis data of mammalian cranial neural crest cells obtained through time-lapse microscopy of cells cultured at 37 °C in a galvanotaxis chamber at ambient pressure. Next, we show that our modeling approach can be used for a variety of cell types and experimental conditions with very limited training data using transfer learning methods. We adapt the model to predict cell behavior for keratocytes (room temperature, ~ 18–20 °C) and keratinocytes (37 °C) under similar experimental conditions with a small dataset (~ 2–5 cells). Finally, this model can be used to perform in silico studies by simulating cell migration lines under time-varying and unseen electric fields. We demonstrate this by simulating feedback control on cell migration using a proportional–integral–derivative (PID) controller. This data-driven approach provides predictive models of cell migration that may be suitable for designing electric field based cellular control mechanisms for applications in precision medicine such as wound healing.

Quantifying the impact of electric fields on single-cell motility

Cell motility in response to environmental cues forms the basis of many developmental processes in multicellular organisms. One such environmental cue is an electric field (EF), which induces a form of motility known as electrotaxis. Electrotaxis has evolved in a number of cell types to guide wound healing and has been associated with different cellular processes, suggesting that observed electrotactic behavior is likely a combination of multiple distinct effects arising from the presence of an EF. To determine the different mechanisms by which observed electrotactic behavior emerges, and thus to design EFs that can be applied to direct and control electrotaxis, researchers require accurate quantitative predictions of cellular responses to externally applied fields. Here, we use mathematical modeling to formulate and parameterize a variety of hypothetical descriptions of how cell motility may change in response to an EF. We calibrate our model to observed data using synthetic likelihoods and Bayesian sequential learning techniques and demonstrate that EFs bias cellular motility through only one of a selection of hypothetical mechanisms. We also demonstrate how the model allows us to make predictions about cellular motility under different EFs. The resulting model and calibration methodology will thus form the basis for future data-driven and model-based feedback control strategies based on electric actuation.

Weakening of resistance force by cell-ECM interactions regulate cell migration directionality and pattern formation

Collective migration of epithelial cells is a fundamental process in multicellular pattern formation. As they expand their territory, cells are exposed to various physical forces generated by cell-cell interactions and the surrounding microenvironment. While the physical stress applied by neighbouring cells has been well studied, little is known about how the niches that surround cells are spatio-temporally remodelled to regulate collective cell migration and pattern formation. Here, we analysed how the spatio-temporally remodelled extracellular matrix (ECM) alters the resistance force exerted on cells so that the cells can expand their territory. Multiple microfabrication techniques, optical tweezers, as well as mathematical models were employed to prove the simultaneous construction and breakage of ECM during cellular movement, and to show that this modification of the surrounding environment can guide cellular movement. Furthermore, by artificially remodelling the microenvironment, we showed that the directionality of collective cell migration, as well as the three-dimensional branch pattern formation of lung epithelial cells, can be controlled. Our results thus confirm that active remodelling of cellular microenvironment modulates the physical forces exerted on cells by the ECM, which contributes to the directionality of collective cell migration and consequently, pattern formation.

The Use of Diffusion Calculations and Monte Carlo Simulations to Understand the Behavior of Cells in Dictyostelium Communities

Microbial communities are the simplest possible model of multicellular tissues, allowing studies of cell-cell interactions to be done with as few extraneous factors as possible. For instance, the eukaryotic microbe Dictyostelium discoideum proliferates as single cells, and when starved, the cells aggregate together and form structures of ~20,000 cells. The cells use a variety of signals to direct their movement, inform each other of their local cell density and whether they are starving, and organize themselves into groups of ~20,000 cells. Mathematical models and computational approaches have been a key check on, and guide of, the experimental work. In this minireview, I will discuss diffusion calculations and Monte Carlo simulations that were used for Dictyostelium studies that offer general paradigms for several aspects of cell-cell communication. For instance, computational work showed that diffusible secreted cell-density sensing (quorum) factors can diffuse away so quickly from a single cell that the local concentration will not build up to incorrectly cause the cell to sense that it is in the presence of a high density of other cells secreting that signal. In another example, computation correctly predicted a mechanism that allows a group of cells to break up into subgroups. These are thus some examples of the power and necessity of computational work in biology.

Maintenance of an undifferentiated state of human-induced pluripotent stem cells through botulinum hemagglutinin-mediated regulation of cell behavior

Applications of human induced pluripotent stem cell (hiPSC) culture are impaired by problems with long term maintenance of pluripotency. In this study, we report that exposure to botulinum hemagglutinin (HA), an E-cadherin function-blocking agent, suppressed deviation from an undifferentiated state in hiPSC colonies. Time-lapse imaging of live cells revealed that cells in central regions of colonies moved slowly and underwent a morphological change to a cobblestone-like shape via interaction between contacting cells, forming dense, multiple layers. Staining and migration analysis showed that actin stress fibers and paxillin spots were diminished in colony central regions, and this was associated with alteration of cellular morphology and migratory behavior. However, in culture with HA exposure, cells in the central and peripheral regions of hiPSC colonies were migratory and arranged in loose monolayers, resulting in relatively uniform dispersion of cells in colonies. We also found that a well-organized network of actin stress fibers was of significance in the central and peripheral regions of a colony, resulting in activation of paxillin and E-cadherin expression in hiPSCs. After routine application of HA for serial passages, hiPSCs remained pluripotent and capable of differentiating into all three germ layers. These observations indicate that relaxation of cell-cell junctions by HA induced rearrangements of the cytoskeleton and cell adhesion in hiPSC colonies by promoting migratory behaviors. These results suggest that this simple and readily reproducible culture strategy is a potentially useful tool for improving the robust and scalable maintenance of undifferentiated hiPSC cultures.