CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Apical constriction requires patterned apical surface remodeling to synchronize cellular deformation

Apical constriction is a basic mechanism for epithelial morphogenesis, making columnar cells into wedge shape and bending a flat cell sheet. It has long been thought that an apically localized myosin generates a contractile force and drives the cell deformation. However, when we tested the increased apical surface contractility in a cellular Potts model simulation, the constriction increased pressure inside the cell and pushed its lateral surface outward, making the cells adopt a drop shape instead of the expected wedge shape. To keep the lateral surface straight, we considered an alternative model in which the cell shape was determined by cell membrane elasticity and endocytosis, and the increased pressure is balanced among the cells. The cellular Potts model simulation succeeded in reproducing the apical constriction, and it also suggested that a too strong apical surface tension might prevent the tissue invagination.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce a novel agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the respective contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism contributing to an increase in migratory speed of the tissue. Model outcomes are validated experimentally using mesendoderm tissue explants.

Competing mechanisms in bacterial invasion of human colon mucus probed with agent-based modeling

The gastrointestinal tract is inhabited by a vast community of microorganisms, termed the gut microbiota. Large colonies can pose a health threat, but the gastrointestinal mucus system protects epithelial cells from microbiota invasion. The human colon features a bilayer of mucus lining. Due to imbalances in intestinal homeostasis, bacteria may successfully penetrate the inner mucus layer, which can lead to severe gut diseases. However, it is hard to tease apart the competing mechanisms that lead to this penetration. To probe the conditions that permit bacteria penetration into the inner mucus layer, we develop an agent-based model consisting of bacteria and an inner mucus layer subject to a constant flux of nutrient fields feeding the bacteria. We find that there are three important variables that determine bacterial invasion: the bacterial reproduction rate, the contact energy between bacteria and mucus, and the rate of bacteria degrading the mucus. Under healthy conditions, all bacteria are naturally eliminated by the constant removal of mucus. In diseased states, imbalances between the rates of bacterial degradation and mucus secretion lead to bacterial invasion at certain junctures. We conduct uncertainty quantification and sensitivity analysis to compare the relative impact between these parameters. The contact energy has the strongest influence on bacterial penetration, which, in combination with bacterial degradation rate and growth rate, greatly accelerates bacterial invasion of the human gut mucus lining. Our findings will serve as predictive indicators for the etiology of intestinal diseases and highlight important considerations when developing gut therapeutics.

Multiscale computational modeling of aortic valve calcification

Calcific aortic valve disease (CAVD) is a common cardiovascular disease that affects millions of people worldwide. The disease is characterized by the formation of calcium nodules on the aortic valve leaflets, which can lead to stenosis and heart failure if left untreated. The pathogenesis of CAVD is still not well understood, but involves several signaling pathways, including the transforming growth factor beta (TGF β ) pathway. In this study, we developed a multiscale computational model for TGF β -stimulated CAVD. The model framework comprises cellular behavior dynamics, subcellular signaling pathways, and tissue-level diffusion fields of pertinent chemical species, where information is shared among different scales. Processes such as endothelial to mesenchymal transition (EndMT), fibrosis, and calcification are incorporated. The results indicate that the majority of myofibroblasts and osteoblast-like cells ultimately die due to lack of nutrients as they become trapped in areas with higher levels of fibrosis or calcification, and they subsequently act as sources for calcium nodules, which contribute to a polydispersed nodule size distribution. Additionally, fibrosis and calcification processes occur more frequently in regions closer to the endothelial layer where the cell activity is higher. Our results provide insights into the mechanisms of CAVD and TGF β signaling and could aid in the development of novel therapeutic approaches for CAVD and other related diseases such as cancer. More broadly, this type of modeling framework can pave the way for unraveling the complexity of biological systems by incorporating several signaling pathways in subcellular models to simulate tissue remodeling in diseases involving cellular mechanobiology.

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce an agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the relative contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism to increase migratory speed of the tissue.

Summary Statement

We present a novel Cellular-Potts model of collective cell migration to investigate the relative roles of cohesotaxis, tissue geometry, and cell intercalation on migration velocity of Xenopus mesendoderm.

Matrix obstructions cause multiscale disruption in collective epithelial migration by suppressing leader cell function

During disease and development, physical changes in extracellular matrix cause jamming, unjamming, and scattering in epithelial migration. However, whether disruptions in matrix topology alter collective cell migration speed and cell-cell coordination remains unclear. We microfabricated substrates with stumps of defined geometry, density, and orientation, which create obstructions for migrating epithelial cells. Here, we show that cells lose their speed and directionality when moving through densely spaced obstructions. Although leader cells are stiffer than follower cells on flat substrates, dense obstructions cause overall cell softening. Through a lattice-based model, we identify cellular protrusions, cell-cell adhesions, and leader-follower communication as key mechanisms for obstruction-sensitive collective cell migration. Our modeling predictions and experimental validations show that cells' obstruction sensitivity requires an optimal balance of cell-cell adhesions and protrusions. Both MDCK (more cohesive) and α-catenin-depleted MCF10A cells were less obstruction sensitive than wild-type MCF10A cells. Together, microscale softening, mesoscale disorder, and macroscale multicellular communication enable epithelial cell populations to sense topological obstructions encountered in challenging environments. Thus, obstruction-sensitivity could define "mechanotype" of cells that collectively migrate yet maintain intercellular communication.

Long-term adherent cell dynamics emerging from energetic and frictional interactions at the interface

Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.

Computational approaches for simulating luminogenesis

Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.

Exact solution for the Anisotropic Ornstein-Uhlenbeck process

Active-Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models also include random noise in particle displacement (a Wiener process), resulting in diffusive motion at short time scales. On the other hand, Ornstein-Uhlenbeck processes apply Langevin dynamics to the particles' velocity and predict motion that is not diffusive at short time scales. Experiments show that migrating cells have gradually varying speeds at intermediate and long time scales, with short-time diffusive behavior. While Ornstein-Uhlenbeck processes can describe the moderate-and long-time speed variation, Active-Matter models for over-damped particles can explain the short-time diffusive behavior. Isotropic models cannot explain both regimes, because short-time diffusion renders instantaneous velocity ill-defined, and prevents the use of dynamical equations that require velocity time-derivatives. On the other hand, both models correctly describe some of the different temporal regimes seen in migrating biological cells and must, in the appropriate limit, yield the same observable predictions. Here we propose and solve analytically an Anisotropic Ornstein-Uhlenbeck process for polarized particles, with Langevin dynamics governing the particle's movement in the polarization direction and a Wiener process governing displacement in the orthogonal direction. Our characterization provides a theoretically robust way to compare movement in dimensionless simulations to movement in experiments in which measurements have meaningful space and time units. We also propose an approach to deal with inevitable finite-precision effects in experiments and simulations.

Supracellular organization confers directionality and mechanical potency to migrating pairs of cardiopharyngeal progenitor cells

Physiological and pathological morphogenetic events involve a wide array of collective movements, suggesting that multicellular arrangements confer biochemical and biomechanical properties contributing to tissue-scale organization. The Ciona cardiopharyngeal progenitors provide the simplest model of collective cell migration, with cohesive bilateral cell pairs polarized along the leader-trailer migration path while moving between the ventral epidermis and trunk endoderm. We use the Cellular Potts Model to computationally probe the distributions of forces consistent with shapes and collective polarity of migrating cell pairs. Combining computational modeling, confocal microscopy, and molecular perturbations, we identify cardiopharyngeal progenitors as the simplest cell collective maintaining supracellular polarity with differential distributions of protrusive forces, cell-matrix adhesion, and myosin-based retraction forces along the leader-trailer axis. 4D simulations and experimental observations suggest that cell-cell communication helps establish a hierarchy to align collective polarity with the direction of migration, as observed with three or more cells in silico and in vivo. Our approach reveals emerging properties of the migrating collective: cell pairs are more persistent, migrating longer distances, and presumably with higher accuracy. Simulations suggest that cell pairs can overcome mechanical resistance of the trunk endoderm more effectively when they are polarized collectively. We propose that polarized supracellular organization of cardiopharyngeal progenitors confers emergent physical properties that determine mechanical interactions with their environment during morphogenesis.

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

Organ morphogenesis is the process of shape acquisition initiated with a small reservoir of undifferentiated cells. In plants, morphogenesis is a complex endeavor that comprises a large number of interacting elements, including mechanical stimuli, biochemical signaling, and genetic prerequisites. Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses. In the last two decades, computational models combined with wet-lab experiments have advanced our understanding of plant organ morphogenesis. Here, we provide a comprehensive review of the most important achievements in the field of computational plant morphodynamics. We present a brief history from the earliest attempts to describe plant forms using algorithmic pattern generation to the evolution of quantitative cell-based models fueled by increasing computational power. We then provide an overview of the most common types of "digital plant" paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics. Finally, we highlight the development of computational frameworks designed to resolve organ shape complexity through integration of mechanical, biochemical, and genetic cues into a quantitative standardized and user-friendly environment.

Modeling oil-water separation with controlled wetting properties

Several oil-water separation techniques have been proposed to improve the capacity of cleaning water. With the technological possibility of producing materials with antagonist wetting behavior, for example, a substrate that repels water and absorbs oil, the understanding of the properties that control this selective capacity has increased with the goal of being used as the mechanism to separate mixed liquids. Besides the experimental advance in this field, less is known from the theoretical side. In this work, we propose a theoretical model to predict the wetting properties of a given substrate and introduce simulations with a four-spin cellular Potts model to study its efficiency in separating water from oil. Our results show that the efficiency of the substrates depends both on the interaction between the liquids and on the wetting behavior of the substrates itself. The water behavior of the droplet composed of both liquids is roughly controlled by the hydrophobicity of the substrate. Predicting the oil behavior, however, is more complex because the substrate being oleophilic does not guarantee that the total amount of oil present on the droplet will be absorbed by the substrate. For both types of substrates considered in this work, pillared and porous with a reservoir, there is always an amount of reminiscent oil on the droplet, which is not absorbed by the substrate due to the interaction with the water and the gas. Both theoretical and numerical models can be easily modified to analyze other types of substrates and liquids.