Dynamic cellular finite-element method for modelling large-scale cell migration and proliferation under the control of mechanical and biochemical cues: a study of re-epithelialization

A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions

In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction-diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface) dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape deformation of the cell during migration. Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic development to cancer invasion. Experimental, theoretical and computational studies have been key to elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques allow for detailed experimental measurements of cell migration pathways, while, on the other, computational approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface mechanobiochemical modelling approach presented in this work, set premises to study single cell migration through complex non-isotropic environments in two- and three-space dimensions.

Dynamic cluster field modeling of collective chemotaxis

Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged experimental, theoretical and computational scientists because cells can sense very small chemoattractant gradients that are tightly controlled by cell-cell interactions and the regulation of the chemoattractant distribution by the cells. Computational models of collective cell migration that offer a high-fidelity resolution of the cell motion and chemoattractant dynamics in the extracellular space have been limited to a small number of cells. Here, we present Dynamic cluster field modeling (DCF), a novel computational method that enables simulations of collective chemotaxis of cellular systems with O ( 1000 ) cells and high-resolution transport dynamics of the chemoattractant in the time-evolving extracellular space. We illustrate the efficiency and predictive capabilities of our approach by comparing our numerical simulations with experiments in multiple scenarios that involve chemoattractant secretion and uptake by the migrating cells, cell migration in confined spaces, regulation of the attractant distribution by cell motion, and interactions of the chemoattractant with an enzyme. The proposed algorithm opens new opportunities to address outstanding problems that involve collective cell migration in the central nervous system, immune response and cancer metastasis.

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.

Bridging systems biology and tissue engineering: Unleashing the full potential of complex 3D in vitro tissue models of disease

Rapid advances in tissue engineering have resulted in more complex and physiologically relevant 3D in vitro tissue models with applications in fundamental biology and therapeutic development. However, the complexity provided by these models is often not leveraged fully due to the reductionist methods used to analyze them. Computational and mathematical models developed in the field of systems biology can address this issue. Yet, traditional systems biology has been mostly applied to simpler in vitro models with little physiological relevance and limited cellular complexity. Therefore, integrating these two inherently interdisciplinary fields can result in new insights and move both disciplines forward. In this review, we provide a systematic overview of how systems biology has been integrated with 3D in vitro tissue models and discuss key application areas where the synergies between both fields have led to important advances with potential translational impact. We then outline key directions for future research and discuss a framework for further integration between fields.

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.

Physical confinement and cell proximity increase cell migration rates and invasiveness: A mathematical model of cancer cell invasion through flexible channels

Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves 12% faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion.

Agent-Based Modeling of Microbial Communities

Microbial communities are complex living systems that populate the planet with diverse functions and are increasingly harnessed for practical human needs. To deepen the fundamental understanding of their organization and functioning as well as to facilitate their engineering for applications, mathematical modeling has played an increasingly important role. Agent-based models represent a class of powerful quantitative frameworks for investigating microbial communities because of their individualistic nature in describing cells, mechanistic characterization of molecular and cellular processes, and intrinsic ability to produce emergent system properties. This review presents a comprehensive overview of recent advances in agent-based modeling of microbial communities. It surveys the state-of-the-art algorithms employed to simulate intracellular biomolecular events, single-cell behaviors, intercellular interactions, and interactions between cells and their environments that collectively serve as the driving forces of community behaviors. It also highlights three lines of applications of agent-based modeling, namely, the elucidation of microbial range expansion and colony ecology, the design of synthetic gene circuits and microbial populations for desired behaviors, and the characterization of biofilm formation and dispersal. The review concludes with a discussion of existing challenges, including the computational cost of the modeling, and potential mitigation strategies.

Cell-substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

During the process of tissue formation and regeneration, cells migrate collectively while remaining connected through intercellular adhesions. However, the roles of cell-substrate and cell-cell mechanical interactions in regulating collective cell migration are still unclear. In this study, we employ a newly developed finite element cellular model to study collective cell migration by exploring the effects of mechanical feedback between cell and substrate and mechanical signal transmission between adjacent cells. Our viscoelastic model of cells consists many triangular elements and is of high resolution. Cadherin adhesion between cells is modeled explicitly as linear springs at subcellular level. In addition, we incorporate a mechano-chemical feedback loop between cell-substrate mechanics and Rac-mediated cell protrusion. Our model can reproduce a number of experimentally observed patterns of collective cell migration during wound healing, including cell migration persistence, separation distance between cell pairs and migration direction. Moreover, we demonstrate that cell protrusion determined by the cell-substrate mechanics plays an important role in guiding persistent and oriented collective cell migration. Furthermore, this guidance cue can be maintained and transmitted to submarginal cells of long distance through intercellular adhesions. Our study illustrates that our finite element cellular model can be employed to study broad problems of complex tissue in dynamic changes at subcellular level.

Predictive Approach Identifies Molecular Targets and Interventions to Restore Angiogenesis in Wounds With Delayed Healing

Impaired angiogenesis is a hallmark of wounds with delayed healing, and currently used therapies to restore angiogenesis have limited efficacy. Here, we employ a computational simulation-based approach to identify influential molecular and cellular processes, as well as protein targets, whose modulation may stimulate angiogenesis in wounds. We developed a mathematical model that captures the time courses for platelets, 9 cell types, 29 proteins, and oxygen, which are involved in inflammation, proliferation, and angiogenesis during wound healing. We validated our model using previously published experimental data. By performing global sensitivity analysis on thousands of simulated wound-healing scenarios, we identified six processes (among the 133 modeled in total) whose modulation may improve angiogenesis in wounds. By simulating knockouts of 25 modeled proteins and by simulating different wound-oxygenation levels, we identified four proteins [namely, transforming growth factor (TGF)-β, vascular endothelial growth factor (VEGF), fibroblast growth factor-2 (FGF-2), and angiopoietin-2 (ANG-2)], as well as oxygen, as therapeutic targets for stimulating angiogenesis in wounds. Our modeling results indicated that simultaneous inhibition of TGF-β and supplementation of either FGF-2 or ANG-2 could be more effective in stimulating wound angiogenesis than the modulation of either protein alone. Our findings suggest experimentally testable intervention strategies to restore angiogenesis in wounds with delayed healing.

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities such as restructuring of extracellular matrix (ECM), stress and force distribution profiles, and reorganization of the cytoskeleton. Therefore, the phenomenon could be understood by an in-depth study of cells' behavior determinants, including but not limited to mechanical cues from the environment and from fellow "travelers". This review article aims to cover the recent development of experimental and computational methods for studying the biomechanics of collective cell migration during cancer progression and invasion. We also summarized the tested hypotheses regarding the mechanism underlying collective cell migration enabled by these methods. Together, the paper enables a broad overview on the methods and tools currently available to unravel the biophysical mechanisms pertinent to cell collective migration as well as providing perspectives on future development toward eventually deciphering the key mechanisms behind the most lethal feature of cancer.

Methods of Micropatterning and Manipulation of Cells for Biomedical Applications

Micropatterning and manipulation of mammalian and bacterial cells are important in biomedical studies to perform in vitro assays and to evaluate biochemical processes accurately, establishing the basis for implementing biomedical microelectromechanical systems (bioMEMS), point-of-care (POC) devices, or organs-on-chips (OOC), which impact on neurological, oncological, dermatologic, or tissue engineering issues as part of personalized medicine. Cell patterning represents a crucial step in fundamental and applied biological studies in vitro, hence today there are a myriad of materials and techniques that allow one to immobilize and manipulate cells, imitating the 3D in vivo milieu. This review focuses on current physical cell patterning, plus chemical and a combination of them both that utilizes different materials and cutting-edge micro-nanofabrication methodologies.