An Agent-Based Discrete Collagen Fiber Network Model of Dynamic Traction Force-Induced Remodeling

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 - 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Click chemistry functionalization of self-assembling peptide hydrogels

Self-assembling peptide (SAP) hydrogels provide a fibrous microenvironment to cells while also giving users control of biochemical and mechanical cues. Previously, biochemical cues were introduced by physically mixing them with SAPs prior to hydrogel assembly, or by incorporating them into the SAP sequence during peptide synthesis, which limited flexibility and increased costs. To circumvent these limitations, we developed "Click SAPs," a novel formulation that can be easily functionalized via click chemistry thiol-ene reaction. Due to its high cytocompatibility, the thiol-ene click reaction is currently used to crosslink and functionalize other types of polymeric hydrogels. In this study, we developed a click chemistry compatible SAP platform by addition of a modified lysine (lysine-alloc) to the SAP sequence, enabling effective coupling of thiol-containing molecules to the SAP hydrogel network. We demonstrate the flexibility of this approach by incorporating a fluorescent dye, a cellular adhesion peptide, and a matrix metalloproteinase-sensitive biosensor using the thiol-ene reaction in 3D Click SAPs. Using atomic force microscopy, we demonstrate that Click SAPs retain the ability to self-assemble into fibers, similar to previous systems. Additionally, a range of physiologically relevant stiffnesses can be achieved by adjusting SAP concentration. Encapsulated cells maintain high viability in Click SAPs and can interact with adhesion peptides and a matrix metalloproteinase biosensor, demonstrating that incorporated molecules retain their biological activity. The Click SAP platform supports easier functionalization with a wider array of bioactive molecules and enables new investigations with temporal and spatial control of the cellular microenvironment.

Unravelling cell migration: defining movement from the cell surface

Cell motility is essential for life and development. Unfortunately, cell migration is also linked to several pathological processes, such as cancer metastasis. Cells' ability to migrate relies on many actors. Cells change their migratory strategy based on their phenotype and the properties of the surrounding microenvironment. Cell migration is, therefore, an extremely complex phenomenon. Researchers have investigated cell motility for more than a century. Recent discoveries have uncovered some of the mysteries associated with the mechanisms involved in cell migration, such as intracellular signaling and cell mechanics. These findings involve different players, including transmembrane receptors, adhesive complexes, cytoskeletal components , the nucleus, and the extracellular matrix. This review aims to give a global overview of our current understanding of cell migration.

Collagen gel contraction assays: From modelling wound healing to quantifying cellular interactions with three-dimensional extracellular matrices

Cells respond to and actively remodel the extracellular matrix (ECM). The dynamic and bidirectional interaction between cells and ECM, especially their mechanical interactions, has been found to play an essential role in triggering a series of complex biochemical and biomechanical signal pathways and in regulating cellular functions and behaviours. The collagen gel contraction assay (CGCA) is a widely used method to investigate cell-ECM interactions in 3D environments and provides a mechanically associated readout reflecting 3D cellular contractility. In this review, we summarize various versions of CGCA, with an emphasis on recent high-throughput and low-consumption CGCA techniques. More importantly, we focus on the technique of force monitoring during the contraction of collagen gel, which provides a quantitative characterization of the overall forces generated by all the resident cells in the collagen hydrogel. Accordingly, we present recent biological applications of the CGCA, which have expanded from the initial wound healing model to other studies concerning cell-ECM interactions, including fibrosis, cancer, tissue repair and the preparation of biomimetic microtissues.

Long-range mechanical coupling of cells in 3D fibrin gels

When seeded in fibrous gels, pairs of cells or cell aggregates can induce bands of deformed gel, extending to surprisingly long distances in the intercellular medium. The formation of bands has been previously shown and studied in collagen systems. In this study, we strive to further our understanding of this fundamental mechanical mechanism in fibrin, a key element in wound healing and angiogenesis processes. We embedded fibroblast cells in 3D fibrin gels, and monitored band formation by real-time confocal microscopy. Quantitative dynamic analysis of band formation revealed a gradual increase in fiber density and alignment between pairs of cells. Such intercellular bands extended into a large-scale network of mechanically connected cells, in which the connected cells exhibited a more spread morphology than the isolated cells. Moreover, computational modeling demonstrated that the direction of cell-induced force triggering band formation can be applied in a wide range of angles relative to a neighboring cell. Our findings indicate that long-range mechanical coupling between cells is an important mechanism in regulating multicellular processes in reconstituted fibrin gels. As such, it should motivate exploration of this mechanism in studies in vivo, in wound healing or angiogenesis, in which fibrin is contracted by fibroblast cells.

Force chains in cell-cell mechanical communication

Force chains (FCs) are a key determinant of the micromechanical properties and behaviour of heterogeneous materials, such as granular systems. However, less is known about FCs in fibrous materials, such as the networks composing the extracellular matrix (ECM) of biological systems. Using a finite-element computational model, we simulated the contraction of a single cell and two nearby cells embedded in two-dimensional fibrous elastic networks and analysed the tensile FCs that developed in the ECM. The role of ECM nonlinear elasticity on FC formation was evaluated by considering linear and nonlinear, i.e. exhibiting 'buckling' and/or 'strain-stiffening', stress-strain curves. The effect of the degree of cell contraction and network coordination value was assessed. We found that nonlinear elasticity of the ECM fibres influenced the structure of the FCs, facilitating the transition towards more distinct chains that were less branched and more radially oriented than the chains formed in linear elastic networks. When two neighbouring cells contract, a larger number of FCs bridged between the cells in nonlinear networks, and these chains had a larger effective rigidity than the chains that did not reach a neighbouring cell. These results suggest that FCs function as a route for mechanical communication between distant cells and highlight the contribution of ECM fibre nonlinear elasticity to the formation of FCs.

Nonlinear Elasticity of the ECM Fibers Facilitates Efficient Intercellular Communication

Biological cells embedded in fibrous matrices have been observed to form intercellular bands of dense and aligned fibers through which they mechanically interact over long distances. Such matrix-mediated cellular interactions have been shown to regulate various biological processes. This study aimed to explore the effects of elastic nonlinearity of the fibers contained in the extracellular matrix (ECM) on the transmission of mechanical loads between contracting cells. Based on our biological experiments, we developed a finite-element model of two contracting cells embedded within a fibrous network. The individual fibers were modeled as showing linear elasticity, compression microbuckling, tension stiffening, or both of the latter two. Fiber compression buckling resulted in smaller loads in the ECM, which were primarily directed toward the neighboring cell. These loads decreased with increasing cell-to-cell distance; when cells were >9 cell diameters apart, no such intercellular interaction was observed. Tension stiffening further contributed to directing the loads toward the neighboring cell, though to a smaller extent. The contraction of two neighboring cells resulted in mutual attraction forces, which were considerably increased by tension stiffening and decayed with increasing cell-to-cell distances. Nonlinear elasticity contributed also to the onset of force polarity on the cell boundaries, manifested by larger contractile forces pointing toward the neighboring cell. The density and alignment of the fibers within the intercellular band were greater when fibers buckled under compression, with tension stiffening further contributing to this structural remodeling. Although previous studies have established the role of the ECM nonlinear mechanical behavior in increasing the range of force transmission, our model demonstrates the contribution of nonlinear elasticity of biological gels to directional and efficient mechanical signal transfer between distant cells, and rehighlights the importance of using fibrous gels in experimental settings for facilitating intercellular communication. VIDEO ABSTRACT.