Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

An entropy-based approach for assessing the directional persistence of cell migration

Cell migration, which is primarily characterized by directional persistence, is essential for the development of normal tissues and organs, as well as for numerous pathological processes. However, there is a lack of simple and efficient tools to analyze the systematic properties of persistence based on cellular trajectory data. Here, we present a novel approach, the entropy of angular distribution , which combines cellular turning dynamics and Shannon entropy to explore the statistical and time-varying properties of persistence that strongly correlate with cellular migration modes. Our results reveal the changes in the persistence of multiple cell lines that are tightly regulated by both intra- and extracellular cues, including Arpin protein, collagen gel/substrate, and physical constraints. Significantly, some previously unreported distinctive details of persistence have also been captured, helping to elucidate how directional persistence is distributed and evolves in different cell populations. The analysis suggests that the entropy of angular distribution-based approach provides a powerful metric for evaluating directional persistence and enables us to better understand the relationships between cellular behaviors and multiscale cues, which also provides some insights into the migration dynamics of cell populations, such as collective cell invasion.

Morphological entropy encodes cellular migration strategies on multiple length scales

Cell migration is crucial for numerous physiological and pathological processes. A cell adapts its morphology, including the overall and nuclear morphology, in response to various cues in complex microenvironments, such as topotaxis and chemotaxis during migration. Thus, the dynamics of cellular morphology can encode migration strategies, from which diverse migration mechanisms can be inferred. However, deciphering the mechanisms behind cell migration encoded in morphology dynamics remains a challenging problem. Here, we present a powerful universal metric, the Cell Morphological Entropy (CME), developed by combining parametric morphological analysis with Shannon entropy. The utility of CME, which accurately quantifies the complex cellular morphology at multiple length scales through the deviation from a perfectly circular shape, is illustrated using a variety of normal and tumor cell lines in different in vitro microenvironments. Our results show how geometric constraints affect the MDA-MB-231 cell nucleus, the emerging interactions of MCF-10A cells migrating on collagen gel, and the critical transition from proliferation to invasion in tumor spheroids. The analysis demonstrates that the CME-based approach provides an effective and physically interpretable tool to measure morphology in real-time across multiple length scales. It provides deeper insight into cell migration and contributes to the understanding of different behavioral modes and collective cell motility in more complex microenvironments.

Subcellular mechano-regulation of cell migration in confined extracellular microenvironment

Cell migration is a highly coordinated cellular event that determines diverse physiological and pathological processes in which the continuous interaction of a migrating cell with neighboring cells or the extracellular matrix is regulated by the physical setting of the extracellular microenvironment. In confined spaces, cell migration occurs differently compared to unconfined open spaces owing to the additional forces that limit cell motility, which create a driving bias for cells to invade the confined space, resulting in a distinct cell motility process compared to what is expected in open spaces. Moreover, cells in confined environments can be subjected to elevated mechanical compression, which causes physical stimuli and activates the damage repair cycle in the cell, including the DNA in the nucleus. Although cells have a self-restoring system to repair damage from the cell membrane to the genetic components of the nucleus, this process may result in genetic and/or epigenetic alterations that can increase the risk of the progression of diverse diseases, such as cancer and immune disorders. Furthermore, there has been a shift in the paradigm of bioengineering from the development of new biomaterials to controlling biophysical cues and fine-tuning cell behaviors to cure damaged/diseased tissues. The external physical cues perceived by cells are transduced along the mechanosensitive machinery, which is further channeled into the nucleus through subcellular molecular linkages of the nucleoskeleton and cytoskeleton or the biochemical translocation of transcription factors. Thus, external cues can directly or indirectly regulate genetic transcriptional processes and nuclear mechanics, ultimately determining cell fate. In this review, we discuss the importance of the biophysical cues, response mechanisms, and mechanical models of cell migration in confined environments. We also discuss the effect of force-dependent deformation of subcellular components, specifically focusing on subnuclear organelles, such as nuclear membranes and chromosomal organization. This review will provide a biophysical perspective on cancer progression and metastasis as well as abnormal cellular proliferation.

Magnetic microrheometry of tumor-relevant stiffness levels and probabilistic quantification of viscoelasticity differences inside 3D cell culture matrices

The progression of breast cancer involves cancer-cell invasions of extracellular matrices. To investigate the progression, 3D cell cultures are widely used along with different types of matrices. Currently, the matrices are often characterized using parallel-plate rheometry for matrix viscoelasticity, or liquid-like viscous and stiffness-related elastic characteristics. The characterization reveals averaged information and sample-to-sample variation, yet, it neglects internal heterogeneity within matrices, experienced by cancer cells in 3D culture. Techniques using optical tweezers and magnetic microrheometry have measured heterogeneity in viscoelasticity in 3D culture. However, there is a lack of probabilistic heterogeneity quantification and cell-size-relevant, microscale-viscoelasticity measurements at breast-tumor tissue stiffness up to ≃10 kPa in Young's modulus. Here, we have advanced methods, for the purpose, which use a magnetic microrheometer that applies forces on magnetic spheres within matrices, and detects the spheres displacements. We present probabilistic heterogeneity quantification using microscale-viscoelasticity measurements in 3D culture matrices at breast-tumor-relevant stiffness levels. Bayesian multilevel modeling was employed to distinguish heterogeneity in viscoelasticity from the effects of experimental design and measurement errors. We report about the heterogeneity of breast-tumor-relevant agarose, GrowDex, GrowDex-collagen and fibrin matrices. The degree of heterogeneity differs for stiffness, and phase angle (i.e. ratio between viscous and elastic characteristics). Concerning stiffness, agarose and GrowDex show the lowest and highest heterogeneity, respectively. Concerning phase angle, fibrin and GrowDex-collagen present the lowest and the highest heterogeneity, respectively. While this heterogeneity information involves softer matrices, probed by ≃30 μm magnetic spheres, we employ larger ≃100 μm spheres to increase magnetic forces and acquire a sufficient displacement signal-to-noise ratio in stiffer matrices. Thus, we show pointwise microscale viscoelasticity measurements within agarose matrices up to Young's moduli of 10 kPa. These results establish methods that combine magnetic microrheometry and Bayesian multilevel modeling for enhanced heterogeneity analysis within 3D culture matrices.

Micromechanical remodeling of the extracellular matrix by invading tumors: anisotropy and heterogeneity

Altered tissue mechanics is an important signature of invasive solid tumors. While the phenomena have been extensively studied by measuring the bulk rheology of the extracellular matrix (ECM) surrounding tumors, micromechanical remodeling at the cellular scale remains poorly understood. By combining holographic optical tweezers and confocal microscopy on in vitro tumor models, we show that the micromechanics of collagen ECM surrounding an invading tumor demonstrate directional anisotropy, spatial heterogeneity and significant variations in time as tumors invade. To test the cellular mechanisms of ECM micromechanical remodeling, we construct a simple computational model and verify its predictions with experiments. We find that collective force generation of a tumor stiffens the ECM and leads to anisotropic local mechanics such that the extension direction is more rigid than the compression direction. ECM degradation by cell-secreted matrix metalloproteinase softens the ECM, and active traction forces from individual disseminated cells re-stiffen the matrix. Together, these results identify plausible biophysical mechanisms responsible for the remodeled ECM micromechanics surrounding an invading tumor.

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.

Nanoscale Tracking Combined with Cell-Scale Microrheology Reveals Stepwise Increases in Force Generated by Cancer Cell Protrusions

In early breast cancer progression, cancer cells invade through a nanoporous basement membrane (BM) as a first key step toward metastasis. This invasion is thought to be mediated by a combination of proteases, which biochemically degrade BM matrix, and physical forces, which mechanically open up holes in the matrix. To date, techniques that quantify cellular forces of BM invasion in 3D culture have been unavailable. Here, we developed cellular-force measurements for breast cancer cell invasion in 3D culture that combine multiple-particle tracking of force-induced BM-matrix displacements at the nanoscale, and magnetic microrheometry of localized matrix mechanics. We find that cancer-cell protrusions exert forces from picoNewtons up to nanoNewtons during invasion. Strikingly, the protrusions extension involves stepwise increases in force, in steps of 0.2 to 0.5 nN exerted from every 30 s to 6 min. Thus, this technique reveals previously unreported dynamics of force generation by invasive protrusions in cancer cells.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

Glycopolymer Engineering of the Cell Surface Changes the Single Cell Migratory Direction and Inhibits the Collective Migration of Cancer Cells

Cancer cell migration is one of the most important processes in cancer metastasis. Metastasis is the major cause of death from most solid tumors; therefore, suppressing cancer cell migration is an important means of reducing cancer mortality. Cell surface engineering can alter the interactions between cells and their microenvironment, thereby offering an effective method of controlling the migration of the cells. This paper reports that modification of the mouse melanoma (B16) cancer cell surface with glycopolymers affects the migration of the cells. Changes in cell morphology, migratory trajectories, and velocity were investigated by time-lapse cell tracking. The data showed that the migration direction is altered and diffusion slows down for modified B16 cells compared to unmodified B16 cells. When modified and unmodified B16 cells were mixed, wound-healing experiments and particle image velocimetry (PIV) analysis showed that the collective migration of unmodified B16 cells was suppressed because of vortexlike motions induced by the modified cells. The work demonstrates the important role of surface properties/modification in cancer cell migration, thereby providing new insights relative to the treatment of cancer metastasis.

Role of RhoC in cancer cell migration

Migration is one of the five major behaviors of cells. Although RhoC-a classic member of the Rho gene family-was first identified in 1985, functional RhoC data have only been widely reported in recent years. Cell migration involves highly complex signaling mechanisms, in which RhoC plays an essential role. Cell migration regulated by RhoC-of which the most well-known function is its role in cancer metastasis-has been widely reported in breast, gastric, colon, bladder, prostate, lung, pancreatic, liver, and other cancers. Our review describes the role of RhoC in various types of cell migration. The classic two-dimensional cell migration cycle constitutes cell polarization, adhesion regulation, cell contraction and tail retraction, most of which are modulated by RhoC. In the three-dimensional cell migration model, amoeboid migration is the most classic and well-studied model. Here, RhoC modulates the formation of membrane vesicles by regulating myosin II, thereby affecting the rate and persistence of amoeba-like migration. To the best of our knowledge, this review is the first to describe the role of RhoC in all cell migration processes. We believe that understanding the detail of RhoC-regulated migration processes will help us better comprehend the mechanism of cancer metastasis. This will contribute to the study of anti-metastatic treatment approaches, aiding in the identification of new intervention targets for therapeutic or genetic transformational purposes.

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.

A computational framework for modeling cell-matrix interactions in soft biological tissues

Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Shannon entropy for time-varying persistence of cell migration

Cell migration, which can be significantly affected by intracellular signaling pathways and extracellular matrix, plays a crucial role in many physiological and pathological processes. Cell migration is typically modeled as a persistent random walk, which depends on two critical motility parameters, i.e., migration speed and persistence time. It is generally very challenging to efficiently and accurately quantify the migration dynamics from noisy experimental data. Here, we introduce the normalized Shannon entropy (SE) based on the FPS of cellular velocity autocovariance function to quantify migration dynamics. The SE introduced here possesses a similar physical interpretation as the Gibbs entropy for thermal systems in that SE naturally reflects the degree of order or randomness of cellular migration, attaining the maximal value of unity for purely diffusive migration (i.e., SE = 1 for the most "random" dynamics) and the minimal value of 0 for purely ballistic dynamics (i.e., SE = 0 for the most "ordered" dynamics). We also find that SE is strongly correlated with the migration persistence but is less sensitive to the migration speed. Moreover, we introduce the time-varying SE based on the WPS of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which typically results from complex and time-varying intra- or extracellular mechanisms. We employ our approach to analyze experimental data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the SE and wavelet transform (i.e., SE-based approach) offers a simple and efficient tool to quantify cell migration dynamics in complex microenvironment.

Dynamically Re-Organized Collagen Fiber Bundles Transmit Mechanical Signals and Induce Strongly Correlated Cell Migration and Self-Organization

Correlated cell migration in fibrous extracellular matrix (ECM) is important in many biological processes. During migration, cells can remodel the ECM, leading to the formation of mesoscale structures such as fiber bundles. However, how such mesoscale structures regulate correlated single-cells migration remains to be elucidated. Here, using a quasi-3D in vitro model, we investigate how collagen fiber bundles are dynamically re-organized and guide cell migration. By combining laser ablation technique with 3D tracking and active-particle simulations, we definitively show that only the re-organized fiber bundles that carry significant tensile forces can guide strongly correlated cell migration, providing for the first time a direct experimental evidence supporting that matrix-transmitted long-range forces can regulate cell migration and self-organization. This force regulation mechanism can provide new insights for studies on cellular dynamics, fabrication or selection of biomedical materials in tissue repairing, and many other biomedical applications.

Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction

Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.

Evaluation of Cell's Passability in the ECM Network

The microstructure of the extracellular matrix (ECM) plays a key role in affecting cell migration, especially nonproteolytic migration. It is difficult, however, to measure some properties of the ECM, such as stiffness and the passability for cell migration. On the basis of a network model of collagen fiber in the ECM, which has been well applied to simulate mechanical behaviors such as the stress-strain relationship, damage, and failure, we proposed a series of methods to study the microstructural properties containing pore size and pore stiffness and to search for the possible migration paths for cells. Finally, with a given criterion, we quantitatively evaluated the passability of the ECM network for cell migration. The fiber network model with a microstructure and the analysis method presented in this study further our understanding of and ability to evaluate the properties of an ECM network.

Simulating flow induced migration in vascular remodelling

Shear stress induces directed endothelial cell (EC) migration in blood vessels leading to vessel diameter increase and induction of vascular maturation. Other factors, such as EC elongation and interaction between ECs and non-vascular areas are also important. Computational models have previously been used to study collective cell migration. These models can be used to predict EC migration and its effect on vascular remodelling during embryogenesis. We combined live time-lapse imaging of the remodelling vasculature of the quail embryo yolk sac with flow quantification using a combination of micro-Particle Image Velocimetry and computational fluid dynamics. We then used the flow and remodelling data to inform a model of EC migration during remodelling. To obtain the relation between shear stress and velocity in vitro for EC cells, we developed a flow chamber to assess how confluent sheets of ECs migrate in response to shear stress. Using these data as an input, we developed a multiphase, self-propelled particles (SPP) model where individual agents are driven to migrate based on the level of shear stress while maintaining appropriate spatial relationship to nearby agents. These agents elongate, interact with each other, and with avascular agents at each time-step of the model. We compared predicted vascular shape to real vascular shape after 4 hours from our time-lapse movies and performed sensitivity analysis on the various model parameters. Our model shows that shear stress has the largest effect on the remodelling process. Importantly, however, elongation played an especially important part in remodelling. This model provides a powerful tool to study the input of different biological processes on remodelling.

Shear stress is known to play a leading role in endothelial cell (EC) migration and hence, vascular remodelling. Vascular remodelling is, however, more complicated than only EC migration. To achieve a better understanding of this process, we developed a computational model in which, shear stress mediated EC migration has the leading role and other factors, such as avascular regions and EC elongation, are also accounted for. We have tested this model for different vessel shapes during remodelling and could study the role that each of these factors play in remodelling. This model gives us the possibility of addition of other factors such as biochemical signals and angiogenesis which will help us in the study of vascular remodelling in both development and disease.

Geometric Dependence of 3D Collective Cancer Invasion

Metastasis of mesenchymal tumor cells is traditionally considered as a single-cell process. Here, we report an emergent collective phenomenon in which the dissemination rate of mesenchymal breast cancer cells from three-dimensional tumors depends on the tumor geometry. Combining experimental measurements and computational modeling, we demonstrate that the collective dynamics is coordinated by the mechanical feedback between individual cells and their surrounding extracellular matrix (ECM). We find the tissue-like fibrous ECM supports long-range physical interactions between cells, which turn geometric cues into regulated cell dissemination dynamics. Our results suggest that migrating cells in three-dimensional ECM represent a distinct class of an active particle system in which the collective dynamics is governed by the remodeling of the environment rather than direct particle-particle interactions.