Predicting Confined 1D Cell Migration from Parameters Calibrated to a 2D Motor-Clutch Model

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

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.

Optimal cell traction forces in a generalized motor-clutch model

Cells exert forces on mechanically compliant environments to sense stiffness, migrate, and remodel tissue. Cells can sense environmental stiffness via myosin-generated pulling forces acting on F-actin, which is in turn mechanically coupled to the environment via adhesive proteins, akin to a clutch in a drivetrain. In this "motor-clutch" framework, the force transmitted depends on the complex interplay of motor, clutch, and environmental properties. Previous mean-field analysis of the motor-clutch model identified the conditions for optimal stiffness for maximal force transmission via a dimensionless number that combines motor-clutch parameters. However, in this and other previous mean-field analyses, the motor-clutch system is assumed to have balanced motors and clutches and did not consider force-dependent clutch reinforcement and catch bond behavior. Here, we generalize the motor-clutch analytical framework to include imbalanced motor-clutch regimes, with clutch reinforcement and catch bonding, and investigate optimality with respect to all parameters. We found that traction force is strongly influenced by clutch stiffness, and we discovered an optimal clutch stiffness that maximizes traction force, suggesting that cells could tune their clutch mechanical properties to perform a specific function. The results provide guidance for maximizing the accuracy of cell-generated force measurements via molecular tension sensors by designing their mechanosensitive linker peptide to be as stiff as possible. In addition, we found that, on rigid substrates, the mean-field analysis identifies optimal motor properties, suggesting that cells could regulate their myosin repertoire and activity to maximize force transmission. Finally, we found that clutch reinforcement shifts the optimum substrate stiffness to larger values, whereas the optimum substrate stiffness is insensitive to clutch catch bond properties. Overall, our work reveals novel features of the motor-clutch model that can affect the design of molecular tension sensors and provide a generalized analytical framework for predicting and controlling cell adhesion and migration in immunotherapy and cancer.

Multiscale models of integrins and cellular adhesions

Computational models of integrin-based adhesion complexes have revealed important insights into the mechanisms by which cells establish connections with their external environment. However, how changes in conformation and function of individual adhesion proteins regulate the dynamics of whole adhesion complexes remains largely elusive. This is because of the large separation in time and length scales between the dynamics of individual adhesion proteins (nanoseconds and nanometers) and the emergent dynamics of the whole adhesion complex (seconds and micrometers), and the limitations of molecular simulation approaches in extracting accurate free energies, conformational transitions, reaction mechanisms, and kinetic rates, that can inform mechanisms at the larger scales. In this review, we discuss models of integrin-based adhesion complexes and highlight their main findings regarding: (i) the conformational transitions of integrins at the molecular and macromolecular scales and (ii) the molecular clutch mechanism at the mesoscale. Lastly, we present unanswered questions in the field of modeling adhesions and propose new ideas for future exciting modeling opportunities.

Challenges in glioblastoma research: focus on the tumor microenvironment

Glioblastoma (GBM) is the most deadly type of malignant brain tumor, despite extensive molecular analyses of GBM cells. In recent years, the tumor microenvironment (TME) has been recognized as an important player and therapeutic target in GBM. However, there is a need for a full and integrated understanding of the different cellular and molecular components involved in the GBM TME and their interactions for the development of more efficient therapies. In this review, we provide a comprehensive report of the GBM TME, which assembles the contributions of physicians and translational researchers working on brain tumor pathology and therapy in France. We propose a holistic view of the subject by delineating the specific features of the GBM TME at the cellular, molecular, and therapeutic levels.

A molecular clock controls periodically driven cell migration in confined spaces

Navigation through a dense, physically confining extracellular matrix is common in invasive cell spread and tissue reorganization but is still poorly understood. Here, we show that this migration is mediated by cyclic changes in the activity of a small GTPase RhoA, which is dependent on the oscillatory changes in the activity and abundance of the RhoA guanine nucleotide exchange factor, GEF-H1, and triggered by a persistent increase in the intracellular Ca²⁺ levels. We show that the molecular clock driving these cyclic changes is mediated by two coupled negative feedback loops, dependent on the microtubule dynamics, with a frequency that can be experimentally modulated based on a predictive mathematical model. We further demonstrate that an increasing frequency of the clock translates into a faster cell migration within physically confining spaces. This work lays the foundation for a better understanding of the molecular mechanisms dynamically driving cell migration in complex environments.

Molecular Mechanisms and Clinical Challenges of Glioma Invasion

Glioma is the most common primary brain tumor, and its prognosis is poor. Glioma cells are highly invasive to the brain parenchyma. It is difficult to achieve complete resection due to the nature of the brain tissue, and tumors that invade the parenchyma often recur. The invasiveness of tumor cells has been studied from various aspects, and the related molecular mechanisms are gradually becoming clear. Cell adhesion factors and extracellular matrix factors have a strong influence on glioma invasion. The molecular mechanisms that enhance the invasiveness of glioma stem cells, which have been investigated in recent years, have also been clarified. In addition, it has been discussed from both basic and clinical perspectives that current therapies can alter the invasiveness of tumors, and there is a need to develop therapeutic approaches to glioma invasion in the future. In this review, we will summarize the factors that influence the invasiveness of glioma based on the environment of tumor cells and tissues, and describe the impact of the treatment of glioma on invasion in terms of molecular biology, and the novel therapies for invasion that are currently being developed.

Modeling and simulation of cell migration on the basis of force equilibrium

To study cell behavior, we developed a cell model to simulate cell movements and the interacting forces among cells and between cells and obstacles. The developed model simulates several cells simultaneously and examines correlations among characteristic parameters between cells and substrates during migration. We modified Odde's model to develop fundamental model, applied Gillespie's stochastic algorithm to design time during in the migration simulation, and employed Keren's membrane theory to analyze the equilibrium at the leading edges. Thus, the proposed model can analyze stresses due to substrate, the intracellular body, and the external interaction between cells and obstacles. Simulation results indicate that cell-cell interaction depends on the equilibrium between the forces at the leading edge of the membrane, namely the cell-substrate interaction force, cell-cell interaction forces, and the cell membrane force. These results also indicate that the migration direction is dependent on the resultant forces. The membrane force and substrate force directions are "low correlation," and the polymerization rate exhibits "little correlative" with the migration direction. We propose a modified cell migration model for simulating allocation and interaction among multiple cells. This model helps indicate the weightings of characteristic parameters that affect the cell migration direction and velocity.

Effects of substrate stiffness on mast cell migration

Mast cells (MCs) play important roles in multiple pathologies, including fibrosis; however, their behaviors in different extracellular matrix (ECM) environments have not been fully elucidated. Accordingly, in this study, the migration of MCs on substrates with different stiffnesses was investigated using time-lapse video microscopy. Our results showed that MCs could appear in round, spindle, and star-like shapes; spindle-shaped cells accounted for 80-90 % of the total observed cells. The migration speed of round cells was significantly lower than that of cells with other shapes. Interestingly, spindle-shaped MCs migrated in a jiggling and wiggling motion between protrusions. The persistence index of MC migration was slightly higher on stiffer substrates. Moreover, we found that there was an intermediate optimal stiffness at which the migration efficiency was the highest. These findings may help to improve our understanding of MC-induced pathologies and the roles of MC migration in the immune system.

The role of vimentin-nuclear interactions in persistent cell motility through confined spaces

The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is composed of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. Here, we develop a minimal model of a cell moving through a microchannel that incorporates explicit effects of actin and vimentin and implicit effects of microtubules. Specifically, the model consists of a cell with an actomyosin cortex and a deformable cell nucleus and mechanical linkages between the two. By decreasing the amount of vimentin, we find that the cell speed increases for vimentin-null cells compared to cells with vimentin. The loss of vimentin increases nuclear deformation and alters nuclear positioning in the cell. Assuming nuclear positioning is a read-out for cell polarity, we propose a new polarity mechanism which couples cell directional motion with cytoskeletal strength and nuclear positioning and captures the abnormally persistent motion of vimentin-null cells, as observed in experiments. The enhanced persistence indicates that the vimentin-null cells are more controlled by the confinement and so less autonomous, relying more heavily on external cues than their wild-type counterparts. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial-mesenchymal transition.

Recursive feedback between matrix dissipation and chemo-mechanical signaling drives oscillatory growth of cancer cell invadopodia

Most extracellular matrices (ECMs) are known to be dissipative, exhibiting viscoelastic and often plastic behaviors. However, the influence of dissipation, in particular mechanical plasticity in 3D confining microenvironments, on cell motility is not clear. In this study, we develop a chemo-mechanical model for dynamics of invadopodia, the protrusive structures that cancer cells use to facilitate invasion, by considering myosin recruitment, actin polymerization, matrix deformation, and mechano-sensitive signaling pathways. We demonstrate that matrix dissipation facilitates invadopodia growth by softening ECMs over repeated cycles, during which plastic deformation accumulates via cyclic ratcheting. Our model reveals that distinct protrusion patterns, oscillatory or monotonic, emerge from the interplay of timescales for polymerization-associated extension and myosin recruitment dynamics. Our model predicts the changes in invadopodia dynamics upon inhibition of myosin, adhesions, and the Rho-Rho-associated kinase (ROCK) pathway. Altogether, our work highlights the role of matrix plasticity in invadopodia dynamics and can help design dissipative biomaterials to modulate cancer cell motility.

Mechanisms of invasion in glioblastoma

PURPOSE OF REVIEW

This review provides an overview of recent updates in understanding the mechanisms by which glioblastoma cells interact with their cellular and molecular partners within the microenvironment.

RECENT FINDINGS

We have now a better knowledge of the cell populations involved in Glioblastoma (GBM) invasion. Recent works discovered the role of new molecular players in GBM invasion, and, most importantly, better models are emerging which better recapitulate GBM invasion.

SUMMARY

Invasive properties of glioblastoma make complete surgical resection impossible and highly invasive cells are responsible for tumor recurrence. In this review, we focus on recent updates describing how invasive cells progress in the surrounding tissue along brain structures. We also provide an overview of the current knowledge on key cells and molecular players within the microenvironment that contribute to the invasive process. VIDEO ABSTRACT.

Adhesion strength and contractility enable metastatic cells to become adurotactic

Significant changes in cell stiffness, contractility, and adhesion, i.e., mechanotype, are observed during a variety of biological processes. Whether cell mechanics merely change as a side effect of or driver for biological processes is still unclear. Here, we sort genotypically similar metastatic cancer cells into strongly adherent (SA) versus weakly adherent (WA) phenotypes to study how contractility and adhesion differences alter the ability of cells to sense and respond to gradients in material stiffness. We observe that SA cells migrate up a stiffness gradient, or durotax, while WA cells largely ignore the gradient, i.e., adurotax. Biophysical modeling and experimental validation suggest that differences in cell migration and durotaxis between weakly and strongly adherent cells are driven by differences in intra-cellular actomyosin activity. These results provide a direct relationship between cell phenotype and durotaxis and suggest how, unlike other senescent cells, metastatic cancer cells navigate against stiffness gradients.

Stick-slip model for actin-driven cell protrusions, cell polarization, and crawling

Cell crawling requires the generation of intracellular forces by the cytoskeleton and their transmission to an extracellular substrate through specific adhesion molecules. Crawling cells show many features of excitable systems, such as spontaneous symmetry breaking and crawling in the absence of external cues, and periodic and propagating waves of activity. Mechanical instabilities in the active cytoskeleton network and feedback loops in the biochemical network of activators and repressors of cytoskeleton dynamics have been invoked to explain these dynamical features. Here, I show that the interplay between the dynamics of cell-substrate adhesion and linear cellular mechanics is sufficient to reproduce many nonlinear dynamical patterns observed in spreading and crawling cells. Using an analytical formalism of the molecular clutch model of cell adhesion, regulated by local mechanical forces, I show that cellular traction forces exhibit stick-slip dynamics resulting in periodic waves of protrusion/retraction and propagating waves along the cell edge. This can explain spontaneous symmetry breaking and polarization of spreading cells, leading to steady crawling or bipedal motion, and bistability, where persistent cell motion requires a sufficiently strong transient external stimulus. The model also highlights the role of membrane tension in providing the long-range mechanical communication across the cell required for symmetry breaking.