On the adhesion-velocity relation and length adaptation of motile cells on stepped fibronectin lanes

Mesenchymal cell migration on one-dimensional micropatterns

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.

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.

Geometry-Sensitive Protrusion Growth Directs Confined Cell Migration

The migratory dynamics of cells can be influenced by the complex microenvironment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their microenvironment. Here, we propose a biophysical mechanism for a geometry-dependent coupling between cellular protrusions and the nucleus that leads to directed migration. We apply our model to geometry-guided cell migration to obtain insights into the origin of directed migration on asymmetric adhesive micropatterns and the polarization enhancement of cells observed under strong confinement. Remarkably, for cells that can choose between channels of different size, our model predicts an intricate dependence for cellular decision making as a function of the two channel widths, which we confirm experimentally.

The senescent mesothelial matrix accentuates colonization by ovarian cancer cells

Ovarian cancer is amongst the most morbid of gynecological malignancies due to its diagnosis at an advanced stage, a transcoelomic mode of metastasis, and rapid transition to chemotherapeutic resistance. Like all other malignancies, the progression of ovarian cancer may be interpreted as an emergent outcome of the conflict between metastasizing cancer cells and the natural defense mounted by microenvironmental barriers to such migration. Here, we asked whether senescence in coelom-lining mesothelia, brought about by drug exposure, affects their interaction with disseminated ovarian cancer cells. We observed that cancer cells adhered faster on senescent human and murine mesothelial monolayers than on non-senescent controls. Time-lapse epifluorescence microscopy showed that mesothelial cells were cleared by a host of cancer cells that surrounded the former, even under sub-confluent conditions. A multiscale computational model predicted that such colocalized mesothelial clearance under sub-confluence requires greater adhesion between cancer cells and senescent mesothelia. Consistent with the prediction, we observed that senescent mesothelia expressed an extracellular matrix with higher levels of fibronectin, laminins and hyaluronan than non-senescent controls. On senescent matrix, cancer cells adhered more efficiently, spread better, and moved faster and persistently, aiding the spread of cancer. Inhibition assays using RGD cyclopeptides suggested the adhesion was predominantly contributed by fibronectin and laminin. These findings led us to propose that the senescence-associated matrisomal phenotype of peritoneal barriers enhances the colonization of invading ovarian cancer cells contributing to the metastatic burden associated with the disease.

Polarity and mixed-mode oscillations may underlie different patterns of cellular migration

In mesenchymal cell motility, several migration patterns have been observed, including directional, exploratory and stationary. Two key members of the Rho-family of GTPases, Rac and Rho, along with an adaptor protein called paxillin, have been particularly implicated in the formation of such migration patterns and in regulating adhesion dynamics. Together, they form a key regulatory network that involves the mutual inhibition exerted by Rac and Rho on each other and the promotion of Rac activation by phosphorylated paxillin. Although this interaction is sufficient in generating wave-pinning that underscores cellular polarization comprised of cellular front (high active Rac) and back (high active Rho), it remains unclear how they interact collectively to induce other modes of migration detected in Chinese hamster Ovary (CHO-K1) cells. We previously developed a six-variable (6V) reaction-diffusion model describing the interactions of these three proteins (in their active/phosphorylated and inactive/unphosphorylated forms) along with other auxiliary proteins, to decipher their role in generating wave-pinning. In this study, we explored, through computational modeling and image analysis, how differences in timescales within this molecular network can potentially produce the migration patterns in CHO-K1 cells and how switching between migration modes could occur. To do so, the 6V model was reduced to an excitable 4V spatiotemporal model possessing three different timescales. The model produced not only wave-pinning in the presence of diffusion, but also mixed-mode oscillations (MMOs) and relaxation oscillations (ROs). Implementing the model using the Cellular Potts Model (CPM) produced outcomes in which protrusions in the cell membrane changed Rac-Rho localization, resulting in membrane oscillations and fast directionality variations similar to those observed experimentally in CHO-K1 cells. The latter was assessed by comparing the migration patterns of experimental with CPM cells using four metrics: instantaneous cell speed, exponent of mean-square displacement ([Formula: see text]-value), directionality ratio and protrusion rate. Variations in migration patterns induced by mutating paxillin's serine 273 residue were also captured by the model and detected by a machine classifier, revealing that this mutation alters the dynamics of the system from MMOs to ROs or nonoscillatory behaviour through variation in the scaled concentration of an active form of an adhesion protein called p21-Activated Kinase 1 (PAK). These results thus suggest that MMOs and adhesion dynamics are the key mechanisms regulating CHO-K1 cell motility.

On multistability and constitutive relations of cell motion on fibronectin lanes

Cell motility on flat substrates exhibits coexisting steady and oscillatory morphodynamics, the biphasic adhesion-velocity relation, and the universal correlation between speed and persistence (UCSP) as simultaneous observations common to many cell types. Their universality and concurrency suggest a unifying mechanism causing all three of them. Stick-slip models for cells on one-dimensional lanes suggest multistability to arise from the nonlinear friction of retrograde flow. This study suggests a mechanical mechanism controlled by integrin signaling on the basis of a biophysical model and analysis of trajectories of MDA-MB-231 cells on fibronectin lanes, which additionally explains the constitutive relations. The experiments exhibit cells with steady or oscillatory morphodynamics and either spread or moving with spontaneous transitions between the dynamic regimes, spread and moving, and spontaneous direction reversals. Our biophysical model is based on the force balance at the protrusion edge, the noisy clutch of retrograde flow, and a response function of friction and membrane drag to integrin signaling. The theory reproduces the experimentally observed cell states, characteristics of oscillations, and state probabilities. Analysis of experiments with the biophysical model establishes a stick-slip oscillation mechanism, and explains multistability of cell states and the statistics of state transitions. It suggests protrusion competition to cause direction reversal events, the statistics of which explain the UCSP. The effect of integrin signaling on drag and friction explains the adhesion-velocity relation and cell behavior at fibronectin density steps. The dynamics of our mechanism are nonlinear flow mechanics driven by F-actin polymerization and shaped by the noisy clutch of retrograde flow friction, protrusion competition via membrane tension, and drag forces. Integrin signaling controls the parameters of the mechanical system.

Understanding How Cells Probe the World: A Preliminary Step towards Modeling Cell Behavior?

Cell biologists have long aimed at quantitatively modeling cell function. Recently, the outstanding progress of high-throughput measurement methods and data processing tools has made this a realistic goal. The aim of this paper is twofold: First, to suggest that, while much progress has been done in modeling cell states and transitions, current accounts of environmental cues driving these transitions remain insufficient. There is a need to provide an integrated view of the biochemical, topographical and mechanical information processed by cells to take decisions. It might be rewarding in the near future to try to connect cell environmental cues to physiologically relevant outcomes rather than modeling relationships between these cues and internal signaling networks. The second aim of this paper is to review exogenous signals that are sensed by living cells and significantly influence fate decisions. Indeed, in addition to the composition of the surrounding medium, cells are highly sensitive to the properties of neighboring surfaces, including the spatial organization of anchored molecules and substrate mechanical and topographical properties. These properties should thus be included in models of cell behavior. It is also suggested that attempts at cell modeling could strongly benefit from two research lines: (i) trying to decipher the way cells encode the information they retrieve from environment analysis, and (ii) developing more standardized means of assessing the quality of proposed models, as was done in other research domains such as protein structure prediction.

Optimization of Mechanosensitive Cross-Talk between Matrix Stiffness and Protein Density: Independent Matrix Properties Regulate Spreading Dynamics of Myocytes

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulates morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin-density-independent increase of the projected cell area until 12 kPa. Additionally, changes in fibronectin density led to an area that was optimum at about 2.6 μg/cm2, which was confirmed by independent F-actin analysis, revealing a maximum actin-filament-to-cell-area ratio of 7.5%. Proliferation evaluation showed an opposite correlation between cell spreading duration and speed to matrix elasticity and protein density, which did not affect cell-cycle duration. In summary, we identified an optimized ECM composition and found that independent matrix properties regulate distinct cell characteristics.

Cell behaviors within a confined adhesive area fabricated using novel micropatterning methods

In the field of cell and tissue engineering, there is an increasing demand for techniques to spatially control the adhesion of cells to substrates of desired sizes and shapes. Here, we describe two novel methods for fabricating a substrate for adhesion of cells to a defined area. In the first method, the surface of the coverslip or plastic dish was coated with Lipidure, a non-adhesive coating material, and air plasma was applied through a mask with holes, to confer adhesiveness to the surface. In the second method, after the surface of the coverslip was coated with gold by sputtering and then with Lipidure; the Lipidure coat was locally removed using a novel scanning laser ablation method. These methods efficiently confined cells within the adhesive area and enabled us to follow individual cells for a longer duration, compared to the currently available commercial substrates. By following single cells within the confined area, we were able to observe several new aspects of cell behavior in terms of cell division, cell–cell collisions, and cell collision with the boundary between adhesive and non-adhesive areas.

Infrared-spectroscopic, dynamic near-field microscopy of living cells and nanoparticles in water

Infrared fingerprint spectra can reveal the chemical nature of materials down to 20-nm detail, far below the diffraction limit, when probed by scattering-type scanning near-field optical microscopy (s-SNOM). But this was impossible with living cells or aqueous processes as in corrosion, due to water-related absorption and tip contamination. Here, we demonstrate infrared s-SNOM of water-suspended objects by probing them through a 10-nm thick SiN membrane. This separator stretches freely over up to 250 µm, providing an upper, stable surface to the scanning tip, while its lower surface is in contact with the liquid and localises adhering objects. We present its proof-of-principle applicability in biology by observing simply drop-casted, living E. coli in nutrient medium, as well as living A549 cancer cells, as they divide, move and develop rich sub-cellular morphology and adhesion patterns, at 150 nm resolution. Their infrared spectra reveal the local abundances of water, proteins, and lipids within a depth of ca. 100 nm below the SiN membrane, as we verify by analysing well-defined, suspended polymer spheres and through model calculations. SiN-membrane based s-SNOM thus establishes a novel tool of live cell nano-imaging that returns structure, dynamics and chemical composition. This method should benefit the nanoscale analysis of any aqueous system, from physics to medicine.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

From the Matrix to the Nucleus and Back: Mechanobiology in the Light of Health, Pathologies, and Regeneration of Oral Periodontal Tissues

Among oral tissues, the periodontium is permanently subjected to mechanical forces resulting from chewing, mastication, or orthodontic appliances. Molecularly, these movements induce a series of subsequent signaling processes, which are embedded in the biological concept of cellular mechanotransduction (MT). Cell and tissue structures, ranging from the extracellular matrix (ECM) to the plasma membrane, the cytosol and the nucleus, are involved in MT. Dysregulation of the diverse, fine-tuned interaction of molecular players responsible for transmitting biophysical environmental information into the cell's inner milieu can lead to and promote serious diseases, such as periodontitis or oral squamous cell carcinoma (OSCC). Therefore, periodontal integrity and regeneration is highly dependent on the proper integration and regulation of mechanobiological signals in the context of cell behavior. Recent experimental findings have increased the understanding of classical cellular mechanosensing mechanisms by both integrating exogenic factors such as bacterial gingipain proteases and newly discovered cell-inherent functions of mechanoresponsive co-transcriptional regulators such as the Yes-associated protein 1 (YAP1) or the nuclear cytoskeleton. Regarding periodontal MT research, this review offers insights into the current trends and open aspects. Concerning oral regenerative medicine or weakening of periodontal tissue diseases, perspectives on future applications of mechanobiological principles are discussed.