Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model

Diffusion model predicts the geometry of actin cytoskeleton from cell morphology

Cells exhibit various morphological characteristics due to their physiological activities, and changes in cell morphology are inherently accompanied by the assembly and disassembly of the actin cytoskeleton. Stress fibers are a prominent component of the actin-based intracellular structure and are highly involved in numerous physiological processes, e.g., mechanotransduction and maintenance of cell morphology. Although it is widely accepted that variations in cell morphology interact with the distribution and localization of stress fibers, it remains unclear if there are underlying geometric principles between the cell morphology and actin cytoskeleton. Here, we present a machine learning system that uses the diffusion model to convert the cell shape to the distribution and alignment of stress fibers. By training with corresponding cell shape and stress fibers datasets, our system learns the conversion to generate the stress fiber images from its corresponding cell shape. The predicted stress fiber distribution agrees well with the experimental data. With this conversion relation, our system allows for performing virtual experiments that provide a visual map showing the probability of stress fiber distribution from the virtual cell shape. Our system potentially provides a powerful approach to seek further hidden geometric principles regarding how the configuration of subcellular structures is determined by the boundary of the cell structure; for example, we found that the stress fibers of cells with small aspect ratios tend to localize at the cell edge while cells with large aspect ratios have homogenous distributions.

Cellular geometry and epithelial-mesenchymal plasticity intersect with PIEZO1 in breast cancer cells

Differences in shape can be a distinguishing feature between different cell types, but the shape of a cell can also be dynamic. Changes in cell shape are critical when cancer cells escape from the primary tumor and undergo major morphological changes that allow them to squeeze between endothelial cells, enter the vasculature, and metastasize to other areas of the body. A shift from rounded to spindly cellular geometry is a consequence of epithelial-mesenchymal plasticity, which is also associated with changes in gene expression, increased invasiveness, and therapeutic resistance. However, the consequences and functional impacts of cell shape changes and the mechanisms through which they occur are still poorly understood. Here, we demonstrate that altering the morphology of a cell produces a remodeling of calcium influx via the ion channel PIEZO1 and identify PIEZO1 as an inducer of features of epithelial-to-mesenchymal plasticity. Combining automated epifluorescence microscopy and a genetically encoded calcium indicator, we demonstrate that activation of the PIEZO1 force channel with the PIEZO1 agonist, YODA 1, induces features of epithelial-to-mesenchymal plasticity in breast cancer cells. These findings suggest that PIEZO1 is a critical point of convergence between shape-induced changes in cellular signaling and epithelial-mesenchymal plasticity in breast cancer cells.

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.

Modelling cell shape in 3D structured environments: A quantitative comparison with experiments

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments.

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.

Cell shape and tension alter focal adhesion structure

Cells are not only anchored to the extracellular matrix via the focal adhesion complex, the focal adhesion complex also serves as a sensor for force transduction. How tension influences the structure of focal adhesions is not well understood. Here, we analyse the effect of tension on the location of key focal adhesion proteins, namely vinculin, paxillin and actin. We use micropatterning on gold surfaces to manipulate the cell shape, to create focal adhesions at specific cell areas, and to perform metal-induced energy transfer (MIET) measurements on the patterned cells. MIET resolves the different protein locations with respect to the gold surface with nanometer accuracy. Further, we use drugs influencing the cellular motor protein myosin or mechanosensitive ion channels to get deeper insight into focal adhesions at different tension states. We show here that in particular actin is affected by the rationally tuned force balance. Blocking mechanosensitive ion channels has a particularly high influence on the actin and focal adhesion architecture, resulting in larger focal adhesions with elevated paxillin and vinculin and strongly lowered actin stress fibres. Our results can be explained by a balance of adhesion tension with cellular tension together with ion channel-controlled focal adhesion homeostasis, where high cellular tension leads to an elevation of vinculin and actin, while high adhesion tension lowers these proteins.

Simulating 3D Cell Shape with the Cellular Potts Model

Computer simulations have become a widely used method for the field of mechanobiology. An important question is whether one can predict the shape and forces of cells as a function of the extracellular environment. Different types of models have been described before to simulate cell and tissue shapes in structured environments. In this chapter, we give a brief overview of commonly used models and then describe the Cellular Potts Model, a lattice-based modelling framework, in more detail. We provide a hands-on guide on how to build a model that simulates the shape of a single cell on a micropattern in three dimensions in different open source software packages using the Cellular Potts framework. A simulation is set up with an initial configuration of generalized cells that change shape and position due to an energy function that incorporates cellular volume and surface area constraints as well as interaction energies between the generalized cells.

Mechanical strain stimulates COPII-dependent secretory trafficking via Rac1

Cells are constantly exposed to various chemical and physical stimuli. While much has been learned about the biochemical factors that regulate secretory trafficking from the endoplasmic reticulum (ER), much less is known about whether and how this trafficking is subject to regulation by mechanical signals. Here, we show that subjecting cells to mechanical strain both induces the formation of ER exit sites (ERES) and accelerates ER-to-Golgi trafficking. We found that cells with impaired ERES function were less capable of expanding their surface area when placed under mechanical stress and were more prone to develop plasma membrane defects when subjected to stretching. Thus, coupling of ERES function to mechanotransduction appears to confer resistance of cells to mechanical stress. Furthermore, we show that the coupling of mechanotransduction to ERES formation was mediated via a previously unappreciated ER-localized pool of the small GTPase Rac1. Mechanistically, we show that Rac1 interacts with the small GTPase Sar1 to drive budding of COPII carriers and stimulates ER-to-Golgi transport. This interaction therefore represents an unprecedented link between mechanical strain and export from the ER.

Intrinsic cell rheology drives junction maturation

A fundamental property of higher eukaryotes that underpins their evolutionary success is stable cell-cell cohesion. Yet, how intrinsic cell rheology and stiffness contributes to junction stabilization and maturation is poorly understood. We demonstrate that localized modulation of cell rheology governs the transition of a slack, undulated cell-cell contact (weak adhesion) to a mature, straight junction (optimal adhesion). Cell pairs confined on different geometries have heterogeneous elasticity maps and control their own intrinsic rheology co-ordinately. More compliant cell pairs grown on circles have slack contacts, while stiffer triangular cell pairs favour straight junctions with flanking contractile thin bundles. Counter-intuitively, straighter cell-cell contacts have reduced receptor density and less dynamic junctional actin, suggesting an unusual adaptive mechano-response to stabilize cell-cell adhesion. Our modelling informs that slack junctions arise from failure of circular cell pairs to increase their own intrinsic stiffness and resist the pressures from the neighbouring cell. The inability to form a straight junction can be reversed by increasing mechanical stress artificially on stiffer substrates. Our data inform on the minimal intrinsic rheology to generate a mature junction and provide a springboard towards understanding elements governing tissue-level mechanics.

Anisotropy profoundly alters stress fields within contractile cells and cell aggregates

Many biological phenomena such as cell proliferation and death are correlated with stress fields within cells. Stress fields are quantified using computational methods which rely on fundamental assumptions about local mechanical properties. Most existing methods such as Monolayer Stress Microscopy assume isotropic properties, yet experimental observations strongly suggest anisotropy. We first model anisotropy in circular cells analytically using Eshelby's inclusion method. Our solution reveals that uniform anisotropy cannot exist in cells due to the occurrence of substantial stress concentration in the central region. A more realistic non-uniform anisotropy model is then introduced based on experimental observations and implemented numerically which interestingly clears out stress concentration. Stresses within the entire aggregate also drastically change compared to the isotropic case, resulting in better agreement with observed biomarkers. We provide a physics-based mechanism to explain the low alignment of stress fibers in the center of cells, which might explain certain biological phenomena e.g., existence of disrupted rounded cells, and higher apoptosis rate at the center of circular aggregates.

Micro-patterned cell populations as advanced pharmaceutical drugs with precise functional control

Human cells are both advanced pharmaceutical drugs and 'drug deliverers'. However, functional control prior to or after cell implantation remains challenging. Micro-patterning cells through geometrically defined adhesion sites allows controlling morphogenesis, polarity, cellular mechanics, proliferation, migration, differentiation, stemness, cell-cell interactions, collective cell behavior, and likely immuno-modulatory properties. Consequently, generating micro-patterned therapeutic cells is a promising idea that has not yet been realized and few if any steps have been undertaken in this direction. This review highlights potential therapeutic applications, summarizes comprehensively the many cell functions that have been successfully controlled through micro-patterning, details the established micro-pattern designs, introduces the available fabrication technologies to the non-specialized reader, and suggests a quality evaluation score. Such a broad review is not yet available but would facilitate the manufacturing of therapeutically patterned cell populations using micro-patterned cell-instructive biomaterials for improved functional control as drug delivery systems in the context of cells as pharmaceutical products.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Methods to quantify endothelial cell front-rear polarity in vivo and in vitro

PURPOSE OF REVIEW

Endothelial cell (EC) front-rear (axial) polarization in response to chemokines and shear stress is fundamental for angiogenesis. This review provides an overview of the in vitro and in vivo methods that are currently available to quantify EC axial polarity.

RECENT FINDINGS

Innovative methodologies and new animal models have been developed to evaluate EC axial polarity. Micropatterning, wound healing and microfluidic assays allow interrogation of signalling mechanisms in vitro. Mouse and zebrafish transgenic lines, in combination with advances in imaging techniques and computational tools, enable interrogation of physiological functions of EC axial polarity in vascular biology during development and in pathology in vivo.

SUMMARY

We present a literature-based review of the methods available to study EC polarity. Further refinement of quantitative methods to analyse EC axial polarity using deep learning-based computational tools will generate new understanding on the aetiology of vascular malformations.

Morphological switch is associated with increase in cell-cell contacts, ALP, and confluence above a minimum island area to perimeter ratio

During osteogenic differentiation in vitro, stem-like cells seeded at a low-density spread and are isolated. As the cells proliferate and mature, they become more cuboidal in shape with more cell-cell contacts. However, the coordination of this switch in cell morphology from elongated to cuboidal, cell-cell contacts, and differentiation is not known. In this work, we present results from experiments and a simulation of cell proliferation on protein-micropatterned islands that, independent of island size (25-1,000 μm) or shape (circles, squares, and hollow squares), shows a distinct morphological switch that is better described as a function of island confluence than time in culture, the standard measure in cell culture experiments. The simulation and experiments show cell morphology and island cell density versus confluence collapse to a single curve for all islands if the island area to perimeter ratio is ≥25 μm. Cell-cell contacts in the simulation and alkaline phosphatase (ALP) expression in experiments, a common marker for osteogenic differentiation, show exponential growth with confluence, rapidly increasing after the switch at ≈0.5 confluence. Furthermore, cell morphology, density, contacts, and ALP are better predicted by confluence than time in culture. The variability with time in culture leads to challenges in not only interpreting data but also in comparing data across research laboratories. This simulation can be used to predict cell behavior on different size and shape islands and to plan and optimize experiments that explore cell behavior as a function of a wide range of island geometries.

Pattern-Based Contractility Screening, a Reference-Free Alternative to Traction Force Microscopy Methodology

The sensing and generation of cellular forces are essential aspects of life. Traction force microscopy (TFM) has emerged as a standard broadly applicable methodology to measure cell contractility and its role in cell behavior. While TFM platforms have enabled diverse discoveries, their implementation remains limited in part due to various constraints, such as time-consuming substrate fabrication techniques, the need to detach cells to measure null force images, followed by complex imaging and analysis, and the unavailability of cells for postprocessing. Here we introduce a reference-free technique to measure cell contractile work in real time, with commonly available substrate fabrication methodologies, simple imaging, and analysis with the availability of the cells for postprocessing. In this technique, we confine the cells on fluorescent adhesive protein micropatterns of a known area on compliant silicone substrates and use the cell deformed pattern area to calculate cell contractile work. We validated this approach by comparing this pattern-based contractility screening (PaCS) with conventional bead-displacement TFM and show quantitative agreement between the methodologies. Using this platform, we measure the contractile work of highly metastatic MDA-MB-231 breast cancer cells that is significantly higher than the contractile work of noninvasive MCF-7 cells. PaCS enables the broader implementation of contractile work measurements in diverse quantitative biology and biomedical applications.

High-Throughput Methods in the Discovery and Study of Biomaterials and Materiobiology

The complex interaction of cells with biomaterials (i.e., materiobiology) plays an increasingly pivotal role in the development of novel implants, biomedical devices, and tissue engineering scaffolds to treat diseases, aid in the restoration of bodily functions, construct healthy tissues, or regenerate diseased ones. However, the conventional approaches are incapable of screening the huge amount of potential material parameter combinations to identify the optimal cell responses and involve a combination of serendipity and many series of trial-and-error experiments. For advanced tissue engineering and regenerative medicine, highly efficient and complex bioanalysis platforms are expected to explore the complex interaction of cells with biomaterials using combinatorial approaches that offer desired complex microenvironments during healing, development, and homeostasis. In this review, we first introduce materiobiology and its high-throughput screening (HTS). Then we present an in-depth of the recent progress of 2D/3D HTS platforms (i.e., gradient and microarray) in the principle, preparation, screening for materiobiology, and combination with other advanced technologies. The Compendium for Biomaterial Transcriptomics and high content imaging, computational simulations, and their translation toward commercial and clinical uses are highlighted. In the final section, current challenges and future perspectives are discussed. High-throughput experimentation within the field of materiobiology enables the elucidation of the relationships between biomaterial properties and biological behavior and thereby serves as a potential tool for accelerating the development of high-performance biomaterials.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

Articular Chondrocyte Phenotype Regulation through the Cytoskeleton and the Signaling Processes That Originate from or Converge on the Cytoskeleton: Towards a Novel Understanding of the Intersection between Actin Dynamics and Chondrogenic Function

Numerous studies have assembled a complex picture, in which extracellular stimuli and intracellular signaling pathways modulate the chondrocyte phenotype. Because many diseases are mechanobiology-related, this review asked to what extent phenotype regulators control chondrocyte function through the cytoskeleton and cytoskeleton-regulating signaling processes. Such information would generate leverage for advanced articular cartilage repair. Serial passaging, pro-inflammatory cytokine signaling (TNF-α, IL-1α, IL-1β, IL-6, and IL-8), growth factors (TGF-α), and osteoarthritis not only induce dedifferentiation but also converge on RhoA/ROCK/Rac1/mDia1/mDia2/Cdc42 to promote actin polymerization/crosslinking for stress fiber (SF) formation. SF formation takes center stage in phenotype control, as both SF formation and SOX9 phosphorylation for COL2 expression are ROCK activity-dependent. Explaining how it is molecularly possible that dedifferentiation induces low COL2 expression but high SF formation, this review theorized that, in chondrocyte SOX9, phosphorylation by ROCK might effectively be sidelined in favor of other SF-promoting ROCK substrates, based on a differential ROCK affinity. In turn, actin depolymerization for redifferentiation would “free-up” ROCK to increase COL2 expression. Moreover, the actin cytoskeleton regulates COL1 expression, modulates COL2/aggrecan fragment generation, and mediates a fibrogenic/catabolic expression profile, highlighting that actin dynamics-regulating processes decisively control the chondrocyte phenotype. This suggests modulating the balance between actin polymerization/depolymerization for therapeutically controlling the chondrocyte phenotype.

Molecular Regulators of Cellular Mechanoadaptation at Cell-Material Interfaces

Diverse essential cellular behaviors are determined by extracellular physical cues that are detected by highly orchestrated subcellular interactions with the extracellular microenvironment. To maintain the reciprocity of cellular responses and mechanical properties of the extracellular matrix, cells utilize a variety of signaling pathways that transduce biophysical stimuli to biochemical reactions. Recent advances in the micromanipulation of individual cells have shown that cellular responses to distinct physical and chemical features of the material are fundamental determinants of cellular mechanosensation and mechanotransduction. In the process of outside-in signal transduction, transmembrane protein integrins facilitate the formation of focal adhesion protein clusters that are connected to the cytoskeletal architecture and anchor the cell to the substrate. The linkers of nucleoskeleton and cytoskeleton molecular complexes, collectively termed LINC, are critical signal transducers that relay biophysical signals between the extranuclear cytoplasmic region and intranuclear nucleoplasmic region. Mechanical signals that involve cytoskeletal remodeling ultimately propagate into the nuclear envelope comprising the nuclear lamina in assistance with various nuclear membrane proteins, where nuclear mechanics play a key role in the subsequent alteration of gene expression and epigenetic modification. These intracellular mechanical signaling cues adjust cellular behaviors directly associated with mechanohomeostasis. Diverse strategies to modulate cell-material interfaces, including alteration of surface rigidity, confinement of cell adhesive region, and changes in surface topology, have been proposed to identify cellular signal transduction at the cellular and subcellular levels. In this review, we will discuss how a diversity of alterations in the physical properties of materials induce distinct cellular responses such as adhesion, migration, proliferation, differentiation, and chromosomal organization. Furthermore, the pathological relevance of misregulated cellular mechanosensation and mechanotransduction in the progression of devastating human diseases, including cardiovascular diseases, cancer, and aging, will be extensively reviewed. Understanding cellular responses to various extracellular forces is expected to provide new insights into how cellular mechanoadaptation is modulated by manipulating the mechanics of extracellular matrix and the application of these materials in clinical aspects.

Of Cell Shapes and Motion: The Physical Basis of Animal Cell Migration

Motile cells have developed a variety of migration modes relying on diverse traction-force-generation mechanisms. Before the behavior of intracellular components could be easily imaged, cell movements were mostly classified by different types of cellular shape dynamics. Indeed, even though some types of cells move without any significant change in shape, most cell propulsion mechanisms rely on global or local deformations of the cell surface. In this review, focusing mostly on metazoan cells, we discuss how different types of local and global shape changes underlie distinct migration modes. We then discuss mechanical differences between force-generation mechanisms and finish by speculating on how they may have evolved.

Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics

Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions.

A Cellular Potts energy-based approach to analyse the influence of the surface topography on single cell motility

The surface shape is an important aspect to take into account to ensure the success of an implant. At the cellular scale level, the cell behaviour, especially its migration, is affected by the specificities of the surface of the substrate, such as the stiffness of the surface and its roughness topography. The latter has been shown to have a great impact on various cell mechanisms, such as the cell adhesion, migration, or proliferation. In fact, the mere presence of micro roughness leads to an improvement of those mechanisms, with a better integration of the implants. However, the phenomena behind those improvements are still not clear. In this paper, we propose a three-dimensional (3D) model of a single cell migration using a Cellular Potts (CP) model to study the influence of the surface topography on cell motility. To do so, various configurations were tested, such as: (i) a substrate with a random roughness, (ii) a substrate with a rectangular groove pattern (parallel and perpendicular to the direction of motion), (ii) a substrate with a sinusoidal groove pattern. To evaluate the influence of the surface topography on cell motility, for each configuration, the cell speed and shape as well as the contact surface between the cell and the substrate have been quantified. Our numerical results demonstrate that, in agreement with the experimental observations of the literature, the substrate topography has an influence on the cell efficiency (i.e. cell speed), orientation and shape. Besides, we also show that the increase of the contact surface alone in presence of roughness is not enough to explain the improvement of cell migration on the various rough surfaces. Finally, we highlight the importance of the roughness dimension on cell motility. This could be a critical aspect to consider for further analyses and applications, such as surface treatments for medical applications.

Mechanical interplay between cell shape and actin cytoskeleton organization

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells.

Extracellular Matrix Geometry and Initial Adhesive Position Determine Stress Fiber Network Organization during Cell Spreading

Three-dimensional matrices often contain highly structured adhesive tracks that require cells to turn corners and bridge non-adhesive areas. Here, we investigate these complex processes using micropatterned cell adhesive frames. Spreading kinetics on these matrices depend strongly on initial adhesive position and are predicted by a cellular Potts model (CPM), which reflects a balance between adhesion and intracellular tension. As cells spread, new stress fibers (SFs) assemble periodically and parallel to the leading edge, with spatial intervals of ∼2.5 μm, temporal intervals of ∼15 min, and characteristic lifetimes of ∼50 min. By incorporating these rules into the CPM, we can successfully predict SF network architecture. Moreover, we observe broadly similar behavior when we culture cells on arrays of discrete collagen fibers. Our findings show that ECM geometry and initial cell position strongly determine cell spreading and that cells encode a memory of their spreading history through SF network organization.

Quasi-periodic migration of single cells on short microlanes

Cell migration on microlanes represents a suitable and simple platform for the exploration of the molecular mechanisms underlying cell cytoskeleton dynamics. Here, we report on the quasi-periodic movement of cells confined in stripe-shaped microlanes. We observe persistent polarized cell shapes and directed pole-to-pole motion within the microlanes. Cells depolarize at one end of a given microlane, followed by delayed repolarization towards the opposite end. We analyze cell motility via the spatial velocity distribution, the velocity frequency spectrum and the reversal time as a measure for depolarization and spontaneous repolarization of cells at the microlane ends. The frequent encounters of a boundary in the stripe geometry provides a robust framework for quantitative investigations of the cytoskeleton protrusion and repolarization dynamics. In a first advance to rigorously test physical models of cell migration, we find that the statistics of the cell migration is recapitulated by a Cellular Potts model with a minimal description of cytoskeleton dynamics. Using LifeAct-GFP transfected cells and microlanes with differently shaped ends, we show that the local deformation of the leading cell edge in response to the tip geometry can locally either amplify or quench actin polymerization, while leaving the average reversal times unaffected.

A Lock Free Approach To Parallelize The Cellular Potts Model: Application To Ductal Carcinoma In Situ

In the field of computational biology, in order to simulate multiscale biological systems, the Cellular Potts Model (CPM) has been used, which determines the actions that simulated cells can perform by determining a hamiltonian of energy that takes into account the influence that neighboring cells exert, under a wide range of parameters. There are some proposals in the literature that parallelize the CPM; in all cases, either lock-based techniques or other techniques that require large amounts of information to be disseminated among parallel tasks are used to preserve data coherence. In both cases, computational performance is limited. This work proposes an alternative approach for the parallelization of the model that uses transactional memory to maintain the coherence of the information. A Java implementation has been applied to the simulation of the ductal adenocarcinoma of breast in situ (DCIS). Times and speedups of the simulated execution of the model on the cluster of our university are analyzed. The results show a good speedup.

Area and Geometry Dependence of Cell Migration in Asymmetric Two-State Micropatterns

Microstructured surfaces provide a unique framework to probe cell migration and cytoskeletal dynamics in a standardized manner. Here, we report on the steady-state occupancy probability of cells in asymmetric two-state microstructures that consist of two fibronectin-coated adhesion sites connected by a thin guidance cue. In these dumbbell-like structures, cells transition between the two sites in a repeated and stochastic manner, and average dwell times in the respective microenvironments are determined from the cell trajectories. We study the dynamics of human breast carcinoma cells (MDA-MB-231) in these microstructures as a function of area, shape, and orientation of the adhesion sites. On square adhesive sites with different areas, we find that the occupancy probability ratio is directly proportional to the ratio of corresponding adhesion site areas. These asymmetries are well captured by a simple model for the stochastic nonlinear dynamics of the cells, which reveals generic features of the motion. Sites of equal area but different shape lead to equal occupancy if shapes are isotropic (e.g., squared or circular). In contrast, an asymmetry in the occupancy is induced by anisotropic shapes like rhombi, triangles, or rectangles that enable motion in the direction perpendicular to the transition axis. Analysis of the two-dimensional motion of cells between two rectangles with orthogonal orientation suggests that cellular transition rates depend on the cell polarization induced by anisotropic micropatterns. Taken together, our results illustrate how two-state micropatterns provide a dynamic migration assay with distinct dwell times and relative cell occupancy as readouts, which may be useful to probe cell-microenvironment interactions.

Mechanisms of endothelial cell coverage by pericytes: computational modelling of cell wrapping and in vitro experiments

Pericytes (PCs) wrap around endothelial cells (ECs) and perform diverse functions in physiological and pathological processes. Although molecular interactions between ECs and PCs have been extensively studied, the morphological processes at the cellular level and their underlying mechanisms have remained elusive. In this study, using a simple cellular Potts model, we explored the mechanisms for EC wrapping by PCs. Based on the observed in vitro cell wrapping in three-dimensional PC-EC coculture, the model identified four putative contributing factors: preferential adhesion of PCs to the extracellular matrix (ECM), strong cell-cell adhesion, PC surface softness and larger PC size. While cell-cell adhesion can contribute to the prevention of cell segregation and the degree of cell wrapping, it cannot determine the orientation of cell wrapping alone. While atomic force microscopy revealed that PCs have a larger Young's modulus than ECs, the experimental analyses supported preferential ECM adhesion and size asymmetry. We also formulated the corresponding energy minimization problem and numerically solved this problem for specific cases. These results give biological insights into the role of PC-ECM adhesion in PC coverage. The modelling framework presented here should also be applicable to other cell wrapping phenomena observed in vivo.

From energy to cellular forces in the Cellular Potts Model: An algorithmic approach

Single and collective cell dynamics, cell shape changes, and cell migration can be conveniently represented by the Cellular Potts Model, a computational platform based on minimization of a Hamiltonian. Using the fact that a force field is easily derived from a scalar energy (F = −∇H), we develop a simple algorithm to associate effective forces with cell shapes in the CPM. We predict the traction forces exerted by single cells of various shapes and sizes on a 2D substrate. While CPM forces are specified directly from the Hamiltonian on the cell perimeter, we approximate the force field inside the cell domain using interpolation, and refine the results with smoothing. Predicted forces compare favorably with experimentally measured cellular traction forces. We show that a CPM model with internal signaling (such as Rho-GTPase-related contractility) can be associated with retraction-protrusion forces that accompany cell shape changes and migration. We adapt the computations to multicellular systems, showing, for example, the forces that a pair of swirling cells exert on one another, demonstrating that our algorithm works equally well for interacting cells. Finally, we show forces exerted by cells on one another in classic cell-sorting experiments.

Cells exert forces on their surroundings and on one another. In simulations of cell shape using the Cellular Potts Model (CPM), the dynamics of deforming cell shapes is traditionally represented by an energy-minimization method. We use this CPM energy, the Hamiltonian, to derive and visualize the corresponding forces exerted by the cells. We use the fact that force is the negative gradient of energy to assign forces to the CPM cell edges, and then extend the results to approximate interior forces by interpolation. We show that this method works for single as well as multiple interacting model cells, both static and motile. Finally, we show favorable comparison between predicted forces and real forces measured experimentally.

Bridging the gap between single-cell migration and collective dynamics

Motivated by the wealth of experimental data recently available, we present a cellular-automaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability; contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology; stress and velocity distributions) at the level of extended tissues.

Spatial integration of mechanical forces by α-actinin establishes actin network symmetry

Cell and tissue morphogenesis depend on the production and spatial organization of tensional forces in the actin cytoskeleton. Actin network architecture is made of distinct modules characterized by specific filament organizations. The assembly of these modules are well described, but their integration in a cellular network is less understood. Here, we investigated the mechanism regulating the interplay between network architecture and the geometry of the extracellular environment of the cell. We found that α-actinin, a filament crosslinker, is essential for network symmetry to be consistent with extracellular microenvironment symmetry. It is required for the interconnection of transverse arcs with radial fibres to ensure an appropriate balance between forces at cell adhesions and across the actin network. Furthermore, this connectivity appeared necessary for the ability of the cell to integrate and to adapt to complex patterns of extracellular cues as they migrate. Our study has unveiled a role of actin filament crosslinking in the spatial integration of mechanical forces that ensures the adaptation of intracellular symmetry axes in accordance with the geometry of extracellular cues.This article has an associated First Person interview with the first author of the paper.

DLITE Uses Cell-Cell Interface Movement to Better Infer Cell-Cell Tensions

Cell shapes and connectivities evolve over time as the colony changes shape or embryos develop. Shapes of intercellular interfaces are closely coupled with the forces resulting from actomyosin interactions, membrane tension, or cell-cell adhesions. Although it is possible to computationally infer cell-cell forces from a mechanical model of collective cell behavior, doing so for temporally evolving forces in a manner robust to digitization difficulties is challenging. Here, we introduce a method for dynamic local intercellular tension estimation (DLITE) that infers such evolution in temporal force with less sensitivity to digitization ambiguities or errors. This method builds upon previous work on single time points (cellular force-inference toolkit). We validate our method using synthetic geometries. DLITE's inferred cell colony tension evolutions correlate better with ground truth for these synthetic geometries as compared to tension values inferred from methods that consider each time point in isolation. We introduce cell connectivity errors, angle estimate errors, connection mislocalization, and connection topological changes to synthetic data and show that DLITE has reduced sensitivity to these conditions. Finally, we apply DLITE to time series of human-induced pluripotent stem cell colonies with endogenously expressed GFP-tagged zonulae occludentes-1. We show that DLITE offers improved stability in the inference of cell-cell tensions and supports a correlation between the dynamics of cell-cell forces and colony rearrangement.

Substrate-rigidity dependent migration of an idealized twitching bacterium

Mechanical properties of the extracellular matrix are important determinants of cellular migration in diverse processes, such as immune response, wound healing, and cancer metastasis. Moreover, recent studies indicate that even bacterial surface colonization can depend on the mechanics of the substrate. Here, we focus on physical mechanisms that can give rise to substrate-rigidity dependent migration. We study a "twitcher", a cell driven by extension-retraction cycles, to idealize bacteria and perhaps eukaryotic cells that employ a slip-stick mode of motion. The twitcher is asymmetric and always pulls itself forward at its front. Analytical calculations show that the migration speed of a twitcher depends non-linearly on substrate rigidity. For soft substrates, deformations do not lead to build-up of significant force and the migration speed is therefore determined by stochastic adhesion unbinding. For rigid substrates, forced adhesion rupture determines the migration speed. Depending on the force-sensitivity of front and rear adhesions, forced bond rupture implies an increase or a decrease of the migration speed. A requirement for the occurrence of rigidity-dependent stick-slip migration is a "sticky" substrate, with binding rates being an order of magnitude larger than unbinding rates in absence of force. Computer simulations show that small stall forces of the driving machinery lead to a reduced movement on high rigidities, regardless of force-sensitivities of bonds. The simulations also confirm the occurrence of rigidity-dependent migration speed in a generic model for slip-stick migration of cells on a sticky substrate.

Bayesian model selection for the Drosophila gap gene network

Background

The gap gene system controls the early cascade of the segmentation pathway in Drosophila melanogaster as well as other insects. Owing to its tractability and key role in embryo patterning, this system has been the focus for both computational modelers and experimentalists. The gap gene expression dynamics can be considered strictly as a one-dimensional process and modeled as a system of reaction-diffusion equations. While substantial progress has been made in modeling this phenomenon, there still remains a deficit of approaches to evaluate competing hypotheses. Most of the model development has happened in isolation and there has been little attempt to compare candidate models.

Results

The Bayesian framework offers a means of doing formal model evaluation. Here, we demonstrate how this framework can be used to compare different models of gene expression. We focus on the Papatsenko-Levine formalism, which exploits a fractional occupancy based approach to incorporate activation of the gap genes by the maternal genes and cross-regulation by the gap genes themselves. The Bayesian approach provides insight about relationship between system parameters. In the regulatory pathway of segmentation, the parameters for number of binding sites and binding affinity have a negative correlation. The model selection analysis supports a stronger binding affinity for Bicoid compared to other regulatory edges, as shown by a larger posterior mean. The procedure doesn’t show support for activation of Kruppel by Bicoid.

Conclusions

We provide an efficient solver for the general representation of the Papatsenko-Levine model. We also demonstrate the utility of Bayes factor for evaluating candidate models for spatial pattering models. In addition, by using the parallel tempering sampler, the convergence of Markov chains can be remarkably improved and robust estimates of Bayes factors obtained.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2888-0) contains supplementary material, which is available to authorized users.

Cellular Response to Surface Morphology: Electrospinning and Computational Modeling

Surface properties of biomaterials, such as chemistry and morphology, have a major role in modulating cellular behavior and therefore impact on the development of high-performance devices for biomedical applications, such as scaffolds for tissue engineering and systems for drug delivery. Opportunely-designed micro- and nanostructures provides a unique way of controlling cell-biomaterial interaction. This mini-review discusses the current research on the use of electrospinning (extrusion of polymer nanofibers upon the application of an electric field) as effective technique to fabricate patterns of micro- and nano-scale resolution, and the corresponding biological studies. The focus is on the effect of morphological cues, including fiber alignment, porosity and surface roughness of electrospun mats, to direct cell migration and to influence cell adhesion, differentiation and proliferation. Experimental studies are combined with computational models that predict and correlate the surface composition of a biomaterial with the response of cells in contact with it. The use of predictive models can facilitate the rational design of new bio-interfaces.

Rotation of sex combs in Drosophila melanogaster requires precise and coordinated spatio-temporal dynamics from forces generated by epithelial cells

The morphogenesis of sex combs (SCs), a male trait in many species of fruit flies, is an excellent system in which to study the cell biology, genetics and evolution of a trait. In Drosophila melanogaster, where the incipient SC rotates from horizontal to a vertical position, three signal comb properties have been documented: length, final angle and shape (linearity). During SC rotation, in which many cellular processes are occurring both spatially and temporally, it is difficult to distinguish which processes are crucial for which attributes of the comb. We have used a novel approach combining simulations and experiments to uncover the spatio-temporal dynamics underlying SC rotation. Our results indicate that 1) the final SC shape is primarily controlled by the inhomogeneity of initial cell size in cells close to the immature comb, 2) the final angle is primarily controlled by later cell expansion and 3) a temporal sequence of cell expansion mitigates the malformations generally associated with longer rotated SCs. Overall, our work has linked together the morphological diversity of SCs and the cellular dynamics behind such diversity, thus providing important insights on how evolution may affect SC development via the behaviours of surrounding epithelial cells.

The sex comb (SC) is a series of modified bristles on the male forelegs of many species of fruit flies. The size, position and shape of these sex combs vary drastically across different fly species. Therefore, SCs are a model system which illustrates the interaction between evolution and organism development influencing phenotypic features. In this work, we use a combined simulation-experimental approach to study the cellular processes involved in the rotation of developing SCs in common fruit flies (D. melanogaster). Our results indicate that despite the appearance of a complicated set of motions of surrounding cells associated with SC rotation, the final SC attributes only depend on a few selected parameters. We showed that changes in the timing and extent of cell size increase in distal cells altered the extent of SC rotation and breakage. Furthermore, these changes were sufficient to account for the observed variations in SC rotation between different fly species. Thus, our computational model has given us important insights on how evolution may use various cellular processes as a means to manifest the diversity of SCs across different fly species.

Biomechanical Control of Lysosomal Secretion Via the VAMP7 Hub: A Tug-of-War between VARP and LRRK1

The rigidity of the cell environment can vary tremendously between tissues and in pathological conditions. How this property may affect intracellular membrane dynamics is still largely unknown. Here, using atomic force microscopy, we show that cells deficient in the secretory lysosome v-SNARE VAMP7 are impaired in adaptation to substrate rigidity. Conversely, VAMP7-mediated secretion is stimulated by more rigid substrate and this regulation depends on the Longin domain of VAMP7. We further find that the Longin domain binds the kinase and retrograde trafficking adaptor LRRK1 and that LRRK1 negatively regulates VAMP7-mediated exocytosis. Conversely, VARP, a VAMP7- and kinesin 1-interacting protein, further controls the availability for secretion of peripheral VAMP7 vesicles and response of cells to mechanical constraints. LRRK1 and VARP interact with VAMP7 in a competitive manner. We propose a mechanism whereby biomechanical constraints regulate VAMP7-dependent lysosomal secretion via LRRK1 and VARP tug-of-war control of the peripheral pool of secretory lysosomes.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Virtual cardiac monolayers for electrical wave propagation

The complex structure of cardiac tissue is considered to be one of the main determinants of an arrhythmogenic substrate. This study is aimed at developing the first mathematical model to describe the formation of cardiac tissue, using a joint in silico-in vitro approach. First, we performed experiments under various conditions to carefully characterise the morphology of cardiac tissue in a culture of neonatal rat ventricular cells. We considered two cell types, namely, cardiomyocytes and fibroblasts. Next, we proposed a mathematical model, based on the Glazier-Graner-Hogeweg model, which is widely used in tissue growth studies. The resultant tissue morphology was coupled to the detailed electrophysiological Korhonen-Majumder model for neonatal rat ventricular cardiomyocytes, in order to study wave propagation. The simulated waves had the same anisotropy ratio and wavefront complexity as those in the experiment. Thus, we conclude that our approach allows us to reproduce the morphological and physiological properties of cardiac tissue.

Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch

During animal development and homeostasis, the structure of tissues, including muscles, blood vessels, and connective tissues, adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form stringlike structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between stringlike patterns and vascular networklike patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation.

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Actomyosin stress fiber mechanosensing in 2D and 3D

Mechanotransduction is the process through which cells survey the mechanical properties of their environment, convert these mechanical inputs into biochemical signals, and modulate their phenotype in response. These mechanical inputs, which may be encoded in the form of extracellular matrix stiffness, dimensionality, and adhesion, all strongly influence cell morphology, migration, and fate decisions. One mechanism through which cells on planar or pseudo-planar matrices exert tensile forces and interrogate microenvironmental mechanics is through stress fibers, which are bundles composed of actin filaments and, in most cases, non-muscle myosin II filaments. Stress fibers form a continuous structural network that is mechanically coupled to the extracellular matrix through focal adhesions. Furthermore, myosin-driven contractility plays a central role in the ability of stress fibers to sense matrix mechanics and generate tension. Here, we review the distinct roles that non-muscle myosin II plays in driving mechanosensing and focus specifically on motility. In a closely related discussion, we also describe stress fiber classification schemes and the differing roles of various myosin isoforms in each category. Finally, we briefly highlight recent studies exploring mechanosensing in three-dimensional environments, in which matrix content, structure, and mechanics are often tightly interrelated. Stress fibers and the myosin motors therein represent an intriguing and functionally important biological system in which mechanics, biochemistry, and architecture all converge.

Modeling cell shape and dynamics on micropatterns

Adhesive micropatterns have become a standard tool to study cells under defined conditions. Applications range from controlling the differentiation and fate of single cells to guiding the collective migration of cell sheets. In long-term experiments, single cell normalization is challenged by cell division. For all of these setups, mathematical models predicting cell shape and dynamics can guide pattern design. Here we review recent advances in predicting and explaining cell shape, traction forces and dynamics on micropatterns. Starting with contour models as the simplest approach to explain concave cell shapes, we move on to network and continuum descriptions as examples for static models. To describe dynamic processes, cellular Potts, vertex and phase field models can be used. Different types of model are appropriate to address different biological questions and together, they provide a versatile tool box to predict cell behavior on micropatterns.

Generalized lattice-gas model for adsorption of functional organic molecules in terms of pair directional interactions

A generalized lattice-gas model that takes into account the directional character of pair interactions between the lattice sites is proposed. It is demonstrated that the proposed model can be successfully used to deeply understand the self-assembly process in adsorption monolayers of functional organic molecules driven by specified directional interactions between such molecules (e.g., hydrogen bonding). To illustrate the idea, representative cases of the general model with different numbers of identical functional groups in the chemical structure of the adsorbed molecule are investigated with Monte Carlo and the transfer-matrix methods. The model reveals that the phase behavior of the adsorption systems considered can be characterized as a hierarchical self-assembly process. It is predicted that in real adsorption systems of this type, the energy of hydrogen bonding sufficiently depends on the mutual orientation of the adsorbed molecules.

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before.

Microsurgery-aided in-situ force probing reveals extensibility and viscoelastic properties of individual stress fibers

Actin-myosin filament bundles (stress fibers) are critical for tension generation and cell shape, but their mechanical properties are difficult to access. Here we propose a novel approach to probe individual peripheral stress fibers in living cells through a microsurgically generated opening in the cytoplasm. By applying large deformations with a soft cantilever we were able to fully characterize the mechanical response of the fibers and evaluate their tension, extensibility, elastic and viscous properties.