Modeling cell shape and dynamics on micropatterns

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.

Revelation of adhesive proteins affecting cellular contractility through reference-free traction force microscopy

Over the past few decades, the critical role played by cellular contractility associated mechanotransduction in the regulation of cell functions has been revealed. In this case, numerous biomaterials have been chemically or structurally designed to manipulate cell behaviors through the regulation of cellular contractility. In particular, adhesive proteins including fibronectin, poly-L-lysine and collagen type I have been widely applied in various biomaterials to improve cell adhesion. Therefore, clarifying the effects of adhesive proteins on cellular contractility has been valuable for the development of biomaterial design. In this study, reference-free traction force microscopy with a well-organized microdot array was designed and prepared to investigate the relationship between adhesive proteins, cellular contractility, and mechanotransduction. The results showed that fibronectin and collagen type I were able to promote the assembly of focal adhesions and further enhance cellular contraction and YAP activity. In contrast, although poly-L-lysine supported cell spreading and elongation, it was inefficient at inducing cell contractility and activating YAP. Additionally, compared with cellular morphogenesis, cellular contraction was essential for YAP activation.

Dynamic Micropatterning Reveals Substrate-Dependent Differences in the Geometric Control of Cell Polarization and Migration

Cells are highly dynamic and adopt variable shapes and sizes. These variations are biologically important but challenging to investigate in a spatiotemporally controlled manner. Micropatterning, confining cells on microfabricated substrates with defined geometries and molecular compositions, is a powerful tool for controlling cell shape and interactions. However, conventional binary micropatterns are static and fail to address dynamic changes in cell polarity, spreading, and migration. Here, a method for dynamic micropatterning is reported, where the non-adhesive surface surrounding adhesive micropatterns is rapidly converted to support specific cell-matrix interactions while allowing simultaneous imaging of the cells. The technique is based on ultraviolet photopatterning of biotinylated polyethylene glycol-grafted poly-L-lysine, and it is simple, inexpensive, and compatible with a wide range of streptavidin-conjugated ligands. Experiments using biotinylation-based dynamic micropatterns reveal that distinct extracellular matrix ligands and bivalent integrin-clustering antibodies support different degrees of front-rear polarity in human glioblastoma cells, which correlates to altered directionality and persistence upon release and migration on fibronectin. Unexpectedly, however, neither an asymmetric cell shape nor centrosome orientation can fully predict the future direction of migration. Taken together, biotinylation-based dynamic micropatterns allow easily accessible and highly customizable control over cell morphology and motility.

Surface nanotopography and cell shape modulate tumor cell susceptibility to NK cell cytotoxicity

Natural killer (NK) cells are innate cytotoxic lymphocytes exerting cytotoxicity against virally infected cells and tumor cells. NK cell cytotoxicity is primarily determined by biochemical signals received from ligands expressed on target cell surfaces, but it is also possible that biophysical environments of tumor cells, such as nanoscale surface topography typically existing on extracellular matrixes (ECMs) or cell morphology determined by ECM spaces or cell density, regulate NK cell cytotoxicity. In this study, micro/nanofabrication technology was applied to examine this possibility. Tumor cells were plated on flat or nanogrooved surfaces, or micropatterned into circular or elliptical geometries, and the effects of surface topography and tumor cell morphology on NK cell cytotoxicity were investigated. NK cells exhibited significantly higher cytotoxicity against tumor cells on nanogrooved surfaces or tumor cells in elliptical patterns than tumor cells on flat surfaces or tumor cells in circular patterns, respectively. The amounts of stress fiber formation in tumor cells positively correlated with NK cell cytotoxicity, indicating that increased cellular tension of tumor cells, either mediated by nanogrooved surfaces or elongated morphologies, was a key factor regulating NK cell cytotoxicity. These results may provide insight into the design of NK cell-based cancer immunotherapy.

Cell-strain-energy costs of active control of contractility

Cell mechanosensing is implicated in the control of a broad range of cell behaviors, with cytoskeletal contractility a key component. Experimentally, it is observed that the contractility of the cell responds to increasing substrate stiffness, showing increased contractile force and changing the distribution of cytoskeletal elements. Here, we show using a theoretical model of active cell contractility that upregulation of contractility need not be energetically expensive, especially when combined with changes in adhesion and contractile distribution. Indeed, we show that a feedback mechanism based on the maintenance of strain energy would require an upregulation in contractile pressure on all but the softest substrates. We consider both the commonly reported substrate strain energy and active work done. We demonstrate substrate strain energy would preferentially select for the experimentally observed clustering of cell adhesions on stiffer substrates which effectively soften the substrate and enable an upregulation of total contractile pressure, while the localization of contractility has the greatest impact on the internal work.

Extracellular Cues Govern Shape and Cytoskeletal Organization in Giant Unilamellar Lipid Vesicles

Spontaneous and induced front-rear polarization and a subsequent asymmetric actin cytoskeleton is a crucial event leading to cell migration, a key process involved in a variety of physiological and pathological conditions such as tissue development, wound healing, and cancer. Migration of adherent cells relies on the balance between adhesion to the underlying matrix and cytoskeleton-driven front protrusion and rear retraction. A current challenge is to uncouple the effect of adhesion and shape from the contribution of the cytoskeleton in regulating the onset of front-rear polarization. Here, we present a minimal model system that introduces an asymmetric actin cytoskeleton in synthetic cells, which are resembled by giant unilamellar lipid vesicles (GUVs) adhering onto symmetric and asymmetric micropatterned surfaces. Surface micropatterning of streptavidin-coated regions with varying adhesion shape and area was achieved by maskless UV photopatterning. To further study the effects of GUV shape on the cytoskeletal organization, actin filaments were polymerized together with bundling proteins inside the GUVs. The micropatterns induce synthetic cell deformation upon adhesion to the surface, with the cell shape adapting to the pattern shape and size. As expected, asymmetric patterns induce an asymmetric deformation in adherent synthetic cells. Actin filaments orient along the long axis of the deformed GUV, when having a length similar to the size of the major axis, whereas short filaments exhibit random orientation. With this bottom-up approach we have laid the first steps to identify the relationship between cell front-rear polarization and cytoskeleton organization in the future. Such a minimal system will allow us to further study the major components needed to create a polarized cytoskeleton at the onset of migration.

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.

Geometric Control of Cell Behavior by Biomolecule Nanodistribution

Many dynamic interactions within the cell microenvironment modulate cell behavior and cell fate. However, the pathways and mechanisms behind cell–cell or cell–extracellular matrix interactions remain understudied, as they occur at a nanoscale level. Recent progress in nanotechnology allows for mimicking of the microenvironment at nanoscale in vitro; electron-beam lithography (EBL) is currently the most promising technique. Although this nanopatterning technique can generate nanostructures of good quality and resolution, it has resulted, thus far, in the production of only simple shapes (e.g., rectangles) over a relatively small area (100 × 100 μm), leaving its potential in biological applications unfulfilled. Here, we used EBL for cell-interaction studies by coating cell-culture-relevant material with electron-conductive indium tin oxide, which formed nanopatterns of complex nanohexagonal structures over a large area (500 × 500 μm). We confirmed the potential of EBL for use in cell-interaction studies by analyzing specific cell responses toward differentially distributed nanohexagons spaced at 1000, 500, and 250 nm. We found that our optimized technique of EBL with HaloTags enabled the investigation of broad changes to a cell-culture-relevant surface and can provide an understanding of cellular signaling mechanisms at a single-molecule level.

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.

Sticking around: Cell adhesion patterning for energy minimization and substrate mechanosensing

Tissue stiffness (Young's modulus) is a key control parameter in cell behavior and bioengineered gels where defined mechanical properties have become an essential part of the toolkit for interrogating mechanotransduction. Here, we show using a mechanical cell model that the effective substrate stiffness experienced by a cell depends, not just on the engineered mechanical properties of the substrate but critically also on the particular arrangement of adhesions between cell and substrate. In particular, we find that cells with different adhesion patterns can experience two different gel stiffnesses as equivalent and will generate the same mean cell deformations. In considering small patches of adhesion, which mimic focal adhesion complexes, we show how the experimentally observed focal adhesion growth and elongation on stiff substrates can be explained by energy considerations. Relatedly, energy arguments also provide a reason why nascent adhesions do not establish into focal adhesions on soft substrates, as has been commonly observed. Fewer and larger adhesions are predicted to be preferred over more and smaller, an effect enhanced by random spot placing with the simulations predicting qualitatively realistic cell shapes in this case.

On the origin of universal cell shape variability in confluent epithelial monolayers

Cell shape is fundamental in biology. The average cell shape can influence crucial biological functions, such as cell fate and division orientation. But cell-to-cell shape variability is often regarded as noise. In contrast, recent works reveal that shape variability in diverse epithelial monolayers follows a nearly universal distribution. However, the origin and implications of this universality remain unclear. Here, assuming contractility and adhesion are crucial for cell shape, characterized via aspect ratio (r), we develop a mean-field analytical theory for shape variability. We find that all the system-specific details combine into a single parameter α that governs the probability distribution function (PDF) of r; this leads to a universal relation between the standard deviation and the average of r. The PDF for the scaled r is not strictly but nearly universal. In addition, we obtain the scaled area distribution, described by the parameter μ. Information of α and μ together can distinguish the effects of changing physical conditions, such as maturation, on different system properties. We have verified the theory via simulations of two distinct models of epithelial monolayers and with existing experiments on diverse systems. We demonstrate that in a confluent monolayer, average shape determines both the shape variability and dynamics. Our results imply that cell shape distribution is inevitable, where a single parameter describes both statics and dynamics and provides a framework to analyze and compare diverse epithelial systems. In contrast to existing theories, our work shows that the universal properties are consequences of a mathematical property and should be valid in general, even in the fluid regime.

Subcellular Dynamic Immunopatterning of Cytosolic Protein Complexes on Microstructured Polymer Substrates

Analysis of protein–protein interactions in living cells by protein micropatterning is currently limited to the spatial arrangement of transmembrane proteins and their corresponding downstream molecules. Here, we present a robust and straightforward method for dynamic immunopatterning of cytosolic protein complexes by use of an artificial transmembrane bait construct in combination with microstructured antibody arrays on cyclic olefin polymer substrates. As a proof, the method was used to characterize Grb2-mediated signaling pathways downstream of the epidermal growth factor receptor (EGFR). Ternary protein complexes (Shc1:Grb2:SOS1 and Grb2:Gab1:PI3K) were identified, and we found that EGFR downstream signaling is based on constitutively bound (Grb2:SOS1 and Grb2:Gab1) as well as on agonist-dependent protein associations with transient interaction properties (Grb2:Shc1 and Grb2:PI3K). Spatiotemporal analysis further revealed significant differences in stability and exchange kinetics of protein interactions. Furthermore, we could show that this approach is well suited to study the efficacy and specificity of SH2 and SH3 protein domain inhibitors in a live cell context. Altogether, this method represents a significant enhancement of quantitative subcellular micropatterning approaches as an alternative to standard biochemical analyses.

Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue

Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical framework for such a system is, therefore, important. Vertex-model (VM) simulations have provided crucial insights into the dynamics of such systems, but their nonequilibrium nature makes theoretical development difficult. The cellular Potts model (CPM) of confluent monolayers provides an alternative model for such systems with a well-defined equilibrium limit. We combine numerical simulations of the CPM and an analytical study based on one of the most successful theories of equilibrium glass, the random first-order transition theory, and develop a comprehensive theoretical framework for a confluent glassy system. We find that the glassy dynamics within the CPM is qualitatively similar to that in the VM. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter P_{0} is varied. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in such systems. The fragility of the system decreases with increasing P_{0} in the low-P_{0} regime, whereas the dynamics is independent of P_{0} in the other regime. The rigidity transition, found in the VM, is absent within the CPM; this difference seems to come from the nonequilibrium nature of the former. We show that the CPM captures the basic phenomenology of glassy dynamics in a confluent biological system via comparison of our numerical results with existing experiments on different systems.

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.

The Research Advance of Cell Bridges in vitro

The microenvironment in which cells reside in vivo dictates their biological and mechanical functioning is associated with morphogenetic and regenerative processes and may find implications in regenerative medicine and tissue engineering. The development of nano- and micro-fabricated technologies, three-dimensional (3D) printing technique, and biomimetic medical materials have enabled researchers to prepare novel advanced substrates mimicking the in vivo microenvironment. Most of the novel morphologies and behaviors of cells, including contact guidance and cell bridges which are observed in vivo but are not perceived in the traditional two-dimensional (2D) culture system, emerged on those novel substrates. Using cell bridges, cell can span over the surface of substrates to maintain mechanical stability and integrity of tissue, as observed in physiological processes, such as wound healing, regeneration and development. Compared to contact guidance, which has received increased attention and is investigated extensively, studies on cell bridges remain scarce. Therefore, in this mini-review, we have comprehensively summarized and classified different kinds of cell bridges formed on various substrates and highlighted possible biophysical mechanisms underlying cell bridge formation for their possible implication in the fields of tissue engineering and regenerative medicine.

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.

Mechanotransduction and Stiffness-Sensing: Mechanisms and Opportunities to Control Multiple Molecular Aspects of Cell Phenotype as a Design Cornerstone of Cell-Instructive Biomaterials for Articular Cartilage Repair

Since material stiffness controls many cell functions, we reviewed the currently available knowledge on stiffness sensing and elucidated what is known in the context of clinical and experimental articular cartilage (AC) repair. Remarkably, no stiffness information on the various biomaterials for clinical AC repair was accessible. Using mRNA expression profiles and morphology as surrogate markers of stiffness-related effects, we deduced that the various clinically available biomaterials control chondrocyte (CH) phenotype well, but not to equal extents, and only in non-degenerative settings. Ample evidence demonstrates that multiple molecular aspects of CH and mesenchymal stromal cell (MSC) phenotype are susceptible to material stiffness, because proliferation, migration, lineage determination, shape, cytoskeletal properties, expression profiles, cell surface receptor composition, integrin subunit expression, and nuclear shape and composition of CHs and/or MSCs are stiffness-regulated. Moreover, material stiffness modulates MSC immuno-modulatory and angiogenic properties, transforming growth factor beta 1 (TGF-β1)-induced lineage determination, and CH re-differentiation/de-differentiation, collagen type II fragment production, and TGF-β1- and interleukin 1 beta (IL-1β)-induced changes in cell stiffness and traction force. We then integrated the available molecular signaling data into a stiffness-regulated CH phenotype model. Overall, we recommend using material stiffness for controlling cell phenotype, as this would be a promising design cornerstone for novel future-oriented, cell-instructive biomaterials for clinical high-quality AC repair tissue.

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.

Disentangling the behavioural variability of confined cell migration

Cell-to-cell variability is inherent to numerous biological processes, including cell migration. Quantifying and characterizing the variability of migrating cells is challenging, as it requires monitoring many cells for long time windows under identical conditions. Here, we observe the migration of single human breast cancer cells (MDA-MB-231) in confining two-state micropatterns. To describe the stochastic dynamics of this confined migration, we employ a dynamical systems approach. We identify statistics to measure the behavioural variance of the migration, which significantly exceeds that predicted by a population-averaged stochastic model. This additional variance can be explained by the combination of an ‘ageing’ process and population heterogeneity. To quantify population heterogeneity, we decompose the cells into subpopulations of slow and fast cells, revealing the presence of distinct classes of dynamical systems describing the migration, ranging from bistable to limit cycle behaviour. Our findings highlight the breadth of migration behaviours present in cell populations.

Stretching of fibroblast cells on micropatterned gelatin on silicone elastomer

Micropatterned gelatin was formed on the silicone elastomer surface. The micropattern enabled cell alignment, regulation of the cell shape, and endowed the cells with resistance against mechanical stress.

Sub-Micropillar Spacing Modulates the Spatial Arrangement of Mouse MC3T3-E1 Osteoblastic Cells

Surface topography is one of the main factors controlling cell responses on implanted devices and a proper definition of the characteristics that optimize cell behavior may be crucial to improve the clinical performances of these implants. Substrate geometry is known to affect cell shape, as cells try to optimize their adhesion by adapting to the irregularities beneath, and this in turn profoundly affects their activity. In the present study, we cultured murine calvaria MC3T3-E1 cells on surfaces with pillars arranged as hexagons with two different spacings and observed their morphology during adhesion and growth. Cells on these highly ordered substrates attached and proliferated effectively, showing a marked preference for minimizing the inter-pillar distance, by following specific pathways across adjacent pillars and displaying consistent morphological modules. Moreover, cell behavior appeared to follow tightly controlled patterns of extracellular protein secretion, which preceded and matched cells and, on a sub-cellular level, cytoplasmic orientation. Taken together, these results outline the close integration of surface features, extracellular proteins alignment and cell arrangement, and provide clues on how to control and direct cell spatial order and cell morphology by simply acting on inter-pillar spacing.

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.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Many studies in cell biology employ global shape descriptors to probe mechanisms of cell morphogenesis. Here, we implement a framework in this paper to profile cellular morphodynamics very locally. We employ the Hilbert-Huang transform (HHT) to extract along the entire cell edge spectra of instantaneous edge motion frequency and magnitude and use them to classify overall cell behavior as well as subcellular edge sectors of distinct dynamics. We find in fibroblast-like COS7 cells that the marked heterogeneity in mobility of an unstimulated population is fully captured by differences in the magnitude spectra, while the frequency spectra are conserved between cells. Using optogenetics to acutely inhibit morphogenetic signaling pathways we find that these molecular shifts are reflected by changes in the frequency spectra but not in the magnitude spectra. After clustering cell edge sectors with distinct morphodynamics we observe in cells expressing a Rac1 activity biosensor that the sectors with different frequency spectra associate with different signaling intensity and dynamics. Together, these observations let us conclude that the frequency spectrum encodes the wiring of the molecular circuitry that regulates edge movements, whereas the magnitude captures the activation level of the circuitry.

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.

How cells respond to environmental cues - insights from bio-functionalized substrates

Biomimetic materials have long been the (he)art of bioengineering. They usually aim at mimicking in vivo conditions to allow in vitro culture, differentiation and expansion of cells. The past decade has witnessed a considerable amount of progress in soft lithography, bio-inspired micro-fabrication and biochemistry, allowing the design of sophisticated and physiologically relevant micro- and nano-environments. These systems now provide an exquisite toolbox with which we can control a large set of physicochemical environmental parameters that determine cell behavior. Bio-functionalized surfaces have evolved from simple protein-coated solid surfaces or cellular extracts into nano-textured 3D surfaces with controlled rheological and topographical properties. The mechanobiological molecular processes by which cells interact and sense their environment can now be unambiguously understood down to the single-molecule level. This Commentary highlights recent successful examples where bio-functionalized substrates have contributed in raising and answering new questions in the area of extracellular matrix sensing by cells, cell-cell adhesion and cell migration. The use, the availability, the impact and the challenges of such approaches in the field of biology are discussed.

Ring-Shaped Microlanes and Chemical Barriers as a Platform for Probing Single-Cell Migration

Quantification and discrimination of pharmaceutical and disease-related effects on cell migration requires detailed characterization of single-cell motility. In this context, micropatterned substrates that constrain cells within defined geometries facilitate quantitative readout of locomotion. Here, we study quasi-one-dimensional cell migration in ring-shaped microlanes. We observe bimodal behavior in form of alternating states of directional migration (run state) and reorientation (rest state). Both states show exponential lifetime distributions with characteristic persistence times, which, together with the cell velocity in the run state, provide a set of parameters that succinctly describe cell motion. By introducing PEGylated barriers of different widths into the lane, we extend this description by quantifying the effects of abrupt changes in substrate chemistry on migrating cells. The transit probability decreases exponentially as a function of barrier width, thus specifying a characteristic penetration depth of the leading lamellipodia. Applying this fingerprint-like characterization of cell motion, we compare different cell lines, and demonstrate that the cancer drug candidate salinomycin affects transit probability and resting time, but not run time or run velocity. Hence, the presented assay allows to assess multiple migration-related parameters, permits detailed characterization of cell motility, and has potential applications in cell biology and advanced drug screening.