Self-polarization and directional motility of cytoplasm

Multiple Mechanisms to Regulate Actin Functions: "Fundamental" Versus Lineage-Specific Mechanisms and Hierarchical Relationships

Eukaryotic actin filaments play a central role in numerous cellular functions, with each function relying on the interaction of actin filaments with specific actin-binding proteins. Understanding the mechanisms that regulate these interactions is key to uncovering how actin filaments perform diverse roles at different cellular locations. Several distinct classes of actin regulatory mechanisms have been proposed and experimentally supported. However, these mechanisms vary in their nature and hierarchy. For instance, some operate under the control of others, highlighting hierarchical relationships. Additionally, while certain mechanisms are fundamental and ubiquitous across eukaryotes, others are lineage-specific. Here, we emphasize the fundamental importance and functional significance of the following actin regulatory mechanisms: the biochemical regulation of actin nucleators, the ATP hydrolysis-dependent aging of actin filaments, thermal fluctuation- and mechanical strain-dependent conformational changes of actin filaments, and cooperative conformational changes induced by actin-binding proteins.

Modelling the effect of cell motility on mixing and invasion in epithelial monolayers

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

Model supports asymmetric regulation across the intercellular junction for collective cell polarization

Symmetry breaking, which is ubiquitous in biological cells, functionally enables directed cell movement and organized embryogenesis. Prior to movement, cells break symmetry to form a well-defined cell front and rear in a process called polarization. In developing and regenerating tissues, collective cell movement requires the coordination of the polarity of the migration machineries of neighboring cells. Though several works shed light on the molecular basis of polarity, fewer studies have focused on the regulation across the cell-cell junction required for collective polarization, thus limiting our ability to connect tissue-level dynamics to subcellular interactions. Here, we investigated how polarity signals are communicated from one cell to its neighbor to ensure coordinated front-to-rear symmetry breaking with the same orientation across the group. In a theoretical setting, we systematically searched a variety of intercellular interactions and identified that co-alignment arrangement of the polarity axes in groups of two and four cells can only be achieved with strong asymmetric regulation of Rho GTPases or enhanced assembly of complementary F-actin structures across the junction. Our results held if we further assumed the presence of an external stimulus, intrinsic cell-to-cell variability, or larger groups. The results underline the potential of using quantitative models to probe the molecular interactions required for macroscopic biological phenomena. Lastly, we posit that asymmetric regulation is achieved through junction proteins and predict that in the absence of cytoplasmic tails of such linker proteins, the likeliness of doublet co-polarity is greatly diminished.

Rigidity percolation and active advection synergize in the actomyosin cortex to drive amoeboid cell motility

Spontaneous locomotion is a common feature of most metazoan cells, generally attributed to the properties of actomyosin networks. This force-producing machinery has been studied down to the most minute molecular details, especially in lamellipodium-driven migration. Nevertheless, how actomyosin networks work inside contraction-driven amoeboid cells still lacks unifying principles. Here, using stable motile blebs from HeLa cells as a model amoeboid motile system, we imaged the dynamics of the actin cortex at the single filament level and revealed the co-existence of three distinct rheological phases. We introduce "advected percolation," a process where rigidity percolation and active advection synergize, spatially organizing the actin network's mechanical properties into a minimal and generic locomotion mechanism. Expanding from our observations on simplified systems, we speculate that this model could explain, down to the single actin filament level, how amoeboid cells, such as cancer or immune cells, can propel efficiently through complex 3D environments.

Light-guided actin polymerization drives directed motility in protocells

Motility is a hallmark of life's dynamic processes, enabling cells to actively chase prey, repair wounds, and shape organs. Recreating these intricate behaviors using well-defined molecules remains a major challenge at the intersection of biology, physics, and molecular engineering. Although the polymerization force of the actin cytoskeleton is characterized as a primary driver of cell motility, recapitulating this process in protocellular systems has proven elusive. The difficulty lies in the daunting task of distilling key components from motile cells and integrating them into model membranes in a physiologically relevant manner. To address this, we developed a method to optically control actin polymerization with high spatiotemporal precision within cell-mimetic lipid vesicles known as giant unilamellar vesicles (GUVs). Within these active protocells, the reorganization of actin networks triggered outward membrane extensions as well as the unidirectional movement of GUVs at speeds of up to 0.43 μm/min, comparable to typical adherent mammalian cells. Notably, our findings reveal a synergistic interplay between branched and linear actin forms in promoting membrane protrusions, highlighting the cooperative nature of these cytoskeletal elements. This approach offers a powerful platform for unraveling the intricacies of cell migration, designing synthetic cells with active morphodynamics, and advancing bioengineering applications, such as self-propelled delivery systems and autonomous tissue-like materials.

Salt Gradient-Induced Phoresis of Vesicles and Enhanced Membrane Fusion in a Crowded Milieu

Phoresis of biocolloidal objects in response to chemical gradients is a matter of interest among diverse scientific disciplines owing to their importance in the spatiotemporal orchestration of biochemical processes. Although there are reports of soft matter transport/phoresis in the gradient of ions or salts in the aqueous system, their phoretic behavior in the presence of macromolecular crowder is largely unexplored. Notably, cellular cytoplasm is illustrated as a crowded milieu and thereby understanding biomolecular phoresis in the presence of polymeric macromolecules would endorse phoretic behavior in a biomimetic environment. Here, we report the phoresis-induced enhanced aggregation and fusion of vesicles in gradients of monovalent (NaCl) and divalent salt (MgCl2), in the presence of polymeric crowder, polyethylene glycol of molecular weight 400 (PEG 400). Apart from diffusiophoresis, depletion force plays a crucial factor in crowded environments to control localized vesicle aggregation in a salt gradient. This demonstration will potentially show the pathway to future research related to spatiotemporally correlated liposomal transport and membrane-dependent function (such as content mixing and signaling) in a physiologically relevant crowded environment.

Ras suppression potentiates rear actomyosin contractility-driven cell polarization and migration

Ras has been extensively studied as a promoter of cell proliferation, whereas few studies have explored its role in migration. To investigate the direct and immediate effects of Ras activity on cell motility or polarity, we focused on RasGAPs, C2GAPB in Dictyostelium amoebae and RASAL3 in HL-60 neutrophils and macrophages. In both cellular systems, optically recruiting the respective RasGAP to the cell front extinguished pre-existing protrusions and changed migration direction. However, when these respective RasGAPs were recruited uniformly to the membrane, cells polarized and moved more rapidly, whereas targeting to the back exaggerated these effects. These unexpected outcomes of attenuating Ras activity naturally had strong, context-dependent consequences for chemotaxis. The RasGAP-mediated polarization depended critically on myosin II activity and commenced with contraction at the cell rear, followed by sustained mTORC2-dependent actin polymerization at the front. These experimental results were captured by computational simulations in which Ras levels control front- and back-promoting feedback loops. The discovery that inhibiting Ras activity can produce counterintuitive effects on cell migration has important implications for future drug-design strategies targeting oncogenic Ras.

Active nuclear positioning and actomyosin contractility maintain leader cell integrity during gonadogenesis

Proper distribution of organelles can play an important role in a moving cell's performance. During C. elegans gonad morphogenesis, the nucleus of the leading distal tip cell (DTC) is always found at the front, yet the significance of this localization is unknown. Here, we identified the molecular mechanism that keeps the nucleus at the front, despite a frictional force that pushes it backward. The Klarsicht/ANC-1/Syne homology (KASH) domain protein UNC-83 links the nucleus to the motor protein kinesin-1 that moves along a polarized acentrosomal microtubule network. Interestingly, disrupting nuclear positioning on its own did not affect gonad morphogenesis. However, reducing actomyosin contractility on top of nuclear mispositioning led to a dramatic phenotype: DTC splitting and gonad bifurcation. Long-term live imaging of the double knockdown revealed that, while the gonad attempted to perform a planned U-turn, the DTC was stretched due to the lagging nucleus until it fragmented into a nucleated cell and an enucleated cytoplast, each leading an independent gonadal arm. Remarkably, the enucleated cytoplast had polarity and invaded, but it could only temporarily support germ cell proliferation. Based on a qualitative biophysical model, we conclude that the leader cell employs two complementary mechanical approaches to preserve its integrity and ensure proper organ morphogenesis while navigating through a complex 3D environment: active nuclear positioning by microtubule motors and actomyosin-driven cortical contractility.

Establishing a conceptual framework for holistic cell states and state transitions

Cell states were traditionally defined by how they looked, where they were located, and what functions they performed. In this post-genomic era, the field is largely focused on a molecular view of cell state. Moving forward, we anticipate that the observables used to define cell states will evolve again as single-cell imaging and analytics are advancing at a breakneck pace via the collection of large-scale, systematic cell image datasets and the application of quantitative image-based data science methods. This is, therefore, a key moment in the arc of cell biological research to develop approaches that integrate the spatiotemporal observables of the physical structure and organization of the cell with molecular observables toward the concept of a holistic cell state. In this perspective, we propose a conceptual framework for holistic cell states and state transitions that is data-driven, practical, and useful to enable integrative analyses and modeling across many data types.

Mesenchymal cell migration on one-dimensional micropatterns

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

A minimal physical model for curvotaxis driven by curved protein complexes at the cell's leading edge

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

Novel Nuclear Roles for Testis-Specific ACTL7A and ACTL7B Supported by In Vivo Characterizations and AI Facilitated In Silico Mechanistic Modeling with Implications for Epigenetic Regulation in Spermiogenesis

A mechanistic role for nuclear function of testis-specific actin related proteins (ARPs) is proposed here through contributions of ARP subunit swapping in canonical chromatin regulatory complexes. This is significant to our understanding of both mechanisms controlling regulation of spermiogenesis, and the expanding functional roles of the ARPs in cell biology. Among these roles, actins and ARPs are pivotal not only in cytoskeletal regulation, but also in intranuclear chromatin organization, influencing gene regulation and nucleosome remodeling. This study focuses on two testis-specific ARPs, ACTL7A and ACTL7B, exploring their intranuclear activities and broader implications utilizing combined in vivo, in vitro, and in silico approaches. ACTL7A and ACTL7B, previously associated with structural roles, are hypothesized here to serve in chromatin regulation during germline development. This study confirms the intranuclear presence of ACTL7B in spermatocytes and round spermatids, revealing a potential role in intranuclear processes, and identifies a putative nuclear localization sequence conserved across mammalian ACTL7B, indicating a potentially unique mode of nuclear transport which differs from conventional actin. Ablation of ACTL7B leads to varied transcriptional changes reported here. Additionally, in the absence of ACTL7A or ACTL7B there is a loss of intranuclear localization of HDAC1 and HDAC3, which are known regulators of epigenetic associated acetylation changes that in turn regulate gene expression. Thus, these HDACs are implicated as contributors to the aberrant gene expression observed in the KO mouse testis transcriptomic analysis. Furthermore, this study employed and confirmed the accuracy of in silico models to predict ARP interactions with Helicase-SANT-associated (HSA) domains, uncovering putative roles for testis-specific ARPs in nucleosome remodeling complexes. In these models, ACTL7A and ACTL7B were found capable of binding to INO80 and SWI/SNF nucleosome remodeler family members in a manner akin to nuclear actin and ACTL6A. These models thus implicate germline-specific ARP subunit swapping within chromatin regulatory complexes as a potential regulatory mechanism for chromatin and associated molecular machinery adaptations in nuclear reorganizations required during spermiogenesis. These results hold implications for male fertility and epigenetic programing in the male-germline that warrant significant future investigation. In summary, this study reveals that ACTL7A and ACTL7B play intranuclear gene regulation roles in male gametogenesis, adding to the multifaceted roles identified also spanning structural, acrosomal, and flagellar stability. ACTL7A and ACTL7B unique nuclear transport, impact on HDAC nuclear associations, impact on transcriptional processes, and proposed mechanism for involvement in nucleosome remodeling complexes supported by AI facilitated in silico modeling contribute to a more comprehensive understanding of the indispensable functions of ARPs broadly in cell biology, and specifically in male fertility.

Friction patterns guide actin network contraction

The shape of cells is the outcome of the balance of inner forces produced by the actomyosin network and the resistive forces produced by cell adhesion to their environment. The specific contributions of contractile, anchoring and friction forces to network deformation rate and orientation are difficult to disentangle in living cells where they influence each other. Here, we reconstituted contractile actomyosin networks in vitro to study specifically the role of the friction forces between the network and its anchoring substrate. To modulate the magnitude and spatial distribution of friction forces, we used glass or lipids surface micropatterning to control the initial shape of the network. We adapted the concentration of Nucleating Promoting Factor on each surface to induce the assembly of actin networks of similar densities and compare the deformation of the network toward the centroid of the pattern shape upon myosin-induced contraction. We found that actin network deformation was faster and more coordinated on lipid bilayers than on glass, showing the resistance of friction to network contraction. To further study the role of the spatial distribution of these friction forces, we designed heterogeneous micropatterns made of glass and lipids. The deformation upon contraction was no longer symmetric but biased toward the region of higher friction. Furthermore, we showed that the pattern of friction could robustly drive network contraction and dominate the contribution of asymmetric distributions of myosins. Therefore, we demonstrate that during contraction, both the active and resistive forces are essential to direct the actin network deformation.

Ras-mediated homeostatic control of front-back signaling dictates cell polarity

Studies in the model systems, Dictyostelium amoebae and HL-60 neutrophils, have shown that local Ras activity directly regulates cell motility or polarity. Localized Ras activation on the membrane is spatiotemporally regulated by its activators, RasGEFs, and inhibitors, RasGAPs, which might be expected to create a stable 'front' and 'back', respectively, in migrating cells. Focusing on C2GAPB in amoebae and RASAL3 in neutrophils, we investigated how Ras activity along the cortex controls polarity. Since existing gene knockout and overexpression studies can be circumvented, we chose optogenetic approaches to assess the immediate, local effects of these Ras regulators on the cell cortex. In both cellular systems, optically targeting the respective RasGAPs to the cell front extinguished existing protrusions and changed the direction of migration, as might be expected. However, when the expression of C2GAPB was induced globally, amoebae polarized within hours. Furthermore, within minutes of globally recruiting either C2GAPB in amoebae or RASAL3 in neutrophils, each cell type polarized and moved more rapidly. Targeting the RasGAPs to the cell backs exaggerated these effects on migration and polarity. Overall, in both cell types, RasGAP-mediated polarization was brought about by increased actomyosin contractility at the back and sustained, localized F-actin polymerization at the front. These experimental results were accurately captured by computational simulations in which Ras levels control front and back feedback loops. The discovery that context-dependent Ras activity on the cell cortex has counterintuitive, unanticipated effects on cell polarity can have important implications for future drug-design strategies targeting oncogenic Ras.

Physical confinement and cell proximity increase cell migration rates and invasiveness: A mathematical model of cancer cell invasion through flexible channels

Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves 12% faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion.

On multistability and constitutive relations of cell motion on fibronectin lanes

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

Small hand-designed convolutional neural networks outperform transfer learning in automated cell shape detection in confluent tissues

Mechanical cues such as stresses and strains are now recognized as essential regulators in many biological processes like cell division, gene expression or morphogenesis. Studying the interplay between these mechanical cues and biological responses requires experimental tools to measure these cues. In the context of large scale tissues, this can be achieved by segmenting individual cells to extract their shapes and deformations which in turn inform on their mechanical environment. Historically, this has been done by segmentation methods which are well known to be time consuming and error prone. In this context however, one doesn't necessarily require a cell-level description and a coarse-grained approach can be more efficient while using tools different from segmentation. The advent of machine learning and deep neural networks has revolutionized the field of image analysis in recent years, including in biomedical research. With the democratization of these techniques, more and more researchers are trying to apply them to their own biological systems. In this paper, we tackle a problem of cell shape measurement thanks to a large annotated dataset. We develop simple Convolutional Neural Networks (CNNs) which we thoroughly optimize in terms of architecture and complexity to question construction rules usually applied. We find that increasing the complexity of the networks rapidly no longer yields improvements in performance and that the number of kernels in each convolutional layer is the most important parameter to achieve good results. In addition, we compare our step-by-step approach with transfer learning and find that our simple, optimized CNNs give better predictions, are faster in training and analysis and don't require more technical knowledge to be implemented. Overall, we offer a roadmap to develop optimized models and argue that we should limit the complexity of such models. We conclude by illustrating this strategy on a similar problem and dataset.

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.

Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a "staircase" pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.

The nonlinear motion of cells subject to external forces

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two different self-propulsion mechanisms, active stresses and treadmilling polymerisation, and we investigate how the active drop motion is altered by these surface forces. We find a highly non-linear response to forces that we characterise using drop velocity, drop shape, and the traction between the drop and the substrate. Each self-propulsion mechanism gives rise to two main modes of motion: a long thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. In each case there is a sharp transition between parabolic, and long thin drops as a function of the applied forces and indications of drop break-up where large forces stretch the drop.

Self-organization in amoeboid motility

Amoeboid motility has come to refer to a spectrum of cell migration modes enabling a cell to move in the absence of strong, specific adhesion. To do so, cells have evolved a range of motile surface movements whose physical principles are now coming into view. In response to external cues, many cells—and some single-celled-organisms—have the capacity to turn off their default migration mode. and switch to an amoeboid mode. This implies a restructuring of the migration machinery at the cell scale and suggests a close link between cell polarization and migration mediated by self-organizing mechanisms. Here, I review recent theoretical models with the aim of providing an integrative, physical picture of amoeboid migration.

Symmetry-breaking, motion and bistability of active drops through polarization-surface coupling

Cell crawling crucially depends on the collective dynamics of the acto-myosin cytoskeleton. However, it remains an open question to what extent cell polarization and persistent motion depend on continuous regulatory mechanisms and autonomous physical mechanisms. Experiments on cell fragments and theoretical considerations for active polar liquids have highlighted that physical mechanisms induce motility through splay and bend configurations in a nematic director field. Here, we employ a simple model, derived from basic thermodynamic principles, for active polar free-surface droplets to identify a different mechanism of motility. Namely, active stresses drive drop motion through spatial variations of polarization strength. This robustly induces parity-symmetry breaking and motility even for liquid ridges (2D drops) and adds to splay- and bend-driven pumping in 3D geometries. Intriguingly, then, stable polar moving and axisymmetric resting states may coexist, reminiscent of the interconversion of moving and resting keratocytes by external stimuli. The identified additional motility mode originates from a competition between the elastic bulk energy and the polarity control exerted by the drop surface. As it already breaks parity-symmetry for passive drops, the resulting back-forth asymmetry enables active stresses to effectively pump liquid and drop motion ensues.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Self-Organization of Cellular Units

The purpose of this review is to explore self-organizing mechanisms that pattern microtubules (MTs) and spatially organize animal cell cytoplasm, inspired by recent experiments in frog egg extract. We start by reviewing conceptual distinctions between self-organizing and templating mechanisms for subcellular organization. We then discuss self-organizing mechanisms that generate radial MT arrays and cell centers in the absence of centrosomes. These include autocatalytic MT nucleation, transport of minus ends, and nucleation from organelles such as melanosomes and Golgi vesicles that are also dynein cargoes. We then discuss mechanisms that partition the cytoplasm in syncytia, in which multiple nuclei share a common cytoplasm, starting with cytokinesis, when all metazoan cells are transiently syncytial. The cytoplasm of frog eggs is partitioned prior to cytokinesis by two self-organizing modules, protein regulator of cytokinesis 1 (PRC1)-kinesin family member 4A (KIF4A) and chromosome passenger complex (CPC)-KIF20A. Similar modules may partition longer-lasting syncytia, such as early Drosophila embryos. We end by discussing shared mechanisms and principles for the MT-based self-organization of cellular units.

Optogenetic control of intracellular flows and cell migration: A comprehensive mathematical analysis with a minimal active gel model

The actin cytoskeleton of cells is in continuous motion due to both polymerization of new filaments and their contraction by myosin II molecular motors. Through adhesion to the substrate, such intracellular flow can be converted into cell migration. Recently, optogenetics has emerged as a new powerful experimental method to control both actin polymerization and myosin II contraction. While optogenetic control of polymerization can initiate cell migration by generating protrusion, it is less clear if and how optogenetic control of contraction can also affect cell migration. Here we analyze the latter situation using a minimal variant of active gel theory into which we include optogenetic activation as a spatiotemporally constrained perturbation. The model can describe the symmetrical flow of the actomyosin system observed in optogenetic experiments, but not the long-lasting polarization required for cell migration. Motile solutions become possible if cytoskeletal polymerization is included through the boundary conditions. Optogenetic activation of contraction can then initiate locomotion in a symmetrically spreading cell and strengthen motility in an asymmetrically polymerizing one. If designed appropriately, it can also arrest motility even for protrusive boundaries.

Cytoskeletal symmetry breaking in animal cells

Symmetry breaking is a crucial step in structure formation and function of all cells, necessary for cell movement, cell division, and polarity establishment. Although the mechanisms of symmetry breaking are diverse, they often share common characteristics. Here we review examples of nematic, polar, and chiral cytoskeletal symmetry breaking in animal cells, and analogous processes in simplified reconstituted systems. We discuss the origins of symmetry breaking, which can arise spontaneously, or involve amplification of a pre-existing external or internal bias to the whole cell level. The underlying mechanisms often involve both chemical and mechanical processes that cooperate to break symmetry in a robust manner, and typically depend on the shape, size, or properties of the cell's boundary.

NK cells integrate signals over large areas when building immune synapses but require local stimuli for degranulation

Immune synapses are large-scale, transient molecular assemblies that serve as platforms for antigen presentation to B and T cells and for target recognition by cytotoxic T cells and natural killer (NK) cells. The formation of an immune synapse is a tightly regulated, stepwise process in which the cytoskeleton, cell surface receptors, and intracellular signaling proteins rearrange into supramolecular activation clusters (SMACs). We generated artificial immune synapses (AIS) consisting of synthetic and natural ligands for the NK cell-activating receptors LFA-1 and CD16 by microcontact printing the ligands into circular-shaped SMAC structures. Live-cell imaging and analysis of fixed human NK cells in this reductionist system showed that the spatial distribution of activating ligands influenced the formation, stability, and outcome of NK cell synapses. Whereas engagement of LFA-1 alone promoted synapse initiation, combined engagement of LFA-1 and CD16 was required for the formation of mature synapses and degranulation. Organizing LFA-1 and CD16 ligands into donut-shaped AIS resulted in fewer long-lasting, symmetrical synapses compared to dot-shaped AIS. NK cells spreading evenly over either AIS shape exhibited similar arrangements of the lytic machinery. However, degranulation only occurred in regions containing ligands that therefore induced local signaling, suggesting the existence of a late checkpoint for degranulation. Our results demonstrate that the spatial organization of ligands in the synapse can affect its outcome, which could be exploited by target cells as an escape mechanism.

Self-organized cell migration across scales - from single cell movement to tissue formation

Self-organization is a key feature of many biological and developmental processes, including cell migration. Although cell migration has traditionally been viewed as a biological response to extrinsic signals, advances within the past two decades have highlighted the importance of intrinsic self-organizing properties to direct cell migration on multiple scales. In this Review, we will explore self-organizing mechanisms that lay the foundation for both single and collective cell migration. Based on in vitro and in vivo examples, we will discuss theoretical concepts that underlie the persistent migration of single cells in the absence of directional guidance cues, and the formation of an autonomous cell collective that drives coordinated migration. Finally, we highlight the general implications of self-organizing principles guiding cell migration for biological and medical research.

Durotaxis: the mechanical control of directed cell migration

Directed cell migration is essential for cells to efficiently migrate in physiological and pathological processes. While migrating in their native environment, cells interact with multiple types of cues, such as mechanical and chemical signals. The role of chemical guidance via chemotaxis has been studied in the past, the understanding of mechanical guidance of cell migration via durotaxis remained unclear until very recently. Nonetheless, durotaxis has become a topic of intensive research and several advances have been made in the study of mechanically guided cell migration across multiple fields. Thus, in this article we provide a state of the art about durotaxis by discussing in silico, in vitro and in vivo data. We also present insights on the general mechanisms by which cells sense, transduce and respond to environmental mechanics, to then contextualize these mechanisms in the process of durotaxis and explain how cells bias their migration in anisotropic substrates. Furthermore, we discuss what is known about durotaxis in vivo and we comment on how haptotaxis could arise from integrating durotaxis and chemotaxis in native environments.

Cell Fragment Formation, Migration, and Force Exertion on Extracellular Mimicking Fiber Nanonets

Cell fragments devoid of the nucleus play an essential role in intercellular communication. Mostly studied on flat 2D substrates, their origins and behavior in native fibrous environments remain unknown. Here, cytoplasmic fragments' spontaneous formation and behavior in suspended extracellular matrices mimicking fiber architectures (parallel, crosshatch, and hexagonal) are described. After cleaving from the parent cell body, the fragments of diverse shapes on fibers migrate faster compared to 2D. Furthermore, while fragments in 2D are mostly circular, a higher number of rectangular and blob-like shapes are formed on fibers, and, interestingly, each shape is capable of forming protrusive structures. Absent in 2D, fibers' fragments display oscillatory migratory behavior with dramatic shape changes, sometimes remarkably sustained over long durations (>20 h). Immunostaining reveals paxillin distribution along fragment body-fiber length, while Forster Resonance Energy Transfer imaging of vinculin reveals mechanical loading of fragment adhesions comparable to whole cell adhesions. Using nanonet force microscopy, the forces exerted by fragments are estimated, and peculiarly small area fragments can exert forces similar to larger fragments in a Rho-associated kinase dependent manner. Overall, fragment dynamics on 2D substrates are insufficient to describe the mechanosensitivity of fragments to fibers, and the architecture of fiber networks can generate entirely new behaviors.

Dynamics of a cell motility model near the sharp interface limit

Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in Berlyand et al. (2017). Rigorous analysis of its sharp interface limit dynamics was completed in Mizuhara et al. (2016) and Mizuhara et al. (2019), where it was observed that persistent cell motion was not stable. In this work we numerically study the pre-limiting phase-field model near the sharp interface limit, to better understand this lack of persistent motion. We find that immobile, persistent, and rotating states are all exhibited in this minimal model, and investigate the loss of persistent motion in the sharp interface limit.

Computational models of migration modes improve our understanding of metastasis

Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell–extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.

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

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

A Stochastic Modelling Framework for Single Cell Migration: Coupling Contractility and Focal Adhesions

The interaction of the actin cytoskeleton with cell–substrate adhesions is necessary for cell migration. While the trajectories of motile cells have a stochastic character, investigations of cell motility mechanisms rarely elaborate on the origins of the observed randomness. Here, guided by a few fundamental attributes of cell motility, I construct a minimal stochastic cell migration model from ground-up. The resulting model couples a deterministic actomyosin contractility mechanism with stochastic cell–substrate adhesion kinetics, and yields a well-defined piecewise deterministic process. Numerical simulations reproduce several experimentally observed results, including anomalous diffusion, tactic migration and contact guidance. This work provides a basis for the development of cell–cell collision and population migration models.

A hybrid stochastic-deterministic mechanochemical model of cell polarization

Polarization is a crucial component in cell differentiation, development, and motility, but its details are not yet well understood. At the onset of cell locomotion, cells break symmetry to form well-defined cell fronts and rears. This polarity establishment varies across cell types: in Dictyostelium discoideum cells, it is mediated by biochemical signaling pathways and can function in the absence of a cytoskeleton, while in keratocytes, it is tightly connected to cytoskeletal dynamics and mechanics. Theoretical models that have been developed to understand the onset of polarization have explored either signaling or mechanical pathways, yet few have explored mechanochemical mechanisms. However, many motile cells rely on both signaling modules and actin cytoskeleton to break symmetry and achieve a stable polarized state. We propose a general mechanochemical polarization model based on coupling between a stochastic model for the segregation of signaling molecules and a simplified mechanical model for actin cytoskeleton network competition. We find that local linear coupling between minimally nonlinear signaling and cytoskeletal systems, separately not supporting stable polarization, yields a robustly polarized cell state. The model captures the essence of spontaneous polarization of neutrophils, which has been proposed to emerge due to the competition between frontness and backness pathways.

Influence of myosin activity and mechanical impact on keratocyte polarization

In cell migration, polarization is the process by which a stationary cell breaks symmetry and initiates motion. Although a lot is known about the mechanisms involved in cell polarization, the role played by myosin contraction remains unclear. In addition, cell polarization by mechanical impact has received little attention. Here, we study the influence of myosin activity on cell polarization and the initiation of motion induced by mechanical cues using a computational model for keratocytes. The model accounts for cell deformation, the dynamics of myosin and the signaling protein RhoA (a member of the Rho GTPases family), as well as the forces acting on the actomyosin network. Our results show that the attainment of a steady polarized state depends on the strength of myosin down- or up-regulation and that myosin upregulation favors cell polarization. Our results also confirm the existence of a threshold level for cell polarization, which is determined by the level of polarization of the Rho GTPases at the time the external stimuli vanish. In all, this paper shows that capturing the interactions between the signaling proteins (Rho GTPases for keratocytes) and the compounds of the motile machinery in a moving cell is crucial to study cell polarization.

Multiscale modelling of motility wave propagation in cell migration

The collective motion of cell monolayers within a tissue is a fundamental biological process that occurs during tissue formation, wound healing, cancerous invasion, and viral infection. Experiments have shown that at the onset of migration, the motility is self-generated as a polarisation wave starting from the leading edge of the monolayer and progressively propagates into the bulk. However, it is unclear how the propagation of this motility wave is influenced by cellular properties. Here, we investigate this question using a computational model based on the Potts model coupled to the dynamics of intracellular polarisation. The model captures the propagation of the polarisation wave and suggests that the cells cortex can regulate the migration modes: strongly contractile cells may depolarise the monolayer, whereas less contractile cells can form swirling movement. Cortical contractility is further found to limit the cells motility, which (i) decelerates the wave speed and the leading edge progression, and (ii) destabilises the leading edge. Together, our model describes how different mechanical properties of cells can contribute to the regulation of collective cell migration.

A minimal mechanosensing model predicts keratocyte evolution on flexible substrates

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis).

How many ways a cell can move: the modes of self-propulsion of an active drop

Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless motion, (ii) the self-propulsion of active components at the substrate, which gives rise to crawling motion, and (iii) a net capillary force, possibly self-generated, and coupled to internal activity. We determine travelling-wave solutions to the lubrication equations as a function of a dimensionless activity parameter for each mode of motion. Numerical simulations are used to characterize the drop motion over a wide range of activity magnitudes, and explicit analytical solutions in excellent agreement with the simulations are derived in the weak-activity regime.

Aligned 3D porous polyurethane scaffolds for biological anisotropic tissue regeneration

A green fabrication process (organic solvent-free) of artificial scaffolds is required in tissue engineering field. In this work, a series of aligned three-dimensional (3D) scaffolds are made from biodegradable waterborne polyurethane (PU) emulsion via directional freeze-drying method to ensure no organic byproducts. After optimizing the concentration of polymer in the emulsion and investigating different freezing temperatures, an aligned PUs scaffold (PU14) generated from 14 wt% polymer content and processed at -196°C was selected based on the desired oriented porous structure (pore size of 32.5 ± 9.3 μm, porosity of 92%) and balanced mechanical properties both in the horizontal direction (strength of 41.3 kPa, modulus of 72.3 kPa) and in the vertical direction (strength of 45.5 kPa, modulus of 139.3 kPa). The response of L929 cells and the regeneration of muscle tissue demonstrated that such pure material-based aligned 3D scaffold can facilitate the development of orientated cells and anisotropic tissue regeneration both in vitro and in vivo. Thus, these pure material-based scaffolds with ordered architecture have great potentials in tissue engineering for biological anisotropic tissue regeneration, such as muscle, nerve, spinal cord and so on.

Motility and morphodynamics of confined cells

We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. In our model, the cell is driven out of equilibrium by an active cytsokeleton force that acts on the membrane. The cell cytoplasm, described as a viscous droplet in the Darcy flow regime, contains a diffusive solute that actively transduces the applied cytoskeleton force. While fairly simple and analytically tractable, this quasi-two-dimensional model predicts a range of compelling dynamic behaviours. A linear stability analysis of the system reveals that solute activity first destabilizes a global polarization-translation mode, prompting cell motility through spontaneous symmetry breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. Altogether, this model offers an analytical paradigm of active deformable systems in which viscous hydrodynamics are coupled to diffusive force transducers.

A minimal computational model for three-dimensional cell migration

During migration, eukaryotic cells can continuously change their three-dimensional morphology, resulting in a highly dynamic and complex process. Further complicating this process is the observation that the same cell type can rapidly switch between different modes of migration. Modelling this complexity necessitates models that are able to track deforming membranes and that can capture the intracellular dynamics responsible for changes in migration modes. Here we develop an efficient three-dimensional computational model for cell migration, which couples cell mechanics to a simple intracellular activator-inhibitor signalling system. We compare the computational results to quantitative experiments using the social amoeba Dictyostelium discoideum. The model can reproduce the observed migration modes generated by varying either mechanical or biochemical model parameters and suggests a coupling between the substrate and the biomechanics of the cell.

Tractionless Self-Propulsion of Active Drops

We report on a new mode of self-propulsion exhibited by compact drops of active liquids on a substrate which, remarkably, is tractionless, i.e., which imparts no mechanical stress locally on the surface. We show, both analytically and by numerical simulation, that the equations of motion for an active nematic drop possess a simple self-propelling solution, with no traction on the solid surface and in which the direction of motion is controlled by the winding of the nematic director field across the drop height. The physics underlying this mode of motion has the same origins as that giving rise to the zero viscosity observed in bacterial suspensions. This topologically protected tractionless self-propusion provides a robust physical mechanism for efficient cell migration in crowded environments like tissues.

Recapitulation of molecular regulators of nuclear motion during cell migration

Cell migration is a highly orchestrated cellular event that involves physical interactions of diverse subcellular components. The nucleus as the largest and stiffest organelle in the cell not only maintains genetic functionality, but also actively changes its morphology and translocates through dynamic formation of nucleus-bound contractile stress fibers. Nuclear motion is an active and essential process for successful cell migration and nucleus self-repairs in response to compression and extension forces in complex cell microenvironment. This review recapitulates molecular regulators that are crucial for nuclear motility during cell migration and highlights recent advances in nuclear deformation-mediated rupture and repair processes in a migrating cell.

Patterning and polarization of cells by intracellular flows

Beginning with Turing’s seminal work [1], decades of research have demonstrated the fundamental ability of biochemical networks to generate and sustain the formation of patterns. However, it is increasingly appreciated that biochemical networks both shape and are shaped by physical and mechanical processes [2, 3, 4]. One such process is fluid flow. In many respects, the cytoplasm, membrane and actin cortex all function as fluids, and as they flow, they drive bulk transport of molecules throughout the cell. By coupling biochemical activity to long range molecular transport, flows can shape the distributions of molecules in space. Here we review the various types of flows that exist in cells, with the aim of highlighting recent advances in our understanding of how flows are generated and how they contribute to intracellular patterning processes, such as the establishment of cell polarity.

Crawling in a Fluid

There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a nonmotile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trends.

Polarization wave at the onset of collective cell migration

Collective cell migration underlies morphogenesis, tissue regeneration, and cancer progression. How the biomechanical coupling between epithelial cells triggers and coordinates the collective migration is an open question. Here, we develop a one-dimensional model for an epithelial monolayer which predicts that after the onset of migration at an open boundary, cells in the bulk of the epithelium are gradually recruited into outward-directed motility, exhibiting traveling-wave-like behavior. We find an exact formula for the speed of this motility wave proportional to the square root of the cells' contractility, which accounts for cortex tension and adhesion between adjacent cells.