Polymer motors: pushing out the front and pulling up the back

Adaptive nonequilibrium design of actin-based metamaterials: Fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control-both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.

Biochemical and mechanical regulation of actin dynamics

Polymerization of actin filaments against membranes produces force for numerous cellular processes, such as migration, morphogenesis, endocytosis, phagocytosis and organelle dynamics. Consequently, aberrant actin cytoskeleton dynamics are linked to various diseases, including cancer, as well as immunological and neurological disorders. Understanding how actin filaments generate forces in cells, how force production is regulated by the interplay between actin-binding proteins and how the actin-regulatory machinery responds to mechanical load are at the heart of many cellular, developmental and pathological processes. During the past few years, our understanding of the mechanisms controlling actin filament assembly and disassembly has evolved substantially. It has also become evident that the activities of key actin-binding proteins are not regulated solely by biochemical signalling pathways, as mechanical regulation is critical for these proteins. Indeed, the architecture and dynamics of the actin cytoskeleton are directly tuned by mechanical load. Here we discuss the general mechanisms by which key actin regulators, often in synergy with each other, control actin filament assembly, disassembly, and monomer recycling. By using an updated view of actin dynamics as a framework, we discuss how the mechanics and geometry of actin networks control actin-binding proteins, and how this translates into force production in endocytosis and mesenchymal cell migration.

Mechanosensitive Ion Channels, Axonal Growth, and Regeneration

Cells sense and respond to mechanical stimuli by converting those stimuli into biological signals, a process known as mechanotransduction. Mechanotransduction is essential in diverse cellular functions, including tissue development, touch sensitivity, pain, and neuronal pathfinding. In the search for key players of mechanotransduction, several families of ion channels were identified as being mechanosensitive and were demonstrated to be activated directly by mechanical forces in both the membrane bilayer and the cytoskeleton. More recently, Piezo ion channels were discovered as a bona fide mechanosensitive ion channel, and its characterization led to a cascade of research that revealed the diverse functions of Piezo proteins and, in particular, their involvement in neuronal repair.

Supracellular organization confers directionality and mechanical potency to migrating pairs of cardiopharyngeal progenitor cells

Physiological and pathological morphogenetic events involve a wide array of collective movements, suggesting that multicellular arrangements confer biochemical and biomechanical properties contributing to tissue-scale organization. The Ciona cardiopharyngeal progenitors provide the simplest model of collective cell migration, with cohesive bilateral cell pairs polarized along the leader-trailer migration path while moving between the ventral epidermis and trunk endoderm. We use the Cellular Potts Model to computationally probe the distributions of forces consistent with shapes and collective polarity of migrating cell pairs. Combining computational modeling, confocal microscopy, and molecular perturbations, we identify cardiopharyngeal progenitors as the simplest cell collective maintaining supracellular polarity with differential distributions of protrusive forces, cell-matrix adhesion, and myosin-based retraction forces along the leader-trailer axis. 4D simulations and experimental observations suggest that cell-cell communication helps establish a hierarchy to align collective polarity with the direction of migration, as observed with three or more cells in silico and in vivo. Our approach reveals emerging properties of the migrating collective: cell pairs are more persistent, migrating longer distances, and presumably with higher accuracy. Simulations suggest that cell pairs can overcome mechanical resistance of the trunk endoderm more effectively when they are polarized collectively. We propose that polarized supracellular organization of cardiopharyngeal progenitors confers emergent physical properties that determine mechanical interactions with their environment during morphogenesis.

Leukocyte transmigration and longitudinal forward-thrusting force in a microfluidic Transwell device

Transmigration of leukocytes across blood vessels walls is a critical step of the immune response. Transwell assays examine transmigration properties in vitro by counting cells passages through a membrane; however, the difficulty of in situ imaging hampers a clear disentanglement of the roles of adhesion, chemokinesis, and chemotaxis. We used here microfluidic Transwells to image the cells' transition from 2D migration on a surface to 3D migration in a confining microchannel and measure cells longitudinal forward-thrusting force in microchannels. Primary human effector T lymphocytes adhering with integrins LFA-1 (α_Lβ₂) had a marked propensity to transmigrate in Transwells without chemotactic cue. Both adhesion and contractility were important to overcome the critical step of nucleus penetration but were remarkably dispensable for 3D migration in smooth microchannels deprived of topographic features. Transmigration in smooth channels was qualitatively consistent with a propulsion by treadmilling of cell envelope and squeezing of cell trailing edge. Stalling conditions of 3D migration were then assessed by imposing pressure drops across microchannels. Without specific adhesion, the cells slid backward with subnanonewton forces, showing that 3D migration under stress is strongly limited by a lack of adhesion and friction with channels. With specific LFA-1 mediated adhesion, stalling occurred at around 3 and 6 nN in 2 × 4 and 4 × 4 μm² channels, respectively, supporting that stalling of adherent cells was under pressure control rather than force control. The stall pressure of 4 mbar is consistent with the pressure of actin filament polymerization that mediates lamellipod growth. The arrest of adherent cells under stress therefore seems controlled by the compression of the cell leading edge, which perturbs cells front-rear polarization and triggers adhesion failure or polarization reversal. Although stalling assays in microfluidic Transwells do not mimic in vivo transmigration, they provide a powerful tool to scrutinize 2D and 3D migration, barotaxis, and chemotaxis.

A Cellular Potts Model for Analyzing Cell Migration across Constraining Pillar Arrays

Cell migration in highly constrained environments is fundamental in a wide variety of physiological and pathological phenomena. In particular, it has been experimentally shown that the migratory capacity of most cell lines depends on their ability to transmigrate through narrow constrictions, which in turn relies on their deformation capacity. In this respect, the nucleus, which occupies a large fraction of the cell volume and is substantially stiffer than the surrounding cytoplasm, imposes a major obstacle. This aspect has also been investigated with the use of microfluidic devices formed by dozens of arrays of aligned polymeric pillars that limit the available space for cell movement. Such experimental systems, in particular, in the designs developed by the groups of Denais and of Davidson, were here reproduced with a tailored version of the Cellular Potts model, a grid-based stochastic approach where cell dynamics are established by a Metropolis algorithm for energy minimization. The proposed model allowed quantitatively analyzing selected cell migratory determinants (e.g., the cell and nuclear speed and deformation, and forces acting at the nuclear membrane) in the case of different experimental setups. Most of the numerical results show a remarkable agreement with the corresponding empirical data.

Sodium Transporters in Human Health and Disease

Sodium (Na+) electrochemical gradients established by Na+/K+ ATPase activity drives the transport of ions, minerals, and sugars in both excitable and non-excitable cells. Na+-dependent transporters can move these solutes in the same direction (cotransport) or in opposite directions (exchanger) across both the apical and basolateral plasma membranes of polarized epithelia. In addition to maintaining physiological homeostasis of these solutes, increases and decreases in sodium may also initiate, directly or indirectly, signaling cascades that regulate a variety of intracellular post-translational events. In this review, we will describe how the Na+/K+ ATPase maintains a Na+ gradient utilized by multiple sodium-dependent transport mechanisms to regulate glucose uptake, excitatory neurotransmitters, calcium signaling, acid-base balance, salt-wasting disorders, fluid volume, and magnesium transport. We will discuss how several Na+-dependent cotransporters and Na+-dependent exchangers have significant roles in human health and disease. Finally, we will discuss how each of these Na+-dependent transport mechanisms have either been shown or have the potential to use Na+ in a secondary role as a signaling molecule.

Analysis of barotactic and chemotactic guidance cues on directional decision-making of Dictyostelium discoideum cells in confined environments

Neutrophils and dendritic cells when migrating in confined environments have been shown to actuate a directional choice toward paths of least hydraulic resistance (barotaxis), in some cases overriding chemotactic responses. Here, we investigate whether this barotactic response is conserved in the more primitive model organism Dictyostelium discoideum using a microfluidic chip design. This design allowed us to monitor the behavior of single cells via live imaging when confronted with bifurcating microchannels, presenting different combinations of hydraulic and chemical stimuli. Under the conditions employed we find no evidence in support of a barotactic response; the cells base their directional choices on the chemotactic cues. When the cells are confronted by a microchannel bifurcation, they often split their leading edge and start moving into both channels, before a decision is made to move into one and retract from the other channel. Analysis of this decision-making process has shown that cells in steeper nonhydrolyzable adenosine- 3', 5'- cyclic monophosphorothioate, Sp- isomer (cAMPS) gradients move faster and split more readily. Furthermore, there exists a highly significant strong correlation between the velocity of the pseudopod moving up the cAMPS gradient to the total velocity of the pseudopods moving up and down the gradient over a large range of velocities. This suggests a role for a critical cortical tension gradient in the directional decision-making process.

Hydrogel systems and their role in neural tissue engineering

Neural tissue engineering (NTE) is a rapidly progressing field that promises to address several serious neurological conditions that are currently difficult to treat. Selecting the right scaffolding material to promote neural and non-neural cell differentiation as well as axonal growth is essential for the overall design strategy for NTE. Among the varieties of scaffolds, hydrogels have proved to be excellent candidates for culturing and differentiating cells of neural origin. Considering the intrinsic resistance of the nervous system against regeneration, hydrogels have been abundantly used in applications that involve the release of neurotrophic factors, antagonists of neural growth inhibitors and other neural growth-promoting agents. Recent developments in the field include the utilization of encapsulating hydrogels in neural cell therapy for providing localized trophic support and shielding neural cells from immune activity. In this review, we categorize and discuss the various hydrogel-based strategies that have been examined for neural-specific applications and also highlight their strengths and weaknesses. We also discuss future prospects and challenges ahead for the utilization of hydrogels in NTE.

Nonmonotonic Stress Relaxation after Cessation of Steady Shear Flow in Supramolecular Assemblies

Stress relaxation upon cessation of shear flow is known to be described by single-mode or multimode monotonic exponential decays. This is considered to be ubiquitous in nature. However, we found that, in some cases, the relaxation becomes anomalous in that an increase in the relaxing stress is observed. Those observations were made for physicochemically very different systems, having in common, however, the presence of self-associating units generating structures at large length scales. The nonmonotonic stress relaxation can be described phenomenologically by a generic model based on a redistribution of energy after the flow has stopped. When broken bonds are reestablished after flow cessation, the released energy is partly used to locally increase the elastic energy by the formation of deformed domains. If shear has induced order such that these elastic domains are partly aligned, the reestablishing of bonds gives rise to an increase of the overall stress.

The Cytoskeleton-A Complex Interacting Meshwork

The cytoskeleton of animal cells is one of the most complicated and functionally versatile structures, involved in processes such as endocytosis, cell division, intra-cellular transport, motility, force transmission, reaction to external forces, adhesion and preservation, and adaptation of cell shape. These functions are mediated by three classical cytoskeletal filament types, as follows: Actin, microtubules, and intermediate filaments. The named filaments form a network that is highly structured and dynamic, responding to external and internal cues with a quick reorganization that is orchestrated on the time scale of minutes and has to be tightly regulated. Especially in brain tumors, the cytoskeleton plays an important role in spreading and migration of tumor cells. As the cytoskeletal organization and regulation is complex and many-faceted, this review aims to summarize the findings about cytoskeletal filament types, including substructures formed by them, such as lamellipodia, stress fibers, and interactions between intermediate filaments, microtubules and actin. Additionally, crucial regulatory aspects of the cytoskeletal filaments and the formed substructures are discussed and integrated into the concepts of cell motility. Even though little is known about the impact of cytoskeletal alterations on the progress of glioma, a final point discussed will be the impact of established cytoskeletal alterations in the cellular behavior and invasion of glioma.

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

Anisotropic mechanics and dynamics of a living mammalian cytoplasm

During physiological processes, cells can undergo morphological changes that can result in a significant redistribution of the cytoskeleton causing anisotropic behavior. Evidence of anisotropy in cells under mechanical stimuli exists; however, the role of cytoskeletal restructuring resulting from changes in cell shape in mechanical anisotropy and its effects remain unclear. In the present study, we examine the role of cell morphology in inducing anisotropy in both intracellular mechanics and dynamics. We change the aspect ratio of cells by confining the cell width and measuring the mechanical properties of the cytoplasm using optical tweezers in both the longitudinal and transverse directions to quantify the degree of mechanical anisotropy. These active microrheology measurements are then combined with intracellular movement to calculate the intracellular force spectrum using force spectrum microscopy (FSM), from which the degree of anisotropy in dynamics and force can be quantified. We find that unrestricted cells with aspect ratio (AR) ∼1 are isotropic; however, when cells break symmetry, they exhibit significant anisotropy in cytoplasmic mechanics and dynamics.

Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path

Surface growth by association or dissociation of material on the boundary of a body is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant challenge in modelling such processes arises due to the inherent coupled interaction between the growth kinetics, the local stresses and the diffusing constituents needed to sustain the growth. Moreover, the volume of the body changes not only due to surface growth but also by variation in solvent concentration within the bulk. In this paper, we present a general theoretical framework that captures these phenomena and describes the kinetics of surface growth while accounting for coupled diffusion. Then, by the combination of analytical and numerical tools, applied to a simple growth geometry, we show that the evolution of such growth processes tends towards a universal path that is independent of initial conditions. This path, on which surface growth and diffusion act harmoniously, can be extended to analytically portray the evolution of a body from inception up to a treadmilling state, in which addition and removal of material are balanced.

Rolling Dynamics of Nanoscale Elastic Shells Driven by Active Particles

Self-propelled elastic shells capable of transducing energy to rolling motion could have potential applications as drug delivery vehicles. To understand the dynamics of the nanoscale size elastic shells, we performed molecular dynamics simulations of shells filled with a mixture of active and passive beads placed in contact with an elastic substrate. The shell skin is made of cross-linked polymer chains. The energy transduction from active beads to elastic shell results in stationary, steady rolling, and accelerating states depending on the strength of the shell-substrate adhesion and the magnitude of a force applied to the active beads. In the stationary state, the torque produced by a friction (rolling resistance) force in the contact area balances that due to the external force generated by the active beads, and the shell sticks to the substrate. In the steady rolling state, a rolling friction force balances the driving force, and the shell maintains a constant rolling velocity. The scaling relationship between the magnitude of the driving force and the shell velocity reflects a viscoelastic nature of the shell skin deformation dynamics. In the accelerating state, the energy supplied to a system by active beads exceeds the energy dissipation due to viscoelastic shell deformation in the contact area. Furthermore, the contact area of the shell with a substrate decreases with increasing shell instantaneous velocity.

Microtubules and Microtubule-Associated Proteins

Microtubules act as "railways" for motor-driven intracellular transport, interact with accessory proteins to assemble into larger structures such as the mitotic spindle, and provide an organizational framework to the rest of the cell. Key to these functions is the fact that microtubules are "dynamic." As with actin, the polymer dynamics are driven by nucleotide hydrolysis and influenced by a host of specialized regulatory proteins, including microtubule-associated proteins. However, microtubule turnover involves a surprising behavior-termed dynamic instability-in which individual polymers switch stochastically between growth and depolymerization. Dynamic instability allows microtubules to explore intracellular space and remodel in response to intracellular and extracellular cues. Here, we review how such instability is central to the assembly of many microtubule-based structures and to the robust functioning of the microtubule cytoskeleton.

The function of TRP channels in neutrophil granulocytes

Neutrophil granulocytes are exposed to widely varying microenvironmental conditions when pursuing their physiological or pathophysiological functions such as fighting invading bacteria or infiltrating cancer tissue. Examples for harsh environmental challenges include among others mechanical shear stress during the recruitment from the vasculature or the hypoxic and acidotic conditions within the tumor microenvironment. Chemokine gradients, reactive oxygen species, pressure, matrix elasticity, and temperature can be added to the list of potential challenges. Transient receptor potential (TRP) channels serve as cellular sensors since they respond to many of the abovementioned environmental stimuli. The present review investigates the role of TRP channels in neutrophil granulocytes and their role in regulating and adapting neutrophil function to microenvironmental cues. Following a brief description of neutrophil functions, we provide an overview of the electrophysiological characterization of neutrophilic ion channels. We then summarize the function of individual TRP channels in neutrophil granulocytes with a focus on TRPC6 and TRPM2 channels. We close the review by discussing the impact of the tumor microenvironment of pancreatic ductal adenocarcinoma (PDAC) on neutrophil granulocytes. Since neutrophil infiltration into PDAC tissue contributes to disease progression, we propose neutrophilic TRP channel blockade as a potential therapeutic option.

Repellent and Attractant Guidance Cues Initiate Cell Migration by Distinct Rear-Driven and Front-Driven Cytoskeletal Mechanisms

Attractive and repulsive cell guidance is essential for animal life and important in disease. Cell migration toward attractants dominates studies [1, 2, 3, 4, 5, 6, 7, 8], but migration away from repellents is important in biology yet relatively little studied [5, 9, 10]. It is widely held that cells initiate migration by protrusion of their front [11, 12, 13, 14, 15], yet this has not been explicitly tested for cell guidance because cell margin displacement at opposite ends of the cell has not been distinguished for any cue. We argue that protrusion of the front, retraction of the rear, or both together could in principle break cell symmetry and start migration in response to guidance cues [16]. Here, we find in the Dictyostelium model [6] that an attractant—cAMP—breaks symmetry by causing protrusion of the front of the cell, whereas its repellent analog—8CPT—breaks symmetry by causing retraction of the rear. Protrusion of the front of these cells in response to cAMP starts with local actin filament assembly, while the delayed retraction of the rear is independent of both myosin II polarization and of motor-based contractility. On the contrary, myosin II accumulates locally in the rear of the cell in response to 8CPT, anticipating retraction and required for it, while local actin assembly is delayed and couples to delayed protrusion at the front. These data reveal an important new concept in the understanding of cell guidance.

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In attractant, cell front protrusion breaks cell symmetry and starts migration

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In repellent, cell rear retraction breaks cell symmetry and starts migration

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Myosin II motor is not required for front-driven migration toward attractant

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Biased myosin II motor contractility drives rear-driven migration away from repellent

Biophysics of Microtubule End Coupling at the Kinetochore

The main physiological function of mitotic kinetochores is to provide durable attachment to spindle microtubules, which segregate chromosomes in order to partition them equally between the two daughter cells. Numerous kinetochore components that can bind directly to microtubules have been identified, including ATP-dependent motors and various microtubule-associated proteins with no motor activity. A major challenge facing the field is to explain chromosome motions based on the biochemical and structural properties of these individual kinetochore components and their assemblies. This chapter reviews the molecular mechanisms responsible for the motions associated with dynamic microtubule tips at the single-molecule level, as well as the activities of multimolecular ensembles called couplers. These couplers enable persistent kinetochore motion even under load, but their exact composition and structure remain unknown. Because no natural or artificial macro-machines function in an analogous manner to these molecular nano-devices, understanding their underlying biophysical mechanisms will require conceptual advances.

Modeling Contact Inhibition of Locomotion of Colliding Cells Migrating on Micropatterned Substrates

In cancer metastasis, embryonic development, and wound healing, cells can coordinate their motion, leading to collective motility. To characterize these cell-cell interactions, which include contact inhibition of locomotion (CIL), micropatterned substrates are often used to restrict cell migration to linear, quasi-one-dimensional paths. In these assays, collisions between polarized cells occur frequently with only a few possible outcomes, such as cells reversing direction, sticking to one another, or walking past one another. Using a computational phase field model of collective cell motility that includes the mechanics of cell shape and a minimal chemical model for CIL, we are able to reproduce all cases seen in two-cell collisions. A subtle balance between the internal cell polarization, CIL and cell-cell adhesion governs the collision outcome. We identify the parameters that control transitions between the different cases, including cell-cell adhesion, propulsion strength, and the rates of CIL. These parameters suggest hypotheses for why different cell types have different collision behavior and the effect of interventions that modulate collision outcomes. To reproduce the heterogeneity in cell-cell collision outcomes observed experimentally in neural crest cells, we must either carefully tune our parameters or assume that there is significant cell-to-cell variation in key parameters like cell-cell adhesion.

Many cells cooperate with their neighbors to move as a group. However, the mechanisms of these cell-cell interactions are not well understood. One experimental tool to analyze interactions is to allow cells to collide with one another, and see what happens. In order to better understand what features these experiments measure, we develop a computational model of cell-cell collisions, and identify the biochemical and mechanical parameters that lead to different outcomes of collisions. We can recreate all known types of collisions seen in experiments, including cells reversing on contact, sticking, or walking past each other. Our model suggests that what happens in a collision may depend strongly on the mechanical forces between the two cells.

Varying effects of EGF, HGF and TGFβ on formation of invadopodia and invasiveness of melanoma cell lines of different origin

The understanding of melanoma malignancy mechanisms is essential for patient survival, because melanoma is responsible for ca. 75% of deaths related to skin cancers. Enhanced formation of invadopodia and extracellular matrix (ECM) degradation are two important drivers of cell invasion, and actin dynamics facilitate protrusive activity by providing a driving force to push through the ECM. We focused on the influence of epidermal growth factor (EGF), hepatocyte growth factor (HGF) and transforming growth factor β (TGFβ) on melanoma cell invasiveness, since they are observed in the melanoma microenvironment. All three factors stimulated invasion of A375 and WM1341D cells derived from primary tumor sites. In contrast, only EGF and HGF stimulated invasion of WM9 and Hs294T cells isolated from lymph node metastasis. Enhanced formation of invadopodia and ECM degradation underlie the increased amount of invasive cells after stimulation with the tested agents. Generally, a rise in invasive potential was accompanied by a decrease in actin polymerization state (F:G ratio). The F:G ratio remained unchanged or was even increased in cell lines from a metastasis treated with TGFβ. Our findings indicate that the effects of stimulation with EGF, HGF and TGFβ on melanoma cell invasiveness could depend on melanoma cell progression stage.

Guidance of Axons by Local Coupling of Retrograde Flow to Point Contact Adhesions

Growth cones interact with the extracellular matrix (ECM) through integrin receptors at adhesion sites termed point contacts. Point contact adhesions link ECM proteins to the actin cytoskeleton through numerous adaptor and signaling proteins. One presumed function of growth cone point contacts is to restrain or "clutch" myosin-II-based filamentous actin (F-actin) retrograde flow (RF) to promote leading edge membrane protrusion. In motile non-neuronal cells, myosin-II binds and exerts force upon actin filaments at the leading edge, where clutching forces occur. However, in growth cones, it is unclear whether similar F-actin-clutching forces affect axon outgrowth and guidance. Here, we show in Xenopus spinal neurons that RF is reduced in rapidly migrating growth cones on laminin (LN) compared with non-integrin-binding poly-d-lysine (PDL). Moreover, acute stimulation with LN accelerates axon outgrowth over a time course that correlates with point contact formation and reduced RF. These results suggest that RF is restricted by the assembly of point contacts, which we show occurs locally by two-channel imaging of RF and paxillin. Further, using micropatterns of PDL and LN, we demonstrate that individual growth cones have differential RF rates while interacting with two distinct substrata. Opposing effects on RF rates were also observed in growth cones treated with chemoattractive and chemorepulsive axon guidance cues that influence point contact adhesions. Finally, we show that RF is significantly attenuated in vivo, suggesting that it is restrained by molecular clutching forces within the spinal cord. Together, our results suggest that local clutching of RF can control axon guidance on ECM proteins downstream of axon guidance cues.

SIGNIFICANCE STATEMENT

Here, we correlate point contact adhesions directly with clutching of filamentous actin retrograde flow (RF), which our findings strongly suggest guides developing axons. Acute assembly of new point contact adhesions is temporally and spatially linked to attenuation of RF at sites of forward membrane protrusion. Importantly, clutching of RF is modulated by extracellular matrix (ECM) proteins and soluble axon guidance cues, suggesting that it may regulate axon guidance in vivo. Consistent with this notion, we found that RF rates of spinal neuron growth cones were slower in vivo than what was observed in vitro. Together, our study provides the best evidence that growth cone-ECM adhesions clutch RF locally to guide axons in vivo.

Force fluctuations in three-dimensional suspended fibroblasts

Cells are sensitive to mechanical cues from their environment and at the same time generate and transmit forces to their surroundings. To test quantitatively forces generated by cells not attached to a substrate, we used a dual optical trap to suspend 3T3 fibroblasts between two fibronectin-coated beads. In this simple geometry, we measured both the cells' elastic properties and the force fluctuations they generate with high bandwidth. Cell stiffness decreased substantially with both myosin inhibition by blebbistatin and serum-starvation, but not with microtubule depolymerization by nocodazole. We show that cortical forces generated by non-muscle myosin II deform the cell from its rounded shape in the frequency regime from 0.1 to 10 Hz. The amplitudes of these forces were strongly reduced by blebbistatin and serum starvation, but were unaffected by depolymerization of microtubules. Force fluctuations show a spectrum that is characteristic for an elastic network activated by random sustained stresses with abrupt transitions.

Mechanochemical regulation of growth cone motility

Neuronal growth cones are exquisite sensory-motor machines capable of transducing features contacted in their local extracellular environment into guided process extension during development. Extensive research has shown that chemical ligands activate cell surface receptors on growth cones leading to intracellular signals that direct cytoskeletal changes. However, the environment also provides mechanical support for growth cone adhesion and traction forces that stabilize leading edge protrusions. Interestingly, recent work suggests that both the mechanical properties of the environment and mechanical forces generated within growth cones influence axon guidance. In this review we discuss novel molecular mechanisms involved in growth cone force production and detection, and speculate how these processes may be necessary for the development of proper neuronal morphogenesis.

A mathematical model of force generation by flexible kinetochore-microtubule attachments

Important mechanical events during mitosis are facilitated by the generation of force by chromosomal kinetochore sites that attach to dynamic microtubule tips. Several theoretical models have been proposed for how these sites generate force, and molecular diffusion of kinetochore components has been proposed as a key component that facilitates kinetochore function. However, these models do not explicitly take into account the recently observed flexibility of kinetochore components and variations in microtubule shape under load. In this paper, we develop a mathematical model for kinetochore-microtubule connections that directly incorporates these two important components, namely, flexible kinetochore binder elements, and the effects of tension load on the shape of shortening microtubule tips. We compare our results with existing biased diffusion models and explore the role of protein flexibility inforce generation at the kinetochore-microtubule junctions. Our model results suggest that kinetochore component flexibility and microtubule shape variation under load significantly diminish the need for high diffusivity (or weak specific binding) of kinetochore components; optimal kinetochore binder stiffness regimes are predicted by our model. Based on our model results, we suggest that the underlying principles of biased diffusion paradigm need to be reinterpreted.

Microtubule plus-end tracking proteins and their roles in cell division

Microtubules are cellular components that are required for a variety of essential processes such as cell motility, mitosis, and intracellular transport. This is possible because of the inherent dynamic properties of microtubules. Many of these properties are tightly regulated by a number of microtubule plus-end-binding proteins or +TIPs. These proteins recognize the distal end of microtubules and are thus in the right context to control microtubule dynamics. In this review, we address how microtubule dynamics are regulated by different +TIP families, focusing on how functionally diverse +TIPs spatially and temporally regulate microtubule dynamics during animal cell division.

Single molecule studies of force-induced S2 site exposure in the mammalian Notch negative regulatory domain

Notch signaling in metazoans is responsible for key cellular processes related to embryonic development and tissue homeostasis. Proteolitic cleavage of the S2 site within an extracellular NRR domain of Notch is a key early event in Notch signaling. We use single molecule force-extension (FX) atomic force microscopy (AFM) to study force-induced exposure of the S2 site in the NRR domain from mouse Notch 1. Our FX AFM measurements yield a histogram of N-to-C termini lengths, which we relate to conformational transitions within the NRR domain. We detect four classes of such conformational transitions. From our steered molecular dynamics (SMD) results, we associate first three classes of such events with the S2 site exposure. AFM experiments yield their mean unfolding forces as 69 ± 42, 79 ± 45, and 90 ± 50 pN, respectively, at 400 nm/s AFM pulling speeds. These forces are matched by the SMD results recalibrated to the AFM force loading rates. Next, we provide a conditional probability analysis of the AFM data to support the hypothesis that a whole sequence of conformational transitions within those three clases is the most probable pathway for the force-induced S2 site exposure. Our results support the hypothesis that force-induced Notch activation requires ligand binding to exert mechanical force not in random but in several strokes and over a substantial period of time.

Motility efficiency and spatiotemporal synchronization in non-metastatic vs. metastatic breast cancer cells

Metastatic breast cancer cells move not only more rapidly and persistently than their non-metastatic variants but in doing so use the mechanical work of the cytoskeleton more efficiently. The efficiency of the cell motions is defined for entire cells (rather than parts of the cell membrane) and is related to the work expended in forming membrane protrusions and retractions. This work, in turn, is estimated by integrating the protruded and retracted areas along the entire cell perimeter and is standardized with respect to the net translocation of the cell. A combination of cross-correlation, Granger causality, and morphodynamic profiling analyses is then used to relate the efficiency to the cell membrane dynamics. In metastatic cells, the protrusions and retractions are highly "synchronized" both in space and in time and these cells move efficiently. In contrast, protrusions and retractions formed by non-metastatic cells are not "synchronized" corresponding to low motility efficiencies. Our work provides a link between the kinematics of cell motions and their energetics. It also suggests that spatiotemporal synchronization might be one of the hallmarks of invasiveness of cancerous cells.

Roles of ion transport in control of cell motility

Cell motility is an essential feature of life. It is essential for reproduction, propagation, embryonic development, and healing processes such as wound closure and a successful immune defense. If out of control, cell motility can become life-threatening as, for example, in metastasis or autoimmune diseases. Regardless of whether ciliary/flagellar or amoeboid movement, controlled motility always requires a concerted action of ion channels and transporters, cytoskeletal elements, and signaling cascades. Ion transport across the plasma membrane contributes to cell motility by affecting the membrane potential and voltage-sensitive ion channels, by inducing local volume changes with the help of aquaporins and by modulating cytosolic Ca(2+) and H(+) concentrations. Voltage-sensitive ion channels serve as voltage detectors in electric fields thus enabling galvanotaxis; local swelling facilitates the outgrowth of protrusions at the leading edge while local shrinkage accompanies the retraction of the cell rear; the cytosolic Ca(2+) concentration exerts its main effect on cytoskeletal dynamics via motor proteins such as myosin or dynein; and both, the intracellular and the extracellular H(+) concentration modulate cell migration and adhesion by tuning the activity of enzymes and signaling molecules in the cytosol as well as the activation state of adhesion molecules at the cell surface. In addition to the actual process of ion transport, both, channels and transporters contribute to cell migration by being part of focal adhesion complexes and/or physically interacting with components of the cytoskeleton. The present article provides an overview of how the numerous ion-transport mechanisms contribute to the various modes of cell motility.

Actin dynamics in growth cone motility and navigation

Motile growth cones lead growing axons through developing tissues to synaptic targets. These behaviors depend on the organization and dynamics of actin filaments that fill the growth cone leading margin [peripheral (P-) domain]. Actin filament organization in growth cones is regulated by actin-binding proteins that control all aspects of filament assembly, turnover, interactions with other filaments and cytoplasmic components, and participation in producing mechanical forces. Actin filament polymerization drives protrusion of sensory filopodia and lamellipodia, and actin filament connections to the plasma membrane link the filament network to adhesive contacts of filopodia and lamellipodia with other surfaces. These contacts stabilize protrusions and transduce mechanical forces generated by actomyosin activity into traction that pulls an elongating axon along the path toward its target. Adhesive ligands and extrinsic guidance cues bind growth cone receptors and trigger signaling activities involving Rho GTPases, kinases, phosphatases, cyclic nucleotides, and [Ca++] fluxes. These signals regulate actin-binding proteins to locally modulate actin polymerization, interactions, and force transduction to steer the growth cone leading margin toward the sources of attractive cues and away from repellent guidance cues.

Processive acceleration of actin barbed-end assembly by N-WASP

Clustered N-WASP binds directly to actin-filament barbed ends and can either slow individual filament growth or processively accelerate the assembly of bundled actin filaments. This novel Arp2/3-independent mechanism of N-WASP likely plays a role in invadopodia and podosome formation, in which both N-WASP and actin filaments are tightly clustered.

Neuronal Wiskott–Aldrich syndrome protein (N-WASP)–activated actin polymerization drives extension of invadopodia and podosomes into the basement layer. In addition to activating Arp2/3, N-WASP binds actin-filament barbed ends, and both N-WASP and barbed ends are tightly clustered in these invasive structures. We use nanofibers coated with N-WASP WWCA domains as model cell surfaces and single-actin-filament imaging to determine how clustered N-WASP affects Arp2/3-independent barbed-end assembly. Individual barbed ends captured by WWCA domains grow at or below their diffusion-limited assembly rate. At high filament densities, however, overlapping filaments form buckles between their nanofiber tethers and myosin attachment points. These buckles grew ∼3.4-fold faster than the diffusion-limited rate of unattached barbed ends. N-WASP constructs with and without the native polyproline (PP) region show similar rate enhancements in the absence of profilin, but profilin slows barbed-end acceleration from constructs containing the PP region. Increasing Mg²⁺ to enhance filament bundling increases the frequency of filament buckle formation, consistent with a requirement of accelerated assembly on barbed-end bundling. We propose that this novel N-WASP assembly activity provides an Arp2/3-independent force that drives nascent filament bundles into the basement layer during cell invasion.

Compare and contrast the reaction coordinate diagrams for chemical reactions and cytoskeletal force generators

Reaction coordinate diagrams are used to relate the free energy changes that occur during the progress of chemical processes to the rate and equilibrium constants of the process. Here I briefly review the application of these diagrams to the thermodynamics and kinetics of the generation of force and motion by cytoskeletal motors and polymer ratchets as they mediate intracellular transport, organelle dynamics, cell locomotion, and cell division. To provide a familiar biochemical context for discussing these subcellular force generators, I first review the application of reaction coordinate diagrams to the mechanisms of simple chemical and enzyme-catalyzed reactions. My description of reaction coordinate diagrams of motors and polymer ratchets is simplified relative to the rigorous biophysical treatment found in many of the references that I use and cite, but I hope that the essay provides a valuable qualitative representation of the physical chemical parameters that underlie the generation of force and motility at molecular scales. In any case, I have found that this approach represents a useful interdisciplinary framework for understanding, researching, and teaching the basic molecular mechanisms by which motors contribute to fundamental cell biological processes.

Mechanism of cell rear retraction in migrating cells

For decades, ever growing data on myosin II provides strong evidence that interaction of myosin-II-motor-domain with actin filaments within cells retracts the cell rear during actin-based cell migration. Now it is clear myosin II motor-activity is not the sole force involved. Alternative force-generating mechanisms within cells clearly also exist to power cell rear retraction during actin-based cell migration. Given that nematode sperm cells migrate without actin and without cytoskeletal motor proteins it is perhaps not surprising other types of force power cell rear retraction in actin-based systems. Here, cell rear retraction driven by actin filament depolymerisation, actin filament crosslinking, cell front protrusion and possibly apparent membrane tension and their importance relative to myosin II-motor-based contractility are discussed.

A Cellular Potts Model simulating cell migration on and in matrix environments

Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.

A mechanochemical model of actin filaments

In eukaryotic cells, actin filaments are involved in important processes such as motility, division, cell shape regulation, contractility, and mechanosensation. Actin filaments are polymerized chains of monomers, which themselves undergo a range of chemical events such as ATP hydrolysis, polymerization, and depolymerization. When forces are applied to F-actin, in addition to filament mechanical deformations, the applied force must also influence chemical events in the filament. We develop an intermediate-scale model of actin filaments that combines actin chemistry with filament-level deformations. The model is able to compute mechanical responses of F-actin during bending and stretching. The model also describes the interplay between ATP hydrolysis and filament deformations, including possible force-induced chemical state changes of actin monomers in the filament. The model can also be used to model the action of several actin-associated proteins, and for large-scale simulation of F-actin networks. All together, our model shows that mechanics and chemistry must be considered together to understand cytoskeletal dynamics in living cells.

Role of ion channels and transporters in cell migration

Cell motility is central to tissue homeostasis in health and disease, and there is hardly any cell in the body that is not motile at a given point in its life cycle. Important physiological processes intimately related to the ability of the respective cells to migrate include embryogenesis, immune defense, angiogenesis, and wound healing. On the other side, migration is associated with life-threatening pathologies such as tumor metastases and atherosclerosis. Research from the last ≈ 15 years revealed that ion channels and transporters are indispensable components of the cellular migration apparatus. After presenting general principles by which transport proteins affect cell migration, we will discuss systematically the role of channels and transporters involved in cell migration.

Impact of cell shape on cell migration behavior on elastic substrate

Cell shape is known to have profound effects on a number of cell behaviors. In this paper we have studied its role in cell migration through modeling the effect of cell shape on the cell traction force distribution, the traction force dependent stability of cell adhesion and the matrix rigidity dependent traction force formation. To quantify the driving force of cell migration, a new parameter called the motility factor, that takes account of the effect of cell shape, matrix rigidity and dynamic stability of cell adhesion, is proposed. We showed that the motility factor depends on the matrix rigidity in a biphasic manner, which is consistent with the experimental observations of the biphasic dependence of cell migration speed on the matrix rigidity. We showed that the cell shape plays a pivotal role in the cell migration behavior by regulating the traction force at the cell front and rear. The larger the cell polarity, the larger the motility factor is. The keratocyte-like shape has a larger motility factor than the fibroblast-like shape, which explains why keratocyte has a much higher migration speed. The motility factor might be an appropriate parameter for a quantitative description of the driving force of cell migration.

Modeling the influence of nucleus elasticity on cell invasion in fiber networks and microchannels

Cell migration in highly constrained extracellular matrices is exploited in scaffold-based tissue engineering and is fundamental in a wide variety of physiological and pathological phenomena, among others in cancer invasion and development. Research into the critical processes involved in cell migration has mainly focused on cell adhesion and proteolytic degradation of the external environment. However, rising evidence has recently shown that a number of cell-derived biophysical and mechanical parameters, among others nucleus stiffness and cell deformability, plays a major role in cell motility, especially in the ameboid-like migration mode in 3D confined tissue structures. We here present an extended cellular Potts model (CPM) first used to simulate a micro-fabricated migration chip, which tests the active invasive behavior of cancer cells into narrow channels. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the migration chamber is composed of channels of different widths. We find that cell motile phenotype and velocity in open spaces (i.e., 2D flat surfaces or large channels) are not significantly influenced by cell elastic properties. On the contrary, the migratory behavior of cells within subcellular and subnuclear structures strongly relies on the deformability of the cytosol and of the nuclear cluster, respectively. Further, we characterize two migration dynamics: a stepwise way, characterized by fluctuations in cell length, within channels smaller than nucleus dimensions and a smooth sliding (i.e., maintaining constant cell length) behavior within channels larger than the nuclear cluster. These resulting observations are then extended looking at cell migration in an artificial fiber network, which mimics cell invasion in a 3D extracellular matrix. In particular, in this case, we analyze the effect of variations in elasticity of the nucleus on cell movement. In order to summarize, with our simulated migration assays, we demonstrate that the dimensionality of the environment strongly affects the migration phenotype and we suggest that the cytoskeletal and nuclear elastic characteristics correlate with the tumor cell's invasive potential.

Mena binds α5 integrin directly and modulates α5β1 function

Mena binds to the cytoplasmic tail of α5 integrin and modulates key α5β1 integrin functions in adhesion, motility, and fibrillogenesis.

Mena is an Ena/VASP family actin regulator with roles in cell migration, chemotaxis, cell–cell adhesion, tumor cell invasion, and metastasis. Although enriched in focal adhesions, Mena has no established function within these structures. We find that Mena forms an adhesion-regulated complex with α5β1 integrin, a fibronectin receptor involved in cell adhesion, motility, fibronectin fibrillogenesis, signaling, and growth factor receptor trafficking. Mena bound directly to the carboxy-terminal portion of the α5 cytoplasmic tail via a 91-residue region containing 13 five-residue “LERER” repeats. In fibroblasts, the Mena–α5 complex was required for “outside-in” α5β1 functions, including normal phosphorylation of FAK and paxillin and formation of fibrillar adhesions. It also supported fibrillogenesis and cell spreading and controlled cell migration speed. Thus, fibroblasts require Mena for multiple α5β1-dependent processes involving bidirectional interactions between the extracellular matrix and cytoplasmic focal adhesion proteins.

Calcineurin-dependent cofilin activation and increased retrograde actin flow drive 5-HT-dependent neurite outgrowth in Aplysia bag cell neurons

Neurite outgrowth in response to soluble growth factors often involves changes in intracellular Ca(2+); however, mechanistic roles for Ca(2+) in controlling the underlying dynamic cytoskeletal processes have remained enigmatic. Bag cell neurons exposed to serotonin (5-hydroxytryptamine [5-HT]) respond with a threefold increase in neurite outgrowth rates. Outgrowth depends on phospholipase C (PLC) → inositol trisphosphate → Ca(2+) → calcineurin signaling and is accompanied by increased rates of retrograde actin network flow in the growth cone P domain. Calcineurin inhibitors had no effect on Ca(2+) release or basal levels of retrograde actin flow; however, they completely suppressed 5-HT-dependent outgrowth and F-actin flow acceleration. 5-HT treatments were accompanied by calcineurin-dependent increases in cofilin activity in the growth cone P domain. 5-HT effects were mimicked by direct activation of PLC, suggesting that increased actin network treadmilling may be a widespread mechanism for promoting neurite outgrowth in response to neurotrophic factors.

'Poking' microtubules bring about nuclear wriggling to position nuclei

Nuclei wriggle in the cells of the follicle epithelium of the Drosophila pre-vitellogenic egg primordia. Although similar phenomena have been reported for a number of cultured cell types and some neurons in the zebrafish embryo, the mechanism and importance of the process have remained unexplained. Wriggling involves successive sudden and random minor turns of the nuclei, approximately three twists per minute with roughly 12° per twist, one of which lasts typically for 14 seconds. Wriggling is generated by the growing microtubules seeded throughout the cell cortex, which, while poking the nuclei, buckle and exert 5-40 piconewtons over ∼16 seconds. While wriggling, the nuclei drift ∼5 µm in a day in the immensely growing follicle cells along the apical-basal axis from the apical to the basal cell region. A >2-fold excess of the microtubules nucleated in the apical cell region, as compared with those seeded in the basal cell cortex, makes the nuclei drift along the apical-basal axis. Nuclear wriggling and positioning appear to be tightly related processes: they cease simultaneously when the nuclei become anchored by the actin cytoskeleton; moreover, colchicine or taxol treatment eliminates both nuclear wriggling and positioning. We propose that the wriggling nuclei reveal a thus far undescribed nuclear positioning mechanism.