Growing an actin gel on spherical surfaces

Harnessing Microbial Effectors for Macrophage-Mediated Drug Delivery

Macrophage-based drug delivery systems are promising, but their development is still in its infancy, with many limitations remaining to be addressed. Our aim was to design a system harnessing microbial effectors to facilitate controlled drug cargo expulsion from macrophages to enable the use of more toxic drugs without adding to the risk of off-target detrimental effects. The pore forming and actin polymerizing Listeria monocytogenes effectors listeriolysin-O (LLO) and actin assembly-inducing protein (ActA) were synthesized using a novel green fluorescent protein (GFP)-linked heterologous expression system. These effectors were coated onto polystyrene beads to generate "synthetic cargo" before loading into primary M1 macrophages. Bead uptake and release from macrophages were evaluated by using high-throughput quantitative imaging flow cytometry and confocal microscopy. In vitro results confirmed appropriate activity of synthesized effectors. Coating of these effector proteins onto polystyrene beads (simulated drug cargo) resulted in changes in cellular morphology, bead content, and intracellular bead localization, which may support an interpretation of the induced release of these beads from the cells. This forms the basis for further investigation to fully elucidate any potential release mechanisms. Bacterial effectors ActA and LLO successfully effectuated actin polarization and protrusions from cell membranes similar to those seen in cells infected with Listeria spp., illustrating the potential of using these effectors and production methods for the development of an endogenous drug delivery system capable of low-risk, targeted release of high potency drugs.

Myosin-I Synergizes with Arp2/3 Complex to Enhance Pushing Forces of Branched Actin Networks

Myosin-Is colocalize with Arp2/3 complex-nucleated actin networks at sites of membrane protrusion and invagination, but the mechanisms by which myosin-I motor activity coordinates with branched actin assembly to generate force are unknown. We mimicked the interplay of these proteins using the "comet tail" bead motility assay, where branched actin networks are nucleated by Arp2/3 complex on the surface of beads coated with myosin-I and the WCA domain of N-WASP. We observed that myosin-I increased bead movement efficiency by thinning actin networks without affecting growth rates. Remarkably, myosin-I triggered symmetry breaking and comet-tail formation in dense networks resistant to spontaneous fracturing. Even with arrested actin assembly, myosin-I alone could break the network. Computational modeling recapitulated these observations suggesting myosin-I acts as a repulsive force shaping the network's architecture and boosting its force-generating capacity. We propose that myosin-I leverages its power stroke to amplify the forces generated by Arp2/3 complex-nucleated actin networks.

Machine learning-enabled constrained multi-objective design of architected materials

Architected materials that consist of multiple subelements arranged in particular orders can demonstrate a much broader range of properties than their constituent materials. However, the rational design of these materials generally relies on experts' prior knowledge and requires painstaking effort. Here, we present a data-efficient method for the high-dimensional multi-property optimization of 3D-printed architected materials utilizing a machine learning (ML) cycle consisting of the finite element method (FEM) and 3D neural networks. Specifically, we apply our method to orthopedic implant design. Compared to uniform designs, our experience-free method designs microscale heterogeneous architectures with a biocompatible elastic modulus and higher strength. Furthermore, inspired by the knowledge learned from the neural networks, we develop machine-human synergy, adapting the ML-designed architecture to fix a macroscale, irregularly shaped animal bone defect. Such adaptation exhibits 20% higher experimental load-bearing capacity than the uniform design. Thus, our method provides a data-efficient paradigm for the fast and intelligent design of architected materials with tailored mechanical, physical, and chemical properties.

The Effect of Magnetic Field Gradient and Gadolinium-Based MRI Contrast Agent Dotarem on Mouse Macrophages

Magnetic resonance imaging (MRI) is widely used in diagnostic medicine. MRI uses the static magnetic field to polarize nuclei spins, fast-switching magnetic field gradients to generate temporal and spatial resolution, and radiofrequency (RF) electromagnetic waves to control the spin orientation. All these forms of magnetic static and electromagnetic RF fields interact with human tissue and cells. However, reports on the MRI technique's effects on the cells and human body are often inconsistent or contradictory. In both research and clinical MRI, recent progress in improving sensitivity and resolution is associated with the increased magnetic field strength of MRI magnets. Additionally, to improve the contrast of the images, the MRI technique often employs contrast agents, such as gadolinium-based Dotarem, with effects on cells and organs that are still disputable and not fully understood. Application of higher magnetic fields requires revisiting previously observed or potentially possible bio-effects. This article focuses on the influence of a static magnetic field gradient with and without a gadolinium-based MRI contrast agent (Dotarem) and the cellular and molecular effects of Dotarem on macrophages.

Non-linear elastic properties of actin patches to partially rescue yeast endocytosis efficiency in the absence of the cross-linker Sac6

Clathrin mediated endocytosis is an essential and complex cellular process involving more than 60 proteins. In yeast, successful endocytosis requires counteracting a large turgor pressure. To this end, yeasts assemble actin patches, which accumulate elastic energy during their assembly. We investigated the material properties of reconstituted actin patches from a wild-type (WT) strain and a mutant strain lacking the cross-linker Sac6 (sac6Δ), which has reduced endocytosis efficiency in live cells. We hypothesized that a change in the viscous properties of the actin patches, which would dissipate more mechanical energy, could explain this reduced efficiency. There was however no significant difference in the viscosity of both types of patches. However, we discovered a significantly different non-linear elastic response. While WT patches had a constant elastic modulus at different stress values, sac6Δ patches had a lower elastic modulus at low stress, before stiffening at higher ones, up to values similar to those of WT patches. To understand the consequences of this discovery, we performed, in vivo, a precise analysis of actin patch dynamics. Our analysis reveals that a small fraction of actin patches successfully complete endocytosis in sac6Δ cells, provided that those assemble an excess of actin at the membrane compared to WT. This observation indicates that the non-linear elastic properties of actin networks in sac6Δ cells contribute to rescue endocytosis, requiring nevertheless more actin material to build-up the necessary stored elastic energy.

Remodelling of membrane tubules by the actin cytoskeleton

Inside living cells, the remodelling of membrane tubules by actomyosin networks is crucial for processes such as intracellular trafficking or organelle reshaping. In this review, we first present various in vivo situations in which actin affects membrane tubule remodelling, then we recall some results on force production by actin dynamics and on membrane tubules physics. Finally, we show that our knowledge of the underlying mechanisms by which actomyosin dynamics affect tubule morphology has recently been moved forward. This is thanks to in vitro experiments that mimic cellular membranes and actin dynamics and allow deciphering the physics of tubule remodelling in biochemically controlled conditions, and shed new light on tubule shape regulation.

Diffusive Interface Model for Actomyosin Driven Cell Oscillations

In this paper, we build phase-field models for the actomyosin driven cell oscillations. In our modeling, an oscillation starts from an actin cortex breakage. After the breakage, due to the unbalanced distribution of actin and myosin, there is unbalanced contraction force in different membrane components, which then results in the lipids transferring to the bulged membrane compartment. As such we can observe a cell oscillation. During the whole process, the actin and myosin polymerization and depolymerization play important roles. We give detailed formulations under the framework of phase-field methodology, in which phase-field functions are used to describe different parts of the cell membrane, integrated with the distribution of the actin and myosin at different components. The whole system is described as a set of time-dependent partial differential equations in three-dimensional space. Forward Euler method is used to solve the system. The spectral method is used for spatial discretizations for efficiency and accuracy purpose. Given carefully selected parameters, three-dimensional simulations are performed and compared with biological images. The simulations prove that actomyosin dynamics are the major reasons for cell oscillations. Further, our method can be easily extended into the simulations of cell polarization. We also compared our numerical simulations with biological experiments. This modeling gives an example of applying diffusive interface methods toward complex biology experiments.

Actin modulates shape and mechanics of tubular membranes

The actin cytoskeleton shapes cells and also organizes internal membranous compartments. In particular, it interacts with membranes for intracellular transport of material in mammalian cells, yeast, or plant cells. Tubular membrane intermediates, pulled along microtubule tracks, are formed during this process and destabilize into vesicles. While the role of actin in tubule destabilization through scission is suggested, literature also provides examples of actin-mediated stabilization of membranous structures. To directly address this apparent contradiction, we mimic the geometry of tubular intermediates with preformed membrane tubes. The growth of an actin sleeve at the tube surface is monitored spatiotemporally. Depending on network cohesiveness, actin is able to entirely stabilize or locally maintain membrane tubes under pulling. On a single tube, thicker portions correlate with the presence of actin. These structures relax over several minutes and may provide enough time and curvature geometries for other proteins to act on tube stability.

Actin shells control buckling and wrinkling of biomembranes

Global changes of cell shape under mechanical or osmotic external stresses are mostly controlled by the mechanics of the cortical actin cytoskeleton underlying the cell membrane. Some aspects of this process can be recapitulated in vitro on reconstituted actin-and-membrane systems. In this paper, we investigate how the mechanical properties of a branched actin network shell, polymerized at the surface of a liposome, control membrane shape when the volume is reduced. We observe a variety of membrane shapes depending on the actin thickness. Thin shells undergo buckling, characterized by a cup-shape deformation of the membrane that coincides with the one of the actin network. Thick shells produce membrane wrinkles, but do not deform their outer layer. For intermediate micrometer-thick shells, wrinkling of the membrane is observed, and the actin layer is slightly deformed. Confronting our experimental results with a theoretical description, we determine the transition between buckling and wrinkling, which depends on the thickness of the actin shell and the size of the liposome. We thus unveil the generic mechanism by which biomembranes are able to accommodate their shape against mechanical compression, through thickness adaptation of their cortical cytoskeleton.

Mechanical stiffness of reconstituted actin patches correlates tightly with endocytosis efficiency

Clathrin-mediated endocytosis involves the sequential assembly of more than 60 proteins at the plasma membrane. An important fraction of these proteins regulates the assembly of an actin-related protein 2/3 (Arp2/3)-branched actin network, which is essential to generate the force during membrane invagination. We performed, on wild-type (WT) yeast and mutant strains lacking putative actin crosslinkers, a side-by-side comparison of in vivo endocytic phenotypes and in vitro rigidity measurements of reconstituted actin patches. We found a clear correlation between softer actin networks and a decreased efficiency of endocytosis. Our observations support a chain-of-consequences model in which loss of actin crosslinking softens Arp2/3-branched actin networks, directly limiting the transmission of the force. Additionally, the lifetime of failed endocytic patches increases, leading to a larger number of patches and a reduced pool of polymerizable actin, which slows down actin assembly and further impairs endocytosis.

This study uses in vitro reconstitution of endocytic actin patches and mechanical measurements with chains of superparamagnetic microbeads to reveal a tight correlation between the stiffness of actin networks and the efficiency of endocytosis in yeast.

Magnetic Field Changes Macrophage Phenotype

Macrophages play a crucial role in homeostasis, regeneration, and innate and adaptive immune responses. Functionally different macrophages have different shapes and molecular phenotypes that depend on the actin cytoskeleton, which is regulated by the small GTPase RhoA. The naive M0 macrophages are slightly elongated, proinflammatory M1 are round, and M2 antiinflammatory macrophages are elongated. We have recently shown in the rodent model system that genetic or pharmacologic interference with the RhoA pathway deregulates the macrophage actin cytoskeleton, causes extreme macrophage elongation, and prevents macrophage migration. Here, we report that an exposure of macrophages to a nonuniform magnetic field causes extreme elongation of macrophages and has a profound effect on their molecular components and organelles. Using immunostaining and Western blotting, we observed that magnetic force rearranges the macrophage actin cytoskeleton, the Golgi complex, and the cation channel receptor TRPM2, and modifies the expression of macrophage molecular markers. We have found that the magnetic-field-induced alterations are very similar to changes caused by RhoA interference. We also analyzed magnetic-field-induced forces acting on macrophages and found that the location and alignment of magnetic-field-elongated macrophages correlate very well with the simulated distribution and orientation of such magnetic force lines.

Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces

Eukaryote cells have flexible membranes that allow them to have a variety of dynamical shapes. The shapes of the cells serve important biological functions, both for cells within an intact tissue, and during embryogenesis and cellular motility. How cells control their shapes and the structures that they form on their surface has been a subject of intensive biological research, exposing the building blocks that cells use to deform their membranes. These processes have also drawn the interest of theoretical physicists, aiming to develop models based on physics, chemistry and nonlinear dynamics. Such models explore quantitatively different possible mechanisms that the cells can employ to initiate the spontaneous formation of shapes and patterns on their membranes. We review here theoretical work where one such class of mechanisms was investigated: the coupling between curved membrane proteins, and the cytoskeletal forces that they recruit. Theory indicates that this coupling gives rise to a rich variety of membrane shapes and dynamics, while experiments indicate that this mechanism appears to drive many cellular shape changes.This article is part of the theme issue 'Self-organization in cell biology'.

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.

A new method to measure mechanics and dynamic assembly of branched actin networks

We measured mechanical properties and dynamic assembly of actin networks with a new method based on magnetic microscopic cylinders. Dense actin networks are grown from the cylinders’ surfaces using the biochemical Arp2/3-machinery at play in the lamellipodium extension and other force-generating processes in the cell. Under a homogenous magnetic field the magnetic cylinders self-assemble into chains in which forces are attractive and depend on the intensity of the magnetic field. We show that these forces, from piconewtons to nanonewtons, are large enough to slow down the assembly of dense actin networks and controlled enough to access to their non linear mechanical responses. Deformations are measured with nanometer-resolution, well below the optical resolution. Self-assembly of the magnetic particles into chains simplifies experiments and allows for parallel measurements. The combination of accuracy and good throughput of measurements results in a method with high potential for cell and cytoskeleton mechanics. Using this method, we observed in particular a strong non linear mechanical behavior of dense branched actin networks at low forces that has not been reported previously.

DNA cytoskeleton for stabilizing artificial cells

Cell-sized liposomes and droplets coated with lipid layers have been used as platforms for understanding live cells, constructing artificial cells, and implementing functional biomedical tools such as biosensing platforms and drug delivery systems. However, these systems are very fragile, which results from the absence of cytoskeletons in these systems. Here, we construct an artificial cytoskeleton using DNA nanostructures. The designed DNA oligomers form a Y-shaped nanostructure and connect to each other with their complementary sticky ends to form networks. To undercoat lipid membranes with this DNA network, we used cationic lipids that attract negatively charged DNA. By encapsulating the DNA into the droplets, we successfully created a DNA shell underneath the membrane. The DNA shells increased interfacial tension, elastic modulus, and shear modulus of the droplet surface, consequently stabilizing the lipid droplets. Such drastic changes in stability were detected only when the DNA shell was in the gel phase. Furthermore, we demonstrate that liposomes with the DNA gel shell are substantially tolerant against outer osmotic shock. These results clearly show the DNA gel shell is a stabilizer of the lipid membrane akin to the cytoskeleton in live cells.

A variational approach to the growth dynamics of pre-stressed actin filament networks

In order to model the growth dynamics of elastic bodies with residual stresses a thermodynamically consistent approach is needed such that the cross-coupling between growth and mechanics can be correctly described. In the present work we apply a variational principle to the formulation of the interfacial growth dynamics of dendritic actin filament networks growing from biomimetic beads, an experimentally well studied system, where the buildup of residual stresses governs the network growth. We first introduce the material model for the network via a strain energy density for an isotropic weakly nonlinear elastic material and then derive consistently from this model the dynamic equations for the interfaces, i.e. for a polymerizing internal interface in contact with the bead and a depolymerizing external interface directed towards the solvent. We show that (i) this approach automatically preserves thermodynamic symmetry-properties, which is not the case for the often cited 'rubber-band-model' (Sekimoto et al 2004 Eur. Phys. J. E 13 247-59, Plastino et al 2004 Eur. Biophys. J. 33 310-20) and (ii) leads to a robust morphological instability of the treadmilling network interfaces. The nature of the instability depends on the interplay of the two dynamic interfaces. Depending on the biochemical conditions the network envelope evolves into a comet-like shape (i.e. the actin envelope thins out at one side and thickens on the opposite side of the bead) via a varicose instability or it breaks the symmetry via higher order zigzag modes. We conclude that morphological instabilities due to mechano-chemical coupling mechanisms and the presences of mechancial pre-stresses can play a major role in locally organizing the cytoskeleton of living cells.

Cell-sized liposome doublets reveal active tension build-up driven by acto-myosin dynamics

Cells modulate their shape to fulfill specific functions, mediated by the cell cortex, a thin actin shell bound to the plasma membrane. Myosin motor activity, together with actin dynamics, contributes to cortical tension. Here, we examine the individual contributions of actin polymerization and myosin activity to tension increase with a non-invasive method. Cell-sized liposome doublets are covered with either a stabilized actin cortex of preformed actin filaments, or a dynamic branched actin network polymerizing at the membrane. The addition of myosin II minifilaments in both cases triggers a change in doublet shape that is unambiguously related to a tension increase. Preformed actin filaments allow us to evaluate the effect of myosin alone while, with dynamic actin cortices, we examine the synergy of actin polymerization and myosin motors in driving shape changes. Our assay paves the way for a quantification of tension changes triggered by various actin-associated proteins in a cell-sized system.

Toward the reconstitution of synthetic cell motility

Cellular motility is a fundamental process essential for embryonic development, wound healing, immune responses, and tissues development. Cells are mostly moving by crawling on external, or inside, substrates which can differ in their surface composition, geometry, and dimensionality. Cells can adopt different migration phenotypes, e.g., bleb-based and protrusion-based, depending on myosin contractility, surface adhesion, and cell confinement. In the few past decades, research on cell motility has focused on uncovering the major molecular players and their order of events. Despite major progresses, our ability to infer on the collective behavior from the molecular properties remains a major challenge, especially because cell migration integrates numerous chemical and mechanical processes that are coupled via feedbacks that span over large range of time and length scales. For this reason, reconstituted model systems were developed. These systems allow for full control of the molecular constituents and various system parameters, thereby providing insight into their individual roles and functions. In this review we describe the various reconstituted model systems that were developed in the past decades. Because of the multiple steps involved in cell motility and the complexity of the overall process, most of the model systems focus on very specific aspects of the individual steps of cell motility. Here we describe the main advancement in cell motility reconstitution and discuss the main challenges toward the realization of a synthetic motile cell.

Pearling instability of membrane tubes driven by curved proteins and actin polymerization

Membrane deformation inside living cells is crucial for the proper shaping of various intracellular organelles and is necessary during the fission/fusion processes that allow membrane recycling and transport (e.g. endocytosis). Proteins that induce membrane curvature play a key role in such processes, mostly by adsorbing to the membrane and forming a scaffold that deforms the membrane according to the curvature of the proteins. In this paper we explore the possibility of membrane tube destabilization through a pearling mechanism enabled by the combined effects of the adsorbed curved proteins and the actin polymerization that they recruit. The pearling instability can serve as the initiation for fission of the tube into vesicles. We find that adsorbed curved proteins are more likely to stabilize the tubes, while the actin polymerization can provide the additional constrictive force needed for the robust instability. We discuss the relevance of the theoretical results to in vivo and in vitro experiments.

Wrinkling of a spherical lipid interface induced by actomyosin cortex

Actomyosin actively generates contractile forces that provide the plasma membrane with the deformation stresses essential to carry out biological processes. Although the contractile property of purified actomyosin has been extensively studied, to understand the physical contribution of the actomyosin contractile force on a deformable membrane is still a challenging problem and of great interest in the field of biophysics. Here, we reconstitute a model system with a cell-sized deformable interface that exhibits anomalous curvature-dependent wrinkling caused by the actomyosin cortex underneath the spherical closed interface. Through a shape analysis of the wrinkling deformation, we find that the dominant contributor to the wrinkled shape changes from bending elasticity to stretching elasticity of the reconstituted cortex upon increasing the droplet curvature radius of the order of the cell size, i.e., tens of micrometers. The observed curvature dependence is explained by the theoretical description of the cortex elasticity and contractility. Our present results provide a fundamental insight into the deformation of a curved membrane induced by the actomyosin cortex.

How capping protein enhances actin filament growth and nucleation on biomimetic beads

Capping protein (CP), which caps the growing ends of actin filaments, accelerates actin-based motility. Recent experiments on biomimetic beads have shown that CP also enhances the rate of actin filament nucleation. Proposed explanations for these phenomena include (i) the actin funneling hypothesis (AFH), in which the presence of CP increases the free-actin concentration, and (ii) the monomer gating model, in which CP binding to actin filament barbed ends makes more monomers available for filament nucleation. To establish how CP increases the rates of filament elongation and nucleation on biomimetic beads, we perform a quantitative modeling analysis of actin polymerization, using rate equations that include actin filament nucleation, polymerization and capping, as modified by monomer depletion near the surface of the bead. With one adjustable parameter, our simulation results match previously measured time courses of polymerized actin and filament number. The results support a version of the AFH where CP increases the local actin monomer concentration at the bead surface, but leaves the global free-actin concentration nearly constant. Because the rate of filament nucleation increases with the monomer concentration, the increased local monomer concentration enhances actin filament nucleation. We derive a closed-form formula for the characteristic CP concentration where the local free-actin concentration reaches half the bulk value, and find it to be comparable to the global Arp2/3 complex concentration. We also propose an experimental protocol for distinguishing branching nucleation of filaments from spontaneous nucleation.

Theoretical study of actin layers attachment and separation

We use the theory of active gels to study theoretically the merging and separation of two actin dense layers akin to cortical layers of animal cells. The layers bind at a distance equal to twice the thickness of a free layer, thus forming a single dense layer, similar in this sense to a lamellipodium. When that unique layer is stretched apart, it is resilient to break apart up to a critical length larger than twice the thickness of a free layer. We show that this behavior can result from the high contractile properties of the actomyosin gel due to the activity of myosin molecular motors. Furthermore, we establish that the stability of the stretched single layer is highly dependent on the properties of the gel. Indeed, the nematic order of the actin filaments along the polymerizing membranes is a destabilizing factor.

Reconstituting the actin cytoskeleton at or near surfaces in vitro

Actin filament dynamics have been studied for decades in pure protein solutions or in cell extracts, but a breakthrough in the field occurred at the turn of the century when it became possible to reconstitute networks of actin filaments, growing in a controlled but physiological manner on surfaces, mimicking the actin assembly that occurs at the plasma membrane during cell protrusion and cell shape changes. The story begins with the bacteria Listeria monocytogenes, the study of which led to the reconstitution of cellular actin polymerization on a variety of supports including plastic beads. These studies made possible the development of liposome-type substrates for filament assembly and micropatterning of actin polymerization nucleation. Based on the accumulated expertise of the last 15 years, many exciting approaches are being developed, including the addition of myosin to biomimetic actin networks to study the interplay between actin structure and contractility. The field is now poised to make artificial cells with a physiological and dynamic actin cytoskeleton, and subsequently to put these cells together to make in vitro tissues. This article is part of a Special Issue entitled: Mechanobiology.

Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechanochemical coupling

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechanochemical coupling mechanisms that guide the growth process are poorly understood, and a general continuum description combining growth and mechanics is lacking. We develop a theory that bridges the gap between mesoscale and continuum limit and propose a general framework providing the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.

Actin dynamics, architecture, and mechanics in cell motility

Tight coupling between biochemical and mechanical properties of the actin cytoskeleton drives a large range of cellular processes including polarity establishment, morphogenesis, and motility. This is possible because actin filaments are semi-flexible polymers that, in conjunction with the molecular motor myosin, can act as biological active springs or "dashpots" (in laymen's terms, shock absorbers or fluidizers) able to exert or resist against force in a cellular environment. To modulate their mechanical properties, actin filaments can organize into a variety of architectures generating a diversity of cellular organizations including branched or crosslinked networks in the lamellipodium, parallel bundles in filopodia, and antiparallel structures in contractile fibers. In this review we describe the feedback loop between biochemical and mechanical properties of actin organization at the molecular level in vitro, then we integrate this knowledge into our current understanding of cellular actin organization and its physiological roles.

Geometrical control of actin assembly and contractility

The actin cytoskeleton is a fundamental player in many cellular processes. Ultrastructural studies have revealed its extremely complex organization, where actin filaments self-organize into defined and specialized structures of distinct functions and, yet, are able to selectively recruit biochemical regulators that are available in the entire cell volume. To overcome this extraordinary complexity, simplified reconstituted systems significantly improve our understanding of actin dynamics and self-organization. However, little is known regarding physical rules governing actin networks organization and to which extent network structure may direct and regulate selective interactions with specific regulators. Here, we describe the first method to direct actin filament assembly to specific 2D motifs with a finely tuned geometry and relative distribution. This method enables the study of how geometrical confinement governs actin network structural organization and how, in return, structural cues can control selective contraction by myosin motor. The protocol relies on the use of surface micropatterning and functionalization procedures in order to selectively direct actin filament assembly to specific sites of nucleation.

Plasma membrane--cortical cytoskeleton interactions: a cell biology approach with biophysical considerations

From a biophysical standpoint, the interface between the cell membrane and the cytoskeleton is an intriguing site where a "two-dimensional fluid" interacts with an exceedingly complex three-dimensional protein meshwork. The membrane is a key regulator of the cytoskeleton, which not only provides docking sites for cytoskeletal elements through transmembrane proteins, lipid binding-based, and electrostatic interactions, but also serves as the source of the signaling events and molecules that control cytoskeletal organization and remolding. Conversely, the cytoskeleton is a key determinant of the biophysical and biochemical properties of the membrane, including its shape, tension, movement, composition, as well as the mobility, partitioning, and recycling of its constituents. From a cell biological standpoint, the membrane-cytoskeleton interplay underlies--as a central executor and/or regulator--a multitude of complex processes including chemical and mechanical signal transduction, motility/migration, endo-/exo-/phagocytosis, and other forms of membrane traffic, cell-cell, and cell-matrix adhesion. The aim of this article is to provide an overview of the tight structural and functional coupling between the membrane and the cytoskeleton. As biophysical approaches, both theoretical and experimental, proved to be instrumental for our understanding of the membrane/cytoskeleton interplay, this review will "oscillate" between the cell biological phenomena and the corresponding biophysical principles and considerations. After describing the types of connections between the membrane and the cytoskeleton, we will focus on a few key physical parameters and processes (force generation, curvature, tension, and surface charge) and will discuss how these contribute to a variety of fundamental cell biological functions.

Influence of substrate curvature on osteoblast orientation and extracellular matrix deposition

Background

The effects of microchannel diameter in hydroxyapatite (HAp) substrates on osteoblast behavior were investigated in this study. Microchannels of 100, 250 and 500 μm diameter were created on hydroxyapatite disks. The changes in osteoblast precursor growth, differentiation, extra cellular matrix (ECM) secretion and cell attachment/orientation were investigated as a function of microchannel diameter.

Results

Curvature did not impact cellular differentiation, however organized cellular orientation was achieved within the 100 and 250 μm microchannels (mc) after 6 days compared to the 12 days it took for the 500mc group, while the flat substrate remained disorganized. Moreover, the 100, 250 and 500mc groups expressed a specific shift in orientation of 17.45°, 9.05°, and 22.86° respectively in 24 days. The secreted/mineralized ECM showed the 100 and 250mc groups to have higher modulus (E) and hardness (h) (E = 42.6GPa; h = 1.6GPa) than human bone (E = 13.4-25.7GPa; h = 0.47-0.74GPa), which was significantly greater than the 500mc and control groups (p < 0.05). It was determined that substrate curvature affects the cell orientation, the time required for initial response, and the shift in orientation with time.

Conclusions

These findings demonstrate the ability of osteoblasts to organize and mineralize differentially in microchannels similar to those found in the osteons of compact bone. These investigations could lead to the development of osteon-like scaffolds to support the regeneration of organized bone.

Physically based principles of cell adhesion mechanosensitivity in tissues

The minimal structural unit that defines living organisms is a single cell. By proliferating and mechanically interacting with each other, cells can build complex organization such as tissues that ultimately organize into even more complex multicellular living organisms, such as mammals, composed of billions of single cells interacting with each other. As opposed to passive materials, living cells actively respond to the mechanical perturbations occurring in their environment. Tissue cell adhesion to its surrounding extracellular matrix or to neighbors is an example of a biological process that adapts to physical cues. The adhesion of tissue cells to their surrounding medium induces the generation of intracellular contraction forces whose amplitude adapts to the mechanical properties of the environment. In turn, solicitation of adhering cells with physical forces, such as blood flow shearing the layer of endothelial cells in the lumen of arteries, reinforces cell adhesion and impacts cell contractility. In biological terms, the sensing of physical signals is transduced into biochemical signaling events that guide cellular responses such as cell differentiation, cell growth and cell death. Regarding the biological and developmental consequences of cell adaptation to mechanical perturbations, understanding mechanotransduction in tissue cell adhesion appears as an important step in numerous fields of biology, such as cancer, regenerative medicine or tissue bioengineering for instance. Physicists were first tempted to view cell adhesion as the wetting transition of a soft bag having a complex, adhesive interaction with the surface. But surprising responses of tissue cell adhesion to mechanical cues challenged this view. This, however, did not exclude that cell adhesion could be understood in physical terms. It meant that new models and descriptions had to be created specifically for these biological issues, and could not straightforwardly be adapted from dead matter. In this review, we present physical concepts of tissue cell adhesion and the unexpected cellular responses to mechanical cues such as external forces and stiffness sensing. We show how biophysical approaches, both experimentally and theoretically, have contributed to our understanding of the regulation of cellular functions through physical force sensing mechanisms. Finally, we discuss the different physical models that could explain how tissue cell adhesion and force sensing can be coupled to internal mechanosensitive processes within the cell body.

Myo1c facilitates G-actin transport to the leading edge of migrating endothelial cells

Addition of actin monomer (G-actin) to growing actin filaments (F-actin) at the leading edge generates force for cell locomotion. The polymerization reaction and its regulation have been studied in depth. However, the mechanism responsible for transport of G-actin substrate to the cell front is largely unknown; random diffusion, facilitated transport via myosin II contraction, local synthesis as a result of messenger ribonucleic acid localization, or F-actin turnover all might contribute. By tracking a photoactivatable, nonpolymerizable actin mutant, we show vectorial transport of G-actin in live migrating endothelial cells (ECs). Mass spectrometric analysis identified Myo1c, an unconventional F-actin-binding motor protein, as a major G-actin-interacting protein. The cargo-binding tail domain of Myo1c interacted with G-actin, and the motor domain was required for the transport. Local microinjection of Myo1c promoted G-actin accumulation and plasma membrane ruffling, and Myo1c knockdown confirmed its contribution to G-actin delivery to the leading edge and for cell motility. In addition, there is no obvious requirement for myosin II contractile-based transport of G-actin in ECs. Thus, Myo1c-facilitated G-actin transport might be a critical node for control of cell polarity and motility.

Directed cytoskeleton self-organization

The cytoskeleton architecture supports many cellular functions. Cytoskeleton networks form complex intracellular structures that vary during the cell cycle and between different cell types according to their physiological role. These structures do not emerge spontaneously. They result from the interplay between intrinsic self-organization properties and the conditions imposed by spatial boundaries. Along these boundaries, cytoskeleton filaments are anchored, repulsed, aligned, or reoriented. Such local effects can propagate alterations throughout the network and guide cytoskeleton assembly over relatively large distances. The experimental manipulation of spatial boundaries using microfabrication methods has revealed the underlying physical processes directing cytoskeleton self-organization. Here we review, step-by-step, from molecules to tissues, how the rules that govern assembly have been identified. We describe how complementary approaches, all based on controlling geometric conditions, from in vitro reconstruction to in vivo observation, shed new light on these fundamental organizing principles.

Impact of branching on the elasticity of actin networks

Actin filaments play a fundamental role in cell mechanics: assembled into networks by a large number of partners, they ensure cell integrity, deformability, and migration. Here we focus on the mechanics of the dense branched network found at the leading edge of a crawling cell. We develop a new technique based on the dipolar attraction between magnetic colloids to measure mechanical properties of branched actin gels assembled around the colloids. This technique allows us to probe a large number of gels and, through the study of different networks, to access fundamental relationships between their microscopic structure and their mechanical properties. We show that the architecture does regulate the elasticity of the network: increasing both capping and branching concentrations strongly stiffens the networks. These effects occur at protein concentrations that can be regulated by the cell. In addition, the dependence of the elastic modulus on the filaments' flexibility and on increasing internal stress has been studied. Our overall results point toward an elastic regime dominated by enthalpic rather than entropic deformations. This result strongly differs from the elasticity of diluted cross-linked actin networks and can be explained by the dense dendritic structure of lamellipodium-like networks.

Choosing orientation: influence of cargo geometry and ActA polarization on actin comet tails

Networks of polymerizing actin filaments can propel intracellular pathogens and drive movement of artificial particles in reconstituted systems. While biochemical mechanisms activating actin network assembly have been well characterized, it remains unclear how particle geometry and large-scale force balance affect emergent properties of movement. We reconstituted actin-based motility using ellipsoidal beads resembling the geometry of Listeria monocytogenes. Beads coated uniformly with the L. monocytogenes ActA protein migrated equally well in either of two distinct orientations, with their long axes parallel or perpendicular to the direction of motion, while intermediate orientations were unstable. When beads were coated with a fluid lipid bilayer rendering ActA laterally mobile, beads predominantly migrated with their long axes parallel to the direction of motion, mimicking the orientation of motile L. monocytogenes. Generating an accurate biophysical model to account for our observations required the combination of elastic-propulsion and tethered-ratchet actin-polymerization theories. Our results indicate that the characteristic orientation of L. monocytogenes must be due to polarized ActA rather than intrinsic actin network forces. Furthermore, viscoelastic stresses, forces, and torques produced by individual actin filaments and lateral movement of molecular complexes must all be incorporated to correctly predict large-scale behavior in the actin-based movement of nonspherical particles.

Spontaneous contractility-mediated cortical flow generates cell migration in three-dimensional environments

We present a model of cell motility generated by actomyosin contraction of the cell cortex. We identify, analytically, dynamical instabilities of the cortex and show that they yield steady-state cortical flows, which, in turn, can induce cell migration in three-dimensional environments. This mechanism relies on the regulation of contractility by myosin, whose transport is explicitly taken into account in the model. Theoretical predictions are compared to experimental data of tumor cells migrating in three-dimensional matrigel and suggest that this mechanism could be a general mode of cell migration in three-dimensional environments.

Actin dynamics counteract membrane tension during clathrin-mediated endocytosis

Clathrin-mediated endocytosis is independent of actin dynamics in many circumstances but requires actin polymerization in others. We show that membrane tension determines the actin dependence of clathrin-coat assembly. As found previously, clathrin assembly supports formation of mature coated pits in the absence of actin polymerization on both dorsal and ventral surfaces of non-polarized mammalian cells, and also on basolateral surfaces of polarized cells. Actin engagement is necessary, however, to complete membrane deformation into a coated pit on apical surfaces of polarized cells and, more generally, on the surface of any cell in which the plasma membrane is under tension from osmotic swelling or mechanical stretching. We use these observations to alter actin dependence experimentally and show that resistance of the membrane to propagation of the clathrin lattice determines the distinction between 'actin dependent and 'actin independent'. We also find that light-chain-bound Hip1R mediates actin engagement. These data thus provide a unifying explanation for the role of actin dynamics in coated-pit budding.

A model actin comet tail disassembling by severing

We use a numerical simulation to model an actin comet tail as it grows from the surface of a small object (a bead) and disassembles by severing. We explore the dependence of macroscopic properties such as the local tail radius and tail length on several controllable properties, namely the bead diameter, the bead velocity, the severing rate per unit length, and the actin gel mesh size. The model predicts an F-actin density with an initial exponential decay followed by an abrupt decay at the edge of the tail, and predicts that the comet tail diameter is constant along the length of the tail. The simulation results are used to fit a formula relating the comet tail length to the control parameters, and it is proposed that this formula offers a means to extract quantitative information on the actin gel mesh size and severing kinetics from simple macroscopic measurements.

Physical model of cellular symmetry breaking

Cells can polarize in response to external signals, such as chemical gradients, cell-cell contacts, and electromagnetic fields. However, cells can also polarize in the absence of an external cue. For example, a motile cell, which initially has a more or less round shape, can lose its symmetry spontaneously even in a homogeneous environment and start moving in random directions. One of the principal determinants of cell polarity is the cortical actin network that underlies the plasma membrane. Tension in this network generated by myosin motors can be relaxed by rupture of the shell, leading to polarization. In this article, we discuss how simplified model systems can help us to understand the physics that underlie the mechanics of symmetry breaking.

Mathematical modeling of endocytic actin patch kinetics in fission yeast: disassembly requires release of actin filament fragments

We report time courses of the accumulation and loss of 16 fluorescent fusion proteins at sites of clathrin-mediated endocytosis in fission yeast. Mathematical modeling shows that dendritic nucleation hypothesis can account for the kinetics of actin assembly in vivo and disassembly requires actin filament severing along with depolymerization.

We used the dendritic nucleation hypothesis to formulate a mathematical model of the assembly and disassembly of actin filaments at sites of clathrin-mediated endocytosis in fission yeast. We used the wave of active WASp recruitment at the site of the patch formation to drive assembly reactions after activation of Arp2/3 complex. Capping terminated actin filament elongation. Aging of the filaments by ATP hydrolysis and γ-phosphate dissociation allowed actin filament severing by cofilin. The model could simulate the assembly and disassembly of actin and other actin patch proteins using measured cytoplasmic concentrations of the proteins. However, to account quantitatively for the numbers of proteins measured over time in the accompanying article (Sirotkin et al., 2010, MBoC 21: 2792–2802), two reactions must be faster in cells than in vitro. Conditions inside the cell allow capping protein to bind to the barbed ends of actin filaments and Arp2/3 complex to bind to the sides of filaments faster than the purified proteins in vitro. Simulations also show that depolymerization from pointed ends cannot account for rapid loss of actin filaments from patches in 10 s. An alternative mechanism consistent with the data is that severing produces short fragments that diffuse away from the patch.

Force generation of curved actin gels characterized by combined AFM-epifluorescence measurements

Polymerization of actin into branched filaments is the driving force behind active migration of eukaryotic cells and motility of intracellular organelles. The site-directed assembly of a polarized branched array forms an expanding gel that generates the force that pushes the membrane. Here, we use atomic force microscopy to understand the relation between actin polymerization and the produced force. Functionalized spherical colloidal probes of varying size and curvature are attached to the atomic force microscopy cantilever and initiate the formation of a polarized actin gel in a solution mimicking the in vivo context. The gel growth is recorded by epifluorescence microscopy both against the cantilever and in the perpendicular (lateral) nonconstrained direction. In this configuration, the gel growth stops simultaneously in both directions at the stall force, which corresponds to a pressure of 0.15 nN/microm(2). The results show that the growth of the gel is limited laterally, in the absence of external force, by internal mechanical stresses resulting from a combination of the curved geometry and the molecular mechanism of site-directed assembly of a cohesive branched filament array.

Reconstruction of aperture functions during full fusion in vesicular exocytosis of neurotransmitters

Individual vesicular exocytosis of adrenaline by dense core vesicles in chromaffin cells is considered here as a paradigm of many situations encountered in biology, nanosciences and drug delivery in which a spherical container releases in the external environment through gradual uncovering of its surface. A procedure for extracting the aperture (opening) function of a biological vesicle fusing with a cell membrane from the released molecular flux of neurotransmitter as monitored by amperometry has been devised based on semi-analytical expressions derived in a former work [C. Amatore, A. I. Oleinick, I. Svir, ChemPhysChem 2009, 10, DOI: 10.1002/cphc.200900646]. This precise analysis shows that in the absence of direct information about the radius of the vesicle or about the concentration of the adrenaline cation stored by the vesicle matrix, current spikes do not contain enough information to determine the maximum aperture angle. Yet, a statistical analysis establishes that this maximum aperture angle is most probably less than a few tens of degrees, which suggests that full fusion is a very improbable event.

Reconstitution of an actin cortex inside a liposome

The composite and versatile structure of the cytoskeleton confers complex mechanical properties on cells. Actin filaments sustain the cell membrane and their dynamics insure cell shape changes. For example, the lamellipodium moves by actin polymerization, a mechanism that has been studied using simplified experimental systems. Much less is known about the actin cortex, a shell-like structure underneath the membrane that contracts for cell movement. We have designed an experimental system that mimicks the cell cortex by allowing actin polymerization to nucleate and assemble at the inner membrane of a liposome. Actin shell growth can be triggered inside the liposome, which offers a useful system for a controlled study. The observed actin shell thickness and estimated mesh size of the actin structure are in good agreement with cellular data. Such a system paves the way for a thorough characterization of cortical dynamics and mechanics.

The actin cytoskeleton in whole mount preparations and sections

In non-muscle cells, the actin cytoskeleton plays a key role by providing a scaffold contributing to the definition of cell shape, force for driving cell motility, cytokinesis, endocytosis, and propulsion of pathogens, as well as tracks for intracellular transport. A thorough understanding of these processes requires insight into the spatial and temporal organisation of actin filaments into diverse higher-order structures, such as networks, parallel bundles, and contractile arrays. Transmission and scanning electron microscopy can be used to visualise the actin cytoskeleton, but due to the delicate nature of actin filaments, they are easily affected by standard preparation protocols, yielding variable degrees of ultrastructural preservation. In this chapter, we describe different conventional and cryo-approaches to visualise the actin cytoskeleton using transmission electron microscopy and discuss their specific advantages and drawbacks. In the first part, we present three different whole mount techniques, which allow visualisation of actin in the peripheral, thinly spread parts of cells grown in monolayers. In the second part, we describe specific issues concerning the visualisation of actin in thin sections. Techniques for three-dimensional visualisation of actin, protein localisation, and correlative light and electron microscopy are also included.

Force-velocity relation for actin-polymerization-driven motility from Brownian dynamics simulations

We report numerical simulation results for the force-velocity relation for actin-polymerization-driven motility. We use Brownian dynamics to solve a physically consistent formulation of the dendritic nucleation model with semiflexible filaments that self-assemble and push a disk. We find that at small loads, the disk speed is independent of load, whereas at high loads, the speed decreases and vanishes at a characteristic stall pressure. Our results demonstrate that at small loads, the velocity is controlled by the reaction rates, whereas at high loads the stall pressure is determined by the mechanical properties of the branched actin network. The behavior is consistent with experiments and with our recently proposed self-diffusiophoretic mechanism for actin-polymerization-driven motility. New in vitro experiments to measure the force-velocity relation are proposed.

In silico reconstitution of actin-based symmetry breaking and motility

Computational modeling and experimentation in a model system for actin-based force generation explain how actin networks initiate and maintain directional movement.

Eukaryotic cells assemble viscoelastic networks of crosslinked actin filaments to control their shape, mechanical properties, and motility. One important class of actin network is nucleated by the Arp2/3 complex and drives both membrane protrusion at the leading edge of motile cells and intracellular motility of pathogens such as Listeria monocytogenes. These networks can be reconstituted in vitro from purified components to drive the motility of spherical micron-sized beads. An Elastic Gel model has been successful in explaining how these networks break symmetry, but how they produce directed motile force has been less clear. We have combined numerical simulations with in vitro experiments to reconstitute the behavior of these motile actin networks in silico using an Accumulative Particle-Spring (APS) model that builds on the Elastic Gel model, and demonstrates simple intuitive mechanisms for both symmetry breaking and sustained motility. The APS model explains observed transitions between smooth and pulsatile motion as well as subtle variations in network architecture caused by differences in geometry and conditions. Our findings also explain sideways symmetry breaking and motility of elongated beads, and show that elastic recoil, though important for symmetry breaking and pulsatile motion, is not necessary for smooth directional motility. The APS model demonstrates how a small number of viscoelastic network parameters and construction rules suffice to recapture the complex behavior of motile actin networks. The fact that the model not only mirrors our in vitro observations, but also makes novel predictions that we confirm by experiment, suggests that the model captures much of the essence of actin-based motility in this system.

Networks of actin filaments provide the force that drives eukaryotic cell movement. In a model system for this kind of force generation, a spherical bead coated with an actin nucleating protein builds and rockets around on an actin “comet tail,” much like the tails observed in some cellular systems. How does a spherically symmetric bead break the symmetry of the actin coat and begin to polymerize actin in a directional manner? A previous theoretical model successfully explained how symmetry breaks, but suggested that the subsequent motion was driven by actin squeezing the bead forwards—a prediction refuted by experiment. To understand how motility occurs, we created a parsimonious computer model that predicted novel experimental behaviors, then performed new experiments inspired by the model and confirmed these predictions. Our model demonstrates how the elastic properties of the actin network explain not only symmetry breaking, but also the details of subsequent motion and how the bead maintains direction.

Transient assembly of F-actin by phagosomes delays phagosome fusion with lysosomes in cargo-overloaded macrophages

Dynamic remodelling of the cortical actin cytoskeleton is required for phagocytic uptake of pathogens and other particles by macrophages. Actin can also be nucleated de novo on membranes of nascent phagosomes, a process that can stimulate or inhibit phagosome fusion with lysosomes. Recently, phagosomes were shown to polymerize actin in transient pulses, called actin ;flashing', whose function remains unexplained. Here, we investigated phagosomal actin dynamics in live macrophages expressing actin tagged with green fluorescent protein (GFP). We show that only immature phagosomes can transiently induce assembly of actin coat, which forms a barrier preventing phagosome-lysosome docking and fusion. The capacity of phagosomes to assemble actin is enhanced in cells exposed to increased phagocytic load, which also exhibit a delay in phagosome maturation. Parallel analysis indicated that polymerization of actin on macropinosomes also induces compression and propulsion. We show that dynamic interactions between membrane elastic tension and compression forces of polymerizing actin can also lead to macropinosome constriction and scission - a process that is obstructed on rigid phagosomes. We hypothesize that the rate of individual phagosome maturation, as well as the biogenesis and remodelling of macropinosomes, can be regulated by the extent and manner of actin assembly on their membrane.