Interplay between activity, elasticity, and liquid transport in self-contractile biopolymer gels.

Active gels play an important role in biology and in inspiring biomimetic active materials, due to their ability to change shape, size, and create their own morphology. We study a particular class of active gels, generated by polymerizing actin in the presence of cross-linkers and clusters of myosin as molecular motors, which exhibit large contractions. The relevant mechanics for these highly swollen gels is the result of the interplay between activity and liquid flow: gel activity yields a structural reorganization of the gel network and produces a flow of liquid that eventually exits from the gel boundary. This dynamics inherits lengthscales that are typical of the liquid flow processes. The analyses we present provide insights into the contraction dynamics, and they focus on the effects of the geometry on both gel velocity and fluid flow.

Self-assembled active actomyosin gels spontaneously curve and wrinkle similar to biological cells and tissues.

Living systems adopt a diversity of curved and highly dynamic shapes. These diverse morphologies appear on many length scales, from cells to tissues and organismal scales. The common driving force for these dynamic shape changes are contractile stresses generated by myosin motors in the cell cytoskeleton, that converts chemical energy into mechanical work. A good understanding of how contractile stresses in the cytoskeleton arise into different three-dimensional (3D) shapes and what are the shape selection rules that determine their final configurations is still lacking. To obtain insight into the relevant physical mechanisms, we recreate the actomyosin cytoskeleton in vitro, with precisely controlled composition and initial geometry. A set of actomyosin gel discs, intrinsically identical but of variable initial geometry, dynamically self-organize into a family of 3D shapes, such as domes and wrinkled shapes, without the need for specific preprogramming or additional regulation. Shape deformation is driven by the spontaneous emergence of stress gradients driven by myosin and is encoded in the initial disc radius to thickness aspect ratio, which may indicate shaping scalability. Our results suggest that while the dynamical pathways may depend on the detailed interactions between the different microscopic components within the gel, the final selected shapes obey the general theory of elastic deformations of thin sheets. Altogether, our results emphasize the importance for the emergence of active stress gradients for buckling-driven shape deformations and provide insights on the mechanically induced spontaneous shape transitions in contractile active matter, revealing potential shared mechanisms with living systems across scales.

Smart design of universally decorated nanoparticles for drug delivery applications driven by active transport.

Targeting the cell nucleus remains a challenge for drug delivery. Here, we present a universal platform for the smart design of nanoparticle (NP) decoration that is based on: (i) a spacer polymer, commonly biotin-polyethylene-glycol-thiol, whose grafting density and molecular weight can be tuned for optimized performance, and (ii) protein binding peptides, such as cell penetrating peptides (CPPs), cancer-targeting peptides, or nuclear localization signal (NLS) peptides, that are linked to the PEG free-end by universal chemistry. We manifested our platform with two different bromo-acetamide (Br-Ac) modified NLSs. We used cell extract-based and live cell assays to demonstrate the recruitment of dynein motor proteins, which drive the NP active transport toward the nucleus, and the enhancement of cellular and nuclear entry, manifesting the properties of NLS as a CPP. Our control of the NP decoration scheme, and the modularity of our platform, carry great advantages for nano-carrier design for drug delivery applications.

The Mechanics of (Poro-)Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton.

Cells can actively change their shapes and become motile, a property that depends on their ability to actively reorganize their internal structure. This feature is attributed to the mechanical and dynamic properties of the cell cytoskeleton, notably, the actomyosin cytoskeleton, which is an active gel of polar actin filaments, myosin motors, and accessory proteins that exhibit intrinsic contraction properties. The usually accepted view is that the cytoskeleton behaves as a viscoelastic material. However, this model cannot always explain the experimental results, which are more consistent with a picture describing the cytoskeleton as a poroelastic active material-an elastic network embedded with cytosol. Contractility gradients generated by the myosin motors drive the flow of the cytosol across the gel pores, which infers that the mechanics of the cytoskeleton and the cytosol are tightly coupled. One main feature of poroelasticity is the diffusive relaxation of stresses in the network, characterized by an effective diffusion constant that depends on the gel elastic modulus, porosity, and cytosol (solvent) viscosity. As cells have many ways to regulate their structure and material properties, our current understanding of how cytoskeleton mechanics and cytosol flow dynamics are coupled remains poorly understood. Here, an in vitro reconstitution approach is employed to characterize the material properties of poroelastic actomyosin gels as a model system for the cell cytoskeleton. Gel contraction is driven by myosin motor contractility, which leads to the emergence of a flow of the penetrating solvent. The paper describes how to prepare these gels and run experiments. We also discuss how to measure and analyze the solvent flow and gel contraction both at the local and global scales. The various scaling relations used for data quantification are given. Finally, the experimental challenges and common pitfalls are discussed, including their relevance to cell cytoskeleton mechanics.

Nano-Particles Carried by Multiple Dynein Motors Self-Regulate Their Number of Actively Participating Motors.

Intra-cellular active transport by native cargos is ubiquitous. We investigate the motion of spherical nano-particles (NPs) grafted with flexible polymers that end with a nuclear localization signal peptide. This peptide allows the recruitment of several mammalian dynein motors from cytoplasmic extracts. To determine how motor-motor interactions influenced motility on the single microtubule level, we conducted bead-motility assays incorporating surface adsorbed microtubules and combined them with model simulations that were based on the properties of a single dynein. The experimental and simulation results revealed long time trajectories: when the number of NP-ligated motors Nm increased, run-times and run-lengths were enhanced and mean velocities were somewhat decreased. Moreover, the dependence of the velocity on run-time followed a universal curve, regardless of the system composition. Model simulations also demonstrated left- and right-handed helical motion and revealed self-regulation of the number of microtubule-bound, actively transporting dynein motors. This number was stochastic along trajectories and was distributed mainly between one, two, and three motors, regardless of Nm. We propose that this self-regulation allows our synthetic NPs to achieve persistent motion that is associated with major helicity. Such a helical motion might affect obstacle bypassing, which can influence active transport efficiency when facing the crowded environment of the cell.

Kinetics of actin networks formation measured by time resolved particle-tracking microrheology.

Actin is one of the most studied cytoskeleton proteins showing a very rich span of structures and functions. For example, adenosine triphosphate (ATP)-assisted polymerization of actin is used to push protrusions forward in a mechanism that enables cells to crawl on a substrate. In this process, the chemical energy released from the hydrolysis of ATP is what enables force generation. We study a minimal model system comprised of actin monomers in an excess of ATP concentration. In such a system polymerization proceeds in three stages: nucleation of actin filaments, elongation, and network formation. While the kinetics of filament growth was characterized previously, not much is known about the kinetics of network formation and the evolution of networks towards a steady-state structure. In particular, it is not clear how the non-equilibrium nature of this ATP-assisted polymerization manifests itself in the kinetics of self-assembly. Here, we use time-resolved microrheology to follow the kinetics of the three stages of self-assembly as a function of initial actin monomer concentration. Surprisingly, we find that at high enough initial monomer concentrations the effective elastic modulus of the forming actin networks overshoots and then relaxes with a -2/5 power law. We attribute the overshoot to the non-equilibrium nature of the polymerization and the relaxation to rearrangements of the network into a steady-state structure.

Finger-like membrane protrusions are favored by heterogeneities in the actin network.

Finger-like protrusions in cells are mostly generated by an active actin cytoskeleton pushing against the cell membrane. Conventional filopodia, localized at the leading edge of the cells, are long and thin protrusions composed of parallel actin filaments that emanate from a branched actin network. In contrast, dendritic filopodia, precursors of dendritic spines in neurons, are entirely filled in with a branched actin network. Here, we investigate in vitro how the dynamics of branched actin structures, polymerized at a membrane surface, trigger the formation of both protrusion types. Using supported bilayers and liposomes, we show that a decrease in the amount of activation sites at the membrane surface leads to the appearance of heterogeneities in the actin network coverage. Such heterogeneities promote the formation of membrane protrusions, and the size of heterogeneity patches matches the one of the protrusion base. Protrusion shape, cylindrical or conical, directly correlates with the absence or the presence of actin branches, respectively.

Deposition of Cellulose Nanocrystals onto Supported Lipid Membranes.

The deposition of cellulose nanocrystals (CNCs) on a supported lipid bilayer (SLB) was investigated at different length scales. Quartz crystal microbalance with dissipation monitoring (QCM-D) was used to probe the bilayer formation and to show for the first time the CNC deposition onto the SLB. Specifically, classical QCM-D measurements gave estimation of the adsorbed hydrated mass and the corresponding film thickness, whereas complementary experiments using D2O as the solvent allowed the quantitative determination of the hydration of the CNC layer, showing a high hydration value. Scanning force microscopy (SFM) and total internal reflection fluorescence microscopy (TIRF) were used to probe the homogeneity of the deposited layers, revealing the structural details at the particle and film length scales, respectively, thus giving information on the effect of CNC concentration on the surface coverage. The results showed that the adsorption of CNCs on the supported lipid membrane depended on lipid composition, CNC concentration, and pH conditions, and that the binding process was governed by electrostatic interactions. Under suitable conditions, a uniform film was formed, with thickness corresponding to a CNC monolayer, which provides the basis for a relevant 2D model of a primary plant cell wall.

Living Matter: Mesoscopic Active Materials.

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with "dead," nonactive matter is presented. This field of research is increasingly denoted as "biological physics" where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function. These include locomotion (cell motility and migration) forces that give rise to cell division, the growth and form of cellular assemblies in development, the beating of heart cells, and the effects of mechanical perturbations such as shear flow (in the bloodstream) or adhesion to other cells or tissues. An introduction to the fundamental concepts and theory with selected experimental examples related to the authors' own research is presented, including red-blood-cell membrane fluctuations, motion of the nucleus within an egg cell, self-contracting acto-myosin gels, and structure and beating of heart cells (cardiomyocytes), including how they can be driven by an oscillating, mechanical probe.

Scale dependence of the mechanics of active gels with increasing motor concentration.

Actin is a protein that plays an essential role in maintaining the mechanical integrity of cells. In response to strong external stresses, it can assemble into large bundles, but it grows into a fine branched network to induce cell motion. In some cases, the self-organization of actin fibers and networks involves the action of bipolar filaments of the molecular motor myosin. Such self-organization processes mediated by large myosin bipolar filaments have been studied extensively in vitro. Here we create active gels, composed of single actin filaments and small myosin bipolar filaments. The active steady state in these gels persists long enough to enable the characterization of their mechanical properties using one and two point microrheology. We study the effect of myosin concentration on the mechanical properties of this model system for active matter, for two different motor assembly sizes. In contrast to previous studies of networks with large motor assemblies, we find that the fluctuations of tracer particles embedded in the network decrease in amplitude as motor concentration increases. Nonetheless, we show that myosin motors stiffen the actin networks, in accordance with bulk rheology measurements of networks containing larger motor assemblies. This implies that such stiffening is of universal nature and may be relevant to a wider range of cytoskeleton-based structures.

Functional Actin Networks under Construction: The Cooperative Action of Actin Nucleation and Elongation Factors.

Cells require actin nucleation factors to catalyze the formation of actin networks and elongation factors to control the rate and extent of actin polymerization. Earlier models suggested that the different factors assemble actin networks independently. However, recent evidence indicates that the assembly of most cellular networks involves multiple nucleation and elongation factors that work in concert. Here, we describe how these different factors cooperate, directly or indirectly, to promote the assembly of functional actin network in cells, both in the cytoplasm and nucleoplasm. We show that, in many cases, multiple factors collaborate to initiate network assembly and growth. The selection of specific sets of key players enables the cells to fine-tune network structure and dynamics, optimizing them for particular cellular functions.

Dynamics in steady state in vitro acto-myosin networks.

It is well known that many biochemical processes in the cell such as gene regulation, growth signals and activation of ion channels, rely on mechanical stimuli. However, the mechanism by which mechanical signals propagate through cells is not as well understood. In this review we focus on stress propagation in a minimal model for cell elasticity, actomyosin networks, which are comprised of a sub-family of cytoskeleton proteins. After giving an overview of th actomyosin network components, structure and evolution we review stress propagation in these materials as measured through the correlated motion of tracer beads. We also discuss the possibility to extract structural features of these networks from the same experiments. We show that stress transmission through these networks has two pathways, a quickly dissipative one through the bulk, and a long ranged weakly dissipative one through the pre-stressed actin network.

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.

Reconstitution of actin-based motility by vasodilator-stimulated phosphoprotein (VASP) depends on the recruitment of F-actin seeds from the solution produced by cofilin.

Vasodilator-stimulated phosphoprotein (VASP) is active in many filopodium-based and cytoskeleton reorganization processes. It is not fully understood how VASP directly functions in actin-based motility and how regulatory proteins affect its function. Here, we combine bead motility assay and single filament experiments. In the presence of a bundling component, actin bundles that grow from the surface of WT-VASP-coated beads induced movement of the beads. VASP promotes actin-based movement alone, in the absence of other actin nucleators. We propose that at physiological salt conditions VASP nucleation activity is too weak to promote motility and bundle formation. Rather, VASP recruits F-actin seeds from the solution and promotes their elongation. Cofilin has a crucial role in the nucleation of these F-actin seeds, notably under conditions of unfavorable spontaneous actin nucleation. We explored the role of multiple VASP variants. We found that the VASP-F-actin binding domain is required for the recruitment of F-actin seeds from the solution. We also found that the interaction of profilin-actin complexes with the VASP-proline-rich domain and the binding of the VASP-F-actin binding domain to the side of growing filaments is critical for transforming actin polymerization into motion. At the single filament level, profilin mediates both filament elongation rate and VASP anti-capping activity. Binding of profilin-actin complexes increases the polymerization efficiency by VASP but decreases its efficiency as an anti-capper; binding of free profilin creates the opposite effect. Finally, we found that an additional component such as methylcellulose or fascin is required for actin bundle formation and motility mediated by VASP.

Extracting the dynamic correlation length of actin networks from microrheology experiments.

The mechanical properties of polymer gels based on cytoskeleton proteins (e.g. actin) have been studied extensively due to their significant role in biological cell motility and in maintaining the cell's structural integrity. Microrheology is the natural method of choice for such studies due to its economy in sample volume, its wide frequency range, and its spatial sensitivity. In microrheology, the thermal motion of tracer particles embedded in a complex fluid is used to extract the fluid's viscoelastic properties. Comparing the motion of a single particle to the correlated motion of particle pairs, it is possible to extract viscoelastic properties at different length scales. In a recent study, a crossover between intermediate and bulk response of complex fluids was discovered in microrheology measurements of reconstituted actin networks. This crossover length was related to structural and mechanical properties of the networks, such as their mesh size and dynamic correlation length. Here we capitalize on this result giving a detailed description of our analysis scheme, and demonstrating how this relation can be used to extract the dynamic correlation length of a polymer network. We further study the relation between the dynamic correlation length and the structure of the network, by introducing a new length scale, the average filament length, without altering the network's mesh size. Contrary to the prevailing assumption, that the dynamic correlation length is equivalent to the mesh size of the network, we find that the dynamic correlation length increases once the filament length is reduced below the crossover distance.

Releasing the brakes while hanging on: Cortactin effects on actin-driven motility.

Actin polymerization plays a major role in many cellular processes, including cell motility, vesicle trafficking, and pathogen propulsion. The transformation of the (protrusive) polymerization forces into directed motion requires that the growing filaments are positioned next to the surface. This is achieved by localization of surface actin nucleators (WASP), which then activate Arp2/3 complex to form new actin branches. Yet, the same surface-bound WASP molecule which initiates the nucleation of new actin branches, also inherently prevents the translation of the polymerization forces into motion, essentially because the WASP molecule has to be in contact with the network during the formation of the new branch. In our recent paper we show that cortactin relaxes this internal inhibition by enhancing the release of WASP-VCA molecule from the new branching site after nucleation is initiated. We show that this enhanced release has two major effects; it increases the turnover rate of branching per WASP molecule, and it decreases the friction-like force caused by the binding of the moving surface with respect to the growing actin network.

Hierarchical self-organization of cytoskeletal active networks.

The structural reorganization of the actin cytoskeleton is facilitated through the action of motor proteins that crosslink the actin filaments and transport them relative to each other. Here, we present a combined experimental-computational study that probes the dynamic evolution of mixtures of actin filaments and clusters of myosin motors. While on small spatial and temporal scales the system behaves in a very noisy manner, on larger scales it evolves into several well distinct patterns such as bundles, asters and networks. These patterns are characterized by junctions with high connectivity, whose formation is possible due to the organization of the motors in 'oligoclusters' (intermediate-size aggregates). The simulations reveal that the self-organization process proceeds through a series of hierarchical steps, starting from local microscopic moves and ranging up to the macroscopic large scales where the steady-state structures are formed. Our results shed light on the mechanisms involved in processes such as cytokinesis and cellular contractility, where myosin motors organized in clusters operate cooperatively to induce the structural organization of cytoskeletal networks.

Cortactin releases the brakes in actin- based motility by enhancing WASP-VCA detachment from Arp2/3 branches.

Cortactin is involved in invadopodia and podosome formation [1], pathogens and endosome motility [2], and persistent lamellipodia protrusion [3, 4]; its overexpression enhances cellular motility and metastatic activity [5-8]. Several mechanisms have been proposed to explain cortactin's role in Arp2/3-driven actin polymerization [9, 10], yet its direct role in cell movement remains unclear. We use a biomimetic system to study the mechanism of cortactin-mediated regulation of actin-driven motility [11]. We tested the role of different cortactin variants that interact with Arp2/3 complex and actin filaments distinctively. We show that wild-type cortactin significantly enhances the bead velocity at low concentrations. Single filament experiments show that cortactin has no significant effect on actin polymerization and branch stability, whereas it strongly affects the branching rate driven by Wiskott-Aldrich syndrome protein (WASP)-VCA fragment and Arp2/3 complex. These results lead us to propose that cortactin plays a critical role in translating actin polymerization at a bead surface into motion, by releasing WASP-VCA from the new branching site. This enhanced release has two major effects: it increases the turnover rate of branching per WASP molecule, and it decreases the friction-like force caused by the binding of the moving surface with respect to the growing actin network.

Cooperative molecular motors moving back and forth.

We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual, Proc. Natl. Acad. Sci. U.S.A. 99, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that develops in the cytoskeletal track due to the joint action of the walking motors. We show, both computationally and analytically, that this additional cooperativity effect leads to a dramatic reduction in the characteristic reversal time of the bidirectional motion, especially in systems with a large number of motors. We also find that bidirectional motion takes place only on (almost) apolar tracks, while on even slightly polar tracks the cooperative motion is unidirectional. We argue that the origin of these observations is the sensitive dependence of the cooperative dynamics on the difference between the number of motors typically working in and against the instantaneous direction of motion.

From branched networks of actin filaments to bundles.

Cross-linking proteins can mediate the emergence of rigid bundles from a dense branched network of actin filaments. To enable their binding, the filaments must first bend towards each other. We derive an explicit criterion for the onset of bundling, in terms of the initial length of filaments L, their spacing b, and cross-linker concentration f, reflecting the balance between bending and binding energies. Our model system contains actin, the branching complex Arp2/3 and the bundling protein fascin. In the first distinct stage, during which only actin and Arp2/3 are active, an entangled aster-like mesh of actin filaments is formed. Tens of seconds later, when filaments at the aster periphery are long and barely branched, a sharp transition takes place into a star-like structure, marking the onset of bundling. Now fascin and actin govern bundle growth; Arp2/3 plays no role. Using kinetic Monte Carlo simulations we calculate the temporal evolution of b and L, and predict the onset of bundling as a function of f. Our predictions are in good qualitative agreement with several new experiments that are reported herein and demonstrate how f controls the aster-star transition and bundle length. We also present two models for aster growth corresponding to different experimental realizations. The first treats filament and bundle association as an irreversible sequence of elongation-association steps. The second, applicable for low f, treats bundling as a reversible self-assembly process, where the optimal bundle size is dictated by the balance between surface and bending energies. Finally, we discuss the relevance of our conclusions for the lamellipodium to filopodia transition in living cells, noting that bundles are more likely nucleated by "tip complex" cross-linkers (e.g. mDia2 or Ena/VASP), whereas fascin is mainly involved in bundle maintenance.