Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions

Systemic cellular migration: The forces driving the directed locomotion movement of cells

Directional motility is an essential property of cells. Despite its enormous relevance in many fundamental physiological and pathological processes, how cells control their locomotion movements remains an unresolved question. Here, we have addressed the systemic processes driving the directed locomotion of cells. Specifically, we have performed an exhaustive study analyzing the trajectories of 700 individual cells belonging to three different species (Amoeba proteus, Metamoeba leningradensis, and Amoeba borokensis) in four different scenarios: in absence of stimuli, under an electric field (galvanotaxis), in a chemotactic gradient (chemotaxis), and under simultaneous galvanotactic and chemotactic stimuli. All movements were analyzed using advanced quantitative tools. The results show that the trajectories are mainly characterized by coherent integrative responses that operate at the global cellular scale. These systemic migratory movements depend on the cooperative nonlinear interaction of most, if not all, molecular components of cells.

Contact guidance as a consequence of coupled morphological evolution and motility of adherent cells

Adherent cells seeded on substrates spread and evolve their morphology while simultaneously displaying motility. Phenomena such as contact guidance, viz. the alignment of cells on patterned substrates, are strongly linked to the coupling of morphological evolution with motility. Here, we employ a recently developed statistical thermodynamics framework for modelling the non-thermal fluctuating response of cells to probe this coupling. This thermodynamic framework is first extended via a Langevin style model to predict temporal responses of cells to unpatterned and patterned substrates. The Langevin model is then shown to not only predict the different experimentally observed temporal scales for morphological observables such as cell area and elongation but also the interplay of morphology with motility that ultimately leads to contact guidance.

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

Reproducing asymmetrical spine shape fluctuations in a model of actin dynamics predicts self-organized criticality

Dendritic spines change their size and shape spontaneously, but the function of this remains unclear. Here, we address this in a biophysical model of spine fluctuations, which reproduces experimentally measured spine fluctuations. For this, we characterize size- and shape fluctuations from confocal microscopy image sequences using autoregressive models and a new set of shape descriptors derived from circular statistics. Using the biophysical model, we extrapolate into longer temporal intervals and find the presence of 1/f noise. When investigating its origins, the model predicts that the actin dynamics underlying shape fluctuations self-organizes into a critical state, which creates a fine balance between static actin filaments and free monomers. In a comparison against a non-critical model, we show that this state facilitates spine enlargement, which happens after LTP induction. Thus, ongoing spine shape fluctuations might be necessary to react quickly to plasticity events.

Predictive assembling model reveals the self-adaptive elastic properties of lamellipodial actin networks for cell migration

Branched actin network supports cell migration through extracellular microenvironments. However, it is unknown how intracellular proteins adapt the elastic properties of the network to the highly varying extracellular resistance. Here we develop a three-dimensional assembling model to simulate the realistic self-assembling process of the network by encompassing intracellular proteins and their dynamic interactions. Combining this multiscale model with finite element method, we reveal that the network can not only sense the variation of extracellular resistance but also self-adapt its elastic properties through remodeling with intracellular proteins. Such resistance-adaptive elastic behaviours are versatile and essential in supporting cell migration through varying extracellular microenvironments. The bending deformation mechanism and anisotropic Poisson's ratios determine why lamellipodia persistently evolve into sheet-like structures. Our predictions are confirmed by published experiments. The revealed self-adaptive elastic properties of the networks are also applicable to the endocytosis, phagocytosis, vesicle trafficking, intracellular pathogen transport and dendritic spine formation.

Anxiety and depression: A matter of stiffness?

Cells react to stress by the universal responses of "fluidization" or "reinforcement" (stiffening) of the cytoplasm, through dramatic re-arrangements of the cytoskeleton. Here it is suggested that, at a supracellular level, the brain exhibits such a fundamental behavior as part of its complex response to stress: it is hypothesized that the soft gel formed by brain cell cytoskeletons and the surrounding extracellular matrix (the "cytoskeletons-matrix system") undergoes transitions either to sol (fluidization) or stiff gel (reinforcement) as a very fundamental and evolutionarily conserved brain response to stress, alongside more sophisticated neural pathways. Sol state corresponds to increased cell activity (a sort of "fight or flight" response), whereas stiff gel state corresponds to inactivity (an "immobility" strategy). Psychological stress, through simple stress signals such as pH changes, would lead to an initial tissue fluidization in key regions of the brain, followed, if the stress stimuli persist, by reinforcement (slow formation of actomyosin stress fibers and matrix stiffening). It is also hypothesized that the cytoskeletons-matrix system is one of the biological correlates of so-called "background feelings", i.e conscious feelings built on inner chemical-physical states of the body. Optimal dynamics of the cytoskeletons-matrix system would contribute to a core feeling of well-being, while shifts towards fluidization (activation) or stiffening (inactivation) would contribute to background feelings at the basis of anxiety and stress-induced depression, respectively. It is suggested that the cytoskeletons-matrix system behaves as a "self-organized critical system", anxiety and depression arising whenever the system is driven too far from the optimal critical point. Finally, some application hints from the proposed ideas are given.

A continuum model for the growth of dendritic actin networks

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here, we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore, a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.

A proteomic approach towards understanding crypoprotective action of Me2SO on the CHO cell proteome

Chinese hamster ovary (CHO) cell lines are the most widely used in vitro cells for research and production of recombinant proteins such as rhGH, tPA, and erythropoietin. We aimed to investigate changes in protein profiles after cryopreservation using 2D-DIGE MALDI-TOF MS and network pathway analysis. The proteome changes that occur in CHO cells between freshly prepared cells and cryopreserved cells with and without Me2SO were compared to determine the key proteins and pathways altered during recovery from cryopreservation. A total of 54 proteins were identified and successfully matched to 37 peptide mass fingerprints (PMF). 14 protein spots showed an increase while 23 showed decrease abundance in the Me2SO free group compared to the control. The proteins with increased abundance included vimentin, heat shock protein 60 kDa, mitochondrial, heat shock 70 kDa protein 9, protein disulfide-isomerase A3, voltage-dependent anion-selective channel protein 2. Those with a decrease in abundance were myotubularin, glutathione peroxidase, enolase, phospho glyceromutase, chloride intracellular channel protein 1. The main canonical functional pathway affected involved the unfolded protein response, aldosterone Signaling in Epithelial Cells, 14-3-3-mediated signaling. 2D-DIGE MALDI TOF mass spectrometry and network pathway analysis revealed the differential proteome expression of FreeStyle CHO cells after cryopreservation with and without 5% Me2SOto involve pathways related to post-translational modification, protein folding and cell death and survival (score = 56, 22 focus molecules). This study revealed, for the first time to our knowledge the proteins and their regulated pathways involved in the cryoprotective action of 5% Me2SO. The use of 5% Me2SO as a cryoprotectant maintained the CHO cell proteome in the cryopreserved cells, similar to that of fresh CHO cells.

DLITE Uses Cell-Cell Interface Movement to Better Infer Cell-Cell Tensions

Cell shapes and connectivities evolve over time as the colony changes shape or embryos develop. Shapes of intercellular interfaces are closely coupled with the forces resulting from actomyosin interactions, membrane tension, or cell-cell adhesions. Although it is possible to computationally infer cell-cell forces from a mechanical model of collective cell behavior, doing so for temporally evolving forces in a manner robust to digitization difficulties is challenging. Here, we introduce a method for dynamic local intercellular tension estimation (DLITE) that infers such evolution in temporal force with less sensitivity to digitization ambiguities or errors. This method builds upon previous work on single time points (cellular force-inference toolkit). We validate our method using synthetic geometries. DLITE's inferred cell colony tension evolutions correlate better with ground truth for these synthetic geometries as compared to tension values inferred from methods that consider each time point in isolation. We introduce cell connectivity errors, angle estimate errors, connection mislocalization, and connection topological changes to synthetic data and show that DLITE has reduced sensitivity to these conditions. Finally, we apply DLITE to time series of human-induced pluripotent stem cell colonies with endogenously expressed GFP-tagged zonulae occludentes-1. We show that DLITE offers improved stability in the inference of cell-cell tensions and supports a correlation between the dynamics of cell-cell forces and colony rearrangement.

Growth and remodelling of living tissues: perspectives, challenges and opportunities

One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

Quantifying dissipation in actomyosin networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

Nonlinear elasticity of incompatible surface growth

Surface growth is a crucial component of many natural and artificial processes, from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility, leading to residual stresses and triggering various instabilities. In a recent paper [G. Zurlo and L. Truskinovsky, Phys. Rev. Lett. 119, 048001 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.048001] we presented a linearized elasticity theory of incompatible surface growth, which provides a quantitative link between deposition protocols and postgrowth states of stress. Here we extend this analysis to account for both physical and geometrical nonlinearities of an elastic solid. This development reveals the shortcomings of the linearized theory, in particular its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities.

Does self-organized criticality drive leading edge protrusion?

Arp2/3 complex nucleates dendritic actin networks and plays a pivotal role in the formation of lamellipodia at the leading edge of motile cells. Mouse fibroblasts lacking functional Arp2/3 complex have the characteristic smooth, veil-like lamellipodial leading edge of wild-type cells replaced by a massive, bifurcating filopodia-like protrusions (FLPs) with fractal geometry. The nanometer-scale actin-network organization of these FLPs can be linked to the fractal geometry of the cell boundary by a self-organized criticality through the bifurcation behavior of cross-linked actin bundles. Despite the pivotal role of the Arp2/3 complex in cell migration, the cells lacking functional Arp2/3 complex migrate at rates similar to wild-type cells. However, these cells display defects in the persistence of a directional movement. We suggest that Arp2/3 complex suppresses the formation of FLPs by locally fine-tuning actin networks and favoring dendritic geometry over bifurcating bundles, giving cells a distinct evolutionary edge by providing the means for a directed movement.

Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM

We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.

Spontaneous symmetry breaking for geometrical trajectories of actin-based motility in three dimensions

Actin-based motility is important for many cellular processes. In this article we extend our previous studies of an actin-propelled circular disk in two dimensions to an actin-propelled spherical bead in three dimensions. We find that for an achiral load the couplings between the motion of the load and the actin network induce a series of bifurcations, starting with a transition from rest to moving state, followed by a transition from straight to planar curves, and finally a further transition from motion in a plane to one with torsion. To address the intriguing, experimentally observed chiral motility of the bacterium Listeria monocytogenes, we also study the motility of a spherical load with a built-in chirality. For such a chiral load, stable circular trajectories are no longer found in numerical simulations. Instead, helical trajectories with handedness that depends on the chirality of the load are found. Our results reveal the relation between the symmetry of actin network and the trajectories of actin-propelled loads.

Gasmin (BV2-5), a polydnaviral-acquired gene in Spodoptera exigua. Trade-off in the defense against bacterial and viral infections

Thousands of Hymenopteran endoparasitoids have developed a unique symbiotic relationship with viruses named polydnavirus (PDVs). These viruses immunocompromise the lepidopteran host allowing the survival of the wasp eggs. In a previous work, we have shown the horizontal transfer of some polydnaviral genes into the genome of the Lepidoptera, Spodoptera exigua. One of these genes, BV2-5 (named gasmin) interferes with actin polymerization, negatively affecting the multiplication of baculovirus in cell culture. In this work, we have focused in the study of the effect of Gasmin expression on different aspects of the baculovirus production. In addition, and since actin polymerization is crucial for phagocytosis, we have studied the effect of Gasmin expression on the larval interaction with bacterial pathogens. Over-expression of Gasmin on hemocytes significantly reduces their capacity to phagocytize the pathogenic bacteria Bacillus thuringiensis. According to these results, gasmin domestication negatively affects baculovirus replication, but increases larvae susceptibility to bacterial infections as pay off. Although the effect of Gasmin on the insect interaction with other pathogens or parasitoids remain unknown, the opposite effects described here could shape the biological history of this species based on the abundance of certain type of pathogens as suggested by the presence of truncated forms of this protein in several regions of the world.

Cell sensing of physical properties at the nanoscale: Mechanisms and control of cell adhesion and phenotype

The chemistry, geometry, topography and mechanical properties of biomaterials modulate biochemical signals (in particular ligand-receptor binding events) that control cells-matrix interactions. In turn, the regulation of cell adhesion by the biochemical and physical properties of the matrix controls cell phenotypes such as proliferation, motility and differentiation. In particular, nanoscale geometrical, topographical and mechanical properties of biomaterials are essential to achieve control of the cell-biomaterials interface. The design of such nanoscale architectures and platforms requires understanding the molecular mechanisms underlying adhesion formation and the assembly of the actin cytoskeleton. This review presents some of the important molecular mechanisms underlying cell adhesion to biomaterials mediated by integrins and discusses the nanoscale engineered platforms used to control these processes. Such nanoscale understanding of the cell-biomaterials interface offers exciting opportunities for the design of biomaterials and their application to the field of tissue engineering.

STATEMENT OF SIGNIFICANCE

Biomaterials design is important in the fields of regenerative medicine and tissue engineering, in particular to allow the long term expansion of stem cells and the engineering of scaffolds for tissue regeneration. Cell adhesion to biomaterials often plays a central role in regulating cell phenotype. It is emerging that physical properties of biomaterials, and more generally the microenvironment, regulate such behaviour. In particular, cells respond to nanoscale physical properties of their matrix. Understanding how such nanoscale physical properties control cell adhesion is therefore essential for biomaterials design. To this aim, a deeper understanding of molecular processes controlling cell adhesion, but also a greater control of matrix engineering is required. Such multidisciplinary approaches shed light on some of the fundamental mechanisms via which cell adhesions sense their nanoscale physical environment.

In search of principles for a Theory of Organisms

Lacking an operational theory to explain the organization and behaviour of matter in unicellular and multicellular organisms hinders progress in biology. Such a theory should address life cycles from ontogenesis to death. This theory would complement the theory of evolution that addresses phylogenesis, and would posit theoretical extensions to accepted physical principles and default states in order to grasp the living state of matter and define proper biological observables. Thus, we favour adopting the default state implicit in Darwin's theory, namely, cell proliferation with variation plus motility, and a framing principle, namely, life phenomena manifest themselves as non-identical iterations of morphogenetic processes. From this perspective, organisms become a consequence of the inherent variability generated by proliferation, motility and self-organization. Morphogenesis would then be the result of the default state plus physical constraints, like gravity, and those present in living organisms, like muscular tension.

Thermodynamic description of Beta amyloid formation using physicochemical scales and fractal bioinformatic scales

Protein function depends on both protein structure and amino acid (aa) sequence. Here we show that modular features of both structure and function can be quantified economically from the aa sequences alone for the small (40,42 aa) plaque-forming (aggregative) amyloid beta fragments. Some edge and center features of the fragments are predicted. Bioinformatic scales based on β strand formation propensities and the thermodynamically second order fractal hydropathicity scale based on evolutionary optimization (self-organized criticality) are contrasted with the standard first order physicochemical scale based on complete protein (water-air) unfolding. The results are consistent with previous studies of these physicochemical factors that show that aggregative properties, even of beta fragments, are driven primarily by near-equilibrium hydropathic forces.

Proteinquakes in the Evolution of Influenza Virus Hemagglutinin (A/H1N1) under Opposing Migration and Vaccination Pressures

Influenza virus contains two highly variable envelope glycoproteins, hemagglutinin (HA) and neuraminidase (NA). Here we show that, while HA evolution is much more complex than NA evolution, it still shows abrupt punctuation changes linked to punctuation changes of NA. HA exhibits proteinquakes, which resemble earthquakes and are related to hydropathic shifting of sialic acid binding regions. HA proteinquakes based on shifting sialic acid interactions are required for optimal balance between the receptor-binding and receptor-destroying activities of HA and NA for efficient virus replication. Our comprehensive results present a historical (1945–2011) panorama of HA evolution over thousands of strains and are consistent with many studies of HA and NA interactions based on a few mutations of a few strains.

Erythrocyte stiffness during morphological remodeling induced by carbon ion radiation

The adverse effect induced by carbon ion radiation (CIR) is still an unavoidable hazard to the treatment object. Thus, evaluation of its adverse effects on the body is a critical problem with respect to radiation therapy. We aimed to investigate the change between the configuration and mechanical properties of erythrocytes induced by radiation and found differences in both the configuration and the mechanical properties with involving in morphological remodeling process. Syrian hamsters were subjected to whole-body irradiation with carbon ion beams (1, 2, 4, and 6 Gy) or X-rays (2, 4, 6, and 12 Gy) for 3, 14 and 28 days. Erythrocytes in peripheral blood and bone marrow were collected for cytomorphological analysis. The mechanical properties of the erythrocytes were determined using atomic force microscopy, and the expression of the cytoskeletal protein spectrin-α1 was analyzed via western blotting. The results showed that dynamic changes were evident in erythrocytes exposed to different doses of carbon ion beams compared with X-rays and the control (0 Gy). The magnitude of impairment of the cell number and cellular morphology manifested the subtle variation according to the irradiation dose. In particular, the differences in the size, shape and mechanical properties of the erythrocytes were well exhibited. Furthermore, immunoblot data showed that the expression of the cytoskeletal protein spectrin-α1 was changed after irradiation, and there was a common pattern among its substantive characteristics in the irradiated group. Based on these findings, the present study concluded that CIR could induce a change in mechanical properties during morphological remodeling of erythrocytes. According to the unique characteristics of the biomechanical categories, we deduce that changes in cytomorphology and mechanical properties can be measured to evaluate the adverse effects generated by tumor radiotherapy. Additionally, for the first time, the current study provides a new strategy for enhancing the assessment of the curative effects and safety of clinical radiotherapy, as well as reducing adverse effects.

Ultrastructure of protrusive actin filament arrays

The actin cytoskeleton is the major force-generating machinery in the cell, which can produce pushing, pulling, and resistance forces. To accomplish these diverse functions, actin filaments, with help of numerous accessory proteins, form higher order ensembles, networks and bundles, adapted to specific tasks. Moreover, dynamic properties of the actin cytoskeleton allow a cell to constantly build, renew, and redesign actin structures according to its changing needs. High resolution architecture of actin filament arrays provides key information for understanding mechanisms of force generation. To generate pushing force, cells use coordinated polymerization of multiple actin filaments organized into branched (dendritic) networks or parallel bundles. This review summarizes our current knowledge of the structural organization of these two actin filament arrays.

Mesoscopic model of actin-based propulsion

Two theoretical models dominate current understanding of actin-based propulsion: microscopic polymerization ratchet model predicts that growing and writhing actin filaments generate forces and movements, while macroscopic elastic propulsion model suggests that deformation and stress of growing actin gel are responsible for the propulsion. We examine both experimentally and computationally the 2D movement of ellipsoidal beads propelled by actin tails and show that neither of the two models can explain the observed bistability of the orientation of the beads. To explain the data, we develop a 2D hybrid mesoscopic model by reconciling these two models such that individual actin filaments undergoing nucleation, elongation, attachment, detachment and capping are embedded into the boundary of a node-spring viscoelastic network representing the macroscopic actin gel. Stochastic simulations of this ‘in silico’ actin network show that the combined effects of the macroscopic elastic deformation and microscopic ratchets can explain the observed bistable orientation of the actin-propelled ellipsoidal beads. To test the theory further, we analyze observed distribution of the curvatures of the trajectories and show that the hybrid model's predictions fit the data. Finally, we demonstrate that the model can explain both concave-up and concave-down force-velocity relations for growing actin networks depending on the characteristic time scale and network recoil. To summarize, we propose that both microscopic polymerization ratchets and macroscopic stresses of the deformable actin network are responsible for the force and movement generation.

There are two major ideas about how actin networks generate force against an obstacle: one is that the force comes directly from the elongation and bending of individual actin filaments against the surface of the obstacle; the other is that a growing actin gel can build up stress around the obstacle to squeeze it forward. Neither of the two models can explain why actin-propelled ellipsoidal beads move with equal bias toward long- and short-axes. We propose a hybrid model by combining those two ideas so that individual actin filaments are embedded into the boundary of a deformable actin gel. Simulations of this model show that the combined effects of pushing from individual filaments and squeezing from the actin network explain the observed bi-orientation of ellipsoidal beads as well as the curvature of trajectories of spherical beads and the force-velocity relation of actin networks.

Crawling motility through the analysis of model locomotors: two case studies

We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.

The role of membrane stiffness and actin turnover on the force exerted by DRG lamellipodia

We used optical tweezers to analyze the effect of jasplakinolide and cyclodextrin on the force exerted by lamellipodia from developing growth cones (GCs) of isolated dorsal root ganglia (DRG) neurons. We found that 25 nM of jasplakinolide, which is known to inhibit actin filament turnover, reduced both the maximal exerted force and maximal velocity during lamellipodia leading-edge protrusion. By using atomic force microscopy, we verified that cyclodextrin, which is known to remove cholesterol from membranes, decreased the membrane stiffness of DRG neurons. Lamellipodia treated with 2.5 mM of cyclodextrin exerted a larger force, and their leading edge could advance with a higher velocity. Neither jasplakinolide nor cyclodextrin affected force or velocity during lamellipodia retraction. The amplitude and frequency of elementary jumps underlying force generation were reduced by jasplakinolide but not by cyclodextrin. The action of both drugs at the used concentration was fully reversible. These results support the notion that membrane stiffness provides a selective pressure that shapes force generation, and confirm the pivotal role of actin turnover during protrusion.

The elementary events underlying force generation in neuronal lamellipodia

We have used optical tweezers to identify the elementary events underlying force generation in neuronal lamellipodia. When an optically trapped bead seals on the lamellipodium membrane, Brownian fluctuations decrease revealing the underlying elementary events. The distribution of bead velocities has long tails with frequent large positive and negative values associated to forward and backward jumps occurring in 0.1-0.2 ms with varying amplitudes up to 20 nm. Jump frequency and amplitude are reduced when actin turnover is slowed down by the addition of 25 nM Jasplakinolide. When myosin II is inhibited by the addition of 20 μM Blebbistatin, jump frequency is reduced but to a lesser extent than by Jasplainolide. These jumps constitute the elementary events underlying force generation.