Analysis of actin filament network organization in lamellipodia by comparing experimental and simulated images

Automatic extraction of actin networks in plants

The actin cytoskeleton is essential in eukaryotes, not least in the plant kingdom where it plays key roles in cell expansion, cell division, environmental responses and pathogen defence. Yet, the precise structure-function relationships of properties of the actin network in plants are still to be unravelled, including details of how the network configuration depends upon cell type, tissue type and developmental stage. Part of the problem lies in the difficulty of extracting high-quality, quantitative measures of actin network features from microscopy data. To address this problem, we have developed DRAGoN, a novel image analysis algorithm that can automatically extract the actin network across a range of cell types, providing seventeen different quantitative measures that describe the network at a local level. Using this algorithm, we then studied a number of cases in Arabidopsis thaliana, including several different tissues, a variety of actin-affected mutants, and cells responding to powdery mildew. In many cases we found statistically-significant differences in actin network properties. In addition to these results, our algorithm is designed to be easily adaptable to other tissues, mutants and plants, and so will be a valuable asset for the study and future biological engineering of the actin cytoskeleton in globally-important crops.

A mechanism with severing near barbed ends andannealing explains structure and dynamics of dendriticactin networks

Single molecule imaging has shown that part of actin disassembles within a few seconds after incorporation into the dendritic filament network in lamellipodia, suggestive of frequent destabilization near barbed ends. To investigate the mechanisms behind network remodeling, we created a stochastic model with polymerization, depolymerization, branching, capping, uncapping, severing, oligomer diffusion, annealing, and debranching. We find that filament severing, enhanced near barbed ends, can explain the single molecule actin lifetime distribution, if oligomer fragments reanneal to free ends with rate constants comparable to in vitro measurements. The same mechanism leads to actin networks consistent with measured filament, end, and branch concentrations. These networks undergo structural remodeling, leading to longer filaments away from the leading edge, at the +/- 35𝑜 orientation pattern. Imaging of actin speckle lifetimes at sub-second resolution verifies frequent disassembly of newly-assembled actin. We thus propose a unified mechanism that fits a diverse set of basic lamellipodia phenomenology.

4polar-STORM polarized super-resolution imaging of actin filament organization in cells

Single-molecule localization microscopy provides insights into the nanometer-scale spatial organization of proteins in cells, however it does not provide information on their conformation and orientation, which are key functional signatures. Detecting single molecules' orientation in addition to their localization in cells is still a challenging task, in particular in dense cell samples. Here, we present a polarization-splitting scheme which combines Stochastic Optical Reconstruction Microscopy (STORM) with single molecule 2D orientation and wobbling measurements, without requiring a strong deformation of the imaged point spread function. This method called 4polar-STORM allows, thanks to a control of its detection numerical aperture, to determine both single molecules' localization and orientation in 2D and to infer their 3D orientation. 4polar-STORM is compatible with relatively high densities of diffraction-limited spots in an image, and is thus ideally placed for the investigation of dense protein assemblies in cells. We demonstrate the potential of this method in dense actin filament organizations driving cell adhesion and motility.

Methods for assessment of membrane protrusion dynamics

Membrane protrusions are a critical facet of cell function. Mediating fundamental processes such as cell migration, cell-cell interactions, phagocytosis, as well as assessment and remodeling of the cell environment. Different protrusion types and morphologies can promote different cellular functions and occur downstream of distinct signaling pathways. As such, techniques to quantify and understand the inner workings of protrusion dynamics are critical for a comprehensive understanding of cell biology. In this chapter, we describe approaches to analyze cellular protrusions and correlate physical changes in cell morphology with biochemical signaling processes. We address methods to quantify and characterize protrusion types and velocity, mathematical approaches to predictive models of cytoskeletal changes, and implementation of protein engineering and biosensor design to dissect cell signaling driving protrusive activity. Combining these approaches allows cell biologists to develop a comprehensive understanding of the dynamics of membrane protrusions.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Cytoskeletal Actin Structure in Osteosarcoma Cells Determines Metastatic Phenotype via Regulating Cell Stiffness, Migration, and Transmigration

Osteosarcoma is the most common primary malignant bone tumor. The cause of death due to osteosarcoma is typically a consequence of metastasis to the lung. Controlling metastasis leads to improved prognosis for osteosarcoma patients. The cell stiffness of several tumor types is involved in metastatic potential; however, it is unclear whether the metastatic potential of osteosarcoma depends on cell stiffness. In this study, we analyzed the cell stiffness of the low metastatic Dunn cell line and its highly metastatic LM8 subline, and compared actin organization, cell proliferation, and metastasis. Actin cytoskeleton, polymerization, stiffness, and other cellular properties were analyzed. The organization of the actin cytoskeleton was evaluated by staining F-actin with Alexa Fluor 488 phalloidin. Cell stiffness was measured using Atomic Force Microscopy (AFM). Cell proliferation, migration, invasion, and adhesion were also evaluated. All experiments were performed using mouse osteosarcoma cell lines cultured in the absence and presence of cytochalasin. In LM8 cells, actin polymerization was strongly suppressed and actin levels were significantly lower than in Dunn cells. Stiffness evaluation revealed that LM8 cells were significantly softer than Dunn. Young’s modulus images showed more rigid fibrillar structures were present in Dunn cells than in LM8 cells. LM8 cells also exhibited a significantly higher proliferation. The migration and invasion potential were also higher in LM8 cells, whereas the adhesion potential was higher in Dunn cells. The administration of cytochalasin resulted in actin filament fragmentation and decreased actin staining intensity and cell stiffness in both LM8 and Dunn cells. Cells with high metastatic potential exhibited lower actin levels and cell stiffness than cells with low metastatic potential. The metastatic phenotype is highly correlated to actin status and cell stiffness in osteosarcoma cells. These results suggest that evaluation of actin dynamics and cell stiffness is an important quantitative diagnostic parameter for predicting metastatic potential. We believe that these parameters represent new reliable quantitative indicators that can facilitate the development of new drugs against metastasis.

Building a dendritic actin filament network branch by branch: models of filament orientation pattern and force generation in lamellipodia

We review mathematical and computational models of the structure, dynamics, and force generation properties of dendritic actin networks. These models have been motivated by the dendritic nucleation model, which provided a mechanistic picture of how the actin cytoskeleton system powers cell motility. We describe how they aimed to explain the self-organization of the branched network into a bimodal distribution of filament orientations peaked at 35° and - 35° with respect to the direction of membrane protrusion, as well as other patterns. Concave and convex force-velocity relationships were derived, depending on network organization, filament, and membrane elasticity and accounting for actin polymerization at the barbed end as a Brownian ratchet. This review also describes models that considered the kinetics and transport of actin and diffuse regulators and mechanical coupling to a substrate, together with explicit modeling of dendritic networks.

Vinculin forms a directionally asymmetric catch bond with F-actin

Vinculin is an actin-binding protein thought to reinforce cell-cell and cell-matrix adhesions. However, how mechanical load affects the vinculin-F-actin bond is unclear. Using a single-molecule optical trap assay, we found that vinculin forms a force-dependent catch bond with F-actin through its tail domain, but with lifetimes that depend strongly on the direction of the applied force. Force toward the pointed (-) end of the actin filament resulted in a bond that was maximally stable at 8 piconewtons, with a mean lifetime (12 seconds) 10 times as long as the mean lifetime when force was applied toward the barbed (+) end. A computational model of lamellipodial actin dynamics suggests that the directionality of the vinculin-F-actin bond could establish long-range order in the actin cytoskeleton. The directional and force-stabilized binding of vinculin to F-actin may be a mechanism by which adhesion complexes maintain front-rear asymmetry in migrating cells.

Physical Model for Stabilization and Repair of Trans-endothelial Apertures

Bacterial toxins that disrupt the stability of contractile structures in endothelial cells promote the opening of large-scale apertures, thereby breaching the endothelium barrier. These apertures are formed by fusion of the basal and apical membranes into a tunnel that spans the height of the cell. Subsequent to the aperture formation, an active repair process, driven by a stimulated polymerization of actin, results in asymmetrical membrane protrusions and, ultimately, the closure of the aperture. Here, we propose a physics-based model for the generation, stabilization and repair of trans-endothelial apertures. Our model is based on the mechanical interplay between tension in the plasma membrane and stresses that develop within different actin structures at the aperture's periphery. We suggest that accumulation of cytoskeletal fragments around the aperture's rim during the expansion phase results in parallel bundles of actin filaments and myosin motors, generating progressively greater contraction forces that resist further expansion of the aperture. Our results indicate that closure of the tunnel is driven by mechanical stresses that develop within a cross-linked actin gel that forms at localized regions of the aperture periphery. We show that stresses within the gel are due to continuous polymerization of actin filaments against the membrane surfaces of the aperture's edges. Based on our mechanical model, we construct a dynamic simulation of the aperture repair process. Our model fully accounts for the phenomenology of the trans-endothelial aperture formation and stabilization, and recaptures the experimentally observed asymmetry of the intermediate aperture shapes during closure. We make experimentally testable predictions for localization of myosin motors to the tunnel periphery and of adhesion complexes to the edges of apertures undergoing closure, and we estimate the minimal nucleation size of cross-linked actin gel that can lead to a successful repair of the aperture.

A Robust Actin Filaments Image Analysis Framework

The cytoskeleton is a highly dynamical protein network that plays a central role in numerous cellular physiological processes, and is traditionally divided into three components according to its chemical composition, i.e. actin, tubulin and intermediate filament cytoskeletons. Understanding the cytoskeleton dynamics is of prime importance to unveil mechanisms involved in cell adaptation to any stress type. Fluorescence imaging of cytoskeleton structures allows analyzing the impact of mechanical stimulation in the cytoskeleton, but it also imposes additional challenges in the image processing stage, such as the presence of imaging-related artifacts and heavy blurring introduced by (high-throughput) automated scans. However, although there exists a considerable number of image-based analytical tools to address the image processing and analysis, most of them are unfit to cope with the aforementioned challenges. Filamentous structures in images can be considered as a piecewise composition of quasi-straight segments (at least in some finer or coarser scale). Based on this observation, we propose a three-steps actin filaments extraction methodology: (i) first the input image is decomposed into a ‘cartoon’ part corresponding to the filament structures in the image, and a noise/texture part, (ii) on the ‘cartoon’ image, we apply a multi-scale line detector coupled with a (iii) quasi-straight filaments merging algorithm for fiber extraction. The proposed robust actin filaments image analysis framework allows extracting individual filaments in the presence of noise, artifacts and heavy blurring. Moreover, it provides numerous parameters such as filaments orientation, position and length, useful for further analysis. Cell image decomposition is relatively under-exploited in biological images processing, and our study shows the benefits it provides when addressing such tasks. Experimental validation was conducted using publicly available datasets, and in osteoblasts grown in two different conditions: static (control) and fluid shear stress. The proposed methodology exhibited higher sensitivity values and similar accuracy compared to state-of-the-art methods.

We propose a novel actin filaments cytoskeleton analysis framework that allows extracting quasi-straight individual fibers in a robust manner, and provides their respective position, orientation, and length as output. The proposed framework is defined as a three-steps processing sequence, that can explicitly cope with high-throughput imaging related issues, such as noise/artifacts presence and heavy blurring, and can similarly process artifacts-free and well-focused images.

MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks

Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN), for simulating active network evolution and dynamics (available at www.medyan.org). This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament’s resulting super-diffusive behavior in the actomyosin-cross-linker system. We discuss the biological implications of these findings for the arc formation in lamellipodium-to-lamellum architectural remodeling. Lastly, our simulations produce force-dependent accumulation of myosin II, which is thought to be responsible for their mechanosensation ability, also spontaneously generating myosin II concentration gradients in the solution phase of the simulation volume.

Active matter systems have the distinct ability to convert energy from their surroundings into mechanical work, which gives rise to them having highly dynamic properties. Modeling active matter systems and capturing their complex behavior has been a great challenge in past years due to the many coupled interactions between their constituent parts, including not only distinct chemical and mechanical properties, but also feedback between them. One of the most intriguing biological active matter systems is the cell cytoskeleton, which can dynamically respond to chemical and mechanical cues to control cell structure and shape, playing a central role in many higher-order cellular processes. To model these systems and reproduce their behavior, we present a new modeling approach which combines the chemical, mechanical, and molecular transport aspects of active matter systems, all represented with equivalent complexity, while also allowing for various forms of mechanochemical feedback. This modeling approach, named MEDYAN, and software implementation is flexible so that a wide range of active matter systems can be simulated with a high level of detail, and ultimately can help to describe active matter phenomena, and in particular, the dynamics of the cell cytoskeleton. In this work, we have used MEDYAN to simulate a cytoskeletal network consisting of actin filaments, cross-linking proteins, and myosin II molecular motors. We found that these systems show rich dynamical behaviors, undergoing alignment and bundling transitions, with an emergent contractility, as the concentrations of myosin II and cross-linking proteins, as well as actin filament turnover rates, are varied.

Actin kinetics shapes cortical network structure and mechanics

The actin cortex of animal cells is the main determinant of cellular mechanics. The continuous turnover of cortical actin filaments enables cells to quickly respond to stimuli. Recent work has shown that most of the cortical actin is generated by only two actin nucleators, the Arp2/3 complex and the formin Diaph1. However, our understanding of their interplay, their kinetics, and the length distribution of the filaments that they nucleate within living cells is poor. Such knowledge is necessary for a thorough comprehension of cellular processes and cell mechanics from basic polymer physics principles. We determined cortical assembly rates in living cells by using single-molecule fluorescence imaging in combination with stochastic simulations. We find that formin-nucleated filaments are, on average, 10 times longer than Arp2/3-nucleated filaments. Although formin-generated filaments represent less than 10% of all actin filaments, mechanical measurements indicate that they are important determinants of cortical elasticity. Tuning the activity of actin nucleators to alter filament length distribution may thus be a mechanism allowing cells to adjust their macroscopic mechanical properties to their physiological needs.

Capping protein regulators fine-tune actin assembly dynamics

Capping protein (CP) binds the fast growing barbed end of the actin filament and regulates actin assembly by blocking the addition and loss of actin subunits. Recent studies provide new insights into how CP and barbed-end capping are regulated. Filament elongation factors, such as formins and ENA/VASP (enabled/vasodilator-stimulated phosphoprotein), indirectly regulate CP by competing with CP for binding to the barbed end, whereas other molecules, including V-1 and phospholipids, directly bind to CP and sterically block its interaction with the filament. In addition, a diverse and unrelated group of proteins interact with CP through a conserved 'capping protein interaction' (CPI) motif. These proteins, including CARMIL (capping protein, ARP2/3 and myosin I linker), CD2AP (CD2-associated protein) and the WASH (WASP and SCAR homologue) complex subunit FAM21, recruit CP to specific subcellular locations and modulate its actin-capping activity via allosteric effects.

Quantitative analysis of F-actin redistribution in astrocytoma cells treated with candidate pharmaceuticals

Actin fibers (F-actin) control the shape and internal organization of cells, and generate force. It has been long appreciated that these functions are tightly coupled, and in some cases drive cell behavior and cell fate. The distribution and dynamics of F-actin is different in cancer versus normal cells and in response to small molecules, including actin-targeting natural products and anticancer drugs. Therefore, quantifying actin structural changes from high resolution fluorescence micrographs is necessary for further understanding actin cytoskeleton dynamics and phenotypic consequences of drug interactions on cells. We applied an artificial neural network algorithm, which used image intensity and anisotropy measurements, to quantitatively classify F-actin subcellular features into actin along the edges of cells, actin at the protrusions of cells, internal fibers and punctate signals. The algorithm measured significant increase in F-actin at cell edges with concomitant decrease in internal punctate actin in astrocytoma cells lacking functional neurofibromin and p53 when treated with three structurally-distinct anticancer small molecules: OSW1, Schweinfurthin A (SA) and a synthetic marine compound 23'-dehydroxycephalostatin 1. Distinctly different changes were measured in cells treated with the actin inhibitor cytochalasin B. These measurements support published reports that SA acts on F-actin in NF1(-/-) neurofibromin deficient cancer cells through changes in Rho signaling. Quantitative pattern analysis of cells has wide applications for understanding mechanisms of small molecules, because many anti-cancer drugs directly or indirectly target cytoskeletal proteins. Furthermore, quantitative information about the actin cytoskeleton may make it possible to further understand cell fate decisions using mathematically testable models.

Contact angle at the leading edge controls cell protrusion rate

Plasma membrane tension and the pressure generated by actin polymerization are two antagonistic forces believed to define the protrusion rate at the leading edge of migrating cells [1-5]. Quantitatively, resistance to actin protrusion is a product of membrane tension and mean local curvature (Laplace's law); thus, it depends on the local geometry of the membrane interface. However, the role of the geometry of the leading edge in protrusion control has not been yet investigated. Here, we manipulate both the cell shape and substrate topography in the model system of persistently migrating fish epidermal keratocytes. We find that the protrusion rate does not correlate with membrane tension, but, instead, strongly correlates with cell roundness, and that the leading edge of the cell exhibits pinning on substrate ridges-a phenomenon characteristic of spreading of liquid drops. These results indicate that the leading edge could be considered a triple interface between the substrate, membrane, and extracellular medium and that the contact angle between the membrane and the substrate determines the load on actin polymerization and, therefore, the protrusion rate. Our findings thus illuminate a novel relationship between the 3D shape of the cell and its dynamics, which may have implications for cell migration in 3D environments.

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.

Unifying autocatalytic and zeroth-order branching models for growing actin networks

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping, and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament numbers. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth-order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, these mechanisms allow cells to grow stable actin networks over a large range of different conditions.

Actin filament elasticity and retrograde flow shape the force-velocity relation of motile cells

Cells migrate through a crowded environment during processes such as metastasis or wound healing, and must generate and withstand substantial forces. The cellular motility responses to environmental forces are represented by their force-velocity relation, which has been measured for fish keratocytes but remains unexplained. Even pN opposing forces slow down lamellipodium motion by three orders of magnitude. At larger opposing forces, the retrograde flow of the actin network accelerates until it compensates for polymerization, and cell motion stalls. Subsequently, the lamellipodium adapts to the stalled state. We present a mechanism quantitatively explaining the cell's force-velocity relation and its changes upon application of drugs that hinder actin polymerization or actomyosin-based contractility. Elastic properties of filaments, close to the lamellipodium leading edge, and retrograde flow shape the force-velocity relation. To our knowledge, our results shed new light on how these migratory responses are regulated, and on the mechanics and structure of the lamellipodium.

Inferring biological structures from super-resolution single molecule images using generative models

Localization-based super resolution imaging is presently limited by sampling requirements for dynamic measurements of biological structures. Generating an image requires serial acquisition of individual molecular positions at sufficient density to define a biological structure, increasing the acquisition time. Efficient analysis of biological structures from sparse localization data could substantially improve the dynamic imaging capabilities of these methods. Using a feature extraction technique called the Hough Transform simple biological structures are identified from both simulated and real localization data. We demonstrate that these generative models can efficiently infer biological structures in the data from far fewer localizations than are required for complete spatial sampling. Analysis at partial data densities revealed efficient recovery of clathrin vesicle size distributions and microtubule orientation angles with as little as 10% of the localization data. This approach significantly increases the temporal resolution for dynamic imaging and provides quantitatively useful biological information.

Excitable actin dynamics in lamellipodial protrusion and retraction

Many animal cells initiate crawling by protruding lamellipodia, consisting of a dense network of actin filaments, at their leading edge. We imaged XTC cells that exhibit flat lamellipodia on poly-L-lysine-coated coverslips. Using active contours, we tracked the leading edge and measured the total amount of F-actin by summing the pixel intensities within a 5-μm band. We observed protrusion and retraction with period 130-200 s and local wavelike features. Positive (negative) velocities correlated with minimum (maximum) integrated actin concentration. Approximately constant retrograde flow indicated that protrusions and retractions were driven by fluctuations of the actin polymerization rate. We present a model of these actin dynamics as an excitable system in which a diffusive, autocatalytic activator causes actin polymerization; F-actin accumulation in turn inhibits further activator accumulation. Simulations of the model reproduced the pattern of actin polymerization seen in experiments. To explore the model's assumption of an autocatalytic activation mechanism, we imaged cells expressing markers for both F-actin and the p21 subunit of the Arp2/3 complex. We found that integrated Arp2/3-complex concentrations spike several seconds before spikes of F-actin concentration. This suggests that the Arp2/3 complex participates in an activation mechanism that includes additional diffuse components. Response of cells to stimulation by fetal calf serum could be reproduced by the model, further supporting the proposed dynamical picture.

Actin branching in the initiation and maintenance of lamellipodia

Using correlated live cell imaging and electron tomography we found that actin branch junctions in protruding and treadmilling lamellipodia are not concentrated at the front as previously supposed, but link actin filament subsets in which there is a continuum of distances from a junction to the filament plus ends, up to at least 1 µm. When branch sites were observed closely spaced on the same filament their separation was commonly a multiple of the actin helical repeat of 36 nm. Image averaging of branch junctions in the tomograms yielded a model for the in vivo branch at 2.9 nm resolution, which compared closely to that derived for the in vitro actin - Arp2/3 complex. Lamellipodia initiation was monitored in an intracellular wound-healing model and involved branching from the sides of actin filaments oriented parallel to the plasmalemma. Many filament plus ends, presumably capped, terminated behind the lamellipodium tip and localized on the dorsal and ventral surfaces of the actin network. These findings reveal how branching events initiate and maintain a network of actin filaments of variable length and provide the first structural model of the branch junction in vivo. A possible role of filament capping in generating the lamellipodium leaflet is discussed and a mathematical model of protrusion is also presented.

THE CYTOSKELETON: AN ACTIVE POLYMER-BASED SCAFFOLD

The motility of cells is a multifaceted and complicated cytoskeletal process. Significant inroads can be made into gaining a more detailed understanding, however, by focusing on the smaller, more simple subunits of the motile system in an effort to isolate the essential protein components necessary to perform a certain task. Identification of such functional modules has proven to be an effective means of working towards a comprehensive understanding of complex, interacting systems. By following a bottom-up approach in studying minimal actin-related sub-systems for keratocyte motility, we revealed several fundamentally important effects ranging from an estimation of the force generated by the polymerization of a single actin filament, to assembly dynamics and the production of force and tension of composite actin networks, to the contraction of actin networks or smaller bundled structures by the motor myosin II. While even motile keratocyte fragments represent a far more complex situation than the simple reconstituted systems presented here, clear parallels can be seen between in vivo cell motility and the idealized in vitro functional modules presented here, giving more weight to their continued focus.

Accounting for diffusion in agent based models of reaction-diffusion systems with application to cytoskeletal diffusion

Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface.

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

Growing networks of actin fibers are able to organize into compact, stiff two-dimensional structures inside lamellipodia of crawling cells. We put forward the hypothesis that the growing actin network is a critically self-organized system, in which long-range mechanical stresses arising from the interaction with the plasma membrane provide the selective pressure leading to organization. We show that a simple model based only on this principle reproduces the stochastic nature of lamellipodia protrusion (growth periods alternating with fast retractions) and several of the features observed in experiments: a growth velocity initially insensitive to the external force; the capability of the network to organize its orientation; a load-history-dependent growth velocity. Our model predicts that the spectrum of the time series of the height of a growing lamellipodium decays with the inverse of the frequency. This behavior is a well-known signature of self-organized criticality and is confirmed by unique optical tweezer measurements performed in vivo on neuronal growth cones.

Simulation of cell motility that reproduces the force-velocity relationship

Many cells crawl by extending an actin-rich pseudopod. We have devised a simulation that describes how the polymerization kinetics of a branched actin filament network, coupled with excluded volume effects, powers the motility of crawling cells such as amoebae and fish keratocytes. Our stochastic simulation is based on the key fundamental properties of actin polymerization, namely growth, shrinkage, capping, branching, and nucleation, and also includes contributions from the creation and breaking of adhesive contacts with the substrate together with excluded volume effects related to filament packing. When reasonable values for appropriate constants were employed, this simulation generated a force-velocity relationship that resembled closely that observed experimentally. Our simulations indicated that excluded volume effects associated with actin filament branching lead to a decreased packing efficiency and resultant swelling of the cytoskeleton gel that contributes substantially to lamellipod protrusion.

A generative model of microtubule distributions, and indirect estimation of its parameters from fluorescence microscopy images

The microtubule network plays critical roles in many cellular processes, and quantitative models of how its organization varies across cell types and conditions are required for understanding those roles and as input to cell simulations. High-throughput image acquisition technologies are potentially valuable for this purpose, but do not provide sufficient resolution for current analysis methods that rely on tracing of individual microtubules. We describe a parametric conditional model of microtubule distribution that can generate a microtubule network in intact cells using a persistent random walk approach. The model parameters are physically meaningful as they directly describe the spatial distribution of microtubules and include the number of microtubules as well as the mean of the length distribution. We also present an indirect method for estimating the parameters of the model from three-dimensional fluorescence microscope images of cells that relies on comparing acquired images with simulated images generated from the model. Our results show that our method can reasonably recover parameters for a given query image, and we present the distributions of parameters estimated by our method for a collection of HeLa cell images. (c) 2010 International Society for Advancement of Cytometry.

Two competing orientation patterns explain experimentally observed anomalies in growing actin networks

The lamellipodium of migrating animal cells protrudes by directed polymerization of a branched actin network. The underlying mechanisms of filament growth, branching, and capping can be studied in in vitro assays. However, conflicting results have been reported for the force-velocity relation of such actin networks, namely both convex and concave shapes as well as history dependencies. Here we model branching as a reaction that is independent of the number of existing filaments, in contrast to capping, which is assumed to be proportional to the number of existing filaments. Using both stochastic network simulations and deterministic rate equations, we show that such a description naturally leads to the stability of two qualitatively different stationary states of the system, namely a +/- 35 degrees and a +70/0/-70 degrees orientation pattern. Changes in network growth velocity induce a transition between these two patterns. For sufficiently different protrusion efficiency of the two network architectures, this leads to hysteresis in the growth velocity of actin networks under force. Dependent on the history of the system, convex and concave regimes are obtained for the force-velocity relation. Thus a simple generic model can explain the experimentally observed anomalies, with far reaching consequences for cell migration.

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.

Coupled myosin VI motors facilitate unidirectional movement on an F-actin network

A combination of experimentation and modeling reveal that multiple myosin VI molecules coordinately transport cargo over the actin filament network.

Unconventional myosins interact with the dense cortical actin network during processes such as membrane trafficking, cell migration, and mechanotransduction. Our understanding of unconventional myosin function is derived largely from assays that examine the interaction of a single myosin with a single actin filament. In this study, we have developed a model system to study the interaction between multiple tethered unconventional myosins and a model F-actin cortex, namely the lamellipodium of a migrating fish epidermal keratocyte. Using myosin VI, which moves toward the pointed end of actin filaments, we directly determine the polarity of the extracted keratocyte lamellipodium from the cell periphery to the cell nucleus. We use a combination of experimentation and simulation to demonstrate that multiple myosin VI molecules can coordinate to efficiently transport vesicle-size cargo over 10 µm of the dense interlaced actin network. Furthermore, several molecules of monomeric myosin VI, which are nonprocessive in single molecule assays, can coordinate to transport cargo with similar speeds as dimers.

Growing actin networks form lamellipodium and lamellum by self-assembly

Many different cell types are able to migrate by formation of a thin actin-based cytoskeletal extension. Recently, it became evident that this extension consists of two distinct substructures, designated lamellipodium and lamellum, which differ significantly in their kinetic and kinematic properties as well as their biochemical composition. We developed a stochastic two-dimensional computer simulation that includes chemical reaction kinetics, G-actin diffusion, and filament transport to investigate the formation of growing actin networks in migrating cells. Model parameters were chosen based on experimental data or theoretical considerations. In this work, we demonstrate the system's ability to form two distinct networks by self-organization. We found a characteristic transition in mean filament length as well as a distinct maximum in depolymerization flux, both within the first 1-2 microm. The separation into two distinct substructures was found to be extremely robust with respect to initial conditions and variation of model parameters. We quantitatively investigated the complex interplay between ADF/cofilin and tropomyosin and propose a plausible mechanism that leads to spatial separation of, respectively, ADF/cofilin- or tropomyosin-dominated compartments. Tropomyosin was found to play an important role in stabilizing the lamellar actin network. Furthermore, the influence of filament severing and annealing on the network properties is explored, and simulation data are compared to existing experimental data.

Migration deficit in monocyte-macrophages in human ovarian cancer

PURPOSE

To examine the migration responses of monocyte/macrophages (MO/MA) expressing complementary receptors to chemokines produced in the tumor environment of epithelial ovarian cancer (EOC).

METHODS

We examined the expression of the chemokine receptors, CCR1, CCR5, and CXCR4, on EOC associated ascitic and blood MO/MA; their response to complementary chemokines in a MO/MA migration assay and the F-actin content in an actin polymerization assay. A validated cDNA microarray assay was then utilized to examine alterations in pathway genes that can be identified with cell migration.

RESULTS

Ascitic and EOC blood MO/MA express CCR1, CCR5 and CXCR4, but differently. Cell surface expression levels for CCR1 and CCR5 were higher in ascites than that of normal blood in contrast to CXCR4 levels in ascitic MO/MA which were lower. EOC associated ascitic or blood MO/MA failed to migrate in response to the CC ligand RANTES and to the CXCR4 reactive chemokine, SDF1 (CXCL12). Ascitic and most EOC blood MO/MA also behaved differently from normal blood MO in the polymerization/depolymerization assay. A cDNA gene analysis of purified ascitic MO/MA demonstrated that a number of genes involved with chemokine production, focal adhesion, actin cytoskeletal function and leukocyte transendothelial migration were down-regulated in the ascitic MO/MA when compared to normal blood MO. Moreover, PBMC cDNA from EOC patients' blood also showed gene profiles similar to that of ascitic MO/MA.

CONCLUSIONS

Defective migration and polymerization/depolymerization activity of MO/MA from EOC patients and a significant down-regulation of critical pathway genes suggest that other mechanisms might be involved in the accumulation of systemically derived MO at the tumor site of EOC patients.

How do in vitro reconstituted actin-based motility assays provide insight into in vivo behavior?

Recent live cell image analysis of actin dynamics in lamellipodia of motile cells has shown that regulated treadmilling, which supports actin-based propulsion of functionalized particles in biomimetic reconstituted motility assays, is also responsible for lamellipodia extension. In both cases, filaments are created by branching with Arp2/3 complex only at the membrane or particle surface, grow transiently and are capped; ADF/cofilin enhances the treadmilling but does not sever filaments in the body of the meshwork. Differences between the cellular and biomimetic systems suggest that additional regulatory mechanisms take place in lamellipodia.