Actin bundling: initiation mechanisms and kinetics

Biomolecular condensation involving the cytoskeleton

Biomolecular condensation of proteins contributes to the organization of the cytoplasm and nucleoplasm. A number of condensation processes appear to be directly involved in regulating the structure, function and dynamics of the cytoskeleton. Liquid-liquid phase separation of cytoskeleton proteins, together with polymerization modulators, promotes cytoskeletal fiber nucleation and branching. Furthermore, the attachment of protein condensates to the cytoskeleton can contribute to cytoskeleton stability and organization, regulate transport, create patterns of functional reaction containers, and connect the cytoskeleton with membranes. Surface-bound condensates can exert and buffer mechanical forces that give stability and flexibility to the cytoskeleton, thus, may play a large role in cell biology. In this review, we introduce the concept and role of cellular biomolecular condensation, explain its special function on cytoskeletal fiber surfaces, and point out potential definition and experimental caveats. We review the current literature on protein condensation processes related to the actin, tubulin, and intermediate filament cytoskeleton, and discuss some of them in the context of neurobiology. In summary, we provide an overview about biomolecular condensation in relation to cytoskeleton structure and function, which offers a base for the exploration and interpretation of cytoskeletal condensates in neurobiology.

Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales

The combination of fluid-structure interactions with stochasticity, due to thermal fluctuations, remains a challenging problem in computational fluid dynamics. We develop an efficient scheme based on the stochastic immersed boundary method, Stokeslets, and multiple timestepping. We test our method for spherical particles and filaments under purely thermal and deterministic forces and find good agreement with theoretical predictions for Brownian Motion of a particle and equilibrium thermal undulations of a semi-flexible filament. As an initial application, we simulate bio-filaments with the properties of F-actin. We specifically study the average time for two nearby parallel filaments to bundle together. Interestingly, we find a two-fold acceleration in this time between simulations that account for long-range hydrodynamics compared to those that do not, suggesting that our method will reveal significant hydrodynamic effects in biological phenomena.

Diamond, graphite, and graphene oxide nanoparticles decrease migration and invasiveness in glioblastoma cell lines by impairing extracellular adhesion

The highly invasive nature of glioblastoma is one of the most significant problems regarding the treatment of this tumor. Diamond nanoparticles (ND), graphite nanoparticles (NG), and graphene oxide nanoplatelets (nGO) have been explored for their biomedical applications, especially for drug delivery. The objective of this research was to assess changes in the adhesion, migration, and invasiveness of two glioblastoma cell lines, U87 and U118, after ND, NG, and nGO treatment. All treatments affected the cell surface structure, adhesion-dependent EGFR/AKT/mTOR, and β-catenin signaling pathways, decreasing the migration and invasiveness of both glioblastoma cell lines. The examined nanoparticles did not show strong toxicity but effectively deregulated cell migration. ND was effectively taken up by cells, whereas nGO and NG strongly interacted with the cell surface. These results indicate that nanoparticles could be used in biomedical applications as a low toxicity active compound for glioblastoma treatment.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Designing highly tunable semiflexible filament networks

Semiflexible polymers can generate a range of filamentous networks significantly different in structure from those seen in conventional polymer solutions. Our coarse-grained simulations with an implicit cross-linker potential show that networks of branching bundles, knotted morphologies, and structural chirality can be generated by a generalized approach independent of specific cross-linkers. Network structure depends primarily on filament flexibility and separation, with significant connectivity increase after percolation. Results should guide the design of engineered semiflexible polymers.

Assembly kinetics determine the architecture of α-actinin crosslinked F-actin networks

The actin cytoskeleton is organized into diverse meshworks and bundles that support many aspects of cell physiology. Understanding the self-assembly of these actin-based structures is essential for developing predictive models of cytoskeletal organization. Here we show that the competing kinetics of bundle formation with the onset of dynamic arrest arising from filament entanglements and cross-linking determine the architecture of reconstituted actin networks formed with α-actinin cross-links. Cross-link mediated bundle formation only occurs in dilute solutions of highly mobile actin filaments. As actin polymerization proceeds, filament mobility and bundle formation are arrested concomitantly. By controlling the onset of dynamic arrest, perturbations to actin assembly kinetics dramatically alter the architecture of biochemically identical samples. Thus, the morphology of reconstituted F-actin networks is a kinetically determined structure similar to those formed by physical gels and glasses. These results establish mechanisms controlling the structure and mechanics in diverse semi-flexible biopolymer networks.

Model of myosin node aggregation into a contractile ring: the effect of local alignment

Actomyosin bundles frequently form through aggregation of membrane-bound myosin clusters. One such example is the formation of the contractile ring in fission yeast from a broad band of cortical nodes. Nodes are macromolecular complexes containing several dozens of myosin-II molecules and a few formin dimers. The condensation of a broad band of nodes into the contractile ring has been previously described by a search, capture, pull and release (SCPR) model. In SCPR, a random search process mediated by actin filaments nucleated by formins leads to transient actomyosin connections among nodes that pull one another into a ring. The SCPR model reproduces the transport of nodes over long distances and predicts observed clump-formation instabilities in mutants. However, the model does not generate transient linear elements and meshwork structures as observed in some wild-type and mutant cells during ring assembly. As a minimal model of node alignment, we added short-range aligning forces to the SCPR model representing currently unresolved mechanisms that may involve structural components, cross-linking and bundling proteins. We studied the effect of the local node alignment mechanism on ring formation numerically. We varied the new parameters and found viable rings for a realistic range of values. Morphologically, transient structures that form during ring assembly resemble those observed in experiments with wild-type and cdc25-22 cells. Our work supports a hierarchical process of ring self-organization involving components drawn together from distant parts of the cell followed by progressive stabilization.

The role of actin bundling proteins in the assembly of filopodia in epithelial cells

The goal of this review is to highlight how emerging new models of filopodia assembly, which include tissue specific actin-bundling proteins, could provide more comprehensive representations of filopodia assembly that would describe more adequately and effectively the complexity and plasticity of epithelial cells.  This review also describes how the true diversity of actin bundling proteins must be considered to predict the far-reaching significance and versatile functions of filopodia in epithelial cells.

The Eps8/IRSp53/VASP network differentially controls actin capping and bundling in filopodia formation

There is a body of literature that describes the geometry and the physics of filopodia using either stochastic models or partial differential equations and elasticity and coarse-grained theory. Comparatively, there is a paucity of models focusing on the regulation of the network of proteins that control the formation of different actin structures. Using a combination of in-vivo and in-vitro experiments together with a system of ordinary differential equations, we focused on a small number of well-characterized, interacting molecules involved in actin-dependent filopodia formation: the actin remodeler Eps8, whose capping and bundling activities are a function of its ligands, Abi-1 and IRSp53, respectively; VASP and Capping Protein (CP), which exert antagonistic functions in controlling filament elongation. The model emphasizes the essential role of complexes that contain the membrane deforming protein IRSp53, in the process of filopodia initiation. This model accurately accounted for all observations, including a seemingly paradoxical result whereby genetic removal of Eps8 reduced filopodia in HeLa, but increased them in hippocampal neurons, and generated quantitative predictions, which were experimentally verified. The model further permitted us to explain how filopodia are generated in different cellular contexts, depending on the dynamic interaction established by Eps8, IRSp53 and VASP with actin filaments, thus revealing an unexpected plasticity of the signaling network that governs the multifunctional activities of its components in the formation of filopodia.

Cells move and interact with the environment by forming migratory structures composed of self organized polymers of actin. These protrusions can be flat and short surfaces, the lamellipodia, or adopt an elongated, finger-like shape called filopodia. In this article, we analyze the ‘computation’ performed by cells when they opt to form filopodia. We focus our attention on some initiators of filopodia that play an essential role due to their interaction with the cell membrane. We analyze the formation of these filopodia initiators in different genotypes, thus providing a way to rationalize the behaviors of different cells in terms of tendency to form filopodia. Our results, based on the combination of experimental and computational approaches, suggest that cells have developed molecular networks that are extremely flexible in their capability to follow the path leading to filopodia formation. In this sense the role of an element of the network, Eps8, is paradigmatic, as this protein can both induce or inhibit the formation of filopodia depending on the cellular context.

Polymorphism of highly cross-linked F-actin networks: probing multiple length scales

The assembly properties of F-actin filaments in the presence of different biological cross-linker concentrations and types have been investigated using a combined approach of fluorescence confocal microscopy and coarse-grained molecular dynamics simulation. In particular for highly cross-linked regimes, new network morphologies are observed. Complex network formation and the details of the resulting structure are strongly dependent on the ratio of cross-linkers to actin monomers and cross-linker shape but only weakly dependent on overall actin concentration and filament length. The work presented here may help to provide some fundamental understanding of how excessive cross-linkers interact with the actin filament solution, creating different structures in the cell under high cross-linker concentrations. F-actin is not only of biological importance but also, as an example of a semiflexible polymer, has attracted significant interest in its physical behavior. In combination with different cross-linkers semiflexible filaments may provide new routes to bio-materials development and act as the inspiration for new hierarchical network-based materials.

Quantifying a pathway: kinetic analysis of actin dendritic nucleation

Progress in uncovering the reaction networks that underlie important cell functions is laying the groundwork for quantitative identification of protein-interaction pathways. Since direct measurement of rate constants is not always feasible, the parameters are often inferred from multiple pieces of data using kinetic analyses based on appropriate mathematical models. The success of this approach relies on the sufficiency of available experimental data for a unique parameterization of the network. The concept of a rate-limiting step is applied to the analysis of experimental data that are usually used to quantify a pathway of actin dendritic nucleation, the Arp2/3-mediated mechanism that enables rapid changes of cell shape in response to external cues. The method yields analytical descriptions of the dynamics of polymerized actin and provides insights into how the experimental curves should be analyzed. It is shown that dynamics measured by pyrene-labeled actin assays with varying Arp2/3 concentrations are equally well described by two different rate-limiting steps: 1), binding of a nucleating complex to the side of a preexisting filament; or 2), its subsequent activation. To distinguish between the alternatives, we propose experiments with varying concentrations of actin monomers, taking advantage of the fact that the number of branches in the two cases depends differently on the initial monomer concentration. The idea is tested by simulating the proposed experiments with the use of spatial stochastic modeling.

Modeling the formation of in vitro filopodia

Filopodia are bundles of actin filaments that extend out ahead of the leading edge of a crawling cell to probe its upcoming environment. In vitro experiments (Vignjevic et al. in J Cell Biol 160:951-962, 2003) have determined the minimal ingredients required for the formation of filopodia from the dendritic-like morphology of the leading edge. We model these experiments using kinetic aggregation equations for the density of growing bundle tips. In mean field, we determine the bundle size distribution to be broad for bundle sizes smaller than a characteristic bundle size above which the distribution decays exponentially. Two-dimensional simulations incorporating both bundling and cross-linking measure a bundle size distribution that agrees qualitatively with mean field. The simulations also demonstrate a nonmonotonicity in the radial extent of the dendritic region as a function of capping protein concentration, as was observed in experiments, due to the interplay between percolation and the ratcheting of growing filaments off a spherical obstacle.

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.

Use of virtual cell in studies of cellular dynamics

The Virtual Cell (VCell) is a unique computational environment for modeling and simulation of cell biology. It has been specifically designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists. The models created with VCell can range from the simple, to evaluate hypotheses or to interpret experimental data, to complex multilayered models used to probe the predicted behavior of spatially resolved, highly nonlinear systems. In this chapter, we discuss modeling capabilities of VCell and demonstrate representative examples of the models published by the VCell users.