Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers towards the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady state solutions.     

Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics: The interplay between diffusion and active transport

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers toward the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady-state solutions.Key words: filopodia, active transport, molecular motors, stochastic process, mean-field theory     

The physics of filopodial protrusion

Filopodium, a spike-like actin protrusion at the leading edge of migrating cells, functions as a sensor of the local environment and has a mechanical role in protrusion. We use modeling to examine mechanics and spatial-temporal dynamics of filopodia. We find that >10 actin filaments have to be bundled to overcome the membrane resistance and that the filopodial length is limited by buckling for 10-30 filaments and by G-actin diffusion for >30 filaments. There is an optimal number of bundled filaments, approximately 30, at which the filopodial length can reach a few microns. The model explains characteristic interfilopodial distance of a few microns as a balance of initiation, lateral drift, and merging of the filopodia. The theory suggests that F-actin barbed ends have to be focused and protected from capping (the capping rate has to decrease one order of magnitude) once every hundred seconds per micron of the leading edge to initiate the observed number of filopodia. The model generates testable predictions about how filopodial length, rate of growth, and interfilopodial distance should depend on the number of bundled filaments, membrane resistance, lamellipodial protrusion rate, and G-actin diffusion coefficient.     

Mechanics and dynamics of actin-driven thin membrane protrusions

Motile cells explore their surrounding milieu by extending thin dynamic protrusions, or filopodia. The growth of filopodia is driven by actin filament bundles that polymerize underneath the cell membrane. We compute the mechanical and dynamical features of the protrusion growth process by explicitly incorporating the flexible plasma membrane. We find that a critical number of filaments are needed to generate net filopodial growth. Without external influences, the filopodium can extend indefinitely up to the buckling length of the F-actin bundle. Dynamical calculations show that the protrusion speed is enhanced by the thermal fluctuations of the membrane; a filament bundle encased in a flexible membrane grows much faster. The protrusion speed depends directly on the number and spatial arrangement of the filaments in the bundle and whether the filaments are tethered to the membrane. Filopodia also attract each other through distortions of the membrane. Spatially close filopodia will merge to form a larger one. Force-velocity relationships mimicking micromanipulation experiments testing our predictions are computed.     

The Diaphanous-related formin dDia2 is required for the formation and maintenance of filopodia

Formins have important roles in the nucleation of actin and the formation of linear actin filaments, but their role in filopodium formation has remained elusive. Dictyostelium discoideum Diaphanous-related formin dDia2 is enriched at the tips of filopodia and interacts with profilin II and Rac1. An FH1FH2 fragment of dDia2 nucleated actin polymerization and removed capping protein from capped filament ends. Genetic studies showed that dDia2 is important for cell migration as well as the formation, elongation and maintenance of filopodia. Here we provide evidence that dDia2 specifically controls filopodial dynamics by regulating actin turnover at the barbed ends of actin filaments.     

Structure and mobility of actin filaments as measured by quasielastic light scattering, viscometry, and electron microscopy

Actin filaments of different lengths were prepared by polymerizing actin in the presence of various concentrations of gelsolin, a protein which accelerates actin polymerization by stabilizing nuclei from which filaments grow and which binds to their fast growing ends. The lengths of the actin filaments following polymerization were measured by electron microscopy and showed that the number-average filament length agreed with the predicted length if each gelsolin molecule acted as a seed for the growth of an actin filament. The distribution of lengths was independent of the actin:gelsolin ratio and was similar to that of actin filaments polymerized in the absence of gelsolin (Lw/Ln = 1.8). The mobility of these filaments in solution was studied by quasielastic light scattering and by viscometry. The translational diffusion constant determined by quasielastic light scattering was in agreement with the infinite dilution values calculated from the dimensions and the distribution of lengths determined by electron microscopy for relatively short filament lengths. Under conditions where overlap of the rotational domains of the filaments would be expected to occur, the measured diffusion rates deviated from their predicted dilute solution values and the solution viscosity increased abruptly. The dependence of the diffusion constant and the solution viscosity on the length of the actin filaments can be explained in terms of a theory that describes the restraints on diffusion of independent rigid rods in semi-dilute solution. The results suggest that the rheology of actin filaments can be accounted for by steric restraints. The length of cytoplasmic actin filaments in some cell types is such that these steric constraints are significant and could produce large changes in physical properties with small changes in filament length.     

Nucleated polymerization of actin from the membrane-associated ends of microvillar filaments in the intestinal brush border

We examined the nucleated polymerization of actin from the two ends of filaments that comprise the microvillus (MV) core in intestinal epithelial cells by electron microscopy. Three different in vitro preparations were used to nucleate the polymerization of muscle G- actin: (a) MV core fragments containing "barbed" and "pointed" filament ends exposed by shear during isolation, (b) isolated, membrane-intact brush borders, and (c) brush borders demembranated with Triton-X 100. It has been demonstrated that MV core fragments nucleate filament growth from both ends with a strong bias for one end. Here we identify the barbed end of the core fragment as the fast growing end by decoration with myosin subfragment one. Both cytochalasin B (CB) and Acanthamoeba capping protein block filament growth from the barbed but not the pointed end of MV core fragments. To examine actin assembly from the naturally occurring, membrane-associated ends of MV core filaments, isolated membrane-intact brush borders were used to nucleate the polymerization of G-actin. Addition of salt (75 mM KCl, 1 mM MgSO4) to brush borders preincubated briefly at low ionic strength with G- actin induced the formation of 0.2-0.4 micron "growth zones" at the tips of microvilli. The dense plaque at the tip of the MV core remains associated with the membrane and the presumed growing ends of the filaments. We also observed filament growth from the pointed ends of core filaments in the terminal web. We did not observe filament growth at the membrane-associated ends of core filaments when the latter were in the presence of 2 microM CB or if the low ionic strength incubation step was omitted. Addition of G-actin to demembranated brush borders, which retain the dense plaque on their MV tips, resulted in filament growth from both ends of the MV core. Again, 2 microM CB blocked filament growth from only the barbed (tip) end of the core. The dense plaque remained associated with the tip-end of the core in the presence of CB but usually was dislodged in control preparations where nucleated polymerization from the tip-end of the core occurred. Our results support the notion that microvillar assembly and changes in microvillar length could occur by actin monomer addition/loss at the barbed, membrane-associated ends of MV core filaments.     

A theoretical analysis of filament length fluctuations in actin and other polymers

Control of the structure and dynamics of the actin cytoskeleton is essential for cell motility and for maintaining the structural integrity of cells. Central to understanding the control of these features is an understanding of the dynamics of actin filaments, first as isolated filaments, then as integrated networks, and finally as networks containing higher-order structures such as bundles, stress fibers and acto-myosin complexes. It is known experimentally that single filaments can exhibit large fluctuations, but a detailed understanding of the transient dynamics involved is still lacking. Here we first study stochastic models of a general system involving two-monomer types that can be analyzed completely, and then we report stochastic simulations on the complete actin model with three monomer types. We systematically examine the transient behavior of filament length dynamics so as to gain a better understanding of the time scales involved in reaching a steady state. We predict the lifetime of a cap of one monomer type and obtain the mean and variance of the survival time of a cap at the filament end, which together determine the filament length fluctuations.     

The regulation of actin polymerization and cross-linking in Dictyostelium

It is clear that the polymerization and organization of actin filament networks plays a critical role in numerous cellular processes. Inhibition of actin polymerization by pharmacological agents will completely prevent chemotactic motility, macropinocytosis, endocytosis, and phagocytosis. Recently there has been great progress in understanding the mechanisms that control the assembly and structure of the actin cytoskeleton. Members of the Rho family of GTPases have been identified as major players in the signal transduction pathway leading from a cell surface signal to actin polymerization. The Arp2/3 complex has been added to the list of means by which new actin filaments can be nucleated. However, it is clear that actin polymerization by Arp2/3 complex is not the whole story. In principle, the final structures formed by actin filaments will depend on factors such as: the length of actin filaments, the degree of branching, how they are cross-linked and the tensions imparted on them. In addition, the means by which actin polymerization generates protrusion of membranes is still controversial. A phagosome, filopodium and a lamellipodium all require polymerization of new actin filaments, but each has a characteristic morphology and cytoskeletal structure. In the following chapter, we will discuss actin polymerization and filament organization, especially as it relates to the machinery of phagocytosis in Dictyostelium.     

Capping Protein Terminates but Does Not Initiate Chemoattractant-induced Actin Assembly in Dictyostelium

The first step in the directed movement of cells toward a chemotactic source involves the extension of pseudopods initiated by the focal nucleation and polymerization of actin at the leading edge of the cell. We have previously isolated a chemoattractant-regulated barbed-end capping activity from Dictyostelium that is uniquely associated with capping protein, also known as cap32/34. Although uncapping of barbed ends by capping protein has been proposed as a mechanism for the generation of free barbed ends after stimulation, in vitro and in situ analysis of the association of capping protein with the actin cytoskeleton after stimulation reveals that capping protein enters, but does not exit, the cytoskeleton during the initiation of actin polymerization. Increased association of capping protein with regions of the cell containing free barbed ends as visualized by exogenous rhodamine-labeled G-actin is also observed after stimulation. An approximate threefold increase in the number of filaments with free barbed ends is accompanied by increases in absolute filament number, whereas the average filament length remains constant. Therefore, a mechanism in which preexisting filaments are uncapped by capping protein, in response to stimulation leading to the generation of free barbed ends and filament elongation, is not supported. A model for actin assembly after stimulation, whereby free barbed ends are generated by either filament severing or de novo nucleation is proposed. In this model, exposure of free barbed ends results in actin assembly, followed by entry of free capping protein into the actin cytoskeleton, which acts to terminate, not initiate, the actin polymerization transient.     

Conformational dynamics of loop 262-274 in G- and F-actin

According to the original Holmes model of F-actin structure, the hydrophobic loop 262-274 stabilizes the actin filament by inserting into a pocket formed at the interface between two protomers on the opposing strand. Using a yeast actin triple mutant, L180C/L269C/C374A [(LC)(2)CA], we showed previously that locking the hydrophobic loop to the G-actin surface by a disulfide bridge prevents filament formation. We report here that the hydrophobic loop is mobile in F- as well as in G-actin, fluctuating between the extended and parked conformations. Copper-catalyzed, brief air oxidation of (LC)(2)CA F-actin on electron microscopy grids resulted in the severing of thin filaments and their conversion to amorphous aggregates. Disulfide, bis(methanethiosulfonate) (MTS), and dibromobimane (DBB) cross-linking reactions proceeded in solution at a faster rate with G- than with F-actin. Cross-linking of C180 to C269 by DBB (4.4 A) in either G- or F-actin resulted in shorter and less stable filaments. The cross-linking with a longer MTS-6 reagent (9.6 A) did not impair actin polymerization or filament structure. Myosin subfragment 1 (S1) and tropomyosin inhibited the disulfide cross-linking of phalloidin-stabilized F-actin. Electron paramagnetic resonance measurements with nitroxide spin-labeled actin revealed strong spin-spin coupling and a similar mean interspin distance ( approximately 10 A) in G- and in F-actin, with a broader distance distribution in G-actin. These results show loop 262-274 fluctuations in G- and F-actin and correlate loop dynamics with actin filament formation and stability.     

Stochastic severing of actin filaments by actin depolymerizing factor/cofilin controls the emergence of a steady dynamical regime

Actin dynamics (i.e., polymerization/depolymerization) powers a large number of cellular processes. However, a great deal remains to be learned to explain the rapid actin filament turnover observed in vivo. Here, we developed a minimal kinetic model that describes key details of actin filament dynamics in the presence of actin depolymerizing factor (ADF)/cofilin. We limited the molecular mechanism to 1), the spontaneous growth of filaments by polymerization of actin monomers, 2), the ageing of actin subunits in filaments, 3), the cooperative binding of ADF/cofilin to actin filament subunits, and 4), filament severing by ADF/cofilin. First, from numerical simulations and mathematical analysis, we found that the average filament length, 〈L〉, is controlled by the concentration of actin monomers (power law: 5/6) and ADF/cofilin (power law: −2/3). We also showed that the average subunit residence time inside the filament, 〈T〉, depends on the actin monomer (power law: −1/6) and ADF/cofilin (power law: −2/3) concentrations. In addition, filament length fluctuations are ∼20% of the average filament length. Moreover, ADF/cofilin fragmentation while modulating filament length keeps filaments in a high molar ratio of ATP- or ADP-P_i versus ADP-bound subunits. This latter property has a protective effect against a too high severing activity of ADF/cofilin. We propose that the activity of ADF/cofilin in vivo is under the control of an affinity gradient that builds up dynamically along growing actin filaments. Our analysis shows that ADF/cofilin regulation maintains actin filaments in a highly dynamical state compatible with the cytoskeleton dynamics observed in vivo.     

The role of actin turnover in retrograde actin network flow in neuronal growth cones

The balance of actin filament polymerization and depolymerization maintains a steady state network treadmill in neuronal growth cones essential for motility and guidance. Here we have investigated the connection between depolymerization and treadmilling dynamics. We show that polymerization-competent barbed ends are concentrated at the leading edge and depolymerization is distributed throughout the peripheral domain. We found a high-to-low G-actin gradient between peripheral and central domains. Inhibiting turnover with jasplakinolide collapsed this gradient and lowered leading edge barbed end density. Ultrastructural analysis showed dramatic reduction of leading edge actin filament density and filament accumulation in central regions. Live cell imaging revealed that the leading edge retracted even as retrograde actin flow rate decreased exponentially. Inhibition of myosin II activity before jasplakinolide treatment lowered baseline retrograde flow rates and prevented leading edge retraction. Myosin II activity preferentially affected filopodial bundle disassembly distinct from the global effects of jasplakinolide on network turnover. We propose that growth cone retraction following turnover inhibition resulted from the persistence of myosin II contractility even as leading edge assembly rates decreased. The buildup of actin filaments in central regions combined with monomer depletion and reduced polymerization from barbed ends suggests a mechanism for the observed exponential decay in actin retrograde flow. Our results show that growth cone motility is critically dependent on continuous disassembly of the peripheral actin network.     

Investigation of the actin-deoxyribonuclease I interaction using a pyrene-conjugated actin derivative

The interaction of deoxyribonuclease I with muscle actin was studied with the aid of a pyrenyl derivative of the actin [Kouyama, T., & Mihashi, K. (1981) Eur. J. Biochem. 114, 33-38] that increases its quantum yield by an order of magnitude on polymerization. It is shown that this derivative copolymerizes with unlabeled G-actin in a random manner and will also bind to deoxyribonuclease with inhibition of enzymic activity. The derivative affords a highly sensitive means of following nucleated polymerization. Preincubation of F-actin with deoxyribonuclease at a concentration of 5% or less of that of total subunits causes inhibition of polymerization of additional G-actin onto the filaments. In red cell membranes that contain stabilized short filaments of actin such that the concentration of filament ends is large relative to monomers, complete inhibition of nucleated polymerization of G-actin is achieved by preincubation with deoxyribonuclease. The results indicate that binding of DNase occurs at the "plus" ends of the actin filaments. Competition with cytochalasin E, which is known to have a high affinity for the plus or preferentially growing ends of F-actin, can be observed. Whereas the activity of deoxyribonuclease in the 1:1 complex with G-actin is inhibited, the enzyme attached to the ends of filaments appears to be fully active. This causes a reduction in the inhibition of enzymic activity with increasing F-actin concentration, presumably by reason of a change in the partition of the enzyme between monomers and filament ends. The degree of inhibition increases with time, however, as the actin depolymerizes. Implications for measurements of actin monomer concentrations by the deoxyribonuclease assay procedure are considered.     

A stochastic analysis of actin polymerization in the presence of twinfilin and gelsolin

We develop an efficient stochastic simulation algorithm for analyzing actin filament growth and decay in the presence of various actin-binding proteins. The evolution of nucleotide profiles of filaments can be tracked and the resulting feedback to actin-binding proteins is incorporated. The computational efficiency of the new method enables us to focus on experimentally realistic problems, and as one example we use it to analyze the experimental data of Helfer et al. [(2006). Mammalian twinfilin sequesters ADP-G-actin and caps filament barbed ends: implications in motility. EMBO J. 25, 1184-1195] on the capping and G-actin sequestering activity of twinfilin. We show that the binding specificity of twinfilin for ADP-G-actin is crucial for the observed biphasic evolution of the filament length distribution in the presence of twinfilin, and we demonstrate that twinfilin can be an essential part of the molecular machinery for regulating filament lengths after a short burst of polymerization. Significantly, our simulations indicate that the pyrenyl-actin fluorescence experiments would fail to report the emergence of large filaments under certain experimental conditions.     

A continuum model of protrusion of pseudopod in leukocytes.

The morphology of human leukocytes, the biochemistry of actin polymerization, and the theory of continuum mechanics are used to model the pseudopod protrusion process of leukocytes. In the proposed model, the pseudopod is considered as a porous solid of F-actin network, the pores of which are full of aqueous solution. G-actin is considered as a "solute" transported by convection and diffusion in the fluid phase. The pseudopod grows as actin filaments elongate at their barbed ends at the tip of the pseudopod. The driving force of extension is hypothesized as being provided by the actin polymerization. It is assumed that elongation of actin filaments, powered by chemical energy liberated from the polymerization reaction, does mechanical work against opposing pressure on the membrane. This also gives rise to a pressure drop in the fluid phase at the tip of the pseudopod, which is formulated by an equation relating the work done by actin polymerization to the local state of pressure. The pressure gradient along the pseudopod drives the fluid filtration through the porous pseudopod according to Darcy's Law, which in turn brings more actin monomers to the growing tip. The main cell body serves as a reservoir of G-actin. A modified first-order equation is used to describe the kinetics of polymerization. The rate of pseudopod growth is modulated by regulatory proteins. A one-dimensional moving boundary problem based on the proposed mechanism has been constructed and approximate solutions have been obtained. Comparison of the solutions with experimental data shows that the model is compatible with available observations. The model is also applicable to growth of other cellular systems such as elongation of acrosomal process in sperm cells.     

ATP hydrolysis stimulates large length fluctuations in single actin filaments

Polymerization dynamics of single actin filaments is investigated theoretically using a stochastic model that takes into account the hydrolysis of ATP-actin subunits, the geometry of actin filament tips, and the lateral interactions between the monomers as well as the processes at both ends of the polymer. Exact analytical expressions are obtained for the mean growth velocity, for the dispersion in the length fluctuations, and the nucleotide composition of the actin filaments. It is found that the ATP hydrolysis has a strong effect on dynamic properties of single actin filaments. At high concentrations of free actin monomers, the mean size of the unhydrolyzed ATP-cap is very large, and the dynamics is governed by association/dissociation of ATP-actin subunits. However, at low concentrations the size of the cap becomes finite, and the dissociation of ADP-actin subunits makes a significant contribution to overall dynamics. Actin filament length fluctuations reach a sharp maximum at the boundary between two dynamic regimes, and this boundary is always larger than the critical concentration for the actin filament's growth at the barbed end, assuming the sequential release of phosphate. Random and sequential mechanisms of hydrolysis are compared, and it is found that they predict qualitatively similar dynamic properties at low and high concentrations of free actin monomers with some deviations near the critical concentration. The possibility of attachment and detachment of oligomers in actin filament's growth is also discussed. Our theoretical approach is successfully applied to analyze the latest experiments on the growth and length fluctuations of individual actin filaments.     

A Combination of Diffusion and Active Translocation Localizes Myosin 10 to the Filopodial Tip

Myosin 10 is an actin-based molecular motor that localizes to the tips of filopodia in mammalian cells. To understand how it is targeted to this distinct region of the cell, we have used total internal reflection fluorescence microscopy to study the movement of individual full-length and truncated GFP-tagged molecules. Truncation mutants lacking the motor region failed to localize to filopodial tips but still bound transiently at the plasma membrane. Deletion of the single α-helical and anti-parallel coiled-coil forming regions, which lie between the motor and pleckstrin homology domains, reduced the instantaneous velocity of intrafilopodial movement but did not affect the number of substrate adherent filopodia. Deletion of the anti-parallel coiled-coil forming region, but not the EKR-rich region of the single α-helical domain, restored intrafilopodial trafficking, suggesting this region is important in determining myosin 10 motility. We propose a model by which myosin 10 rapidly targets to the filopodial tip via a sequential reduction in dimensionality. Molecules first undergo rapid diffusion within the three-dimensional volume of the cell body. They then exhibit periods of slower two-dimensional diffusion in the plane of the plasma membrane. Finally, they move in a unidimensional, highly directed manner along the polarized actin filament bundle within the filopodium becoming confined to a single point at the tip. Here we have observed directly each phase of the trafficking process using single molecule fluorescence imaging of live cells and have quantified our observations using single particle tracking, autocorrelation analysis, and kymographs.     

A Highlights from MBoC Selection: Cell type–dependent mechanisms for formin-mediated assembly of filopodia

Filopodia are finger-like protrusions from the plasma membrane and are of fundamental importance to cellular physiology, but the mechanisms governing their assembly are still in question. One model, called convergent elongation, proposes that filopodia arise from Arp2/3 complex–nucleated dendritic actin networks, with factors such as formins elongating these filaments into filopodia. We test this model using constitutively active constructs of two formins, FMNL3 and mDia2. Surprisingly, filopodial assembly requirements differ between suspension and adherent cells. In suspension cells, Arp2/3 complex is required for filopodial assembly through either formin. In contrast, a subset of filopodia remains after Arp2/3 complex inhibition in adherent cells. In adherent cells only, mDia1 and VASP also contribute to filopodial assembly, and filopodia are disproportionately associated with focal adhesions. We propose an extension of the existing models for filopodial assembly in which any cluster of actin filament barbed ends in proximity to the plasma membrane, either Arp2/3 complex dependent or independent, can initiate filopodial assembly by specific formins.     

Mechanism of filopodia initiation by reorganization of a dendritic network

Afilopodium protrudes by elongation of bundled actin filaments in its core. However, the mechanism of filopodia initiation remains unknown. Using live-cell imaging with GFP-tagged proteins and correlative electron microscopy, we performed a kinetic-structural analysis of filopodial initiation in B16F1 melanoma cells. Filopodial bundles arose not by a specific nucleation event, but by reorganization of the lamellipodial dendritic network analogous to fusion of established filopodia but occurring at the level of individual filaments. Subsets of independently nucleated lamellipodial filaments elongated and gradually associated with each other at their barbed ends, leading to formation of cone-shaped structures that we term Lambda-precursors. An early marker of initiation was the gradual coalescence of GFP-vasodilator-stimulated phosphoprotein (GFP-VASP) fluorescence at the leading edge into discrete foci. The GFP-VASP foci were associated with Lambda-precursors, whereas Arp2/3 was not. Subsequent recruitment of fascin to the clustered barbed ends of Lambda-precursors initiated filament bundling and completed formation of the nascent filopodium. We propose a convergent elongation model of filopodia initiation, stipulating that filaments within the lamellipodial dendritic network acquire privileged status by binding a set of molecules (including VASP) to their barbed ends, which protect them from capping and mediate association of barbed ends with each other.