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.     

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.     

Single-molecule imaging of IQGAP1 regulating actin filament dynamics

IQGAP is a conserved family of actin-binding proteins with essential roles in cell motility, cytokinesis, and cell adhesion, yet there remains a limited understanding of how IQGAP proteins directly influence actin filament dynamics. To close this gap, we used single-molecule and single-filament total internal reflection fluorescence microscopy to observe IQGAP regulating actin dynamics in real time. To our knowledge, this is the first study to do so. Our results demonstrate that full-length human IQGAP1 forms dimers that stably bind to actin filament sides and transiently cap barbed ends. These interactions organize filaments into thin bundles, suppress barbed end growth, and inhibit filament disassembly. Surprisingly, each activity depends on distinct combinations of IQGAP1 domains and/or dimerization, suggesting that different mechanisms underlie each functional effect on actin. These observations have important implications for how IQGAP functions as an actin regulator in vivo and how it may be regulated in different biological settings.     

Arabidopsis actin depolymerizing factor4 modulates the stochastic dynamic behavior of actin filaments in the cortical array of epidermal cells

Actin filament arrays are constantly remodeled as the needs of cells change as well as during responses to biotic and abiotic stimuli. Previous studies demonstrate that many single actin filaments in the cortical array of living Arabidopsis thaliana epidermal cells undergo stochastic dynamics, a combination of rapid growth balanced by disassembly from prolific severing activity. Filament turnover and dynamics are well understood from in vitro biochemical analyses and simple reconstituted systems. However, the identification in living cells of the molecular players involved in controlling actin dynamics awaits the use of model systems, especially ones where the power of genetics can be combined with imaging of individual actin filaments at high spatial and temporal resolution. Here, we test the hypothesis that actin depolymerizing factor (ADF)/cofilin contributes to stochastic filament severing and facilitates actin turnover. A knockout mutant for Arabidopsis ADF4 has longer hypocotyls and epidermal cells when compared with wild-type seedlings. This correlates with a change in actin filament architecture; cytoskeletal arrays in adf4 cells are significantly more bundled and less dense than in wild-type cells. Several parameters of single actin filament turnover are also altered. Notably, adf4 mutant cells have a 2.5-fold reduced severing frequency as well as significantly increased actin filament lengths and lifetimes. Thus, we provide evidence that ADF4 contributes to the stochastic dynamic turnover of actin filaments in plant cells.     

Cofilin tunes the nucleotide state of actin filaments and severs at bare and decorated segment boundaries

Actin-based motility demands the spatial and temporal coordination of numerous regulatory actin-binding proteins (ABPs), many of which bind with affinities that depend on the nucleotide state of actin filament. Cofilin, one of three ABPs that precisely choreograph actin assembly and organization into comet tails that drive motility in vitro, binds and stochastically severs aged ADP actin filament segments of de novo growing actin filaments. Deficiencies in methodologies to track in real time the nucleotide state of actin filaments, as well as cofilin severing, limit the molecular understanding of coupling between actin filament chemical and mechanical states and severing. We engineered a fluorescently labeled cofilin that retains actin filament binding and severing activities. Because cofilin binding depends strongly on the actin-bound nucleotide, direct visualization of fluorescent cofilin binding serves as a marker of the actin filament nucleotide state during assembly. Bound cofilin allosterically accelerates P(i) release from unoccupied filament subunits, which shortens the filament ATP/ADP-P(i) cap length by nearly an order of magnitude. Real-time visualization of filament severing indicates that fragmentation scales with and occurs preferentially at boundaries between bare and cofilin-decorated filament segments, thereby controlling the overall filament length, depending on cofilin binding density.     

Nonequilibrium Self-Assembly of a Filament Coupled to ATP/GTP Hydrolysis

We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: two phases of unbounded growth: a rapidly growing phase and an intermediate phase, and one bounded growth phase. We analyze all these phases, with an emphasis on the bounded growth phase. We also discuss how hydrolysis affects force-velocity curves. The bounded growth phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero (i.e., to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations.     

Annealing accounts for the length of actin filaments formed by spontaneous polymerization

We measured the lengths of actin filaments formed by spontaneous polymerization of highly purified actin monomers by fluorescence microscopy after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of approximately 7 microm (2600 subunits). This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: 1) filaments formed from a wide range of highly purified actin monomer concentrations, and 2) filaments formed from 24 microM actin over a range of CapZ concentrations.     

Quantitative analysis of extension-torsion coupling of actin filaments

Actin filaments have a double-helix structure consisting of globular actin molecules. In many mechanical cellular activities, such as cell movement, division, and shape control, modulation of the extensional and torsional dynamics of the filament has been linked to regulatory actin-binding protein functions. Therefore, it is important to quantitatively evaluate extension-torsion coupling of filament to better understand the actin filament dynamics. In the present study, the extension-torsion coupling was investigated using molecular dynamics simulations. We constructed a model for the actin filament consisting of 14 actin subunits in an ionic solvent as a minimal functional unit, and analyzed longitudinal and twisting Brownian motions of the filament. We then derived the expected value of energy associated with extension and torsion at equilibrium, and evaluated the extension-torsion stiffness of the filament from the thermal fluctuations obtained from the MD simulations. The results demonstrated that as the analyzed sampling-window duration was increased, the extension-torsion coupling stiffness evaluated on a nanosecond scale tended to converge to a value of 7.6×10(-11) N. The results obtained from this study will contribute to the understanding of biomechanical events, under mechanical tension and torque, involving extension-torsion coupling of filaments.     

From solution to surface to filament: actin flux into branched networks

The actin cytoskeleton comprises a set of filament networks that perform essential functions in eukaryotic cells. The idea that actin filaments incorporate monomers directly from solution forms both the “textbook picture” of filament elongation and a conventional starting point for quantitative modeling of cellular actin dynamics. Recent work, however, reveals that filaments created by two major regulators, the formins and the Arp2/3 complex, incorporate monomers delivered by nearby proteins. Specifically, actin enters Arp2/3-generated networks via binding sites on nucleation-promoting factors clustered on membrane surfaces. Here, we describe three functions of this surface-associated actin monomer pool: (1) regulating network density via product inhibition of the Arp2/3 complex, (2) accelerating filament elongation as a distributive polymerase, and (3) converting profilin-actin into a substrate for the Arp2/3 complex. These linked functions control the architecture of branched networks and explain how capping protein enhances their growth.     

Thin filaments elongate from their pointed ends during myofibril assembly in Drosophila indirect flight muscle.

Tropomodulin (Tmod) is an actin pointed-end capping protein that regulates actin dynamics at thin filament pointed ends in striated muscle. Although pointed-end capping by Tmod controls thin filament lengths in assembled myofibrils, its role in length specification during de novo myofibril assembly is not established. We used the Drosophila Tmod homologue, sanpodo (spdo), to investigate Tmod's function during muscle development in the indirect flight muscle. SPDO was associated with the pointed ends of elongating thin filaments throughout myofibril assembly. Transient overexpression of SPDO during myofibril assembly irreversibly arrested elongation of preexisting thin filaments. However, the lengths of thin filaments assembled after SPDO levels had declined were normal. Flies with a preponderance of abnormally short thin filaments were unable to fly. We conclude that: (a) thin filaments elongate from their pointed ends during myofibril assembly; (b) pointed ends are dynamically capped at endogenous levels of SPDO so as to allow elongation; (c) a transient increase in SPDO levels during myofibril assembly converts SPDO from a dynamic to a permanent cap; and (d) developmental regulation of pointed-end capping during myofibril assembly is crucial for specification of final thin filament lengths, myofibril structure, and muscle function.     

Actin filament severing by cofilin

Cofilin is essential for cell viability and for actin-based motility. Cofilin severs actin filaments, which enhances the dynamics of filament assembly. We investigated the mechanism of filament severing by cofilin with direct fluorescence microscopy observation of single actin filaments in real time. In cells, actin filaments are likely to be attached at multiple points along their length, and we found that attaching filaments in such a manner greatly increased the efficiency of filament severing by cofilin. Cofilin severing increased and then decreased with increasing concentration of cofilin. Together, these results indicate that cofilin severs the actin filament by a mechanism of allosteric and cooperative destabilization. Severing is more efficient when relaxation of this cofilin-induced instability of the actin filament is inhibited by restricting the flexibility of the filament. These conclusions have particular relevance to cofilin function during actin-based motility in cells and in synthetic systems.     

Computational Analysis of Viscoelastic Properties of Crosslinked Actin Networks

Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks. Two methods were employed, bulk rheology and segment-tracking rheology, where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. It was demonstrated that the storage shear modulus (G′) increases more by the addition of ACPs that form orthogonal crosslinks than by those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G′ as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a ‘supportive framework,’ as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain.     

Actin filament dynamics in the actomyosin VI complex is regulated allosterically by calcium-calmodulin light chain

The contractile and enzymatic activities of myosin VI are regulated by calcium binding to associated calmodulin (CaM) light chains. We have used transient phosphorescence anisotropy to monitor the microsecond rotational dynamics of erythrosin-iodoacetamide-labeled actin with strongly bound myosin VI (MVI) and to evaluate the effect of MVI-bound CaM light chain on actin filament dynamics. MVI binding lowers the amplitude but accelerates actin filament microsecond dynamics in a Ca²⁺- and CaM-dependent manner, as indicated from an increase in the final anisotropy and a decrease in the correlation time of transient phosphorescence anisotropy decays. MVI with bound apo-CaM or Ca²⁺-CaM weakly affects actin filament microsecond dynamics, relative to other myosins (e.g., muscle myosin II and myosin Va). CaM dissociation from bound MVI damps filament rotational dynamics (i.e., increases the torsional rigidity), such that the perturbation is comparable to that induced by other characterized myosins. Analysis of individual actin filament shape fluctuations imaged by fluorescence microscopy reveals a correlated effect on filament bending mechanics. These data support a model in which Ca²⁺-dependent CaM binding to the IQ domain of MVI is linked to an allosteric reorganization of the actin binding site(s), which alters the structural dynamics and the mechanical rigidity of actin filaments. Such modulation of filament dynamics may contribute to the Ca²⁺- and CaM-dependent regulation of myosin VI motility and ATP utilization.     

Kinetic analysis of F-actin depolymerization in polymorphonuclear leukocyte lysates indicates that chemoattractant stimulation increases actin filament number without altering the filament length distribution

The rate of filamentous actin (F-actin) depolymerization is proportional to the number of filaments depolarizing and changes in the rate are proportional to changes in filament number. To determine the number and length of actin filaments in polymorphonuclear leukocytes and the change in filament number and length that occurs during the increase in F-actin upon chemoattractant stimulation, the time course of cellular F-actin depolymerization in lysates of control and peptide-stimulated cells was examined. F-actin was quantified by the TRITC-labeled phalloidin staining of pelletable actin. Lysis in 1.2 M KCl and 10 microM DNase I minimized the effects of F-actin binding proteins and G-actin, respectively, on the kinetics of depolymerization. To determine filament number and length from a depolymerization time course, depolymerization kinetics must be limited by the actin monomer dissociation rate. Comparison of time courses of depolymerization in the presence (pointed ends free) or absence (barbed and pointed ends free) of cytochalasin suggested depolymerization occurred from both ends of the filament and that monomer dissociation was rate limiting. Control cells had 1.7 +/- 0.4 x 10(5) filaments with an average length of 0.29 +/- 0.09 microns. Chemo-attractant stimulation for 90 s at room temperature with 0.02 microM N-formylnorleucylleucylphenylalanine caused a twofold increase in F-actin and about a two-fold increase in the total number of actin filaments to 4.0 +/- 0.5 x 10(5) filaments with an average length of 0.27 +/- 0.07 microns. In both cases, most (approximately 80%) of the filaments were quite short (less than or equal to 0.18 micron). The length distributions of actin filaments in stimulated and control cells were similar.     

Interplay between Brownian motion and cross-linking controls bundling dynamics in actin networks

Morphology changes in cross-linked actin networks are important in cell motility, division, and cargo transport. Here, we study the transition from a weakly cross-linked network of actin filaments to a heavily cross-linked network of actin bundles through microscopic Brownian dynamics simulations. We show that this transition occurs in two stages: first, a composite bundle network of small and highly aligned bundles evolves from cross-linking of individual filaments and, second, small bundles coalesce into the clustered bundle state. We demonstrate that Brownian motion speeds up the first stage of this process at a faster rate than the second. We quantify the time to reach the composite bundle state and show that it strongly increases as the mesh size increases only when the concentration of cross-links is small and that it remains roughly constant if we decrease the relative ratio of cross-linkers as we increase the actin concentration. Finally, we examine the dependence of the bundling timescale on filament length, finding that shorter filaments bundle faster because they diffuse faster.     

High microfilament concentration results in barbed-end ADP caps.

Current theory and experiments describing actin polymerization suggest that site-specific cleavage of bound nucleotide following F-actin filament formation causes the barbed ends of microfilaments to be capped first with ATP subunits, then with ADP bound to inorganic phosphate (ADP.Pi) at steady-state. The barbed ends of depolymerizing filaments consist of ADP subunits. The decrease in stability of the barbed-end cap accompanying the transition from ADP.Pi to ADP allows nucleotide hydrolysis and subsequent loss of Pi to regulate F-actin filament dynamics. We describe a novel computational model of nucleotide capping that simulates both the spatial and temporal properties of actin polymerization. This model has been used to test the effects of high filament concentration on the behavior of the ATP hydrolysis cycle observed during polymerization. The model predicts that under conditions of high microfilament concentration an ADP cap can appear during steady-state at the barbed ends of filaments. We show that the presence of the cap can be accounted for by a kinetic model and predict the relationship between the nucleotide concentration ratio [ATP]/[ADP], the F-actin filament concentration, and the steady-state distribution of barbed-end ADP cap lengths. The possible consequences of this previously unreported phenomenon as a regulator of cytoskeletal behavior are discussed.     

The organization and regulation of the macrophage actin skeleton

To move, leukocytes extend portions of their cortical cytoplasm as pseudopods. These pseudopods are filled with a three-dimensional actin filament skeleton, the reversible assembly of which in response to receptor stimulation is thought to play a major role in providing the mechanical force for these protrusive movements. The organization of this actin skeleton occurs at different levels within the cell, and a number of macrophage proteins have been isolated and shown to affect the architecture, assembly, stability, and length of actin filaments in vitro. The architecture of cytoplasmic actin is regulated by proteins that cross-link filaments in higher-order structures. Actin-binding protein plays a major role in defining network structure by cross-linking actin filaments into orthogonal networks. Gelsolin may have a central role in regulating network structure. It binds to the sides of actin filaments and severs them, and binds the "barbed" filament end, thereby blocking monomer addition at this end. Gelsolin is activated to bind actin filaments by microM calcium. Dissociation of gelsolin bound on filament ends occurs in the presence of the polyphosphoinositides, PIP and PIP2. Calcium and PIP2 have been shown to be intracellular messengers of cell stimulation.     

Organization and dynamics of cross-linked actin filaments in confined environments

The organization of the actin cytoskeleton is impacted by the interplay between physical confinement, features of cross-linking proteins, and deformations of semiflexible actin filaments. Some cross-linking proteins preferentially bind filaments in parallel, although others bind more indiscriminately. However, a quantitative understanding of how the mode of binding influences the assembly of actin networks in confined environments is lacking. Here we employ coarse-grained computer simulations to study the dynamics and organization of semiflexible actin filaments in confined regions upon the addition of cross-linkers. We characterize how the emergent behavior is influenced by the system shape, the number and type of cross-linking proteins, and the length of filaments. Structures include isolated clusters of filaments, highly connected filament bundles, and networks of interconnected bundles and loops. Elongation of one dimension of the system promotes the formation of long bundles that align with the elongated axis. Dynamics are governed by rapid cross-linking into aggregates, followed by a slower change in their shape and connectivity. Cross-linking decreases the average bending energy of short or sparsely connected filaments by suppressing shape fluctuations. However, it increases the average bending energy in highly connected networks because filament bundles become deformed, and small numbers of filaments exhibit long-lived, highly unfavorable configurations. Indiscriminate cross-linking promotes the formation of high-energy configurations due to the increased likelihood of unfavorable, difficult-to-relax configurations at early times. Taken together, this work demonstrates physical mechanisms by which cross-linker binding and physical confinement impact the emergent behavior of actin networks, which is relevant both in cells and in synthetic environments.     

Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: curvature as an indicator of the torque

ATP synthase (F-ATPase) operates as an electrochemical-to-mechanical-to-chemical energy transducer with an astounding 360 degrees rotary motion of subunits epsilongammac(10-14) (rotor) against delta(alphabeta)(3)ab(2) (stator). The enzyme's torque as a function of the angular reaction coordinate in relation to ATP-synthesis/hydrolysis, internal elasticity, and external load has remained an important issue. Fluorescent actin filaments of micrometer length have been used to detect the rotation as driven by ATP hydrolysis. We evaluated the viscoelastic dynamics of actin filaments under the influence of enzyme-generated torque, stochastic Langevin force, and viscous drag. Modeling with realistic parameters revealed the dominance of the lowest normal mode. Because of its slow relaxation (approximately 100 ms), power strokes of the enzyme were expected to appear strongly damped in recordings of the angular velocity of the filament. This article describes the theoretical background for the alternative use of the filament as a spring balance. The enzyme's angular torque profile under load can be gauged by measuring the average curvature and the stochastic fluctuations of actin filaments. Pertinent experiments were analyzed in the companion paper.