Emergence and maintenance of variable-length actin filaments in a limiting pool of building blocks

Actin is one of the key structural components of the eukaryotic cytoskeleton that regulates cellular architecture and mechanical properties. Dynamic regulation of actin filament length and organization is essential for the control of many physiological processes including cell adhesion, motility and division. While previous studies have mostly focused on the mechanisms controlling the length of single actin filaments, it remains poorly understood how distinct actin filament populations in cells maintain different lengths using the same set of molecular building blocks. Here, we develop a theoretical model for the length regulation of multiple actin filaments by nucleation and growth-rate modulation by actin-binding proteins in a limiting pool of monomers. We first show that spontaneous nucleation of actin filaments naturally leads to heterogeneities in filament length distribution. We then investigate the effects of filament growth inhibition by capping proteins and growth promotion by formin proteins on filament length distribution. We find that filament length heterogeneity can be increased by growth inhibition, whereas growth promoters do not significantly affect length heterogeneity. Interestingly, a competition between filament growth inhibitors and growth promoters can give rise to bimodal filament length distribution as well as a highly heterogeneous length distribution with large statistical dispersion. We quantitatively predict how heterogeneity in actin filament length can be modulated by tuning filamentous actin nucleation and growth rates in order to create distinct filament subpopulations with different lengths.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

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.     

Cytochalasin B and the structure of actin gels

We analyzed the structure of gels formed when macrophage actin-binding protein crosslinks skeletal muscle actin polymers and the effect of the fungal metabolite cytochalasin B on this structure. Measurement of the actin filament length distribution permitted calculation of the critical concentration of crosslinker theoretically required for gelation of actin polymer networks. The experimentally determined critical concentration of actin-binding protein agreed sufficiently with the theoretical to conclude that F-actin-actin-binding protein gels are networks composed of isotropically oriented filaments crosslinked at intervals. The effects of cytochalasin B on these actin networks fits this model. Cytochalasin B (1) bound to F-actin (but not to actin-binding protein), (2) decreased the length of actin filaments without increasing the quantity of monomeric actin, (3) decreased the rigidity of actin networks both in the presence and absence of crosslinking proteins and (4) increased the critical concentration of actin-binding protein required for incipient gelation by a magnitude predicted from network theory if filaments were divided and shortened by the extents observed. The effects of cytochalasin B on gelation were highly dependent on actin concentration and were inhibited by the actin-stabilizing agent phalloidin. Therefore, cytochalasin B diminishes actin gel structure by severing actin filaments at limited sites. The demonstration of gel-sol transformations in actin networks caused by limited actin filament cleavage suggests a new mechanism for the control of cytoplasmic structure.     

Form-Finding Model Shows How Cytoskeleton Network Stiffness Is Realized

In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network’s stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein’s relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.     

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.     

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.     

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.     

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 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.     

Three-dimensional structure of actin filaments and of an actin gel made with actin-binding protein

Purified muscle actin and mixtures of actin and actin-binding protein were examined in the transmission electron microscope after fixation, critical point drying, and rotary shadowing. The three-dimensional structure of the protein assemblies was analyzed by a computer-assisted graphic analysis applicable to generalized filament networks. This analysis yielded information concerning the frequency of filament intersections, the filament length between these intersections, the angle at which filaments branch at these intersections, and the concentration of filaments within a defined volume. Purified actin at a concentration of 1 mg/ml assembled into a uniform mass of long filaments which overlap at random angles between 0 degrees and 90 degrees. Actin in the presence of macrophage actin-binding protein assembled into short, straight filaments, organized in a perpendicular branching network. The distance between branch points was inversely related to the molar ratio of actin-binding protein to actin. This distance was what would be predicted if actin filaments grew at right angles off of nucleation sites on the two ends of actin-binding protein dimers, and then annealed. The results suggest that actin in combination with actin-binding protein self-assembles to form a three- dimensional network resembling the peripheral cytoskeleton of motile cells.     

Action of cytochalasin D on cytoskeletal networks

Extraction of SC-1 cells (African green monkey kidney) with the detergent Triton X-100 in combination with stereo high-voltage electron microscopy of whole mount preparations has been used as an approach to determine the mode of action of cytochalasin D on cells. The cytoskeleton of extracted BSC-1 cells consists of substrate-associated filament bundles (stress fibers) and a highly cross-linked network of four major filament types extending throughout the cell body; 10-nm filaments, actin microfilaments, microtubules, and 2- to 3-nm filaments. Actin filaments and 2- to 3-nm filaments form numerous end- to-side contacts with other cytoskeletal filaments. Cytochalasin D treatment severely disrupts network organization, increases the number of actin filament ends, and leads to the formation of filamentous aggregates or foci composed mainly of actin filaments. Metabolic inhibitors prevent filament redistribution, foci formation, and cell arborization, but not disorganization of the three-dimensional filament network. In cells first extracted and then treated with cytochalasin D, network organization is disrupted, and the number of free filament ends is increased. Supernates of preparations treated in this way contain both short actin filaments and network fragments (i.e., actin filaments in end-to-side contact with other actin filaments). It is proposed that the dramatic effects of cytochalasin D on cells result from both a direct interaction of the drug with the actin filament component of cytoskeletal networks and a secondary cellular response. The former leads to an immediate disruption of the ordered cytoskeletal network that appears to involve breaking of actin filaments, rather than inhibition of actin filament-filament interactions (i.e., disruption of end-to-side contacts). The latter engages network fragments in an energy-dependent (contractile) event that leads to the formation of filament foci.     

Affinity of alpha-actinin for actin determines the structure and mechanical properties of actin filament gels.

Proteins that cross-link actin filaments can either form bundles of parallel filaments or isotropic networks of individual filaments. We have found that mixtures of actin filaments with alpha-actinin purified from either Acanthamoeba castellanii or chicken smooth muscle can form bundles or isotropic networks depending on their concentration. Low concentrations of alpha-actinin and actin filaments form networks indistinguishable in electron micrographs from gels of actin alone. Higher concentrations of alpha-actinin and actin filaments form bundles. The threshold for bundling depends on the affinity of the alpha-actinin for actin. The complex of Acanthamoeba alpha-actinin with actin filaments has a Kd of 4.7 microM and a bundling threshold of 0.1 microM; chicken smooth muscle has a Kd of 0.6 microM and a bundling threshold of 1 microM. The physical properties of isotropic networks of cross-linked actin filaments are very different from a gel of bundles: the network behaves like a solid because each actin filament is part of a single structure that encompasses all the filaments. Bundles of filaments behave more like a very viscous fluid because each bundle, while very long and stiff, can slip past other bundles. We have developed a computer model that predicts the bundling threshold based on four variables: the length of the actin filaments, the affinity of the alpha-actinin for actin, and the concentrations of actin and alpha-actinin.     

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.     

Effect of tensile force on the mechanical behavior of actin filaments

Actin filaments are the most abundant components of the cellular cytoskeleton, and play critical roles in various cellular functions such as migration, division and shape control. In these activities, mechanical tension causes structural changes in the double-helical structure of the actin filament, which is a key modulator of cytoskeletal reorganization. This study performed large-scale molecular dynamics (MD) and steered MD simulations to quantitatively analyze the effects of tensile force on the mechanical behavior of actin filaments. The results revealed that when a tensile force of 200pN was applied to a filament consisting of 14 actin subunits, the twist angle of the filament decreased by approximately 20°, corresponding to a rotation of approximately -2° per subunit, representing a critical structural change in actin filaments. Based on these structural changes, the variance in filament length and twist angle was found to decrease, leading to increases in extensional and torsional stiffness. Torsional stiffness increased significantly under the tensile condition, and the ratio of filament stiffness under tensile force to that under no external force increased significantly on longer temporal scales. The results obtained from this study contribute to the understanding of mechano-chemical interactions concerning actin dynamics, showing that increased tensile force in the filament prevents actin regulatory proteins from binding to the filament.     

F actin assembly modulated by villin: Ca++-dependent nucleation and capping of the barbed end

We have studied the mechanism of Ca++-dependent restriction of actin filament length by villin, one of the major actin-associated proteins of intestinal microvilli microfilament bundles. Villin acts, even at a ratio of 1 to 1000 with respect to actin, very efficiently as a Ca++-dependent nucleation factor on actin assembly. This gives rise to unidirectional assembly, with the morphologically defined "barbed" end of the resulting filament being capped. Consequently, at steady state treadmilling of actin monomers through the filament is inhibited. Increase of the villin-to-actin ratio enhances the number of nucleated filaments necessarily shorter in length. This results finally in nonsedimentable F actin and a low molecular weight complex of one villin and three monomeric actins, which itself is a potent nucleator. Thus restriction of actin assembly by villin is not due to a direct inhibition of assembly but arises as the consequence of strongly enhanced nucleation followed by unidirectional elongation at the pointed end of the nucleated filaments. In addition, in the presence of Ca++-villin, but not the villin-actin complex, seems able to "break" or "sever" preformed F actin filaments. Thus a variety of cellular phenomena-nucleation, unidirectional assembly, filament end capping, nonpolymerizable actin and F actin bundles-can be observed in vitro in a two-protein component system modulated by the concentration of free Ca++.     

Effect of filamin and controlled linear shear on the microheterogeneity of F-actin/gelsolin gels

We have previously established [Cortese and Frieden, J. Cell Biol. 107:1477-1487, 1988] that actin gels formed under shear are microheterogeneous. In this study, the effect of cross-linking (by chicken gizzard filamin), severing (by plasma gelsolin), and shear on actin microheterogeneity are investigated using fluorescence photobleaching recovery and video microscopy. We find that filamin and shear form microheterogeneous F-actin:gelsolin gels by different mechanisms. Bundling of actin:gelsolin filaments by filamin can be explained by an increase in the apparent length of the filaments due to interfilament binding, resulting in a decrease of the polymer number concentration at which filaments organize into anisotropic phases. Some intrafilament binding of filamin to actin filaments may also be present, and those filaments coated with filamin immobilize more slowly than actin under the same polymerization conditions. The length of F-actin/gelsolin filaments seems to be a major factor in controlling the extent of bundling relative to network formation. In contrast, the effect of shear on the microheterogeneity of actin:gelsolin filaments is consistent with our previous proposal that shear aligns actin filaments, allowing filament-filament interactions and phase formation to occur. Short filaments are unable to organize into branched actin networks, but they can create large aggregates under low shear. Longer actin filaments will exist as networks with variable levels of branching and are less sensitive to shear. The effect of the intensity of a shear field on the spatial distribution of actin may involve a progressively more random orientation of actin molecules and bundles. A regular pattern develops across the sample at low shear rates (0.04-1.39 s-1), and becomes very irregular at higher shear rates (greater than 10 s-1). We suggest here that actin-binding proteins and shear can control the transition between isotropic networks and anisotropic phases by their effect on apparent length and local filament concentration, and also that this transition can have substantial effects on the resistance of cells to mechanical stress.     

Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape

Microtubules are long, proteinaceous filaments that perform structural functions in eukaryotic cells by defining cellular shape and serving as tracks for intracellular motor proteins. We report the first accurate measurements of the flexural rigidity of microtubules. By analyzing the thermally driven fluctuations in their shape, we estimated the mean flexural rigidity of taxol-stabilized microtubules to be 2.2 x 10(-23) Nm2 (with 6.4% uncertainty) for seven unlabeled microtubules and 2.1 x 10(-23) Nm2 (with 4.7% uncertainty) for eight rhodamine-labeled microtubules. These values are similar to earlier, less precise estimates of microtubule bending stiffness obtained by modeling flagellar motion. A similar analysis on seven rhodamine-phalloidin- labeled actin filaments gave a flexural rigidity of 7.3 x 10(-26) Nm2 (with 6% uncertainty), consistent with previously reported results. The flexural rigidity of these microtubules corresponds to a persistence length of 5,200 microns showing that a microtubule is rigid over cellular dimensions. By contrast, the persistence length of an actin filament is only approximately 17.7 microns, perhaps explaining why actin filaments within cells are usually cross-linked into bundles. The greater flexural rigidity of a microtubule compared to an actin filament mainly derives from the former's larger cross-section. If tubulin were homogeneous and isotropic, then the microtubule's Young's modulus would be approximately 1.2 GPa, similar to Plexiglas and rigid plastics. Microtubules are expected to be almost inextensible: the compliance of cells is due primarily to filament bending or sliding between filaments rather than the stretching of the filaments themselves.     

A direct interaction between actin and vimentin filaments mediated by the tail domain of vimentin

The assembly and organization of the three major eukaryotic cytoskeleton proteins, actin, microtubules, and intermediate filaments, are highly interdependent. Through evolution, cells have developed specialized multifunctional proteins that mediate the cross-linking of these cytoskeleton filament networks. Here we test the hypothesis that two of these filamentous proteins, F-actin and vimentin filament, can interact directly, i.e. in the absence of auxiliary proteins. Through quantitative rheological studies, we find that a mixture of vimentin/actin filament network features a significantly higher stiffness than that of networks containing only actin filaments or only vimentin filaments. Maximum inter-filament interaction occurs at a vimentin/actin molar ratio of 3 to 1. Mixed networks of actin and tailless vimentin filaments show low mechanical stiffness and much weaker inter-filament interactions. Together with the fact that cells featuring prominent vimentin and actin networks are much stiffer than their counterparts lacking an organized actin or vimentin network, these results suggest that actin and vimentin filaments can interact directly through the tail domain of vimentin and that these inter-filament interactions may contribute to the overall mechanical integrity of cells and mediate cytoskeletal cross-talk.     

The variable twist of actin and its modulation by actin-binding proteins

Previous studies demonstrated that actin filaments have variable twist in which the intersubunit angles vary by approximately +/- 10 degrees within a filament. In this work we show that this variability was unchanged when different methods were used to prepare filaments for electron microscopy. We also show that actin-binding proteins can modulate the variability in twist. Three preparations of actin filaments were photographed in the electron microscope: negatively stained filaments, replicas of rapidly frozen, etched filaments, and frozen hydrated filaments. In addition, micrographs of actin + tropomyosin + troponin (thin filaments), of actin + myosin S1 (decorated filaments), and of filaments frayed from the acrosomal process of Limulus sperm (Limulus filaments) were obtained. We used two independent methods to measure variable twist based on Fourier transforms of single filaments. The first involved measuring layer line intensity versus filament length and the second involved measuring layer line position. We measured a variability in the intersubunit angle of actin filaments of approximately 12 degrees independent of the method of preparation or of measurement. Thin filaments have 15 degrees of variability, but the increase over pure actin is not statistically significant. Decorated filaments and Limulus filaments, however, have significantly less variability (approximately 2 and 1 degree, respectively), indicating a torsional stiffening relative to actin. The results from actin alone using different preparative methods are evidence that variable twist is a property of actin in solution. The results from actin filaments in the presence of actin-binding proteins suggest that the angular variability can be modulated, depending on the biological function.