Distribution of actin filament lengths measured by fluorescence microscopy

Small organic osmolytes accelerate actin filament assembly and stiffen filaments

Actin filament assembly and mechanics are crucial for maintenance of cell structure, motility, and division. Actin filament assembly occurs in a crowded intracellular environment consisting of various types of molecules, including small organic molecules known as osmolytes. Ample evidence highlights the protective functions of osmolytes such as trimethylamine-N-oxide (TMAO), including their effects on protein stability and their ability to counteract cellular osmotic stress. Yet, how TMAO affects individual actin filament assembly dynamics and mechanics is not well understood. We hypothesize that, owing to its protective nature, TMAO will enhance filament dynamics and stiffen actin filaments due to increased stability. In this study, we investigate osmolyte-dependent actin filament assembly and bending mechanics by measuring filament elongation rates, steady-state filament lengths, and bending persistence lengths in the presence of TMAO using total internal reflection fluorescence microscopy and pyrene assays. Our results demonstrate that TMAO increases filament elongation rates as well as steady-state average filament lengths, and enhances filament bending stiffness. Together, these results will help us understand how small organic osmolytes modulate cytoskeletal protein assembly and mechanics in living cells.

Chronic lactate exposure promotes cardiomyocyte cytoskeleton remodelling

We investigated the effect of growing on lactate instead of glucose in human cardiomyocyte assessing their viability, cell cycle activity, oxidative stress and metabolism by a proteomic and metabolomic approach. In previous studies performed on elite players, we found that adaptation to exercise is characterized by a chronic high plasma level of lactate. Lactate is considered not only an energy source but also a signalling molecule and is referred as "lactormone"; heart is one of the major recipients of exogenous lactate. With this in mind, we used a cardiac cell line AC16 to characterize the lactate metabolic profile and investigate the metabolic flexibility of the heart. Interestingly, our data indicated that cardiomyocytes grown on lactate (72 h) show change in several proteins and metabolites linked to cell hypertrophy and cytoskeleton remodelling. The obtained results could help to understand the effect of this metabolite on heart of high-performance athletes.

Cytosolic actin isoforms form networks with different rheological properties that indicate specific biological function

The implications of the existence of different actins expressed in epithelial cells for network mechanics and dynamics is investigated by microrheology and confocal imaging. γ-actin predominately found in the apical cortex forms stiffer networks compared to β-actin, which is preferentially organized in stress fibers. We attribute this to selective interactions with Mg2+-ions interconnecting the filaments' N-termini. Bundling propensity of the isoforms is different in the presence of Mg2+-ions, while crosslinkers such as α-actinin, fascin, and heavy meromyosin alter the mechanical response independent of the isoform. In the presence of myosin, β-actin networks show a large number of small contraction foci, while γ-actin displays larger but fewer foci indicative of a stronger interaction with myosin motors. We infer that subtle changes in the amino acid sequence of actin isoforms lead to alterations of the mechanical properties on the network level with potential implications for specific biological functions.

Topological mechanism in the nonlinear power-law relaxation of cell cortex

Different types of cells exhibit a universal power-law rheology, but the mechanism underneath is still unclear. Based on the exponential distribution of actin filament length, we treat the cell cortex as a collection of chains of crosslinkers with exponentially distributed binding energy, and show that the power-law exponent of its stress relaxation should scale with the chain length. Through this model, we are able to explain how the exponent can be regulated by the crosslinker number and imposed strain during cortex relaxation. Network statistics show that the average length of filament-crosslinker chains decreases with the crosslinker number, which endows a denser network with lower exponent. Due to gradual molecular alignment with the stretch direction, the number of effectively stretched crosslinkers in the network is found to increase with the imposed strain. This effective growth in network density diminishes the exponent under large strain. By incorporating the inclined angle of crosslinkers into the model without in-series structure, we show that the exponent cannot be altered by crosslinker rotation directly, refining our previous conjectures. This work may help to understand cellular mechanics from the molecular perspective.

Network dynamics of the nonlinear power-law relaxation of cell cortex

Living cells are known to exhibit universal power-law rheological behaviors, but their underlying biomechanical principles are still not fully understood. Here, we present a network dynamics picture to decipher the nonlinear power-law relaxation of cortical cytoskeleton. Under step strains, we present a scaling relation between instantaneous differential stiffness and external stress as a result of chain reorientation. Then, during the relaxation, we show how the scaling law theoretically originates from an exponential form of cortical disorder, with the scaling exponent decreased by the imposed strain or crosslinker density in the nonlinear regime. We attribute this exponent variation to the molecular realignment along the stretch direction or the transition of network structure from in-series to in-parallel modes, both solidifying the network toward our one-dimensional theoretical limit. In addition, the rebinding of crosslinkers is found to be crucial for moderating the relaxation speed under small strains. Together with the disorder nature, we demonstrate that the structural effects of networks provide a unified interpretation for the nonlinear power-law relaxation of cell cortex, and may help to understand cell mechanics from the molecular scale.

A statistical mechanics model for determining the length distribution of actin filaments under cellular tensional homeostasis

Tensional homeostasis is a cellular process whereby nonmuscle cells such as fibroblasts keep a constant level of intracellular tension and signaling activities. Cells are allowed thanks to tensional homeostasis to adapt to mechanical stress, but the detailed mechanism remains unclear. Here we address from a theoretical point of view what is required for maintaining cellular tensional homeostasis. A constrained optimization problem is formulated to analytically determine the probability function of the length of individual actin filaments (AFs) responsible for sustaining cellular tension. An objective function composed of two entropic quantities measuring the extent of formation and dispersion of AFs within cells is optimized under two constraint functions dictating a constant amount of actin molecules and tension that are arguably the two most salient features of tensional homeostasis. We then derive a specific probability function of AFs that is qualitatively consistent with previous experimental observations, in which short AF populations preferably appear. Regarding the underlying mechanism, our analyses suggest that the constraint for keeping the constant tension level makes long AF populations smaller in number because long AFs have a higher chance to be involved in bearing larger forces. The specific length distribution of AFs is thus required for achieving the constrained objectives, by which individual cells are endowed with the ability to stably maintain a homeostatic tension throughout the cell, thereby potentially allowing cells to locally detect deviation in the tension, keep resulting biological functions, and hence enable subsequent adaptation to mechanical stress. Although minimal essential factors are included given the actual complexity of cells, our approach would provide a theoretical basis for understanding complicated homeostatic and adaptive behavior of the cell.

Hydrodynamic and Polyelectrolyte Properties of Actin Filaments: Theory and Experiments

Actin filament’s polyelectrolyte and hydrodynamic properties, their interactions with the biological environment, and external force fields play an essential role in their biological activities in eukaryotic cellular processes. In this article, we introduce a unique approach that combines dynamics and electrophoresis light-scattering experiments, an extended semiflexible worm-like chain model, and an asymmetric polymer length distribution theory to characterize the polyelectrolyte and hydrodynamic properties of actin filaments in aqueous electrolyte solutions. A fitting approach was used to optimize the theories and filament models for hydrodynamic conditions. We used the same sample and experimental conditions and considered several g-actin and polymerization buffers to elucidate the impact of their chemical composition, reducing agents, pH values, and ionic strengths on the filament translational diffusion coefficient, electrophoretic mobility, structure factor, asymmetric length distribution, effective filament diameter, electric charge, zeta potential, and semiflexibility. Compared to those values obtained from molecular structure models, our results revealed a lower value of the effective G-actin charge and a more significant value of the effective filament diameter due to the formation of the double layer of the electrolyte surrounding the filaments. Contrary to the data usually reported from electron micrographs, the lower values of our results for the persistence length and average contour filament length agree with the significant difference in the association rates at the filament ends that shift to sub-micro lengths, which is the maximum of the length distribution.

Myosin-driven actin-microtubule networks exhibit self-organized contractile dynamics

The cytoskeleton is a dynamic network of proteins, including actin, microtubules, and their associated motor proteins, that enables essential cellular processes such as motility, division, and growth. While actomyosin networks are extensively studied, how interactions between actin and microtubules, ubiquitous in the cytoskeleton, influence actomyosin activity remains an open question. Here, we create a network of co-entangled actin and microtubules driven by myosin II. We combine dynamic differential microscopy, particle image velocimetry, and particle tracking to show that both actin and microtubules undergo ballistic contraction with unexpectedly indistinguishable characteristics. This contractility is distinct from faster disordered motion and rupturing that active actin networks exhibit. Our results suggest that microtubules enable self-organized myosin-driven contraction by providing flexural rigidity and enhanced connectivity to actin networks. Beyond the immediate relevance to cytoskeletal dynamics, our results shed light on the design of active materials that can be precisely tuned by the network composition.

Gelsolin-mediated actin filament severing in crowded environments

Gelsolin is a calcium-regulated actin binding protein that severs and caps actin filaments. Gelsolin's severing activity is important for regulating actin filament assembly dynamics that are required for cell motility as well as survival. The majority of in vitro studies of gelsolin have been performed in dilute buffer conditions which do not simulate the molecular interactions occurring in the crowded intracellular environment. We hypothesize that crowding results in greater gelsolin severing activity due to induced conformational changes in actin filaments and/or gelsolin. In this study, we evaluated the effects of crowding on gelsolin-mediated actin filament severing and gelsolin binding to actin filaments in crowded solutions, utilizing total internal reflection fluorescence (TIRF) microscopy and co-sedimentation assays. Our data indicates that the presence of crowders causes a decrease in the rate of gelsolin severing as well as a decrease in the amount of gelsolin bound to actin filaments, with greater effects caused by the polymeric crowder. Despite the severing rate decrease, gelsolin-mediated filament severing is increased in the presence of crowders. Understanding the crowding effect on gelsolin-mediated actin filament severing offers insight into the interactions between gelsolin and actin that occur inside the crowded cytoplasm.

The elastic properties and deformation mechanisms of actin filament networks crosslinked by filamins

As a substructure of cell cytoskeleton, the crosslinked actin filament networks (CAFNs) play a major role in different cell functions, however, the elastic properties and the deformation mechanisms of CAFNs still remain to be understood. In this paper, a novel three-dimensional (3D) finite element (FE) model has been developed to mimic the mechanical properties of actin filament (F-actin) networks crosslinked by filamin A (FLNA). The simulation results indicate that although the Young's modulus of CAFNs varies in different directions for each random model, the statistical mean value is in-plane isotropic. The crosslinking density and the actin filament volume fraction are found to strongly affect the in-plane shear modulus of CAFNs. The simulation results agree well with the relevant experimental results. In addition, an L-shaped cantilever beam model has been developed for dimensional analysis on the shear stiffness of CAFNs and for quantifying the deformation mechanisms. It has been demonstrated that the in-plane shear modulus of CAFNs is mainly dominated by FLNA (i.e., cross-linkers), and that the bending and torsion deformations of FLNA have almost the same contribution to the stiffness of CAFNs. It has also been found that the stiffness of CAFNs is almost insensitive to the variation of the Poisson's ratios of FLNA and actin filament in the range from 0.29 to 0.499.

Cardiac troponin and tropomyosin bind to F-actin cooperatively, as revealed by fluorescence microscopy

In cardiac muscle, binding of troponin (Tn) and tropomyosin (Tpm) to filamentous (F)‐actin forms thin filaments capable of Ca²⁺‐dependent regulation of contraction. Tpm binds to F‐actin in a head‐to‐tail fashion, while Tn stabilizes these linkages. Valuable structural and functional information has come from biochemical, X‐ray, and electron microscopy data. However, the use of fluorescence microscopy to study thin filament assembly remains relatively underdeveloped. Here, triple fluorescent labeling of Tn, Tpm, and F‐actin allowed us to track thin filament assembly by fluorescence microscopy. It is shown here that Tn and Tpm molecules self‐organize on actin filaments and give rise to decorated and undecorated regions. Binding curves based on colocalization of Tn and Tpm on F‐actin exhibit cooperative binding with a dissociation constant K_d of ~ 0.5 µm that is independent of the Ca²⁺ concentration. Binding isotherms based on the intensity profile of fluorescently labeled Tn and Tpm on F‐actin show that binding of Tn is less cooperative relative to Tpm. Computational modeling of Tn‐Tpm binding to F‐actin suggests two equilibrium steps involving the binding of an initial Tn‐Tpm unit (nucleation) and subsequent recruitment of adjacent Tn‐Tpm units (elongation) that stabilize the assembly. The results presented here highlight the utility of employing fluorescence microscopy to study supramolecular protein assemblies.

On the mechanical response of the actomyosin cortex during cell indentations

A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

Binding partner- and force-promoted changes in αE-catenin conformation probed by native cysteine labeling

Adherens Junctions (AJs) are cell-cell adhesion complexes that sense and propagate mechanical forces by coupling cadherins to the actin cytoskeleton via β-catenin and the F-actin binding protein αE-catenin. When subjected to mechanical force, the cadherin•catenin complex can tightly link to F-actin through αE-catenin, and also recruits the F-actin-binding protein vinculin. In this study, labeling of native cysteines combined with mass spectrometry revealed conformational changes in αE-catenin upon binding to the E-cadherin•β-catenin complex, vinculin and F-actin. A method to apply physiologically meaningful forces in solution revealed force-induced conformational changes in αE-catenin when bound to F-actin. Comparisons of wild-type αE-catenin and a mutant with enhanced vinculin affinity using cysteine labeling and isothermal titration calorimetry provide evidence for allosteric coupling of the N-terminal β-catenin-binding and the middle (M) vinculin-binding domain of αE-catenin. Cysteine labeling also revealed possible crosstalk between the actin-binding domain and the rest of the protein. The data provide insight into how binding partners and mechanical stress can regulate the conformation of full-length αE-catenin, and identify the M domain as a key transmitter of conformational changes.

Quantifying dissipation in actomyosin networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

Triggered disassembly and reassembly of actin networks induces rigidity phase transitions

Non-equilibrium soft materials, such as networks of actin proteins, have been intensely investigated over the past decade due to their promise for designing smart materials and understanding cell mechanics. However, current methods are unable to measure the time-dependent mechanics of such systems or map mechanics to the corresponding dynamic macromolecular properties. Here, we present an experimental approach that combines time-resolved optical tweezers microrheology with diffusion-controlled microfluidics to measure the time-evolution of microscale mechanical properties of dynamic systems during triggered activity. We use these methods to measure the viscoelastic moduli of entangled and crosslinked actin networks during chemically-triggered depolymerization and repolymerization of actin filaments. During disassembly, we find that the moduli exhibit two distinct exponential decays, with experimental time constants of ∼169 min and ∼47 min. Conversely, during reassembly, measured moduli initially exhibit power-law increase with time, after which steady-state values are achieved. We develop toy mathematical models that couple the time-evolution of filament lengths with rigidity percolation theory to shed light onto the molecular mechanisms underlying the observed mechanical transitions. The models suggest that these two distinct behaviors both arise from phase transitions between a rigidly percolated network and a non-rigid regime. Our approach and collective results can inform the general principles underlying the mechanics of a large class of dynamic, non-equilibrium systems and materials of current interest.

Shear Deformation Dissipates Energy in Biofilaments

Thermally fluctuating biofilaments possessing porous structures or viscoelastic properties exhibit energy losses from internal friction as well as external friction from drag. Prior models for internal friction account for energy dissipation solely from the dynamic bending of filaments. In this paper, we present a new energy dissipation model that captures the important effects of dynamic shear in addition to bending. Importantly, we highlight that shear-induced friction plays a major role in energy dissipation for shorter filaments and for shorter wavelengths (larger wavenumbers). The new model exhibits coupled shear-bending energy relaxation on two distinct time scales in lieu of a single time scale predicted by bending alone. We employ this model to interpret results from prior experiments on the internal friction of thermally fluctuating chromosomes and the drag-induced friction of thermally fluctuating microtubules. The examples confirm the energy relaxation on two time scales associated with internal friction and on two length scales associated with external friction. Overall, this new model that accounts for shear deformation yields superior estimates of energy dissipation for fluctuating biofilaments.

Cholesterol-Dependent Phase-Demixing in Lipid Bilayers as a Switch for the Activity of the Phosphoinositide-Binding Cytoskeletal Protein Gelsolin

The lateral distribution of phosphatidylinositol 4,5-bisphosphate (PIP2) in lipid bilayers is affected both by divalent cation-mediated attractions and cholesterol-dependent phase demixing. The effects of lateral redistribution of PIP2 within a membrane on PIP2-protein interactions are explored with an N-terminal fragment of gelsolin (NtGSN) that severs actin in a Ca(2+)-insensitive manner. The extent of NtGSN inhibition by PIP2-containing large unilamellar vesicles (LUVs) depends on the lateral organization of the membrane as quantified by an actin-severing assay. At a fixed PIP2 mole fraction, the inhibition is largely enhanced by the segregation of liquid ordered/liquid disordered (Lo/Ld) phases that is induced by altering either cholesterol content or temperature, whereas the presence of Ca(2+) only slightly improves the inhibition. Inhibition of gelsolin induced by demixed LUVs is more effective with decreasing temperature, coincident with increasing membrane order as determined by Laurdan generalized polarization and is reversible as the temperature increases. This result suggests that PIP2-mediated inhibition of gelsolin function depends not only on changes in global concentration but also on lateral distribution of PIP2. These observations imply that gelsolin, and perhaps other PIP2-regulated proteins, can be activated or inactivated by the formation of nanodomains or clusters without changing PIP2 bulk concentration in the cell membrane.

Nano-assembly of nanodiamonds by conjugation to actin filaments

Fluorescent nanodiamonds (NDs) are remarkable objects. They possess unique mechanical and optical properties combined with high surface areas and controllable surface reactivity. They are non-toxic and hence suited for use in biological environments. NDs are also readily available and commercially inexpensive. Here, the exceptional capability of controlling and tailoring their surface chemistry is demonstrated. Small, bright diamond nanocrystals (size ˜30 nm) are conjugated to protein filaments of actin (length ˜3-7 µm). The conjugation to actin filaments is extremely selective and highly target-specific. These unique features, together with the relative simplicity of the conjugation-targeting method, make functionalised nanodiamonds a powerful and versatile platform in biomedicine and quantum nanotechnologies. Applications ranging from using NDs as superior biological markers to, potentially, developing novel bottom-up approaches for the fabrication of hybrid quantum devices that would bridge across the bio/solid-state interface are presented and discussed.

DeFiNe: an optimisation-based method for robust disentangling of filamentous networks

Thread-like structures are pervasive across scales, from polymeric proteins to root systems to galaxy filaments, and their characteristics can be readily investigated in the network formalism. Yet, network links usually represent only parts of filaments, which, when neglected, may lead to erroneous conclusions from network-based analyses. The existing alternatives to detect filaments in network representations require tuning of parameters over a large range of values and treat all filaments equally, thus, precluding automated analysis of diverse filamentous systems. Here, we propose a fully automated and robust optimisation-based approach to detect filaments of consistent intensities and angles in a given network. We test and demonstrate the accuracy of our solution with contrived, biological, and cosmic filamentous structures. In particular, we show that the proposed approach provides powerful automated means to study properties of individual actin filaments in their network context. Our solution is made publicly available as an open-source tool, "DeFiNe", facilitating decomposition of any given network into individual filaments.

A bibenzyl from Dendrobium ellipsophyllum inhibits migration in lung cancer cells

Metastatic cancer cells have been shown to have aggressive behaviors accounting for the high incidence of chemotherapeutic failure and mortality. Because migration and invasion are crucial behaviors for cancer cell dissemination, promising compounds exhibiting potential antimigration effects are of interest for metastasis-based therapeutic approaches. This study aimed to evaluate the activity of a bibenzyl, 4,5,4'-trihydroxy-3,3'-dimethoxybibenzyl (TDB), isolated from Dendrobium ellipsophyllum Tang and Wang, in the suppression of migration in human lung cancer cells. TDB at nontoxic concentrations (1 and 5 µM) significantly inhibited the motility of lung cancer cells in scratch-wound assay. Chemotaxis-induced migration and invasion assays also revealed that the cell motility dramatically diminished in the cells treated with 1-5 µM TDB. Western blot analysis provided the underlying molecular mechanism, showing that TDB reduced such cell migration and invasion by decreasing migration-regulating proteins, including integrins αv, α4, β1, β3 and β5, as well as downstream signaling proteins, such as activated focal adhesion kinase (pFAK), activated Ras-related C3 botulinum toxin substrate 1 (Rac1-GTP) and cell division control protein 42 (Cdc42). As the presence of cellular protrusion, called filopodia, has been indicated as a hallmark of migrating cells, we showed that the reduction of the mentioned proteins correlated well with the disappearance of filopodia. In summary, this study demonstrates the promising activity of TDB and its mechanism in the inhibition of lung cancer cell migration, which might be useful for encouraging the development of this compound for antimetastatic approaches.

Real-time dynamics of emerging actin networks in cell-mimicking compartments

Understanding the cytoskeletal functionality and its relation to other cellular components and properties is a prominent question in biophysics. The dynamics of actin cytoskeleton and its polymorphic nature are indispensable for the proper functioning of living cells. Actin bundles are involved in cell motility, environmental exploration, intracellular transport and mechanical stability. Though the viscoelastic properties of actin-based structures have been extensively probed, the underlying microstructure dynamics, especially their disassembly, is not fully understood. In this article, we explore the rich dynamics and emergent properties exhibited by actin bundles within flow-free confinements using a microfluidic set-up and epifluorescence microscopy. After forming entangled actin filaments within cell-sized quasi two-dimensional confinements, we induce their bundling using three different fundamental mechanisms: counterion condensation, depletion interactions and specific protein-protein interactions. Intriguingly, long actin filaments form emerging networks of actin bundles via percolation leading to remarkable properties such as stress generation and spindle-like intermediate structures. Simultaneous sharing of filaments in different links of the network is an important parameter, as short filaments do not form networks but segregated clusters of bundles instead. We encounter a hierarchical process of bundling and its subsequent disassembly. Additionally, our study suggests that such percolated networks are likely to exist within living cells in a dynamic fashion. These observations render a perspective about differential cytoskeletal responses towards numerous stimuli.

Rotational motion of rhodamine 6G tethered to actin through oligo(ethylene glycol) linkers studied by frequency-domain fluorescence anisotropy

Investigation of the rotational motion of a fluorescent probe tethered to a protein helps to elucidate the local properties of the solvent and protein near the conjugation site of the probe. In this study, we have developed an instrument for frequency-domain fluorescence (FDF) anisotropy measurements, and studied how the local properties around a protein, actin, can be elucidated from the rotational motion of a dye tethered to actin. Rhodamine 6G (R6G) was attached to Cys-374 using newly-synthesized R6G-maleimide with three different oligo(ethylene glycol) (OEG) linker lengths. The time-resolved anisotropy decay of R6G tethered to G-actin was revealed to be a combination of the two modes of the wobbling motion of R6G and the tumbling motion of G-actin. The rotational diffusion coefficient (RDC) of R6G wobbling was ~0.1 ns⁻¹ at 20°C and increased with OEG linker length. The use of the three R6G-actin conjugates of different linker lengths was useful to not only figure out the linker length dependence of the rotational motion of R6G but also validate the analyses. In the presence of a cosolvent of glycerol, although the tumbling motion of G-actin was retarded in response to the bulk viscosity, the wobbling motion of R6G tethered to actin exhibited an increase of RDC as glycerol concentration increased. This finding suggests an intricate relationship between the fluid properties of the bulk solvent and the local environment around actin.

Analysis of flexural rigidity of actin filaments propelled by surface adsorbed myosin motors

Actin filaments are central components of the cytoskeleton and the contractile machinery of muscle. The filaments are known to exist in a range of conformational states presumably with different flexural rigidity and thereby different persistence lengths. Our results analyze the approaches proposed previously to measure the persistence length from the statistics of the winding paths of actin filaments that are propelled by surface-adsorbed myosin motor fragments in the in vitro motility assay. Our results suggest that the persistence length of heavy meromyosin propelled actin filaments can be estimated with high accuracy and reproducibility using this approach provided that: (1) the in vitro motility assay experiments are designed to prevent bias in filament sliding directions, (2) at least 200 independent filament paths are studied, (3) the ratio between the sliding distance between measurements and the camera pixel-size is between 4 and 12, (4) the sliding distances between measurements is less than 50% of the expected persistence length, and (5) an appropriate cut-off value is chosen to exclude abrupt large angular changes in sliding direction that are complications, e.g., due to the presence of rigor heads. If the above precautions are taken the described method should be a useful routine part of in vitro motility assays thus expanding the amount of information to be gained from these.

A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis

The mechanical properties of a cell are defined mainly by the cytoskeleton. One contributor within this three-dimensional structure is the actin cortex which is located underneath the lipid bilayer. It forms a nearly isotropic and densely cross-linked protein network. We present a continuum mechanical formulation for describing the mechanical properties of in vitro model systems based on their micro-structure, i.e. the behavior of a single filament and its spatial arrangement. The network is considered elastic, viscous effects being neglected. Filamentous actin is a biopolymer with a highly nonlinear force-stretch relationship. This can be well described by a worm-like chain model that includes extensibility of the filament, which we call the β-model. A comparison with experimental data shows good agreement with values for the physically interpretable parameters. To make these properties applicable to three dimensions we used a non-affine micro-sphere network, which accounts for filaments, equally distributed in space. The assembled model results in a strain-energy density which is a function of the deformation gradient, and it is validated with experimental data from rheological experiments of in vitro reconstituted actin networks. The Cauchy stress and elasticity tensors are obtained within the continuum mechanics framework and implemented into a finite element program to solve boundary-value problems.

Actin filament length tunes elasticity of flexibly cross-linked actin networks

Networks of the cytoskeletal biopolymer actin cross-linked by the compliant protein filamin form soft gels that stiffen dramatically under shear stress. We demonstrate that the elasticity of these networks shows a strong dependence on the mean length of the actin polymers, unlike networks with small, rigid cross-links. This behavior is in agreement with a model of rigid filaments connected by multiple flexible linkers.

Reaction-diffusion systems in intracellular molecular transport and control

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

Bending flexibility of actin filaments during motor-induced sliding

Muscle contraction and other forms of cell motility occur as a result of cyclic interactions between myosin molecules and actin filaments. Force generation is generally attributed to ATP-driven structural changes in myosin, whereas a passive role is ascribed to actin. However, some results challenge this view, predicting structural changes in actin during motor activity, e.g., when the actin filaments slide on a myosin-coated surface in vitro. Here, we analyzed statistical properties of the sliding filament paths, allowing us to detect changes of this type. It is interesting to note that evidence for substantial structural changes that led to increased bending flexibility of the filaments was found in phalloidin-stabilized, but not in phalloidin-free, actin filaments. The results are in accordance with the idea that a high-flexibility structural state of actin is a prerequisite for force production, but not the idea that a low-to-high flexibility transition of the actin filament should be an important component of the force-generating step per se. Finally, our data challenge the general view that phalloidin-stabilized filaments behave as native actin filaments in their interaction with myosin. This has important implications, since phalloidin stabilization is a routine procedure in most studies of actomyosin function.

Effect of short-range forces on the length distribution of fibrous cytoskeletal proteins

The length distribution of cytoskeletal filaments is an important physical parameter, which can modulate physiological cell functions. In both eukaryotic and prokaryotic cells various biological cytoskeletal polymers form supramolecular structures due to short-range forces induced mainly by molecular crowding or cross linking proteins, but their in vivo length distribution remains difficult to measure. In general, based on experimental evidence and mathematical modeling of actin filaments in aqueous solutions, the steady state length distribution of fibrous proteins is believed to be exponential. We performed in vitro TIRF- and electron-microscopy to demonstrate that in the presence of short-range forces, which are an integral part of any living cell, the steady state length distributions of the eukaryotic cytoskeletal biopolymer actin, its prokaryotic homolog ParM and microtubule homolog FtsZ deviate from the classical exponential and are either double-exponential or Gaussian, as recent theoretical modeling predicts. Double exponential or Gaussian distributions opposed to exponential can change for example the visco-elastic properties of actin networks within the cell, influence cell motility by decreasing the amount of free ends at the leading edge of the cell or effect the assembly of FtsZ into the bacterial Z-ring thus modulating membrane constriction.

Nonequilibrium microtubule fluctuations in a model cytoskeleton

Biological activity gives rise to nonequilibrium fluctuations in the cytoplasm of cells; however, there are few methods to directly measure these fluctuations. Using a reconstituted actin cytoskeleton, we show that the bending dynamics of embedded microtubules can be used to probe local stress fluctuations. We add myosin motors that drive the network out of equilibrium, resulting in an increased amplitude and modified time dependence of microtubule bending fluctuations. We show that this behavior results from steplike forces on the order of 10 pN driven by collective motor dynamics.

A quantitative analysis of contractility in active cytoskeletal protein networks

Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of purified F-actin, muscle myosin II motors, and alpha-actinin cross-linkers. We show that contractility occurs above a threshold motor concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of approximately 1 microN, or approximately 100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the (local) activity of molecular motors and the cross-linker density and binding affinity.

Protein osmotic pressure modulates actin filament length distribution

On these bases, we propose that the length distribution of the actin filaments is regulated by (a) the free energy of hydrolysis of ATP and (b) the macromolecular osmotic pressure.

Structure-function analysis of the filamentous actin binding domain of the neuronal scaffolding protein spinophilin

Spinophilin, a neuronal scaffolding protein, is essential for synaptic transmission, and functions to target protein phosphatase-1 to distinct subcellular locations in dendritic spines. It is vital for the regulation of dendritic spine formation and motility, and functions by regulating glutamatergic receptors and binding to filamentous actin. To investigate its role in regulating actin cytoskeletal structure, we initiated structural studies of the actin binding domain of spinophilin. We demonstrate that the spinophilin actin binding domain is intrinsically unstructured, and that, with increasing C-terminal length, the domain shows augmented secondary structure content. Further characterization confirmed the previously known crosslinking activity and uncovered a novel filamentous actin pointed-end capping activity. Both of these functions seem to be fully contained within residues 1-154 of spinophilin.

Crowded surfaces change annealing dynamics of actin filaments

Changes in cell shape that occur in many cellular processes are thought to arise from polymerization of actin filaments near the cell membrane. End-to-end annealing of actin filaments is believed to play only a minor role in this process, as annealing in solution was shown to be a slow process, which is not typical for a bimolecular reaction, its rate constant decreasing over time, being inversely proportional to the filament length. Furthermore, in vitro studies on f-actin solutions were found to display an exponential steady-state length distribution. In the cell, many physiologically important parameters, such as mechanical strength or viscoelastic response are a direct function of the physical properties of the underlying actin cytoskeleton, such as actin filament length distribution and dynamics. How the underlying physical parameters of the actin cytoskeleton may be influenced by the cell surface or molecular crowding remains poorly understood. Using total internal reflection fluorescence (TIRF) microscopy we reinvestigated actin end-to-end annealing in vitro in a more realistic environment. We studied the process near a hydrophilic surface together with crowding agents, in order to mimic the physiological media near the cell membrane, which has substantial amounts of macromolecules present. We find that actin end-to-end annealing changes in three ways near a crowded hydrophilic surface as compared to solution. First the annealing rate becomes a factor of 20 faster than in solution. Second the rate of annealing becomes typical of a bimolecular reaction, shows no length dependence and is basically just a function of the square of the concentration of ends. Lastly the length distribution is Gaussian throughout the entire annealing process. This implicates that dynamic rearrangement of actin filaments by annealing near the leading edge of the cell, could change physical parameters like the mechanical response and contribute significantly to cell motility.

Size distribution of linear and helical polymers in actin solution analyzed by photon counting histogram

Actin is a ubiquitous protein that is a major component of the cytoskeleton, playing an important role in muscle contraction and cell motility. At steady state, actin monomers and filaments (F-actin) coexist, and actin subunits continuously attach and detach at the filament ends. However, the size distribution of actin oligomers in F-actin solution has never been clarified. In this study, we investigated the size distribution of actin oligomers using photon-counting histograms. For this purpose, actin was labeled with a fluorescent dye, and the emitted photons were detected by confocal optics (the detection volume was of femtoliter (fL) order). Photon-counting histograms were analyzed to obtain the number distribution of actin oligomers in the detection area from their brightness, assuming that the brightness of an oligomer was proportional to the number of protomers. We found that the major populations at physiological ionic strength were 1-5mers. For data analysis, we successfully applied the theory of linear and helical aggregations of macromolecules. The model postulates three states of actin, i.e., monomers, linear polymers, and helical polymers. Here we obtained three parameters: the equilibrium constants for polymerization of linear polymers, K(l)=(5.2 +/- 1.1) x 10(6) M(-1), and helical polymers, K(h)=(1.6 +/- 0.5) x 10(7) M(-1); and the ratio of helical to linear trimers, gamma = (3.6 +/- 2.3) x 10(-2). The excess free energy of transforming a linear trimer to a helical trimer, which is assumed to be a nucleus for helical polymers, was calculated to be 2.0 kcal/mol. These analyses demonstrate that the oligomeric phase at steady state is predominantly composed of linear 1-5mers, and the transition from linear to helical polymers occurs on the level of 5-7mers.

Orientational order parameter of the nematic liquid crystalline phase of F-actin

We measured the orientational order parameter of F-actin traversing the isotropic-nematic phase transition using a combination of techniques, including fluorescence imaging, local birefringence measurements, and small-angle x-ray scattering. The order parameter approaches a saturated value of 0.75 for actin concentrations above the region of the isotropic-nematic phase transition. This result implies a significant extent of misalignment and consequently entanglement among long actin filaments, even in the nematic phase. We determine the specific birefringence of completely aligned F-actin to be Deltan(0)=2.3 x 10(-5) ml/mg. At concentrations slightly below the isotropic-nematic transition, nonzero values of the order parameter are detected for hours following an initial alignment, indicating extremely slow rotational kinetics of F-actin in the entangled networks.

High-frequency stress relaxation in semiflexible polymer solutions and networks

We measure the linear viscoelasticity of sterically entangled and chemically cross-linked networks of actin filaments over more than five decades of frequency. The high-frequency response reveals rich dynamics unique to semiflexible polymers, including a previously unobserved relaxation due to rapid axial tension propagation. For high molecular weight, and for cross-linked gels, we obtain quantitative agreement with predicted shear moduli in both amplitude and frequency dependence.

Dynamic changes in the length distribution of actin filaments during polymerization can be modulated by barbed end capping proteins

During actin polymerization, it has been theorized that the actin filament length distribution initially grows in the form of a Gaussian before converting to produce that of an exponential. However, it has been difficult to demonstrate this experimentally. In this study, we use modern fluorescence microscopy techniques to observe the changing actin filament length distribution during and subsequent to the polymerization process. Nucleated actin filament growth using barbed end capping proteins (gelsolin and erythrocyte capping protein) leads to Gaussian length distributions that are relatively stable. As predicted, nucleated actin filament growth using actin/spectrin complexes follows a similar process until polymerization reaches equilibrium whereafter the Gaussian length distribution rapidly converts to that of an exponential. This study provides direct confirmation of the original theories for the mode of actin polymerization but raises doubts regarding the mechanism of the length distribution conversion from Gaussian to exponential.

The effect of alpha-actinin on the length distribution of F-actin

Actin filament length distribution in cells is often regulated to fit specific tasks. In comparison to the well-studied regulation of the average filament length (e.g., using capping proteins), controlling the width of the distribution is less well understood. We utilize two complementary methods to measure the effect of alpha-actinin on the width of the distribution of lengths of F-actin in vitro. Analyzing transmission electron micrographs shows that crosslinking by alpha-actinin reduces the width of the length distribution of F-actin, decreasing the coefficient of variation by two- to threefold. Analysis of fluorescence data from depolymerization assays confirms this observation. We suggest a mechanistic molecular model in which a local (weak) stabilization of crosslinked monomers in the filament is the physical origin of the decrease in the variance of lengths. Although alpha-actinin is known to bind reversibly to F-actin, our model shows that even weak binding can produce this effect, and that in fact it persists throughout a wide range of binding strengths.

Real-time measurements of actin filament polymerization by total internal reflection fluorescence microscopy

Understanding the mechanism of actin polymerization and its regulation by associated proteins requires an assay to monitor polymerization dynamics and filament topology simultaneously. The only assay meeting these criteria is total internal reflection fluorescence microscopy (Amann and Pollard, 2001; Fujiwara et al., 2002). The fluorescence signal is fourfold stronger with actin labeled on Cys-374 with Oregon green rather than rhodamine. To distinguish growth at barbed and pointed ends we used image drift correction and maximum intensity projections to reveal points where single N-ethylmaleimide inactivated myosins attach filaments to the glass coverslip. We estimated association rates at high actin concentrations and dissociation rates near and below the critical actin concentration. At the barbed end, the association rate constant for Mg-ATP-actin is 7.4 microM(-1) s(-1) and the dissociation rate constant is 0.89 s(-1). At the pointed end the association and dissociation rate constants are 0.56 microM(-1) s(-1) and 0.19 s(-1). When vitamin D binding protein sequesters all free monomers, ADP-actin dissociates from barbed ends at 1.4 s(-1) and from pointed ends at 0.16 s(-1) regardless of buffer nucleotide.

Reversible polymerizations and aggregations

The aggregation of monomers into polymers, whether by covalent or noncovalent interactions, is often reversible and frequently occurs with the entropy and enthalpy of the aggregation sharing the same sign. In such a case, the aggregation goes forward or reverses, depending on such variables as temperature and composition, rather like a phase transition. We explore the physical chemistry of three such systems: an organic monomer (alpha-methylstyrene), an inorganic monomer (sulfur), and a biopolymer (actin). We compare the available theories and experiments and list issues still open.

ATPase activity and conformational changes in the regulation of actin

The eukaryotic microfilament system is regulated in part through the nucleotide- and cation-dependent conformation of the actin molecule. In this review, recent literature on the crystal and solution structures of actin and other actin-superfamily proteins is summarized. Furthermore, the structure of the nucleotide binding cleft is discussed in terms of the mechanism of ATP hydrolysis and P(i) release. Two distinct domain movements are suggested to participate in the regulation of actin. (1) High-affinity binding of Mg(2+) to actin induces a rearrangement of side chains in the nucleotide binding site leading to an increased ATPase activity and polymerizability, as well as a rotation of subdomain 2 which is mediated by the hydroxyl of serine-14. (2) Hydrolysis of ATP and subsequent release of inorganic phosphate lead to a butterfly-like opening of the actin molecule brought about by a shearing in the interdomain helix 135-150. These domain rearrangements modulate the interaction of actin with a variety of different proteins, and conversely, protein binding to actin can restrict these conformational changes, with ultimate effects on the assembly state of the microfilament system.

Conformational and dynamic differences between actin filaments polymerized from ATP- or ADP-actin monomers

Conformational and dynamic properties of actin filaments polymerized from ATP- or ADP-actin monomers were compared by using fluorescence spectroscopic methods. The fluorescence intensity of IAEDANS attached to the Cys(374) residue of actin was smaller in filaments from ADP-actin than in filaments from ATP-actin monomers, which reflected a nucleotide-induced conformational difference in subdomain 1 of the monomer. Radial coordinate calculations revealed that this conformational difference did not modify the distance of Cys(374) from the longitudinal filament axis. Temperature-dependent fluorescence resonance energy transfer measurements between donor and acceptor molecules on Cys(374) of neighboring actin protomers revealed that the inter-monomer flexibility of filaments assembled from ADP-actin monomers were substantially greater than the one of filaments from ATP-actin monomers. Flexibility was reduced by phalloidin in both types of filaments.

Effect of capping protein, CapZ, on the length of actin filaments and mechanical properties of actin filament networks

We report on how physiological concentrations of capping protein shorten actin filaments and on the remarkably fluid nature of solutions of such short filaments even at the high concentrations that exist in cells. 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 about 7 microm (2600 subunits). As observed previously with less quantitative assays, copolymerization with the actin capping protein, CapZ, reduces the length of the filaments. At cellular concentrations of capping protein, one filament forms for each molecule of capping protein and the population of filaments is uniformly short. Using CapZ to vary the length of actin filaments, we measured how their mechanical properties depend on length. The stiffness (elastic modulus) of actin filament networks depends steeply on the length, with long filaments contributing far out of proportion to their numbers to the stiffness. Even at physiological concentrations (300 microM), networks of filaments limited to lengths observed in cells with a 1 to 500 molar ratio of CapZ are more fluid and much less elastic than lower concentrations of longer actin filaments. Thus the high concentration of short actin filaments in cells must be crosslinked to produce the observed stiffness of the cortex.

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.

Microvillar Ca++ signaling: a new view of an old problem

Proceeding from the recent finding that the main components of the Ca++ signal pathway are located in small membrane protrusions on the surface of differentiated cells, called microvilli, a novel concept of cellular Ca++ signaling was developed. The main features of this concept can be summarized as follows: Microvilli are formed on the cell surface of differentiating or resting cells from exocytic membrane domains, growing out from the cell surface by elongation of an internal bundle of actin filaments. The microvillar tip membranes contain all functional important proteins synthesized such as ion channels and transporters for energy-providing substrates and structural components, which are, in rapidly growing undifferentiated cells, distributed over the whole cell surface by lateral diffusion. The microvillar shaft structure, a bundle of actin filaments, forms a dense cytoskeletal matrix tightly covered by the microvillar lipid membrane and represents an effective diffusion barrier separating the microvillar tip compartment (entrance compartment) from the cytoplasm. This diffusion barrier prevents the passage of low molecular components such as Ca++ glucose and other relevant substrates from the entrance compartment into the cytoplasm. The effectiveness of the actin-based diffusion barrier is modulated by various signal pathways and effectors, most importantly, by the actin-depolymerizing/reorganizing activity of the phospholipase C (PLC)-coupled Ca++ signaling. Moreover, the microvillar bundle of actin filaments plays a dual role in Ca++ signaling. It combines the function of a diffusion barrier, preventing Ca++ influx into the resting cell, with that of a high-affinity, ATP-dependent, and IP3-sensitive Ca++ store. Activation of Ca++ signaling via PLC-coupled receptors simultaneously empties Ca++ stores and activates the influx of external Ca++. The presented concept of Ca++ signaling is compatible with all established data on Ca++ signaling. Properties of Ca++ signaling, that could not be reconciled with the basic principles of the current hypothesis, are intrinsic properties of the new concept. Quantal Ca++ release, Ca(++)-induced Ca++ release (CICR), the coupling phenomen between the filling state of the Ca++ store and the activity of the Ca++ influx pathway, as well as the various yet unexplained complex kinetics of Ca++ uptake and release can be explained on a common mechanistic basis.

Defining actin filament length in striated muscle: rulers and caps or dynamic stability?

Actin filaments (thin filaments) are polymerized to strikingly uniform lengths in striated muscle sarcomeres. Yet, actin monomers can exchange dynamically into thin filaments in vivo, indicating that actin monomer association and dissociation at filament ends must be highly regulated to maintain the uniformity of filament lengths. We propose several hypothetical mechanisms that could generate uniform actin filament length distributions and discuss their application to the determination of thin filament length in vivo. At the Z line, titin may determine the minimum extent and tropomyosin the maximum extent of thin filament overlap by regulating alpha-actinin binding to actin, while a unique Z filament may bind to capZ and regulate barbed end capping. For the free portion of the thin filament, we evaluate possibilities that thin filament components (e.g. nebulin or the tropomyosin/troponin polymer) determine thin filament lengths by binding directly to tropomodulin and regulating pointed end capping, or alternatively, that myosin thick filaments, together with titin, determine filament length by indirectly regulating tropomodulin's capping activity.

Influence of tightly bound Mg2+ and Ca2+, nucleotides, and phalloidin on the microsecond torsional flexibility of F-actin

To better understand the relationship between structure and molecular dynamics in F-actin, we have monitored the torsional flexibility of actin filaments as a function of the type of tightly bound divalent cation (Ca2+ or Mg2+) or nucleotide (ATP or ADP), the level of inorganic phosphate and analogues, KCl concentration, and the level of phalloidin. Torsional flexibility on the microsecond time scale was monitored by measuring the steady-state phosphorescence emission anisotropy (rFA) of the triplet probe erythrosin-5-iodoacetamide covalently bound to Cys-374 of skeletal muscle actin; extrapolations to an infinite actin concentration corrected the measured anisotropy values for the influence of variable amounts of rotationally mobile G-actin in solution. The type of tightly bound divalent cation modulated the torsional flexibility of F-actin polymerized in the presence of ATP; filaments with Mg2+ bound (rFA = 0.066) at the active site cleft were more flexible than those with Ca2+ bound (rFA = 0.083). Filaments prepared from G-actin in the presence of MgADP were more flexible (rFA = 0.051) than those polymerized with MgATP; the addition of exogenous inorganic phosphate or beryllium trifluoride to ADP filaments, however, decreased the filament flexibility (increased the anisotropy) to that seen in the presence of MgATP. While variations in KCl concentration from 0 to 150 mM did not modulate the torsional flexibility of the filament, the binding of phalloidin decreased the torsional flexibility of all filaments regardless of the type of cation or nucleotide bound at the active site. These results emphasize the dynamic malleability of the actin filament, the role of the cation-nucleotide complex in modulating the torsional flexibility, and suggest that the structural differences that have previously been seen in electron micrographs of actin filaments manifest themselves as differences in torsional flexibility of the filament.