Lateral Motion and Bending of Microtubules Studied with a New Single-Filament Tracking Routine in Living Cells

The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.     

Lateral Motion and Bending of Microtubules Studied with a New Single-Filament Tracking Routine in Living Cells

The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.     

Origin of Twist-Bend Coupling in Actin Filaments

Actin filaments are semiflexible polymers that display large-scale conformational twisting and bending motions. Modulation of filament bending and twisting dynamics has been linked to regulatory actin-binding protein function, filament assembly and fragmentation, and overall cell motility. The relationship between actin filament bending and twisting dynamics has not been evaluated. The numerical and analytical experiments presented here reveal that actin filaments have a strong intrinsic twist-bend coupling that obligates the reciprocal interconversion of bending energy and twisting stress. We developed a mesoscopic model of actin filaments that captures key documented features, including the subunit dimensions, interaction energies, helicity, and geometrical constraints coming from the double-stranded structure. The filament bending and torsional rigidities predicted by the model are comparable to experimental values, demonstrating the capacity of the model to assess the mechanical properties of actin filaments, including the coupling between twisting and bending motions. The predicted actin filament twist-bend coupling is strong, with a persistence length of 0.15-0.4 μm depending on the actin-bound nucleotide. Twist-bend coupling is an emergent property that introduces local asymmetry to actin filaments and contributes to their overall elasticity. Up to 60% of the filament subunit elastic free energy originates from twist-bend coupling, with the largest contributions resulting under relatively small deformations. A comparison of filaments with different architectures indicates that twist-bend coupling in actin filaments originates from their double protofilament and helical structure.     

Apparent stiffness of vimentin intermediate filaments in living cells and its relation with other cytoskeletal polymers

The cytoskeleton is a complex network of interconnected biopolymers intimately involved in the generation and transmission of forces. Several mechanical properties of microtubules and actin filaments have been extensively explored in cells. In contrast, intermediate filaments (IFs) received comparatively less attention despite their central role in defining cell shape, motility and adhesion during physiological processes as well as in tumor progression. Here, we explored relevant biophysical properties of vimentin IFs in living cells combining confocal microscopy and a filament tracking routine that allows localizing filaments with ~20 nm precision. A Fourier-based analysis showed that IFs curvatures followed a thermal-like behavior characterized by an apparent persistence length (lp*) similar to that measured in aqueous solution. Additionally, we determined that certain perturbations of the cytoskeleton affect lp* and the lateral mobility of IFs as assessed in cells in which either the microtubule dynamic instability was reduced or actin filaments were partially depolymerized. Our results provide relevant clues on how vimentin IFs mechanically couple with microtubules and actin filaments in cells and support a role of this network in the response to mechanical stress.     

Cofilin increases the bending flexibility of actin filaments: implications for severing and cell mechanics

We determined the flexural (bending) rigidities of actin and cofilactin filaments from a cosine correlation function analysis of their thermally driven, two-dimensional fluctuations in shape. The persistence length of actin filaments is 9.8 μm, corresponding to a flexural rigidity of 0.040 pN μm². Cofilin binding lowers the persistence length ∼5-fold to a value of 2.2 μm and the filament flexural rigidity to 0.0091 pN μm². That cofilin-decorated filaments are more flexible than native filaments despite an increased mass indicates that cofilin binding weakens and redistributes stabilizing subunit interactions of filaments. We favor a mechanism in which the increased flexibility of cofilin-decorated filaments results from the linked dissociation of filament-stabilizing ions and reorganization of actin subdomain 2 and as a consequence promotes severing due to a mechanical asymmetry. Knowledge of the effects of cofilin on actin filament bending mechanics, together with our previous analysis of torsional stiffness, provide a quantitative measure of the mechanical changes in actin filaments associated with cofilin binding, and suggest that the overall mechanical and force-producing properties of cells can be modulated by cofilin activity.     

Force Production by a Bundle of Growing Actin Filaments Is Limited by Its Mechanical Properties

Bundles of actin filaments are central to a large variety of cellular structures such as filopodia, stress fibers, cytokinetic rings, and focal adhesions. The mechanical properties of these bundles are critical for proper force transmission and force bearing. Previous mathematical modeling efforts have focused on bundles’ rigidity and shape. However, it remains unknown how bundle length and buckling are controlled by external physical factors. In this work, we present a biophysical model for dynamic bundles of actin filaments submitted to an external load. In combination with in vitro motility assays of beads coated with formins, our model allowed us to characterize conditions for bead movement and bundle buckling. From the deformation profiles, we determined key biophysical properties of tethered actin bundles such as their rigidity and filament density.     

Mechanically tuning actin filaments to modulate the action of actin-binding proteins

In cells, the actin cytoskeleton is regulated by an interplay between mechanics and biochemistry. A key mechanism, which has emerged based on converging indications from structural, cellular, and biophysical data, depicts the actin filament as a mechanically tunable substrate: mechanical stress applied to an actin filament induces conformational changes, which modify the binding and the regulatory action of actin-binding proteins. For a long time, however, direct evidence of this mechanotransductive mechanism was very scarce. This situation is changing rapidly, and recent in vitro single-filament studies using different techniques have revealed that several actin-binding proteins are able to sense tension, curvature, and/or torsion, applied to actin filaments. Here, we discuss these recent advances and their possible implications.     

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.     

Tracking single particles and elongated filaments with nanometer precision

Recent developments in image processing have greatly advanced our understanding of biomolecular processes in vitro and in vivo. In particular, using Gaussian models to fit the intensity profiles of nanometer-sized objects have enabled their two-dimensional localization with a precision in the one-nanometer range. Here, we present an algorithm to precisely localize curved filaments whose structures are characterized by subresolution diameters and micrometer lengths. Using surface-immobilized microtubules, fluorescently labeled with rhodamine, we demonstrate positional precisions of ∼2 nm when determining the filament centerline and ∼9 nm when localizing the filament tips. Combined with state-of-the-art single particle tracking we apply the algorithm 1), to motor-proteins stepping on immobilized microtubules, 2), to depolymerizing microtubules, and 3), to microtubules gliding over motor-coated surfaces.     

Nucleation limits the lengths of actin filaments assembled by formin

Formins stimulate actin polymerization by promoting both filament nucleation and elongation. Because nucleation and elongation draw upon a common pool of actin monomers, the rate at which each reaction proceeds influences the other. This interdependent mechanism determines the number of filaments assembled over the course of a polymerization reaction, as well as their equilibrium lengths. In this study, we used kinetic modeling and in vitro polymerization reactions to dissect the contributions of filament nucleation and elongation to the process of formin-mediated actin assembly. We found that the rates of nucleation and elongation evolve over the course of a polymerization reaction. The period over which each process occurs is a key determinant of the total number of filaments that are assembled, as well as their average lengths at equilibrium. Inclusion of formin in polymerization reactions speeds filament nucleation, thus increasing the number and shortening the lengths of filaments that are assembled over the course of the reaction. Modulation of the elongation rate produces modest changes in the equilibrium lengths of formin-bound filaments. However, the dependence of filament length on the elongation rate is limited by the number of filament ends generated via formin’s nucleation activity. Sustained elongation of small numbers of formin-bound filaments, therefore, requires inhibition of nucleation via monomer sequestration and a low concentration of activated formin. Our results underscore the mechanistic advantage for keeping formin’s nucleation efficiency relatively low in cells, where unregulated actin assembly would produce deleterious effects on cytoskeletal dynamics. Under these conditions, differences in the elongation rates mediated by formin isoforms are most likely to impact the kinetics of actin assembly.     

Multi-Platform Compatible Software for Analysis of Polymer Bending Mechanics

Cytoskeletal polymers play a fundamental role in the responses of cells to both external and internal stresses. Quantitative knowledge of the mechanical properties of those polymers is essential for developing predictive models of cell mechanics and mechano-sensing. Linear cytoskeletal polymers, such as actin filaments and microtubules, can grow to cellular length scales at which they behave as semiflexible polymers that undergo thermally-driven shape deformations. Bending deformations are often modeled using the wormlike chain model. A quantitative metric of a polymer''s resistance to bending is the persistence length, the fundamental parameter of that model. A polymer''s bending persistence length is extracted from its shape as visualized using various imaging techniques. However, the analysis methodologies required for determining the persistence length are often not readily within reach of most biological researchers or educators. Motivated by that limitation, we developed user-friendly, multi-platform compatible software to determine the bending persistence length from images of surface-adsorbed or freely fluctuating polymers. Three different types of analysis are available (cosine correlation, end-to-end and bending-mode analyses), allowing for rigorous cross-checking of analysis results. The software is freely available and we provide sample data of adsorbed and fluctuating filaments and expected analysis results for educational and tutorial purposes.     

Mechanism of Calponin Stabilization of Cross-Linked Actin Networks

The actin-binding protein calponin has been previously implicated in actin cytoskeletal regulation and is thought to act as an actin stabilizer, but the mechanism of its function is poorly understood. To investigate this underlying physical mechanism, we studied an in vitro model system of cross-linked actin using bulk rheology. Networks with basic calponin exhibited a delayed onset of strain stiffening (10.0% without calponin, 14.9% with calponin) and were able to withstand a higher maximal strain before failing (35% without calponin, 56% with calponin). Using fluorescence microscopy to study the mechanics of single actin filaments, we found that calponin increased the flexibility of actin filaments, evident as a decrease in persistence length from 17.6 μm without to 7.7 μm with calponin. Our data are consistent with current models of affine strain behavior in semiflexible polymer networks, and suggest that calponin stabilization of actin networks can be explained purely by changes in single-filament mechanics. We propose a model in which calponin stabilizes actin networks against shear through a reduction of persistence length of individual filaments.     

Bending dynamics of fluctuating biopolymers probed by automated high-resolution filament tracking

Microscope images of fluctuating biopolymers contain a wealth of information about their underlying mechanics and dynamics. However, successful extraction of this information requires precise localization of filament position and shape from thousands of noisy images. Here, we present careful measurements of the bending dynamics of filamentous (F-)actin and microtubules at thermal equilibrium with high spatial and temporal resolution using a new, simple but robust, automated image analysis algorithm with subpixel accuracy. We find that slender actin filaments have a persistence length of approximately 17 microm, and display a q(-4)-dependent relaxation spectrum, as expected from viscous drag. Microtubules have a persistence length of several millimeters; interestingly, there is a small correlation between total microtubule length and rigidity, with shorter filaments appearing softer. However, we show that this correlation can arise, in principle, from intrinsic measurement noise that must be carefully considered. The dynamic behavior of the bending of microtubules also appears more complex than that of F-actin, reflecting their higher-order structure. These results emphasize both the power and limitations of light microscopy techniques for studying the mechanics and dynamics of biopolymers.     

Relationship between the flexibility and the motility of actin filaments: effects of pH

Both the sliding velocity of fluorescently labeled actin filament and its persistence length as an index of the bending flexibility of the filament were examined in the motility assay as varying the pH values of the solution for preparing actin filaments. When the pH value was varied from 5.0 to 9.0 in the solution in which actin filaments were formed from the constituent monomers, the motile performance of Mg²⁺ bound actin filaments (Mg-F-actin) was apparently suppressed compared to the case of Ca²⁺ bound ones (Ca-F-actin). The persistence length for Ca-F-actin gradually increased with the increase of the pH value while the similar length for Mg-F-actin remained rather independent of the value. The largest sliding velocity of the filament, on the other hand, obtained at the persistence length of roughly 6 μm for both cases of Mg-F-actin and Ca-F-actin.     

A mechanochemical model of actin filaments

In eukaryotic cells, actin filaments are involved in important processes such as motility, division, cell shape regulation, contractility, and mechanosensation. Actin filaments are polymerized chains of monomers, which themselves undergo a range of chemical events such as ATP hydrolysis, polymerization, and depolymerization. When forces are applied to F-actin, in addition to filament mechanical deformations, the applied force must also influence chemical events in the filament. We develop an intermediate-scale model of actin filaments that combines actin chemistry with filament-level deformations. The model is able to compute mechanical responses of F-actin during bending and stretching. The model also describes the interplay between ATP hydrolysis and filament deformations, including possible force-induced chemical state changes of actin monomers in the filament. The model can also be used to model the action of several actin-associated proteins, and for large-scale simulation of F-actin networks. All together, our model shows that mechanics and chemistry must be considered together to understand cytoskeletal dynamics in living cells.     

Mechanotransduction down to individual actin filaments

The actin cytoskeleton plays an essential role in a cell's ability to generate and sense forces, both internally and in interaction with the outside world. The transduction of mechanical cues into biochemical reactions in cells, in particular, is a multi-scale process which requires a variety of approaches to be understood. This review focuses on understanding how mechanical stress applied to an actin filament can affect its assembly dynamics. Today, experiments addressing this issue at the scale of individual actin filaments are emerging and bring novel insight into mechanotransduction. For instance, recent data show that actin filaments can act as mechanosensors, as an applied tension or curvature alters their conformation and their affinity for regulatory proteins. Filaments can also transmit mechanical tension to other proteins, which consequently change the way they interact with the filaments to regulate their assembly. These results provide evidence for mechanotransduction at the scale of individual filaments, showing that forces participate in the regulation of filament assembly and organization. They bring insight into the elementary events coupling mechanics and biochemistry in cells. The experiments presented here are linked to recent technical developments, and certainly announce the advent of more exciting results in the future.     

Modulation of actin mechanics by caldesmon and tropomyosin

The ability of cells to sense and respond to physiological forces relies on the actin cytoskeleton, a dynamic structure that can directly convert forces into biochemical signals. Because of the association of muscle actin-binding proteins (ABPs) may affect F-actin and hence cytoskeleton mechanics, we investigated the effects of several ABPs on the mechanical properties of the actin filaments. The structural interactions between ABPs and helical actin filaments can vary between interstrand interactions that bridge azimuthally adjacent actin monomers between filament strands (i.e. by molecular stapling as proposed for caldesmon) or, intrastrand interactions that reinforce axially adjacent actin monomers along strands (i.e. as in the interaction of tropomyosin with actin). Here, we analyzed thermally driven fluctuations in actin's shape to measure the flexural rigidity of actin filaments with different ABPs bound. We show that the binding of phalloidin increases the persistence length of actin by 1.9-fold. Similarly, the intrastrand reinforcement by smooth and skeletal muscle tropomyosins increases the persistence length 1.5- and 2- fold respectively. We also show that the interstrand crosslinking by the C-terminal actin-binding fragment of caldesmon, H32K, increases persistence length by 1.6-fold. While still remaining bound to actin, phosphorylation of H32K by ERK abolishes the molecular staple (Foster et al. 2004. J Biol Chem 279;53387-53394) and reduces filament rigidity to that of actin with no ABPs bound. Lastly, we show that the effect of binding both smooth muscle tropomyosin and H32K is not additive. The combination of structural and mechanical studies on ABP-actin interactions will help provide information about the biophysical mechanism of force transduction in cells.     

Assessing the flexibility of intermediate filaments by atomic force microscopy

Eukaryotic cells contain three cytoskeletal filament systems that exhibit very distinct assembly properties, supramolecular architectures, dynamic behaviour and mechanical properties. Microtubules and microfilaments are relatively stiff polar structures whose assembly is modulated by the state of hydrolysis of the bound nucleotide. In contrast, intermediate filaments (IFs) are more flexible apolar structures assembled from a approximately 45 nm long coiled-coil dimer as the elementary building block. The differences in flexibility that exist among the three filament systems have been described qualitatively by comparing electron micrographs of negatively stained dehydrated filaments and by directly measuring the persistence length of F-actin filaments (approximately 3-10 microm) and microtubules (approximately 1-8 mm) by various physical methods. However, quantitative data on the persistence length of IFs are still missing. Toward this goal, we have carried out atomic force microscopy (AFM) in physiological buffer to characterise the morphology of individual vimentin IFs adsorbed to different solid supports. In addition, we compared these images with those obtained by transmission electron microscopy (TEM) of negatively stained dehydrated filaments. For each support, we could accurately measure the apparent persistence length of the filaments, yielding values ranging between 0.3 microm and 1 microm. Making simple assumptions concerning the adsorption mechanism, we could estimate the persistence length of an IF in a dilute solution to be approximately 1 microm, indicating that the lower measured values reflect constraints induced by the adsorption process of the filaments on the corresponding support. Based on our knowledge of the structural organisation and mechanical properties of IFs, we reason that the lower persistence length of IFs compared to that of F-actin filaments is caused by the presence of flexible linker regions within the coiled-coil dimer and by postulating the occurrence of axial slipping between dimers within IFs.     

Regulation of Actin by Ion-Linked Equilibria

Actin assembly, filament mechanical properties, and interactions with regulatory proteins depend on the types and concentrations of salts in solution. Salts modulate actin through both nonspecific electrostatic effects and specific binding to discrete sites. Multiple cation-binding site classes spanning a broad range of affinities (nanomolar to millimolar) have been identified on actin monomers and filaments. This review focuses on discrete, low-affinity cation-binding interactions that drive polymerization, regulate filament-bending mechanics, and modulate interactions with regulatory proteins. Cation binding may be perturbed by actin post-translational modifications and linked equilibria. Partial cation occupancy under physiological and commonly used in vitro solution conditions likely contribute to filament mechanical heterogeneity and structural polymorphism. Site-specific cation-binding residues are conserved in Arp2 and Arp3, and may play a role in Arp2/3 complex activation and actin-filament branching activity. Actin-salt interactions demonstrate the relevance of ion-linked equilibria in the operation and regulation of complex biological systems.     

Fragmentation is crucial for the steady-state dynamics of actin filaments

Despite the recognition that actin filaments are important for numerous cellular processes, and decades of investigation, the dynamics of in vitro actin filaments are still not completely understood. Here, we follow the time evolution of the length distribution of labeled actin reporter filaments in an unlabeled F-actin solution via fluorescence microscopy. Whereas treadmilling and diffusive length fluctuations cannot account for the observed dynamics, our results suggest that at low salt conditions, spontaneous fragmentation is crucial.