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1.
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.  相似文献   

2.
Origin of Twist-Bend Coupling in Actin Filaments   总被引:1,自引:0,他引:1  
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.  相似文献   

3.
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.  相似文献   

4.
《Biophysical journal》2022,121(10):1813-1822
Cytoskeletal filaments, such as microtubules and actin filaments, play important roles in the mechanical integrity of cells and the ability of cells to respond to their environment. Measuring the mechanical properties of cytoskeletal structures is crucial for gaining insight into intracellular mechanical stresses and their role in regulating cellular processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring filament deformations, such as Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature distributions can be used as an alternative tool to quantify biofilament deformations, and investigate how the apparent stiffness of filaments depends on the resolution and noise of the imaging system. We present analytical calculations of the scaling curvature distributions as a function of filament discretization, and test our predictions by comparing Monte Carlo simulations with results from existing techniques. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of nonfunctional motors, and calculate the persistence length of these filaments. The presented curvature analysis is significantly more accurate compared with existing approaches for small data sets, and can be readily applied to both in vitro and in vivo filament data through the use of the open-source codes we provide.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
A theory and graphical presentation for the analysis of helix structure and deformations in oligonucleotides is presented. The parameters “persistence” and “flexibility” as defined in the configurational statistics of polymers of infinite length are reformulated at the oligonucleotide level in an extension of J. A. Schellman's method [(1974) Biopolymers, Vol. 17, pp. 217–226], and used as a basis for a systematic “Persistence Analysis” of the helix deformation properties for all possible subsequences in the structure. The basis for the analysis is a set of link vectors referenced to individual base pairs, and is limited to sequences exhibiting only perturbed rod-like behavior, i.e., below the threshold for supercoiling. The present application of the method is concerned with a physical model for the angular component of bending, so the link vectors are defined as the unit components of a global helix axis obtained by the procedure “Curves” of R. Lavery and H. Sklenar [(1988) J. Biomol. Struct. Dynam., Vol. 6, pp. 63–91; (1989) J. Biomol. Struct. Dynam., Vol. 6, pp. 655–667]. A discussion, of the relationship between global bending and relative orientation of base pairs is provided. Our approach is illustrated by analysis of some model oligonucleotide structures with intrinsic kinks, the crystal structure of the dodecamer d (CGCGAATTCGCG)2, and the results of two molecular dynamics simulations on this dodecamer using two variations of the GROMOS force field. The results indicate that essentially all aspects of curvature in short oligonucleotides can be determined, such as the position and orientation of each bend, the sharpness or smoothness, and the location and linearity of subsequences. In the case of molecular dynamics simulations, where a Boltzmann ensemble of structures is analyzed, the spatial extent of the deformations (flexibility) is also considered. © 1993 John Wiley & Sons, Inc.  相似文献   

8.
Abstract

The conformation of single stranded oligonucleotides is analysed by measurements of their rotation time constants. The oligomers are aligned to some degree by short electric field pulses; after pulse termination the transition to a random orientation is followed by measurements of the linear dichroism. An efficient deconvolution procedure is developed for evaluation of the experimental data obtained in the ns-time range. The increase of rotation time constants observed for chain lengths in the range from 14 to 22 residues are interpreted according to a weakly bending rod model providing a persistence length and a Stokes' diameter. The Stokes' diameters obtained for ribo- and deoxyriboadenylates are about 13Å, in approximate agreement with the expectation for a single stranded helix. The persistence length L = 53Å corresponding to ~16 nucleotide residues found for riboadenylates at 2°C appears to reflect relatively strong stacking interactions at this temperature. However, a comparison with the average length of stacked residues evaluated from available thermodynamic parameters of base stacking indicate that unstacked residues are not completely flexible. Apparently the ribose-phosphate chain provides an essential contribution to the stiffness of oligomers and polymers, even when the bases are unstacked. Addition of 100μM Mg2+ leads to an increase of the persistence length to 88Å. Corresponding measurements with deoxyriboadenylates show a slightly lower value of the persistence length than that found for riboadenylates. Addition of LysTrpLys and LysTyrLys to A(pA)19 leads to an increase of the rotation time constant, which corresponds approximately to a length increment by one residue per bound peptide. Since controls performed with LysLeuLys do not show any similar effect, the increase of the time constants induced by LysTrpLys and LysTyrLys is attributed to intercalation of the aromatic amino acids.  相似文献   

9.
Mechanical manipulation of single cytoskeleton filaments and their monitoring over long times is difficult because of fluorescence bleaching or phototoxic protein degradation. The integration of label-free microscopy techniques, capable of imaging freely diffusing, weak scatterers such as microtubules (MTs) in real-time, and independent of their orientation, with optical trapping and tracking systems, would allow many new applications. Here, we show that rotating-coherent-scattering microscopy (ROCS) in dark-field mode can also provide strong contrast for structures far from the coverslip such as arrangements of isolated MTs and networks. We could acquire thousands of images over up to 30 min without loss in image contrast or visible photodamage. We further demonstrate the combination of ROCS imaging with fast and nanometer-precise 3D interferometric back-focal-plane tracking of multiple beads in time-shared optical traps using acoustooptic deflectors to specifically construct and microrheologically probe small microtubule networks with well-defined geometries. Thereby, we explore the frequency-dependent elastic response of single microtubule filaments between 0.5 Hz and 5 kHz, which allows for investigating their viscoelastic response up to the fourth-order bending mode. Our spectral analysis reveals constant filament stiffness at low frequencies and frequency-dependent stiffening following a power law ~ωp with a length-dependent exponent p(L). We find further evidence for the dependence of the MT persistence length on the contour length L, which is still controversially debated. We could also demonstrate slower stiffening at high frequencies for longer filaments, which we believe is determined by the molecular architecture of the MT. Our results shed new light on the nanomechanics of this essential, multifunctional cytoskeletal element and pose new questions about the adaptability of the cytoskeleton.  相似文献   

10.
Single actin filaments were analyzed in solutions ranging from dilute (0.2 microgram/ml), where filaments interact only with solvent, to concentrations (4.0 mg/ml) at which F-actin forms a nematic phase. A persistence length of approximately 1.8 microns and an average length of approximately 22 microns (Kaufmann et al., 1992) identify actin as a model for studying the dynamics of semiflexible polymers. In dilute solutions the filaments exhibit thermal bending undulations in addition to diffusive motion. At higher semidilute concentrations (1.4 mg/ml) three-dimensional reconstructions of confocal images of fluorescently labeled filaments in a matrix of unlabeled F-actin reveal steric interactions between filaments, which account for the viscoelastic behavior of these solutions. The restricted undulations of these labeled chains reveal the virtual tube formed around a filament by the surrounding actin. The average tube diameter <a> scales with monomer concentration c as <a> varies; is directly proportional to c-(0.5 +/- 0.15). The diffusion of filaments in semidilute solutions (c = (0.1-2.0) mg/ml) is dominated by diffusion along the filament contour (reptation), and constraint release by remodeling of the surrounding filaments is rare. The self-diffusion coefficient D parallel along the tube decreases linearly with the chain length for semidilute solutions. For concentrations > 2.5 mg/ml a transition occurs from an isotropic entangled phase to a coexistence between isotropic and nematic domains. Analysis of the molecular motions of filaments suggests that the filaments in the aligned domains are in thermal equilibrium and that the diffusion coefficient parallel to the director D parallel is nearly independent of filament length. We also report the novel direct observation of u-shaped defects, called hairpins, in the nematic domains.  相似文献   

11.
The actin regulatory protein, cofilin, increases the bending and twisting elasticity of actin filaments and severs them. It has been proposed that filaments partially decorated with cofilin accumulate stress from thermally driven shape fluctuations at bare (stiff) and decorated (compliant) boundaries, thereby promoting severing. This mechanics-based severing model predicts that changes in actin filament compliance due to cofilin binding affect severing activity. Here, we test this prediction by evaluating how the severing activities of vertebrate and yeast cofilactin scale with the flexural rigidities determined from analysis of shape fluctuations. Yeast actin filaments are more compliant in bending than vertebrate actin filaments. Severing activities of cofilactin isoforms correlate with changes in filament flexibility. Vertebrate cofilin binds but does not increase the yeast actin filament flexibility, and does not sever them. Imaging of filament thermal fluctuations reveals that severing events are associated with local bending and fragmentation when deformations attain a critical angle. The critical severing angle at boundaries between bare and cofilin-decorated segments is smaller than in bare or fully decorated filaments. These measurements support a cofilin-severing mechanism in which mechanical asymmetry promotes local stress accumulation and fragmentation at boundaries of bare and cofilin-decorated segments, analogous to failure of some nonprotein materials.  相似文献   

12.
The bacterial cytoskeleton guides the synthesis of cell wall and thus regulates cell shape. Because spatial patterning of the bacterial cytoskeleton is critical to the proper control of cell shape, it is important to ask how the cytoskeleton spatially self-organizes in the first place. In this work, we develop a quantitative model to account for the various spatial patterns adopted by bacterial cytoskeletal proteins, especially the orientation and length of cytoskeletal filaments such as FtsZ and MreB in rod-shaped cells. We show that the combined mechanical energy of membrane bending, membrane pinning, and filament bending of a membrane-attached cytoskeletal filament can be sufficient to prescribe orientation, e.g., circumferential for FtsZ or helical for MreB, with the accuracy of orientation increasing with the length of the cytoskeletal filament. Moreover, the mechanical energy can compete with the chemical energy of cytoskeletal polymerization to regulate filament length. Notably, we predict a conformational transition with increasing polymer length from smoothly curved to end-bent polymers. Finally, the mechanical energy also results in a mutual attraction among polymers on the same membrane, which could facilitate tight polymer spacing or bundling. The predictions of the model can be verified through genetic, microscopic, and microfluidic approaches.  相似文献   

13.
Despite the fundamental role of thick filaments in muscle contraction, little is known about the mechanical behavior of these filaments and how myosin-associated proteins dictate differences between muscle types. In this study, we used atomic force microscopy to study the morphological and mechanical properties of fully hydrated native thick filaments isolated from indirect flight muscle (IFM) of normal and mutant Drosophila lacking flightin (fln0). IFM thick filaments from newly eclosed (0-1 h old) wild-type flies have a mean length of 3.04 ± 0.05 μm. In contrast, IFM thick filaments from newly eclosed fln0 flies are more variable in length and, on average, are significantly longer (3.90 ± 1.33 μm) than wild-type filaments from flies of the same age. In the absence of flightin, thick filaments can attain lengths > 300% of wild-type filaments, indicating that flightin is required for setting the proper filament length in vivo. Filaments lacking flightin are structurally compromised, and filament preparations from fully matured 3- to 5-day-old adult fln0 IFM yielded fragments of variable length much shorter than 3.20 ± 0.04 μm, the length obtained from wild-type flies of similar age. The persistence length, an index of bending stiffness, was calculated from measurements of filament end-to-end length and contour length. We show that the presence of flightin increases persistence length by more than 40% and that wild-type filaments increase in stiffness with age. These results indicate that flightin fulfills an essential role in defining the structural and mechanical properties of IFM thick filaments.  相似文献   

14.
《Biophysical journal》2023,122(1):30-42
The organization of the actin cytoskeleton is impacted by the interplay between physical confinement, features of cross-linking proteins, and deformations of semiflexible actin filaments. Some cross-linking proteins preferentially bind filaments in parallel, although others bind more indiscriminately. However, a quantitative understanding of how the mode of binding influences the assembly of actin networks in confined environments is lacking. Here we employ coarse-grained computer simulations to study the dynamics and organization of semiflexible actin filaments in confined regions upon the addition of cross-linkers. We characterize how the emergent behavior is influenced by the system shape, the number and type of cross-linking proteins, and the length of filaments. Structures include isolated clusters of filaments, highly connected filament bundles, and networks of interconnected bundles and loops. Elongation of one dimension of the system promotes the formation of long bundles that align with the elongated axis. Dynamics are governed by rapid cross-linking into aggregates, followed by a slower change in their shape and connectivity. Cross-linking decreases the average bending energy of short or sparsely connected filaments by suppressing shape fluctuations. However, it increases the average bending energy in highly connected networks because filament bundles become deformed, and small numbers of filaments exhibit long-lived, highly unfavorable configurations. Indiscriminate cross-linking promotes the formation of high-energy configurations due to the increased likelihood of unfavorable, difficult-to-relax configurations at early times. Taken together, this work demonstrates physical mechanisms by which cross-linker binding and physical confinement impact the emergent behavior of actin networks, which is relevant both in cells and in synthetic environments.  相似文献   

15.
Membrane nanotubes, ubiquitous in cellular systems, adopt a spectrum of curvatures and shapes that are dictated by their intrinsic physical characteristics as well as their interactions with the local cellular environment. A high bending flexibility is needed in the crowded cytoplasm where tubes often need to bend significantly in the axial direction at sub-micron length scales. We find the stiffness of spontaneously formed membrane nanotubes by measuring the persistence length of reconstituted membrane nanotubes freely suspended in solution and imaged by fluorescence microscopy. By quantifying the tube diameter we demonstrate for the first time that the persistence length scales linearly with radius. Although most tubes are uni-lamellar, the predicted linear scaling between tube radius and persistence length allows us to identify tubes that spontaneously form as multilamellar structures upon hydration. We provide the first experimental evidence that illumination of lipid fluorophores can have a profound effect on the lipid bilayer which we sensitively detect as a continuous change in the tube persistence length with time. The novel assay and methodology here presented has potential for quantification of the structural reinforcement of membrane tubes by scaffolding proteins.  相似文献   

16.
Microtubules (MTs) are dynamic cytoskeletal elements involved in numerous cellular processes. Although they are highly rigid polymers with a persistence length of 1–8 mm, they may exhibit a curved shape at a scale of few micrometers within cells, depending on their biological functions. However, how MT flexural rigidity in cells is regulated remains poorly understood. Here we ask whether MT-associated proteins (MAPs) could locally control the mechanical properties of MTs. We show that two major cross-linkers of the conserved MAP65/PRC1/Ase1 family drastically decrease MT rigidity. Their MT-binding domain mediates this effect. Remarkably, the softening effect of MAP65 observed on single MTs is maintained when MTs are cross-linked. By reconstituting physical collisions between growing MTs/MT bundles, we further show that the decrease in MT stiffness induced by MAP65 proteins is responsible for the sharp bending deformations observed in cells when they coalign at a steep angle to create bundles. Taken together, these data provide new insights into how MAP65, by modifying MT mechanical properties, may regulate the formation of complex MT arrays.  相似文献   

17.
Single-molecule imaging is widely used to determine statistical distributions of molecular properties. One such characteristic is the bending flexibility of biological filaments, which can be parameterized via the persistence length. Quantitative extraction of persistence length from images of individual filaments requires both the ability to trace the backbone of the chains in the images and sufficient chain statistics to accurately assess the persistence length. Chain tracing can be a tedious task, performed manually or using algorithms that require user input and/or supervision. Such interventions have the potential to introduce user-dependent bias into the chain selection and tracing. Here, we introduce a fully automated algorithm for chain tracing and determination of persistence lengths. Dubbed “AutoSmarTrace,” the algorithm is built off a neural network, trained via machine learning to identify filaments within images recorded using atomic force microscopy. We validate the performance of AutoSmarTrace on simulated images with widely varying levels of noise, demonstrating its ability to return persistence lengths in agreement with input simulation parameters. Persistence lengths returned from analysis of experimental images of collagen and DNA agree with previous values obtained from these images with different chain-tracing approaches. Although trained on atomic-force-microscopy-like images, the algorithm also shows promise to identify chains in other single-molecule imaging approaches, such as rotary-shadowing electron microscopy and fluorescence imaging.  相似文献   

18.
We determined and correlated the rigidity of Salmonella typhimurium, Escherichia coli, and Rhizobium lupini flagellar filaments representing various structural and polymorphic states (plain, complex, straight, superhelical, and right- and left-handed). Persistence length, from which the filament's rigidity and other parameters (Young's modulus, bending force constant, buckling persistence length, flexural deformation, and flexural time) were derived, was determined from electron micrographs of isolated, negatively stained filaments. Outer diameters and radii of strong intersubunit connectivity were determined from three-dimensional image reconstructions and radial mass density profiles from scanning transmission electron microscopy. All filaments appear to be highly rigid with no evident correlation with their helical sense or superhelicity. The complex filament of R. lupini is rigid to the extent that it becomes brittle. The overall flexibility of the flagellum seems to stem mainly from the hook and not from the filament. Polymorphism is probably related to the propelling properties and hydrodynamic shape of the filament rather than to its rigidity.  相似文献   

19.
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.  相似文献   

20.
Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarly on the interaction strength between the filament and the support: i) For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii) For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a ‘trapping’ mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these ‘ideal’ adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica (‘ideal’ trapping) and on glass (‘ideal’ equilibrated) with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions.  相似文献   

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