Measurement of the persistence length of cytoskeletal filaments using curvature distributions

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.     

Cardiac Myosin Binding Protein-C Is Essential for Thick-Filament Stability and Flexural Rigidity

Using atomic force microscopy, we examined the contribution of cardiac myosin binding protein-C (cMyBP-C) to thick-filament length and flexural rigidity. Native thick filaments were isolated from the hearts of transgenic mice bearing a truncation mutation of cMyBP-C (t/t) that results in no detectable cMyBP-C and from age-matched wild-type controls (+/+). Atomic force microscopy images of these filaments were evaluated with an automated analysis algorithm that identified filament position and shape. The t/t thick-filament length (1.48 ± 0.02 μm) was significantly (P < 0.01) shorter than +/+ (1.56 ± 0.02 μm). This 5%-shorter thick-filament length in the t/t was reflected in 4% significantly shorter sarcomere lengths of relaxed isolated cardiomyocytes of the t/t (1.97 ± 0.01 μm) compared to +/+ (2.05 ± 0.01 μm). To determine if cMyBP-C contributes to the mechanical properties of thick filaments, we used statistical polymer chain mechanics to calculate a per-filament-specific persistence length, an index of flexural rigidity directly proportional to Young's modulus. Thick-filament-specific persistence length in the t/t (373 ± 62 μm) was significantly lower than in +/+ (639 ± 101 μm). Accordingly, Young's modulus of t/t thick filaments was ∼60% of +/+. These results provide what we consider a new understanding for the critical role of cMyBP-C in defining normal cardiac output by sustaining force and muscle stiffness.     

Interactive measurement and characterization of DNA molecules by analysis of AFM images.

BACKGROUND: In the past few years, computer-based analysis of atomic-force microscopic images has acquired increasing importance for studying biomolecules such as DNA. On the one hand, fully automated methods do not allow analysis of complex shapes; on the other hand, manual methods are usually time consuming and inaccurate. The semiautomated approach presented in this report overcomes the drawbacks of both methods. METHODS: Two kinds of images were analyzed: computer-generated filaments that modeled circular DNA molecules on a surface and real atomic-force microscopic images of DNA molecules adsorbed on an appropriate substrate surface. RESULTS: The algorithm was tested on a group of 140 simulated and 189 real plasmids with a nominal length of 913 nm. The accuracy of the length measurement was statistically evaluated on the ensemble of molecules, with particular attention to the influence of the noise. Mean contour lengths of 912 +/- 5 nm and 910 +/- 47 nm were found for simulated and real plasmids, respectively. The measured end-to-end distance of lambda-DNA molecules as a function of their contour length is reported, from which it is possible to estimate the stiffness of the DNA molecules adsorbed onto a surface; the value obtained for the DNA persistence length (42 +/- 5 nm) is consistent with values measured by other imaging techniques. CONCLUSIONS: An interactive algorithm for DNA molecule measurements based on the detection of the filament ridge line in a digitized image is presented. The simulation of artificial filaments combined with the experimental data demonstrates that the proposed method can be a valuable tool for the DNA contour length evaluation, especially in the case of complex shapes where the use of automatic methods is not possible.     

F-actin, a model polymer for semiflexible chains in dilute, semidilute, and liquid crystalline solutions.

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.     

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.     

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.     

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.     

Monte Carlo generation of polypeptide random coil conformations; the persistence vector and the chain vector distribution

Polypeptide random coil conformations of various chain lenghts (N = 5, 10, 20, 40, 80 peptide units) are generated by a Monte Carlo procedure. The characteristic ratio obtained for the sets of generated conformations is identical with the exact value calculated with the average transformation matrix procedure, indicating the equivalence of the two treatments. On the basic of the generated sets of conformations the length and direction of the persistence vector (the averaged chain vector expressed in the reference frame of the first two skeletal bonds) are investigated for various chain lengths. The radial distribution function for the chain vector shows the length of the chain vector for small polypeptides (N = 5, 10) not to deviate far from its most probable value. Also for larger chains up to chains of 80 peptide units very significant deviations from a gaussian distribution are observed.The distribution of the length of the vector connecting the remote end of the chain with the end of the persistence vector exhibited behavior much doser to the gaussian approximation, an improvement especially significant for the short chains.     

Automated segmentation of electron tomograms for a quantitative description of actin filament networks

Cryo-electron tomography allows to visualize individual actin filaments and to describe the three-dimensional organization of actin networks in the context of unperturbed cellular environments. For a quantitative characterization of actin filament networks, the tomograms must be segmented in a reproducible manner. Here, we describe an automated procedure for the segmentation of actin filaments, which combines template matching with a new tracing algorithm. The result is a set of lines, each one representing the central line of a filament. As demonstrated with cryo-tomograms of cellular actin networks, these line sets can be used to characterize filament networks in terms of filament length, orientation, density, stiffness (persistence length), or the occurrence of branching points.     

A Monte-Carlo estimate of DNA loop formation

The ends of rather short double-helical DNA segments (approximately two persistence lengths) can be enzymatically joined to form closed circles. Such covalent closure into circles is a measure of the likelihood of the two ends of the DNA coming into close contact. There is a length of DNA for which loop formation is most likely to occur. We have determined the chain-length dependence of loop formation for stiff chains using computer-generated chains of cylinders. The distribution from which the values for the angles between cylinders were chosen relates the chain parameters to a given chain persistence. Our results are compared with those of other theories, including a statistical wormlike chain model, and with the experimental measurements for ring closure of DNA restriction fragments.     

Filamentous Biopolymers on Surfaces: Atomic Force Microscopy Images Compared with Brownian Dynamics Simulation of Filament Deposition

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.     

Deconstructing the late phase of vimentin assembly by total internal reflection fluorescence microscopy (TIRFM)

Quantitative imaging of intermediate filaments (IF) during the advanced phase of the assembly process is technically difficult, since the structures are several μm long and therefore they exceed the field of view of many electron (EM) or atomic force microscopy (AFM) techniques. Thereby quantitative studies become extremely laborious and time-consuming. To overcome these difficulties, we prepared fluorescently labeled vimentin for visualization by total internal reflection fluorescence microscopy (TIRFM). In order to investigate if the labeling influences the assembly properties of the protein, we first determined the association state of unlabeled vimentin mixed with increasing amounts of labeled vimentin under low ionic conditions by analytical ultracentrifugation. We found that bona fide tetrameric complexes were formed even when half of the vimentin was labeled. Moreover, we demonstrate by quantitative atomic force microscopy and electron microscopy that the morphology and the assembly properties of filaments were not affected when the fraction of labeled vimentin was below 10%. Using fast frame rates we observed the rapid deposition of fluorescently labeled IFs on glass supports by TIRFM in real time. By tracing their contours, we have calculated the persistence length of long immobilized vimentin IFs to 1 μm, a value that is identical to those determined for shorter unlabeled vimentin. These results indicate that the structural properties of the filaments were not affected significantly by the dye. Furthermore, in order to analyze the late elongation phase, we mixed long filaments containing either Alexa 488- or Alexa 647-labeled vimentin. The 'patchy' structure of the filaments obtained unambiguously showed the elongation of long IFs through direct end-to-end annealing of individual filaments.     

Atomic force microscopy of long and short double-stranded, single-stranded and triple-stranded nucleic acids.

Atomic force microscopy (AFM, also called scanning force microscopy) is proving to be a useful technique for imaging DNA. Thus it is important to push the limits of AFM imaging in order to explore both what types of DNA can be reliably imaged and identified and also what substrates and methods of sample preparation are suitable. The following advances in AFM of DNA are presented here. (i) DNA molecules as short as 25 bases can be seen by AFM. The short single-stranded DNAs imaged here (25 and 50 bases long) appeared globular in the AFM, perhaps because they are all capable of intramolecular base pairing and because the DNAs were in a Mg(ll) buffer, which facilitates intramolecular cross-bridging. (ii) AFM images in air of short double-stranded DNA molecules, 100-200 bp, gave lengths consistent with A-DNA. (iii) AFM images of poly (A) show both short bent lumpy molecules with an apparent persistence length of 40 nm and long straight molecules with an apparent persistence length of 600 nm. For comparison, the apparent persistence length for double-stranded DNA from phX-174 under the same conditions was 80 nm. (iv) Structures believed to be triple- stranded DNA were seen in samples of poly(dA.poly(dT) and poly (dG).poly(dC). These structures were twice as high as double-stranded DNA and the same width. (v) Entire molecules of lambda DNA, approx. 16 micron long, were imaged clearly in overlapping scans. (vi) Plasmid DNA was imaged on oxidized silicon, although less clearly than on mica.     

Mechanics and structure of titin oligomers explored with atomic force microscopy

Titin is a giant polypeptide that spans half of the striated muscle sarcomere and generates passive force upon stretch. To explore the elastic response and structure of single molecules and oligomers of titin, we carried out molecular force spectroscopy and atomic force microscopy (AFM) on purified full-length skeletal-muscle titin. From the force data, apparent persistence lengths as long as approximately 1.5 nm were obtained for the single, unfolded titin molecule. Furthermore, data suggest that titin molecules may globally associate into oligomers which mechanically behave as independent wormlike chains (WLCs). Consistent with this, AFM of surface-adsorbed titin molecules revealed the presence of oligomers. Although oligomers may form globally via head-to-head association of titin, the constituent molecules otherwise appear independent from each other along their contour. Based on the global association but local independence of titin molecules, we discuss a mechanical model of the sarcomere in which titin molecules with different contour lengths, corresponding to different isoforms, are held in a lattice. The net force response of aligned titin molecules is determined by the persistence length of the tandemly arranged, different WLC components of the individual molecules, the ratio of their overall contour lengths, and by domain unfolding events. Biased domain unfolding in mechanically selected constituent molecules may serve as a compensatory mechanism for contour- and persistence-length differences. Variation in the ratio and contour length of the component chains may provide mechanisms for the fine-tuning of the sarcomeric passive force response.     

Mechanics and structure of titin oligomers explored with atomic force microscopy

Titin is a giant polypeptide that spans half of the striated muscle sarcomere and generates passive force upon stretch. To explore the elastic response and structure of single molecules and oligomers of titin, we carried out molecular force spectroscopy and atomic force microscopy (AFM) on purified full-length skeletal-muscle titin. From the force data, apparent persistence lengths as long as ∼1.5 nm were obtained for the single, unfolded titin molecule. Furthermore, data suggest that titin molecules may globally associate into oligomers which mechanically behave as independent wormlike chains (WLCs). Consistent with this, AFM of surface-adsorbed titin molecules revealed the presence of oligomers. Although oligomers may form globally via head-to-head association of titin, the constituent molecules otherwise appear independent from each other along their contour. Based on the global association but local independence of titin molecules, we discuss a mechanical model of the sarcomere in which titin molecules with different contour lengths, corresponding to different isoforms, are held in a lattice. The net force response of aligned titin molecules is determined by the persistence length of the tandemly arranged, different WLC components of the individual molecules, the ratio of their overall contour lengths, and by domain unfolding events. Biased domain unfolding in mechanically selected constituent molecules may serve as a compensatory mechanism for contour- and persistence-length differences. Variation in the ratio and contour length of the component chains may provide mechanisms for the fine-tuning of the sarcomeric passive force response.     

Scanning tunneling microscopy of mercapto-hexyl-oligonucleotides attached to gold.

6-mercapto hexyl-oligonucleotides bind to a gold surface strongly enough to permit imaging by a scanning tunneling microscope (STM). STM images showed worm-like chains that were approximately 12-(A-wide for single-stranded DNA and 20-(A-wide for double-stranded DNA. The chain lengths corresponded to 3.4 +/- 0.4 A per basepair for double-stranded DNA and 2.2 +/- 0.4 A per base for single-stranded DNA. This unexpectedly short length for single-stranded DNA was confirmed using oligomers with both single- and double-stranded regions. When the attachment of the samples was weakened (by imaging in water or scraping with the STM tip) the images changed to pairs of "blobs," apparently reflecting the attachment points of the molecules to the gold surface. Given this interpretation, images of DNA containing a five-base bulge imply that the bulge bends the oligomer by 90 degrees +/- 20 degrees.     

Pig cardiac myosin isoenzymes

Pig heart myosins isolated from the free wall of the right ventricle and the free wall of the left ventricle were compared with respect to structural and enzymatic properties. The following parameters were studied (1) activation of myosin ATase by Ca2+ and K+j(2) molecular weight of the heavy and light chains of myosins as determined by electrophoretic migration in polyacrylamide sodium dodecyl sulfate (SDS) gels; (3) ability of the heavy chains to form aggregates at low ionic strength as revealed by electron microscopy; (4) sensitivity to the action of chymotrypsin. Differences were observed between left and right ventricular myosins (L-myosin and R-myosin) for all these parameters except for the molecular weight of heavy and light chains. The existence of large amounts of short synthetic filaments for R-myosin compared with L-myosin as revealed by the length repartition of the filaments, and the production of smaller quantities of HMM-S by chymotryptic digestion for R-myosin, strongly suggest the presence of different cardiac myosin heavy chain species.     

Hierarchical extensibility in the PEVK domain of skeletal-muscle titin

Titin is the main determinant of passive muscle force. Physiological extension of titin derives largely from its PEVK (Pro-Glu-Val-Lys) domain, which has a different length in different muscle types. Here we characterized the elasticity of the full-length, human soleus PEVK domain by mechanically manipulating its contiguous, recombinant subdomain segments: an N-terminal (PEVKI), a middle (PEVKII), and a C-terminal (PEVKIII) one third. Measurement of the apparent persistence lengths revealed a hierarchical arrangement according to local flexibility: the N-terminal PEVKI is the most rigid and the C-terminal PEVKIII is the most flexible segment within the domain. Immunoelectron microscopy supported the hierarchical extensibility within the PEVK domain. The effective persistence lengths decreased as a function of ionic strength, as predicted by the Odijk-Skolnick-Fixman model of polyelectrolyte chains. The ionic strength dependence of persistence length was similar in all segments, indicating that the residual differences in the elasticity of the segments derive from nonelectrostatic mechanisms.     

Chain-length specificities of maize starch synthase I enzyme: studies of glucan affinity and catalytic properties

It is widely known that some of the starch synthases and starch-branching enzymes are trapped inside the starch granule matrix during the course of starch deposition in amyloplasts. The objective of this study was to use maize SSI to further our understanding of the protein domains involved in starch granule entrapment and identify the chain-length specificities of the enzyme. Using affinity gel electrophoresis, we measured the dissociation constants of maize SSI and its truncated forms using various glucans. The enzyme has a high degree of specificity in terms of its substrate-enzyme dissociation constant, but has a greatly elevated affinity for increasing chain lengths of alpha-1, 4 glucans. Deletion of the N-terminal arm of SSI did not affect the Kd value. Further small deletions of either N- or C-terminal domains resulted in a complete loss of any measurable affinity for its substrate, suggesting that the starch-affinity domain of SSI is not discrete from the catalytic domain. Greater affinity was displayed for the amylopectin fraction of starch as compared to amylose, whereas glycogen revealed the lowest affinity. However, when the outer chain lengths (OCL) of glycogen were extended using the phosphorylase enzyme, we found an increase in affinity for SSI between an average OCL of 7 and 14, and then an apparently exponential increase to an average OCL of 21. On the other hand, the catalytic ability of SSI was reduced several-fold using these glucans with extended chain lengths as substrates, and most of the label from [14C]ADPG was incorporated into shorter chains of dp < 10. We conclude that the rate of catalysis of SSI enzyme decreases with the OCL of its glucan substrate, and it has a very high affinity for the longer glucan chains of dp approximately 20, rendering the enzyme catalytically incapable at longer chain lengths. Based on the observations in this study, we propose that during amylopectin synthesis shorter A and B1 chains are extended by SSI up to a critical chain length that soon becomes unsuitable for catalysis by SSI and hence cannot be elongated further by this enzyme. Instead, SSI is likely to become entrapped as a relatively inactive protein within the starch granule. Further glucan extension for continuation of amylopectin synthesis must require a handover to other SS enzymes which can extend the glucan chains further or for branching by branching enzymes. If this is correct, this proposal provides a biochemical basis to explain how the specificities of various SS enzymes determine and set the limitations on the length of A, B, C chains in the starch granule.     

Structure and mobility of actin filaments as measured by quasielastic light scattering, viscometry, and electron microscopy

Actin filaments of different lengths were prepared by polymerizing actin in the presence of various concentrations of gelsolin, a protein which accelerates actin polymerization by stabilizing nuclei from which filaments grow and which binds to their fast growing ends. The lengths of the actin filaments following polymerization were measured by electron microscopy and showed that the number-average filament length agreed with the predicted length if each gelsolin molecule acted as a seed for the growth of an actin filament. The distribution of lengths was independent of the actin:gelsolin ratio and was similar to that of actin filaments polymerized in the absence of gelsolin (Lw/Ln = 1.8). The mobility of these filaments in solution was studied by quasielastic light scattering and by viscometry. The translational diffusion constant determined by quasielastic light scattering was in agreement with the infinite dilution values calculated from the dimensions and the distribution of lengths determined by electron microscopy for relatively short filament lengths. Under conditions where overlap of the rotational domains of the filaments would be expected to occur, the measured diffusion rates deviated from their predicted dilute solution values and the solution viscosity increased abruptly. The dependence of the diffusion constant and the solution viscosity on the length of the actin filaments can be explained in terms of a theory that describes the restraints on diffusion of independent rigid rods in semi-dilute solution. The results suggest that the rheology of actin filaments can be accounted for by steric restraints. The length of cytoplasmic actin filaments in some cell types is such that these steric constraints are significant and could produce large changes in physical properties with small changes in filament length.