Coarse-grained modeling of the actin filament derived from atomistic-scale simulations

A coarse-grained (CG) procedure that incorporates the information obtained from all-atom molecular dynamics (MD) simulations is presented and applied to actin filaments (F-actin). This procedure matches the averaged values and fluctuations of the effective internal coordinates that are used to define a CG model to the values extracted from atomistic MD simulations. The fluctuations of effective internal coordinates in a CG model are computed via normal-mode analysis (NMA), and the computed fluctuations are matched with the atomistic MD results in a self-consistent manner. Each actin monomer (G-actin) is coarse-grained into four sites, and each site corresponds to one of the subdomains of G-actin. The potential energy of a CG G-actin contains three bonds, two angles, and one dihedral angle; effective harmonic bonds are used to describe the intermonomer interactions in a CG F-actin. The persistence length of a CG F-actin was found to be sensitive to the cut-off distance of assigning intermonomer bonds. Effective harmonic bonds for a monomer with its third nearest neighboring monomers are found to be necessary to reproduce the values of persistence length obtained from all-atom MD simulations. Compared to the elastic network model, incorporating the information of internal coordinate fluctuations enhances the accuracy and robustness for a CG model to describe the shapes of low-frequency vibrational modes. Combining the fluctuation-matching CG procedure and NMA, the achievable time- and length scales of modeling actin filaments can be greatly enhanced. In particular, a method is described to compute the force-extension curve using the CG model developed in this work and NMA. It was found that F-actin is easily buckled under compressive deformation, and a writhing mode is developed as a result. In addition to the bending and twisting modes, this novel writhing mode of F-actin could also play important roles in the interactions of F-actin with actin-binding proteins and in the force-generation process via polymerization.     

Viscoelasticity of F-actin and F-actin/gelsolin complexes

Actin is the major protein of eukaryote peripheral cytoplasm where its mechanical effects could determine cell shape and motility. The mechanical properties of purified F-actin, whether it is a viscoelastic fluid or an elastic solid, have been a subject of controversy. Mainstream polymer theory predicts that filaments as long as those found in purified F-actin are so interpenetrated as to appear immobile in measurements over a reasonable time with available instrumentation and that the fluidity of F-actin could only be manifest if the filaments were shortened. We show that the static and dynamic elastic moduli below a critical degree of shear strain are much higher than previously reported, consistent with extreme interpenetration, but that higher strain or treatment with very low concentrations of the F-actin severing protein gelsolin greatly diminish the moduli and cause F-actin to exhibit rheologic behavior expected for independent semidilute rods, and defined by the dimensions of the filaments, including shear rate independent viscosity below a critical shear rate. The findings show that shortening of actin filaments sufficiently to permit reasonable measurements brings out their viscoelastic fluid properties. Since gelsolin shortens F-actin, it is likely that the effect of high strain is also to fragment a population of long actin filaments. We confirmed recent findings that the viscosity of F-actin is inversely proportional to the shear rate, consistent with an indeterminate fluid, but found that gelsolin abolishes this unusual shear rate dependence, indicating that it results from filament disruption during the viscosity measurements.(ABSTRACT TRUNCATED AT 250 WORDS)     

Dynamic light-scattering study of muscle F-actin. II

By dynamic light scattering, the intensity autocorrelation function, G2(tau) = B[1 + beta[g1(tau)[2], was obtained over the scattering angles (theta) from 30 to 130 degrees in steps of 10 degrees for semidilute solutions of muscle F-actin and of F-actin complexed with heavy meromyosin in the absence of ATP (acto-HMM), where B is the baseline and beta a constant. The main findings were: (1) A 0.5 mg/ml F-actin solution gave nonreproducible spectra at theta less than or equal to 40 degrees but quite reproducible spectra at theta greater than or equal to 50 degrees, with beta = 0.9-0.8 at all theta values. Nonreproducibility of spectra at low theta values was concluded to be due to restricted motions of very long filaments confined in cages or zig-zag tubing formed by a major fraction of filaments, where the very long filaments were those at a distant tail of an exponential length distribution and the major fraction of filaments were those with lengths around Ln-2Ln, Ln being the number-average length. Spectral widths were compared with theoretical ones for rigid rods averaged over the length distribution with Ln = 900 nm, and were suggested to be largely contributed at high theta values from bending motions of filaments. (2) Acto-HMM solutions at 0.5 mg/ml F-actin and at weight ratios of HMM to F-actin of 0.5-2 gave spectra which, with respect to theta, behaved very similarly to those of F-actin alone. The spectral widths, however, drastically decreased with the weight ratio up to unity and stayed virtually constant above unity. In contrast to a previous study (F.D. Carlson and A.B. Fraser, J. Mol. Biol. 89 (1974) 273), beta values of acto-HMM were as large as those of F-actin alone. Acto-HMM was concluded to travel a distance far greater than 1/K with a mobility smaller than that of F-actin, where K = (4 pi/lambda) sin(theta/2), lambda being the wavelength of light in the medium. These results suggest that acto-HMM gels are very soft even though they did not pour from an inverted cell. Based on several intuitive models which give a mutual relationship between the beta value and modes of motion of scatterers, we discuss the restricted motions responsible for nonreproducibility of spectra at low angles and large beta values of acto-HMM gels at all theta values and weight ratios so far studied.     

Directional movement of F-actin in vitro

By a fluorescence microscopic method for visualizing single filaments of F-actin in solutions, we have investigated movement of F-actin in a motility system in vitro. It was found that, when F-actin and myosin were mixed in the presence of Mg2+-ATP under appropriate conditions, individual F-actin filaments continued moving in different directions, but in parallel to their length, for a long period of time. The actin filaments did not reverse their direction of movement and had a distribution of speed with the maximum at about 5 micron per second (at 27 degrees C).     

The role of shape in determining molecular motions

We examined the role of molecular shape in determining the patterns of low-frequency deformational motions of biological macromolecules. The low-frequency subspace of eigenvectors in normal mode analysis was found to be robustly similar upon randomization of the Hessian matrix elements as long as the structure of the matrix is maintained, which indicates that the global shape of molecules plays a more dominant role in determining the highly anisotropic low-frequency motions than the absolute values of stiffness and directionality of local interactions. The results provided a quantitative foundation for the validity of elastic normal mode analysis.     

Tracer diffusion through F-actin: effect of filament length and cross-linking.

We have determined diffusion coefficients for small (50- to 70-nm diameter) fluorescein-thiocarbamoyl-labeled Ficoll tracers through F-actin as a function of filament length and cross-linking. fx45 was used to regulate filament length and avidin/biotinylated actin or ABP-280 was used to prepare cross-linked actin gels. We found that tracer diffusion was generally independent of filament length in agreement with theoretical predictions for diffusion through solutions of rods. However, in some experiments diffusion was slower through short (< or = 1.0 micron) filaments, although this result was not consistently reproducible. Measured diffusion coefficients through unregulated F-actin and filaments of lengths > 1.0 micron were more rapid than predicted by theory for tracer diffusion through rigid, random networks, which was consistent with some degree of actin bundling. Avidin-induced cross-linking of biotinylated F-actin did not affect diffusion through unregulated F-actin, but in cases where diffusion was slower through short filaments this cross-linking method resulted in enhanced tracer diffusion rates indistinguishable from unregulated F-actin. This finding, in conjunction with increased turbidity of 1.0-micron filaments upon avidin cross-linking, indicated that this cross-linking method induces F-actin bundling. By contrast, ABP-280 cross-linking retarded diffusion through unregulated F-actin and decreased turbidity. Tracer diffusion under these conditions was well approximated by the diffusion theory. Both cross-linking procedures resulted in gel formation as determined by falling ball viscometry. These results demonstrate that network microscopic geometry is dependent on the cross-linking method, although both methods markedly increase F-actin macroscopic viscosity.     

Viral capsid equilibrium dynamics reveals nonuniform elastic properties

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.     

Length distribution of F-actin in Dictyostelium discoideum

Inhibition of deoxyribonuclease I activity was used to assay the actin monomers and the pointed ends of actin filaments in lysates of Dictyostelium discoideum. The KD for the binding reaction was 0.2-0.3 nM. Total cellular actin was 93 microM in monomers (approximately 0.1 fmol/cell) of which roughly half was initially polymeric. Essentially all of the filamentous actin (F-actin) was readily pelleted in the microcentrifuge and was therefore presumed to be in the cytoskeleton. Free F-actin barbed ends, measured as pelletable [3H]cytochalasin B, numbered 1.8 x 10(5)/cell; nuclei for the polymerization of rabbit muscle globular (monomeric) actin numbered 2.0 x 10(5)/cell; and pointed ends, determined by their inhibition of deoxyribonuclease I, numbered 3.6 x 10(5)/cell. These values suggest that half the barbed ends might be occluded. On average, the filaments contained approximately 76 subunits and were therefore about 0.2 micron long. The distribution of their lengths was estimated from the time course of depolymerization following vast dilution. Three populations were defined. In one experiment, the smallest population contained 71% of the F-actin mass and 96% of the pointed ends; these filaments averaged 80 subunits or 0.22 microns in length. An intermediate population contained 14% of the F-actin mass and 3% of the filaments; these were roughly 460 subunits (1.3 microns) long. The largest population contained 15% of the F-actin mass in about 0.3% of the filaments; these were 13 microns in length, about the diameter of the cell. The numerous short filaments might populate a cortical mesh, while the long filaments might constitute endoplasmic bundles.     

Stochastic simulation of actin dynamics reveals the role of annealing and fragmentation

Recent observations of F-actin dynamics call for theoretical models to interpret and understand the quantitative data. A number of existing models rely on simplifications and do not take into account F-actin fragmentation and annealing. We use Gillespie's algorithm for stochastic simulations of the F-actin dynamics including fragmentation and annealing. The simulations vividly illustrate that fragmentation and annealing have little influence on the shape of the polymerization curve and on nucleotide profiles within filaments but drastically affect the F-actin length distribution, making it exponential. We find that recent surprising measurements of high length diffusivity at the critical concentration cannot be explained by fragmentation and annealing events unless both fragmentation rates and frequency of undetected fragmentation and annealing events are greater than previously thought. The simulations compare well with experimentally measured actin polymerization data and lend additional support to a number of existing theoretical models.     

The utrophin actin-binding domain binds F-actin in two different modes: implications for the spectrin superfamily of proteins

Utrophin, like its homologue dystrophin, forms a link between the actin cytoskeleton and the extracellular matrix. We have used a new method of image analysis to reconstruct actin filaments decorated with the actin-binding domain of utrophin, which contains two calponin homology domains. We find two different modes of binding, with either one or two calponin-homology (CH) domains bound per actin subunit, and these modes are also distinguishable by their very different effects on F-actin rigidity. Both modes involve an extended conformation of the CH domains, as predicted by a previous crystal structure. The separation of these two modes has been largely dependent upon the use of our new approach to reconstruction of helical filaments. When existing information about tropomyosin, myosin, actin-depolymerizing factor, and nebulin is considered, these results suggest that many actin-binding proteins may have multiple binding sites on F-actin. The cell may use the modular CH domains found in the spectrin superfamily of actin-binding proteins to bind actin in manifold ways, allowing for complexity to arise from the interactions of a relatively few simple modules with actin.     

Binding of actin filaments to connectin

The binding of actin filaments to connectin, a muscle elastic protein, was investigated by means of turbidity and sedimentation measurements and electron microscopy. In the presence of less than 0.12 M KCl at pH 7.0, actin filaments bound to connectin. Long actin filaments formed bundles. Short actin filaments also aggregated into irregular bundles or a meshwork, and were frequently attached perpendicularly to long bundles. The binding of F-actin to connectin was saturated at an equal weight ratio (molar ratio, 50 : 1), as determined by a cosedimentation assay. Larger amounts of sonicated short actin filaments appeared to bind to connectin than intact F-actin. Myosin S1-decorated actin filaments did not bind to connectin. The addition of S1 to connectin-induced actin bundles resulted in partial disaggregation. Thus, connectin does not appear to interfere with actin-myosin interactions, since myosin S1 binds to actin more strongly than connectin.     

Counterion-induced actin ring formation

Actin filaments form rings and loops when > 20 mM divalent cations are added to very dilute solutions of phalloidin-stabilized filamentous actin (F-actin). Some rings consist of very long single actin filaments partially overlapping at their ends, and others are formed by small numbers of filaments associated laterally. In some cases, undulations of the rings are observed with amplitudes and dynamics similar to those of the thermal motions of single actin filaments. Lariat-shaped aggregates also co-exist with rings and rodlike bundles. These polyvalent cation-induced actin rings are analogous to the toroids of DNA formed by addition of polyvalent cations, but the much larger diameter of actin rings reflects the greater bending stiffness of F-actin. Actin rings can also be formed by addition of streptavidin to crosslink sparsely biotinylated F-actin at very low concentrations. The energy of bending in a ring, calculated from the persistence length of F-actin and the ring diameter, provides an estimate for the adhesion energy mediated by the multivalent counterions, or due to the streptavidin-biotin bonds, required to keep the ring closed.     

Quantitation of liquid-crystalline ordering in F-actin solutions.

Actin filaments (F-actin) are important determinants of cellular shape and motility. These functions depend on the collective organization of numerous filaments with respect to both position and orientation in the cytoplasm. Much of the orientational organization arises spontaneously through liquid crystal formation in concentrated F-actin solutions. In studying this phenomenon, we found that solutions of purified F-actin undergo a continuous phase transition, from the isotropic state to a liquid crystalline state, when either the mean filament length or the actin concentration is increased above its respective threshold value. The phase diagram representing the threshold filament lengths and concentrations at which the phase transition occurs is consistent with that predicted by Flory's theory on solutions of noninteracting, rigid cylinders (Flory, 1956b). However, in contrast to other predictions based on this model, we found no evidence for the coexistence of isotropic and anisotropic phases. Furthermore, the phase transition proved to be temperature dependent, which suggests the existence of orientation-dependent interfilament interactions or of a temperature-dependent filament flexibility. We developed a simple method for growing undistorted fluorescent acrylodan-labeled F-actin liquid crystals; and we derived a simple theoretical treatment by which polarization-of-fluorescence measurements could be used to quantitate, for the first time, the degree of spontaneous filament ordering (nematic order parameter) in these F-actin liquid crystals. This order parameter was found to increase monotonically with both filament length and concentration. Actin liquid crystals can readily become distorted by a process known as "texturing." Zigzaging and helicoidal liquid crystalline textures which persisted in the absence of ATP were observed through the polarizing microscope. Possible texturing mechanisms are discussed.     

Kinetic analysis of F-actin depolymerization in polymorphonuclear leukocyte lysates indicates that chemoattractant stimulation increases actin filament number without altering the filament length distribution

The rate of filamentous actin (F-actin) depolymerization is proportional to the number of filaments depolarizing and changes in the rate are proportional to changes in filament number. To determine the number and length of actin filaments in polymorphonuclear leukocytes and the change in filament number and length that occurs during the increase in F-actin upon chemoattractant stimulation, the time course of cellular F-actin depolymerization in lysates of control and peptide-stimulated cells was examined. F-actin was quantified by the TRITC-labeled phalloidin staining of pelletable actin. Lysis in 1.2 M KCl and 10 microM DNase I minimized the effects of F-actin binding proteins and G-actin, respectively, on the kinetics of depolymerization. To determine filament number and length from a depolymerization time course, depolymerization kinetics must be limited by the actin monomer dissociation rate. Comparison of time courses of depolymerization in the presence (pointed ends free) or absence (barbed and pointed ends free) of cytochalasin suggested depolymerization occurred from both ends of the filament and that monomer dissociation was rate limiting. Control cells had 1.7 +/- 0.4 x 10(5) filaments with an average length of 0.29 +/- 0.09 microns. Chemo-attractant stimulation for 90 s at room temperature with 0.02 microM N-formylnorleucylleucylphenylalanine caused a twofold increase in F-actin and about a two-fold increase in the total number of actin filaments to 4.0 +/- 0.5 x 10(5) filaments with an average length of 0.27 +/- 0.07 microns. In both cases, most (approximately 80%) of the filaments were quite short (less than or equal to 0.18 micron). The length distributions of actin filaments in stimulated and control cells were similar.     

Dynamic and elastic properties of F-actin: a normal-modes analysis.

We examine the dynamic, elastic, and mechanical consequences of the proposed atomic models of F-actin, using a normal mode analysis. This initial analysis is done in vacuo and assumes that all monomers are rigid and equivalent. Our computation proceeds from the atomic level and, relying on a single fitting parameter, reproduces various experimental results, including persistence lengths, elastic moduli, and contact energies. The computations reveal modes of motion characteristic to all polymers, such as longitudinal pressure waves, torsional waves, and bending, as well as motions unique to F-actin. Motions typical to actin include a "groove-swinging" motion of the two long-pitch helices, as well as an axial slipping motion of the two strands. We prepare snapshots of thermally activated filaments and quantify the accumulation of azimuthal angular "disorder," variations in cross-over lengths, and various other fluctuations. We find that the orientation of a small number of select residues has a surprisingly large effect on the filament flexibility and elasticity characteristics.     

Bundling of actin filaments by alpha-actinin depends on its molecular length

Cross-linking of actin filaments (F-actin) into bundles and networks was investigated with three different isoforms of the dumbbell-shaped alpha-actinin homodimer under identical reaction conditions. These were isolated from chicken gizzard smooth muscle, Acanthamoeba, and Dictyostelium, respectively. Examination in the electron microscope revealed that each isoform was able to cross-link F-actin into networks. In addition, F-actin bundles were obtained with chicken gizzard and Acanthamoeba alpha-actinin, but not Dictyostelium alpha-actinin under conditions where actin by itself polymerized into disperse filaments. This F-actin bundle formation critically depended on the proper molar ratio of alpha-actinin to actin, and hence F-actin bundles immediately disappeared when free alpha-actinin was withdrawn from the surrounding medium. The apparent dissociation constants (Kds) at half-saturation of the actin binding sites were 0.4 microM at 22 degrees C and 1.2 microM at 37 degrees C for chicken gizzard, and 2.7 microM at 22 degrees C for both Acanthamoeba and Dictyostelium alpha-actinin. Chicken gizzard and Dictyostelium alpha-actinin predominantly cross-linked actin filaments in an antiparallel fashion, whereas Acanthamoeba alpha-actinin cross-linked actin filaments preferentially in a parallel fashion. The average molecular length of free alpha-actinin was 37 nm for glycerol-sprayed/rotary metal-shadowed and 35 nm for negatively stained chicken gizzard; 46 and 44 nm, respectively, for Acanthamoeba; and 34 and 31 nm, respectively, for Dictyostelium alpha-actinin. In negatively stained preparations we also evaluated the average molecular length of alpha-actinin when bound to actin filaments: 36 nm for chicken gizzard and 35 nm for Acanthamoeba alpha-actinin, a molecular length roughly coinciding with the crossover repeat of the two-stranded F-actin helix (i.e., 36 nm), but only 28 nm for Dictyostelium alpha-actinin. Furthermore, the minimal spacing between cross-linking alpha-actinin molecules along actin filaments was close to 36 nm for both smooth muscle and Acanthamoeba alpha-actinin, but only 31 nm for Dictyostelium alpha-actinin. This observation suggests that the molecular length of the alpha-actinin homodimer may determine its spacing along the actin filament, and hence F-actin bundle formation may require "tight" (i.e., one molecule after the other) and "untwisted" (i.e., the long axis of the molecule being parallel to the actin filament axis) packing of alpha-actinin molecules along the actin filaments.     

Analyzing the normal mode dynamics of macromolecules by the component synthesis method: Residue clustering and multiple-component approach

A study of the component synthesis method (CSM) for analyzing the normal mode dynamics of macromolecules is reported. The procedure involves a reduction of the dimensions of the normal mode problems for large molecular systems and the accurate extraction of the low-frequency modes. A macromolecule is divided into small components based on a hierarchical clustering of the residues in the structure. Interactions between coupled components are treated by the method of static correlation. The normal modes of the components are obtained first, and a fraction of the low-frequency normal modes of the components under mutual correlations are then used as a reduced basis for solving for the normal modes of the whole molecule. Multiple components are introduced for large macromolecules so that the dimensions of the eigenvalue problems at the component level are small. The method is applied to the protein crambin. In test calculations in which the dimensions of the eigenvalue equations are reduced to 1/6 of their natural size, the errors in the normal mode frequencies calculated by the CSM procedure are only about 1–2% when compared with the exact values. The rms fluctuations of all atoms in crambin calculated by the CSM procedure are basically identical to the exact results. The CSM procedure is shown to be accurate for calculating the normal modes of large macromolecules with a significant reduction of the size of the problem. © 1994 John Wiley & Sons, Inc.     

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.     

Heavy meromyosin induces sliding movements between antiparallel actin filaments

Suzuki et al. [Biochemistry 28, 6513-6518 (1989)] have shown that, when F-actin is mixed with inert high polymer, a large number of actin filaments closely align in parallel with overlaps to form a long and thick bundle. The bundle may be designated non-polar, as the constituent filaments are random in polarity (Suzuki et al. 1989). I prepared non-polar bundles of F-actin using methylcellulose (MC) as the high polymer, exposed them to heavy meromyosin (HMM) in the presence of ATP under a light microscope, and followed their morphological changes in the continuous presence of MC. It was found that bundles several tens of micrometers long contracted to about one-third the initial length, while becoming thicker, in half a minute after exposure to HMM. Subsequently, each bundle was split longitudinally into several bundles in a stepwise manner, while the newly formed ones remained associated together at one of the two ends. The product, an aster-like assembly of actin bundles, was morphologically quiescent; that is, individual bundles never contracted upon second exposure to HMM and ATP, although they were still longer than the F-actin used. Bundles in this state consisted of filaments with parallel polarity as examined by electron microscopy. This implies that non-polar bundles were transformed into assemblies of polar bundles with ATP hydrolysis by HMM. Importantly, myosin subfragment-1 caused neither contraction nor transformation. These results are interpreted as follows. In the presence of ATP, the two-headed HMM molecule was able to cross-bridge antiparallel actin filaments, as well as parallel ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

Rapid formation and high diffusibility of actin-cofilin cofilaments at low pH.

Cofilin is a small actin-binding protein that is known to bind both F-actin and G-actin, severing the former. The interaction of cofilin with actin is pH-sensitive, F-actin being preferentially bound at low pH and G-actin at higher pH, within the physiological range. Diffusion coefficients of F-actin with cofilin were measured by the fluorescence recovery after photobleaching (FRAP) technique. This has the potential for simultaneous and direct measurement of average polymer length via the average diffusion coefficient of the polymers (DLM) as well as the fraction of polymerized actin, fLM, present in solution. In the range of cofilin-actin ratios up to 1 : 1 and at both pH 6.5 and pH 8.0, the diffusion coefficients of the polymers increased with the amount of cofilin present in the complex, in a co-operative manner to a plateau. We interpret this as indicating co-operative binding/severing and that filaments less than a certain length cannot be severed further. Under the conditions used here, filaments were found to be more motile at pH 6.5 than at pH 8.0. At pH 8.0, some actin is expected to be sequestered as ADP-actin-cofilin complexes, with the remaining actin being present as long slowly diffusing filaments. At pH 6.5, however, cofilin binds to F-actin to form short rapidly diffusing cofilaments. These filaments form very rapidly from cofilin-actin monomeric complexes, possibly indicating that this complex is able to polymerize without dissociation. These findings may be relevant to the nuclear import of actin-cofilin complexes.