Refinement of F-Actin Model against Fiber Diffraction Data by Long-Range Normal Modes

The atomic model of F-actin was refined against fiber diffraction data using long-range normal modes as adjustable parameters to account for the collective long-range filamentous deformations. To determine the effect of long-range deformations on the refinement, each of the four domains of G-actin was treated as a rigid body. It was found that among all modes, the bending modes make the most significant contributions to the improvement of the refinement. Inclusion of only 7–9 bending modes as adjustable parameters yielded a lowest R-factor of 6.3%. These results demonstrate that employing normal modes as refinement parameters has the advantage of using a small number of adjustable parameters to achieve a good fitting efficiency. Such a refinement procedure may therefore prevent the refinement from overfitting the structural model. More importantly, the results of this study demonstrate that, for any fiber diffraction data, a substantial amount of refinement error is due to long-range deformations, especially the bending, of the filaments. The effects of these intrinsic deformations cannot be easily compensated for by adjusting local structural parameters, and must be properly accounted for in the refinement to achieve improved fit of refined models with experimental diffraction data.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data.

A dynamic structure refinement method for X-ray crystallography, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the low-frequency normal modes whose amplitudes and eigenvectors are experimentally optimized in the process of the crystallographic refinement. In this model, the atomic fluctuations are treated as anisotropic and concerted. The normal modes of the external motion (TLS model) are also introduced to cover the factors other than the internal fluctuations, such as the lattice disorder and diffusion. A program for the normal mode refinement (NM-REF) has been developed. The method has first been tested against simulated diffraction data for human lysozyme calculated by a Monte Carlo simulation. Applications of the method have demonstrated that the normal mode refinement has: (1) improved the fitting to the diffraction data, even with fewer adjustable parameters; (2) distinguished internal fluctuations from external ones; (3) determined anisotropic thermal factors; and (4) identified concerted fluctuations in the protein molecule.     

Solution structure and dynamics of ADF from Toxoplasma gondii

Toxoplasma gondii ADF (TgADF) belongs to a functional subtype characterized by strong G-actin sequestering activity and low F-actin severing activity. Among the characterized ADF/cofilin proteins, TgADF has the shortest length and is missing a C-terminal helix implicated in F-actin binding. In order to understand its characteristic properties, we have determined the solution structure of TgADF and studied its backbone dynamics from ¹⁵N-relaxation measurements. TgADF has conserved ADF/cofilin fold consisting of a central mixed β-sheet comprised of six β-strands that are partially surrounded by three α-helices and a C-terminal helical turn. The high G-actin sequestering activity of TgADF relies on highly structurally and dynamically optimized interactions between G-actin and G-actin binding surface of TgADF. The equilibrium dissociation constant for TgADF and rabbit muscle G-actin was 23.81 nM, as measured by ITC, which reflects very strong affinity of TgADF and G-actin interactions. The F-actin binding site of TgADF is partially formed, with a shortened F-loop that does not project out of the ellipsoid structure and a C-terminal helical turn in place of the C-terminal helix α4. Yet, it is more rigid than the F-actin binding site of Leishmania donovani cofilin. Experimental observations and structural features do not support the interaction of PIP2 with TgADF, and PIP2 does not affect the interaction of TgADF with G-actin. Overall, this study suggests that conformational flexibility of G-actin binding sites enhances the affinity of TgADF for G-actin, while conformational rigidity of F-actin binding sites of conventional ADF/cofilins is necessary for stable binding to F-actin.     

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.     

Biomechanics of actin filaments: a computational multi-level study

The actin microfilament (F-actin) is a structural and functional component of the cell cytoskeleton. Notwithstanding the primary role it plays for the mechanics of the cell, the mechanical behaviour of F-actin is still not totally explored. In particular, the relationship between the mechanics of F-actin and its molecular architecture is not completely understood. In this study, the mechanical properties of F-actin were related to the molecular topology of its building monomers (G-actin) by employing a computational multi-level approach. F-actins with lengths up to 500 nm were modelled and characterized, using a combination of equilibrium molecular dynamics (MD) simulations and normal mode analysis (NMA). MD simulations were performed to analyze the molecular rearrangements of G-actin in physiological conditions; NMA was applied to compute the macroscopic properties of F-actin from its vibrational modes of motion. Results from this multi-level approach showed that bending stiffness, bending modulus and persistence length are independent from the length of F-actin. On the contrary, the orientations and motions of selected groups of residues of G-actin play a primary role in determining the filament flexibility. In conclusion, this study (i) demonstrated that a combined computational approach of MD and NMA allows to investigate the biomechanics of F-actin taking into account the molecular topology of the filament (i.e., the molecular conformations of G-actin) and (ii) that this can be done using only crystallographic G-actin, without the need of introducing experimental parameters nor of reducing the number of residues.     

Crystallographic studies of the chicken gizzard G-actin X DNase I complex at 5A resolution

The structure of the chicken gizzard G-actin X DNase I complex has been determined at 5 A resolution by an X-ray diffraction method. Protein phases were computed by the multiple isomorphous replacement method using four heavy atom derivatives. The mean figure of merit was 0.65. Dimensions of the three molecular species, the complex, G-actin and DNase I, were determined based on the "cypress wood" models derived from the electron density map. The natures of the heavy atom binding sites are discussed in relation to the distinction between the two component molecules. The pattern of successive contacts between actin molecules observed in the present crystal seems unrelated to that found in F-actin.     

An assessment of the models of thin filament of the sarcomere using small-angle X-ray data on rabbit relaxed muscle

Models of a thin filament based on various G-actin atomic structures and modes of their packing into helical structures were considered. The calculated intensities of actin layer lines were compared with the X-ray data for thin fiber bundles of a relaxed rabbit skeletal muscle. The effect of the main components of thin filament on the intensity of actin layer lines was also analyzed. The F-actin PDB 3BYH model gave the best fit to the experimental data.     

Computational prediction of actin–actin interaction

Actin is one of the most abundant proteins in eukaryotic cells, where it plays key roles in cell shape, motility, and regulation. Actin is found in globular (G) and filamentous (F) structure in the cell. The helix of actin occurs as a result of polymerization of monomeric G-actin molecules through sequential rowing, is called F-actin. Recently, the crystal structure of an actin dimer has been reported, which details molecular interface in F-actin. In this study, the computational prediction model of actin and actin complex has been constructed base on the atomic model structure of G-actin. To this end, a docking simulation was carried out using predictive docking tools to obtain modeled structures of the actin–actin complex. Following molecular dynamics refinement, hot spots interactions at the protein interface were identified, that were predicted to contribute substantially to the free energy of binding. These provided a detailed prediction of key amino acid interactions at the protein–protein interface. The obtained model can be used for future experimental and computational studies to draw biological and functional conclusions. Also, the identified interactions will be used for designing next studies to understand the occurrence of F-actin structure.     

Differences in internal dynamics of actin under different structural states detected by neutron scattering

F-actin, a helical polymer formed by polymerization of the monomers (G-actin), plays crucial roles in various aspects of cell motility. Flexibility of F-actin has been suggested to be important for such a variety of functions. Understanding the flexibility of F-actin requires characterization of a hierarchy of dynamical properties, from internal dynamics of the actin monomers through domain motions within the monomers and relative motions between the monomers within F-actin to large-scale motions of F-actin as a whole. As a first step toward this ultimate purpose, we carried out elastic incoherent neutron scattering experiments on powders of F-actin and G-actin hydrated with D₂O and characterized the internal dynamics of F-actin and G-actin. Well established techniques and analysis enabled the extraction of mean-square displacements and their temperature dependence in F-actin and in G-actin. An effective force constant analysis with a model consisting of three energy states showed that two dynamical transitions occur at ∼150 K and ∼245 K, the former of which corresponds to the onset of anharmonic motions and the latter of which couples with the transition of hydration water. It is shown that behavior of the mean-square displacements is different between G-actin and F-actin, such that G-actin is “softer” than F-actin. The differences in the internal dynamics are detected for the first time between the different structural states (the monomeric state and the polymerized state). The different behavior observed is ascribed to the differences in dynamical heterogeneity between F-actin and G-actin. Based on structural data, the assignment of the differences observed in the two samples to dynamics of specific loop regions involved in the polymerization of G-actin into F-actin is proposed.     

Binding of actin to liver cell membranes: the state of membrane-bound actin

Previous work has shown that actin binds specifically and saturably to liver membranes stripped of endogenous actin (Tranter, M. P., S. P. Sugrue, and M. A. Schwartz. 1989. J. Cell Biol. 109:2833-2840). Scatchard plots of equilibrium binding data were linear, indicating that binding is not cooperative, as would be expected for F- or G-actin. To determine the state of membrane-bound actin, we have analyzed the binding of F- and G-actin to liver cell membranes. G-actin in low salt depolymerization buffer and EF-actin, a derivative that polymerizes very poorly in solution, bind to liver cell membranes as well as untreated actin in polymerization buffer. Phalloidin-stabilized F-actin binds, but to a lesser extent. The binding of F- and G-actins are mutually competitive and are inhibited by ATP, suggesting that both forms of actin bind to the same sites. For untreated actin in polymerization buffer, the time course of binding is biphasic, with an initial rapid component which is followed by a plateau phase, then a second, slower component. The binding kinetics of pure F-actin and pure G-actin are both monophasic and match the fast and slower components, respectively, of untreated actin. In the reconstituted system, membrane-bound actin does not stain with rhodamine-phalloidin, nor are actin filaments detected by EM. Distinct regions of amorphous material, however, are visible, which stain with an anti-actin antibody. The exact nature of this material has yet to be determined. A model of actin binding is presented.     

The critical concentration of actin in the presence of ATP increases with the number concentration of filaments and approaches the critical concentration of actin.ADP

F-actin at steady state in the presence of ATP partially depolymerized to a new steady state upon mechanical fragmentation. The increase in critical concentration with the number concentration of filaments has been quantitatively studied. The data can be explained by a model in which the preferred pathway for actin association-dissociation reactions at steady state in the presence of ATP involves binding of G-actin . ATP to filaments, ATP hydrolysis, and dissociation of G-actin . ADP which is then slowly converted to G-actin . ATP. As a consequence of the slow exchange of nucleotide on G-actin, the respective amounts of G-actin . ATP and G-actin . ADP coexisting with F-actin at steady state depend on the filament number concentration. G-actin coexisting with F-actin at zero number concentration of filaments would then consist of G-actin . ATP only, while the critical concentration obtained at infinite number of filaments would be that for G-actin . ADP. Values of 0.35 and 8 microM, respectively, were found for these two extreme critical concentrations for skeletal muscle actin at 20 degrees C, pH 7.8, 0.1 mM CaCl2, 1 mM MgCl2, and 0.2 mM ATP. The same value of 8 microM was directly measured for the critical concentration of G-actin . ADP polymerized in the presence of ADP and absence of ATP, and it was unaffected by fragmentation. These results have important implications for experiments in which critical concentrations are compared under conditions that change the filament number concentrations.     

Two distinct regions of calponin share common binding sites on actin resulting in different modes of calponin–actin interaction

Calponins are a small family of proteins that alter the interaction between actin and myosin II and mediate signal transduction. These proteins bind F-actin in a complex manner that depends on a variety of parameters such as stoichiometry and ionic strength. Calponin binds G-actin and F-actin, bundling the latter primarily through two distinct and adjacent binding sites (ABS1 and ABS2). Calponin binds other proteins that bind F-actin and considerable disagreements exist as to how calponin is located on the filament, especially in the presence of other proteins. A study (Galkin, V.E., Orlova, A., Fattoum, A., Walsh, M.P. and Egelman, E.H. (2006) J. Mol. Biol. 359, 478–485.), using EM single-particle reconstruction has shown that there may be four modes of interaction, but how these occur is not yet known. We report that two distinct regions of calponin are capable of binding some of the same sites on actin (such as 18–28 and 360–372 in subdomain 1). This accounts for the finding that calponin binds the filament with different apparent geometries. We suggest that the four modes of filament binding account for differences in stoichiometry and that these, in turn, arise from differential binding of the two calponin regions to actin. It is likely that the modes of binding are reciprocally influenced by other actin-binding proteins since members of the α-actinin group also adopt different actin-binding positions and bind actin principally through a domain that is similar to calponin's ABS1.     

Effect of Hypothyroidism on Different Forms of Actin in Rat Cerebral Neuronal Cultures Studied by an Improved DNase I Inhibition Assay

An improved DNase I inhibition assay for the filamentous actin (F-actin) and monomeric actin (G-actin) in brain cells has been developed. Unlike other methods, the cell lysis conditions and postlysis treatments, established by us, inhibited the temporal inactivation of actin in the cell lysate and maintained a stable F-actin/G-actin ratio for at least 4-5 h after lysis. The new procedure allowed separate quantitation of the noncytoskeletal F-actin in the Triton-soluble fraction (12,000 g, 10 min supernatant) that did not readily sediment with the Triton-insoluble cytoskeletal F-actin (12,000 g, 10 min pellet). We have applied this modified assay system to study the effect of hypothyroidism on different forms of actin using primary cultures of neurons derived from cerebra of neonatal normal and hypothyroid rats. Our results showed a 20% increase in the Triton-insoluble cytoskeletal F-actin in cultures from hypothyroid brain relative to normal controls. In the Triton-soluble fraction, containing the G-actin and the noncytoskeletal F-actin, cultures from hypothyroid brain showed a 15% increase in G-actin, whereas the F-actin remained unaltered. The 10% increase in total actin observed in this fraction from hypothyroid brain could be totally accounted for by the enhancement of G-actin. The mean F-actin/G-actin ratio in this fraction was about 30% higher in the cultures from normal brain compared to that of the hypothyroid system, which indicates that hypothyroidism tends to decrease the proportion of noncytoskeletal F-actin relative to G-actin.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. II. Application to human lysozyme.

The dynamic structure of a protein, human lysozyme, is determined by the normal mode refinement of X-ray crystal structure. This method uses the normal modes of both internal and external motions to distinguish the real internal dynamics from the external terms such as lattice disorder, and gives an anisotropic and concerted picture of atomic fluctuations. The refinement is carried out with diffraction data of 5.0 to 1.8 A resolution, which are collected on an imaging plate. The results of the refinement show: (1) Debye-Waller factor consists of two parts, highly anisotropic internal fluctuations and almost isotropic external terms. The former is smaller than the latter by a factor of 0.72 in the scale of B-factor. Therefore, the internal dynamics cannot be recognized directly from the apparent electron density distribution. (2) The internal fluctuations show basically similar features as those predicted by the normal mode analysis, with almost the same amplitude and a similar level of anisotropy. (3) Correlations of fluctuations are detected between two lobes forming the active site cleft, which move simultaneously in opposite directions. This corresponds to the hinge-bending motion of lysozyme.     

Activation of heavy meromyosin adenosine triphosphatase by various states of actin.

F-actin monomer (F-monomer) is formed upon the addition of neutral salt to G-actin. Since F-monomer has a digestibility similar to that of F-actin and much lower than that of G-actin, it has been proposed that F-monomer has a conformation different from that of G-actin and similar to the conformation of the subunits in F-actin. To examine whether F-monomer will enhance the magnesium-activated myosin adenosine triphosphatase (Mg2+-ATPase) as much as F-actin, the ability of partially polymerized actin populations at equilibrium to activate the Mg2+-ATPase of heavy meromyosin was investigated. Correlations were made between ATPase activities and the polymerization state of actin as determined by measurements of viscosity and digestibility. No significant activation of the heavy meromyosin ATPase was observed under conditions where G-actin or mixtures of G-actin and F-monomer were present. As polymer formation occurred at higher actin concentrations, or with increased KCl concentrations, substantial activation characteristic of F-actin was observed. The data suggest that F-monomer may undergo a further conformational change as it forms nuclei or joins onto polymers. Alternatively, the site of actin which activates the myosin ATPase may involve the crevice between two adjacent actin subunits.     

State of actin in gastric parietal cells

Remodeling of theapical membrane-cytoskeleton has been suggested to occur when gastricparietal cells are stimulated to secrete HCl. The present experimentsassayed the relative amounts of F-actin and G-actin in gastric glandsand parietal cells, as well as the changes in the state of actin onstimulation. Glands and cells were treated with a Nonidet P-40extraction buffer for separation into detergent-soluble (supernatant)and detergent-insoluble (pellet) pools. Two actin assays were used toquantitate actin: the deoxyribonuclease I binding assay to measureG-actin and F-actin content in the two pools and a simple Western blotassay to quantitate the relative amounts of actin in the pools.Functional secretory responsiveness was assayed by aminopyrineaccumulation. About 5% of the total parietal cell protein is actin,with about 90% of the actin present as F-actin. Stimulation of acidsecretion resulted in no measurable change in the relative amounts ofG-actin and cytoskeletal F-actin. Treatment of gastric glands withcytochalasin D inhibited acid secretion and resulted in a decrease inF-actin and an increase in G-actin. No inhibition of parietal cellsecretion was observed when phalloidin was used to stabilize actinfilaments. These data are consistent with the hypothesis thatmicrofilamentous actin is essential for membrane recruitment underlyingparietal cell secretion. Although the experiments do not eliminate theimportance of rapid exchange between G- and F-actin for the secretoryprocess, the parietal cell maintains actin in a highly polymerizedstate, and no measurable changes in the steady-state ratio of G-actin to F-actin are associated with stimulation to secrete acid.

     

Mechanism of regulation of actin polymerization by Physarum profilin

Physarum profilin reduces the rates of nucleation and elongation of F- actin and also reduces the extent of polymerization of actin at the steady state in a concentration-dependent fashion. The apparent critical concentration for polymerization of actin is increased by the addition of profilin. These results can be explained by the idea that Physarum profilin forms a 1:1 complex with G-actin and decreases the concentration of actin available for polymerization. The dissociation constant for binding of profilin to G-actin is estimated from the kinetics of polymerization of G-actin and elongation of F-actin nuclei and from the increase of apparent critical concentration in the presence of profilin. The dissociation constants for binding of Physarum profilin to Physarum and muscle actins under physiological ionic conditions are in the ranges of 1.4-3.7 microM and 11.3-28.5 microM, respectively. When profilin is added to an F-actin solution, profilin binds to G-actin which co-exists with F-actin, and then G- actin is dissociated from F-actin to compensate for the decrease of the concentration of free G-actin and to keep it constant at the critical concentration. At the steady state, free G-actin of the critical concentration is in equilibrium not only with F-actin but also with profilin-G-actin complex. The stoichiometry of 1:1 for the formation of complex between profilin and G-actin is directly shown by means of chemical cross-linking.     

Solution structure of human cofilin: actin binding, pH sensitivity, and relationship to actin-depolymerizing factor

Human actin-depolymerizing factor (ADF) and cofilin are pH-sensitive, actin-depolymerizing proteins. Although 72% identical in sequence, ADF has a much higher depolymerizing activity than cofilin at pH 8. To understand this, we solved the structure of human cofilin using nuclear magnetic resonance and compared it with human ADF. Important sequence differences between vertebrate ADF/cofilins were correlated with unique structural determinants in the F-actin-binding site to account for differences in biochemical activities of the two proteins. Cofilin has a short beta-strand at the C terminus, not found in ADF, which packs against strands beta3/beta4, changing the environment around Lys96, a residue essential for F-actin binding. A salt bridge involving His133 and Asp98 (Glu98 in ADF) may explain the pH sensitivity of human cofilin and ADF; these two residues are fully conserved in vertebrate ADF/cofilins. Chemical shift perturbations identified residues that (i) differ in their chemical environments between wild type cofilin and mutants S3D, which has greatly reduced G-actin binding, and K96Q, which does not bind F-actin; (ii) are affected when G-actin binds cofilin; and (iii) are affected by pH change from 6 to 8. Many residues affected by G-actin binding also show perturbation in the mutants or in response to pH. Our evidence suggests the involvement of residues 133-138 of strand beta5 in all of the activities examined. Because residues in beta5 are perturbed by mutations that affect both G-actin and F-actin binding, this strand forms a "boundary" or "bridge" between the proposed F- and G-actin-binding sites.     

A role for γS-crystallin in the organization of actin and fiber cell maturation in the mouse lens

γS-crystallin (γS) is a highly conserved component of the eye lens. To gain insights into the functional role(s) of this protein, the mouse gene (Crygs) was deleted. Although mutations in γS can cause severe cataracts, loss of function of γS in knockout (KO) mice produced no obvious lens opacity, but was associated with focusing defects. Electron microscopy showed no major differences in lens cell organization, suggesting that the optical defects are primarily cytoplasmic in origin. KO lenses were also grossly normal by light microscopy but showed evidence of incomplete clearance of cellular organelles in maturing fiber cells. Phalloidin labeling showed an unusual distribution of F-actin in a band of mature fiber cells in KO lenses, suggesting a defect in the organization or processing of the actin cytoskeleton. Indeed, in wild-type lenses, γS and F-actin colocalize along the fiber cell plasma membrane. Relative levels of F-actin and G-actin in wild-type and KO lenses were estimated from fluorescent staining profiles and from isolation of actin fractions from whole lenses. Both methods showed a two-fold reduction in the F-actin/G-actin ratio in KO lenses, whereas no difference in tubulin organization was detected. In vitro experiments showed that recombinant mouse γS can directly stabilize F-actin. This suggests that γS may have a functional role related to actin, perhaps in 'shepherding' filaments to maintain the optical properties of the lens cytoplasm and normal fiber cell maturation.