Actin bundles have profound effects on cellular shape, division, adhesion, motility, and signaling. Fimbrin belongs to a large family of actin-bundling proteins and is involved in the formation of tightly ordered cross-linked bundles in the brush border microvilli and in the stereocilia of inner ear hair cells. Polymorphism in these three-dimensional (3D) bundles has prevented the detailed structural characterization required for in-depth understanding of their morphogenesis and function. Here, we describe the structural characterization of two-dimensional arrays of actin cross-linked with human T-fimbrin. Structural information obtained by electron microscopy, x-ray crystallography, and homology modeling allowed us to build the first molecular model for the complete actin–fimbrin cross-link. The restriction of the arrays to two dimensions allowed us to deduce the spatial relationship between the components, the mode of fimbrin cross-linking, and the flexibility within the cross-link. The atomic model of the fimbrin cross-link, the cross-linking rules deduced from the arrays, and the hexagonal packing of actin bundles in situ were all combined to generate an atomic model for 3D actin–fimbrin bundles. Furthermore, the assembly of the actin–fimbrin arrays suggests coupling between actin polymerization, fimbrin binding, and crossbridge formation, presumably achieved by a feedback between conformational changes and changes in affinity.

Introduction

Cells organize their actin filaments into three-dimensional (3D) bundles using a large repertoire of actin–cross-linking proteins (Ayscough 1998; Puius et al. 1998; Bartles 2000). Actin bundles support and stabilize cellular protrusions, invaginations, or domains of the plasma membrane and thus have profound effects on cellular shape, division, adhesion, motility, and signaling. The actin cross-linkers are conserved throughout the eukaryotic kingdom and found to have a modular organization (Matsudaira 1991). They are composed of a pair of actin-binding domains (ABDs), variable spacer domains, and sometimes a regulatory domain. In one cross-linking class, the conserved ABDs consist of tandem pairs of calponin homology (CH) domains (Castresana and Saraste 1995; Banuelos et al. 1998). Proteins containing tandem pairs of CH domains include α-actinin, dystrophin, fimbrin, spectrin, and utrophin. The simplest modular arrangement within the cross-linkers of this family is found in fimbrin, where two ABDs are arranged on the same polypeptide chain without any spacers, directing the formation of densely packed bundles. In the rest of the family, tandem organization of two ABDs is achieved through protein dimerization.

In vivo, fimbrin is involved in the formation of actin bundles in the microvilli of the brush border epithelia cells and in the hair cell stereocilia of the inner ear (Tilney et al. 1989, Tilney et al. 1992). The tightly packed arrays of the microvilli amplify the apical surface of the absorptive epithelial cells, and the stereocilia serve as mechanosensory devices implicated in transduction of sound-induced motion. Fimbrin is the major actin-bundling protein of the hair cell stereocilia. Fimbrin and villin are the major cross-linkers of the microvilli core. However, ultrastructural studies of intestinal microvilli in villin-null mice indicate that villin is not a critical determinant for bundle assembly (Pinson et al. 1998; Ferrary et al. 1999). Microvilli as well as stereocilia bundles contain parallel actin filaments that share the same polarity and are packed in a hexagonal lattice with their filament barbed ends facing the cell surface (DeRosier and Tilney 1982; Tilney et al. 1983, Tilney et al. 2000). The actin-bundling activity of fimbrin is inhibited by calcium (Namba et al. 1992; Lin et al. 1994).

Understanding the mechanism of bundle assembly and function requires detailed structural information. However, disorder and polymorphism limit the structural information that can be extracted from actin bundles directly. To constrain this polymorphism, here we restricted the cross-linking to two dimensions and analyzed the structural organization of actin and of actin arrays cross-linked with human T-fimbrin. In the cross-linked arrays we found two distinct types of cross-link conformations, leading to straight or slanted crossbands. The actin filaments in these arrays are unipolar, consistent with the organization observed in bundles in vivo (DeRosier and Tilney 2000). In addition, the distance (∼120 Å) between adjacent filaments in the fimbrin–cross-linked arrays agrees with the average distance reported for microvilli bundles (Matsudaira et al. 1983; Coluccio and Bretscher 1989). The assembly of the two-dimensional (2D) actin–fimbrin arrays in our experimental setting suggests coupling between actin polymerization, fimbrin binding, and crossbridge formation.

The structural information derived from the arrays and the structure of an actin–fimbrin (ABD) complex (Hanein et al. 1998) were used to generate the first atomic model of complete actin–fimbrin cross-links. The model provides evidence for flexibility of the actin–fimbrin cross-link, that can be accommodated by the torsional freedom of actin filaments (Egelman and DeRosier 1992; Orlova and Egelman 2000) and rearrangements at the interface between the two ADBs of fimbrin. The observed flexibility of the cross-link, the resulting constraints on the cross-linking rules, and the hexagonal packing of actin bundles in situ (Tilney et al. 1983, DeRosier and Tilney 2000) allowed us to build an atomic model for actin–fimbrin bundles. This model supports a mechanism for bundle bending through tilting of the crossbridges, consistent with the observations of bent stereocilia bundles in which the actin filaments slide past each other and do not stretch or compress (Tilney et al. 1983). In vivo, bending of the bundle occurs during stereocilia stimulation by sound and motion.

Materials and Methods

Protein Purification

β-Actin was purified by Dr. I. Correia (Whitehead Institute, Cambridge, MA) (Rozycki et al. 1991). The G-actin was flash frozen in liquid nitrogen and stored as 1-mg aliquots at −80°C. Before use, aliquots were thawed, dialyzed against G-actin buffer (2 mM Tris, pH 8.0, 0.2 mM CaCl2, 0.2 mM ATP, and 1 mM DTT), and clarified at 7.0 × 104 rpm for 30 min in a Beckman-Coulter TLA-100 rotor.

Human T-fimbrin was expressed in BL21 bacterial cells grown in 2X YT/Amp media, concentrated by centrifugation, and lysed in a French press. The 3/7 ammonium sulfate precipitate from a 18k × g supernatant of the cell lysate was resuspended in column buffer (50 mM NaCl, 1 mM EDTA, 1 mM DTT, 1 mM NaN3, and 10 mM Tris, pH 8.0) and chromatographed through an AcA34 gel filtration column. Fimbrin-containing fractions were pooled and loaded onto a DEAE Sepharose fast flow column equilibrated in column buffer. The column was developed with a 0–300 mM gradient of NaCl in column buffer, and the fimbrin-containing fractions were pooled and diluted to 50 mM NaCl in column buffer. The fimbrin-containing fractions were loaded onto an fast protein liquid chromatography Q-HR Sepharose column and eluted with a 0–500 mM NaCl gradient in 1 mM EDTA, 1 mM DTT, 10 mM Pipes, pH 7.0. The fimbrin fractions were pooled and concentrated in a Centricon concentrator. By SDS-PAGE, the protein was at least 95% pure.

2D Arrays

Arrays were grown (8–24 h) at 4°C on positively charged lipid layers consisting of a 3:7 wt/wt solution of dilaurylphosphatidylcholine (Avanti Polar Lipids, Inc.) and didodecyldimethylammonium bromide (DDDMA; Acros Organic) dissolved in chloroform (Taylor and Taylor 1994). The lipid–surfactant mixture (0.5 μl drop containing 0.5 μg lipids) was layered over the polymerization buffer before the injection of G-actin (∼0.5 μM) for producing the F-actin arrays. The polymerization buffer contained 20 mM PO4, pH 6.5, 40 mM KCl, 1 mM MgCl2, 1 mM ATP, and 0.2 mM EGTA. For producing the actin–fimbrin arrays, the lipid–surfactant mixture was layered over the polymerization buffer containing fimbrin (∼1 μM) before the injection of G-actin (∼0.5 μM).

Electron Microscopy

Specimens were transferred to 400-mesh copper grids coated with holey carbon films (Kubalek et al. 1991). Specimens were washed with polymerization buffer before staining using 2% aqueous uranyl acetate and air dried. The samples stained and not washed had 3D bundles intersecting the 2D arrays. Specimens were examined on a CM12 electron microscope (FEI) under low-dose conditions. Low-dose images were recorded using 120 keV, at a nominal magnification of 60,000× and ∼0.5-μm defocus (electron dose ∼10 e Å−2).

Image Processing

Images were scanned at a raster of 7 μm pixel−1 using a SCAI scanner and an O2 workstation (SGI). 40 arrays of actin–fimbrin and 20 of fimbrin-free actin were chosen for image processing. The arrays were selected, boxed, and displayed with a modified version of Ximdisp (Smith 1999). Fourier transforms were calculated using the Brandeis helical imaging package (Owen et al. 1996). All measurements (e.g., tilt and distance) relating to row-line offsets to determine rotational and translational relationships between neighboring filaments were done relative to the direction of the layer lines. This ensures that no bias is introduced by misalignment of the arrays in respect to the image coordinate system. Fourier filtering was done using the 2D crystallography software in the MRC image-processing package (Crowther et al. 1996).

Homology Modeling

Homology modeling was achieved using the program MODELLER4 (Sali and Blundell 1993). We used the crystal structures of the fimbrin (PDB code 1AOA) and utrophin (1QAG) NH2-terminal ABDI , and of the CH domain of β-spectrin (1AA2) for the modeling of the COOH-terminal ABD of fimbrin (ABD2). We used 48 EF-hand structures to model the NH2-terminal calcium-binding domain.

Sequence Similarity

The sequence similarity between the residues of ABD1 and ABD2 was evaluated using a scoring matrix (PAM250, as used in FASTA; Pearson 1990). The numbers in the scoring matrix are derived from the probability of substitution. The higher this number, the higher the sequence similarity. 68 residues were assigned as prospective interface residues using interaction probabilities for ABD1 (Hanein et al. 1998). The residues in ABD1 and ABD2 that were assigned to interact were identical in 29.4% of the cases; the ones in the remaining set were identical in 23.2% of the cases. The average similarity score for the interface residues was 2.265, and that for the remainder was 0.584. A t test reveals that this difference is statistically significant at a confidence level of 99.5% (p-value < 0.005).

Results

2D Arrays of Actin Filaments Cross-linked with Human T-Fimbrin

We polymerized G-actin on positively charged lipid surfaces (Ward et al. 1990; Taylor and Taylor 1994) in the absence (Fig. 1 A) and in the presence (Fig. 1, B–C) of human T-fimbrin. In the cross-linked arrays the crossbridges appear as regularly spaced bands either perpendicular or slanted relative to the axis of the actin filaments. Washing the preformed actin arrays with fimbrin resulted in sparse formation of cross-links and an appearance with no regular crossbands. A stoichiometry of one crossbridge per crossover (about every 13.5 actin monomers, 375 Å apart) is measured in gels (data not shown) as well as directly from the images.

Polarity and Spatial Relationships between Neighboring Filaments in the Fimbrin-free 2D Arrays.

The filament arrays of actin in the absence of fimbrin are tightly packed and give rise to well-ordered computed diffraction patterns (Fig. 1 A). These patterns consist of spots lying on a series of horizontal lines called layer lines. These layer lines arise from the helical symmetry of the actin filaments (Fig. 2 A). Single filaments give rise to continuous layer lines. The sampling of the layer lines, at intersections with so-called row lines, is due to the paracrystalline order of the filaments (Fig. 2A and Fig. B). The way the layer lines are sampled (tilt and distance of the row lines) gives information on the spatial relationship between neighboring filaments, i.e., orientation, the relative rotation, and axial shift (Sukow and DeRosier 1998). The actin and actin–fimbrin arrays are highly ordered, as can be assessed from the clear visibility of individual F-actin monomers in the Fourier-filtered images and the resolution of diffraction patterns of individual arrays (Fig. 1B and Fig. C, ∼35 Å). This resolution is clearly sufficient to unambiguously determine the tilt and the distance of the row lines and thus the spatial relationship between neighboring filaments. Within the 20 fimbrin-free arrays analyzed, the interfilament distance between successive actin filaments is ∼75–80 Å. The diameter of actin filaments in projection is ∼90 Å. The fact that the interfilament distance is smaller than the projection diameter means that the packing must be extremely tight with relatively close contact distances between actin monomers of adjacent filaments. Within the actin arrays, we observe both unipolar and bipolar organization of adjacent filaments, with some preference to unipolar. We detect bipolar arrays by the occurrence of diffraction spots on the layer lines halfway in between the spots for unipolar arrays (Fig. 1 A). This additional sampling in the bipolar arrays results from the reduced symmetry generated by neighboring filaments having their polarities reversed (Sukow and DeRosier 1998). The tilting of the row lines in the diffraction pattern indicates that adjacent actin filaments are rotated counter clockwise by 30–40°.

Polarity and Spatial Relationships between Neighboring Filaments in the Cross-linked 2D Arrays.

In the fimbrin cross-linked arrays (Fig. 1B and Fig. C), the spacing between the filaments as measured in real and reciprocal space is 115–120 Å, consistent with the distance of 120 Å measured by solution x-ray scattering from microvilli bundles (Matsudaira et al. 1983). This interfilament distance is also consistent with the distance predicted by the atomic model of the actin–fimbrin ABD complex (Hanein et al. 1998). In contrast, the interfilament distance of 2D actin arrays cross-linked with α-actinin, which is found in actin gels and networks, is ∼390 Å (Taylor et al. 2000).

Contrary to the fimbrin-free actin arrays, the actin arrays cross-linked by fimbrin are always unipolar. Two lines of evidence support this unipolar organization of the filaments. First, inspection of the computed diffraction patterns of 40 cross-linked arrays shows that all layer lines are separated by a distance equal to the interfilament spacing (Fig. 1B and Fig. C). No spots appear halfway in between. Second, where a filament ends within an array, the two neighboring filaments are cross-linked with no disruption to the array or alteration in the orientation of the crossbridges (Fig. 1 D). This indicates that the spatial relationship between the filament that ends and its two neighboring filaments is identical to the spatial relationship between the two neighboring filaments. This is only possible if the polarity of the three filaments is the same. In vivo, microvilli and stereocilia actin–fimbrin bundles have also been shown to have unidirectional polarity (Tilney et al. 1980).

Crossbridge Conformations and Flexibility.

We observed two types of crossbridge conformations, one producing straight crossbands (Fig. 1 B), the other producing slanted crossbands (Fig. 1 C). Only these two types of conformations exist, and both conformations can be easily identified by eye. We did not observe mixed arrays. Both arrays are distinct from actin arrays in the absence of fimbrin (Fig. 1 A). The slanted arrays display handedness and are always slanted in the same direction as shown in Fig. 1 C. The handedness in the slanted arrays indicates a preference of one side of the array for the lipid surface. As a consequence of their helical symmetry, actin filaments appear the same from all directions. Therefore, the preference of one side of the array for the lipid must result from the spatial relationship between the interfilament cross-link and the lipid. Handedness in arrays with straight crossband appearance, if it exists, cannot be assessed visually.

The diffraction patterns of the straight crossband conformation indicate that adjacent actin filaments are in register (Fig. 1 B). The rotation angle between adjacent filaments in the array can be deduced from the analysis of their corresponding diffraction patterns (Sukow and DeRosier 1998). For the analyzed straight crossband arrays, these angles ranged beteen to −5° and +5° with a mean value close to zero. The diffraction patterns of the slanted crossbridge conformation indicate a clockwise rotation of ∼27° between adjacent filaments (Fig. 1 C). The angles for all slanted arrays investigated fell into the range between 22° and 32°. Due to the helical symmetry of actin, a 26.66° rotation is equivalent to a translation of 55 Å towards its barbed end (Fig. 2 C). Thus, a transformation from the spatial relationship between adjacent filaments in the straight crossband array (in register) to the spatial relationship in the slanted crossband arrays can be simply achieved by sliding the neighboring filament down by 55 Å. If a cross-link in the straight crossband array is rotated by 180° and is bound to the same actin units on one filament, the free binding site of the cross-linker, due to fimbrin's geometry (Fig. 3), faces now in the same direction as before (towards the second filament), only transitionally shifted downwards by 55 Å. Thus, a similar cross-linker conformation can accommodate both crossband patterns if the cross-linker is rotated by 180° around its center of mass, and the roles of ABD1 and ABD2 are exchanged.

Can Fimbrin's ADBs Exchange Roles?

Structural studies of F-actin complexes of α-actinin (McGough et al. 1994), fimbrin (ABD1) (Hanein et al. 1997), and utrophin (Moores et al. 2000) have all suggested that the conserved ABDs of this cross-linker superfamily (Matsudaira 1994; Castresana and Saraste 1995) bind a similar surface on actin. Results of peptide deletion studies and suppressor mutant analysis for fimbrin and several other members of the superfamily also indicate that the ABDs of this family bind a similar surface on actin (Mimura and Asano 1987; Lebart et al. 1990; Bresnick et al. 1991; Levine et al. 1992; Fabbrizio et al. 1993; Corrado et al. 1994; Holtzman et al. 1994; Honts et al. 1994; Brower et al. 1995). Sequence similarity between fimbrin residues proposed to interact with actin (Fig. 4A and Fig. B) is significantly higher (p-value < 0.005) than the similarity between residues not involved in actin binding, further supporting the notion that the roles of ABD1 and ABD2 can be exchanged. However, despite the high sequence similarity, there is relatively low sequence identity (29.4%) in the residues involved in actin binding, indicating that ABD1 and ABD2 may generate non-identical interactions with actin. This is consistent with the identification of two separate dissociation constants for plant fimbrin from Arabidopsis thaliana, presumably one for each ABD (Kovar et al. 2000), and results obtained by suppressor mutant studies of yeast fimbrin. A tryptophan residue that is absolutely conserved in all ABDs of the superfamily show different levels of suppression for equivalent mutations in ABD1 (W252C, human T-fimbrin sequence) and ABD2 (W499C, human T-fimbrin sequence) (Fig. 4C and Fig. D) (Brower et al. 1995).

As a consequence of the filament symmetry (∼2.16 actin monomers per turn, 27.5 Å rise per monomer), the exact spatial relationship needed for the formation of the crossbridge only occurs every fourth crossover (every 54 monomers). The three crossovers in between are offset from this spatial relationship (Fig. 2 D, and its respective legend). The observed crossband patterns and the biochemical analysis indicate one crossbridge per crossover. How can this be accomplished? The straight crossbridge formation can be achieved with an angular deviation of only 6.66° by allowing direction reversal of the crossbridges every 27 monomers. The slanted crossband conformation needs deviations up to 20° since it cannot be built with reversal of the crossbridge direction due to its handedness. The existence of the slanted crossbridge conformation therefore necessitates that the actin cross-linker complex can be deformed to accommodate a ≤20° difference over four crossovers. However, the flexibility of the actin cross-linker system must be <26.66°, otherwise the cross-linker can accommodate both crossband patterns within the same array, i.e., a slanted crossband pattern in arrays with filaments in register. The later type of crossband pattern is not observed experimentally. The torsional freedom in actin, which expresses itself in a 5°–6° root-mean-square random change in the twist per monomer (Egelman and DeRosier 1992; Orlova and Egelman 2000), is likely to be a contributor to the actin cross-linker flexibility that allows the binding at the offset monomers. The variable twist of the actin filaments together with the flexibility of fimbrin give enough freedom to accommodate the observed range of crossbridge conformations while maintaining specific actin–fimbrin interactions. Crystal structures of the ABDs of several members of the superfamily have shown different dimer arrangements (Keep et al. 1999, Norwood et al. 2000), suggesting that the flexibility of fimbrin can be achieved through rearrangements of the ABD1-ABD2 interface.

Actin–Fimbrin Cross-link

We provided measurement of stoichiometry of fimbrin in 2D arrays (one crossbridge per crossover), the polarity (unipolar) and the spacing between adjacent cross-linked filaments (115-120 Å), the conformations of the crossbridge, and flexibility of the actin–fimbrin cross-link. We used this information to deduce the spatial relationships between the components of the cross-link. The knowledge of the spatial relationships allows us to build a model of the 2D arrays by putting the components together in a way that satisfies these relationships. To build the atomic model of an interfilament cross-link, we also need atomic models for the components. The crystal structure of the NH2-terminal ABD1 of fimbrin (Goldsmith et al. 1997), as well as an atomic model of the actin-ABD1 complex (Hanein et al. 1998), is available. The atomic structures of the ABD2 and the NH2-terminal regulatory domain of fimbrin are still not known. Therefore in this study, we generated models of both domains through the use of homology modeling (Sali and Blundell 1993).

Homology Modeling of the NH2-terminal Calcium-binding Domain.

Sequence analysis shows that there are two tentative EF-hand motifs in the NH2-terminal regulatory calcium-binding domain of fimbrin (de Arruda et al. 1990). There are currently more than 90 EF-hand structures in the Protein Data Bank. 48 of these have sequence identity larger than 37.5%. Using these structures as the basis for the homology modeling, we obtained an atomic model of the domain (Fig. 4 E). Although the secondary structure of the NH2-terminal domain is well defined by the high homology with other EF-hand motifs, the exact spatial arrangement of these structural elements remains uncertain. The relative orientation between the helices of the EF-hand motifs is known to be flexible (Yap et al. 1999). We initially modeled the relative orientation according to troponin C, the structure with the highest sequence identity (47.9%), and refined it later using spatial constraints from the rest of the structural domains of the model.

Homology Modeling of ABD2.

We modeled the two CH domains that make up ABD2 independently. We used CH domains from the crystal structures of the fimbrin ABD1 (Goldsmith et al. 1997), utrophin ABD1 (Keep et al. 1999), and the CH domain of β-spectrin (Carugo et al. 1997), making a total of five known CH domain structures. ABD1 of fimbrin was used as a scaffold for the relative conformation of the two CH domains of ABD2 (Fig. 4 A). The decision to use fimbrin's ABD1 as a scaffold rather than utrophin's ABD1 was guided by the observations that ABD1 and ABD2 share a similar binding site on actin (Holtzman et al. 1994; Honts et al. 1994; Brower et al. 1995). This can only be achieved if ABD2 is in a fimbrin-ABD1–like conformation.

Building a Cross-link. Spatial Relationship between ABD1, ABD2, and the Calcium-binding Domain.

The spatial relationship between ABD1 and the calcium-binding domain was provided through the fitting of ADB1 crystal structure into helical reconstructions of actin decorated with N375 (fimbrin ABD1 plus calcium-binding domain) (Hanein et al. 1998). A prominent peak, calculated from the difference between the observed density and the docked atomic model, localized the calcium-binding domain at the interface between the CH domains of ABD1 on the side facing away from the actin filament. This spatial arrangement places constraints on the relative orientation of the EF-hand helices, narrowing the possibilities down to a small number of relative arrangements. We selected one arrangement that fulfills these spatial constraints and also places both Ca++ binding sites exposed to solvent. The spatial relationship between the actin filaments and ABD1 as well as the actin-ABD1 residues involved in binding have been also establish (Hanein et al. 1998). The distance between filaments in the 2D arrays helps to define the distance between the ABDs. There are two ways in which to add ABD2 and a second actin filament to form a complete interfilament cross-link. One arrangement leads to clashes between ABD2 and the calcium-binding domain, but the other one does not. Our model in Fig. 3 corresponds to the model without clashes. We cannot deduce from the data whether the handedness of the slanted crossband conformation is due to a preferred distance or a preferred orientation of the crossbridges relative to the lipid layer. The arrangement in Fig. 3 shows a similar relative distance of the crossbridges from the lipid interface in the straight crossband conformation and the slanted conformation (Fig. 3B and Fig. F). The distance is the more likely cause for handedness, since we do not observe excess fimbrin bound to the lipid. However, a similar relative orientation, i.e., exposing the same surface patch of fimbrin to the lipid, can be achieved by simply flipping the straight array in Fig. 3 by 180° parallel to the actin filament axis (around the paper plane), without altering the crossbridge model or the relative orientations between actin and the crossbridges. Our model is fully compatible with the observed diffraction patterns (compare the patterns calculated from the model in Fig. 3D and Fig. I, with the observed ones in Fig. 1B and Fig. C) as well as with the real space images of the 2D arrays (Fig. 3E and Fig. H).

Discussion

2D Assembly Mechanism

Fimbrin imposes a regularity on the cross-linked array that is different from that observed in fimbrin-free actin arrays. It is interesting to note that fimbrin does not incorporate well into preformed actin arrays. We observed only a partial formation of cross-links and no regular crossbands in this case (data not shown). The regular appearance of the crossbands within the arrays (slanted or straight) indicates that the binding of fimbrin to actin occurs only at very specific binding sites and not in a random manner. The observation that regular crossbands only form when filaments are polymerized in the presence of fimbrin suggests that array formation requires coupling between actin polymerization and cross-link assembly. This notion is supported by the fact that in vitro yeast fimbrin (Sac6p) restores polymerization and bundle formation of a polymerization-defective yeast actin (GG-actin) (Cheng et al. 1999). Sac6p is also required for cell viability in the GG-actin phenotype in vivo (Cheng et al. 1999). In addition, the sedimentation behavior of F-actin from A. thaliana in the presence and absence of fimbrin suggests that fimbrin may promote actin polymerization and is capable of cross-linking very short segments of actin filaments (Kovar et al. 2000).

How can specific binding of fimbrin generate the observed crossband patterns? One possibility is that either fimbrin or actin (or both) sense the presence of a bound molecule at the opposite side of the actin filament. It is known that ABD1 binding initiates conformational changes within F-actin (Hanein et al. 1997), providing a possible mechanism for communication from one binding site on F-actin to another. In this setting the initial affinity of fimbrin and F-actin would be relatively low (Fig. 5, gray actin monomers), allowing fimbrin to detach easily. This hypothesis is consistent with the observation that ABD1 decorates single filaments only partially (Hanein et al. 1997; Rost et al. 1998). However, the presence of the first bound monomer may increase the affinity of the opposite F-actin–binding site (Fig. 5 B, yellow), increasing the probability of binding a second fimbrin molecule at that site. Binding of the second fimbrin molecule is then in turn sensed by the first binding site (Fig. 5 C, now also yellow), lowering the likelihood of detachment for the first-bound fimbrin molecule, i.e., increasing its affinity to actin. The next actin filament, sharing the same polarity with the first fimbrin-bound filament, can contact the bound fimbrin only in relatively fixed geometry due to limited crossbridge flexibility (maximum ∼20°). Whether this geometry produces straight or slanted crossbands would depend on which ABD binds first to the filament: One will result in straight crossbands (Fig. 5, top), whereas the other will result in slanted crossbands (Fig. 5, bottom). The lack of mixed arrays suggests that actin senses whether ABD1 or ABD2 is bound at the opposite site, allowing only one type of ABD (the one that is not bound at the original binding site) to bind at the unoccupied binding site. That actin distinguishes between the two ABDs is supported by the relatively small sequence identity in fimbrin residues involved in actin binding, by different levels of suppression (Brower et al. 1995) for equivalent mutations in ABD1 and ABD2, and by the identification of two distinct dissociation constants for actin–fimbrin interactions in A. thaliana (Kovar et al. 2000).

We observe only very little fimbrin decoration of single isolated actin filaments, and these were not incorporated in the arrays. The rareness of single filament decoration suggests that affinity is higher when another filament is bound to the fimbrin at the opposite binding site. As a consequence of this hypothesis, one should be able to observe regular fimbrin decoration at the edge of intact arrays (side decoration). These actin-bound fimbrin molecules would not form crossbridges due to the absence of adjacent actin filaments. Indeed, we observed exactly that in our electron micrographs (Fig. 1 E). The fact that this side decoration is much more abundant than decoration of two opposite fimbrin molecules on single filaments indicates that the bonds on array sides are stronger than on single filaments. This is consistent with our proposal that the unoccupied binding site on actin not only senses the presence of fimbrin on the opposite site but also whether this fimbrin is bound to a second actin or not. The extension of this proposed mechanism into three dimensions may provide the necessary specificity for precise organization of the bundles in vivo.

3D Actin–Fimbrin Bundles

We built a 3D atomic model of actin–fimbrin bundles using the atomic model of the 2D cross-link and the bonding rules. In summary, three aspects of the bonding rules can be deduced from the data and the modeling. One, ABD1 and ABD2 bind a similar interface on actin. Two, the flexibility within the actin cross-linker complex, through the offset between allowed binding sites, is at least 20°. On the other side this flexibility needs to be <26.66°, as we do not observe slanted crossbands while filaments are in register. Three, the lack of mixed arrays and the regularity of the crossband patterns suggest that only different fimbrin ABDs (e.g., ABD1 and ABD2) can bind to the two opposite sides of the filament (not ABD1 and ABD1 or ABD2 and ABD2).

In vivo, actin–fimbrin bundles such as in the stereocilium from the hair cells of bird cochlea were shown to be organized in a hexagonal lattice, to be unipolar, and to have their filaments in register (DeRosier and Tilney 1982). This geometry indicates that the geometry of slanted arrays (neighboring filaments not in register) does not appear in vivo. Three regularly spaced crossbands per crossover are visible in the stereocilia. Is this information consistent with our model? The three crossbands observed in these stereocilium bundles indicate that each neighboring filament in the hexagonal lattice is crossbridged once per crossover (Fig. 6 A). Starting at actin monomer 0 (located near the red crossbridge in Fig. 6 A) as the reference and using our cross-linking rules, the next crossbridge would be possible at the fourth monomer (located near the green crossbridge in Fig. 6 A) with a 6.66° counter clockwise offset from the reference position. The next crossbridge would occur at the ninth monomer with the reference geometry, but pointing in a different direction (near the blue crossbridge in Fig. 6 A). A crossbridge could then occur at the next crossover point at monomer 13 (cross-linking the same filaments as at actin monomer 0, similar to the straight 2D array) with a 6.66° counter clockwise offset from the reference position. The next crossbridge would occur at monomer 18, again with the geometry of actin monomer 0, but with reversed direction from the crossbridge at monomer 4 (compare 4 with 18 in Fig. 6C and Fig. D). The following crossbridge at monomer 22 is offset 6.66° counter clockwise from the reference position at monomer 9. The next crossbridge at monomer 27 would again be in reference geometry, but with reversed direction from the very first crossbridge at monomer 0. The emerging pattern is an alternation between one crossbridge every 4 and every 5 monomers with 6.66° offset between them, a deviation that can be easily achieved by the variability in the actin twist (∼6° root-mean-square deviation) alone. The rest of the cross-link's flexibility, which can accommodate ∼20° offset in total, is then still available for accommodating the necessary bending and flexibility required from these mechanoelectrical signal transducer bundles. The mechanical deformation of the hair cells is required for the depolarization and subsequent neurotransmitter release at the synapses. In situ observations show that the crossbridges tilt in respect to the filament axis when stereocilia bend (Tilney et al. 1983), indicating that the main source of flexibility is deformation of the cross-links. This flexibility of the cross-links is most likely due to the variable twist of the actin filaments actin and rearrangements at ABD1-ABD2 interface.

Structural characterization of 2D actin and actin–fimbrin arrays obtained by electron microscopy and image analysis, combined with information derived from x-ray crystallography and homology modeling, allowed us to build the first molecular model of an actin–fimbrin cross-link. Our structural model for the cross-link is in excellent agreement with the crossband patterns and interfilament spacing of stereocilia of the inner ear (DeRosier and Tilney 1982) and of other actin bundles (DeRosier et al. 1977; Spudich and Amos 1979; DeRosier and Censullo 1981; Cohen et al. 1982). The data support an assembly mechanism that relies on long-range communication between the individual components of the arrays, presumably achieved by a feedback between conformational changes and changes in affinity. The regularity of the cross-linked assembly appears to be achieved through coupling between actin polymerization and cross-link formation. The model predicts the existence of flexibility within the fimbrin molecule that is consistent with a mechanism for bundle bending through tilting of the crossbridges (Tilney et al. 1983), allowing to explain how an actin bundle can be a mechanosensory machine.

Acknowledgments

We thank Dr. I. Correia for β-actin. N. Volkmann and D. Hanein thank L. Bankston for her valuable comments on the manuscript.

This work was supported by National Institutes of Health grants to D. DeRosier (GM26357) and to P. Matsudaira (CA44703). The authors acknowledge funds from the W.M. Keck Foundation.

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Abbreviations used in this paper: 2D, two-dimensional; 3D, three-dimensional; ABD, actin-binding domain; ABD1, NH2-terminal ABD of fimbrin; ABD2, COOH-terminal ABD of fimbrin; CH, calponin homology.