Gelsolin binds to polymeric actin at a low rate.

Association of gelsolin with actin filament subunits was investigated by the decrease of the fluorescence intensity of a 7-nitro-2-oxa-1,3-diazole (NBD) label covalently linked to gelsolin. The rate constant of this reaction was found to be 4 x 10(3) M-1 s-1. Binding of NBD-labeled gelsolin to monomeric actin proceeds at a similar low rate. The rate of association of gelsolin that was unmodified to actin filament subunits was estimated too. Unmodified gelsolin was added to a mixture of actin filaments and actin-DNase I complex. The fractions of gelsolin that bound to actin filament subunits or to actin-DNase I complex depended on the relative rates of these two competing reactions. In this way it was possible to estimate the rate constant of association of unmodified gelsolin with actin filament subunits (2 x 10(4) M-1 s-1). Thus, gelsolin associates with actin filament subunits at a rate that is considerably slower than diffusion-controlled and similar to the rate of binding of gelsolin to monomeric actin.     

Coarse-Graining Provides Insights on the Essential Nature of Heterogeneity in Actin Filaments

Experiments have shown that actin is structurally polymorphic, but knowledge of the details of molecular level heterogeneity in both the dynamics of a single subunit and the interactions between subunits is still lacking. Here, using atomistic molecular dynamics simulations of the actin filament, we identify domains of atoms that move in a correlated fashion, quantify interactions between these domains using coarse-grained (CG) analysis methods, and perform CG simulations to explore the importance of filament heterogeneity. The persistence length and torsional stiffness calculated from molecular dynamics simulation data agree with experimental values. We additionally observe that distinct actin conformations coexist in actin filaments. The filaments also exhibit random twist angles that are broadly distributed. CG analysis reveals that interactions between equivalent CG pairs vary from one subunit to another. To explore the importance of heterogeneity on filament dynamics, we perform CG simulations using different methods of parameterization to show that only by including heterogeneous interactions can we reproduce the twist angles and related properties. Free energy calculations further suggest that in general the actin filament is best represented as a set of subunits with differing CG sites and interactions, and the incorporating heterogeneity into the CG interactions is more important than including that in the CG sites. Our work therefore presents a systematic method to explore molecular level detail in this large and complex biopolymer.     

The structural basis for the intrinsic disorder of the actin filament: the "lateral slipping" model

Three-dimensional (3-D) helical reconstructions computed from electron micrographs of negatively stained dispersed F-actin filaments invariably revealed two uninterrupted columns of mass forming the "backbone" of the double-helical filament. The contact between neighboring subunits along the thus defined two long-pitch helical strands was spatially conserved and of high mass density, while the intersubunit contact between them was of lower mass density and varied among reconstructions. In contrast, phalloidinstabilized F-actin filaments displayed higher and spatially more conserved mass density between the two long-pitch helical strands, suggesting that this bicyclic hepta-peptide toxin strengthens the intersubunit contact between the two strands. Consistent with this distinct intersubunit bonding pattern, the two long-pitch helical strands of unstabilized filaments were sometimes observed separated from each other over a distance of two to six subunits, suggesting that the intrastrand intersubunit contact is also physically stronger than the interstrand contact. The resolution of the filament reconstructions, extending to 2.5 nm axially and radially, enabled us to reproducibly "cut out" the F-actin subunit which measured 5.5 nm axially by 6.0 nm tangentially by 3.2 nm radially. The subunit is distinctly polar with a massive "base" pointing towards the "barbed" end of the filament, and a slender "tip" defining its "pointed" end (i.e., relative to the "arrowhead" pattern revealed after stoichiometric decoration of the filaments with myosin subfragment 1). Concavities running approximately parallel to the filament axis both on the inner and outer face of the subunit define a distinct cleft separating the subunit into two domains of similar size: an inner domain confined to radii less than or equal to 2.5-nm forms the uninterrupted backbone of the two long-pitch helical strands, and an outer domain placed at radii of 2-5-nm protrudes radially and thus predominantly contributes to the outer part of the massive base. Quantitative evaluation of successive crossover spacings along individual F-actin filaments revealed the deviations from the mean repeat to be compensatory, i.e., short crossovers frequently followed long ones and vice versa. The variable crossover spacings and diameter of the F-actin filament together with the local unraveling of the two long-pitch helical strands are explained in terms of varying amounts of compensatory "lateral slipping" of the two strands past each other roughly perpendicular to the filament axis. This intrinsic disorder of the actin filament may enable the actin moiety to play a more active role in actin-myosin-based force generation than merely act as a rigid passive cable as has hitherto been assumed.     

Angular disorder in actin: is it consistent with general principles of protein structure?

Harold Erickson has recently provided a useful analysis of helical structures having one class versus two classes of intersubunit bonds. His analysis is based upon an assumption that the subunits themselves are essentially unchanged upon bond formation (polymerization). He shows that such a structure having two classes of bonds (i.e. one in which each subunit interacts with four of its neighbors rather than two) can explain some of the features of actin. While he acknowledges that for actin there could be a conformational change and that, in principle, it could explain such features, he argues that the allowed magnitude of such a conformational change is inadequate. Since kinetics and thermodynamics cannot distinguish between the energy derived from the formation of a bond from that due to a conformational change, the question of whether the features of F-actin are derived from a conformational change or a system of two classes of bonds or both must be answered with high-resolution structural information. Recent studies by K. C. Holmes and others suggest that the second possibility might be closest to the truth. The heart of our disagreement is not whether Erickson's thermodynamic analysis is correct, given rigid subunits, but whether all protein polymers are characterized by rigid subunits with rigid intersubunit contacts. Erickson maintains that the observation of an angular disorder of 12 degrees per subunit within the actin filament conflicts with his formalism of rigid subunit interfaces and must therefore result from the erroneous interpretation of measurements. He presents an alternative model to explain the observations. His model, however, does not account for the observations and we will argue that, ultimately, like the resolution of the matter of the number of classes of bonds and the extent of their contact, the amount of angular disorder will require higher-resolution structural studies.     

Three-dimensional structure of a single filament in the Limulus acrosomal bundle: scruin binds to homologous helix-loop-beta motifs in actin

Frozen, hydrated acrosomal bundles from Limulus sperm were imaged with a 400 kV electron cryomicroscope. Segments of this long bundle can be studied as a P1 crystal with a unit cell containing an acrosomal filament with 28 actin and 28 scruin molecules in 13 helical turns. A novel computational procedure was developed to extract single columns of superimposed acrosomal filaments from the distinctive crystallographic view. Helical reconstruction was used to generate a three-dimensional structure of this computationally isolated acrosomal filament. The scruin molecule is organized into two domains which contact two actin subunits in different strands of the same actin filament. A correlation of Holmes' actin filament model to the density in our acrosomal filament map shows that actin subdomains 1, 2, and 3 match the model density closely. However, actin subdomain 4 matches rather poorly, suggesting that interactions with scruin may have altered actin conformation. Scruin makes extensive interactions with helix-loop-beta motifs in subdomain 3 of one actin subunit and in subdomain 1 of a consecutive actin subunit along the genetic filament helix. These two actin subdomains are structurally homologous and are closely spaced along the actin filament. Our model suggests that scruin, which is derived from a tandemly duplicated gene, has evolved to bind structurally homologous but non-identical positions across two consecutive actin subunits.     

Polylysine induces an antiparallel actin dimer that nucleates filament assembly: crystal structure at 3.5-A resolution

An antiparallel actin dimer has been proposed to be an intermediate species during actin filament nucleation. We now show that latrunculin A, a marine natural product that inhibits actin polymerization, arrests polylysine-induced nucleation at the level of an antiparallel dimer, resulting in its accumulation. These dimers, when composed of pyrene-labeled actin subunits, give rise to a fluorescent excimer, permitting detection during polymerization in vitro. We report the crystallographic structure of the polylysine-actin-latrunculin A complex at 3.5-A resolution. The non-crystallographic contact is consistent with a dimeric structure and confirms the antiparallel orientation of its subunits. The crystallographic contacts reveal that the mobile DNase I binding loop of one subunit of a symmetry-related antiparallel actin dimer is partially stabilized in the interface between the two subunits of a second antiparallel dimer. These results provide a potential explanation for the paradoxical nucleation of actin filaments that have exclusively parallel subunits by a dimer containing antiparallel subunits.     

A new internal mode in F-actin helps explain the remarkable evolutionary conservation of actin's sequence and structure

Actin is one of the most highly conserved eukaryotic proteins. There are no amino acid changes between the chicken and human skeletal muscle isoforms, and the most dissimilar actins still share more than 85% sequence identity [1]. We suggest that large discrete internal modes of freedom within the actin filament may account for a significant component of this conservation, since each subunit must make multiple specific interactions with neighboring subunits. In support of this, we find that the same state of tilt of the actin subunit exists in both yeast and vertebrate striated muscle actin, and that in both the two domains undergo a "propeller rotation." A similar movement of domains has also been seen in hexokinase, Hsc70, and Arp2/3, all structural homologs of actin, suggesting that such an interdomain hinge motion is common to proteins in this superfamily. Subunit-subunit interactions within the actin filament involve sequence insertions that are not present in MreB, a bacterial homolog of actin. Remarkably, we find that in the tilted state actin subunits make new contacts with neighboring subunits that also involve these inserts, suggesting a key role for these elements in F-actin polymorphism.     

Structure of a Longitudinal Actin Dimer Assembled by Tandem W Domains: Implications for Actin Filament Nucleation

Actin filament nucleators initiate polymerization in cells in a regulated manner. A common architecture among these molecules consists of tandem WASP homology 2 domains (W domains) that recruit three to four actin subunits to form a polymerization nucleus. We describe a low-resolution crystal structure of an actin dimer assembled by tandem W domains, where the first W domain is cross-linked to Cys374 of the actin subunit bound to it, whereas the last W domain is followed by the C-terminal pointed end-capping helix of thymosin β4. While the arrangement of actin subunits in the dimer resembles that of a long-pitch helix of the actin filament, important differences are observed. These differences result from steric hindrance of the W domain with intersubunit contacts in the actin filament. We also determined the structure of the first W domain of Vibrio parahaemolyticus VopL cross-linked to actin Cys374 and show it to be nearly identical with non-cross-linked W-Actin structures. This result validates the use of cross-linking as a tool for the study of actin nucleation complexes, whose natural tendency to polymerize interferes with most structural methods. Combined with a biochemical analysis of nucleation, the structures may explain why nucleators based on tandem W domains with short inter-W linkers have relatively weak activity, cannot stay bound to filaments after nucleation, and are unlikely to influence filament elongation. The findings may also explain why nucleation-promoting factors of the Arp2/3 complex, which are related to tandem-W-domain nucleators, are ejected from branch junctions after nucleation. We finally show that the simple addition of the C-terminal pointed end-capping helix of thymosin β4 to tandem W domains can change their activity from actin filament nucleation to monomer sequestration.     

Determinants of Formin Homology 1 (FH1) domain function in actin filament elongation by formins

Formin-mediated elongation of actin filaments proceeds via association of Formin Homology 2 (FH2) domain dimers with the barbed end of the filament, allowing subunit addition while remaining processively attached to the end. The flexible Formin Homology 1 (FH1) domain, located directly N-terminal to the FH2 domain, contains one or more stretches of polyproline that bind the actin-binding protein profilin. Diffusion of FH1 domains brings associated profilin-actin complexes into contact with the FH2-bound barbed end of the filament, thereby enabling direct transfer of actin. We investigated how the organization of the FH1 domain of budding yeast formin Bni1p determines the rates of profilin-actin transfer onto the end of the filament. Each FH1 domain transfers actin to the barbed end independently of the other and structural evidence suggests a preference for actin delivery from each FH1 domain to the closest long-pitch helix of the filament. The transfer reaction is diffusion-limited and influenced by the affinities of the FH1 polyproline tracks for profilin. Position-specific sequence variations optimize the efficiency of FH1-stimulated polymerization by binding profilin weakly near the FH2 domain and binding profilin more strongly farther away. FH1 domains of many other formins follow this organizational trend. This particular sequence architecture may optimize the efficiency of FH1-stimulated elongation.     

Evidence for S2 flexibility by direct visualization of quantum dot–labeled myosin heads and rods within smooth muscle myosin filaments moving on actin in vitro

Myosins in muscle assemble into filaments by interactions between the C-terminal light meromyosin (LMM) subdomains of the coiled-coil rod domain. The two head domains are connected to LMM by the subfragment-2 (S2) subdomain of the rod. Our mixed kinetic model predicts that the flexibility and length of S2 that can be pulled away from the filament affects the maximum distance working heads can move a filament unimpeded by actin-attached heads. It also suggests that it should be possible to observe a head remain stationary relative to the filament backbone while bound to actin (dwell), followed immediately by a measurable jump upon detachment to regain the backbone trajectory. We tested these predictions by observing filaments moving along actin at varying ATP using TIRF microscopy. We simultaneously tracked two different color quantum dots (QDs), one attached to a regulatory light chain on the lever arm and the other attached to an LMM in the filament backbone. We identified events (dwells followed by jumps) by comparing the trajectories of the QDs. The average dwell times were consistent with known kinetics of the actomyosin system, and the distribution of the waiting time between observed events was consistent with a Poisson process and the expected ATPase rate. Geometric constraints suggest a maximum of ∼26 nm of S2 can be unzipped from the filament, presumably involving disruption in the coiled-coil S2, a result consistent with observations by others of S2 protruding from the filament in muscle. We propose that sufficient force is available from the working heads in the filament to overcome the stiffness imposed by filament-S2 interactions.     

Subunit coupling and kinetic co-operativity of polymeric enzymes. Amplification, attenuation and inversion effects

The principles of structural kinetics, as applied to dimeric enzymes, allow us to understand how the strength of subunit coupling controls both substrate-binding co-operativity, under equilibrium conditions, and kinetic co-operativity, under steady state conditions. When subunits are loosely coupled, positive substrate-binding co-operativity may result in either an inhibition by excess substrate or a positive kinetic co-operativity. Alternatively, negative substrate-binding co-operativity is of necessity accompanied by negative kinetic co-operativity. Whereas the extent of negative kinetic co-operativity is attenuated with respect to the corresponding substrate-binding co-operativity, the positive kinetic co-operativity is amplified with respect to that of the substrate-binding co-operativity. Strong kinetic co-operativity cannot be generated by a loose coupling of subunits. If subunit is propagated to the other, the dimeric enzyme may display apparently surprising co-operativity effects. If the strain of the active sites generated by subunit coupling is relieved in the non-liganded and fully-liganded states, both substrate-binding co-operativity and kinetic co-operativity cannot be negative. If the strain of the active sites however, is not relieved in these states, negative substrate-binding co-operativity is accompanied by either a positive or a negative co-operativity. The possible occurrence of a reversal of kinetic co-operativity, with respect to substrate-binding co-operativity, is the direct consequence of quaternary constraints in the dimeric enzyme. Moreover, tight coupling between subunits may generate a positive kinetic co-operativity which is not associated with any substrate-binding co-operativity. In other words a dimeric enzyme may well bind the substrate in a non co-operative fashion and display a positive kinetic co-operativity generated by the strain of the active sites.     

Three-dimensional reconstruction of an actin bundle

We present the three-dimensional structure of an actin filament bundle from the sperm of Limulus. The bundle is a motile structure which by changing its twist, converts from a coiled to an extended form. The bundle is composed of actin plus two auxiliary proteins of molecular masses 50 and 60 kD. Fraying the bundle with potassium thiocyanate created three classes of filaments: actin, actin plus the 60-kD protein, and actin plus both the auxiliary proteins. We examined these filaments by transmission electron microscopy and scanning transmission electron microscopy (STEM). Three-dimensional reconstructions from electron micrographs allowed us to visualize the actin subunit and the 60- and 50-kD subunits bound to it. The actin subunit appears to be bilobed with dimensions 70 X 40 X 35 A. The inner lobe of the actin subunit, located at 20 A radius, is a prolate ellipsoid, 50 X 25 A; the outer actin lobe, at 30 A radius, is a 35-A-diam spheroid. Attached to the inner lobe of actin is the 60-kD protein, an oblate spheroid, 55 X 40 A, at 50 A radius. The armlike 50-kD protein, at 55 A radius, links the 60-kD protein on one of actin's twin strands to the outer lobe of the actin subunit on the opposite strand. We speculate that the 60-kD protein may be a bundling protein and that the 50-kD protein may be responsible for the change in twist of the filaments which causes extension of the bundle.     

ADF/cofilin use an intrinsic mode of F-actin instability to disrupt actin filaments

Proteins in the ADF/cofilin (AC) family are essential for rapid rearrangements of cellular actin structures. They have been shown to be active in both the severing and depolymerization of actin filaments in vitro, but the detailed mechanism of action is not known. Under in vitro conditions, subunits in the actin filament can treadmill; with the hydrolysis of ATP driving the addition of subunits at one end of the filament and loss of subunits from the opposite end. We have used electron microscopy and image analysis to show that AC molecules effectively disrupt one of the longitudinal contacts between protomers within one helical strand of F-actin. We show that in the absence of any AC proteins, this same longitudinal contact between actin protomers is disrupted at the depolymerizing (pointed) end of actin filaments but is prominent at the polymerizing (barbed) end. We suggest that AC proteins use an intrinsic mechanism of F-actin's internal instability to depolymerize/sever actin filaments in the cell.     

Troponin-I interacts with the Met47 region of skeletal muscle actin. Implications for the mechanism of thin filament regulation by calcium

Striated muscles are regulated by Ca(2+) via the thin filament proteins troponin (Tn) and tropomyosin (Tm). In the absence of Ca(2+), contraction is inhibited, whereas myosin-actin interaction and contraction can take place in its presence. Although it is well established that the interaction of troponin-I (TnI), the inhibitory subunit of Tn, with actin is required for the inhibition process and that there are two separate actin-binding regions in TnI that interact with actin, the molecular mechanism of this inhibition process is still not clear. Using TnI mutants with photocrosslinking probes attached to genetically engineered cysteine residues in each of the two actin-binding regions, we show that both regions are close to Met47 of actin in its outer domain. It has been proposed that the Ca(2+)-induced activation of contraction involves the movement of Tm from the outer to the inner domain of the actin filament. On the basis of our results presented here, we propose that the position of Tm at the outer domain of actin in the Ca(2+)-free state is stabilized by the presence of TnI over actin's outer domain via mutual interactions of all three components. In the presence of Ca(2+), TnI's actin-binding regions dissociate from actin allowing Tm to move toward actin's inner domain.     

Binding of myotrophin/V-1 to actin-capping protein: implications for how capping protein binds to the filament barbed end

The heterodimeric actin-capping protein (CP) regulates actin assembly and cell motility by binding tightly to the barbed end of the actin filament. Here we demonstrate that myotrophin/V-1 binds directly to CP in a 1:1 molar ratio with a Kd of 10-50 nm. V-1 binding inhibited the ability of CP to cap the barbed ends of actin filaments. The actin-binding COOH-terminal region, the "tentacle," of the CP beta subunit was important for binding V-1, with lesser contributions from the alpha subunit COOH-terminal region and the body of the protein. V-1 appears to be unable to bind to CP that is on the barbed end, based on the observations that V-1 had no activity in an uncapping assay and that the V-1.CP complex had no capping activity. Two loops of V-1, which extend out from the alpha-helical backbone of this ankyrin repeat protein, were necessary for V-1 to bind CP. Parallel computational studies determined a bound conformation of the beta tentacle with V-1 that is consistent with these findings, and they offered insight into experimentally observed differences between the alpha1 and alpha2 isoforms as well as the mutant lacking the alpha tentacle. These results support and extend our "wobble" model for CP binding to the actin filament, in which the two COOH-terminal regions of CP bind independently to the actin filament, and bound CP is able to wobble when attached only via its mobile beta-subunit tentacle. This model is also supported by molecular dynamics simulations of CP reported here. The existence of the wobble state may be important for actin dynamics in cells.     

Location of the disulfide bonds in human coagulation factor XI: the presence of tandem apple domains

Factor XI is a plasma glycoprotein that participates in the blood coagulation cascade. Of the 19 disulfide bonds present in each of the subunits of the human protein, 16 were determined by amino acid sequence analysis of peptide fragments produced by chemical and enzymatic digestion. Four apple domains of 90 or 91 amino acids were identified in the tandem repeats present in the amino-terminal portion of each subunit of factor XI. The disulfide bonds in the carboxyl-terminal portion of the molecule were similar to those in the catalytic region of other serine proteases. The two identical subunits of factor XI were connected by a single disulfide bond at Cys321 linking each of the fourth apple domains while each of the Cys residues at position 11 in the first apple domains forms a disulfide bond with another Cys residue.     

Evidence for an extended hydrogen bond network in the binding site of the nicotinic receptor: role of the vicinal disulfide of the alpha1 subunit

The defining feature of the α subunits of the family of nicotinic acetylcholine receptors is a vicinal disulfide between Cys-192 and Cys-193. Although this structure has played a pivotal role in a number of pioneering studies of nicotinic receptors, its functional role in native receptors remains uncertain. Using mutant cycle analysis and unnatural residue mutagenesis, including backbone mutagenesis of the peptide bond of the vicinal disulfide, we have established the presence of a network of hydrogen bonds that extends from that peptide NH, across a β turn to another backbone hydrogen bond, and then across the subunit interface to the side chain of a functionally important Asp residue in the non-α subunit. We propose that the role of the vicinal disulfide is to distort the β turn and thereby properly position a backbone NH for intersubunit hydrogen bonding to the key Asp.     

Effect of the state of oxidation of cysteine 190 of tropomyosin on the assembly of the actin-tropomyosin complex

Tropomyosin, cross-linked at cysteine 190, was found to bind more weakly to actin filaments than uncross-linked tropomyosin. Cross-linking of tropomyosin can cause actin filaments nearly completely covered with tropomyosin to be uncovered almost completely. The critical monomer concentration of actin is not significantly changed by binding of cross-linked or uncross-linked tropomyosin to actin filaments. The binding curves were analyzed quantitatively, thereby taking into account the polar end-to-end contact of tropomyosin molecules bound by actin and the overlap of the seven subunit binding sites along the actin filament. Under the conditions of the experiment (80 mM KCl, 1 mM MgCl2, pH 7.5, 38-42 degrees C), the equilibrium constant for isolated binding of tropomyosin to actin filaments is in the range 1 x 10(3)-3 x 10(3) M-1. The equilibrium constants for binding of tropomyosin to binding sites along the actin filament with one or two neighbouring tropomyosin molecules are in the range of 10(6) or 10(8) to 10(9) M-1, respectively. The equilibrium constants for binding of tropomyosin to binding sites along the actin filament with one or two neighbouring tropomyosin molecules are in the range of 10(6) or 10(8) to 10(9) M-1, respectively. The equilibrium constants for cross-linked and uncross-linked tropomyosin differ by a factor of only about two. Owing to the highly cooperative binding, these differences are sufficient so that actin filaments nearly completely covered with uncross-linked tropomyosin are uncovered almost completely by cross-linking tropomyosin at cysteine 190.     

ADF/cofilin weakens lateral contacts in the actin filament.

Observed in vivo motility rates can only be accounted for if the rate of actin filament treadmilling in cells is considerably greater than has been quantified for purified actin in vitro. ADF/cofilin is uniquely suited to promote actin dynamics in cells, owing to its remarkable ability to change actin filament structure. In earlier work we showed that human cofilin chanRges filament twist by about 5 degrees per subunit and suggested that this contributes to increased filament turnover. Our initial structural modeling provided some insights into how the longitudinal actin-actin contacts might be disrupted following cofilin-induced twisting. Here we present direct evidence that cofilin also disrupts lateral actin-actin contacts in the filament and suggest a model showing how this could contribute to cofilin's novel effects on actin filament dynamics and assembly.     

Interaction of tropomyosin-troponin with actin filaments

The assembly of actin filaments with tropomyosin-troponin was investigated by means of light scattering. Binding curves of tropomyosin-troponin [consisting of all three subunits (holotroponin)] and of tropomyosin-troponin-T-I to actin filaments were analyzed by separating the affinity of tropomyosin-troponin for actin filaments and the affinity for the end-to-end contact of tropomyosin molecules. Under the experimental conditions (42.4 degrees C, 300 mM KCl), tropomyosin-holotroponin in the absence of calcium and tropomyosin-troponin-T-I had similar affinities for actin filaments whereas tropomyosin-holotroponin in the presence of calcium was found to bind more weakly. Tropomyosin-holotroponin and tropomyosin-troponin-T-I bound about 200-300-fold more strongly to binding sites with adjacent tropomyosin-troponin units than to isolated sites on actin filaments. The equilibrium constant for isolated association with actin filaments was more than 2-fold higher for tropomyosin-holotroponin in the absence of calcium (15 400 M-1) and tropomyosin-troponin-T-I (17 500 M-1) than for tropomyosin-holotroponin in the presence of calcium (6600 M-1). Binding curves of mixtures of tropomyosin-holotroponin in the presence of calcium and of tropomyosin-troponin-T-I were measured and analyzed on the basis of a model of cooperative binding of two types of large ligands to a one-dimensional homogeneous lattice. The results provided information on the strength of the end-to-end contacts of tropomyosin-troponin units in different positions on an actin filament. It was found that a tropomyosin-troponin unit binds adjacently to another unit in a different position on an actin filament about 2-fold more weakly than adjacent to a unit in the same position. With the aid of these results, it was possible to obtain information of the equilibrium distribution of tropomyosin-troponin in the two positions on actin filaments. Generation of a sequence of tropomyosin-troponin units in a different position on actin filaments was found to be 4-fold less favored than elongation of an existing sequence (cooperativity parameter sigma = 1/4). Shifting of tropomyosin-troponin on actin filaments appears to be accompanied by small free-energy changes in the various interactions of the components of actin-tropomyosin-troponin filaments and not to be an all-or-none reaction