Linear dichroism of acrylodan-labeled tropomyosin and myosin subfragment 1 bound to actin in myofibrils.

Muscle contraction can be activated by the binding of myosin heads to the thin filament, which appears to result in thin filament structural changes. In vitro studies of reconstituted muscle thin filaments have shown changes in tropomyosin-actin geometry associated with the binding of myosin subfragment 1 to actin. Further information about these structural changes was obtained with fluorescence-detected linear dichroism of tropomyosin, which was labeled at Cys 190 with acrylodan and incorporated into oriented ghost myofibrils. The fluorescence from three sarcomeres of the fibril was collected with the high numerical aperture objective of a microscope and the dichroic ratio, R (0/90 degrees), for excitation parallel/perpendicular to the fibril, was obtained, which gave the average probe dipole polar angle, Theta. For both acrylodan-labeled tropomyosin bound to actin in fibrils and in Mg2+ paracrystals, Theta congruent to 52 degrees +/- 1.0 degrees, allowing for a small degree of orientational disorder. Binding of myosin subfragment 1 to actin in fibrils did not change Theta; i.e., the orientation of the rigidly bound probe on tropomyosin did not change relative to the actin axis. These data indicate that myosin subfragment 1 binding to actin does not appreciably perturb the structure of tropomyosin near the probe and suggest that the geometry changes are such as to maintain the parallel orientation of the tropomyosin and actin axes, a finding consistent with models of muscle regulation. Data are also presented for effects of MgADP on the orientation of labeled myosin subfragment 1 bound to actin in myofibrils.     

Fluorescence studies of the conformation of pyrene-labeled tropomyosin: effects of F-actin and myosin subfragment 1

The fluorescence of pyrene-TM [rabbit skeletal tropomyosin (TM) labeled at Cys with N-(1-pyrenyl)maleimide] consists of monomer and excimer bands [Betcher-Lange, S., & Lehrer, S.S. (1978) J. Biol. Chem. 253, 3757-3760]; an increase in excimer fluorescence with temperature is due to a shift in equilibrium from a chain-closed state (N) to a chain-open state (X) associated with a helix pretransition [Graceffa, P., & Lehrer, S.S. (1980) J. Biol. Chem. 255, 11296-11300]. In this study, we show that the presence of appreciable excimer fluorescence at temperatures below the N----X pretransition (initial excimer) is due to perturbation of the TM chain-chain interaction by the pyrenes at Cys-190. Fluorescence and ATPase titrations indicated that the label caused a decrease in TM binding to F-actin primarily due to reduced end to end TM interactions on the actin filament. Under conditions where pyrene-TM was bound to F-actin, however, the excimer fluorescence did not increase with temperature, indicating that F-actin stabilizes tropomyosin by inhibiting the N----X transition. The binding of myosin subfragment 1 (S1) to pyrene-TM-F-actin at low ratios to actin caused time-dependent changes in fluorescence. After equilibrium was reached, the initial excimer fluorescence was markedly reduced and remained constant over the pretransition temperature range. Further stabilization of tropomyosin conformation on F-actin is therefore associated with S1 binding. Effects of the binding of S1 to the F-actin-tropomyosin thin filament on the state of tropomyosin were studied by monitoring the monomer fluorescence of pyrene-TM.(ABSTRACT TRUNCATED AT 250 WORDS)     

Regulation of the interaction between actin and myosin subfragment 1: evidence for three states of the thin filament.

Equilibrium titrations and kinetic experiments were used to define the cooperative binding of myosin subfragment 1 (S1) to actin-troponin-tropomyosin. Both types of experiment require an equilibrium between two states of the thin filament in which one state (the off state) binds S1 less readily than the other. Equilibrium titrations are compatible with > 95% of the actin7.Tn.Tm units being in the off state in the absence of calcium and 80% in the off state in the presence of calcium. Kinetic binding data suggest that the presence of calcium switches the thin filament from 70% in the off state to < 5%. The two experiments, therefore, define quite different populations of the off states. We propose a three-state model of the thin filament. A "blocked state" which is unable to bind S1, a "closed state" which can only bind S1 relatively weakly and an "open state" in which the S1 can both bind and undergo an isomerization to a more strongly bound rigor-like conformation. The equilibrium between the three states is calcium-dependent; KB = [closed]/[blocked] = 0.3 and > or = 16 and KT = [open]/[closed] = 0.09 and 0.25 in the absence and presence of calcium, respectively. This model can account for both types of experimental data.     

Dynamic interaction between actin and myosin subfragment 1 in the presence of ADP

The equilibrium and dynamics of the interaction between actin, myosin subfragment 1 (S1), and ADP have been investigated by using actin which has been covalently labeled at Cys-374 with a pyrene group. The results are consistent with actin binding to S1.ADP (M.D) in a two-step reaction, A + M.D K1 equilibrium A-M.D K2 equilibrium A.M.D, in which the pyrene fluorescence only monitors the second step. In this model, K1 = 2.3 X 10(4) M-1 (k+1 = 4.6 X 10(4) M-1 s-1) and K2 = 10 (k+2 less than or equal to 4 s-1); i.e., both steps are relatively slow compared to the maximum turnover of the ATPase reaction. ADP dissociates from both M.D and A-M.D at 2 s-1 and from A.M.D at greater than or equal to 500 s-1; therefore, actin only accelerates the release of product from the A.M.D state. This model is consistent with the actomyosin ATPase model proposed by Geeves et al. [(1984) J. Muscle Res. Cell Motil. 5, 351]. The results suggest that A-M.D cannot break down at a rate greater than 4 s-1 by dissociation of ADP, by dissociation of actin, or by isomerizing to A.M.D. It is therefore unlikely to be significantly occupied in a rapidly contracting muscle, but it may have a role in a muscle contracting against a load where the ATPase rate is markedly inhibited. Under these conditions, this complex may have a role in maintaining tension with a low ATP turnover rate.     

Subtilisin-cleaved actin: polymerization and interaction with myosin subfragment 1

Homogeneous preparations of actin cleaved into two fragments, the N-terminal 9- and C-terminal 36-kDa peptides, were achieved by proteolysis of G-actin with subtilisin at 23 degrees C at a 1:1000 (w/w) ratio of enzyme to actin. The subtilisin cleavage site was identified by sequence analysis to be between Met-47 and Gly-48. Although under nondenaturing conditions the two fragments remained associated to one another, the cleavage affected macromolecular interactions of actin. The rates of cleaved actin polymerization by MgCl2, KCl, and myosin subfragment 1 (S-1) were slower and the critical concentrations for this process were higher than in intact protein. Intact and cleaved actin formed morphologically indistinguishable filaments and copolymerized in the presence of MgCl2. The affinity of actin for S-1 was decreased by about 10-fold due to subtilisin cleavage, but the S-1 ATPase activity was activated to the same Vmax value by both intact and cleaved actins. DNase I inhibition measurements revealed lower affinity of cleaved actin for DNase I than that of intact protein. These results are discussed in terms of actin's structure.     

Proteolysis and binding of myosin subfragment 1 to actin

Rates of proteolytic cleavage of myosin subfragment 1 were measured in the absence and presence of different amounts of actin. The rates of tryptic digestion at the 50K/20K junction and papain digestion at the 25K/50K junction of the myosin head were progressively inhibited with increasing substoichiometric molar ratios of actin to myosin subfragment 1. The percentage inhibitions of digestion reactions corresponded precisely to the molar compositions of actin-subfragment 1 solutions and demonstrated that equimolar complexes of these proteins were responsible for the observed changes in the proteolysis of myosin heads.     

Nucleotide-induced states of myosin subfragment 1 cross-linked to actin

Actomyosin interactions and the properties of weakly bound states in carbodiimide-cross-linked complexes of actin and myosin subfragment 1 (S-1) were probed in tryptic digestion, fluorescence, and thiol modification experiments. Limited proteolysis showed that the 50/20K junction on S-1 was protected in cross-linked acto-S-1 from trypsin even under high-salt conditions in the presence of MgADP, MgAMPPNP, and MgPPi (mu = 0.5 M). The same junction was exposed to trypsin by MgATP and MgATP gamma S but mainly on S-1 cross-linked via its 50K fragment to actin. p-Phenylenedimaleimide-bridged S-1, when cross-linked to actin, yielded similar tryptic cleavage patterns to those of cross-linked S-1 in the presence of MgATP. By using p-nitrophenylenemaleimide, it was found that the essential thiols of cross-linked S-1 were exposed to labeling in the presence of MgATP and MgATP gamma S in a state-specific manner. In contrast to this, the reactive thiols were protected from modification in the presence of MgADP, MgAMPPNP, and MgPPi at mu = 0.5 M. These modifications were compared with similar reactions on isolated S-1. Experiments with pyrene-actin cross-linked to S-1 showed enhancement of fluorescence intensity upon additions of MgATP and MgATP gamma S, indicating the release of the pyrene probe on actin from the sphere of S-1 influence. The results of this study contrast the "open" structure of weakly bound actomyosin states to the "tight" conformation of rigor complexes.     

Alteration of the ATP hydrolysis and actin binding properties of thrombin-cut myosin subfragment 1

We have characterized various structural and enzymatic properties of the (68K-30K)-S-1 derivative obtained by thrombic cleavage [Chaussepied, P., Mornet, D., Audemard, E., Derancourt, J., & Kassab, R. (1986) Biochemistry (preceding paper in this issue)]. The far-ultraviolet CD spectra and thiol reactivity measurements indicated an unchanged overall polypeptide conformation of the enzyme whereas the CD spectra in the near-ultraviolet region suggested a local change in the environments of phenylalanine side chains; the latter finding was rationalized by considering the existence of about five of these amino acids in the vicinity of the cleavage sites. When the binding of Mg2+-ATP and Mg2+-ADP to the derivative was assessed by CD spectroscopy, distinct spectra were obtained with the two nucleotides as with native subfragment 1 (S-1), but some spectral features were unique to the nicked S-1. Stern-Volmer fluorescence quenching studies using acrylamide and the analogues 1,N6-ethenoadenosine 5'-triphosphate and 1,N6-ethenoadenosine 5'-diphosphate indicated that the complexes formed with the modified S-1 have a solute quencher accessibility close to that observed for the complexes with the normal S-1. However, in contrast to the parent enzyme, the thrombin-cut S-1 was unable to bind irreversibly Mg2+-ATP, nor did it form a stable Mg2+-ADP-sodium vanadate complex or achieve the entrapping of Mg2+-ADP after cross-linking of SH1 and SH2 with N,N'-p-phenylenedimaleimide. Additionally, the amplitude of the Pi burst was very low, indicating that the inactivation of the proteolyzed S-1 was linked to the suppression of the hydrolysis step in the ATPase cycle.(ABSTRACT TRUNCATED AT 250 WORDS)     

Interaction of myosin subfragment 1 with forms of monomeric actin

The ability of myosin subfragment 1 to interact with monomeric actin complexed to sequestering proteins was tested by a number of different techniques such as affinity absorption, chemical cross-linking, fluorescence titration, and competition procedures. For affinity absorption, actin was attached to agarose immobilized DNase I. Both chymotryptic subfragment 1 isoforms (S1A1 and S1A2) were retained by this affinity matrix. Fluorescence titration employing pyrenyl-actin in complex with deoxyribonuclease I (DNase I) or thymosin beta4 demonstrated S1 binding to these actin complexes. A K(D) of 5 x 10(-8) M for S1A1 binding to the actin-DNase I complex was determined. Fluorescence titration did not indicate binding of S1 to actin in complex with gelsolin segment 1 (G1) or vitamin D-binding protein (DBP). However, fluorescence competition experiments and analysis of tryptic cleavage patterns of S1 indicated its interaction with actin in complex with DBP or G1. Formation of the ternary DNase I-acto-S1 complex was directly demonstrated by sucrose density sedimentation. S1 binding to G-actin was found to be sensitive to ATP and an increase in ionic strength. Actin fixed in its monomeric state by DNase I was unable to significantly stimulate the Mg2+-dependent S1-ATPase activity. Both wild-type and a mutant of Dictyostelium discoideum myosin II subfragment 1 containing 12 additional lysine residues within an insertion of 20 residues into loop 2 (K12/20-Q532E) were found to also interact with actin-DNase I complex. Binding of the K12/20-Q532E mutant to the actin-DNase I complex occurred with higher affinity than wild-type S1 and was less sensitive to mono- and divalent cations.     

Nucleotide-induced changes in the interaction of myosin subfragment 1 with actin: detection by antibodies against the N-terminal segment of actin

The binding of myosin subfragment 1 (S-1) to actin in the presence and absence of nucleotides was determined under conditions of partial saturation of actin, up to 80%, by Fab(1-7), the antibodies against the first seven N-terminal residues on actin. In the absence of nucleotides, the binding constant of S-1 to actin (2 x 10(7) M-1) was decreased by 1 order of magnitude by Fab(1-7). The binding of S-1 to actin caused only limited displacement of Fab, and between 30 and 50% of actin appeared to bind both proteins. In the presence of MgAMP.PNP, MgADP, and MgPPi and at low S-1 concentrations, the same antibodies caused a large decrease in the binding of S-1 to actin. However, the binding of S-1.nucleotide to actin in the presence of Fab(1-7) increased cooperatively with the increase in S-1 concentration. Also, in contrast to rigor conditions, there was no indication for the binding of Fab(1-7) and S-1.nucleotide to the same actin molecules. These results show a nucleotide-induced transition in the actomyosin interface, most likely related to the different roles of the N-terminal segment of actin in the binding of S-1 and S-1.nucleotide. The possible implications of these findings to the regulation of actomyosin interactions are discussed.     

Kinetic model for the interaction of myosin subfragment 1 with regulated actin

A one-dimensional kinetic Ising model is developed to describe the binding of myosin subfragment 1 (SF-1) to regulated actin. The model allows for cooperative interactions between individual actin sites with bound SF-1 ligands rather than assuming that groups of actin monomer sites change their state in a cooperative fashion. With the triplet closure approximation, the model yields a set of 16 independent differential (master) equations which may be solved numerically to yield the extent of binding as a function of time. The predictions of the model are compared with experiments on the transient binding of SF-1 to regulated actin in the presence of Ca2+ and in the absence of Ca2+ with varying amounts of SF-1 prebound to the actin filament and on the equilibrium binding of SF-1 X ADP to regulated actin in the absence of Ca2+. In all cases, the calculations fit the data to within the experimental errors. In the case of SF-1 X ADP, the results suggest that a repulsive interaction exists between adjacently bound SF-1 at the ends of two neighboring seven-site actin units.     

Interaction of fluorescently labeled myosin subfragment 1 with nucleotides and actin

Isolated myosin heads (subfragment 1) were modified by covalent attachment of 5-(iodoacetamido)fluorescein or 5-(iodoacetamido)salicylic acid to the essential sulfhydryl group SH1. The extrinsic fluorescence of the modified proteins was sensitive to binding of nucleotides and F-actin. With the fluorescein derivative [subfragment 1 (S1) modified with 5-(iodoacetamido)fluorescein (IAF) at SH1 (S1-AF)], association with MgADP decreased the probe fluorescence by 30%, whereas binding to actin increased the emission by a factor of 2. In the ternary complex acto-S1-AF X MgADP, the effect of nucleotide on the intensity of the attached fluorescein canceled the effect of actin. The fluorescence state of this ternary complex was similar to that of S1-AF X MgADP. The emission of S1-AF was resolved into two components with lifetimes of 4.3 and 0.6 ns and relative contributions of 33% and 67%, respectively. Interaction of S1-AF with nucleotides and actin did not alter the lifetimes but significantly shifted their fractional contributions. Quenching studies showed that the short lifetime likely arose from the fluorescein moiety statically quenched by internal groups. Binding of MgADP to the salicylate derivative [S1 modified with 5-(iodoacetamido)salicylic acid at SH1 (S1-SAL)] induced a 25% enhancement of the probe fluorescence, whereas formation of acto-S1-SAL decreased the emission by 10% regardless of whether MgADP was bound to the protein. Both labeled S1 species bound MgADP with a similar affinity, comparable to that of unmodified S1 previously reported by other investigators.(ABSTRACT TRUNCATED AT 250 WORDS)     

Interaction of maleimidobenzoyl actin with myosin subfragment 1 and tropomyosin-troponin.

A chemical modification of G-actin with (m-maleimidobenzoyl)-N-hydroxysuccinimide ester (MBS) impairs actin polymerization [Bettache, N., Bertrand, R., & Kassab, R. (1989) Proc. Natl. Acad. Sci. U.S.A. 86, 6028-6032]. MBS-actin recovers the ability to polymerize when a 2-fold molar excess of phalloidin is added in 30 mM KCl/2 mM MgCl2/20 mM Tris-HCl (pH 7.6). The resulting polymer (MBS-P-actin) is highly potentiated so that it activates the Mg(2+)-ATPase of S1 more strongly than native F-actin. The affinity of MBS-P-actin for S1 in the presence of ATP (KATPase) is about four times higher than that of native F-actin, although the maximum velocity at infinite actin concentration (Vmax) is almost the same. This high activation is not due to a cross-linking between MBS-P-actin and the S1 heavy chain, since no substantial amount of cross-linking was observed in SDS gel electrophoresis. Direct binding studies and ATPase measurements showed that the modification of actin with MBS impairs the binding of tropomyosin. Tropomyosin binding can be improved considerably by the addition of troponin. However, the regulation mechanism of the acto-S1 ATPase activity by troponin-tropomyosin is damaged. The addition of troponin-tropomyosin reduces the S1 ATPase activation by MBS-P-actin to the same level as that of native F-actin in 30 mM KCl/2.5 mM ATP/2 mM MgCl2, but there is no difference in the ATPase activation in the presence and absence of Ca2+.(ABSTRACT TRUNCATED AT 250 WORDS)     

Fluorescence resonance energy transfer within the complex formed by actin and myosin subfragment 1. Comparison between weakly and strongly attached states

Fluorescence resonance energy transfer measurements have been made between Cys-374 on actin and Cys-177 on the alkali light chain of myosin subfragment 1 (S1) using several pairs of donor-acceptor chromophores. The labeled light chain was exchanged into subfragment 1 and the resulting fluorescently labeled subfragment 1 isolated by ion-exchange chromatography on SP-Trisacryl. The efficiency of energy transfer was measured by steady-state fluorescence in a strong binding complex of acto-S1 and found to represent a spatial separation between the two probes of 5.6-6.3 nm. The same measurements were then made with weak binding acto-S1 complexes generated in two ways. First, actin was complexed with p-phenylenedimaleimide-S1, a stable analogue of S1-adenosine 5'-triphosphate (ATP), obtained by cross-linking the SH1 and SH2 heavy-chain thiols of subfragment 1 [Greene, L. E., Chalovich, J. M., & Eisenberg, E. (1986) Biochemistry 25, 704-709]. Large increases in transfer efficiency indicated that the two probes had moved closer together by some 3 nm. Second, weak binding complexes were formed between subfragment 1 and actin in the presence of the regulatory proteins troponin and tropomyosin, the absence of calcium, and the presence of ATP [Chalovich, J. M., & Eisenberg, E. (1982) J. Biol. Chem. 257, 2432-2437]. The measured efficiency of energy transfer again indicated that the distance between the two labeled sites had moved closer by about 3 nm. These data support the idea that there is a considerable difference in the structure of the acto-S1 complex between the weakly and strongly bound states.     

Preparation and characterization of frog muscle myosin subfragment 1 and actin.

The preparation, structural and steady-state kinetic characteristics of contractile proteins from the leg muscle of frogs Rana temporaria and Rana pipiens are described. Actin and myosin from the two frog species are indistinguishable. The proteins have structural and steady-state kinetic properties similar to those from rabbit fast-twitch skeletal muscle. Chymotrypsin digestion of frog myosin or myofibrils in the presence of EDTA yields subfragment 1, which is separated by chromatography into two components that are distinguished by their alkali light-chain content.     

The ends of tropomyosin are major determinants of actin affinity and myosin subfragment 1-induced binding to F-actin in the open state

Tropomyosin (TM) is thought to exist in equilibrium between two states on F-actin, closed and open [Geeves, M. A., and Lehrer, S. S. (1994) Biophys. J. 67, 273-282]. Myosin shifts the equilibrium to the open state in which myosin binds strongly and develops force. Tropomyosin isoforms, that primarily differ in their N- and C-terminal sequences, have different equilibria between the closed and open states. The aim of the research is to understand how the alternate ends of TM affect cooperative actin binding and the relationship between actin affinity and the cooperativity with which myosin S1 promotes binding of TM to actin in the open state. A series of rat alpha-tropomyosin variants was expressed in Escherichia coli that are identical except for the ends, which are encoded by exons 1a or 1b and exons 9a, 9c or 9d. Both the N- and C-terminal sequences, and the particular combination within a TM molecule, determine actin affinity. Compared to tropomyosins with an exon 1a-encoded N-terminus, found in long isoforms, the exon 1b-encoded sequence, expressed in 247-residue nonmuscle tropomyosins, increases actin affinity in tropomyosins expressing 9a or 9d but has little effect with 9c, a brain-specific exon. The relative actin affinities, in decreasing order, are 1b9d > 1b9a > acetylated 1a9a > 1a9d > 1a9a > or = 1a9c congruent with 1b9c. Myosin S1 greatly increases the affinity of all tropomyosin variants for actin. In this, the actin affinity is the primary factor in the cooperativity with which myosin S1 induces TM binding to actin in the open state; generally, the higher the actin affinity, the lower the occupancy by myosin required to saturate the actin with tropomyosin: 1b9d >1a9d> 1b9a > or = acetylated 1a9a > 1a9a > 1a9c congruent with 1b9c.     

Intracellular motility: myosin and tropomyosin in actin cable flow

A new study has found that retrograde flow of budding yeast actin cables is facilitated by myosin II but is inhibited by a specific tropomyosin isoform (Tpm2p). Budding yeast therefore contains a minimal component system for elucidating the mechanistic details of retrograde actin flow.     

Binding between maleimidobenzoyl-G-actin and myosin subfragment 1.

It is well known that the structural interactions between S-1 moieties of myosin molecules ("cross bridges") and actin molecules in polymerized ("F") form are thought to underlie muscle contraction. It is surmised that such interactions are unitary (actin:S-1 = 1:1), but actual demonstration thereof is handicapped by intrinsic properties of the proteins. Recently, it has been reported that chemically modified [with m-maleimidobenzoyl-N-hydroxysuccinimide ester (MBS)] actin maintains its monomeric ("G") form and makes a stable unitary complex with S-1 but does not activate the S-1 ATPase [Bettache, N., Bertrand, R., & Kassab, R. (1989) Proc. Natl. Acad. Sci. U.S.A. 86, 6028-6032]. However, we recently showed that when MBS-G-actin and S-1 are covalently cross-linked by 1-ethyl-3-[3-(dimethylamino)propyl]-carbodiimide (EDC), ATPase activity is restored [Hozumi, T. (1991) Biochem. Int. 23, 835-843]. Here we investigated the interface between MBS-G-actin and S-1 using the techniques of tryptic digestion and EDC-cross-linking. MBS-G-actin specifically protected the N-terminal region of S-1 heavy chain against tryptic cleavage at the 25 kDa/50 kDa junction, which is different from the effect that a protomer within F-actin has on the protection of the 25 kDa/50 kDa junction. In addition, the cross-linking pattern between MBS-G-actin and S-1 was different from that between F-actin and S-1. When MBS-G actin was cross-linked to trypsin-treated S-1, no cross-linked product was observed.(ABSTRACT TRUNCATED AT 250 WORDS)     

Studies on co-operative properties of tropomyosin-actin and tropomyosin-troponin-actin complexes by the use of N-ethylmaleimide-treated and untreated species of myosin subfragment 1

When subfragment-1 of rabbit skeletal myosin was extensively modified with N-ethylmaleimide, the protein became strongly associable to actin in the presence of MgATP at low ionic strength, while the ATPase ceased to be activated by actin. Various concentrations of the modified protein were mixed with 10 μmol of pure actin or actin complexed with tropomyosin, and the fraction β of actin saturated with the modified protein in each mixture was determined by an ultracentrifugal method. We then added 0.3 μmol of unmodified subfragment-1 to the same sets of mixtures as used in the above experiments and determined the rate of ATP hydrolysis V by unmodified subfragment-1 as a function of β. A biphasic V-β relation was obtained for the tropomyosin-actin complex: when β was increased continuously from zero, the rate first increased substantially, had a maximum value more than tenfold larger than the initial at β ～- 0.3, and finally decreased to zero. In contrast, the V-β profile for pure actin deviated downwards from a linear relation, showing that there was a weak repulsive interaction between the modified and unmodified subfragment-1 species bound to the actin filament. The occurrence of such a repulsion was interpreted in terms of a steric hinderance model. Assuming that the same kind of repulsion underlay the biphasic V-β relation for the tropomyosin-actin complex, we calculated the relation of V′-β in an ideal case where it was absent. The result was also biphasic. We studied regulated actin in the presence and absence of Ca²⁺ by the same method and obtained biphasic V′-β relations in both cases.The experimental results were analyzed by a two-state model based on the proposal of Bremel & Weber (1972) that, within tropomyosin-actin or the regulated actin complex, n actin monomers undergo “off”/“on” transitions as a unit. Interactions between units were ignored in order to estimate the apparent size n, as well as the equilibrium constant L for the transition in the absence of myosin heads. Within the framework of allosteric theory (Monod et al., 1965), we derived formulae fit for data analysis, found a satisfactory agreement of the experimental and theoretical results, and obtained values of n = 11, and L = 37 for the tropomyosin-actin complex, and n = 16, L = 9 for regulated actin in the presence of Ca²⁺. The parameters in its absence could not be determined separately from the V?β relation which, however, was well-approximated with a combination of n = 16 and L = 10,000. It was also shown that tropomyosin-actin complex in the “on” state activated subfragment-1 ATPase eightfold more strongly than pure actin, and 2.2 to 2.6-fold more strongly than regulated actin in the “on” state. The results are compared with those provided by Greene & Eisenberg (1980), Hill et al. (1980) and Trybus & Taylor (1980) and discussed in conjunction with the double helical structure of tropomyosin-actin and regulated actin filaments.A simple allosteric calculation is presented in the Appendix to explain the well-known biphasic dependence on substrate concentration of the rate of regulated actin-subfragment-1 MgATPase (Bremel et al., 1972; Weber & Murray, 1973), with a reference to Deshcherevsky (1977).