The Flexibility of Actin Filaments as Revealed by Fluorescence Resonance Energy Transfer

The temperature profile of the fluorescence resonance energy transfer efficiency normalized by the fluorescence quantum yield of the donor in the presence of acceptor, f′, was measured in a way allowing the independent investigation of (i) the strength of interaction between the adjacent protomers (intermonomer flexibility) and (ii) the flexibility of the protein matrix within actin protomers (intramonomer flexibility). In both cases the relative increase as a function of temperature in f′ is larger in calcium-F-actin than in magnesium-F-actin in the range of 5–40 °C, which indicates that both the intramonomer and the intermonomer flexibility of the actin filaments are larger in calcium-F-actin than those in magnesium-F-actin. The intermonomer flexibility was proved to be larger than the intramonomer one in both the calcium-F-actin and the magnesium-F-actin. The distance between Gln41 and Cys374 residues was found to be cation-independent and did not change during polymerization at 21 °C. The steady-state fluorescence anisotropy data of fluorophores attached to the Gln41 or Cys374 residues suggest that the microenvironments around these regions are more rigid in the magnesium-loaded actin filament than in the calcium-loaded form.

The tension generation in the striated muscle is performed through a series of chemical reactions by cyclic interaction of myosin with ATP and actin, and at least six intermediates are proposed for actomyosin ATPase in solution (1)(2)(3). On a cellular level in supramolecular complexes where stabilizing forces may modulate the hydrolysis process, some contribution from actin flexibility and dynamics to the contraction process cannot be excluded. This statement is supported by earlier and recent suggestions about the role of actin during the force development in muscle (4).
Flexural rigidity experiments suggested that the actin filament was extensible (5). These findings were supported by electron microscopic measurements on the sarcomere in rigor fibers (6). The extensibility of the thin filaments was also suggested by the changes of the spacings of the x-ray diffraction pattern during contraction (4,7). Actin filaments were shown to be elastic and extensible by measuring the stiffness of the actin-tropomyosin complex with in vitro nanomanipulation (8).
Polarization studies using fluorescent phalloidine on skinned rabbit psoas fibers have demonstrated that the generation of force was associated with a conformational change in the actin filament (9). The sliding of actin filaments is diminished by the cross-linking of actin subunits (10). Egelman et al. (11) and later the workgroup in DeRosier's laboratory (12) emphasized the existence of variations in the twist along the axes of isolated filaments, which increases the fluctuations of approximately 10°in the azimuthal angle between adjacent monomers. The fluctuations, bending and twisting motions, are modulated by myosin and actin-binding proteins (13,14). The tighter binding of myosin to actin reduces the torsional motion of a small section of F-actin, as reported by standard transfer-EPR measurements (13,15). The change of the orientation of spin labels on F-actin during interaction with heavy meromyosin was also reported (10,16). It is also known that the actin monomers undergo conformational changes or slight rotation during contraction (17). The large free energy change caused by binding of the myosin head to actin is also able to generate conformational change in actin (18).
Experimental evidences suggest that the exchange of the bound cation can also modify the dynamic and conformational state of the actin filament. Cation-dependent changes in the mobility of the N-terminal segment (first 21 amino acids) of actin were observed performing nuclear magnetic resonance (NMR) experiments (19). The torsional rigidity of actin filaments is sensitive to the nature of the bound cation, since this parameter is larger in calcium-F-actin than in magnesium-F-actin (20). Orlova and Egelman (21) have shown that the bending flexibility of filaments polymerized from magnesium-actin is approximately four times larger than in the case of calcium-F-actin. Contrary to these data, other laboratories found no essential change in the filament flexibility using dynamic light scattering measurements (22) or various other techniques to determine the persistence length of the filaments (23,24). The direct measurement of the flexibility of single actin filaments corroborates this latter conclusion (20). Using fluorescence methods Miki et al. (25) observed that the binding of Ca 2ϩ to actin increased the mobility of the fluorophore attached to Cys 374 . The results of our spectroscopic experiments indicated that filaments polymerized in the presence of Ca 2ϩ were more flexible than the filaments of magnesium-actin (26).
The recently published actin powerstroke model was based on the length changes in actin filaments, which require conformational transitions in each monomer (27). During the ATP hydrolysis cycle the myosin heads can adopt more than one conformation in interaction with actin, and the multiple modes of binding can relate to different actin conformations. Recently, the negative experimental results of the rotating cross-bridge model have led to suggestions of a more complex model of the muscle contraction. This model involves large scale conformational changes of myosin head in the light chain-binding domain that rotates relative to the actin-binding portion of the catalytic domain (28 -30). The closure of the cleft on the actinbinding domains, which follows the release of the P i , results in a specific interaction between the two proteins, and this interaction might be modulated by the actual dynamic and conformational states of both proteins.
Although there are strong indications that actin is an active part of the contracting system, we are still far from understanding the details of the biological function of this abundant protein. The lack of complete understanding of the function of the actin in the contracting system can emphasize the importance of further investigations dealing with this matter.
The principal aim of this study was to characterize the effect of divalent cations on the internal flexibility and the conformational states of actin filaments using the method of fluorescence resonance energy transfer. According to the fluorescence resonance energy transfer data presented in this paper, the calcium-F-actin is proved to be more flexible than the magnesium-F-actin in either the intermonomer or the intramonomer protein flexibility. The intermonomer flexibility is larger than the intramonomer one, regardless of the nature of the bound cation. In accordance with these flexibility data the steadystate anisotropy experiments indicate that the microenvironments of the Gln 41 and Cys 374 residues are more rigid in the Mg 2ϩ -saturated filaments than in calcium-F-actin.
Protein Preparation-Acetone-dried powder of rabbit skeletal muscle was obtained as described by Feuer et al. (31). Rabbit skeletal muscle actin was prepared according to the method of Spudich and Watt (32) and stored in 2 mM Tris/HCl buffer (pH 8.0) containing 0.2 mM ATP, 0.1 mM CaCl 2 , 0.1 mM ␣-mercaptoethanol, and 0.02% NaN 3 (buffer A).
Labeling of the Cys 374 residue ( Fig. 1A) with IAEDANS was performed as described earlier (33), and F-actin (2 mg/ml) was incubated with 10-fold molar excess of IAEDANS for 1 h at room temperature. Labeling of the same residue in separate samples with IAF was carried out in the following way: monomeric actin (2 mg/ml) was mixed with the 10-fold molar excess of IAF over the protein and incubated for 3-4 h at room temperature. Then the actin was polymerized for 12-16 h at 4°C. After the labeling procedures, the samples were centrifuged at 100,000 ϫ g for 2 h at 4°C. The pellets were dissolved in buffer A and dialyzed overnight against buffer A (in the case of IAF-labeled actin the dialyzing buffer contained 1% (v/v) dimethylformamide as well). The Gln 41 residue (Fig. 1A) was modified with FC by the use of the procedure of Takashi (34), and G-actin was incubated with 10-fold molar excess of the dye in the presence of 1 mg/ml TGase. The labeling was carried out for 16 h at 4°C. Unbound FC was removed similarly as described in the case of IAEDANS and IAF labeling procedures.
The G-actin concentration was determined with a Shimadzu UV-2100 spectrophotometer by using the absorption coefficient of 0.63 mg ml Ϫ1 cm Ϫ1 at 290 nm (35). In the case of IAEDANS-labeled G-actin the measured absorbance at 290 nm was corrected for the contribution of the fluorescence label (using A (290 nm) ϭ 0.21 ϫ A (336 nm) for the bound IAEDANS). Relative molecular mass of 42,300 Da was used for monomeric actin (36). Occasionally, the actin concentration was also determined by using Bradford (Coomassie Blue) protein assay reagent (37). The assay was calibrated as described by the manufacturer using unlabeled monomeric actin. The concentrations determined according to the two methods were identical within the limits of experimental error. The concentration of the IAEDANS, IAF, and FC in the protein solution was determined by using the absorption coefficient of 6100 M Ϫ1 cm Ϫ1 at 336 nm (38), 77,000 M Ϫ1 cm Ϫ1 at 496 nm (39), and 75,500 M Ϫ1 cm Ϫ1 at 493 nm (40), respectively. The extent of labeling for IAEDANS, IAF, and FC was determined to be 0.83 Ϯ 0.02, 0.55 Ϯ 0.04, and 0.8 Ϯ 0.03, respectively.
Sample Preparation and Polymerization-Studying the intermonomer flexibility, part of the actin sample was labeled with the donor molecule (IAEDANS), and the remaining part was modified separately with the acceptor (IAF). After the labeling procedure, the two samples were mixed to obtain the molar ratio of the donor labeled and not donor labeled (acceptor labeled and unlabeled) monomers of minimum 1:10 ( Fig. 1B). In order to measure the intramonomer flexibility, the actin monomer was double-labeled (i.e. labeled with both the donor (IAE-DANS) and the acceptor (FC)). Then the solution of labeled actin was mixed with a solution of unlabeled actin monomers to adjust the labeled:unlabeled actin ratio to a minimum of 1:10 ( Fig. 1C). After the appropriate mixture of labeled and unlabeled actin monomers the polymerization process was initiated.
Magnesium-G-actin was obtained according to the method of Strzelecka-Golaszewska et al. (41). The solution of calcium-G-actin was dialyzed exhaustively against buffer A in which the concentration of CaCl 2 was decreased to 50 M. EGTA and MgCl 2 were added and adjusted to final concentrations of 0.2 and 0.1 mM, respectively. The sample was stirred at room temperature for 10 min.
Polymerization of either calcium-G-actin or magnesium-G-actin was initiated by the addition of 100 mM KCl and 2 mM of the appropriate cation (CaCl 2 or MgCl 2 ) to the solutions of calcium-G-actin or magnesium-G-actin, respectively. The samples were incubated at room temperature for 2 h, then dialyzed overnight against the appropriate polymerization buffer (buffer A supplemented with 100 mM KCl and 2 mM divalent cation, while in the case of magnesium-actin, the buffer also contained 0.1 mM EGTA).
Fluorescence Experiments-The concentration of actin was between 30 and 40 M, unless stated otherwise. The fluorescence emission spectra of the donor were recorded at temperatures ranging between 5 and 40°C with a Perkin-Elmer LS50B luminescence spectrometer in the presence and the absence of the appropriate acceptor (FC in the experiments dealing with intramonomer flexibility and IAF in the study of intermonomer flexibility). The excitation wavelength for the IAEDANS was 360 nm. The slits were set to 3 nm in both the excitation and emission paths. The spectra were corrected for the inner filter effect as described earlier (42). To calculate fluorescence resonance energy transfer efficiency (see Equation 2), the under-curve areas of these emission spectra were calculated between 380 and 460 nm. In this wavelength range, the contribution of the acceptor (either the FC or the IAF) to the measured fluorescence is negligible.
The steady-state fluorescence anisotropy of the donor and acceptor molecules was calculated from the polarized emission components (F VV , F VH , F HV , and F HH , where the subscripts indicate the orientation of the excitation and emission polarizers) as follows, where G ϭ F HV /F HH . In the case of actin-bound IAEDANS, the excitation wavelength was 360 nm, and the emission wavelength was 460 nm, while for the fluorescein derivatives the excitation monochromator was set to 493 nm, and the emission was measured at 520 nm. The slits were set to 3 nm. In these experiments the concentration of the actin was decreased to 5 M after the polymerization by diluting the sample with the appropriate buffer. In this way the depolarizing effect of light scattering was reduced to a negligible level. The corrected fluorescence emission spectra of IAEDANS-F-actin was recorded in the absence of the acceptor at an excitation wavelength of 360 nm to obtain the fluorescence quantum yield of the donor molecule. The quantum yield of quinine sulfate (0.53 in 0.1 N H 2 SO 4 ) was used as a reference (43).
To test the reversibility of the temperature-induced changes in fluorescence, the samples were re-measured by cooling back the solution to the initial low temperature (7°C) or repeating the measurements after overnight dialysis. The errors of the measured data presented in this paper are mean Ϯ S.E. calculated from the results of three to five independent experiments.
Donor-Acceptor Distance-The transfer efficiency of the fluorescence resonance energy transfer occurring between a single donor and single acceptor can be calculated from the fluorescence intensities as follows, where F DA and F D are the fluorescence intensities of the donor molecule in the presence and the absence of the acceptor, respectively; ␤ symbolizes the acceptor/monomer molar ratio. c D and c DA are the concentrations of the donor molecule in the samples indicated by the subscripts. By knowing the fluorescence energy transfer efficiency (E), it is possible to determine the distance (R) between the donor and acceptor molecules from the following equation: where R o is the Förster's critical distance defined as the donor-acceptor distance where the fluorescence resonance energy transfer efficiency is 50%. The use of Equation 3 requires the calculation of R o as follows, where n is the refractive index of the medium, 2 characterizes the relative orientation of the donor and acceptor molecules, ⌽ D is the fluorescence quantum yield of the IAEDANS in the absence of acceptor, and J is the overlap integral given in M Ϫ1 cm Ϫ1 nm 4 . The overlap integral (J) is defined as follows, where F D () is the corrected fluorescence emission spectra of the donor, and ⑀ A () is the molar extinction coefficient of the acceptor.
Normalized Transfer Efficiency-The temperature profile of the normalized energy transfer parameter f (defined as the ratio of the transfer efficiency and the fluorescence quantum yield of the donor in the presence of acceptor) is proportional to the mean value of the energy transfer rate constant, Ͻk ti Ͼ, which has been shown to be an appropriate parameter for monitoring intramolecular fluctuations and/or conformational changes of a macromolecule (44), where ⌽ DA is the fluorescence quantum yield of the donor in the presence of acceptor, and k f is the rate constant of the fluorescence emission. According to earlier publications the value of k f is fairly constant under a wide variety of experimental conditions (see e.g. Ref. 45), therefore here its value is taken as constant. The subscript "i" indicates the value of the given parameter for the i th population, taking a momentary picture, and C is a constant involving the refractive index (n) and the overlap integral (J), which were assumed to be constant (44). The sensitivity of this parameter to temperature is able to provide information regarding the flexibility of the protein matrix between the two fluorophores. It should be noted that f is sensitive to changes in the donor-acceptor distance originating from any kind of intramolecular motions. Thus, the temperature profile of this parameter provides information about the average flexibility of the protein matrix located between the two labels. The method was developed for systems where the energy transfer occurred between a single donor and a single acceptor (44). However, in the present experiments dealing with intermonomer energy transfer, one should take into account that the donor can transfer energy to acceptors located on more than one neighboring actin protomers, i.e. the transfer is directed to a multiple acceptor system. Considering the helical structure of the actin filament, it seems reasonable that the acceptor population can be divided into two characteristically different groups: 1) acceptors on the closest protomer in the single-started genetic helix and 2) acceptors affecting the fluorescence of the donor from the double-started long-pitch helix. It is also assumed that acceptors on more distant protomers are not efficient in the reduction of the donor fluorescence. Accordingly, the donor-acceptor system can be described with two different equilibrium donor-acceptor distance distributions. It could be easily shown by using simple mathematical transformations that the measured normalized energy transfer parameter of the system having a single donor interacting with two different groups of acceptor molecules is the sum of the normalized energy transfer efficiencies characterized by the individual donor-acceptor systems (see also Ref. 46), Considering that the value of the fluorescence quantum yield is proportional to the fluorescence intensity measured at a given wave-length, it is usually more convenient to determine the value of the fЈ, which is defined as follows (44), where F DA is the fluorescence intensity of the donor in the presence of acceptor, and CЈ is a constant that is proportional to the C used in Equation 6.

RESULTS AND DISCUSSION
The actin monomer has one high-affinity and three or more lower-affinity (i.e. intermediate-and low-affinity) cation-binding sites (see Ref. 47 for review). It is very likely that in vivo the high-affinity site is occupied by Mg 2ϩ , and the Mg 2ϩ and K ϩ ions compete for the lower-affinity binding sites (47). The ion composition of the buffer that was used in this study to prepare magnesium-F-actin can be considered as a reasonable model for the free ion concentrations of Mg 2ϩ and K ϩ in the cytosol (47). This preparation resulted in a magnesium-F-actin that contains Mg 2ϩ at the high-affinity binding site and probably either Mg 2ϩ or K ϩ at the lower-affinity sites. According to earlier publications the type of the cation at the lower-affinity binding sites might have an important biological effect (48). The calcium-actin filaments were polymerized in the presence of millimolar concentration (2 mM) of CaCl 2 . Following this procedure the Ca 2ϩ in calcium-F-actin, similar to the Mg 2ϩ in magnesium-F-actin samples, occupies the high-affinity binding site and probably competes with the K ϩ for the lower-affinity binding sites.
In the present work we explored the differences between flexibilities of filaments polymerized from calcium-actin and magnesium-actin by investigating separately the intermonomer and the intramonomer flexibilities. To examine intermonomer flexibilities the donor IAEDANS and the acceptor IAF are attached to different actin protomers within the filament. The relatively low donor ratio in these samples (compared with that of actin without the donor) assures that there is no acceptor in the actin filament, which is in resonance transfer with two donor molecules (see Fig. 1B). Accordingly, in these experiments one is dealing with a single donor-multiple acceptor system (see "Materials and Methods"). In a different experimental setup, the double labeling of the actin monomer makes it possible to study intramonomer flexibility within the actin filament. In this case it was necessary to dilute the samples with unlabeled actin to exclude the possibility of interaction between donor and acceptor molecules located on neighboring protomers. Considering the atomic model of the actin filament (49), it is very likely that the 10-fold dilution of the double labeled actin monomers with unlabeled monomers accurately separates the labeled monomers within the double helix of actin filaments (Fig. 1C). The experiments designed to monitor the reversibility of the temperature-induced changes in the fluorescence parameters gave evidence that the changes were reversible.
The distance between the donor (IAEDANS at Cys 374 ) and acceptor (FC at Gln 41 ) molecules is 4.46 Ϯ 0.07 nm and 4.49 Ϯ 0.06 nm in the Ca 2ϩ -and Mg 2ϩ -loaded forms of the monomer, respectively, indicating that the exchange of the bound cation does not influence the relative position of the Gln 41 and Cys 374 residues in the actin monomer. The data are in good accordance with the results of Moraczewska et al. (50), who found that the replacement of Ca 2ϩ with Mg 2ϩ produced no essential change in the distance between Gln 41 and Cys 374 . These results are also in agreement with our recent observation that the distance between Lys 61 and Cys 374 of the actin monomer is cation-independent (51). The distance between Gln 41 (C␣) and Cys 374 (S␥) residues is 4.1 nm according to the x-ray diffraction experiments (52). The value of this parameter resolved in our experiments is somewhat longer. The relatively small difference between the x-ray and the fluorescence data might be due to the size of the applied fluores-cent probes.
The donor-acceptor distances (between residues Cys 374 and Gln 41 ) in the filament at room temperature are 4.45 Ϯ 0.08 nm and 4.59 Ϯ 0.09 nm in calcium-F-actin and magnesium-F-actin, respectively (Table I.), which indicates that the polymerization does not affect significantly the donor-acceptor distance. This is in agreement with Miki's conclusion (53) that the small domain in the actin monomer is substantially rigid and compact and only slightly sensitive to the binding of DNase I or myosin subfragment 1 or tropomyosin-troponin or polymerization. Above we speculate on the basis of the filament model (49) that the 10-fold dilution of doubly labeled actin samples with unlabeled actin diminishes the intermonomer resonance energy transfer. The lack of the effect of polymerization on the donoracceptor distance implies that this assumption was correct. The distance between the two labeled residues of the small domain was temperature-independent in magnesium-F-actin (Table I). This statement is apparently not true for the calcium-F-actin (Table I), since the value of the donor-acceptor distance shows a decreasing tendency with increasing temperature (for discussion, see below).
The cation dependence of the flexibility of the actin protomer within the filament can be characterized by measuring the temperature profile of the normalized transfer efficiency (Equations 6 and 8). In experiments dealing with intraprotomer interactions the temperature dependence of the relative fЈ is proved to be substantially larger in calcium-F-actin than in magnesium-F-actin between 5 and 40°C ( Fig. 2A). The total change of 5% in the Mg 2ϩ -saturated form faces the 30% increase in the Ca 2ϩ -saturated form. The data set suggests that the protomer structure is more flexible in the Ca 2ϩ -loaded form of the actin filament than that in the magnesium-loaded form. The change in the relative fЈ is very similar in calcium-F-actin to what was observed in the case of actin monomer by using a similar donor-acceptor pair (51). Accordingly, the flexibility of the small domain does not seem to be sensitive to polymerization in calcium-actin. Contrary to this, the relative change of fЈ is smaller in magnesium-F-actin than that in magnesium-Gactin (51), indicating that in the Mg 2ϩ -loaded form this protein segment is more rigid in the filament than it is in the monomer.
According to the results of intermonomer transfer experiments, the change of the relative fЈ is larger in the calcium-Factin than in the magnesium-F-actin (Fig. 2B), which suggests that the strength of the intermonomer interaction is stronger in the Mg 2ϩ -saturated filament. By comparing the data obtained in the experiments addressing intramonomer and intermonomer fluorescence energy transfer, one can conclude that the intramonomer flexibility is smaller than the intermonomer flexibility for both the calcium-F-actin and magnesium-F-actin (Fig. 2, A and B). Considering that in intermonomer energy transfer the contributions of the two kinds of acceptor populations (see also "Materials and Methods") to the measured fluorescence energy transfer efficiency are probably similar (49), in these experiments it is not possible to separate the flexural  properties of the genetic helix and the two-started long-pitch helix. The increase in the amplitude of the relative fluctuation of the donor and acceptor molecules should result in an increase of the mean value of the energy transfer rate constant, Ͻk ti Ͼ and therefore the measurable donor-acceptor distance, even if the equilibrium distance between the two labels remains unchanged (44). In the light of our present data regarding the cation-dependent flexural properties of the filament, it seems possible that the slight temperature dependence of the donoracceptor distance measured in the calcium-F-actin is partly the result of a temperature-induced increase in the amplitude of the relative fluctuation of the donor and acceptor molecules. The interpretation of the results described above requires further spectral considerations. Both the temperature-and cation-induced changes in the shape of the emission spectra of the donor and the absorption spectra of the acceptor are negligible (data are not shown). Accordingly, the value of the overlap integral (Equation 5.) depends on neither the temperature nor the nature of the bound cation. Therefore it cannot contribute to the observed changes of fЈ in the filaments. However, the value of the fЈ, and hence the relative fЈ, might depend on the orientation factor ( 2 ). Although this is the only parameter in the fluorescence energy transfer experiments which cannot be measured properly, the measurements of the steady-state anisotropy of both the donor and the acceptor molecules might provide information regarding the behavior of 2 . The anisotropy of IAEDANS and FC is cation-dependent in the actin filament (Fig. 3, A and B). The measured anisotropy values are larger in the Mg 2ϩ -saturated form than in the Ca 2ϩsaturated one for both IAEDANS and FC, which can be taken as an indication of conformational differences between the calcium-F-actin and magnesium-F-actin. Interestingly, similar cation-induced change was not observed in the case of IAF (Fig.  3C). Taking into account that both IAEDANS and IAF are connected to the same amino acid (Cys 374 ), the different cation sensitivity possibly originates from the application of different fluorophores. According to the results of Orlova and Egelman  (54), there is a high-density bridge between the two strands of filament when the high-affinity cation-binding sites are occupied by Ca 2ϩ . This density bridge was not observed in magnesium-F-actin. They proposed that the presence of this bridge could be the result of the shift in the position of the C terminus. Therefore, the cation dependence of the fluorescence anisotropy in the case of IAEDANS and FC might reflect the cationinduced intramolecular rearrangement of the C-terminal segment within the actin filament. Although the exact nature of this rearrangement is not known, it seems to be possible that the formation of the density bridge in calcium-F-actin involves the modification of some of the connections between the Cterminal segment and the small domain of either the same or the neighboring protomers. The subdomain 1 (involving the Cys 374 residue) is in close contact with the subdomain 2 (which contains the Gln 41 residue) of the subsequent protomer within the long-pitch helix (49). Accordingly, the formation of the high-density bridge in calcium-F-actin can result in a conformation where the microenvironments of the Cys 374 and the Gln 41 residues are more flexible than these microenvironments in the magnesium-F-actin.
The temperature sensitivity of the fluorescence anisotropy of all fluorophores is similar (Fig. 3, A-C), which suggests that the temperature-induced change in the value of the orientation factor is also similar in these cases. Accordingly, the change in the 2 is probably not the source of the apparent cation-dependent variation in the value of the relative fЈ in either the intermonomer or the intramonomer energy transfer experiments. All these data allow the conclusion that both the intramonomer and intermonomer flexibilities are larger in calcium-F-actin than in magnesium-F-actin. Furthermore, the results of the steady-state anisotropy measurements support the conclusion that the microenvironments of the Gln 41 and Cys 374 residues are more rigid in the magnesium-F-actin than in the calcium-F-actin.
The bending and torsional flexibility of calcium-F-actin was found to be smaller (21) or similar (28 -31) to that of magnesium-F-actin. However, we have shown here and in our previous work (26) that the flexibility characteristic for intramolecular motions on a nanosecond time scale is larger in calcium-F-actin than in the Mg 2ϩ -saturated form of the filament. We have suggested (26) that the apparent conflict could be resolved considering that the methods applied in our experiments and those used in the cited articles (21, 28 -31) provide information about intramolecular motions on a substantially different time scales.
The structure of the magnesium-F-actin can be taken as a model of the thin filament in the relaxed state. The changes in the actin-associated layer lines in x-ray diffraction pattern during muscle activation (56,57) and the differences of the layer lines observed between magnesium-F-actin and calcium-F-actin (54) are similar. Relying on these data Egelman and Orlova (58) proposed that the structure of the calcium-F-actin was corresponding to the thin filaments in the activated state. It is very likely that due to the slow exchange of the tightly bound divalent cation in actin the replacement of Mg 2ϩ by Ca 2ϩ does not occur under physiological conditions (47). Accordingly, Egelman and Orlova (58) concluded that the activated state of the thin filament was probably induced by the binding of myosin. One might assume that the similarity of the structure of calcium-F-actin and the structure of the F-actin in the activated thin filaments can extend to intramolecular dynamic events occurring on a nanosecond timescale. Thus, considering that actin-myosin interaction can possibly utilize the strain energy stored in actin filaments (59), the divalent cation-dependent changes in the intramolecular flexibility described in this study might be important in the efficient energy transduction of the muscle contraction.