371

Journal of Muscle Research and Cell Motility 22: 371±378, 2001. Ó 2001 Kluwer Academic Publishers. Printed in the Netherlands.

Phalloidin a€ects the myosin-dependent sliding velocities of actin ®laments in a bound-divalent cation dependent manner KIYOTAKA TOKURAKU1,2,* and TARO Q. P. UYEDA2 1 Department of Chemical Science and Engineering, Miyakonojo National College of Technology, 473-1 Yoshio-cho, Miyakonojo, Miyazaki 885-8567; 2Gene Discovery Research Center, National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8562, Japan Received 3 July 2001; accepted in revised form 15 August 2001

Abstract We examined sliding velocities in vitro of four types of actin ®laments, that is, ®laments with Ca2‡ or Mg2‡ bound at the high anity metal binding site, each with rhodamine phalloidin bound with a high or low stoichiometry. When surfaces coated with a high density of heavy meromyosin (HMM) were used, high stoichiometric concentrations of rhodamine phalloidin reduced sliding velocities of only Ca2‡-actin ®laments, by 40%. As the HMM density on surfaces was reduced, continuous movement of actin ®laments became dependent on the presence of methylcellulose and sliding velocities of all four types became progressively slower. Interestingly, Ca2‡-actin ®laments with a high stoichiometric concentration of rhodamine phalloidin were the fastest among the four types of ®laments on sparse HMM surfaces. In contrast, phalloidin did not a€ect steady state ATPase activities of HMM in the presence of Ca2‡- or Mg2‡-actin ®laments. We speculate that the reversal of the order of sliding velocities among the four types of actin ®laments between high and low densities of HMM relates with di€erent axial elasticity of the actin ®laments, so that sti€er ®laments move slower on dense HMM surfaces, but faster on sparse surfaces, than elastic ones.

Introduction Phalloidin, a cellular toxin of fungal origin, binds to actin with a high anity (Kd is 10)8 M) at a 1:1 stoichiometric concentration (Wieland et al., 1975). Upon the binding, actin polymerization is promoted (Dancker et al., 1975) and the actin ®laments are stabilized against depolymerization (Low et al., 1975; Estes et al., 1981). Fluorescently-labeled phalloidin has been widely used in in vitro motility assays, in order to stabilize and visualize actin ®laments sliding on myosincoated surfaces. Binding of phalloidin a€ects various other properties of actin ®laments as well. For example, phalloidin binding reduces bending and torsional ¯exibility of actin ®laments (Isambert et al., 1995; Rebello and Ludescher, 1998). It is known that binding of myosin to actin ®laments is coopearative, so that bound myosin molecules tend to form clusters along actin ®laments when myosin is present at very low stoichiometric concentration against actin subunits (Woodrum et al., 1975). There is evidence that bound phalloidin interferes with this cooperative binding between myosin and actin ®laments (Orlova and Egelman, 1997). It was reported that phalloidin has an activating e€ect on striated muscle (Bukatina and Fuchs, 1994; Bukatina et al., *To whom correspondence should be addressed: Tel.: ‡81-986-47-1221; Fax: ‡81-986-47-1231; E-mail: [email protected]

1995), but a recent analysis failed to detect e€ects of phalloidin on in vitro actomyosin sliding and ATPase activities (VanBuren et al., 1998). Thus, consequences of phalloidin bound to actin on the actomyosin interactions remain elusive. Divalent cations also bind actin. Either Ca2‡ or Mg2‡ bind to the single divalent cation binding site of actin with a high-anity (Kd  10)8 M for both Ca2‡ and Mg2‡) (Estes et al., 1992), and the type of bound cation a€ects various properties of actin as well. For instance, the polymerization kinetics of Ca2‡-actin were di€erent from those of Mg2‡-actin (Carlier et al., 1986) and the tertiary structures of actin ®laments can be altered depending on the type of tightly bound divalent cation (Orlova and Egelman, 1992, 1993, 1995; Orlova et al., 1995). Moreover, torsional ¯exibility of Ca2‡-actin ®laments is di€erent from those of Mg2‡-actin ®laments (Yasuda et al., 1996; Rebello and Ludescher, 1998). E€ects of myosin-binding on dynamic rotational motion of actin ®laments is also di€erent between Ca2‡- and Mg2‡-actin ®laments (Rebello and Ludescher, 1999). With respect to the cooperative binding between actin and myosin, bound Mg2‡ abolishes this cooperativity (Orlova and Egelman, 1997). Consequently, there is a considerable degree of overlap among the published e€ects of actin-bound Ca2‡/Mg2‡ and phalloidin on structural and biochemical parameters such as ®lament ¯exibility and cooperative binding with myosin. Yet, the physiological or

372 functional signi®cances of binding Ca2‡/Mg2‡ and phalloidin to actin ®laments has not been elucidated. We were interested to know if the actomyosin sliding mechanism is a€ected by bound Ca2‡/Mg2‡ and phalloidin, and if it is, whether it is correlated with the cooperativity of actin±myosin binding, or the sti€ness of actin ®laments. Therefore, we have examined the sliding velocities in vitro of actin ®laments carrying either Ca2‡ or Mg2‡, and with a high or low stoichiometric concentrations of bound rhodamine phalloidin. We found that Ca2‡/Mg2‡, and rhodamine phalloidin a€ect actomyosin sliding velocity in a manner well correlated with the elasticity of actin ®laments.

Acto-HMM ATPase assays were carried out in reaction solutions which contained 0.1 lM HMM, various concentrations of Ca2‡- or Mg2‡-actin ®laments, with or without phalloidin, and 2 mM ATP in the Mg2‡-bu€er at 30°C. The liberated Pi was quanti®ed by a modi®ed malachite green method (Kodama et al., 1986). Ca2‡- or Mg2‡-actin ®laments were added to the mixture immediately before the reaction was started by the addition of ATP.

Materials and methods

E€ects of rhodamine phalloidin on sliding velocities

Protein preparation

We ®rst examined whether binding of rhodamine phalloidin a€ects sliding velocity of Ca2‡- or Mg2‡actin ®laments. The labeled actin ®laments were diluted in the Mg2‡-bu€er, and immediately introduced into ¯ow chambers that consisted of a glass slide, pairs of spacers, and a nitrocellulose-coated coverslip on which a high density of HMM had been absorbed. After incubating for 1 min at 30°C, the Mg2‡-bu€er containing 2 mM ATP was introduced to initiate the movement. When the concentration of rhodamine phalloidin was low, yielding the stoichiometric ratio of rhodamine phalloidin to actin subunits of 1:20 (RP0.05), sliding velocities of both Ca2‡- and Mg2‡-actin ®lament were approximately 9 lm/s (Figure 1A). Sliding velocity of Mg2‡-actin ®laments slightly decreased with the increase of concentration of rhodamine phalloidin (Figure 1A, circles). In contrast, a stoichiometric concentration of rhodamine phalloidin (RP1)a decreased velocity of Ca2‡-actin ®laments by more than 30% to 6 lm/s (Figure 1A, squares). Increasing the concentration of rhodamine phalloidin to twofold molar excess over the actin subunits further decreased sliding velocities of Ca2‡-actin ®laments to 5 lm/s, which is a 40% decrease compared with RP0.05. Additional increase of the concentration of rhodamine phalloidin was not feasible due to very high background ¯uorescence during observation. Therefore, to investigate possible e€ects of large excess of phalloidin on sliding velocities, 200-fold molar excess of unlabeled phalloidin was added to actin ®laments that had been labeled with a stoichiometric concentration of rhodamine phalloidin (shown at RP/actin of 200 in Figure 1A). These actin ®laments moved at speeds similar to those labeled with twofold molar excess of rhodamine phalloidin, indicating that twofold molar excess is saturating in terms of slowing the sliding velocities of Ca2‡-actin ®laments. The concentration of actin subunits is extremely low after dilution in preparation for the

Actin and myosin were prepared from rabbit skeletal muscle by the standard methods (Pardee and Spudich, 1982; Hynes et al., 1987). G-actin was further puri®ed by gel ®ltration chromatography using Superose 6 (Amersham Pharmacia Biotech, Buckinghamshire, UK) in 5 mM Tris±Cl, 0.2 mM DTT, 0.1 mM CaCl2, 1.5 mM NaN3, 0.2 mM ATP, pH 7.8. Rabbit skeletal muscle heavy meromyosin (HMM) and myosin subfragment 1 (S1) were prepared by the method of Okamoto and Sekine (1985). Protein concentrations were determined by the method of Lowry et al. (1951) using bovine albumin as the standard. Ca2‡- or Mg2‡actin monomer was prepared according to Yasuda et al. (1996). To polymerize Ca2‡- or Mg2‡-actin ®laments, G-actin (Ca2‡- or Mg2‡-) was dialyzed against Ca2‡bu€er (4 mM CaCl2, 25 mM Imidazole, 25 mM KCl, and 1 mM DTT, pH 7.4) or Mg2‡-bu€er (4 mM MgCl2, 25 mM Imidazole, 25 mM KCl, and 1 mM DTT, pH 7.4) containing 0.1 mM ATP for 3 h. Ca2‡- or Mg2‡actin ®laments were labeled with rhodamine phalloidin at various stoichiometries by incubating them in either Ca2‡- or Mg2‡-bu€er containing various concentrations of rhodamine phalloidin (Molecular Probes, Eugene, USA) overnight on ice. The concentration of actin during the labeling reaction was 100 lg/ml. Immediately before use these solutions of labeled actin ®laments were diluted 100-fold in the Mg2‡-bu€er. In vitro motility assay In vitro motility assays were carried out according to Kron et al. (1991) using the Mg2‡-bu€er containing 2 mM ATP at 30°C. For assays on surfaces only sparsely coated with HMM, 0.8% methylcellulose was added to the assay bu€er to suppress lateral di€usion of actin ®laments away from the surfaces (Uyeda et al., 1990). Sliding velocities of actin ®laments were determined manually by tracking the leading edges of the actin ®laments at intervals of 0.5 s during the period of 1.5 s.

Acto-HMM ATPase assay

Results

a

Rhodamine phalloidin was present at a stoichiometric concentration of 1:1 with respect to actin subunits during the labeling reaction.

373

Fig. 1. E€ect of rhodamine phalloidin on sliding velocity in vitro. A, Ca2‡-actin ®laments (h) and Mg2‡-actin ®laments (s) were labeled with various stoichiometries of rhodamine phalloidin and their sliding velocities on HMM surfaces were measured (concentration of HMM in the absorption bu€er was 0.8 lM). The motility assays were carried out in the Mg2‡-Bu€er. Vertical axis and horizontal axes are sliding velocities of each type of ®laments (n ˆ 25) and the stoichiometric concentration of rhodamine phalloidin to actin, respectively. The exceptions are data points at RP/actin of 200, as explained in the text. Error bars denote standard deviations. Sliding velocities of Ca2‡-actin ®laments (n) and Mg2‡-actin ®laments (d) were also measured on S1 surfaces (concentration of S1 in the absorption bu€er was 1 lM). Error bars of the data points for S1 are hidden behind the symbols. B, Ca2‡-actin ®laments (h) and Mg2‡-actin ®laments (s) were labeled with various stoichiometries of rhodamine phalloidin and the images were observed under a ¯uorescence microscope. Fluorescence intensity along a unit axial length of each actin ®lament (n ˆ 20) was measured by analyzing digitized images using the NIH image software.

motility assay, and we speculate that higher stoichiometric concentrations of rhodamine phalloidin or unlabeled phalloidin prevents their dissociation from actin ®laments after this dilution step. To eliminate the possibility that the weak inhibitory e€ect of rhodamine phalloidin on sliding movement of Mg2‡-actin ®laments was caused by its lower anity for Mg2‡-actin ®laments, we compared relative anities of rhodamine phalloidin between these two types of actin. The anities were estimated by measuring ¯uorescence intensities of rhodamine phalloidin-labeled ®laments observed under a ¯uorescence microscope (Figure 1B).

Fluorescence intensity of the actin ®laments increased with the increase of stoichiometric concentrations of rhodamine phalloidin, and saturated when stoichiometric concentration was more than 1.5. The ¯uorescence intensity curves of Ca2‡- and Mg2‡-actin ®laments were practically indistinguishable from each other, indicating that the anities of phalloidin for Ca2‡- and Mg2‡actin ®laments are the same. Taken together, we conclude that rhodamine phalloidin bound to Ca2‡actin ®laments exerts a large inhibitory e€ect on the movement while that bound to Mg2‡-actin ®laments has negligible e€ects. There was a concern that Ca2‡ bound to actin may be replaced by Mg2‡ in the Mg2‡-bu€er during the assay, and the velocities of ®laments that we thought were Ca2‡-actin ®laments were in fact those of Mg2‡-actin ®laments. This does not appear to be the case, as earlier biochemical studies have shown that the exchange of divalent cations bound to the high anity metal binding sites of actin ®laments is an extremely slow process (Kasai and Oosawa, 1969; Estes et al., 1992). Furthermore, Ca2‡-actin ®laments with a high stoichiometric concentrations of rhodamine phalloidin consistently moved at a slower speed than Mg2‡-actin ®laments with the same stoichiometric concentration of rhodamine phalloidin, and this speed di€erence did not change within a time span of up to 10 min (data not shown), indicating that the exchange of bound Ca2‡ with Mg2‡ did not occur at appreciable levels under our experimental conditions. We also carried out in vitro motility assays using S1 instead of HMM. The sliding velocities of Ca2‡-actin (RP1) and Mg2‡-actin (RP1) were 1.1 and 1.8 lm/s, respectively. These sliding velocities were much lower than that over HMM-coated surfaces, as has been reported previously by Toyoshima et al. (1987). Notably, the ratio of velocities between the two types of actin ®laments on S1-coated surfaces (approximately 1.6) was similar to that over HMM-coated surfaces (1.5), suggesting that a common mechanism, not directly related to the motor function, is a€ecting the sliding velocities in both cases. E€ects of HMM densities on sliding velocities We next examined e€ects of changing HMM densities on assay surfaces (Figure 2). Our initial attempt to prepare surfaces of uniform, low densities of motors by simply introducing diluted HMM solutions into ¯ow chambers was not very successful, with the tendency to result in higher densities of motors near the intake of the ¯ow chamber than other parts of the surface (result not shown). We have therefore modi®ed the procedure to absorb HMM on nitrocellulose surfaces. First, two pieces of double-sided adhesive tape were placed on a glass slide, and a drop of the Mg2‡-bu€er containing diluted HMM was placed between these spacers. A coverslip with nitrocellulose coating was quickly placed

374 (RP1) or low (RP0.05) stoichiometric concentration of rhodamine phalloidin, were measured and plotted against the concentrations of HMM in the initial absorption solution (Figure 2A). At the same time, the number of sliding actin ®laments in 1 mm2 were counted, and were plotted against the concentration of HMM (Figure 2B). When HMM concentration was less than 0.18 lM, all actin ®laments were released from the surface upon addition of ATP (Figure 2B). The release of actin ®laments caused their di€usion away from the surface by Brownian movements (Uyeda et al., 1990). Above HMM concentrations of 0.18 lM, Ca2‡-actin ®laments (RP1) showed the lowest sliding velocity as compared with the other three types of actin ®laments (Figure 2A). HMM concentration did not have significant e€ects on sliding velocities of each type actin ®laments, as long as the density of HMM molecules are above a certain threshold value. E€ects of low HMM densities on sliding velocities in the presence of methylcellulose

Fig. 2. E€ect of HMM density on sliding velocity. Sliding velocities of Ca2‡-actin ®laments (RP1) (j), Ca2‡-actin ®laments (RP0.05) (h), Mg2‡-actin ®laments (RP1) (d), and Mg2‡-actin ®laments (RP0.05) (s) were measured on surfaces with various densities of HMM in the absence of methylcellulose. The velocities were measured between 1 and 3 min after the addition of ATP. A, Sliding velocities of actin ®laments (n ˆ 25) were plotted against the concentrations of HMM in the absorption bu€er. All ®laments were released from the surfaces when HMM concentration was less than 0.18 lM (- - -). B, Number of actin ®laments per 1 mm2 at 1 to 3 min after the addition of ATP was plotted against the concentrations of HMM in the absorption bu€er. Error bars denote standard deviations.

over the HMM solution and the spacers, and a ¯ow chamber was constructed. After incubation for 1 min at 30°C, a blocking solution which consisted of the Mg2‡bu€er and 1 mg/ml bovine serum albumin was introduced from one of the two openings. Surfaces prepared in this way had relatively uniform densities of motors, as judged by the uniformity of sliding velocities at di€erent parts of the same ¯ow chamber (not shown). Hereafter, we use the concentration of HMM in the solution used in the initial absorption, rather than the actual density of HMM molecules on the surface, to refer to the surface density of HMM. Sliding velocities of four types of actin ®laments, Ca2‡- or Mg2‡-actin ®laments, each labeled with a high

To measure sliding velocities over surfaces with low HMM densities, which cannot support continuous sliding movement under standard in vitro motility assay conditions, we carried out assays in the presence of 0.8% methylcellulose (Figure 3). When HMM concentration was higher than 0.3 lM (data not shown), sliding velocities were similar to those without methylcellulose (Figure 2). Sliding velocities of Ca2‡-actin ®laments (RP0.05) (Figure 3A) and Mg2‡actin ®laments (both RP1 and RP0.05) (Figure 3B) remained relatively constant, independent of the HMM concentration, when it was higher than approximately 0.08 lM. On the other hand, sliding velocity of Ca2‡actin ®laments (RP1) increased with the decrease of HMM concentration when HMM concentration was between 0.3 and 0.06 lM, and the maximum velocity was achieved at 0.06 lM of HMM concentration (Figure 3A). This maximum velocity at the HMM concentration of 0.06 lM was similar to velocities of other types of actin ®laments at the same HMM density. When HMM concentration was reduced below 0.06 lM, sliding velocity of Ca2‡-actin ®laments (RP1) declined, but at a rate smaller than that of the other types of ®laments. Notably, this resulted in the reversal of the order of velocities among the four types of actin ®laments, and Ca2‡-actin ®laments (RP1) were the fastest at very low HMM densities. When HMM concentration was 0.02 lM, sliding velocities of Ca2‡actin ®laments (RP1) and Ca2‡-actin ®laments (RP0.05) were 2.9 and 2.1 lm/s, respectively (Figure 3B). The di€erence between these two velocities is small, but is statistically signi®cant (P < 0:01). This reversal in the order of velocities was also observed when rhodamine phalloidin was present at a twofold molar excess over actin subunits (data not shown).

375 Table 1. Kapp and Vmax of actomyosin ATPase Kapp (lM)

Vmax (s)1)

Ca2‡-actin (P1) Ca2‡-actin (P0.05)

22.8 ‹ 6.2 19.4 ‹ 3.7

16.8 ‹ 6.0 14.4 ‹ 3.5

Mg2‡-actin (P1) Mg2‡-actin (P0.05)

16.1 ‹ 1.1 17.5 ‹ 1.6

10.0 ‹ 0.8 10.0 ‹ 1.1

with a high (P1)b or low (P0.05)c stoichiometric concentration of phalloidin. To exclude possible e€ects of di€erent cations on HMM, all assays were carried out in a common bu€er (Mg2‡-bu€er). Concentrated Ca2‡actin ®laments maintained in the Ca2‡-bu€er were added to the assay mixture immediately before the onset of the reaction, and the reactions were terminated within 10 min. In vitro motility assays had demonstrated that the exchange of actin-bound Ca2‡ with Mg2‡ is negligible in 10 min. Kapp for actin and Vmax of acto-HMM ATPase using Ca2‡-actin ®laments were di€erent from those using Mg2‡-actin ®laments. However, phalloidin had no e€ect on ATPase activities using either Ca2‡- or Mg2‡-actin ®laments. These results indicated that actin-bound cation a€ects ATPase activities but phalloidin has no relevance to the steady state ATPase activities in solution. Discussion

Fig. 3. Sliding velocities on surfaces with low HMM densities. To measure sliding velocities on low HMM density surfaces, assays were carried out in the presence of 0.8% methylcellulose. A, Sliding velocities of Ca2‡-actin ®laments (RP1) (j) and Ca2‡-actin ®laments (RP0.05) (h) were plotted against HMM concentrations in the absorption bu€er. B, Magni®ed plot of the low HMM concentration region from A (Ca2‡-actin ®laments). C, Sliding velocities of Mg2‡-actin ®laments (RP1) (d) and Mg2‡-actin ®laments (RP0.05) (s) were plotted against concentrations of HMM in the absorption bu€er. Error bars denote standard deviations (n ˆ 25).

E€ects of phalloidin on acto-HMM ATPase activities Finally we examined whether phalloidin a€ects actoHMM ATPase activities (Table 1). Acto-HMM ATPase activities were measured by a modi®ed malachite green method (Kodama et al., 1986) using four types of actin ®laments, Ca2‡- or Mg2‡-actin ®laments each labeled b

Phalloidin was present at a stoichiometric concentration of 1:1 with respect to actin subunits during the labeling reaction.

In this paper, we have characterized four types of actin ®laments, that is, actin ®laments with Ca2‡ or Mg2‡ bound at the high anity divalent cation binding site, each labeled with a high (1:1) or low (1:0.05) stoichiometric concentration of phalloidin or rhodamine phalloidin, in in vitro motility and steady state ATPase assays. The results demonstrated that rhodamine phalloidin a€ects actomyosin sliding velocity without impacting the ATPase activity. The e€ect of rhodamine phalloidin on sliding of Ca2‡-actin ®laments was larger than that on Mg2‡-actin ®laments. In the presence of a high density of HMM on surfaces (Table 2, concentration of HMM in the absorption bu€er = 0.5 lM), velocity of Ca2‡-actin ®laments (RP1) was reduced by one third when compared with those bound with a smaller stoichiometric concentration of rhodamine phalloidin, and was the slowest among the four types of ®laments. However, when HMM density was low (Table 2, concentration of HMM in the absorption bu€er = 0.02 lM), Ca2‡-actin ®laments (RP1) were the fastest among the four types of ®laments. Rhodamine phalloidin used in this study contains four stereo-isomers. However, the di€erences are outside the actin binding region of the molecules, and the anities of these isomers to actin ®laments are more or less c

Phalloidin was present at a stoichiometric concentration of 1:20 with respect to actin subunits during the labeling reaction.

376 Table 2. Sliding velocity and torsional ¯exibility of actin ®lament Velocity (lm/s) HMM 0.5 lMc

HMM 0.02 lMd

a rFA

Torsional rigidityb (Nm2)

Ca2‡-actin (RP1) Ca2‡-actin (RP0.05)

5.0 ‹ 0.5 8.3 ‹ 0.5

4.6 ‹ 0.8 3.0 ‹ 0.5

0.098 ‹ 0.005 0.083 ‹ 0.002

8.5 ‹ 1.3 ´ 10)26 ±

Mg2‡-actin (RP1) Mg2‡-actin (RP0.05)

8.8 ‹ 0.6 9.0 ‹ 0.9

2.9 ‹ 0.6 2.1 ‹ 0.3

0.080 ‹ 0.005 0.066 ‹ 0.002

2.8 ‹ 0.3 ´ 10)26 ±

a

Phosphorescence emission anisotropies that were reported by Rebello and Ludescher (1998). Torsional rigidities that were reported Yasuda et al. (1996). c Means of velocities ‹ standard deviations of 25 ®laments from Figure 2. d Means of velocities ‹ standard deviations of 25 ®laments from Figure 3. b

similar to each other (Faulstich et al., 1988). Therefore, we do not think that the existence of the isomers should have much to do with the di€erential e€ects rhodamine phalloidin exerted on Ca2‡- and Mg2‡-actin ®laments. How then is this complex behavior of Ca2‡-actin ®laments (RP1) in the motility assays related to its structural or biochemical property? Video microscopic and electron microscopic observations of actin ®laments failed to detect di€erences in ¯exural ¯exibility of Ca2‡and Mg2‡-actin ®laments (Isambert et al., 1995; Yasuda et al., 1996; Steinmetz et al., 1997). However, Yasuda et al. (1996) estimated the torsional rigidity of actin ®laments on the millisecond to second time scales by observing motion of beads attached to the ®laments, and found that phalloidin-stabilized Ca2‡-actin ®laments are three times torsionally more rigid than phalloidin-stabilized Mg2‡-actin ®laments (Table 2). More recently, Rebello and Ludescher (1998) estimated torsional ¯exibility of actin ®laments on the micro- to milli-second time scale by measuring phosphorescence emission anisotropy (Table 2). They reported that Mg2‡-actin ®laments (rFA = 0.066) were more ¯exible than Ca2‡-actin ®laments (rFA = 0.083). They also reported that phalloidin lowered the ¯exibility of both Mg2‡-actin ®laments (rFA = 0.080) and Ca2‡-actin ®laments (rFA = 0.098) (Table 2). Considering the double-helical nature of actin ®laments, the di€erence in torsional rigidity between Ca2‡- and Mg2‡-actin ®laments suggests a di€erence in the extensile elasticity of ®laments along the axial direction. In other words, it is probable that Ca2‡-actin ®laments, particularly Ca2‡-actin ®laments (RP1), may be less elastic than Mg2‡-actin ®laments. Elasticity of phalloidin-stabilized Mg2‡-actin ®laments has been directly measured by nanomanipulation techniques (Kojima et al., 1994), but an experimental comparison of elasticity between Ca2‡and Mg2‡-actin ®laments and examination of the possible e€ects of bound phalloidin have not been reported so far. Based on the assumption that bound Ca2‡ or Mg2‡ and phalloidin a€ects elasticity of actin ®laments, we propose a hypothesis which qualitatively explains the complex e€ects phalloidin binding exerts on sliding velocities. When HMM density is high, one ®lament simultaneously interacts strongly with multiple myosin

heads. Those myosin heads which have ®nished the power stroke but are still strongly attached to the ®lament would experience negative strain and impose a load on the movement of ®laments, which is powered by other strongly bound heads performing power strokes or in the positive strain (Huxley, 1957). Such mechanical interference between heads that are producing positive and negative strains is mediated by the sti€ness of actin ®laments, and sti€er ®laments should be more prone to this interference, and hence to the load imposed by negatively-strained heads. This may be the reason why the velocity of Ca2‡-actin ®laments (RP1) is the slowest among the four types of actin ®laments moving over high density HMM surfaces. This scenario also explains why its sliding velocities increase when the HMM concentration in the absorption bu€er was decreased from 0.25 to 0.06 lM and the average distance between heads that are strongly bound along actin ®laments increases (Figure 3A). When the HMM density is very low, each actin ®lament would interact strongly with only one or a small number of myosin heads at a moment. Under such conditions, interference between strongly bound heads becomes infrequent and less of a problem. Instead, displacement generated at one point along the length of an actin ®lament is more eciently transmitted to other parts of the ®lament, if the ®lament is sti€er. A larger fraction of the local displacement of a ®lament should be dissipated in compression or stretching of the ®lament for more elastic ®laments. Thus it is expected that the sti€est, Ca2‡-actin ®laments (RP1) move fastest on sparse HMM surfaces (Figure 3B). Orlova and Egelman (1997) reported that the cooperativity of binding between myosin and actin ®laments is larger with Ca2‡-actin ®laments than with Mg2‡-actin ®laments. This ®nding is particularly intriguing because cooperative binding has a potential to promote actomyosin interactions and a€ect the sliding velocity. However, di€erence in the cooperativity of binding does not seem to be the cause of the observed di€erent sliding velocities between Ca2‡- and Mg2‡-actin ®laments (RP1), since the e€ect of phalloidin binding on the cooperativity and that on the sliding velocity do not correlate with each other. Cooperative binding between HMM and Ca2‡-actin ®laments was abolished by a high

377 stoichiometric concentration of bound phalloidin, so that phalloidin-bound Ca2‡-actin ®laments were similar to phalloidin-bound Mg2‡-actin ®laments in terms of the poor cooperativity (Orlova and Egelman, 1997). In contrast, the di€erence in sliding velocities between Ca2‡- and Mg2‡-actin ®laments was larger in the presence of a high stoichiometric concentration of rhodamine phalloidin. Alternatively, the complex e€ect of phalloidin binding on sliding velocity may be an indirect consequence of its impact on the kinetics of myosin ATPase. However, we do not think this scenario very likely for the following three reasons. First, the kinetic alteration model is unable to explain why phalloidin a€ects sliding velocity of Ca2‡-actin ®laments in opposite directions depending on the density of HMM on surfaces. Second, the kinetic alteration model is not consistent with the fact that the ratio between the sliding velocities of the Ca2‡- and Mg2‡-actin ®laments (RP1) over S1-coated surfaces and that over HMM-coated surfaces were very similar to each other, even though the absolute values of the sliding velocities, and hence kinetic parameters which determine the sliding velocities, were di€erent by a factor of ®ve. Third, we were unable to ®nd evidence to suggest that the kinetics is altered by phalloidin. Each myosin head alternates between strongly-bound and weakly-bound states with actin in each ATPase cycle. The length of the strongly bound state is relatively short, but the length of this state, rather than the length of the total cycle time, primarily determines the sliding velocity (Harada et al., 1990; Uyeda et al., 1990). The ratio of the length of the strongly bound state to that of the total cycle time is called the duty ratio. Thus, even though phalloidin does not a€ect the steady state ATPase activity in the presence of Ca2‡-actin ®laments, it could alter the length of the strongly bound state and the duty ratio simultaneously, and hence, the sliding velocity. Therefore, we have performed an indirect assessment of whether phalloidin binding a€ects the duty ratio. In conventional sliding ®lament-type in vitro motility assays without viscous additives such as methylcellulose, continuous sliding movement of ®laments requires that each ®lament is always held by at least one motor molecule in the strongly bound state. The number of motor molecules strongly interacting with a unit length of a ®lament is proportional to the surface density of motors and to the duty ratio. Consequently, there is a threshold density of motors on surfaces that is required to support continuous movement of ®laments, and the threshold density is a function of the duty ratio (Toyoshima et al., 1990). We have demonstrated that all four types of actin ®laments became unable to move continuously and di€use away from surfaces at the same HMM density (Figure 2B). This result indicates that the duty ratio, and hence the length of the strongly bound state, is una€ected by phalloidin binding. VanBuren et al. (1998) reported that ¯uorescent phalloidin has no e€ect on sliding velocity of actin

®laments on HMM surfaces. They carried out in vitro motility assays using Mg2‡-actin ®laments in a Mg2‡containing bu€er. We have con®rmed these results that rhodamine phalloidin has only a minor e€ect on sliding velocity of Mg2‡-actin ®laments. However, our data demonstrated that sliding velocity of Ca2‡-actin ®laments is signi®cantly a€ected and lowered by more than 40% by rhodamine phalloidin. These results indicate that sliding velocities in vitro are a€ected by multiple factors in a complex manner, and that, for quantitative analyses, attention should be paid regarding what divalent cation is bound to actin, and to what extent actin ®lament is labeled with phalloidin.

Acknowledgements We thank Mr Leonardo Mendoza for reading the manuscript. This work is supported by Japan Science and Technology Corporation and a Grants-in-Aid to T. U. from the Ministry of Education, Science, Culture of Japan.

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