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SKELETAL MUSCLE AND EXERCISE |
1 Department of Anatomy and Cell Biology, College of Medicine, University of Iowa, Iowa City, IA 52242, USA
2 Department of Physics, School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
3 Medical Biophysics Unit, Institute of Physiology and Pathophysiology, Ruprecht-Karls-Universität, Im Neuenheimer Feld 326, 69120 Heidelberg, Germany
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Abstract |
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23Tm, diminishes force and velocity. These results are consistent with the hypothesis that Tm in the presence of Tn and Ca2+ exerts a positive allosteric effect on actin to make actomyosin linkage more secure so that larger forces can be generated.
(Received 14 April 2006;
accepted after revision 16 May 2006;
first published online 18 May 2006)
Corresponding author M. Kawai: Department of Anatomy and Cell Biology, University of Iowa, Iowa City, IA 52242, USA. Email: masataka-kawai{at}uiowa.edu
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Introduction |
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To evaluate these hypotheses, a number of experiments have been performed by using skinned fibres and single molecules. Our skinned fibre experiments demonstrated that the step that generates force is endothermic, hence its equilibrium shifts significantly to the force-generating state at a higher temperature, thus supporting the first hypothesis (Zhao & Kawai, 1994; Wang & Kawai, 2001). It was also shown that this step accompanies a large entropy increase, which is based on burial of a large surface area consisting of hydrophobic amino acid residues (Murphy et al. 1996). Our experiment on single molecules using heavy meromyosin (HMM) and actin filaments demonstrated that force generated at the level of single molecules was independent of the temperature (Kawai et al. 2000), which is consistent with the first hypothesis.
However, our later experiments on reconstituted myocardium have demonstrated that, without regulatory proteins tropomyosin (Tm) and troponin complex (Tn), the temperature effect on isometric tension is much reduced, indicating a possibility that the temperature effect is enhanced by regulatory proteins (Fujita & Kawai, 2002). Thus, it has become important to carry out a temperature study in the presence of Tm and Tn in single-molecule experiments, which is the main focus of this report. For this reason, we performed in vitro motility studies and measured force as the ambient temperature was changed in the range 20–35°C. Our results demonstrate that the single molecular force remains the same as temperature is changed, supporting the first hypothesis.
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Methods |
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The experimental set-up used here was the same as that reported by Kawai et al. (2000) and mounted on a pneumatic isolation table (Herz Kogyo KK, Tokyo, Japan) as previously described (Miyata et al. 1994, 1995; Nishizaka et al. 1995a, 1995b, 2000; Nishizaka, 1996; Ishiwata, 1998). In brief, an inverted microscope (TMD-300, Nikon, Tokyo, Japan) was used for the central optical system. The light from an Nd-YLF laser (1053 nm, 1 W; Amoco Laser, Naperville, IL, USA) was led through the x100 oil-immersion objective lens (n.a. = 1.3) and trapped a polystyrene bead in the flow cell to work as optical tweezers. The image of the flow cell and activities within were recorded by the CCD camera with the light originating from a halogen lamp filtered at 380–520 nm. Fluorescent light (> 590 nm) was led into the image intensifier (KS 1381, Video Scope, Washington, DC, USA) and recorded by another CCD camera (CCD-72, DAGE MTI, Michigan City, IN, USA). These were videotaped (Hi8 Video, Sony Corp, Tokyo, Japan) for later analysis.
Flow cell
Both surfaces of a large coverslip (24 x 60 mm; thickness, 0.12–0.17 mm) were coated with collodion dissolved in 3-methylbutyl acetate (1:20). A small coverslip (18 x 18 mm; thickness, 0.12–0.17 mm) was glued to the large coverslip with Vaseline and two spacers (thickness, 50 µm) along the two sides. The total volume of the flow cell was about 25 µl. From an open side, 25 µl of HMM solution (5 µg ml–1 for rigor; otherwise 30 µg ml–1 in DHMM) was applied and left to settle for 60 s to allow the HMM molecules to be adsorbed onto the collodion-coated glass surface. Another 25 µl of HMM solution was applied from the other side and allowed to settle for 60 s. Subsequently, 25 µl of rhodamine-phalloidin-labelled regulated actin filaments in an experimental solution (Table 1) were applied twice from the same direction. Actin filaments were attached to polystyrene beads (see below), and then Tm and Tn were added to reconstitute the thin filaments. For this reconstitution, we did not need an annealing treatment (10 min at 45°C; longer time is needed if at lower temperatures), because the protein concentrations were low (Ishiwata, 1973). The two open sides were then sealed by Vaseline, and the flow cell was placed in the experimental apparatus.
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The compositions of solutions are listed in Table 1. After mixing solutions, doubly distilled water was depressurized for 10 min by aspirator to minimize dissolved O2. ATP was added as Na2H2ATP·2H2O, Pi as H1.5Na1.5PO4, EGTA as H4EGTA and calcium as CaCl2, and pH was adjusted to 7.40.
Polystyrene beads
Polystyrene beads (polybead carboxylate; catalogue number 08226; diameter, 1 µm) to which a carboxyl group (–COOH) was attached were purchased from Polysciences Inc. (Warrington, PA, USA). They were washed by Na-carbonate buffer (200 mM, pH 9.6), followed by Na-phosphate buffer (20 mM, pH 4.5). 1-ethyl-3-(3-dimethyl-aminopropyl)-carbodiimide (EDC) (208 mM) was then added to the beads in the phosphate buffer, and mixed gently for 2 h at room temperature. EDC reacts with the carboxyl group of the beads. The beads were then washed by Na-borate buffer (200 mM, pH 8.4). Gelsolin (10 µg ml–1), freshly prepared G-actin (10 µg ml–1), TMR-(tetramethyl rhodamine)-BSA (17 µg ml–1), BSA (303 µg ml–1) and Na-borate (30 mM) were then added and gently mixed overnight at 2°C. This procedure results in a covalent bond between the carboxyl group of the beads and the amino group of gelsolin. G-Actin was bound to the gelsolin, presumably because of stereospecific (both ionic and hydrophobic) interactions: gelsolin is an actin-binding protein that caps the barbed end of actin filaments. TMR-BSA was attached to the beads to make them fluorescent. 2-Aminoethanol (20 mM) was added and mixed for 30 min at 2°C, and the beads were washed by the Na-borate buffer and stored in Na-phosphate buffer (200 mM, pH 7.4).
Proteins
G-Actin, HMM and a Tm–Tn complex were isolated from rabbit white skeletal muscles as previously described (Suzuki et al. 1996; Fujita et al. 1996). Rabbits were killed by decapitation after anaesthetizing with sodium pentobarbital (150 mg/kg) by IV injection; this method was approved by the Institutional Review Committee on Animal Experimentation at Waseda University. G-Actin (0.1 mg ml–1) was polymerized to result in F-actin, rhodamine-conjugated phalloidin was bound to the F-actin, and then the F-actin (50 µg ml–1) was attached to polystyrene beads (1.1 x 1010 particles ml–1) via G-actin and gelsolin, which were previously attached to the beads as the nucleus (see above). Gelsolin was prepared from bovine serum by the method described by Kurokawa et al. (1990). The Tm–Tn complex was then added to the bead-tailed F-actin solution at a concentration of 1 mg ml–1 in a 500 µl test tube, and agitated for 30–60 min in a cold room on ice (0°C). This concentration is in excess of stoichiometric binding of Tm (about 12 µg ml–1) and Tn (about 14 µg ml–1) to F-actin (50 µg ml–1).
Temperature control
The inverted microscope, including the stage and the flow cell, was enclosed by a Nikon-Plexiglass cover and the internal temperature was controlled by sending warm air from one side and by cooling with frozen antifreeze (1,2-ethanediole)–water mixture (1:1) on the other side. The temperature was measured by a thermister probe attached to the microscope stage at the flow cell and regulated within ± 0.5°C of the desired experimental temperature. The temperature in the cell was also estimated from thermal quenching of the fluorescence from rhodamine–maleimide conjugated to tubulin subunits of microtubule (Kawaguchi & Ishiwata, 2000, 2001) in a similar manner to that reported earlier (Kato et al. 1999).
Velocity measurement
A record consisting of 3 s (30 frames s–1) was randomly selected from the video image, and the sliding velocity was calculated by using a computer program developed in Heidelberg for PC (Uttenweiler et al. 2000). This program uses a structure–tensor-based algorithm to identify a group of pixels moving together, follows its trajectory with time, and calculates the velocity of the pixel group.
Force measurement
To measure force, a bead to which a regulated actin filament was attached was caught by optical tweezers and placed several micrometres above the HMM-coated glass surface. The glass was moved horizontally to align the filament parallel to the surface. Then the bead was lowered close to the surface and filament–HMM interaction was initiated (Fig. 1 of Kawai et al. 2000). The displacement of the bead from the trap centre was measured from the video image. Force was calculated as Force = kP x displacement, where P is the power of the incident Nd-YLF laser beam at the level of the sample, which was measured by a power meter (Model LM-3, Coherent, Santa Clara, CA, USA) and ranged from 100 to 300 mW; k is the proportionality constant (k = 0.531 fN mW–1 nm–1); and kP is the spring constant of the optical tweezers. The laser power could be attenuated to 30 or 50% by inserting a neutral density filter. The length of filaments was measured from the video image. Since force generated is proportional to the length of the filament (Kishino & Yanagida, 1988), the force value was divided by the length value to obtain force per unit length.
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Results |
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Regulated actin filaments (reconstituted thin filaments) were placed on the HMM-coated glass surface and first bathed in the EGTA relaxing solution in the presence of MgATP (2 mM). Then the mobility of the filaments was examined. There were no overall movements, demonstrating a good regulation by Tm and Tn. These filaments, however, exhibited a segmental motion, presumably caused by thermal bombardment of H2O molecules on filaments, indicating that the actomyosin interaction is weak to nonexistent. When the regulated actin filaments were placed in the Ca2+ activating solution, they started sliding, demonstrating the presence of the Ca2+ activation mechanism. When the regulated actin filaments were placed in the rigor solution, there were no overall or segmental movements, demonstrating the strong interaction between the filaments and HMM molecules. In contrast, unregulated actin filaments moved regardless of the presence of Ca2+ as long as MgATP was present.
Effect of temperature on the sliding velocity
Regulated actin filaments were placed on the HMM-coated glass surface in the activating solution and then the sliding velocity was observed at four different temperatures (20, 25, 30 and 35°C). The experiments were carried out under unloaded conditions and in the presence of 2 mM ATP at pCa 4.74. For this series of experiments, the standard 30 µg ml–1 HMM was used to coat the glass surface. The velocity was measured as described in the Methods. The result is the number of pixel groups moving at a given velocity forming a velocity distribution, such as shown in Figs 1 and 2. Ten to twenty records from the same condition were analysed. We noticed that there were often two peaks in the distribution (Fig. 1). On visual inspection of the video images, it was apparent that the slower peak corresponds to the filaments with irregular movements that had an appearance of sticking to the glass surface. These presumably correspond to thin filaments interacting with partially denatured HMM molecules. Depending on the velocity distribution, a record is classified into three groups: (A) those with only fast-moving filaments; (B) those with both fast- and slow-moving filaments; and (C) those with only slow-moving filaments. The records were summated within each group, and plotted in Fig. 1. Because it is considered that the slow-moving group is based on denatured proteins with irregular movements, we have used only records with fast-moving filaments for subsequent analyses.
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6 µm s–1 (25°C) with a half-width of about 3 µm s–1, but there is a long trailing tail at a larger velocity up to 25 µm s–1, which may not be realistic. It turned out that this trailing tail was an artifact of the velocity calculation system, because a distribution of the velocity in the relaxing solution (absence of Ca2+) or rigor solution (absence of MgATP) exhibited a similar trailing tail (data not shown). For this reason, only the velocity data within a half-width of the distribution were used to calculate the average velocity. The data were analysed for four different temperatures, and the results are plotted in Fig. 3 together with the standard deviation. This figure demonstrates that the velocity increased with an increase in the temperature. The temperature coefficient over a 10°C temperature range (Q10) of the velocity was 1.46 ± 0.03 (n
= 3) in the range 20°C to 35°C (where n is the number of data points).
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Figure 4 represents a typical displacement of the bead position in the presence of Ca2+ and MgATP. Figure 5 represents averaged force plotted against the temperature in the control activating solution (Table 1). As seen in Fig. 5, force was about the same at 20–25°C, but a gradual increase in force was observed as the temperature was raised from 25 to 35°C. From Fig. 5, the averaged Q10 was calculated to be 1.43 ± 0.19 (n = 3). This result is similar to that observed for unregulated actin filaments (Kawai et al. 2000).
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Because it is possible that the number of cross-bridges available for interaction with the regulated actin filament may vary at different temperatures, we decided to count the number of cross-bridges as described by Nishizaka et al. (2000). This experiment was carried out under rigor conditions in which no ATP was added (Table 1), since it is difficult to count the number of cross-bridges during Ca2+ activation. We reduced the concentration of HMM from 30 to 5 µg ml–1, since counting becomes impractical when too many cross-bridges are interacting at the same time. It has been shown that the number of cross-bridges and the HMM concentration are proportionately related if the HMM concentration is less than 200 µg ml–1 (Nishizaka, 1996).
In Fig. 6A, a bead with a regulated actin filament that is interacting with HMM on the glass surface was caught by the optical tweezers. Care was taken to search for a linear filament, because subsequent data analysis is easier with a linear filament than a bent filament. If the bead was adsorbed onto the glass surface, it was first peeled off from the surface when possible. Then the bead was elevated at a constant speed (30–50 nm s–1; Fig. 6A) and its horizontal position was monitored by phase-contrast microscope. Calculation of the bead position was carried out based on videotaped images. An example of the bead displacement is shown in Fig. 6C. As shown in this figure, the bead was displaced almost horizontally at a constant velocity as it was raised, and suddenly the bead was brought back to an earlier position. This is the time when a rigor cross-bridge breaks (Fig. 6B); hence, by counting the number of breaks, the number of available cross-bridges can be determined. The example of Fig. 6C has 10 break points, indicating 10 cross-bridges. If this number is divided by the length of the filament, then the cross-bridge density (equivalent to the available number of cross-bridges per unit length) on the filament can be obtained.
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10 and 15 s. These were the times when the filament was slack because the neighbouring HMM molecules were distant. It is also interesting to note that the time of break and the break distance (horizontal drop of the displacement) are irregular. This fact implies that adjacent HMM molecules are not periodically spaced and/or consistently orientated. The main reason that the slope is nearly the same in all places (40 nm s–1 in Fig. 6C) is that the angle formed by the glass surface and the HMM–bead vector did not vary much and the bead was elevated at a constant speed. The number of cross-bridges is plotted in Fig. 7 as a function of the temperature. As seen in this figure, there is a small increase from 20 to 30°C and a significantly large increase from 30 to 35°C. These results demonstrate that the cross-bridge number increases as the temperature is increased with an average Q10 of 1.49 ± 0.31 (n = 3). This temperature dependence is similar to that in our earlier report (Kawai et al. 2000), which used a different method for counting the number of cross-bridges, in which Q10 = 1.5 ± 0.2 (n = 3) was found. It is to be noted, however, that the present method detected roughly twice as many cross-bridges, presumably because of the differences in the HMM concentration and procedure used for preparing the flow cell.
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Because the number of cross-bridges available for interaction with the regulated actin filament increased with the temperature (Fig. 7), the data of Fig. 5 were divided by the data of Fig. 7, and results are plotted in Fig. 8. The errors in Figs 5 and 7 were appropriately propagated and entered in Fig. 8 as described (Kawai et al. 2000). Figure 8 demonstrates that force per cross-bridge does not change much with the temperature in the range 20–35°C. From Fig. 8, the averaged Q10 was calculated to be 1.03 ± 0.25 (n = 3).
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In skinned fibres (or myofibrils), force is reduced as a low millimolar concentration of Pi is added to the activating solution (Cooke & Pate, 1985; Kawai, 1986; Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992; Tesi et al. 2002). For this reason, 8 mM Pi was added to the activating solution (by keeping ionic strength constant), and force and velocity were measured at 25°C (Table 2). Force was 2.08 pN µm–1 in the absence of added Pi, and 2.04 pN µm–1 in the presence of 8 mM Pi, indicating that there was no significant force attenuation as Pi was introduced to the activating solution. Similarly, there was no detectable difference in the velocity when 8 mM Pi was introduced to the activating solution. This result is consistent with our earlier results that used unregulated actin filaments (Kawai et al. 2000). The velocity result is consistent with the shortening velocity measurement on muscle fibres of Cooke & Pate (1985), but the force result is not consistent with that of muscle fibres (or myofibrils) reported by many investigators (Cooke & Pate, 1985; Kawai, 1986; Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992; Tesi et al. 2002).
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For the next series of experiments, the force and velocity were compared in the absence and presence of a regulatory system at 25°C. As shown in Table 2, the velocity was 2.95 µm s–1 in the absence and 5.49 µm s–1 in the presence of the regulatory system. Thus, we conclude that the velocity was almost doubled by the regulatory system. The same table demonstrates that force was 1.89 pN µm–1 in the absence of the regulatory system and increased to 2.08 pN µm–1 in its presence. Thus, we conclude that force is enhanced by 10% by the regulatory system.
To demonstrate that force and velocity are indeed influenced by the regulatory proteins, a truncated Tm mutant, AS-23Tm (Hitchcock-DeGregori & Varnell, 1990), was used instead of normal Tm. AS-23Tm lacks regions 2 and 3 out of 7 quasi-repeat regions that exist in normal Tm. Since AS-23Tm is synthesized by E. coli, it lacks N-terminal acetylation that is normally present in mammalian Tm and which is necessary for its polymerization. To compensate for this effect, Ala-Ser- (AS-) was added at the N-terminus (Monteiro et al. 1994) and used as a control. We observed that the reconstituted thin filament with AS-Tm or AS-23Tm was regulated by Ca2+ (see also Hitchcock-DeGregori & Varnell, 1990; Lu et al. 2003). Force developed with AS-23Tm was 1.15 pN µm–1, and only 43% of AS-Tm (2.68 pN µm–1; Table 2). Sliding velocity of AS-23Tm was 1.98 µm s–1, and 52% of AS-Tm (3.80 µm s–1; Table 2).
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Discussion |
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The velocity of the thin filament sliding on HMM was measured to compare the results with those measured previously. Our value (4.7–8.3 µm s–1; Fig. 3) is similar to those observed by Honda & Asakura (1989) or by Homsher et al. (1992) in the same temperature range (20–35°C). These investigators used regulated actin filaments. Our velocity value is larger than those of Anson (1992) in rabbit fast-twitch muscles, and of Rossi et al. (2005) in rat type IIB muscles. This difference is likely to be related to the absence of regulatory proteins. The velocity nearly doubles with an addition of regulatory proteins (Table 2; see below).
As the temperature was elevated, we observed a moderate increase in force (Fig. 5; see also Kato et al. 1999). There are two possibilities to explain this finding: (1) the number of cross-bridges available for force generation increases with temperature; and (2) average force per cross-bridge increases with temperature. For this reason, we determined the number of cross-bridges in rigor conditions. This number increased in a similar manner to tension as the temperature was raised (Fig. 7). Therefore, we conclude that (1) is the case. There are several possibilities to account for the increase of the number of cross-bridges with temperature: (a) the Brownian motion of the HMM molecules may release more head domains from the glass surface at higher temperature without releasing the attached end; (b) the increased thermal motion of the thin filament could reach a larger number of HMM molecules, thereby forming the increased number of cross-bridges at higher temperature; and (c) the interaction between actin and myosin may be promoted at higher temperatures, because it is an endothermic reaction (Tonomura et al. 1962; Highsmith, 1977). However, whether this increase in the number of available cross-bridges is a physiological phenomenon is still an open question (Kato et al. 1999).
To calculate force per cross-bridge, we divided the force value in Fig. 5 by the number of cross-bridges (Fig. 7), and plotted the result in Fig. 8. This figure demonstrates that force per cross-bridge does not change with temperature when regulated actin filaments are used, and it averages 1.57 ± 0.07 pN (n = 4; Fig. 8, dashed line). This conclusion is consistent with our earlier results using unregulated actin filaments (Kawai et al. 2000). The force plotted in Fig. 8 is not the averaged unitary force. This is because the concentration of HMM used in Fig. 5 is 30 µg ml–1, whereas that used in Fig. 7 is 5 µg ml–1. Because the HMM concentration and the number of cross-bridges are proportional within this range (Nishizaka, 1996), the value in Fig. 8 must be divided by 6 (= 30/5) to obtain average unitary force, i.e. 0.26 pN can be deduced. If we assume that the duty ratio is about 0.1 (Howard, 1997), we can then conclude that the unitary force is about 2.6 pN. This value is within the range of those previously reported in single-molecule experiments (1–6 pN: Finer et al. 1994; Miyata et al. 1995; Molloy et al. 1995; Ishijima et al. 1996).
In muscle fibre studies, it has been reported that an increase in temperature resulted in increased isometric tension in maximally activated mammalian skeletal muscle fibres (Goldman et al. 1987; Bershitsky & Tsaturyan, 1992, 2002; Zhao & Kawai, 1994; Ranatunga, 1996; Coupland et al. 2001; Wang & Kawai, 2001) as well as in cardiac muscle fibres (Ranatunga, 1999; Fujita & Kawai, 2002). This process is called ‘endothermic’ because higher temperature favours larger force, which is consistent with the fact that heat is absorbed on force generation. There are two mechanisms proposed to account for this temperature effect. The first mechanism is a shift of equilibrium between the force-generating state(s) and the non-force-generating state(s) (Zhao & Kawai, 1994; Head et al. 1995; Coupland et al. 2001; Wang & Kawai, 2001). The second mechanism is an increase in the force per cross-bridge, but the number of force-generating cross-bridges does not change (Goldman et al. 1987; Kraft & Brenner, 1997; Bershitsky & Tsaturyan, 2002; Piazzesi et al. 2003; Linari et al. 2005). The first mechanism was proposed because the equilibrium constant of the force generation step increased with temperature (Zhao & Kawai, 1994; Wang & Kawai, 2001), and the tension–temperature plot can be predicted based on the equilibrium shift argument (Kawai, 2003). This mechanism is consistent with the hydrophobic interaction, the endothermic reaction, the positive standard entropy change and the negative heat capacity change, as observed in the muscle fibre system (Zhao & Kawai, 1994; Murphy et al. 1996; Wang & Kawai, 2001) and as reviewed by Kawai (2003). The second mechanism was proposed because stiffness did not change much with the temperature (Bershitsky et al., 1997), or the change was less in stiffness than in tension. However, it has been found that series compliance plays a significant role in measured stiffness (Huxley et al. 1994; Kojima et al. 1994; Wakabayashi et al. 1994; Higuchi et al. 1995), and that the stiffness–temperature plot can be predicted based on a series compliance model in which 50% of the compliance is placed in the series elements (Kawai, 2003). Most temperature studies (other than ours) were carried out in the absence of added Pi, a condition that increases the number of force-generating cross-bridges (Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992), thereby maximizing the stiffness in the overlap zone of the thick and the thin filaments. In this condition, a further increase in the number of force-generating cross-bridges with temperature may not be detected as a stiffness increase because of the series compliance. Our present result using the in vitro system is consistent with the first mechanism in the sense that the unitary force does not change with temperature.
The force and velocity are not modified much when 8 mM Pi is added in the activating solution in single molecules, and this result is the same whether the regulatory system is included (Table 2) or not (Kawai et al. 2000). These results using single molecules are very different from those using single fibres (or myofibrils), where addition of several millimolar Pi diminishes isometric force (Cooke & Pate, 1985; Kawai, 1986; Fortune et al. 1991; Kawai & Halvorson, 1991; Dantzig et al. 1992; Tesi et al. 2002). The cause of this discrepancy is not immediately apparent, but it is possible that the low ionic strength condition (50 mM) used in the in vitro motility system makes a difference to the results; muscle fibre experiments are typically carried out at around physiological ionic strength (180–200 mM). Because the electrostatic interaction is stronger at low ionic strength, it is possible that the negatively charged Pi ion may be trapped by positively charged amino acid residues of myosin before reaching the Pi-binding site. It is also possible that the presence of a large-scale co-operativity may modify the Pi-binding process.
When the regulatory system is added, both force and velocity increased (Table 2). These results are consistent with those of other investigators using single molecules (Gordon et al. 1998; VanBuren et al. 1999; Bing et al. 2000a,b; Homsher et al. 2000, 2003) and single fibres (Fujita et al. 2002, 2004; Fujita & Kawai, 2002). These results are in accord with the hypothesis that Tm and Tn apply a positive allosteric effect on the actomyosin interaction. This hypothesis is further supported by the experiment using a truncated mutant Tm. When AS-23Tm is used, both force and velocity decrease to 43 and 52% of control values, respectively (Table 2). This observation demonstrates a presence of the negative allosteric effect of AS-23Tm on the actomyosin interaction. These results are also consistent with those that measured ATP hydrolysis rate (Hitchcock-DeGregori & Varnell, 1990), in vitro motility assay (Landis et al. 1999), and reconstituted cardiac fibres (Lu et al. 2003), which compared the effect of native Tm, AS-Tm and AS-23Tm.
The fact that the unitary force is independent of the temperature was also reported in the kinesin–microtubule system in the temperature range 15–35°C (Kawaguchi & Ishiwata, 2000). This fact may imply that the temperature insensitivity of the single molecular force is a fundamental property of a motor protein, and supports the hypothesis that force is associated with a particular molecular structure of the motor, which is consistent with the current knowledge of the mechanisms of force generation. In myosin, force is generated as a result of a swing of the lever arm (Dominguez et al. 1998; Geeves & Holmes, 1999; Holmes et al. 2004). Therefore, the force (F) generated by a single molecule is:
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| (1) |
L is the swing of the lever arm, which is known as the step size, and 
is the stiffness of series elements, including that of cross-bridges. The size of the lever arm is determined by the molecular structure of myosin, and it does not vary with temperature. The step size is determined by the length of the lever arm, hence the step size does not vary with temperature. is approximately independent of temperature because it is determined by the molecular structure of the myosin head and in-series elements to the head. Therefore, we can appreciate from eqn (1) that F must be independent of the temperature. In conclusion, we have demonstrated that force per cross-bridge does not change with temperature in experiments using regulated actin filaments and HMM.
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23Tm and AS Tm, to Dr Daisuke Sasaki for the gift of Tm and Tn, and to Dr Madoka Suzuki for technical help. This work was carried out during the tenure of a long-term fellowship to M.K. awarded by the Japan Society for Promotion of Science in the spring of 2003. This work was supported in part by an NIH grant HL70041 to M.K., and by an LFSP Baden-Württemberg grant to R.H.A.F. This research was also supported in part by Grants-in-Aid for Specially Promoted Research and for the 21st century COE program (Physics of Self-organization Systems) at Waseda University from the Ministry of Education, Sports, Culture, Science and Technology of Japan to S.I. The contents of this work are solely the responsibility of the authors and do not necessarily represent the official view of awarding organizations. This article has been cited by other articles:
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  P. P. de Tombe and G. J. M. Stienen Impact of temperature on cross-bridge cycling kinetics in rat myocardium J. Physiol., October 15, 2007; 584(2): 591 - 600. [Abstract] [Full Text] [PDF]
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