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Tetanus responses under rapid bath solution change: Electrotonic depolarization of transverse tubules may release Ca2+ from sarcoplasmic reticulum of Rana japonica skeletal muscle
Camp. Biochem. Physiol.Vol. 103A, No. 4, pp. 661466, 1992
Printed in Great
Britain
0
0300-9629/92 $5.00 + 0.00 1992 Pergamon Press Ltd
TETANUS RESPONSES UNDER RAPID BATH SOLUTION CHANGE: ELECTROTONIC DEPOLARIZATION OF TRANSVERSE TUBULES MAY RELEASE Ca2+ FROM SARCOPLASMIC RETICULUM OF RANA JAPONICA SKELETAL MUSCLE NAOJI FUJISHIROand HIROSHI KAWATA Department of Physiology, School of Medicine, Fukuoka University, 45-l-7 Nanakuma, Jonan-ku, Fukuoka 814-01, Japan (Received 14 April 1992; accepted 22 May 1992)
Abstract-l. Single skeletal muscle fibers were transferred from a normal Ringer solution to Na + ion free. solution, and vice versa, and tetanus responses were recorded immediately after the transfer. 2. Fractional tetanus tension recorded immediately after the displacement from the Na+ ion free solution to normal Ringer solution was dependent on fiber diameter. 3. Diffusion of Na + ions along the transverse tubules was simulated [apparent diffusion constant was 3.11 x 10m6(cm*/s)]. 4. Our results suggest that the electrotonic spreading of membrane potential, caused by an action potential in the transverse tubules, could release Ca *+ ions from sarcoplasmic reticulum.
INTRODUaION
MATERIALSAND METHODS
Depolarization of transverse tubule membranes releases Ca*+ ions from the sarcoplasmic reticulum in skeletal muscle. Action potentials generated on the surface membrane of muscle fibers are conducted along the transverse tubules (Costantin, 1970; Bezanilla et al., 1972; Bastian and Nakajima, 1974; Nakajima and Gilai, 1980) and depolarize the membrane. Bastian and Nakajima (1974) confirmed that part of the twitch and tetanus tension was generated by the electrotonic spreading of depolarization into the transverse tubules. In a local activation experiment, activation of a muscle fiber caused by the passive spreading of subthreshold depolarization was observed (Huxley and Taylor, 1958; Huxley, 1971). The area in front of the action potential is depolarized by the electrotonic spreading of membrane potential. It is unknown whether or not such depolarization can release Ca*+ ions from the sarcoplasmic reticulum. To examine this problem we used a method of rapid solution change. Hodgkin and Horowitz (1960), and Nakajima er al. (1975) achieved sudden changes of external solution with a rapidly flowing bathing solution. In our experiments single skeletal muscle fibers were transferred from one trough to another, and were stimulated immediately after the transfer. Carefully prepared single fibers were not damaged by the air-water interface. Our results suggested that the conduction of the action potential into the transverse tubules was necessary to induce full activation of the muscle fiber, and that the area in the transverse tubules in front of the conducted action potential was activated. These results suggest that the electrotonic spreading of membrane depolarization caused by an action potential could release Ca*+ ions from the sarcoplasmic reticulum.
Single muscle fibers were isolated from dissected semitendinosus muscles of Rano japonica. One end of each fiber was connected via the tendon to a tension-sensitive hook of a strain gauge (TDS-101. Fuii-Keisoku) while the other end was co&&& to a fixed hook. Fibers were stretched to 1.2 times the slack length. The single fibers were placed in a small Lucite trough which was bathed in temperature controlled water maintained at 20°C. Single fibers were transferred from one trough to another so as to change solution rapidly. An electrical stimulus (rectangle pulse, 0.5 msec duration, 1.5 times threshold, 1OOHz for 0.2-0.5~~) was applied to the fiber immediately after the transfer. The stimulator (SEN-7103, Nihon Kohden) was triggered by a signal which monitored the touching of the hook to the bath solution (Fig. 1). The signal which triggered the stimulator was the potential change caused by a 75 pA d.c. current that flowed between the hook and the bath solution. The potential
WATER+ +
& Fig. I. Apparatus for rapid solution change. Single fibers were fixed between two hooks and placed in a trough filled with normal Ringer solution. Another trough was filled with Na+ ion free solution. The troughs were bathed with temperature controlled water at 20°C. The trough could move up, down, right and left. 661
NAOJI FUIISHIROand
662
HIROSHIKAWATA C
NR +ONa
_---J
ONa
L_---!~_
NR
-+
J
\
1 0.5 mN
II
500
msec
Fig. 2. Contractions induced by tetanic stimulation immediately after solution change. Trace (a) shows the tetanic response in normal Ringer solution. Trace (b) shows the tetanic response when the fiber was transferred from normal Ringer to Na + ion free solution. Trace (c) shows the tetanic response when the solution was changed from Na+ ion free solution to normal Ringer. In records (b) and (c), the middle trace indicates the duration of stimulation and the bottom trace the trigger signal resulting from the touching of the hook, to which the fiber was fixed, to the bath solution. The bottom trace does not correspond to the time course of the bath solution change.
change was monitored using a low-pass filter, so that the signal increased slowly (Fig. 2). However, the moment at which the hook touched the bath solution could be easily determined. Single fibers were transferred from normal Ringer solution (11 I .2 mM NaCl, 3 mM KCl, 2 mM CaCI,, 5 mM HEPES, pH 7.2) to Na+ ion free solution (NaCl was replaced with choline chloride) and vice versa. Fibers were immersed for
at least 10 min in one solution before transfer to the other solution. Recorded tensions were stored on FM tapes (MR-10, TEAC) and monitored by a computer (PC9801 VM2, NEC) using an AD converter (analog pro DMA, Canopus Elec. Corp.) at a sampling rate of 800 Hz. Various parameters were determined by computer using the software DSS type IV (Canopus Elec. Corp.).
ONa -$
NR
Fig. 3. Paired tetanic stimulation. Control responses in normal Ringer solution, and responses initiated immediately after changing solution from Na+ ion free to normal Ringer are shown. The second stimulus was applied 350 msec after the first. In (A) the fiber diameter was 50 pm. In (B) the fiber diameter was IlOpm. The middle and the bottom traces of each panel are as for Fig. 2.
Tetanus responses of single muscle fiber RESULTS
Rapid solution change and tetanus response
Figure 2 shows tetanus responses recorded in a single fiber stimulated immediately after transfer from normal Ringer (NR) solution to Na + ion free solution (ONa) and vice versa (these conditions are abbreviated as “from NR to ONa” or “from ONa to NR” from here on). The bottom traces are the monitored trigger signal resulting from the hook touching the bath solution. The upward deflection of the signal indicates that the hook had touched the bath solution, it does not mean that fibers were immersed in the bath solution during the time course of the signal. The middle trace indicates the period of tetanic stimulation. There was a slight delay between the hook touching the bath solution and the onset of tetanic stimulation, resulting from the time taken for the signal to exceed the trigger level of the stimulator. Single muscle fibers started to contract on average 57.9 msec (N = 6) after the hook touched the bath solution under the condition from NR to ONa. On the other hand, under the condition from ONa to NR, contraction started on average 142.3 msec
663
after the hook touched the bath solution in the same fiber. When single fibers were continuously stimulated under the condition from NR to ONa, contraction ceased after some time (Fig. 2b). Diffusion of Na+ ions away from the cell surface may have caused this inhibition of contraction. On the other hand, when single fibers were stimulated under the condition from ONa to NR, the duration of contraction corresponded to the duration of stimulation, although the amplitude of the tetanic tension was smaller than that recorded under the condition from NR to ONa (Fig. 2~). Fractional tensions (i.e. relative to control tensions recorded in Ringer solution) recorded under the condition from NR to ONa were nearly identical in each fiber (mean + SEM, 0.82 + 0.05, N = 14), however, those recorded under the condition from ONa to NR were very different from fiber to fiber (see below). Contraction induced by paired stimulation under the condition from ONa to NR
Tension recorded under the condition from ONa to NR was smaller than that recorded under the condition from NR to ONa (Fig. 2). This means that
A
a
b
il,
I\
bmN
500 msec
I&
50 msec Fig. 4. Superimposition of paired tetanic contractions resulting from paired stimuli with varying inter-stimuli recovery periods. In trace (A-a), five recordings are superimposed. Intervals between the first and second stimuli are 200, 500, 800, 1000 and 1500msec. In trace (A-b), tetanic responses induced by paired stimuli separated by 1500msec in normal Ringer solution are shown. Fiber diameter was 92.5 pm. In trace (B-a), three recordings are superimposed. Inter-stimuli intervals were 100, 150 and 200 msec. In trace (B-b), tetanic responses induced by paired stimuli separated by 200 msec in normal Ringer solution are shown. Fiber diameter was 57.5 pm.
NAOIIFUIISHIRO and HIR~~HIKAWATA
664
some parts of the fiber were not activated under the condition from ONa to NR. This reduced area of activation may have resulted from an impaired diffusion of Na+ ions into the transverse tubules under this condition. Thus a paired stimulation protocol was employed. If Na + ions diffused into the transverse tubules during the recovery period between the paired stimuli, then the contraction induced by the second stimulus would be larger than the first contraction. Initially a delay of 350 msec separated the paired stimuli. Figures 3A and B illustrate two examples of contractions obtained with the paired stimuli. The second contraction was larger than the first, however, the amplitude of the second contraction was still smaller than the control contraction in some fibers, as shown in Fig. 3B. Therefore the duration of the recovery period between the paired stimuli was varied. Figure 4 illustrates the results obtained in this experiment. In every fiber the second contraction reached the control level when fibers were stimulated after a sufficient long recovery period. This recovery period was different from fiber to fiber (1.5 set in Fig. 4A and 200 msec in Fig. 4B). These results suggested that the size of activated area under the condition from ONa to NR depended on the diffusion of Na+ ions into the transverse tubules. Dependence of fractional tension on jiber radius recorded under the condition from ONa to NR
Fractional tension (relative to control) recorded under the condition from ONa to NR was different from fiber to fiber. Isometric tetanic tension is known to be correlated with the activated area of fiber (Elzinga et al., 1989). Thus, under the assumption that the entire area of the fiber from the cell surface to depth x was activated under the condition from ONa to NR, fractional tension could be estimated by equation (1). Transformations of equation (1) yielded equations (2) and (3). )‘=
Jl
-y
=
r2n - (r - x)2n r27t
-xr +1
1:
L;
L
0.2
t
0
0
. 0.01
0.02
0.03
l/RADIUS
(/I-‘)
k. 0.04
l
0.05
Fig. 5. A plot of ,/l --y vs l/r. Open circles indicate contractions resulting from the first stimuli in the paired stimuli protocol. Filled circles indicate contractions resulting from the second stimuli. Continuous lines were obtained by a least squares method.
area increased by 10.8pm (23.2 - 12.4 = 10.8) in 200msec (the time between tetanic stimuli). Impaired transverse -tubular diffusion of Na + ions during contraction
The diffusion of Na+ ions into transverse tubules during contraction was examined. Fibers were stimulated under the condition from ONa to NR with two pulse protocols. In the first, paired stimuli at 100 Hz of 200 msec duration were separated by 100 msec, whereas in the second a 100 Hz stimulus was applied continuously for 500 msec. If Na + ions diffused into transverse tubules during contraction, it follows that the maximal tension produced by the second protocol would be same as the tension resulting from the second contraction under the first protocol. However, the tensions were not the same as shown in Fig. 6. The tension resulting from the second contraction under the first protocol was greater than the tension
(1)
I
0.25 mN
(3)
where y is the fractional tension, r is the radius of fiber and x is the depth of activated area from the cell surface. Thus J 1 - y was plotted against l/r according to equation (3). Figure 5 illustrates these results. The open circles are the values obtained from the first contraction while the closed circles are the values obtained from the second contraction when the stimuli were separated by 200 msec. Lines of best fit were obtained with a least squares method and gave values of x = 12.4 pm for the open circles (correlation coefficient = 0.72), and x = 23.2 pm for the closed circles (correlation coefficient = 0.84). Since each line crossed the vertical axis near 1.Oand there was a good correlation between I/r and ,/l - y, the following two conclusions are suggested. Firstly, when fibers were stimulated immediately after transfer from ONa to NR, an area up to 12 pm in depth from the fiber surface could be activated. Secondly, the activated
20oYsec Fig. 6. Contractions resulting in a fiber stimulated tetanically immediately after transfer from a Nat ion free solution to a normal Ringer solution. Contractions resulting from two protocols are superimposed. The first protocol consisted of two paired stimuli of 200 msec duration separated by 100 msec, as shown in the second trace. The second protocol consisted of continuous stimulation for 500 msec as shown in the third trace. The fourth trace is the trigger signal which monitored the hook touching the solution.
Tetanus responses of single muscle fiber resulting second diffusion impaired
from the continued stimulation under the protocol. This result suggested that the of Na+ ions into the transverse tubules is during muscle contraction.
Simulation of increasing tension with the second tetanic contraction As described above, fractional tension obtained under the condition from ONa to NR depended on fiber radius. This analysis suggested that the smaller the fiber radius, the bigger the fractional tension would be under the condition from ONa to NR. Thus full activation was generated rapidly in thin fibers as shown in Figs 3A and 4B. The time course for recovery of tension during the second contraction shown in Fig. 4, probably corresponded to the increasing area of the muscle fiber activated by the diffusion of Na+ ions into the transverse tubules. This time course of recovery was simulated using data from thick fibers (radius 47-55 grn, mean 50 pm, N = 4, Fig. 7). The following diffusion equation, described by Hill (1928, equation 45) was employed.
665
Thus the diffusion constants for several C/C, values using t = 200 msec and x = 10.8 pm were calculated. Next, from the obtained parameters C/C’, and D, the value of t at each x was calculated according to equation (4). By substituting each value of x in equation (2), the fractional tension at each time t was determined. Figure 7 illustrates the results obtained with this simulation (continuous lines). These results indicated the need to modify the model, which was subsequently modified in two ways. Firstly, in the simulation, at time t = 0 Na+ ions had not diffused into the transverse tubules, whereas in the experiments, time t = 0 was the time when contractions were first initiated. Therefore, if the first contraction occurred after Na+ ions had already diffused into the transverse tubules, these results could not be plotted on the same axis as the simulated data. Secondly, it is possible that the electrotonic spreading of membrane potential might activate a wider area than that activated an action potential in the transverse tubules. If the first modification is accepted, the experimental data must be shifted to the right as shown in Fig. 8A (the experimental data was right-shifted by 133 msec). Acceptance of the second modification, requires that equation (2) be modified as follows.
y=1_(1_q2) where C is the concentration of Na + ions at point x, C, is the concentration of Na+ ions at x = 0 (constant), J0 and J, are Bessel functions, r is the fiber radius, D is the diffusion constant, t is the time, GI,is the n th root of J,,(a,) = 0, and n is an integer. In this simulation, fiber radius was assumed to be 50 pm and n was fixed at 5 (there was no change in the results even if a larger number than 5 was used). In the model it was assumed that if the concentration of Na + ions at a point x in the transverse tubules was over a threshold level, then the area from the fiber surface to that point would activate. As discussed above, Na+ ions do not diffuse significantly during contraction, while the distance along the transverse tubule which is capable of activation increases by 1O.Bpm during a 200 msec resting period. It could be speculated that Na + ions diffuse 10.8 pm in 200 msec.
where 1 is the difference in the distance between the activated depth from the cell surface and the position
A 1.0
r
0
0.2
0.4
0.6
TIME 1.0
a b c
(5)
B
0.6
1.0
1.2
Csec)
1.0
5 9 y 2
0.e
0.6
g
0.4
c u a
0.2
E 0
0 0
0.2
0.4
TIME
0.6
0.6
1.0
(set)
Fig. 7. Simulation of Na+ ion diffusion into T-tubules. Open circles are the mean fractional tensions (N = 4) obtained with the paired stimuli. Continuous lines are the theoretical curves obtained using the following diffusion constants and fractional Na + ion concentrations (relative to normal Ringer solution) in the transverse tubules: (a) 1.28 x IO+, 0.5; (b) 3.11 x W6, 0.4; (c) 2.20 x IO+, 0.3.
0
0.2
0.4
0.6
TIME
(sex)
0.6
1.0
Fig. 8. (A) Modification of the simulation shown in Fig. 7. Open circles are the experimental data points moved 133 msec to the right. The theoretical curve is best fit to the experimental data with parameters D and C/C,, as follows, D = 3.11 x 10m6,and C/C,, = 0.4. (B) The continuous line is the modified theoretical curve (D = 3.11 x 10m6,C/C,, = 0.4 and I = 4.3 pm according to equation 5).
NAOJIFUJ~SHIRO and HIROSHIKAWATA
666
where the action potential arrived in the transverse tubules. Figure 8B shows the results of the second modification where it was postulated that an area 4.3 pm ahead of the action potential was activated by electrotonic spreading of membrane potential (D =3.11 x 10-G and C/C,=O.4). The second modification produced a better fit than the first modification. D~SCU~ION
Experimental data was fitted to the diffusion equation developed by Hill (1928) using the simulation of Nakajima et al. (1975). The diffusion constant for Na+ ions obtained in this study (3.11 x 10e6 cm’/ set) was about twice that reported by Nakajima et al. (1975). However, it was smaller than the diffusion constant for Na+ ions in aqueous solution (1.48 x 10~‘5cm2/sec at 25°C; Robinson and Stokes, 1958). The difference in the value of the diffusion constant obtained in the current study and that reported by Robinson and Stokes might be caused by the complexity of the structure of the transverse tubules. Transverse tubules in frog make a network along the longitudinal axis of the muscle fiber (cf. Peachey, 1983). This complex structure might decrease the rate of diffusion of Na + ions. In the simulation employed in this study, transverse tubule membranes initiated action potentials when the Na + ion concentration in the tubules was 40% (C/C,, = 0.4) of that in Ringer solution. Bezanilla et al. (1972) showed that peak tetanus tension in a solution with half normal Na+ concentration was similar to that in normal Ringer solution. Thus the results of the current simulation are consistent. The analysis of the experimental data, and simulation presented in this study suggest that the attenuated tetanic tension recorded under the condition from ONa to NR was caused by a partial activation of the muscle fiber. The simulation suggested that an area preceding the action potential could be activated by an electrotonic spreading of membrane depolarization. As described in the results section, contraction under the condition from ONa to NR started 142.3 msec on average after the hook touched the solution, and after 57.9 msec on average under the condition from NR to ONa. If the results of the simulation are accepted, the diffusion distance of Na + ions in the 84.4 msec (= 142.3-57.9) could be calculated to be 6.5 pm under the conditions D = 3.11 x 10-6, C/C, = 0.4, and radius = 50 pm. In this caIculation, the unstirred layer at the fiber surface was ignored. Diffusion speed of Na + ions may be slower in the unstirred layer, and therefore the actual distance might be shorter than
6.5 pm. However the analysis presented in this study revealed that a depth 12 pm from the cell surface of the muscle fibers was activated (see results section). This means that a deeper area of the transverse tubules than the area at which the action potential arrived was activated under the condition from ONa to NR. Huxley and Taylor (1958) observed that activation of muscle fiber spread as far as 10 pm along transverse tubules in a local activation experiment, and thought that this spread was a passive process (Huxley and Taylor, 1958; Huxley, 1971). Their observation may correspond to the results obtained in this study. Acknowledgements-We
thank Drs P. Palade and B. Simon for their critical comments on this paper. We are indebted to Dr D. Hill for his kind check and comments on this paper.
REFERENCES
Bastian J. and Nakajima S. (1974) Action potential in the transverse tubules and its role in the activation of skeletal muscle. J. gen. Physiot. 63, X7-278. Bezanilla F., Caputo C., Gonzalez-Serratos H. and Venosa R. A. (1972) Sodium dependence of the inward spread of activation in isolated twitch muscle fibers of the frog. J. Physiol. 223, 507.--523.
Costantin L. L., (1970) The role of sodium current in the radial spread of contraction in frog muscle fibers. J. gen. Physiol. 55, 703--l 15.
Elzinga G., Howarth J. V., Rail J. A., Wilson M. G. A. and Woledge R. C. (I 989) Variation in the normalized tetanic force of single frog muscle fibers. J. Physic/. 410, 1577170. Hill A. V. (1928) The diffusion of oxygen and lactic acid through tissues. Proc. R. Sot. B Biol. Sci. 184, 39-96. Hodgkin A. L. and Horowicz P. (1960) The effect of sudden changes in ionic con~ntrations on the membrane potential of single muscle fibers. J. Phvsiol. 153. 370-385. Huxfey A. F. (1971) The activation of striated muscle and its mechanical response. Prof. R. Sot. London. B. 178, t-27. Huxley A. F. and Taylor R. E. (1958) Local activation of striated muscle fibres. J. Physiol. 144, 426-441. Nakajima S. and Gilai A. (1980) Radial propagation of muscle action potential along the tubular system examined by potential-sensitive dyes. J. gen. Physiol. 76, 751~-762. Nakaiima S.. Nakaiima Y. and Bastian J. (1975) Effects of sudden changes in external sodium concentration on twitch tension in isolated muscle fibers. J. ge:en. Physiol. 65, 459-482.
Peachey L. D. (1983) Structure and function of membrane systems of skeletal muscle cells. In ~~dbook of physiology, Sect. 10, pp. 23-71. Am. Physiol. Sot. Bethesda, MD. Robinson R. A. and Stokes R. H. (1959) Electrolyte so&ions. Butterworths, London.
Printed in Great
Britain
0
0300-9629/92 $5.00 + 0.00 1992 Pergamon Press Ltd
TETANUS RESPONSES UNDER RAPID BATH SOLUTION CHANGE: ELECTROTONIC DEPOLARIZATION OF TRANSVERSE TUBULES MAY RELEASE Ca2+ FROM SARCOPLASMIC RETICULUM OF RANA JAPONICA SKELETAL MUSCLE NAOJI FUJISHIROand HIROSHI KAWATA Department of Physiology, School of Medicine, Fukuoka University, 45-l-7 Nanakuma, Jonan-ku, Fukuoka 814-01, Japan (Received 14 April 1992; accepted 22 May 1992)
Abstract-l. Single skeletal muscle fibers were transferred from a normal Ringer solution to Na + ion free. solution, and vice versa, and tetanus responses were recorded immediately after the transfer. 2. Fractional tetanus tension recorded immediately after the displacement from the Na+ ion free solution to normal Ringer solution was dependent on fiber diameter. 3. Diffusion of Na + ions along the transverse tubules was simulated [apparent diffusion constant was 3.11 x 10m6(cm*/s)]. 4. Our results suggest that the electrotonic spreading of membrane potential, caused by an action potential in the transverse tubules, could release Ca *+ ions from sarcoplasmic reticulum.
INTRODUaION
MATERIALSAND METHODS
Depolarization of transverse tubule membranes releases Ca*+ ions from the sarcoplasmic reticulum in skeletal muscle. Action potentials generated on the surface membrane of muscle fibers are conducted along the transverse tubules (Costantin, 1970; Bezanilla et al., 1972; Bastian and Nakajima, 1974; Nakajima and Gilai, 1980) and depolarize the membrane. Bastian and Nakajima (1974) confirmed that part of the twitch and tetanus tension was generated by the electrotonic spreading of depolarization into the transverse tubules. In a local activation experiment, activation of a muscle fiber caused by the passive spreading of subthreshold depolarization was observed (Huxley and Taylor, 1958; Huxley, 1971). The area in front of the action potential is depolarized by the electrotonic spreading of membrane potential. It is unknown whether or not such depolarization can release Ca*+ ions from the sarcoplasmic reticulum. To examine this problem we used a method of rapid solution change. Hodgkin and Horowitz (1960), and Nakajima er al. (1975) achieved sudden changes of external solution with a rapidly flowing bathing solution. In our experiments single skeletal muscle fibers were transferred from one trough to another, and were stimulated immediately after the transfer. Carefully prepared single fibers were not damaged by the air-water interface. Our results suggested that the conduction of the action potential into the transverse tubules was necessary to induce full activation of the muscle fiber, and that the area in the transverse tubules in front of the conducted action potential was activated. These results suggest that the electrotonic spreading of membrane depolarization caused by an action potential could release Ca*+ ions from the sarcoplasmic reticulum.
Single muscle fibers were isolated from dissected semitendinosus muscles of Rano japonica. One end of each fiber was connected via the tendon to a tension-sensitive hook of a strain gauge (TDS-101. Fuii-Keisoku) while the other end was co&&& to a fixed hook. Fibers were stretched to 1.2 times the slack length. The single fibers were placed in a small Lucite trough which was bathed in temperature controlled water maintained at 20°C. Single fibers were transferred from one trough to another so as to change solution rapidly. An electrical stimulus (rectangle pulse, 0.5 msec duration, 1.5 times threshold, 1OOHz for 0.2-0.5~~) was applied to the fiber immediately after the transfer. The stimulator (SEN-7103, Nihon Kohden) was triggered by a signal which monitored the touching of the hook to the bath solution (Fig. 1). The signal which triggered the stimulator was the potential change caused by a 75 pA d.c. current that flowed between the hook and the bath solution. The potential
WATER+ +
& Fig. I. Apparatus for rapid solution change. Single fibers were fixed between two hooks and placed in a trough filled with normal Ringer solution. Another trough was filled with Na+ ion free solution. The troughs were bathed with temperature controlled water at 20°C. The trough could move up, down, right and left. 661
NAOJI FUIISHIROand
662
HIROSHIKAWATA C
NR +ONa
_---J
ONa
L_---!~_
NR
-+
J
\
1 0.5 mN
II
500
msec
Fig. 2. Contractions induced by tetanic stimulation immediately after solution change. Trace (a) shows the tetanic response in normal Ringer solution. Trace (b) shows the tetanic response when the fiber was transferred from normal Ringer to Na + ion free solution. Trace (c) shows the tetanic response when the solution was changed from Na+ ion free solution to normal Ringer. In records (b) and (c), the middle trace indicates the duration of stimulation and the bottom trace the trigger signal resulting from the touching of the hook, to which the fiber was fixed, to the bath solution. The bottom trace does not correspond to the time course of the bath solution change.
change was monitored using a low-pass filter, so that the signal increased slowly (Fig. 2). However, the moment at which the hook touched the bath solution could be easily determined. Single fibers were transferred from normal Ringer solution (11 I .2 mM NaCl, 3 mM KCl, 2 mM CaCI,, 5 mM HEPES, pH 7.2) to Na+ ion free solution (NaCl was replaced with choline chloride) and vice versa. Fibers were immersed for
at least 10 min in one solution before transfer to the other solution. Recorded tensions were stored on FM tapes (MR-10, TEAC) and monitored by a computer (PC9801 VM2, NEC) using an AD converter (analog pro DMA, Canopus Elec. Corp.) at a sampling rate of 800 Hz. Various parameters were determined by computer using the software DSS type IV (Canopus Elec. Corp.).
ONa -$
NR
Fig. 3. Paired tetanic stimulation. Control responses in normal Ringer solution, and responses initiated immediately after changing solution from Na+ ion free to normal Ringer are shown. The second stimulus was applied 350 msec after the first. In (A) the fiber diameter was 50 pm. In (B) the fiber diameter was IlOpm. The middle and the bottom traces of each panel are as for Fig. 2.
Tetanus responses of single muscle fiber RESULTS
Rapid solution change and tetanus response
Figure 2 shows tetanus responses recorded in a single fiber stimulated immediately after transfer from normal Ringer (NR) solution to Na + ion free solution (ONa) and vice versa (these conditions are abbreviated as “from NR to ONa” or “from ONa to NR” from here on). The bottom traces are the monitored trigger signal resulting from the hook touching the bath solution. The upward deflection of the signal indicates that the hook had touched the bath solution, it does not mean that fibers were immersed in the bath solution during the time course of the signal. The middle trace indicates the period of tetanic stimulation. There was a slight delay between the hook touching the bath solution and the onset of tetanic stimulation, resulting from the time taken for the signal to exceed the trigger level of the stimulator. Single muscle fibers started to contract on average 57.9 msec (N = 6) after the hook touched the bath solution under the condition from NR to ONa. On the other hand, under the condition from ONa to NR, contraction started on average 142.3 msec
663
after the hook touched the bath solution in the same fiber. When single fibers were continuously stimulated under the condition from NR to ONa, contraction ceased after some time (Fig. 2b). Diffusion of Na+ ions away from the cell surface may have caused this inhibition of contraction. On the other hand, when single fibers were stimulated under the condition from ONa to NR, the duration of contraction corresponded to the duration of stimulation, although the amplitude of the tetanic tension was smaller than that recorded under the condition from NR to ONa (Fig. 2~). Fractional tensions (i.e. relative to control tensions recorded in Ringer solution) recorded under the condition from NR to ONa were nearly identical in each fiber (mean + SEM, 0.82 + 0.05, N = 14), however, those recorded under the condition from ONa to NR were very different from fiber to fiber (see below). Contraction induced by paired stimulation under the condition from ONa to NR
Tension recorded under the condition from ONa to NR was smaller than that recorded under the condition from NR to ONa (Fig. 2). This means that
A
a
b
il,
I\
bmN
500 msec
I&
50 msec Fig. 4. Superimposition of paired tetanic contractions resulting from paired stimuli with varying inter-stimuli recovery periods. In trace (A-a), five recordings are superimposed. Intervals between the first and second stimuli are 200, 500, 800, 1000 and 1500msec. In trace (A-b), tetanic responses induced by paired stimuli separated by 1500msec in normal Ringer solution are shown. Fiber diameter was 92.5 pm. In trace (B-a), three recordings are superimposed. Inter-stimuli intervals were 100, 150 and 200 msec. In trace (B-b), tetanic responses induced by paired stimuli separated by 200 msec in normal Ringer solution are shown. Fiber diameter was 57.5 pm.
NAOIIFUIISHIRO and HIR~~HIKAWATA
664
some parts of the fiber were not activated under the condition from ONa to NR. This reduced area of activation may have resulted from an impaired diffusion of Na+ ions into the transverse tubules under this condition. Thus a paired stimulation protocol was employed. If Na + ions diffused into the transverse tubules during the recovery period between the paired stimuli, then the contraction induced by the second stimulus would be larger than the first contraction. Initially a delay of 350 msec separated the paired stimuli. Figures 3A and B illustrate two examples of contractions obtained with the paired stimuli. The second contraction was larger than the first, however, the amplitude of the second contraction was still smaller than the control contraction in some fibers, as shown in Fig. 3B. Therefore the duration of the recovery period between the paired stimuli was varied. Figure 4 illustrates the results obtained in this experiment. In every fiber the second contraction reached the control level when fibers were stimulated after a sufficient long recovery period. This recovery period was different from fiber to fiber (1.5 set in Fig. 4A and 200 msec in Fig. 4B). These results suggested that the size of activated area under the condition from ONa to NR depended on the diffusion of Na+ ions into the transverse tubules. Dependence of fractional tension on jiber radius recorded under the condition from ONa to NR
Fractional tension (relative to control) recorded under the condition from ONa to NR was different from fiber to fiber. Isometric tetanic tension is known to be correlated with the activated area of fiber (Elzinga et al., 1989). Thus, under the assumption that the entire area of the fiber from the cell surface to depth x was activated under the condition from ONa to NR, fractional tension could be estimated by equation (1). Transformations of equation (1) yielded equations (2) and (3). )‘=
Jl
-y
=
r2n - (r - x)2n r27t
-xr +1
1:
L;
L
0.2
t
0
0
. 0.01
0.02
0.03
l/RADIUS
(/I-‘)
k. 0.04
l
0.05
Fig. 5. A plot of ,/l --y vs l/r. Open circles indicate contractions resulting from the first stimuli in the paired stimuli protocol. Filled circles indicate contractions resulting from the second stimuli. Continuous lines were obtained by a least squares method.
area increased by 10.8pm (23.2 - 12.4 = 10.8) in 200msec (the time between tetanic stimuli). Impaired transverse -tubular diffusion of Na + ions during contraction
The diffusion of Na+ ions into transverse tubules during contraction was examined. Fibers were stimulated under the condition from ONa to NR with two pulse protocols. In the first, paired stimuli at 100 Hz of 200 msec duration were separated by 100 msec, whereas in the second a 100 Hz stimulus was applied continuously for 500 msec. If Na + ions diffused into transverse tubules during contraction, it follows that the maximal tension produced by the second protocol would be same as the tension resulting from the second contraction under the first protocol. However, the tensions were not the same as shown in Fig. 6. The tension resulting from the second contraction under the first protocol was greater than the tension
(1)
I
0.25 mN
(3)
where y is the fractional tension, r is the radius of fiber and x is the depth of activated area from the cell surface. Thus J 1 - y was plotted against l/r according to equation (3). Figure 5 illustrates these results. The open circles are the values obtained from the first contraction while the closed circles are the values obtained from the second contraction when the stimuli were separated by 200 msec. Lines of best fit were obtained with a least squares method and gave values of x = 12.4 pm for the open circles (correlation coefficient = 0.72), and x = 23.2 pm for the closed circles (correlation coefficient = 0.84). Since each line crossed the vertical axis near 1.Oand there was a good correlation between I/r and ,/l - y, the following two conclusions are suggested. Firstly, when fibers were stimulated immediately after transfer from ONa to NR, an area up to 12 pm in depth from the fiber surface could be activated. Secondly, the activated
20oYsec Fig. 6. Contractions resulting in a fiber stimulated tetanically immediately after transfer from a Nat ion free solution to a normal Ringer solution. Contractions resulting from two protocols are superimposed. The first protocol consisted of two paired stimuli of 200 msec duration separated by 100 msec, as shown in the second trace. The second protocol consisted of continuous stimulation for 500 msec as shown in the third trace. The fourth trace is the trigger signal which monitored the hook touching the solution.
Tetanus responses of single muscle fiber resulting second diffusion impaired
from the continued stimulation under the protocol. This result suggested that the of Na+ ions into the transverse tubules is during muscle contraction.
Simulation of increasing tension with the second tetanic contraction As described above, fractional tension obtained under the condition from ONa to NR depended on fiber radius. This analysis suggested that the smaller the fiber radius, the bigger the fractional tension would be under the condition from ONa to NR. Thus full activation was generated rapidly in thin fibers as shown in Figs 3A and 4B. The time course for recovery of tension during the second contraction shown in Fig. 4, probably corresponded to the increasing area of the muscle fiber activated by the diffusion of Na+ ions into the transverse tubules. This time course of recovery was simulated using data from thick fibers (radius 47-55 grn, mean 50 pm, N = 4, Fig. 7). The following diffusion equation, described by Hill (1928, equation 45) was employed.
665
Thus the diffusion constants for several C/C, values using t = 200 msec and x = 10.8 pm were calculated. Next, from the obtained parameters C/C’, and D, the value of t at each x was calculated according to equation (4). By substituting each value of x in equation (2), the fractional tension at each time t was determined. Figure 7 illustrates the results obtained with this simulation (continuous lines). These results indicated the need to modify the model, which was subsequently modified in two ways. Firstly, in the simulation, at time t = 0 Na+ ions had not diffused into the transverse tubules, whereas in the experiments, time t = 0 was the time when contractions were first initiated. Therefore, if the first contraction occurred after Na+ ions had already diffused into the transverse tubules, these results could not be plotted on the same axis as the simulated data. Secondly, it is possible that the electrotonic spreading of membrane potential might activate a wider area than that activated an action potential in the transverse tubules. If the first modification is accepted, the experimental data must be shifted to the right as shown in Fig. 8A (the experimental data was right-shifted by 133 msec). Acceptance of the second modification, requires that equation (2) be modified as follows.
y=1_(1_q2) where C is the concentration of Na + ions at point x, C, is the concentration of Na+ ions at x = 0 (constant), J0 and J, are Bessel functions, r is the fiber radius, D is the diffusion constant, t is the time, GI,is the n th root of J,,(a,) = 0, and n is an integer. In this simulation, fiber radius was assumed to be 50 pm and n was fixed at 5 (there was no change in the results even if a larger number than 5 was used). In the model it was assumed that if the concentration of Na + ions at a point x in the transverse tubules was over a threshold level, then the area from the fiber surface to that point would activate. As discussed above, Na+ ions do not diffuse significantly during contraction, while the distance along the transverse tubule which is capable of activation increases by 1O.Bpm during a 200 msec resting period. It could be speculated that Na + ions diffuse 10.8 pm in 200 msec.
where 1 is the difference in the distance between the activated depth from the cell surface and the position
A 1.0
r
0
0.2
0.4
0.6
TIME 1.0
a b c
(5)
B
0.6
1.0
1.2
Csec)
1.0
5 9 y 2
0.e
0.6
g
0.4
c u a
0.2
E 0
0 0
0.2
0.4
TIME
0.6
0.6
1.0
(set)
Fig. 7. Simulation of Na+ ion diffusion into T-tubules. Open circles are the mean fractional tensions (N = 4) obtained with the paired stimuli. Continuous lines are the theoretical curves obtained using the following diffusion constants and fractional Na + ion concentrations (relative to normal Ringer solution) in the transverse tubules: (a) 1.28 x IO+, 0.5; (b) 3.11 x W6, 0.4; (c) 2.20 x IO+, 0.3.
0
0.2
0.4
0.6
TIME
(sex)
0.6
1.0
Fig. 8. (A) Modification of the simulation shown in Fig. 7. Open circles are the experimental data points moved 133 msec to the right. The theoretical curve is best fit to the experimental data with parameters D and C/C,, as follows, D = 3.11 x 10m6,and C/C,, = 0.4. (B) The continuous line is the modified theoretical curve (D = 3.11 x 10m6,C/C,, = 0.4 and I = 4.3 pm according to equation 5).
NAOJIFUJ~SHIRO and HIROSHIKAWATA
666
where the action potential arrived in the transverse tubules. Figure 8B shows the results of the second modification where it was postulated that an area 4.3 pm ahead of the action potential was activated by electrotonic spreading of membrane potential (D =3.11 x 10-G and C/C,=O.4). The second modification produced a better fit than the first modification. D~SCU~ION
Experimental data was fitted to the diffusion equation developed by Hill (1928) using the simulation of Nakajima et al. (1975). The diffusion constant for Na+ ions obtained in this study (3.11 x 10e6 cm’/ set) was about twice that reported by Nakajima et al. (1975). However, it was smaller than the diffusion constant for Na+ ions in aqueous solution (1.48 x 10~‘5cm2/sec at 25°C; Robinson and Stokes, 1958). The difference in the value of the diffusion constant obtained in the current study and that reported by Robinson and Stokes might be caused by the complexity of the structure of the transverse tubules. Transverse tubules in frog make a network along the longitudinal axis of the muscle fiber (cf. Peachey, 1983). This complex structure might decrease the rate of diffusion of Na + ions. In the simulation employed in this study, transverse tubule membranes initiated action potentials when the Na + ion concentration in the tubules was 40% (C/C,, = 0.4) of that in Ringer solution. Bezanilla et al. (1972) showed that peak tetanus tension in a solution with half normal Na+ concentration was similar to that in normal Ringer solution. Thus the results of the current simulation are consistent. The analysis of the experimental data, and simulation presented in this study suggest that the attenuated tetanic tension recorded under the condition from ONa to NR was caused by a partial activation of the muscle fiber. The simulation suggested that an area preceding the action potential could be activated by an electrotonic spreading of membrane depolarization. As described in the results section, contraction under the condition from ONa to NR started 142.3 msec on average after the hook touched the solution, and after 57.9 msec on average under the condition from NR to ONa. If the results of the simulation are accepted, the diffusion distance of Na + ions in the 84.4 msec (= 142.3-57.9) could be calculated to be 6.5 pm under the conditions D = 3.11 x 10-6, C/C, = 0.4, and radius = 50 pm. In this caIculation, the unstirred layer at the fiber surface was ignored. Diffusion speed of Na + ions may be slower in the unstirred layer, and therefore the actual distance might be shorter than
6.5 pm. However the analysis presented in this study revealed that a depth 12 pm from the cell surface of the muscle fibers was activated (see results section). This means that a deeper area of the transverse tubules than the area at which the action potential arrived was activated under the condition from ONa to NR. Huxley and Taylor (1958) observed that activation of muscle fiber spread as far as 10 pm along transverse tubules in a local activation experiment, and thought that this spread was a passive process (Huxley and Taylor, 1958; Huxley, 1971). Their observation may correspond to the results obtained in this study. Acknowledgements-We
thank Drs P. Palade and B. Simon for their critical comments on this paper. We are indebted to Dr D. Hill for his kind check and comments on this paper.
REFERENCES
Bastian J. and Nakajima S. (1974) Action potential in the transverse tubules and its role in the activation of skeletal muscle. J. gen. Physiot. 63, X7-278. Bezanilla F., Caputo C., Gonzalez-Serratos H. and Venosa R. A. (1972) Sodium dependence of the inward spread of activation in isolated twitch muscle fibers of the frog. J. Physiol. 223, 507.--523.
Costantin L. L., (1970) The role of sodium current in the radial spread of contraction in frog muscle fibers. J. gen. Physiol. 55, 703--l 15.
Elzinga G., Howarth J. V., Rail J. A., Wilson M. G. A. and Woledge R. C. (I 989) Variation in the normalized tetanic force of single frog muscle fibers. J. Physic/. 410, 1577170. Hill A. V. (1928) The diffusion of oxygen and lactic acid through tissues. Proc. R. Sot. B Biol. Sci. 184, 39-96. Hodgkin A. L. and Horowicz P. (1960) The effect of sudden changes in ionic con~ntrations on the membrane potential of single muscle fibers. J. Phvsiol. 153. 370-385. Huxfey A. F. (1971) The activation of striated muscle and its mechanical response. Prof. R. Sot. London. B. 178, t-27. Huxley A. F. and Taylor R. E. (1958) Local activation of striated muscle fibres. J. Physiol. 144, 426-441. Nakajima S. and Gilai A. (1980) Radial propagation of muscle action potential along the tubular system examined by potential-sensitive dyes. J. gen. Physiol. 76, 751~-762. Nakaiima S.. Nakaiima Y. and Bastian J. (1975) Effects of sudden changes in external sodium concentration on twitch tension in isolated muscle fibers. J. ge:en. Physiol. 65, 459-482.
Peachey L. D. (1983) Structure and function of membrane systems of skeletal muscle cells. In ~~dbook of physiology, Sect. 10, pp. 23-71. Am. Physiol. Sot. Bethesda, MD. Robinson R. A. and Stokes R. H. (1959) Electrolyte so&ions. Butterworths, London.