amplitude, it has more effect than the other agents on the rate of decay. The Ca2+ transients in indo-1-loaded rat ventricular myocytes.

Transcription

1 Journal of Physiology (1993), 468, pp With 11 figures Printed in Great Britain THE EFFECTS OF INHIBITORS OF SARCOPLASMIC RETICULUM FUNCTION ON THE SYSTOLIC Ca2l TRANSIENT IN RAT VENTRICULAR MYOCYTES BY N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER From the Department of Veterinary Preclinical Sciences, University of Liverpool, Liverpool L69 3BX (Received 5 May 1992) SUMMARY 1. The effects of thapsigargin, ryanodine and caffeine were examined on systolic Ca2+ transients in indo-1-loaded rat ventricular myocytes. 2. Thapsigargin (1-1,tM) decreased the magnitude of the Ca2+ transient. This was accompanied by a decrease of the rate constant of decay of the transient. 3. Ryanodine (1-1 /4M) decreased the magnitude of the Ca2+ transient. Initially there was no change in the rate of decay but further reduction of the magnitude was accompanied by a slowing. 4. Caffeine ( 5-1 mm) decreased the magnitude of the Ca2+ transient and its rate of decay. These effects were graded with caffeine concentration. 5. For a given submaximal reduction of the magnitude of the Ca2+ transient, the effect on the rate of decay was greatest for thapsigargin, least for ryanodine and intermediate for caffeine. 6. The above data are reproduced by a model in which all three agents decrease the magnitude of the Ca2+ transient by decreasing the calcium content of the sarcoplasmic reticulum (SR) (thapsigargin by inhibiting the Ca2+ pump and ryanodine and caffeine by increasing the leak of Ca2+ from the SR). The decreased contribution of the SR will thereby slow relaxation. The fact that thapsigargin inhibits the SR Ca2+ pump accounts for the observation that, for a given decrease of amplitude, it has more effect than the other agents on the rate of decay. The difference between caffeine and ryanodine is suggested to arise because caffeine potentiates Ca2+ release from the SR and thereby attenuates the effect of the decreased SR calcium content on the magnitude of the Ca2+ transient. INTRODUCTION The rise of intracellular calcium concentration ([Ca2+]i) which activates contraction in cardiac muscle comes from two sources: (i) Ca2+ entry across the surface membrane; (ii) Ca2+ release from the sarcoplasmic reticulum (SR). Relaxation results as Ca2+ is pumped both out of the cell (primarily by Na+-Ca2+ exchange) and back into the SR (by the Ca-ATPase). These sources and sinks for Ca2+ thereby determine both the magnitude and time course of the Ca2+ transient. For the heart to function MS 1338

2 36 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER effectively as a pump it must relax between contractions. It is therefore important, not only that the level to which [Ca2+]i rises during systole is controlled but also that the rate of decay of the systolic [Ca2+]i transient is appropriate. The overall rate of decay of the Ca2+ transient will be expected to depend, not only on the rates of Ca2+ pumping by the SR and surface membrane, but also on the relative contributions of these two sinks. The calcium content of the SR and therefore its ability to pump Ca2+ and contribute to relaxation can be regulated in two ways: (i) by controlling the Ca- ATPase which is stimulated by phosphorylation of phospholamban (Tada, Kirchberger, Repke & Katz, 1974); and (ii) by controlling the Ca2+ efflux from the SR which is influenced by cytoplasmic factors such as [ATP], calmodulin or [Ca2+]i (Meissner & Henderson, 1987). The aim of the present paper was to investigate experimentally how altering the contribution of the SR to relaxation by these two methods alters the rate of recovery of the calcium transient. It is easy to see that an increase of the rate of the SR Ca-ATPase will increase the rate of recovery of the calcium transient. However, it is less obvious what effect modulation of the opening of the Ca2+ release channel will have. We have compared the actions of three agents which would be expected to affect the Ca2+ content of the SR. (i) Thapsigargin inhibits the isolated SR Ca-ATPase in cardiac muscle (Kijima, Ogunbunmi & Fleischer, 1991) and also the Ca-ATPase of the sarcoplasmic or endoplasmic reticulum in many other cell types (Takemura, Hughes, Thastrup & Putney, 1989; Thastrup, Cullen, Drobak, Hanley & Dawson, 199). The effects of thapsigargin have been compared with those of (ii) ryanodine which partially opens the SR Ca2+ release channel (Meissner, 1986; Rousseau, Smith & Meissner, 1987) and (iii) caffeine which promotes Ca2+-induced release of Ca2+ from the SR (Rousseau & Meissner, 1989; Sitsapesan & Williams, 199). The results show that the maximal effect of all three agents is to decrease both the magnitude and rate constant of decay of the Ca2+ transient. However, the intermediate effects of the three agents are different and are analysed in terms of a model for the control of systolic [Ca2+]i. A preliminary account of some of these data has been presented to the Physiological Society (O'Neill, Lamont, Negretti & Eisner, 1992). METHODS The experiments were performed on rat ventricular myocytes isolated as described previously using a collagenase and protease dissociation (Eisner, Nichols, O'Neill, Smith & Valdeolmillos, 1989). Rats were killed by stunning and cervical dislocation. Isolated cells were loaded with the acetoxymethyl (AM) ester of indo-1 and fluorescence measured using apparatus described previously (O'Neill, Donoso & Eisner, 199). Indo-1 was used 199; O'Neill & to measure both [Ca2+]1 and the intracellular caffeine concentration (O'Neill et al. Eisner, 199). Briefly cells were placed in a bath on the stage of an inverted microscope. The cells were stimulated by field electrodes in the bath and fluorescence was excited at 34 nm and collected at 4 and 5 nm. In the diagrams presented we have not expressed the indo- 1 measurements in terms of absolute levels of [Ca2+]i. This is because of the problems of calibrating indo-1 when it is loaded as the AM ester (Highsmith, Bloebaum & Snowdowne, 1986). Instead the results are presented in terms of the ratio of light emission at 4 nm to that at 5 nm. This ratio increases with an increase of [Ca2+]i. One problem with the use of the AM ester is that some of it is incorporated into organelles such as the mitochondrion. Total mitochondrial calcium content (as measured by electron microprobe

3 SR FUNCTION IN HEART 37 analysis) increases during the transient (Wendt-Gallitelli & Isenberg, 1991). However, the fluorescence of indicator incorporated into the mitochondria does not appear to change during a systolic Ca2l transient (Miyata, Silverman, Sollott, Lakatta, Stern & Hansford, 1991) and therefore should not affect the time course of the Ca2+ transient. A 1. - Thapsigargin LI.5- a b c d B 1 min oc C F Ii O_4L~~~~ s Fig. 1. The effects of thapsigargin on [Ca2+]i. A, time course. The record shows [Ca2+], as measured from the 4:5 nm ratio of indo-1. The cell was stimulated at -1 Hz and thapsigargin (2-5 SM) was applied as indicated above. B, specimen transients. These are the average of the periods indicated on A. The transients have rate constants of decay of 3-2 (a), 1 7 (b), 1X4 (c) and -6 s-1 (d). C, normalized transients. These show records a, b and d normalized to the same magnitude. The smooth curves are best-fit single exponentials. Despite the above reservations, we have performed some experiments in which the cell membrane was made permeable to Ca2+ with a high concentration (5 UM) of the ionophore ionomycin. The cell was then exposed to Ca2+-free (2 mm EGTA) and Ca2+-containing (3 mm) solutions in order to estimate the maximum (Rmax) and minimum (Rmin) indo-1 ratios. Values obtained were respectively and In these experiments, the mean ratios at diastole and systole were respectively and It should be noted that this means that, even at systolic [Ca2+]i, indo-1 is far from saturation. Indeed we calculate (assuming a dissociation constant, Kd, for the indicator of 25nM) that diastolic and systolic [Ca2+], are respectively 59 and 38 nm. The comparatively small size of the calcium transient may reflect buffering due to the indo-1. Solutions. The experimental solution contained (mm): NaCl, 134; KCl, 4; MgCl2, 1; Hepes, 1; glucose, 11; CaCl2, 1; titrated to ph 7-4 with NaOH and equilibrated with air. All experiments were carried out at 27 C. All statistics are presented as means+ S.E.M. Statistical significance was assessed by two-tailed t tests. RESULTS Figure 1 shows the effects of thapsigargin (2-5 /LM) on field-stimulated systolic Ca2` transients. The upper trace shows that thapsigargin decreases the magnitude of the [Ca2+]i transient. This record also shows that, in thapsigargin, the smaller Ca21

4 38 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER I1 1 Le) * cc Ca Control -a...l.,a S.1...-AL nit 1 k Thapsigargin P^.51 1 I ) Cl) O _ li 2 s Fig. 2. The effects of thapsigargin on [Ca2+]1 and contraction. In both panels the traces show [Ca2+]i (top) and contraction (bottom). The cell was stimulated at 1 Hz. Panels show: control (left) and after 1 min exposure to 2-5 /LM thapsigargin (right). A Caffeine Caffeine.9 Lfl co.e. B.5 1 min.f 1 s Fig. 3. The effects of thapsigargin on the response to rapid application of caffeine. A, time course. The trace shows [Ca2+]i. Caffeine (1 mm) was applied for the periods shown by the filled bars and thapsigargin (1 /tm) as shown by the open bars. The cell was initially stimulated at 33 Hz. Stimulation was discontinued during the exposure to caffeine and for 3 s after. B, normalized responses to caffeine. This shows the two caffeine responses from A normalized to the same amplitude.

5 SR FUNCTION IN HEART transients decay more slowly than the control records. This point is emphasized in Fig. lb which shows sample Ca2+ transients on an expanded time scale. A control record (a) and three records obtained after various periods of exposure to thapsigargin (b-d) are shown. Records a, b and d have been normalized to the same 39 A Ryanodine.4 Ld a b c B 1.2-1min o a b c d 1.2- r s Ca c \h Ad a, b,c 1 s Fig. 4. The effects of ryanodine on [Ca2+]1. A, time course. Ryanodine (1 FM) was added for the period shown by the bar. Stimulation rate, -83 Hz. There is a 27 min duration break in the record before the final five transients. B, specimen records. These are single transients obtained at the points indicated on A with rate constants of 3-4 (a), 3-8 (b), 3-6 (c) and -6 s-1 (d). C, normalized records. The smooth curves are best-fit exponentials. amplitude and superimposed in Fig. 1 C. All the transients are fitted well by single exponentials. It is clear that the rate constant of decay of transient b is lower than that of the control (a) and that the final transient in thapsigargin (d) decays even more slowly. Such results were obtained consistently; in particular when the magnitude of the Ca2` transient had been decreased by thapsigargin it was always found to be slower to decay. The effects of thapsigargin were not reversed by washing off the drug for periods of up to 3 min (not shown). Each of the concentrations of thapsigargin (1-1 szm) used in this study produced a similar slowing and reduction in magnitude of the Ca2+ transient; only the time taken to reach the steady state varied. The decrease in amplitude and decay rate of the Ca21 transient was accompanied by a similar effect on contraction (Fig. 2). The decrease in both magnitude and rate constant of decay of the transient can qualitatively be accounted for by an inhibition of the SR Ca-ATPase. This would decrease the rate of pumping of Ca2+ back into the SR and thereby decrease its calcium content as a larger proportion of the systolic calcium would be pumped out of the cell. Evidence that the SR calcium content is,

6 4 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER indeed, decreased is presented in Fig. 3. This shows the effects of rapid application of caffeine (1 mm) both under control conditions and after thapsigargin (1,UM) had been applied for long enough for the Ca2l transient to be decreased to less than 5 % of its control size. It is clear that, consistent with a depletion of the SR, the A mm caffeine 1 mm caffeine.6 a b c 1 mi B m- C a 6-1 s 1 S Fig. 5. The effects of caffeine on [Ca2"],. A, time course. Caffeine (2-5 or 1 mm) was added as shown above. The cell was electrically stimulated (-1 Hz) except for the period just before and for the first period of the addition of caffeine. The arrow indicates the smallest Ca21 transient on removal of 2-5 mm caffeine. B, specimen Ca21 transients. These are averages (n = 6-8) obtained at the points indicated on A. Transient a includes three transients recorded immediately before the record begins. C, normalized Ca21 transients. The smooth curves drawn through the points are best-fit single exponentials with rate constants of 5-7 (a), 4-2 (b) and 1-2 s-' (c). magnitude of the caffeine response is decreased by previous exposure to thapsigargin. Figure 3B shows the two caffeine responses normalized to the same magnitude. The fact that these normalized traces superimpose indicates that thapsigargin has no effect on the rate of decay. As the recovery of the caffeine response is thought to be mediated largely by Na+'Ca2+ exchange with some contribution from the sarcolemmal Ca-ATPase (Bers & Bridge, 1989; O'Neill, Valdeolmillos, Lamont, Donoso & Eisner, 1991) this result suggests that neither of these mechanisms is affected by thapsigargin. Figure 3 also shows that thapsigargin increases the diastolic level of [Ca21],. This effect is largely due to the slowing of the decay of the Ca2+ transient, i.e. if stimulation was discontinued (not shown) [Ca2+], fell towards control. This effect was less apparent in experiments such as those of Figs 1 and 2 which were carried out at lower stimulation rates.

7 SR FUNCTION IN HEART 41 The effects of ryanodine The effects of ryanodine are shown in Fig. 4. The application of ryanodine produces a gradual decrease of the magnitude of the systolic Ca2+ transient. The final records obtained in ryanodine show that the calcium transient is eventually greatly A 1. Caffeine Thapsigargin 5L a b L.. c 1 min B 1. 1 LoL 4 a, C.5 1 s 1 s Fig. 6. A direct comparison of the effects of caffeine and thapsigargin. A, time course. Caffeine (2-5 mm) and thapsigargin (5 #M) were added as shown above. The stimulation rate was -83 Hz. B, specimen Ca2+ transients. These show averaged (n = 7-9) records obtained at the points shown in A. C, normalized transients. slowed. However the specimen records (Fig. 4B) and especially the normalized traces (Fig. 4C) show that, initially, reduction of the magnitude of the transient is not accompanied by a slowing. This contrasts with the effects of thapsigargin described above where the decrease of magnitude was always accompanied by a slowing of the decay of the transient. As has been previously shown (Hansford & Lakatta, 1987) ryanodine causes a maintained increase in the diastolic [Ca2+]i which they suggested represented the leak of calcium from the SR. However, a maintained increase like this cannot arise from a leak of calcium from a finite store such as the SR and therefore the origin of this increase is not clear.

8 42 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER The effects of caffeine Figure 5 shows the effects of two concentrations of caffeine. In these experiments stimulation was discontinued while caffeine was added. The addition of 2-5 mm caffeine initially produced a series of Ca2" oscillations. When stimulation was A 1.- LOl S.2 5 L a b c 1L B 1. 1min o a b c.5 2s L Fig. 7. The effects of caffeine removal on the time course of the Ca2+ transient. A, time course. Traces show [Ca21]i (top) and [caffeine], (bottom). B, specimen transients obtained at the points indicated on A. The dashed line on transient b indicates the time course of transient c (immediately post-caffeine). recommenced the Ca2+ transient was somewhat smaller than the control and, as emphasized by the specimen transients, was also slightly slower. When caffeine is removed the Ca2+ transient declines before recovering to control levels. This transient decrease of the magnitude of the Ca2+ transient will be discussed later. The application of 1 mm caffeine produces a large transient rise of [Ca2+]i. Subsequent Ca2+ transients are smaller than control and recover more slowly. Thus like thapsigargin but unlike the initial effects of ryanodine, the decrease of the magnitude of the systolic Ca2+ transient produced by caffeine is accompanied by a decrease of the rate constant of decay. Figure 6 shows, however, that there is a quantitative difference between thapsigargin and caffeine. For a similar submaximal reduction of the magnitude of the Ca2+ transient, caffeine produces much less slowing of the decay of the transient than does thapsigargin. The above experiments in caffeine have shown that, the smaller the Ca2+ transient, the slower its rate of decay. It appears, however, that the rate of decay is not simply a function of the size of the transient. Figure 7 shows that 1 mm caffeine decreases

9 SR FUNCTION IN HEART the rate of decay of the Ca2+ transient as well as decreasing its magnitude. When caffeine is removed it takes several beats for the magnitude of the transient to recover to control levels. However, the rate constant of decay of the first transient on caffeine removal (c) is already much faster than that in caffeine. A o ii o 3i J W n+ 3 Control Caffeine Thapsigargin 43 B 2 s LO o CDI 9 F Control Caffeine Ryanodine.5-2 s Fig. 8. Comparison of the final effects of thapsigargin, caffeine and ryanodine on the Ca2+ transient. A, comparison of the effects of caffeine and thapsigargin. Panels show (from left to right) control, caffeine (1 mm), and thapsigargin (after 5 min exposure to 1,M); the right-hand panel shows the traces normalized to the same amplitude. The relative magnitudes of the caffeine and thapsigargin traces have not been altered. The magnitudes and time courses of the caffeine and thapsigargin transients are so similar that they appear as a single trace. Stimulation rate, -2 Hz throughout. B, comparison of the effects of caffeine and ryanodine. The panels are as in A except that ryanodine (1 min exposure to 1,UM) rather than thapsigargin was tested. Stimulation rate, -1 Hz. The results presented above show that, when applied at sufficiently high concentrations, or for a sufficient time, caffeine, ryanodine and thapsigargin each produces a decrease of the magnitude and a slowing of the decay of the Ca2+ transient. The experiment illustrated in Fig. 8 was designed to investigate whether these agents produce equivalent reductions in size and rate of recovery. As the effects of both thapsigargin and ryanodine are irreversible it was impossible to compare all three compounds on the same cell. Instead thapsigargin and ryanodine were each tested on a cell which had previously been exposed to caffeine. Figure 8A shows Ca2+ transients recorded first under control conditions and then in the presence of either caffeine (1 mm) or when thapsigargin had had its final effect. It is clear that both thapsigargin and caffeine slow the recovery and decrease the magnitude of the Ca2+ transient. The right-hand panel shows the caffeine and thapsigargin traces magnified (with no change in their relative size) and the control normalized to have the same

10 44 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER apparent amplitude as these transients. This emphasizes that the caffeine and thapsigargin transients have similar amplitudes and time courses. Figure 8B shows that caffeine and ryanodine also produce quantitatively similar effects transient. on the Ca2+ A B Ryanodine Ryano1ine U 8 8 Ryanodine Caffeine' C; 4 Thapsigargin 4 Thapsigargin Size of Ca transient(% control) Size of Ca2+ transient(% control) Fig. 9. The effects of caffeine, ryanodine and thapsigargin on the relationship between the magnitude and rate constant of decay of the calcium transients. A, uncorrected data. The ordinate shows the rate constant of the transient normalized to that in the absence of any of the drugs. The abscissa is the similarly normalized magnitude of the transient. E, thapsigargin;, caffeine;*, ryanodine. For caffeine the symbols represent (from right to left) the mean effects of the following concentrations (mm), with the number of cells in parentheses: 5 (3), 1. (5), 2-5 (15), 5 (7) and 1 (16). For thapsigargin and ryanodine the data were binned by the magnitude of the effect at any one time. The number of cells for each point (from right to left) are, for thapsigargin, 17, 9, 8 and 13, and for ryanodine, 4,5,4 and 4. For all three drugs the horizontal and vertical error bars denote S.E.M. B, corrected data. This graph is identical to that of A except that the caffeine data were corrected as follows (see also Discussion p. 45). For the corrected data the rate constant is that actually measured. However, the value of the magnitude is that obtained on the smallest Ca2+ transient after returning to control (zero caffeine). The above results have shown that thapsigargin, caffeine and ryanodine each eventually decreases both the magnitude and rate of decay of the systolic Ca2+ transient. It is also apparent that before the maximum effects are observed the different compounds have different relative effects on the magnitude and the rate constant. For example thapsigargin decreases the magnitude and rate constant of decay of the Cal+ transient together whereas, at first, ryanodine decreases the magnitude rather than the rate constant. These comparisons are facilitated by the plot of Fig. 9A which shows the rate constant of decay of the Ca2+ transient plotted as a function of its magnitude. Each point in Fig. 9 represents the mean of several cells (n values in legend) in different caffeine concentrations or after different times in supramaximal concentrations of ryanodine or thapsigargin. The relation for thapsigargin shows an upward curvature. Starting at the control point the rate constant initially decreases by a greater fraction than does the magnitude. In contrast the curvature of the ryanodine plot is in the opposite direction: there is initially a much greater effect on the magnitude than on the rate constant. The plot for caffeine is intermediate between those for ryanodine and thapsigargin. From Fig. 8 it would appear that the maximum effects of the three agents are identical. However, when data from several cells are pooled some significant

11 SR FUNCTION IN HEART differences can be seen. Table 1 shows statistical comparisons of the size and rate constants of the calcium transients in (i) 1 mm caffeine, (ii) after the full effect of ryanodine and (iii) after the full effect of thapsigargin. No significant differences were found between the sizes in the three agents or between the rate constants in caffeine and ryanodine. The rate constants of recovery in caffeine and in ryanodine were each TABLE 1. Sizes and rate constants of recovery of transients in 1 mm caffeine and in the steady state achieved in ryanodine and thapsigargin Ca2+ transient size Rate constant (% control) (% control) Caffeine (n = 16) * Ryanodine (n = 4) * Thapsigargin (n = 13) Values shown are means + S.E.M. * The rate constants in caffeine and ryanodine were significantly different from that measured in thapsigargin (P < 5). There were no significant differences between the sizes of any of the transients or between the rate constants in caffeine and ryanodine. significantly different from that in thapsigargin (P < -5). This finding is also reproduced by the model (see later). 45 DISCUSSION The results of this paper show that ryanodine, caffeine and thapsigargin all decrease the rate constant and magnitude of the systolic Ca2+ transient. The decrease of magnitude is easily accounted for as all three of these drugs will decrease the calcium content of the SR. Figure 3 shows that thapsigargin does decrease the SR calcium content, as judged by the decrease in the size of the response to caffeine. It is, however, rather more complicated to analyse the reduction of the rate constant of decay. Thapsigargin would be expected to decrease the rate of decay as it has been shown to inhibit the Ca-ATPase of cardiac SR (Kijima et al. 1991). The question then arises as to how caffeine and ryanodine, which are thought to make the SR leaky to Ca2' rather than affecting the SR Ca-ATPase, slow the rate of decay of the Ca2+ transient. Previous work has also found that caffeine and ryanodine can slow the rate of decay of the Ca2+ transient (Allen & Kurihara, 198; Wier, Yue & Marban, 1985; Smith, Valdeolmillos, Eisner & Allen, 1988). Indeed in order to account for the slowing of the decay of contraction and the Ca2+ transient, it has been suggested that caffeine does inhibit the SR Ca-ATPase (Blinks, Olson, Jewell & Braveny, 1972; Hess & Wier, 1984). The slowing of the decay of the calcium transient produced by ryanodine has also been attributed to a slowing of inactivation of the sarcolemmal calcium current (Wier et al. 1985). We must therefore consider how caffeine and ryanodine can slow the decay of the Ca2+ transient if their only action is to make the SR leaky to Ca2. It seems probable that this arises because, when the SR leak is sufficiently high, the SR will play no role in either Ca2' release or reuptake. Under these conditions Ca2+ removal from the cytoplasm will be controlled by the surface membrane alone and the recovery will be slower. Therefore if the SR is completely emptied (either by inhibiting the Ca-ATPase or by increasing the leak) the Ca2+

12 46 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER transient will be slowed (see Fig. 8). We now develop a quantitative model of this hypothesis. Model for the effects of SR inhibitors on the systolic Ca2" transient In order to analyse the effects of manoeuvres which interfere with SR function we make use of a simple model which is similar to that previously presented (Baro, O'Neill & Eisner, 1993). The fluxes of Ca2+ across the surface membrane are represented by: (i) a constant leak inward of magnitude J; (ii) a Na'-Ca2 exchange which pumps Ca2" out of the cell of magnitude m[ca2+]i where m is a constant, independent of [Ca2+]i (Beuckelmann & Wier, 1989). The Ca2+ current activated during each action potential is represented as an instantaneous increase of total cell calcium of magnitude ica. The fluxes across the SR membrane are: (i) a Ca-ATPase of rate k[ca2+]i where k is independent of [Ca2+]i and (ii) a leak of Ca2+ out of the SR of magnitude p([ca2 ] -[Ca2+]1) where [Ca2+]s is the Ca2+ concentration in the SR. The linear dependence of the SR Ca2+ pump rate on [Ca2+]i is a reasonable approximation given the Kd of 1-5 ItM (Tada et al. 1974). This model assumes that the SR Ca2+ pump is only affected by cytoplasmic [Ca2+]i. It is likely that the pump will be subject to product inhibition by elevated [Ca2+] (Inesi & De Meis, 1989). For simplicity, no account is taken of this possibility in the model. The products of the volumes and buffering power of the cytoplasm and SR are taken to be V, and K, respectively. In other words we assume that the Ca2+ buffers do not saturate over the experimental range. Estimates of the likely Ca2+ buffers (Fabiato, 1983) suggest that the total calcium bound will be a reasonable linear function of [Ca2+]i over the relevant range. The present model treats the calcium influx as an instantaneous function and ignores the fact that it may continue during the action potential and both it and the Na+-Ca2+ exchange will be affected by the changes of membrane potential during the action potential. We assume that systole results from the addition of the component due to the calcium current and the equilibration of Ca2+ between the SR and cytoplasm. After this [Ca2+]i will decrease as Ca2+ ions are pumped both into the SR and out of the cell. The process can be described by the following equations. V, d[ca2+]i/dt = p([ca2+]. -[Ca2+]i) - k[ca2+]i + J-m[Ca2+]i, (1) V. d[ca2+]s/dt = k[ca2+]i-p([ca2+].- [Ca2+]i). (2) In the steady state, [Ca2+]i is controlled simply -by the surface membrane. Therefore J = m[ca2+] and, in the steady state, [Ca2+]i = J/m. The pre-stimulation value of [Ca2+]s is given by the steady-state solution of eqn (2) (d[ca2+]s/dt = ): [Ca2+]s [Ca2+]i = (k+p)/p. (3) Therefore a decrease of the SR Ca2+ pump rate (decreased k) or an increase of the leak (increased p) will decrease the Ca content of the SR. At the peak of systole: [Ca2+]i= [Ca2+]s=[Ca=2+]SySt It can be shown that: [Ca2+]syst = (J/m){ Vc + Vs(k + p)/p}/( Vs + Vc) + ica/ (Vs + VcI) ( (4)

13 SR FUNCTION IN HEART It is clear from eqn (4) that increasing p or decreasing k will decrease [Ca2+] st. In the limit when either (i) p is very large or (ii) k very small then: [Ca2+]SYSt = J/m + ica/( Vs + VcD)' and only the Ca2+ current contributes to the systolic rise of [Ca2+]j. These two cases correspond to (i) high [ryanodine] and (ii) high [thapsigargin], respectively. These 47 i 3 N Cu a k= 2.8- k= 1.4- b 1s 1s 1 c d :3 CD p=.28- p=.56- p=.28- O L p= Fig. 1. Model for the effects of changing the SR Ca2+ leak or pump. All four panels show three traces. The continuous transient with the largest magnitude is a control (k = 2-8, p = 28). The smaller continuous transient is calculated by changing either the pump parameter (k) or the leak parameter (p) to the value indicated. Finally, the dashed line is the result of normalizing the modified transient to the control size. The modified transients represent pump parameter (k) decreased from 2-8 to 1-4 (a), pump parameter (k) decreased from 2-8 to (b), leak parameter (p) increased from -28 to -56 (c), and leak parameter (p) increased from -28 to 1 (d). In all panels the values of the other parameters were: VK = V, = 1 arbitrary volume unit, J 95 #smol s-1, = m = 95 arbitrary volume units s-1, = ic. 1 umol. equations have been solved numerically in Fig. 1. The values for the various parameters were assigned as follows. The Na'-Ca2+ exchange parameter (m) was adjusted to give the correct rate constant for the decay of the thapsigargin Ca2+ transient where it is assumed that only the surface membrane contributes to removal of Ca2+ from the cytoplasm during systole. The value for the inward Ca2+ leak (J) was adjusted to give a resting [Ca2+]i of 1 nm. The SR Ca2+ pump parameter (k) was set to give the correct rate constant of decay of the control Ca2+ transient. The control value of the leak p was set to give a reasonable size for the Ca2+ transient. The actual value of the parameters are given in the legend to Fig. 1.

14 48 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER Predicted effects on sy8tolic [Ca2+]i of altering SR pump and leak In the model calculations we adjust, separately, the values of k and p. The control condition has the parameters k and p equal to 2-8 and -28 respectively. Figure 1a shows the effects of decreasing the SR pump coefficient (k) from 2-8 to 1-4. This 15) 1 A B Leak L"\leak /n 5 r v- Control V Control v- LP Pump Pump [Ca2J8sy8t (,um) [Ca2+]Syst (pm) Fig. 11. The predicted relationship between the magnitude and rate of decay of the Ca2+ transients. Both graphs show the calculated rate constant (here expressed as the reciprocal of the half-time, l/to.5) as a function of the calculated magnitude of the Ca2+ transient. The control point has parameters k = 2-8 and p = 28. The continuous line shows the effect of decreasing k (at constant p) from 2-8 to. The dashed line shows the effect of increasing the leak (p) from -28 to 1 at constant k. A, simple model as used for Fig. 1. B, model with a saturating Ca2+ buffer in the SR. The amount of this buffer was adjusted to make the SR total calcium content for the control case (k = 2-8, p = 28) the same as that in A. decreases the magnitude of the systolic rise of [Ca2+]i to about -6 of its initial value. The dashed line shows the k = 1-4 transient normalized to the control. It is clear that its decay is slowed with respect to the control. The effects of a larger decrease of k (to zero) are shown in Fig. lob. The Ca2+ transient is further decreased and, as shown by the normalized trace, is greatly slowed. The effects of increasing the SR leak parameter (p) by either a small (from 28 to 56) or a large amount (to 1) are shown in Fig. loc and d. Despite the fact that the small increase of p decreases the magnitude by as much as did the small decrease of k (Fig. 1a), it has little effect on the time course of the transient. In contrast the large increase of p greatly slows the Ca2+ transient, as does reducing k to. The model can therefore account for the observation that, although the maximal effect of both thapsigargin and ryanodine is to slow the rate of decay of the Ca2+ transient, ryanodine initially has little effect on the time course of the transient whereas thapsigargin slows it. In terms of the model, the final effect of either is to empty the SR which therefore no longer contributes to Ca2+ regulation. Computations over a wider range of conditions are summarized in Fig. 11. Figure 1 IA shows the rate of decay of the Ca2+ transient plotted as a function of the magnitude. The initial point is the control (k = 2-8, p = 28). The continuous line shows the relationship between magnitude and rate constant as the pump parameter

15 SR FUNCTION IN HEART (k) is gradually decreased to zero. The dashed line shows an equivalent plot for increasing the leak p (from -28 to 1). Both manoeuvres eventually decrease the rate constant and magnitude. However when k is decreased rate constant and magnitude fall together. In contrast when p is increased, the magnitude declines greatly before the rate constant decreases. The model can therefore account for the different effects of thapsigargin and ryanodine on the rate vs. magnitude graphs. It should be noted that the results of the model are presented in terms of [Ca2+]i whereas the experimental results are given (for reasons explained in Methods) as the indo-1 ratio. We have, however, found that the general shape of the model predictions of Fig. 11 are not greatly changed by using the ratio rather than [Ca2+]i (not shown). Figure 11 A also shows that a small fractional increase of the rate constant results from moderate increases of p. The explanation of this acceleration appears to be that, as p is increased, for a given [Ca2+]i, the SR holds less Ca2+. This will therefore decrease the net Ca2+ efflux from the SR at a given [Ca2+]i. This effect dominates over that of the increased p. Therefore, as p is increased, at a given [Ca2+]i there is a smaller Ca2+ efflux from the SR opposing the SR Ca2+ pump and [Ca2+]i therefore falls faster. This effect is eventually lost as the SR becomes less and less important in controlling the rate of recovery of the Ca2+ transient. The effects of thapsigargin One obvious difference between the calculated and observed effects of thapsigargin is that the experimental data show that for thapsigargin, at first, the rate constant declines by more than does the amplitude whereas the model predicts that both parameters should fall in proportion. This discrepancy can be accounted for if one allows for the presence of the saturating Ca2+ buffer calsequestrin in the SR (Mitchell, Simmerman & Jones, 1988). Under these conditions, moderate inhibition of the SR Ca2+ pump will produce a proportional decrease of the free Ca2+ in the SR but not of the total content. Therefore the magnitude will be affected less than the rate. The curves in Fig. 11B show the predictions of a model in which the SR contains a buffer which is 85 % saturated with calcium before Ca2+ release (under control conditions). It can be seen that the relationship between rate constant and magnitude is curved as is the experimental thapsigargin data. It should be noted that the model is expressed in terms of [Ca2+]i whereas the experimental data show the indo fluorescence ratio which will be a function of [Ca2+]i. One must therefore consider whether the difference between the observed and predicted effects of thapsigargin (reproduced above by the addition of buffer in the SR) might be due to the non-linear relationship between [Ca2+]i and indo-1 ratio. As discussed in Methods, the systolic increase of [Ca2+]i produces changes of the indo-1 ratio far below the maximum possible value (O'Neill et al. 199). Saturation of the dye should, therefore, not be a problem. Furthermore, computations (not shown) which allow for such non-linearity indicate that this cannot explain the observed difference. This can be seen intuitively as follows. If the Ca2+ transient reaches levels of [Ca2+]i at which indo-1 is markedly saturated then, if the [Ca2+]i transient is reduced in magnitude with no change of time course, the magnitude of the indo-1 ratio trace will change by a smaller fraction than that of [Ca2+]i. However, because 49

16 5 N. NEGRETTI, S. C. O'NEILL AND D. A. EISNER the indo- 1 will be less saturated during the smaller transient, the ratio will decay more quickly. Therefore the indo- 1 non-linearity will appear to accelerate the rate of decay of smaller transients. In contrast the thapsigargin transients decay more slowly than predicted by the original version of the model. The maximal effect of thapsigargin, ryanodine and caffeine When the contribution of the SR to the systolic increase of [Ca2+]i has been abolished either by increasing the leak or decreasing the pump rate, the model predicts that the size of the transient will be the same in both cases. However, the rate of recovery of the transient will depend on the intervention: increased leak slows the transient more than does pump inhibition (Figs 1 and 11). This behaviour in the model arises because there is an equilibrium of cytosolic and SR calcium after addition of the calcium current component. Indeed, with the starting condition that [Ca2+]i is equal to [Ca2±]s, the calcium contributed by the calcium current will produce an initial increase of [Ca2+]r (and [Ca21]i) on equilibration. If the pump has been inhibited and the leak is normal the rate of efflux of calcium into the cytoplasm is low. Under this condition [Ca21]i will fall faster than [Ca2+]. This will lead to a faster initial lowering of [Ca2+]i and an apparently faster calcium transient (the slower tail on the transient also implied in this would be more difficult to see). In contrast, if the leak from the SR has been greatly increased there would be a free communication between the SR and cytoplasm and the surface membrane will decrease [Ca2+]i and [Ca2+] equally. The differences between the rate constants of the experimental transients in ryanodine or caffeine on the one hand and in thapsigargin on the other is not as marked as the model would predict. Indeed observations on single cells show little difference (Fig. 8). However, the pooled data (Fig. 9 and Table 1) show that the rate constant of decay of the thapsigargin transient is, indeed, faster than that for caffeine or ryanodine. The sizes are not, however, significantly different. Comparison between caffeine and ryanodine The final point to consider is the difference in the caffeine and ryanodine plots of rate constant vs. magnitude. Whereas the ryanodine data (Fig. 9A) appear similar to the model predictions for increasing the leak, caffeine produces a roughly linear relationship between rate constant and magnitude. One explanation of the caffeine effects is suggested by the fact that caffeine (unlike either thapsigargin or ryanodine) changes the relationship between SR calcium content and Ca2+ release. Specifically, caffeine increases the fraction of the SR calcium content released by the action potential (O'Neill & Eisner, 199). Therefore a concentration of caffeine which produces the same submaximal reduction of the SR calcium content as does ryanodine will decrease the magnitude of the systolic Ca2+ transient less. Since both will affect the rate of decay of the Ca2+ transient similarly, the result will be to change the shape of the relationship between magnitude and rate constant in the direction observed. The curves for caffeine and ryanodine ought, therefore, to be identical if the rate constant of decay were plotted against SR calcium content rather than Ca2+ transient magnitude. This hypothesis for the difference between caffeine and ryanodine can be tested. When caffeine is removed there is a transient undershoot of the magnitude of the

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