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¹ Département de physiologie et biophysique, Université de Sherbrooke Faculté de médicine et des Sciences de la Santé, 3001, 12^e Avenue Nord, Sherbrooke, Québec, Canada J1H5 N4

	Abstract

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C Appendix D Appendix E References

 
Calsequestrin is a large-capacity Ca-binding protein located in the terminal cisternae of sarcoplasmic reticulum (SR) suggesting a role as a buffer of the concentration of free Ca in the SR ([Ca²⁺]_SR) serving to maintain the driving force for SR Ca²⁺ release. Essentially all of the functional studies on calsequestrin to date have been carried out on purified calsequestrin or on disrupted muscle preparations such as terminal cisternae vesicles. To obtain information about calsequestrin's properties during physiological SR Ca²⁺ release, experiments were carried out on frog cut skeletal muscle fibres using two optical methods. One – the EGTA–phenol red method – monitored the content of total Ca in the SR ([Ca_T]_SR) and the other used the low affinity Ca indicator tetramethylmurexide (TMX) to monitor the concentration of free Ca in the SR. Both methods relied on a large concentration of the Ca buffer EGTA (20 mM), in the latter case to greatly reduce the increase in myoplasmic [Ca²⁺] caused by SR Ca²⁺ release thereby almost eliminating the myoplasmic component of the TMX signal. By releasing almost all of the SR Ca, these optical signals provided information about [Ca_T]_SR versus [Ca²⁺]_SR as [Ca²⁺]_SR varied from its resting level ([Ca²⁺]_SR,R) to near zero. Since almost all of the Ca in the SR is bound to calsequestrin, this information closely resembles the binding curve of the Ca–calsequestrin reaction. Calcium binding to calsequestrin was found to be cooperative (estimated Hill coefficient = 2.95) and to have a very high capacity (at the start of Ca²⁺ release, 23 times more Ca was estimated to initiate from calsequestrin as opposed to the pool of free Ca in the SR). The latter result contrasts with an earlier report that only 25% of released Ca²⁺ comes from calsequestrin and 75% comes from the free pool. The value of [Ca²⁺]_SR,R was close to the K_D for calsequestrin, which has a value near 1 mM in in vitro studies. Other evidence indicates that [Ca²⁺]_SR,R is near 1 mM in cut fibres. These results along with the known rapid kinetics of the Ca–calsequestrin binding reaction indicate that calsequestrin's properties are optimized to buffer [Ca²⁺]_SR during rapid, physiological SR Ca²⁺ release. Although the results do not entirely rule out a more active role in the excitation–contraction coupling process, they do indicate that passive buffering of [Ca²⁺]_SR is a very important function of calsequestrin.

(Received 13 December 2006; accepted after revision 28 February 2007; first published online 1 March 2007)
Corresponding author P. C. Pape: Département de physiologie et biophysique, Université de Sherbrooke Faculté de médicine, 3001, 12e Avenue Nord, Sherbrooke, Québec, Canada J1H5 N4.  Email: paul.pape{at}usherbrooke.ca

	Introduction

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C Appendix D Appendix E References

 
Calsequestrin is a high-capacity Ca binding protein located in the terminal cisternae of the sarcoplasmic reticulum (SR) of skeletal muscle (MacLennan & Wong, 1971). One function proposed for calsequestrin is that it rapidly buffers [Ca²⁺] in the sarcoplasmic reticulum (denoted [Ca²⁺]_SR). In this way, local depletion of Ca²⁺ would be avoided and the driving force for Ca²⁺ release maintained. In support of this idea, the in vitro kinetics of the Ca–calsequestrin binding reaction appear to be fast (‘rates of calcium association and dissociation are faster than 1 ms^–1; Prieto et al. 1994) indicating that they would not be rate limiting for physiological SR Ca²⁺ release. Therefore, unless its kinetic properties change significantly in intact muscle, calsequestrin should essentially be in instantaneous equilibrium with [Ca²⁺]_SR during physiological stimulation. The ability of calsequestrin to act as a local buffer should then depend on the amount of calsequestrin, its steady-state binding curve with Ca, and the location on this curve determined by [Ca²⁺]_SR. Essentially all of the information on calsequestrin's binding properties thus far has come from studies with purified calsequestrin or with disrupted preparations, principally terminal cisternae vesicles. The main aim of this article is to evaluate these properties under more physiological conditions during depolarization-induced Ca²⁺ release.

The main experiments in this article involved measurements of two optical signals in response to voltage-clamp stimulation, one signal approximately proportional to total SR Ca content and the other driven by changes in [Ca²⁺]_SR. The concentration of total SR Ca content (denoted [Ca_T]_SR) were obtained from absorbance measurements of phenol red (the first optical signal) with the EGTA–phenol red method (Pape et al. 1995). [Ca²⁺]_SR was monitored with the absorbance indicator-dye tetramethylmurexide (TMX, the second optical signal), an application suggested by the results of Maylie et al. (1987). They described TMX-related absorbance changes (A_TMX) from cut muscle fibres equilibrated with a low concentration of EGTA (0.1 mM) in response to action-potential stimulation. The A_TMX signal had two components, an early transient component consistent with an increase in [Ca²⁺] in the myoplasm followed by a rapid decrease to a somewhat maintained signal of opposite sign to the initial transient component. They proposed that the maintained signal was due to a decrease in [Ca²⁺]_SR. In a subsequent study, measurements were carried out using modified Ca²⁺ indicators which were essentially TMX or a similar dye, murexide, with two charged groups added to prevent their entry into the SR (Hirota et al. 1989). As predicted, the action-potential-generated, dye-related A signals showed a rapid transient component that rapidly decayed to zero – consistent with a myoplasmic Ca²⁺ transient and no subsequent SR component. Due to their low affinities and negligible binding to intracellular components, these indicators have provided the most reliable estimate to date of the magnitude of the myoplasmic Ca²⁺ transient (Hirota et al. 1989; Konishi & Baylor, 1991). In the present study with TMX and 20 mM EGTA in the internal solution, the A_TMX signal was consistent with a decrease in [Ca²⁺]_SR with no apparent myoplasmic component in response to step depolarizations. This and other results indicate that TMX can be used to monitor [Ca²⁺]_SR if myoplasmic [Ca²⁺] is significantly reduced, as it was in this case with 20 mM EGTA. In summary, experiments were carried out with two indicators that monitored [Ca_T]_SR(t) and [Ca²⁺]_SR(t) signals in response to stimulations that released almost all of the Ca in the SR. Since most of the Ca in the SR is expected to be bound to calsequestrin (confirmed in this study), a plot of [Ca_T]_SR versus [Ca²⁺]_SR should closely resemble the binding curve for Ca with calsequestrin ([CaCalsequestrin] versus [Ca²⁺]_SR). Therefore, the main experiments in this article provide information about the buffering properties of calsequestrin when [Ca²⁺]_SR varies from the resting state, [Ca²⁺]_SR,R, to zero. The results indicate significant cooperativity in the binding of Ca to calsequestrin and that [Ca²⁺]_SR,R is near to calsequestrin's K_D. The results also indicated that calsequestrin is the source of almost all of the Ca²⁺ released from the SR at the start of the release process. This is opposite to the conclusion reached by Volpe & Simon (1991) that the free Ca pool in the SR is the main source. An update of the estimate of [Ca²⁺]_SR,R in the study of Maylie et al. (1987) is also provided, taking into account a slow loss of TMX across the surface/T-system membranes (Konishi & Baylor, 1991).

Another problem addressed in this article concerns a possible active role of calsequestrin during excitation–contraction (E–C) coupling. Electron-micrograph studies of Franzini-Armstrong et al. (1987) indicated that calsequestrin molecules are localized near the inner surface of the SR membrane where Ca²⁺ release channels (RyRs) are located, suggesting the possibility of physical contact between the two proteins. Later results indicated that they are, in fact, linked via two intermediary proteins, triadin (Guo & Cambell, 1995) and junctin (Jones et al. 1995). Based in part on this physical link, several researchers have suggested possible functional interactions between calsequestrin and SR Ca²⁺ release channels (e.g. see review of literature in Beard et al. 2005). One of these possible interactions involves an active role of calsequestrin in E–C coupling as proposed by Ikemoto et al. (1991). In their study, Ca²⁺ release from SR vesicles was stimulated by a ‘releasing agent’, polylysine. As in this article, [Ca²⁺]_SR was monitored with TMX in the presence of 20 mM EGTA outside the SR. Their results showed a clear increase in [Ca²⁺]_SR in response to polylysine at concentrations of 1 or 2.5 µg ml^–1. This occurred with almost negligible or low rates of Ca²⁺ release as detected with ⁴⁵Ca flux measurements. At the highest concentration (5 µg ml^–1), the early positive [Ca²⁺]_SR component was not observed, though it would probably have been masked by a much more rapid decrease in [Ca²⁺]_SR in response to Ca²⁺ leaving the SR. Their interpretation was that activation of the ryanodine receptor changes the conformation of the calsequestrin via a mechanical link thereby lowering its affinity and releasing Ca²⁺ from calsequestrin into the terminal cisternae. Such a mechanism would enhance SR Ca²⁺ release by increasing [Ca²⁺]_SR, the presumed driving force for Ca²⁺ release. If such a process also occurs during physiological E–C coupling, small voltage-clamp steps – in analogy to the requirement for low polylysine concentrations – should produce an early positive A_TMX signal. This possibility is evaluated in experiments using a recently completed setup providing a significantly improved signal-to-noise ratio.

	Methods

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C Appendix D Appendix E References

 
Cut fibres from frog (Rana temporaria) leg muscles were mounted in the same apparatus and subjected to essentially the same experimental protocols described in Pape & Carrier (1998). Briefly, frogs were decapitated and double pithed using a protocol approved by the Comité d'éthique de l'expérimentation animale at the Université de Sherbrooke. Fast-twitch fibres from a semitendinosus or ileofibularis muscle were mounted in a double-Vaseline gap chamber (Hille & Campbell, 1976; Irving et al. 1987) designed for both electrical and optical measurements. Fibres were stretched to a sarcomere spacing of 3.5–3.9 µm and maintained at 16–17°C. In all but the experiments described with Fig. 9, the voltage in one end pool (V1) was maintained at –90 mV in the resting state by injecting current (the holding current or I_h) into the other end pool and collecting it in the central pool.

View larger version (20K): [in this window] [in a new window]   Figure 9.  Estimation of the permeability of the SR for TMX Details of this experiment are given in the text. The best fit function shown in D is 0.003825 + 0.0003226 min–1·(t – tsaponin) + 0.01407·exp(–(t – tsaponin)/0.767min, where tsaponin is the time of saponin addition to the central pool. Fibre reference, 623062; fibre diameter, 89.9 µm; TMX added 20 min after saponin treatment of end pools; tsaponin was 52.9 min.

Unless indicated, the end-pool solutions for the voltage-clamp experiments contained (mM): 45 caesium glutamate, 20 EGTA, 6.8 MgSO₄, 5 Cs₂-ATP, 20 Cs₂-creatine phosphate, 5 Cs₃-phospho(enol)pyruvate, 5 3-(N-morpholino)-propanesulphonic acid (Mops), and 1.76 mM Ca. The pH was adjusted to 7.0 with CsOH. The estimated value of [Mg²⁺] was 0.86 mM and that of [Ca²⁺] was 32 nM. Values for [Mg²⁺] and [Ca²⁺] were calculated by iteratively adjusting their values to match the concentrations of total Ca and Mg added to the solution using an excel program similar to that of Fabiato (1988). Values for the affinity constants at 15°C were taken from the literature (Godt & Lindley, 1982 for ATP, creatine phosphate and EGTA; Wold & Ballou, 1957 for phospho(enol)pyruvate; Windhoz et al. 1983 for glutamate).

The zero Ca internal solution used for the bottom two pairs of traces in Fig. 8B had the same composition as that just described except that no Ca was added.

View larger version (15K): [in this window] [in a new window]   Figure 8.  Additional results with low SR Ca contents A shows the best fit values of n versus assumed values of pHR from least-squares fits of [CaT]SR,model to [CaT]SR derived from A signals after the usual 5 min resting period (shown in Fig. 7A) and after the short-term decrease in SR Ca content (shown in Fig. 7B). The symbols above and below the dashed lines were obtained from the A signals in Fig. 7A and B, respectively. See the text for further explanation. In B, the two superimposed voltage traces at the top were from stimulations before and after a long-term depletion in SR Ca content. The 2nd pair of traces (from the top) show the APR(570) and ATMX(480) signals from the earlier stimulation before the Ca-free internal solution was introduced into the end pools. The 3rd pair of traces show the [CaT]SR and best fit [CaT]SR,model signals derived from the corresponding A signals. The 4th and 5th pair of traces are analogous to those shown in the 2nd and 3rd pair of traces, respectively, except they were obtained later in the experiment after a long-term reduction in SR Ca content. The APR(570) signals in the 2nd and 4th pair of traces were scaled by 0.67 and 1.22, respectively, as indicated. These scaling factors were determined by minimizing the sum of squares between the two APR and ATMX signals during the period 50–200 ms after the start of the pulse to –45 mV. See text for more details. Fibre reference, 423021. Values before and after long-term depletion: time after saponin treatment, 76.4 and 130.1 min; time after adding dyes, 51.9 and 105.6 min; holding current, –31.9 and –31.7 nA; ATMX(480)min, –0.00844 and –0.00391; pHR, 7.340 and 7.260; k, 1.096 x 10–4 and 2.065 x 10–4 pH units ms–1; pHmin, –0.2247 and –0.0160; QT, 24.0 and 24.0 mM; [Ca2+]SR,R, 1.12 and 0.25; [CaT]SR,R 15.45 and 1.10 mM.

Compositions are given in Table 1 of Irving et al. (1987) for the relaxing solution used in the experiment of Fig. 9 and the potassium internal and normal Ringer solutions used in the action-potential experiment in Fig. 11A. The normal Ringer external solution was also used in the action-potential experiment of Fig. 11B. Internal solutions containing 8 mM BAPTA in addition to 20 mM EGTA were used in Fig. 11B and C. The caesium internal solution with 8 mM BAPTA used in Fig. 11C had the same composition as the caesium internal solution above except that it contained 33 mM caesium glutamate and 3.32 mM Ca. The estimated values of [Mg²⁺] and [Ca²⁺] were the same as the BAPTA-free caesium internal solutions, 0.86 mM and 32 nM, respectively. The potassium internal solution with 8 mM BAPTA used in Fig. 11B was the same as the caesium internal solution with BAPTA just described except that K replaced Cs throughout.

View larger version (10K): [in this window] [in a new window]   Figure 11.  Evaluation of a possible active coupling mechanism between RyRs and calsequestrin The top trace in A shows an action potential measured under current-clamp conditions and the bottom trace shows the corresponding ATMX signal. B shows similar traces from another experiment except that 8 mM BAPTA was present in the internal solution. C shows the signal averaged voltage and ATMX signals from 4 stimulations of a voltage-clamp experiment with the caesium internal solution containing 8 mM BAPTA. See text for more details. For A: fibre reference, 127061; time after saponin, 184.5 min; time after dye, 121.0 min; fibre diameter, 148.5 µm, holding current, –48.2 nA. For B: fibre reference, 207062; time after saponin, 106.4 min; time after dye, 88.9 min; fibre diameter, 50.0 µm, holding current, –12.4 nA. For C: fibre reference, 327062; time after saponin, 90.2–110.2 min; time after dye, 65.2–85.2 min; fibre diameter, 84.3–85.5 µm; holding current, –112.8 to –121.6 nA.

Optical measurements

All of the results until Fig. 11 in this article were obtained with the optical apparatus for measuring light intensity at three wavelengths, described in Pape & Carrier (1998), with one modification. The beam splitter cube between the last two interference filters (positions F2 and F3 in Fig. 1 of Pape & Carrier, 1998) was replaced with a dichroic mirror which reflected (transmitted) most of the light of wavelength shorter (longer) than 610 nm (model 610DRLP, Omega Optical, Brattleboro, VT, USA) This modification increased the light intensities at these last two positions by about a factor of two.

All of the filters below with 30 nm bandwidths were obtained from Omega Optical and those with 10 nm bandwidths were obtained from Edmund Optics (Barrington, NJ, USA).

The experiment in Fig. 11 was done on a recently completed setup which gave an approximately 4-fold improvement in the signal-to-noise ratio for the active absorbance signals compared with the optical apparatus above. Briefly, this new setup is based on an X95 optical rail (Newport Instruments; Irvine, CA, USA) for gross positioning of optical elements. Fine positioning is achieved with micromanipulator stages, also from Newport Instruments. The setup is very similar to that illustrated in Fig. 1 of Pape & Carrier (1998) except that dichroic mirrors replace the beam splitters and light is sampled at four wavelengths instead of three. Also, light is focused on the fibre with a 40 x water-immersion objective (N.A. 0.55; product no. 140025; Nikon, Japan) and collected with an 80 x ultra working-distance objective (Mitutoyo, M plan Apo SL series, N.A. 0.5; Edmund Scientific, Barrington, NJ, USA) The improvement in the signal-to-noise ratio is mainly attributable to the extra light obtained with this arrangement.

In all experiments, a 690(30) nm interference filter (having a nominal 690 nm centre wavelength and 30 nm bandwidth) was used to monitor the intrinsic absorbance since neither of the two indicator dyes used in this study absorbed in this wavelength band. Intrinsic absorbances at shorter wavelengths – extrapolated from the 690 nm signal – were subtracted from raw absorbance measurements to yield the dye-related resting absorbance (A_D) and the dye-related absorbance change (A_D) in response to stimulation, as described and justified in Irving et al. (1987). As their description applied to measurements with polarized light (our A measurements correspond to their A(1: 1) measurements) and included at least one method not used in our laboratory, the approach adapted is repeated here. This description is also useful for the interpretation of the results in Fig. 9.

The first step for obtaining the value of A_D at wavelength was to calculate the raw absorbance (A_raw) given by

(1)

where I is the intensity of trans-illuminating light at passing through a circular area (or, in the case of Fig. 11, a rectangular area) focused on the centre of the fibre and I_{spot_off} is the intensity at with the fibre moved out of the field of view. The value of I_{spot_off} is determined by linear interpolation between measurements made at times before and after the measurement of I, usually at the start and end of the experiment. There was generally very little change in light intensity, so that the effect of a possible difference in the bracketing I_{spot_off} measurements on A_raw was minor in relation to the intrinsic and dye-related absorbances given below. The next step was to calculate a spot-on corrected absorbance (A_SOC) which is given by

(2)

where

(3)

and where I_{no_dye} is the light intensity measured with no dye at the optical recording site. I_{no_dye} is determined near the start of the experiment with the spot focused on the fibre and either just before or within 2 min of adding dye to the end pools (before dye has had a chance to reach the optical recording site, 550 µm from the end pools). (The I_{spot_off} values in eqns (1) and (3) are for different times, so they do not necessarily cancel when eqns (1) and (3) are substituted into eqn (2). The dye-related absorbance (A_D) is given by

(4)

where the second term on the right-hand side is the spot-on corrected absorbance at a long wavelength (_long) beyond which any dye species present has any detectable absorbance. In the case of this article, _long was 690 nm. It is noted that A_SOC(_long) corrects for changes in intrinsic absorbance that occur following the spot-on measurement. It assumes that there is no wavelength dependence of the change in intrinsic absorbance. Irving et al. (1987) found that there was, in fact, essentially no wavelength dependence for long-term changes in the intrinsic absorbance in 2 of the 3 fibres they studied. The possibility of a wavelength dependence for changes in the intrinsic absorbance is the main uncertainty with the approach adapted, an uncertainty that can account for one aspect of the results in Fig. 9.

From eqn (1), the change in raw absorbance during a stimulation is given by:

(5)

where I is the change in intensity during stimulation. Expanding this in a Taylor series yields:

(6)

Our procedure in the past was to ignore the second and subsequent terms in eqn (6) yielding the approximation

(7)

Equation (7) has been referred to as the differential form (cf. eqn (2) in Irving et al. 1987). As all but one of the results yielded maximum values of |A_raw| of 0.012 or less (see column 3 of Table 2), the differential form would have overestimated the final level by only 1.4% or less (evaluated with eqn (6)). However, one of the |A_raw| signals had a maximum value near 0.03 which would have produced an overestimation of 3.5%. Therefore, eqn (5) was used for results in this article and will also be used in future studies from our laboratory.

(8)

[see their eqn (20)]. As noted above, _long was 690 nm in the case of this article. The value of n was fixed at 1.1, the average value from the nine experiments in Irving et al. (1987; column 6 in their Table 3).

View this table: [in this window] [in a new window]   Table 3.  Results of linear-least-squares best fits of [CaT]SR,model to [CaT]SR

Similar calibrations were carried out for phenol red. The effective extinction coefficients for both the protonated and unprotonated forms of phenol red for the 480(10) nm filter were taken to be 11 000 M^–1cm^–1, the value at the isosbestic wavelength of 480 nm (Lisman & Strong, 1979). As for the 520(10) nm filter in the TMX calibrations, the 480(10) nm filter served as the reference for the other filters. For the unprotonated form of phenol red, the effective extinction coefficient for our 480(30) and 570(30) nm filters were 11 209 and 22 594 M^–1 cm^–1, respectively (denoted _PR(480) and _PR(570) below). For the protonated form, the effective extinction coefficient for our 480(30) and 570(30) nm filters were 9470 and 1647 M^–1 cm^–1, respectively (denoted _HPR(480) and _HPR(570) below).

Phenol red-related and TMX-related A signals

When both TMX and phenol red are present in the internal solution, the dye-related A signals at the two active wavelengths are given by

(9)

and

(10)

where A_TMX and A_PR are the TMX and phenol red-related changes in absorbance, respectively. With the spectral dependence of the TMX and phenol red active signals defined by

(11)

and

(12)

respectively, the solution of eqns (9) and (10) yields that

(13)

and

(14)

The values of and can be calculated from the relationships

(15)

and

(16)

With the effective extinction coefficients above, = –0.4594, = 0.0830 and eqns (13) and (14) become

(17)

and

(18)

It is noted that the A_TMX(480) signal is almost the same as the dye-related active signal with only a small (8%) correction needed. This correction arises because the effective centre wavelength (CWL) of the 480(30) nm filter is somewhat greater than its nominal value of 480 nm, the isosbestic wavelength for phenol red (see above).

Estimation of f_R

It was of interest to compare two methods for estimating the fraction of total TMX in a fibre that is complexed with Ca in the resting state, denoted by f_R and given by

(19)

(subscript R refers to resting and subscript T to the sum of the Ca-free and Ca-bound forms of TMX). With R defined as the ratio of resting absorbance of TMX at wavelength to that at the isosbestic wavelength (R = A()/A(_iso)) or (R = A()÷A(_iso)), it follows (after substituting in Beer's Law, A = cl, and rearranging) that

(20)

where R₀ and R are the values of R with [Ca²⁺] = 0 and , respectively. This method – using resting absorbance values – is the same as that used by Maylie et al. (1987) to estimate f_R.

In response to stimulation, the change in f (f) is given by

(21)

With 20 mM EGTA present in the myoplasm in this study, it was possible to release almost all of the Ca from the SR with a sufficiently long stimulation (denoted fully depleting stimulation or nearly fully depleting stimulation where appropriate). In addition, with TMX being such a low affinity dye and with EGTA buffering myoplasmic [Ca²⁺], there should be essentially no detectable amount of CaTMX in the myoplasm before and after a fully depleting stimulation when the rate of Ca²⁺ release is negligible. If these conditions are met, f should be zero at the end of a fully depleting stimulation and f_R should be given by the relationship

(22)

where R_max is the change in R in response to a fully depleting stimulation. Results in Table 1 do in fact indicate that f_R = –f_max, as described later. This means that one can estimate the resting absorbance due to CaTMX at 480 nm (denoted A_CaTMX,R(480)) from the relationship

(23)

where A_TMX,max(480) is the TMX-related absorbance change at 480 nm in response to a fully depleting stimulation. Values for R(480) and R₀(480) – calculated from the effective extinction coefficients for TMX given above – were 1.398 and 0.509, respectively.

As described later, a first step in this article was to estimate the time courses of the free and total Ca concentrations in the SR ([Ca²⁺]_SR and [Ca_T]_SR, respectively) from the TMX and phenol red signals, respectively. The [Ca²⁺]_SR signal was then used to estimate binding of Ca to calsequestrin and TMX in the SR to give a second estimate of [Ca_T]_SR, denoted [Ca_T]_SR,model. The main aim was to obtain information about calsequestrin's properties by determining the set of model parameters that gave the best fit of [Ca_T]_SR,model to [Ca_T]_SR. This section gives information about this fitting procedure and two methods used to evaluate the ‘goodness of fit’. The first method was the chi-square (²) maximum likelihood estimation. The second method was based on a ‘visual’ approach.

The fitting procedure involved finding the model parameters that minimized the sum of squares of the difference between the [Ca_T]_SR,model and [Ca_T]_SR signals, denoted SSQs and given by the equation

(24)

where N is the number of points and t_i is the time of the ith point. In this and the following functions, the terms y_model and y are substituted for [Ca_T]_SR,model and [Ca_T]_SR, respectively. The related ² statistic is given by

(25)

where is the standard deviation associated with the measurement error. (This form assumes that is independent of [Ca_T]_SR.) The value of was estimated from the baseline points before the first depolarization in a stimulation, i.e. before SR Ca²⁺ release commenced. It was determined with the relationship

(26)

where N_baseline is the number of baseline points. With the assumption of constant , ² is proportional to SSQs so that the least-squares-fitting procedure is the same as minimizing ², the basis of the maximum likelihood estimation (e.g. Chapter 15 in Press et al. 1992). Use of the ² statistic also requires knowledge of the degrees of freedom, , given by

(27)

where M is the number of fitted parameters.

The second approach for assessing the goodness of fit – the ‘visual’ approach – was to evaluate a value indicative of the difference between the two signals, denoted and given by

(28)

In this case, y_max is [Ca_T]_SR,R – the resting total Ca content of the SR – which is the maximum possible value for both the [Ca_T]_SR,model(t) and [Ca_T]_SR(t) signals. The second term in the brackets on the right-hand side subtracts the expected average difference due to measurement noise. As a result, is the average of the absolute values of the differences between the model and data signals above that expected due to measurement noise, expressed as a percentage of their maximum value. This value should semi-quantitatively reflect the visual difference between the [Ca_T]_SR,model and [Ca_T]_SR signals. Such a difference could be due to an inadequate model and/or at least four other reasons discussed in the section on the goodness of fit in Results.

Statistical tests of significance

Sets of results were considered significantly different if the Student's two-tailed t test parameter P was = 0.05.

	Results

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C Appendix D Appendix E References

 
A signals with only TMX present

In order to interpret the A_D signals in the presence of the two indicator dyes (TMX and phenol red) shown later, it was important to confirm the wavelength dependence of the A_TMX signal with only TMX present. Figure 1 shows results obtained 57 min after adding TMX to the end pools. The top trace in panel A shows the change in voltage in the V1 end pool. The bottom three traces show the simultaneously measured A_raw signals at the three wavelengths indicated. Neither TMX nor CaTMX absorb at 690 nm, and the relatively small signal at this wavelength should be due to a change in intrinsic absorbance only. Both the positive A_raw signal at 570 nm and the negative A_raw at 480 nm are indicative of a decrease in [Ca²⁺] (cf. the difference spectrum for TMX in Fig. 4 of Maylie et al. 1987). Figure 1B shows the corresponding A_TMX signals at 570 and 480 nm obtained by subtracting the intrinsic component, determined from the A_raw(690) signal by eqn (8). There are two signals superimposed at 570 nm. The trace labelled with arrows is the A_TMX(480) signal scaled by –0.540. The other trace is the measured A_TMX(570) trace. The scaling factor was obtained from a least-squares fit of the A_TMX(480) to the A_TMX(570) trace. The average of this scaling factor and those obtained from the two other fibres was –0.480 (S.E.M. = 0.032). This factor is not significantly different than the value of –0.4594 predicted from the effective extinction coefficients for the interference filters (see value of given by eqn (15) above). This agreement suggests that the spectral properties of TMX are not significantly altered in vivo – as might occur if TMX bound to intracellular constituents – thereby supporting the idea that the active signal does, in fact, indicate a change in [Ca²⁺]_SR. On the other hand, the scatter in the scaling factor values from the three experiments (–0.54, –0.46 and –0.43) could be due to modest differences in the spectral properties in different fibres or different conditions. Nevertheless, the in vitro value of –0.4594 was used to correct for the TMX component of the A(570) signal in all of the analyses in this article involving the two indicators, TMX and phenol red.

View larger version (10K): [in this window] [in a new window]   Figure 1.  A signals with TMX in response to voltage-clamp stimulations In both panels, the top trace shows the voltage signal. In this and later figures, the values shown above the pulses are the command potentials in mV. A, the bottom three traces show the Araw signals measured at 570, 690 and 480 nm, as indicated. B, the middle trace not indicated by arrows and the bottom trace are the ATMX signals at 570 and 480 nm, respectively. The middle trace indicated by arrows is the ATMX(480) signal scaled as described in the text. Fibre reference 226031; time after saponin treatment, 86 min; time after adding TMX, 68 min; sarcomere length, 3.9 µm; fibre diameter, 94 µm; holding current, –133 nA; concentration of TMX at the optical site, 1.2 mM; fraction of TMX complexed with Ca at rest, 0.117; interval of time between data points, 0.96 ms.

Table 1 compares the two estimates in Methods of f_R, the fraction of TMX bound with Ca in the resting state (eqn (19)) in fibres containing only TMX. Column 2 gives the value of f_R determined from the dye-related resting absorbances at 480 and 520 nm using eqn (20). The average value 0.113 (S.E.M. 0.007) is not significantly different than the average value of 0.13 (S.E.M. 0.012, N = 3) obtained by Maylie et al. (1987) in fibres containing only 0.1 mM EGTA and solutions appropriate for action-potential stimulation. Column 3 gives the value of –f_max estimated with eqn (22). The value of A_TMX,max(480) for this calculation was determined by extrapolation to infinite time of an exponential function fit to the final part of A(480) signal during the last pulse when the SR approaches full depletion. As noted in Methods, –f_max should equal f_R if the part of the A_TMX signal attributed to CaTMX is, in fact, due to CaTMX and not some other source such as spectral changes due to TMX binding to proteins. Since the average value for –f_max in column 3 of 0.107 is not significantly different from that of f_R in column 2 of 0.113, these results add additional support to the idea that TMX is a reliable indicator of [Ca²⁺]_SR. (If the signal had been due to some artefact such as a change in binding to a protein, it is unlikely that all of it would have been converted to the TMX form in response to a fully depleting stimulation.)

Column 4 in Table 1 gives the ratio of –f_max to f_R (column 3 to column 2). The average value close to unity indicates that –f_max can be used to estimate f_R under the conditions of this experiment (20 mM EGTA and a fully depleting stimulation). It may be noted, however, that there was some variability and the ratio was somewhat low in two experiments (0.604 and 0.677). This may be due in part to a small wavelength-dependent change in the resting intrinsic absorbance during the course of an experiment which would affect the estimate of f_R based on resting absorbances, but not –f_max. Therefore, –f_max should provide a more reliable estimate of f_R.

A signals with both TMX and phenol red present

Figure 2 shows signals obtained with both phenol red and TMX in the fibre. The top trace in panel A shows the measured V1 signal and the bottom two signals show dye-related A signals at 570 and 480 nm, as indicated. A feature of particular importance to note for the A_D(570) signal is its reversal of direction shortly after the start of the pulse to –20 mV. As it was not observed in the A_D(480) signal which is almost all due to TMX (since 480 nm is the isosbestic wavelength for phenol red), this feature is an indication of different time courses for the two components of opposite polarities making up the A_D(570) signal, namely A_PR(570) and A_TMX(570). The traces labelled A_TMX(480) and A_PR(570) in Fig. 2B were determined by a linear combination of the A_D(480) and A_D(570) signals in panel A as given by eqns (17) and (18), respectively. The main features to note are that the A_TMX and A_PR signals more or less superimpose at the start and that the A_TMX signal is much more pronounced later during the stimulation protocol. These relationships between the time courses of A_TMX and A_PR were observed in all of the experiments and they are the main experimental finding of this article.

View larger version (9K): [in this window] [in a new window]   Figure 2.  Dye-related A signals with both phenol red and TMX present This figure shows signals obtained from a voltage-clamp stimulation applied 68 min after exchanging the dye-free, end-pool solution with the internal solution containing TMX and phenol red at nominal concentrations of 2 mM and 1 mM, respectively. A, the top trace shows the voltage signal. The middle and bottom traces show the AD signals at 570 and 480 nm, respectively. B shows signals from the same stimulation shown in A. The trace indicated by arrows is the APR(570) signal obtained from the AD(570) and AD(480) signals in A as described in the text. The ATMX(480) signal was scaled by 1.466, the value obtained by a linear-least squares fit up to the start of the pulse to –20 mV. Fibre reference 211021; time after saponin treatment, 95 min; sarcomere length, 3.9 µm; fibre diameter, 85 µm; holding current, –28 nA; interval of time between data points, 1.50 ms.

Essentially all of the A_TMX signal comes from the SR

Although a positive component in the A_TMX(480) signal was not observed in Fig. 2B, such a component could have been present, though hidden by the superimposed and much larger negative A_TMX(480) signal. This section evaluates the likely magnitude of such a hidden positive component. Any myoplasmic component of A_TMX would have been maximal at the peak rate of SR Ca²⁺ release. This peak would have occurred during the pulse to –20 mV at which point [Ca²⁺] in the myoplasm ([Ca²⁺]_myo) should have been significantly less than 2 µM (cf. Fig. 4 in Jong et al. 1995). With [Ca²⁺]_myo of 2 µM, the peak of the myoplasmic A_TMX(480) signal calculated with Beer's Law would be 0.00013 (K_D for TMX = 2.6 mM; fibre diameter = 85 µm; (480) = 14 040 M^–1 cm^–1; ratio of myoplasmic volume to total fibre volume = 0.7; assumed [TMX_T] = 2 mM). This value is less than 5% of the scale bar in Fig. 2A so that the myoplasmic component should have made an almost negligible contribution to the A_TMX(480). Therefore, [CaTMX]_SR should be very nearly linearly related to the A_TMX(480) signal. In the processing of the A_TMX signal that follows, we assume that they are proportional.

Determination and apparent reversal of the pH signal

This section describes how the pH signal was calculated from the A_PR(570) signal. This was done previously in Irving et al. (1989) and Pape et al. (1995) for experiments in which phenol red was the only indicator dye present. Irving et al. (1989) noted that pH is closely approximated by the relationship

(29)

where f_u is the fraction of phenol red in the unprotonated form and A_PR,R(570) is the resting absorbance of phenol red at 570 nm. Since f_u is about 0.1 during rest for the pH of the experiments in this study, the second factor (1 – f_u)^–1) is close to one and it can not change much during a stimulation. Therefore, pH is approximately proportional to A_PR(570). Another important thing to note is that the determination of pH depends on a good estimate of A_PR,R(570). Since the spectra of the four dye species present in these experiments (unprotonated and protonated phenol red and Ca-free and Ca-bound TMX) differ enough, it should be possible to estimate the absorbance related to each species from measurements of resting dye-related absorbances at four or more wavelengths. Despite a significant effort, however, we did not succeed in reliably estimating A_PR,R(570) with this approach when TMX was present. This is because the expected value of A_PR,R(570) is small relative to the value of A_TMX,R(570) for the concentrations of phenol red and TMX species present in the fibres. Appendix A describes the approach adopted to estimate A_PR,R(570). The approach uses the values for resting absorbance at 480 and 570 nm, the final level of the A_TMX(480) signal and an assumed value of resting pH (pH_R).

The A_PR(570) and A_TMX(480) traces in Fig. 3A were obtained in the same way as those shown in Fig. 2B but from a stimulation done 15 min earlier. The signal labelled pH was determined from the A_PR(570) signal as described in the preceding paragraph and in Appendix A. An important feature to note about the pH signal is that it reaches a minimum during the pulse to –20 mV and then starts to increase well before the end of the pulse. This feature was previously observed in experiments with the EGTA–phenol red method indicating that it is not due to the estimation of A_PR(570) with TMX present. (See myoplasmic [Ca_T] traces in Fig. 2 of Pape & Carrier, 1998; Fig. 1 in Pape et al. 2002 and Fig. 1 in Fénelon & Pape, 2002. For this comparison with earlier studies, note that the pH and [Ca_T]_myo signals are linearly related as given by eqn (B2) in this article, [Ca_T]_myo = –/2·pH). One explanation for the reversal of the pH signal (or [Ca_T] signal) during the final pulse is that Ca²⁺ release somehow terminates even though the fibre is still depolarized and that the SR Ca²⁺ pump is removing Ca from the myoplasm. However, the monotonically decreasing A_TMX(480) signal indicates that [CaTMX] in the SR continued to decline up to the end of the final pulse to –20 mV. Another possibility is that there is an alkalization associated with counter-ion movements of protons into the SR during Ca²⁺ release. Results of Pape et al. (1990; their Fig. 5), however, indicate that there should be a relatively short delay (no more than a few milliseconds) between the release of Ca²⁺ and the positive pH signal associated with counter-ion movements. As a result, any positive pH signal due to counter-ion movements would be expected to have approximately the same time course as the negative pH signal due to Ca²⁺ release (see also Pape et al. 1995). Therefore, a simple scaling of the pH signal should provide a fairly good correction for counter-ion movements of protons so that it seems unlikely that counter-ion movements could explain the reversal of the pH signal. These arguments indicate that a process other than Ca²⁺ transport or counter-ion movements across the SR membrane was involved. Another observation (not shown) supporting a mechanism unrelated to the Ca²⁺ release or counter-ion movements is that any reversal of the pH signal tends to disappear during the course of experiments – generally within 2 h of the saponin treatment – even if Ca²⁺ release remains relatively stable. Our hypothesis is that there is some type of active transport of protons out of the myoplasm (either into the SR or out of cell) whose activity depends on the magnitude of the acidification. The next section describes the approach used to account for whatever process might be causing the reversal of the pH signal.

View larger version (12K): [in this window] [in a new window]   Figure 3.  Determination of the pH signal and its correction A, the APR(570) and ATMX(480) signals were obtained as described for Fig. 2B. The ATMX(480) signal was scaled by 1.442. The pH signal was determined from the APR(570) signal as described in the text and in Appendix A. B, the pH signal is the same as that shown in A. The method for determining the –pHlost and pHcorrected signals is described in the text. The lower vertical scale bar on the left is for the A signals and the one on the right is for the pH signals in both panels. The signals in this figure were obtained from the same fibre in Fig. 2, but 15 min earlier. Fibre reference 211021; time after saponin treatment, 80 min; additional information given in the legend of Fig. 2 and in Table 2.

View larger version (21K): [in this window] [in a new window]   Figure 5.  Comparison of measured and modelled [CaT]SR signals A, the voltage and the [Ca2+]SR traces are the same as those shown in Fig. 4A, the latter obtained with the assumption that [Ca2+]SR,R was 0.71 mM. The trace labelled [CaT]SR in the top pair of traces was calculated by scaling the pHcorrected trace in Fig. 3B as described in the text; its scale bar is on the right of the trace. The trace labelled [CaT]SR in the bottom pair of traces is the same trace shown on a somewhat expanded scale. The trace labelled [CaT]SR,model was calculated from the [Ca2+]SR trace as described in the text and Appendix B. B shows the Ca–calsequestrin binding curve used for the determination of [CaT]SR,model in A. The traces in C are the same as the corresponding traces in A except that [Ca2+]SR was from Fig. 4B, which was obtained with the assumption that [Ca2+]SR,R was 3 mM. D, the curve with the sigmoidal shape and labelled ‘KD,CSQ = 1 mM’ is the Ca–calsequestrin binding curve used for the calculation of [CaT]SR,model trace at the bottom of C. The other curve in D, which is labelled ‘KD,CSQ = 2.50 mM’, is the Ca–calsequestrin binding curve associated with the fit in which [Ca2+]SR,R was again fixed at 3 mM, but KD,CSQ was an adjustable parameter; see text for details.

Correction for reversal of pH signal before the end of a fully depleting stimulation

As discussed in the previous section, it appears that there is some unknown process involved in removing protons from the myoplasm causing a change in pH, denoted by pH_lost. We assume that the rate of proton loss is proportional to pH so that

(30)

pH_lost is given by the integral of eqn (30). Figure 3B shows the application of this approach. The pH_lost component starts at zero; it is shifted vertically to show that it can account for the final part of the pH signal. The signal labelled pH_corrected is given by pH + pH_lost. The value of k was adjusted to give a zero slope for the line least-squares-fitted to the pH_corrected signal during the last 600 ms of the pulse to –20 mV. In addition to accounting for the final part of the pH signal, this removal model also mostly corrects for the positive slope of the pH signals after the early short pulses to –45 mV.

As indicated by the non-zero slope in the A_TMX signal at the end of the pulse to –20 mV in Fig. 3A, some SR Ca²⁺ release was apparently still occurring at the end of the pulse. As described later, the value of k was adjusted iteratively to account for this small slope. The zero-slope condition for the pH_corrected signal, however, served as a very good, first approximation.

Although the reversal of the pH signal during the end of the fully depleting pulse was observed in earlier studies with the EGTA–phenol red method (see above), taking it into account with the approach described in this section should not change any of the conclusions reached in earlier studies. This correction procedure is more important in this case since it partially accounts for the difference in the time courses of the A_TMX and A_PR signals.

Summary of fibre properties and dye-related information from six experiments

Table 2 gives information about the six fibres used in following analyses. Column 1 gives the fibre reference. Column 2 gives the time after saponin treatment for permeabilizing the fibre membranes in the end pools. The restricted time period of 71–80 min was to limit possible differences in fibre condition associated with the time of the experiment. The period also allowed enough time for dye to diffuse from the end pools to the optical recording site at the centre of the fibre. Column 3 gives the final level of the A_TMX(480) signal obtained by extrapo