The relaxation rate of fast skeletal muscles at the end of tetanic stimulation critically depends on tetanus duration. Rate is maximal after a very short tetanus (< 0.2 s) but is rapidly reduced as tetanus duration is prolonged to 2–3 s, while maximal isometric tension remains unaffected. This early fast decline of relaxation rate has been thoroughly studied in frog muscles but is also present in mouse muscles. It is to be distinguished from further slowing of relaxation, which appears as tetanization is prolonged, and is accompanied by force decline or ‘fatigue’, with numerous underlying biochemical changes (acidosis, increased concentration of Pi and lactate; Westerblad & Allen, 1994).
Fast skeletal muscles from lower vertebrates and from small mammals contain high concentrations (∼0.5 mm) of the cytosolic Ca2+-Mg2+ binding protein parvalbumin (PV) which presents a ∼104 higher affinity for Ca2+ over Mg2+. It has been estimated that, at rest, parvalbumin is essentially in the form of the Mg-PV complex, given the values of cytosolic [Ca2+] and [Mg2+] (Gillis et al. 1982; Maughan & Recchia, 1985). During stimulation, when the cytosolic Ca2+ concentration steeply increases, Ca2+ binding to PV is thought to occur progressively. However, as shown by computer simulation, the formation of the Ca-PV complex is limited by two conditions: (1) the Ca2+ binding rate to PV cannot occur faster than the much slower dissociation of Mg2+ from PV and (2) the Ca2+ binding capacity is limited by the PV concentration (Gillis et al. 1982). It has been proposed that the early slowing of relaxation, as tetanus duration increases, reflects the progressive saturation of PV by Ca2+ and that this saturation is rate limited by the kinetics of the Ca2+-Mg2+ exchange (Gillis et al. 1982; Woledge et al. 1985; Cannell, 1986). Considerable experimental evidence supports this saturation model in frog (Hou et al. 1991; Westerblad & Allen, 1996) and in rat (Garcia & Schneider, 1993; Carroll et al. 1997). Indeed, in frog muscles, the rate constants of relaxation slowing and of the Ca2+-Mg2+ exchange are remarkably similar, have the same temperature dependence and the resulting increase of [Mg2+]i occurs with the expected magnitude (Hou et al. 1991). For reviews of PV in skeletal muscle, see Gillis (1985) and Rall (1996).
This proposed role of PV in tetanus relaxation has been challenged in the case of mammalian muscles (Westerblad & Allen, 1994). The slowing of relaxation has been ascribed either to a reduced rate of Ca2+ dissociation from troponin or to a slowed cross-bridge turnover. PV loading by Ca2+ during tetanic contraction was not disputed but was seen as a non-causal, purely concomitant event, because the authors did not observe a correlation between the slowing of relaxation and the initial decline of [Ca2+]i in the flexor digitorum brevis (FDB) muscle of the mouse. In a more recent study on the rat FDB, however, a class of fibres was identified where the initial decline of [Ca2+]i at the end of the tetanus was markedly reduced as tetanus duration was increased (Carroll et al. 1997).
Recently, we developed a mouse strain where the parvalbumin gene had been knocked out (Schwaller et al. 1999) and reported a decrease of the relaxation rate of the twitch in vivo. Tetanus relaxation, however, was not investigated. PV-free muscles offer a unique opportunity to check if PV saturation does play an important role in the slowing of relaxation with increased tetanus duration.
We report here that, in two different fast muscles of PV-deficient mice, the relaxation rate was slow and unaffected by tetanus duration in the range of 0.2 to 2–3 s, while normal muscles showed a marked decrease. This direct comparison brings new evidence which strongly supports the role of PV saturation in slowing the relaxation rate of fast skeletal muscles in mammals. Moreover, the comparison also suggests that diffusion of Ca2+ from myofibrils to the sarcoplasmic reticulum could be facilitated by formation of the Ca-PV complex. A slowing of the relaxation rate for the longest duration of tetani occurred in both strains, thus was unrelated to the presence of parvalbumin.
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In this paper, we report how the presence of parvalbumin, a cytosolic Ca2+ binding protein, affects the rate of relaxation in muscles submitted to tetanus stimulations of increasing duration. The study is based on the comparison of muscles (EDL and FDB) coming from either normal (wild-type) mice, thus with a high parvalbumin content, or from genetically modified mice where the parvalbumin gene had been inactivated. This modification does not significantly alter the fast phenotype of the muscles. The major determinants of the rate of relaxation, MHC composition, cross-bridge kinetics and Ca2+ pumping rate by the SR, were all found to be unaffected by the inactivation of the parvalbumin gene. The comparison of WT versus PVKO thus offered far better conditions to study the role of parvalbumin in muscle relaxation than by comparing muscles in which different parvalbumin contents occur together with different myosin isoform compositions, e.g. the comparison of EDL versus soleus.
We first confirmed previous studies that in two mouse muscles, namely EDL and FDB, increased tetanus duration slowed down the rate of relaxation until an approximately constant value was obtained (Berquin & Lebacq, 1992; Westerblad & Allen, 1994). Similar results have been observed in fast frog muscles (Hou et al. 1991). Here a stable value for relaxation was obtained after 1.6 s of tetanic stimulation (125 Hz) of the EDL, and somewhat earlier (∼1 s) in FDB. It is remarkable that while the relaxation process is clearly slower in FDB than in EDL (due to different myosin isoform composition), the effect on relaxation with increasing tetanus duration concerned essentially the same first 50 ms period after the last stimulus, affecting the t20–t5 interval in EDL and mainly the t5–t0 interval in FDB.
In contrast to normal muscles, parvalbumin-deficient muscles (EDL and FDB) display a slow relaxation rate, even after the shortest tetanus duration studied, and this rate remained essentially constant over the duration range where slowing of relaxation was observed in normal muscles. For tetanus duration longer than 3 s, relaxation rate and isometric tension (not shown) slowly decreased in a similar way, in EDL from both WT and PVKO mice (Fig. 5A). This late effect on relaxation was thus unrelated to the parvalbumin presence and probably results from other, yet unidentified, effects which, according to Berquin & Lebacq (1992), become significant after 2 s (see also Westerblad & Allen, 1994).
The present results fully support, at least qualitatively, the saturation model where, as tetanus duration is prolonged, progressive Ca2+ binding to parvalbumin diminishes its ability to contribute to Ca2+ removal from the cytosol and thus to promote fast relaxation. The simplest form of the PV saturation model supposes that the rate constant of relaxation slowing cannot be faster than the rate constant of Mg2+ dissociation from PV (as subsequent Ca2+ binding is very fast). As the rate constant of Mg2+ dissociation has not been determined for mouse PV, this hypothesis could not be tested in this study, but in frog muscles, Rall and his collaborators (Hou et al. 1991, 1992) have shown that, at 0°C, the rate constants of relaxation slowing and of Mg2+ dissociation from PV were almost identical (1.18 vs. 0.93 s−1, respectively). At 10°C however, some differences seemed to appear: 2.96 vs. 1.76 s−1; thus, in frog, at higher temperatures, the slowing of relaxation appeared to advance with a faster rate than the PV saturation. Most probably, at a higher temperature, the effect of tetanus duration on the relaxation rate is more complex: parvalbumin saturation will depend not only on the effect of temperature on the Mg2+ dissociation constant, but also on the rate at which cytosolic Ca2+ is actively removed by the SR, together with the contribution of other factor(s) with a high Q10 (H+ and Pi accumulation, change of the free energy available from ATP) which tends to slow down relaxation.
This emphasizes the importance of comparing WT versus PVKO, by a point-to-point subtraction, which allows us to isolate the specific effect of parvalbumin, in otherwise identical experimental conditions, information that previous studies were not able to provide. With this approach, it is assumed that the rate constant of the relaxation slowing is an indirect measurement of the rate-limiting reaction in parvalbumin saturation i.e. the rate constant of Mg2+ dissociation. Here, for the EDL (20°C), this was calculated to be 1.10 s−1 (see Fig. 5B). Direct measurements of the rate constant of Mg2+ dissociation for frog parvalbumin is around 3 s−1 at 20°C (Hou et al. 1992), but no value for mouse parvalbumin is available so far.
The tetanus duration necessary to eliminate the contribution of parvalbumin to relaxation is expected to increase with the PV concentration. This duration was about 1 s in FDB and 1.5 s in EDL, in agreement with the fact that the average parvalbumin content of EDL muscle was about 1.4 times higher. Similarly, the initial fast removal of Ca2+ levelled off after 0.5 s of stimulation in the rat FDB (Carroll et al. 1997) in accordance with the fact that the PV content of rat fast muscles is about one-half of that of the mouse (Heizmann et al. 1982).
The recovery protocol is the counterpart of the saturation protocol. Progressive dissociation of the PV-Ca complex as Ca2+ is re-accumulated actively in the SR during the recovery interval, regenerates the pool of the PV-Mg complex and therefore allows fast relaxation again. Thus the recovery kinetics depend both on the rate constant of Ca2+ dissociation from PV and on the turnover rate of the Ca2+-ATPase of the SR. However, during the recovery intervals, other effects of tetanic stimulation are also progressively reversed and this too may contribute to the recovery of the original fast relaxation. Here again, the point-to-point subtraction of PVKO results from those of WT allows us to determine the specific effect of PV recovery on the return to a fast relaxation (Fig. 7B). This procedure yielded a rate constant of 0.05 s−1. This value is close to the rate constant of 0.12 s−1 calculated for the recovery of the 1/(t20–t5), in frog muscles at 0°C (Hou et al. 1991). This suggests that Ca2+ dissociation from mouse PV is either genuinely slower or shows only a small temperature dependence.
The WT versus PVKO comparisons (Fig. 5B and D) have revealed an effect of parvalbumin on relaxation which was not expected from the ‘saturation-recovery model’. We observed that in all conditions, the relaxation rates of muscles from PVKO were always slower than from WT. Relaxation rates of WT and PVKO did not merge, even after long tetani when PV was supposed to be Ca2+-saturated. This suggests that calcium removal from the cytosol was accelerated by the mere presence of parvalbumin. We previously proposed that parvalbumin could act as a ‘shuttle’, transporting calcium from myofibrils to the sarcoplasmic reticulum (Gillis & Gerday, 1977; Gillis et al. 1979), a model inspired by the role of myoglobin in accelerating oxygen diffusion from capillaries to muscle mitochondria (Wittenberg, 1970). Parvalbumin was seen dynamically as a diffusible Ca2+ buffer ‘commuting’ between two immobile Ca2+-binding sites: troponin C on myofibrils and the Ca2+-ATPase of the sarcoplasmic reticulum (calcium uptake within the latter imposing the direction of the calcium flux). The kinetics of calcium traffic in situations involving both diffusible and immobile calcium buffers or binding sites have been studied by computer simulations to mimic the intracellular [Ca2+] response to a short Ca2+ pulse (Nowycky & Pinter, 1993). It turned out that, in the absence of diffusible buffers, the presence of fixed Ca2+ binding sites greatly retards calcium diffusion and that, once the Ca2+ pulse is over, these binding sites act as a source of calcium which prolongs the time when Ca2+ is elevated in their close surroundings. On the contrary, the presence of competing diffusible buffers speeds up calcium diffusion (in a bound state). Similar conclusions were reached after modelling the facilitated diffusion of calcium by the intestinal calcium binding protein in aiding calcium entry at the luminal side and calcium exit at the serosal side of enterocytes (Kretsinger et al. 1982). We thus propose that the increase of relaxation rate in the presence of parvalbumin, irrespective of tetanus duration, reflects its effect in speeding up calcium traffic between myofibrils and the SR, an effect which may be further enhanced if parvalbumin interacts with the SR and stimulates calcium uptake as proposed by Ushio & Watabe (1994). Most probably, such calcium traffic, in a parvalbumin-bound state, would largely escape detection by the usual calcium indicators and it would be rate limited by the value of the diffusion coefficient of parvalbumin. Indeed, direct measurements of the diffusion coefficient of 45Ca2+ injected into frog fibres (thus containing PV) (Kushmerick & Podolsky, 1969) and of parvalbumin are identical (Maughan & Godt, 1999).
In summary, the comparison between parvalbumin-deficient muscles and the corresponding normal, parvalbumin-containing muscles has demonstrated the specific contribution of parvalbumin in accelerating the rate of tetanus relaxation of fast mouse muscles. This contribution seems adequately described by the combination of the ‘saturation-recovery model’ together with the ‘shuttle model’. The physiological advantage conferred by an elevated parvalbumin content is to provide very fast relaxation for very short bursts of activity.