• We investigated the relationship between the action potential, Ca²⁺ and phasic force in intact guinea-pig ureter, following physiological activation.
• The action potential elicited a Ca²⁺ transient consisting of three components: a fast increment, associated with the first action potential spike, a slower increment, associated with subsequent spikes and the initial part of the plateau component, and a steady-state phase associated with the plateau.
• Prolongation of the plateau, by agonists, prolonged the third component of the Ca²⁺ transient and increased force amplitude and duration.
• The force-Ca²⁺ relationship during phasic contractions showed hysteresis; more force was produced as Ca²⁺ declined than when it rose. Paired pulse stimuli suggested that the delay between Ca²⁺ and force was not due to mechanical properties. Wortmannin, which has been shown to selectively inhibit force and myosin light chain (MLC) phosphorylation in the guinea-pig ureter, did not affect electrical activity or Ca²⁺ but significantly increased the delay, suggesting that myosin phosphorylation is a major contributor to it.
• Prolongation of the duration of the [Ca²⁺]_i transient, at unchanged amplitude, increased force. The rise of [Ca²⁺]_i did not limit the rate of contraction. Slowing of the rate of [Ca²⁺]_i rise abolished the hysteresis between Ca²⁺ and force.
• Cooling reduced force, increased the delay and hysteresis between Ca²⁺ and force, but did not affect the rate of rise of Ca²⁺. The reduction in force could be compensated, by increasing the duration of the Ca²⁺ transient.
• We suggest that in vivo, steady-state force-Ca²⁺ relationships are not applicable in phasic smooth muscles. Furthermore, agonists increase force mainly by prolonging the action potential, which increases the duration of the [Ca²⁺] signal.

The second objective was to determine the relationship between the Ca²⁺ signal and force production in the ureter, as clearly an accurate determination of this relationship is essential for the understanding of excitation-contraction coupling. Permeabilised smooth muscle preparations have been useful in studying the steady-state force-Ca²⁺ relationship, as the environment around the myofilaments can be controlled (Nishimura et al. 1988; Kitazawa et al. 1989; Smith & Crichton, 1993). It has, however, been noted that the sensitivity of the myofilaments to [Ca²⁺]_i may be decreased (Smith & Crichton, 1993). There therefore remains a concern that the force-Ca²⁺ relationship has been disturbed and that study in intact muscles would be advantageous. There have been studies of the steady-state (tonic) force-Ca²⁺ relationship in intact smooth muscles (DeFoe & Morgan, 1985; Himpens et al. 1988; Himpens & Casteels, 1990). However, it was reported that during prolonged stimulation, the Ca²⁺ sensitivity of the contractile machinery could be altered (Himpens et al. 1988; Boland et al. 1992). In addition, the Ca²⁺ transients accompanying phasic contractions may be so brief that the force and [Ca²⁺]_i changes cannot be described by a steady-state relationship. In single smooth muscle cells the force-Ca²⁺ relationship displayed a strong hysteresis, indicating no equilibrium between the rapidly changing [Ca²⁺]_i and force (Yagi et al. 1988). Thus it is not clear that findings from tonic smooth muscles can be applied to phasic ones. We have therefore measured and manipulated the force and Ca²⁺ in intact ureter following physiological stimulation to determine their relationship.

In both tonic and phasic smooth muscles there is a considerable latency (300–500 ms) between stimulation or rise of [Ca²⁺]_i and the onset of force development. This delay is partially attributed to the mechanical compliance in series with the contractile apparatus (Singer & Murphy, 1987; Horiuti et al. 1989; Zimmermann et al. 1995), and also to pre-phosphorylation steps linking [Ca²⁺]_i rise to myosin light chain phosphorylation, i.e. recruitment of, and binding to, calmodulin, and attachment of Ca²⁺-calmodulin to myosin light chain kinase (MLCK) followed by isomerisation and activation (Miller-Hance et al. 1988; Zimmermann et al. 1995; Stull et al. 1997). As phasic muscles generate relatively fast and short-lasting Ca²⁺ transients, these pre-phosphorylation delays may be expected to have a large influence on the force-Ca²⁺ relationship. Thus in order to increase our understanding of the mechanisms involved, we have used altered temperature to determine the temperature-sensitive mechanisms operating in excitation-contraction coupling and wortmannin to inhibit MLCK and myosin light chain phosphorylation, and assessed their effects on the delay and force-Ca²⁺ relationship in the ureter.

We find that the rising phase of the Ca²⁺ transient is mostly associated with the generation of the spike component of the action potential while the plateau component mainly controls the duration of the Ca²⁺ transient. The major mechanism modulating the amplitude of the phasic contraction during stimulation by agonists is an increase in the duration of the Ca²⁺ transient at its peak level. This in turn is controlled by the duration of the plateau component of the action potential. This mechanism is effective because under control conditions there is no steady state between the Ca²⁺ signal and the mechanisms activating force.

Guinea-pigs (~300 g) were anaesthetised with CO₂ and killed by cervical dislocation. The ureters were dissected, cleared of fat and cut into strips 4–5 mm in length. Tissues were rinsed and placed in a 200 μl bath on the stage of an inverted Nikon microscope. One end of the tissue was fixed and the other end attached to a force transducer with a self-resonant frequency of 75–100 Hz, and an overall compliance of 1 μm mN⁻¹. The maximal force that could be developed by the ureteric preparations was in the range of 2–3 mN. Care was taken to produce minimal damage when securing the tissue. We found that using silk knots or aluminium foil clips as muscle end attachments produced no difference in the temporal characteristics of the force development, but deliberate crushing of the ends of the preparation increased the compliance. At the beginning of the experiments the length at which steady passive force was maintained at 1–2 % of the maximal isometric force was determined, and taken as a measure of L₀ (resting length). Normally at this length the preparations showed maximal force responses. In the organ bath experiments the tissue was stimulated by silver electrodes, 3–5 V (duration 50–100 ms; Burdyga et al. 1995), and superfused with oxygenated, buffered Krebs solution (pH 7.4), of the following composition (mM): NaCl, 154; KCl, 5.9; CaCl₂, 2; MgSO₄, 1.2; glucose, 11.5; Hepes, 11. When K⁺ was increased up to 140 mM, this was done by isosmotically substituting K⁺ for Na⁺. Na⁺-free solutions were made by replacement of Na⁺ with Tris. Na⁺-loading of tissues was achieved by exposing the ureter to ouabain (0.1 mM) for 60 min (Aickin et al. 1984; Lamont et al. 1998). Histamine (10 μM), carbachol (100 μM) and tetraethylammonium (TEA, 5 mM) were used in some experiments. In other experiments, detailed in the text, single cells were studied. These were obtained by enzymatic digestion of the ureter as described elsewhere (Smith et al. 1998). Experiments were carried out at 34–36°C, unless stated otherwise. When the temperature was changed this was usually done by altering the temperature of the superfusate. For one set of data (Fig. 11), rapid changes were required. These were achieved by rapidly injecting a bolus of solution via a porthole in the side of the tissue bath. The temperature in the bath was monitored throughout via a thermister tip, positioned in the bath. Chemicals were from Sigma, unless otherwise mentioned.

Figure 11 The effect of a temperature jump on force

For [Ca²⁺]_i measurements, tissues were loaded with 15 μM and single cells with 5 μM of the membrane-permeant form of indo-1 (Calbiochem), for 2–3 h and 15–30 min, respectively, at room temperature (see Burdyga et al. 1996 for details). These conditions were determined in preliminary experiments to provide the best signal-to-noise Ca²⁺ records, without slowing Ca²⁺ changes, i.e. no significant Ca²⁺ buffering occurred. In addition, as reported previously (Burdyga et al. 1995), no perturbation of the force signal was produced by indo-1 loading, as judged by identical force records obtained before and after loading. The tissue was excited at 340 nm and the fluorescence emission signals at 400 and 500 nm recorded at 100 Hz. The ratio of these signals (F₄₀₀:F₅₀₀) provides a measure of [Ca²⁺]_i. Due to the well-recognised difficulties, we did not calibrate our Ca²⁺ signals in the majority of experiments. In some experiments (n = 15), however, an in situ calibration was performed, as described by Himpens et al. (1988). This was to verify that the indo-1 signals were not saturated, that there was a linear relationship between indo-1 and [Ca²⁺] over the experimental range encountered, and that there was a close match between [Ca²⁺] vs. time and indo-1 ratio vs. time. Briefly, after increasing pH to 8.6 in control solution, a Ca²⁺-free, pH 8.6 solution was applied, which contained 50 μM ionomycin. This was normally associated with a transient increase in [Ca²⁺]_i, which was followed by the decline of the two emission signals to their minimum levels (R_min). Immediately after determining R_min the solution was replaced by Na⁺-free, high-K⁺ (150 mM) solution with 10 mM Ca²⁺ and the maximum fluorescence (R_max) determined (Fig. 1). When the fluorescence reached steady state, 10 mM Mn²⁺ was applied to the tissue to quench fluorescence and measure the background fluorescence for both wavelengths. These values were subtracted from the raw changes and the ratio of emission signals at 400 and 500 nm obtained (Fig. 1B). The [Ca²⁺]_i was calculated from the ratio (F₄₀₀/F₅₀₀) according to the formula of Grynkiewicz et al. (1985):

Figure 1 Calcium changes in intact ureter

The delay (t_d), i.e. time between the rise in [Ca²⁺]_i and the onset of the force development, was measured by fitting a line to the steepest portion of the Ca²⁺ transient and force traces and t_d was the time between the baseline intercepts of these two lines (Fig. 2).

Figure 2 The relationship between force and Ca2+ in ureter smooth muscle

Values are given as means ±s.e.m., and n is the number of animals or cells. Significant differences were tested for using Student's t test.

Before examining the relationship between action potentials, force and Ca²⁺, it is necessary to show that these signals are being recorded from the same regions of the ureter. We choose the guinea-pig ureter because it is a thin preparation that loads evenly with fluorescence indicators, and can be uniformly excited by action potentials (Shuba, 1981; Aickin et al. 1984; Burdyga et al. 1995). The Ca²⁺ signals gave excellent correspondence with the force measurement throughout the strip. However, given the importance of this point to the data, we compared the Ca²⁺ transient recorded in our multicellular preparation with those from single isolated cells. The time course, shape and kinetics of the Ca²⁺ transient obtained from the multicellular and single cell preparations were identical (Fig. 2A). We also simultaneously recorded electrical activity, Ca²⁺ and force, using a combination of the double-sucrose gap method and Ca²⁺ fluorimetry (Burdyga & Wray, 1997). We found a close correlation between the temporal characteristics of the action potential, recorded from the whole portion of the ureter in the test gap (2 mm in width which is less than the 2.5 mm space constant for this muscle) and the Ca²⁺ transient (see Fig. 2B). Thus we are confident that the methods are in place to study the relationship between force, [Ca²⁺] and electrical activity.

The Ca²⁺ signal associated with the normal action potential was found to have three distinct phases, which are shown in more detail in Fig. 3A. There was an initial fast increment of Ca²⁺, which peaked within 40–60 ms and was associated with the upstroke of the first spike of the action potential (labelled i on Fig. 3A). This rapid increment of Ca²⁺ was followed by a much slower Ca²⁺ increase, which lasted for 200–300 ms (ii on Fig. 3A), and was associated with the generation of the subsequent spikes and plateau component of the action potential. This was followed by a third phase of maintenance of the Ca²⁺ signal at its peak level, which was associated with the generation of the plateau component of the action potential (iii on Fig. 3A). The duration of this steady-state component of the Ca²⁺ signal was exclusively dependent on the duration of the plateau component of the action potential. This is well illustrated in Fig. 4, which shows the action potential and concomitant Ca²⁺ signal recorded in the presence of TEA, histamine and 0 Na⁺ solution (described below).

Figure 3 The time course of intracellular Ca2+ changes

Figure 4 Modulation of the ureteric action potential

Three distinct phases of the Ca²⁺ transient were also observed in single cells (n = 4) stimulated by long depolarising steps (from −80 to 0 mV) under voltage clamp conditions (Fig. 3B). The Ca²⁺ transient started to rise at a time when I_Ca had already reached its peak level. The first increment of Ca²⁺ rise was, again, always fast (time to peak, 40–50 ms) and reached its peak at a time when I_Ca had fallen to 70–80 % of its peak (i on Fig. 3B). This Ca²⁺ rise was followed by a second phase, which was slower than the first increment and occurred as I_Ca declined from 70–80 % to 40–50 % of its peak level (ii on Fig. 3B). This second phase could last 70–200 ms. A third phase, when the Ca²⁺ transient was at its steady state, was associated with a further decline in I_Ca which was approaching steady state (iii on Fig. 3B).

When the ureter muscle was placed in 0 Na⁺ solution, the plateau-type action potentials were converted into single spikes and little or no plateau (Fig. 4C, typical of 5 others). The spikes were associated with the generation of Ca²⁺ transients that also had a simple spike-like configuration, with a time to peak of 40–60 ms. These Ca²⁺ transients lasted for 30–50 ms and quickly decayed in a monoexponential manner (Fig. 4C). The amplitude of the Ca²⁺ transient associated with the single spike was 50–70 % (n = 6) of the normal Ca²⁺ transient induced by generation of the normal action potential (Fig. 4C).

Thus these data clearly show that both the spike and plateau components of the action potential are contributing to the generation of the Ca²⁺ signal and that the rising phase of the Ca²⁺ signal is associated mainly with the spike component. The plateau component of the action potential is mainly associated with the maintenance of the Ca²⁺ signal at its peak level.

The above data clearly showed a delay between the rise in [Ca²⁺]_i and the onset of force development. A useful approach to study the relationship between [Ca²⁺]_i and force, is to plot force against Ca²⁺, i.e. a phase-plane plot (Ashley et al. 1985; Yagi et al. 1988). A hysteresis between the contraction and relaxation limbs of the plot implies that [Ca²⁺]_i is not in equilibrium with myofilament force production when peak [Ca²⁺]_i is achieved. In contrast, a common trajectory for the contraction and relaxation limbs, implies that there is equilibrium between [Ca²⁺]_i and force.

Figure 2E shows a phase-plane plot of the force and Ca²⁺ changes during the contractions illustrated in Fig. 2B. For each contraction the phase-plane diagram forms an anti-clockwise loop, with force development shown by the up arrows. During contraction the force at any given [Ca²⁺]_i is less than during the relaxation phase. This hysteresis suggests that, at least during the rising phase of a normal phasic contraction, [Ca²⁺]_i and force do not reach steady state.

Figure 4A and B shows typical changes in the parameters of the action potential and force during TEA and histamine stimulation. It can be seen that in both cases the duration of the plateau component of the action potential was increased, along with the duration of the Ca²⁺ transient at its peak level. The amplitude and duration of the phasic contractions were also increased. TEA increased the duration of the Ca²⁺ transient 5- to 9-fold (Fig. 4A) in all twelve preparations studied. The contractions were also greatly prolonged, 5- to 6-fold. The amplitude of the contractions was always increased (1.58 ± 0.12 times). This occurred despite little (n = 5) or no (n = 7) change in the amplitude of the Ca²⁺ transient. It can be seen that, in the presence of TEA, both [Ca²⁺]_i and force reached steady state. The mean times for [Ca²⁺]_i and force to reach steady state were 0.83 ± 0.17 and 3.34 ± 0.4 s, respectively. The phase-plane plots (Fig. 4D) showed that under these conditions much force developed at a time when there was little or no change in the amplitude of the Ca²⁺ transient; 62 ± 5 % of the force development occurred at a time when no further change in the amplitude of [Ca²⁺]_i occurred.

Histamine and carbachol also potentiated force by increasing the duration of the Ca²⁺ transient at its peak level. Histamine increased the duration of the plateau component 3–12 times and this was associated with a slight or no increase in the amplitude, but a 3–12 times increase in the duration of the Ca²⁺ transient (n = 7, Fig. 4B). The amplitude of force in the presence of histamine increased 1.6–2.3 times. As in the case of TEA, the phase-plane diagram showed that most of the force development, in the presence of histamine, occurred at a time when Ca²⁺ remained at its peak level (Fig. 4E). Carbachol also potentiated force (1.4–1.7 times, n = 5), mostly by increasing the duration of the Ca²⁺ transient at its peak level 1.4–2.2 times, which was associated with the 1.4–2.1 times increase in the duration of the plateau component of the action potential (data not shown).

These data suggest (i) that the amplitude of contraction can be altered at unchanged [Ca²⁺]_i, if the duration of the [Ca²⁺]_i signal is altered and (ii) that the longer duration of the [Ca²⁺]_i signal is allowing the myofilaments to come into equilibrium with the peak level of [Ca²⁺]_i, and hence more force is obtained.

When the ureter was treated by experimental manoeuvres, which shortened the duration of the plateau component of the action potential, this was associated with a decrease not only in the duration but also in the amplitude of the Ca²⁺ signal. This is illustrated in Fig. 4C, which shows the effect of Na⁺-free solution, which eliminates the plateau component of the action potential in the guinea-pig ureter (Shuba, 1977). As discussed above, it can be seen that the amplitude and duration of the Ca²⁺ transient associated with the single spike were significantly smaller in comparison to control Ca²⁺ signals, and were associated with a significant decrease in the amplitude of the force response. This can also be seen in the phase-plane plot (Fig. 4F). Thus these data clearly indicate that, in the guinea-pig ureter, modulation of the duration of the Ca²⁺ transient, which is controlled by the duration of the plateau component of the action potential, is playing a key role in the modulation of the amplitude of the phasic contraction.

Figure 5 Effect of compliance

In order to investigate this important point, Ca²⁺ transients and contractions were evoked by paired stimuli. The interval between the stimuli was adjusted so that the second pulse could be applied at a time when the muscle had already developed maximal force (Fig. 5B, typical of 3). One could expect that during the development of the first contraction the passive elements had already been substantially stretched and the contribution of the SEC to the delay of the second contraction should therefore be significantly less. However, the delays between the rise in [Ca²⁺]_i and onset of force development of the first and secondary force developments were practically the same, as can be seen in the normalised and superimposed data (Fig. 5D). These data suggest that the visco-elastic elements contribute little to the delay between the [Ca²⁺]_i rise and force development in the ureter and, furthermore, that they cannot explain the hysteresis between force and Ca²⁺. Figure 5B also showed that the amplitude of the second Ca²⁺ transient (b) was practically the same as that of the first transient (a). However, paired stimuli always evoked larger contractions than a single stimulus. Thus an increase in the duration of [Ca²⁺]_i, at unchanged amplitude, was associated with increased force.

Figure 6A shows that 50 % Na⁺ reduction produced a slow and small rise in [Ca²⁺]_i, which was associated with a small and slow development of force (n = 3). When the tissue was activated by Na⁺-free solution, the Ca²⁺ transient rose faster and reached higher levels. This was associated with a faster rate and larger amplitude of force development (n = 6). Figure 6B illustrates changes in force and [Ca²⁺]_i obtained during stimulation of the Na⁺-loaded ureter with 50 % Na⁺ or 0 Na⁺ solutions, normalised to force and [Ca²⁺]_i obtained during normal phasic contraction, produced by an action potential.

Figure 6 The effect of altering Ca2+ kinetics

The rate of rise in [Ca²⁺]_i was 16–20 times slower with 0 Na⁺ solution (n = 6) and 60–110 times slower with 50 % Na⁺ solution (n = 3) than that during normal phasic contraction (ii, iii and i, respectively, in Fig. 6B). The ratios of the maximal normalised rate of force and Ca²⁺ rise during Na⁺-free contractions were close to 1 (0.38 ± 0.06 and 0.39 ± 0.05 arbitrary units, respectively; n = 6). Thus the rate of force development (dF/dt) was linearly related to the rate of change of intracellular Ca²⁺ during the development of the slow low-Na⁺ or Na⁺-free contractions. In contrast, during the normal fast phasic contractions, this ratio was close to 4 (2.56 ± 0.22 and 10.6 ± 2.1, for force and Ca²⁺, respectively), suggesting that the rate of force development was not limited by the rate of [Ca²⁺]_i rise. The restoration of [Ca²⁺]_i and force to basal levels were also comparatively slow processes.

When the force-Ca²⁺ relationship was plotted for contractions obtained in 50 % Na⁺ or 0 Na⁺ solutions (Fig. 6C), it was essentially linear and followed the same trajectory during the rising and relaxation phases, i.e. no hysteresis. This suggests that, firstly, during slow changes of [Ca²⁺]_i, the mechanisms of force activation can keep pace with the rate of increase in [Ca²⁺]_i and, secondly, with slow changes of [Ca²⁺]_i the rates of contraction and relaxation are controlled exclusively by the rate of rise and fall of the Ca²⁺ transient, and steady-state conditions apply.

Figure 7A (typical of 6 others) shows that wortmannin caused a time-dependent inhibition of force, despite unaltered Ca²⁺ transients. Figure 7B shows superimposed traces of the initial phase of the force development seen under control conditions (i in Fig. 7B) and in the presence of wortmannin, which were normalised to their maximum amplitude. The time of delay in the presence of wortmannin increased more than 2-fold to 302 ± 63 ms (n = 7, compared with 115 ± 12 ms in controls). The half-time of force development was also significantly increased (1.48 ± 0.71-fold), while the Ca²⁺ signals remained practically unaltered (n = 7).

Figure 7 Effect of wortmannin on the Ca2+ transient and phasic contractions

Figure 8 The effect of cooling on ureteric force

The rising phase of the Ca²⁺ transient was little affected by moderate cooling (Fig. 8B), and the Q₁₀ was 1.4 (7.85 ± 0.18 at 35°C and 5.66 ± 0.28 at 25°C). The rate of decay of the Ca²⁺ transient, however, was significantly effected by cooling; the Q₁₀ was 2.7 and the maximal rate decreased from 1.95 ± 0.43 at 35°C to 0.71 ± 0.22 s at 25°C. These data indicate that the mechanisms controlling Ca²⁺ rise are passive while those responsible for the restoration of the [Ca²⁺]_i are energy dependent.

Figure 9A shows the effect of cooling when parameters of the Ca²⁺ signal are similar. It can be seen that significantly less force was produced when the ureter was cooled, despite the parameters of the Ca²⁺ signal being very similar. From Fig. 9B, where superimposed traces are presented on a faster time scale, it can be clearly seen that cooling significantly increased the time of the delay and the rate of force development, while having no effect on the rising phase of the Ca²⁺ transient. From the phase-plane plot of the relationship between dF/dt vs. normalised force (Fig. 9D), it can be seen that cooling significantly slowed the rate of both contraction and relaxation. Thus by increasing the time of delay and decreasing the rate of force development, cooling significantly enhanced the hysteresis in the force-Ca²⁺ relationship (Fig. 9C).

Figure 9 The effect of temperature on the force-Ca2+ relationship

These data showed that less force is produced at low temperature when the parameters of the Ca²⁺ transient were practically identical. In the next set of experiments we investigated what duration of Ca²⁺ transients would be required, at low temperature, to enable comparable levels of force to be obtained at the two temperatures. Figure 10 shows that both histamine (A) and TEA (B) were able to reverse the negative ionotropic effect of cooling. Since they both take time to develop their maximal effect on ureteric muscle, there was a period when the amplitude of force at room temperature in the presence of TEA or histamine, was similar to that seen under control conditions at 35°C. Thus it was possible to compare the temporal characteristics of the Ca²⁺ transient associated with the same level of force obtained at two temperatures (Fig. 10A and B, contractions a and c).

Figure 10 The effect of agonists at low temperature

It can be seen that in order to achieve the same level of force at room temperature the duration of the Ca²⁺ transient at its peak level must be increased more than 4 times (n = 5 for histamine; n = 9 for TEA). However, the time for force to reach steady state was more than 8 times longer at 20°C than at 35°C (27.6 ± 4.7 s vs. 3.3 ± 0.4 s, n = 9, TEA). Longer periods in histamine or TEA produced even longer duration Ca²⁺ transients and this was associated with even greater force, which could surpass that of the control contraction (Fig. 10A and B, contraction d).

These data also indicate that moderate cooling had only a small effect on the mechanism controlling the rate of rise of [Ca²⁺], in contrast to its strong influence on the rate of force development (Figs 8 and 9). So, whatever steps in force activation are affected by cooling, and lead to an increase in the delay (t_d) and a decrease in the rate of force development, they do not appear to be limited by the mechanisms controlling the kinetics of the rising phase of the Ca²⁺ signal.

In order to test this further, the effect of an instantaneous rise of temperature (‘temperature jump’) on the kinetics of the force development was examined. This jump was applied at a time when [Ca²⁺]_i had already reached its peak level (to exclude a possible influence of cooling on the kinetics of the Ca²⁺ transient) and the rate of force development had already achieved its maximum value. The data obtained are illustrated in Fig. 11 and are presented in the form of superimposed original records (Fig. 11A) and the phase-plane plots of the phasic contraction (dF/dt vs. force; Fig. 11B). It can be seen that the temperature jump produced an immediate and selective effect on the parameters of the phasic contraction; an increase in the amplitude and the rate of force development (Fig. 11A and B). These data indicate that it is possible to achieve larger rates of force development and larger force, at the same level of Ca²⁺, and for the same period of time, by speeding up the events which control the rate of force development per se. These data also indicate that the apparent upper limit on force development rate does not reflect limits imposed by the contractile machinery; a temperature jump, applied at a time when the maximal rate of force development had already being achieved, could rapidly increase it.

These data emphasised that the rate of force development was not limited by the rate of [Ca²⁺] elevation but by the speed of the energy-dependent events linking [Ca²⁺] with force development. These events play an important role in controlling the level of force development in phasic smooth muscles, which generate a fast and relatively short Ca²⁺ transient.

The data in this paper are some of the first to show how the action potential configuration relates to changes in [Ca²⁺]_i and in turn, how the parameters of the Ca²⁺ signal, i.e. its rate of rise and duration, affect the phasic contractions of an intact phasic smooth muscle, during the transient changes that occur with normal physiological activity and temperature. The data lead us to propose that under physiological conditions the brief, rapid Ca²⁺ transient associated with phasic contractions will not be long enough to allow [Ca²⁺]_i to come into dynamic equilibrium with the mechanisms of force activation in ureteric smooth muscle. Thus (1) there is a marked hysteresis between [Ca²⁺]_i and force during the rising and falling phases of the twitch contraction. (2) If the rate of rise of [Ca²⁺]_i is slowed, then the myofilament can come into equilibrium with peak [Ca²⁺], hysteresis is not seen, and greater force may be obtained. (3) If the [Ca²⁺]_i signal during the development of phasic contraction is prolonged, a new equilibrium is obtained, and much greater force can be produced by the muscle. We further suggest that, at least in the ureter, modulation of the duration of the [Ca²⁺]_i peak is an important physiological means by which agonists exert their effect on the amplitude of contraction.

Before discussing our data further it is first necessary to briefly address the limitations of our technique. In intact preparations the environment around the myofilaments is not controlled, in contrast to permeabilised preparations. However, we were measuring [Ca²⁺]_i, the most important regulator of force, and studying normal phasic activity. The advantage of the intact preparation is that no constituents of the intracellular environment are lost or changed and hence the sensitivity of the myofilaments to [Ca²⁺]_i is not altered. Multicellular preparations may potentially suffer from non-uniformity and the presence of the series elastic component (SEC), the compliance of which can affect the temporal relationship between calcium and force. We chose the guinea-pig ureter because it is a thin (100–200 μm) preparation that loads evenly with fluorescence indicators, and can be uniformly excited by action potentials (Shuba, 1981; Aickin et al. 1984; Burdyga et al. 1995). Figure 2 demonstrates the good correspondence between both Ca²⁺ and electrical activity and force transients in multicellular and single cell preparations. Thus non-uniformity is not a problem in the multicellular ureteric smooth muscle strips.

The SEC, measured in maximally activated ureteric muscle using the quick release method, was found to be relatively small (about 2–3 % of L₀), while the maximal shortening velocity (V₀) of the contractile element (CE), derived from the force-velocity curve fitted with a rectangular hyperbola, gave values exceeding 1 L₀ s⁻¹ (T. V. Burdyga and R. M. Maass, unpublished data). Thus we assume that the contribution of the SEC to the time of delay will be in the range of 20–30 % (discussed later). The advantage of our preparation is that the tissue is close to its in vivo state and can be stimulated by action potentials and respond to agonists, and thus the information obtained is physiologically relevant.

By simultaneously measuring electrical activity and intracellular [Ca²⁺], we were able to elucidate how the electrical signal is translated to changes in [Ca²⁺]_i. Three clear components of the Ca²⁺ transient were discerned in both intact strips and single cells. The final component, a steady phase associated with the plateau phase of the action potential, was found to be the component which was modulated by agonists to affect force production. The guinea-pig ureter action potential has been well studied, and it is therefore possible to relate its components to the underlying ionic mechanisms. Opening of L-type Ca²⁺ channels is produced by the upstroke of the action potential (Lang, 1989; Imaizumi et al. 1989; Sui & Kao, 1997), which we found to be associated with an initial, rapid increment of Ca²⁺. The action potential subsequently consists of some repolarisation and a further series of spikes and a long plateau phase (Shuba, 1981). The outward currents have been shown to be largely due to Ca²⁺-activated K⁺ channels (Lang, 1989; Imaizumi et al. 1989). The long plateau phase of the ureteric action potential has been attributed to the very slow rate of inactivation of the Ca²⁺ channel (Kao, 1997). As shown by us and others (Kao, 1997), inhibition of K⁺ channels by TEA, produces a prolongation of the plateau phase. Thus Ca²⁺ entry will continue throughout the action potential and, as we show here, takes the form of a slower Ca²⁺ increase (compared to that produced by the initial spike) lasting 200–300 ms, and then a maintained, peak Ca²⁺ signal clearly associated with the action potential plateau. We found the duration of this maintained peak Ca²⁺ to be associated with the duration of the plateau phase. Thus agonists that can prolong the plateau phase will maintain the Ca²⁺ signal at its peak level for longer and, as described below, produce greater ureteric force. Similar results were also reported for gastric smooth muscle which also generates a plateau-type action potential (Ozaki et al. 1991). Similarly, changes which reduce the duration of the plateau phase shortened the time for which peak Ca²⁺ is produced. It is also likely that the sarcoplasmic reticulum (SR) contributes to the changes in cytoplasmic [Ca²⁺]_i, but recent evidence suggests that this is via effects on surface membrane excitability, e.g. by spontaneous Ca²⁺ release activating K⁺ and Cl⁻ channels, rather than as a direct source of Ca²⁺ for the myofilaments (Maggi et al. 1995; Burdyga & Wray, 1999). When the action potential was reduced to a single spike, as occurred in 0 Na⁺ solution, then only the initial rapid increment of Ca²⁺ occurred.

The slower kinetics of force development, compared to the fast Ca²⁺ transient during phasic contractions, also suggest that even if the rate of rise of the Ca²⁺ transient and its amplitude are unaltered, but the [Ca²⁺]_i signal maintained, it should be possible for [Ca²⁺]_i and force to enter a new equilibrium associated with increased force production. The experiments with paired pulses, histamine and TEA to prolong [Ca²⁺]_i, convincingly supported this prediction; with increased duration of the [Ca²⁺]_i signal the amplitude of force was significantly increased. During twitch contractions of barnacle skeletal muscle (Ashley et al. 1985) and ileal smooth muscle (Ito et al. 1988), where there is also a lag between [Ca²⁺]_i and force, a prolongation of the duration of [Ca²⁺]_i signal also increased force. The physiological significance of the long delay between Ca²⁺ rise and force development is also illustrated in the present experiments by the data at low temperatures. Despite no decrease in the amplitude of the Ca²⁺ transients, but an increased delay, force is reduced, as it starts to develop mostly during the declining phase of the Ca²⁺ transient. This contrasts with the situation at 35°C, when up to 20 % of maximal force can be developed during the rising phase of the Ca²⁺ transient. Thus at low temperature the myofilaments will ‘miss’ the initial stage of the [Ca²⁺]_i rise during normal phasic contractions, and will not have sufficient time to reach a steady state with [Ca²⁺]_i at its peak value. The temperature data obtained in the presence of TEA and histamine showed that with prolongation of the [Ca²⁺]_i peak, this effect can be overcome – hence more force can be produced at 20°C in TEA than during a normal phasic contraction at 35°C. It is worth noting that many agonists that affect ureteric contractility do so predominantly by prolonging the action potential, e.g. histamine can increase it 14-fold (Shuba, 1981). This presumably is a more effective way of modulating ureteric force than increasing action potential frequency.

Our data also suggest that the rate of rise of [Ca²⁺]_i is not going to limit the contractile ability of the ureter under physiological conditions, since during normal phasic contractions the rate of rise of Ca²⁺ was 4 times that of force. Only when the rate of rise of Ca²⁺ was significantly reduced (20-fold), e.g. in 0 Na⁺ experiments, did the rate of force development show a dependence on Ca²⁺ rise. The upper limit of myofilament kinetic responsiveness to rapidly changing Ca²⁺ may therefore be a more important modulator of the rate of rise of force than is the rate of Ca²⁺ rise.

Some of the delay will be due to the presence of the SEC, but this is not considered to be a major contributor for the following reasons. (1) Cooling which increases stiffness of the SEC (Stephens et al. 1977; Peiper et al. 1978) did not shorten, but in fact significantly increased, the latency, although cooling will also influence shortening velocity. (2) Wortmannin, an inhibitor of MLCK, also produced a significant increase in the time of delay. (3) The hysteresis disappears if the change in Ca²⁺ is slowed. (4) The hysteresis does not disappear if the SEC has already been stretched (paired pulse data). (5) Thiophosphorylation of the MLC shortens the time of delay to 30 ms in tonic and 20 ms in phasic smooth muscles (Horiuti et al. 1989; Zimmermann et al. 1995). (6) When a movement artefact was deliberately introduced by setting the muscle up at a slack length, a clear temporal difference could be seen between the initiation of the Ca²⁺ signal and the mechanical response, and furthermore, the movement artefact coincided with force measurement. This suggested that the delay was due to force activation mechanisms rather than extension of the SEC. However, during slack conditions the load is effectively zero and the SEC is not extended. As described by Murphy (1976), the time needed to take up the mechanical slack, i.e. to stretch the SEC, can be roughly calculated, assuming instantaneous and full activation, as a percentage of L₀ and V₀, e.g. with a SEC of 5 % of L₀ and V₀ of 0.5 L₀ s⁻¹, the delay would be 100 ms. In the ureter the maximum value of SEC is about 2–3 % of L₀ and V₀ is about 1 L₀ s⁻¹ at 37°C and 0.5 L₀ s⁻¹ at room temperature. Thus it can be calculated that the time needed to stretch the SEC in ureteric muscle will be around 20–30 ms at 37°C and 40–60 ms at room temperature. Thus about 20–30 % of the time delay we find in the ureter is likely to be produced by the SEC. Thus we conclude that SEC does not account for the majority of the delay between the rise of Ca²⁺ and force development. What is responsible then?

Information from several studies would suggest that the delay resides in one or more of the steps leading to myosin phosphorylation, particularly the activation of MLCK by Ca²⁺-calmodulin (Kamm & Stull, 1986; Miller-Hance et al. 1988). These steps include: (i) recruitment of calmodulin, (ii) binding of Ca²⁺ to calmodulin, (iii) Ca²⁺-calmodulin binding to MLCK, (iv) isomerisation of the Ca²⁺- calmodulin-MLCK complex, and (v) MLCK phosphorylation of myosin. Steps (ii), (iii) and (v) are all fast and not considered to be rate limiting (Adelstein & Klee, 1981; Torok & Trentham, 1994; Zimmermann et al. 1995). In contrast steps (i) and (iv) may make significant contributions to the delay. For example Zimmerman et al. (1995) calculate that the recruitment of a slowly diffusable component of total cytoplasmic calmodulin takes around 200 ms. It is possible that, at resting [Ca²⁺]_i, the two C-terminal Ca²⁺ binding sites of calmodulin may be saturated with Ca²⁺ and thus calmodulin is bound to, but does not activate MLCK (Bayley et al. 1996; Johnson et al. 1996). If this is the case, activation would consist of just three steps: (i) Ca²⁺ binding to the N-terminal sites of calmodulin, (ii) a resultant conformational change in calmodulin and isomerisation of the Ca²⁺-calmodulin-MLCK complex, and (iii) phosphorylation of myosin. Step (ii) of this process would be rate limiting. A complication to this, and other studies, is that the measured changes of Ca²⁺ are global. Thus if Ca²⁺ is at a lower concentration around the myofilament than in the rest of the cytoplasm, this will not be apparent.

Wortmannin, an inhibitor of MLCK, completely and selectively inhibited force development in this muscle (Burdyga & Wray, 1998, and present data). It was without effect on the Ca²⁺ transient and previous data have shown it was also without effect on electrical activity (Burdyga & Wray, 1998). Whereas MLC phosphorylation was reduced to less than 1 % of control levels (T. V. Burdyga & R. W. Mitchell, unpublished observation). The significant increase in the delay between Ca²⁺ and force and the slowing of force development highlights the role of phosphorylation in these processes. One can speculate that the phosphorylation-Ca²⁺ relationship in ureteric smooth muscle is also far from equilibrium, as was found in trachea and uterine smooth muscle (Word et al. 1990), and thus by prolongation of the Ca²⁺ signal a larger degree of myosin light chain phosphorylation may occur at the same level of [Ca²⁺]_i. So, as has been appreciated for many years, the inter-relations between Ca²⁺, phosphorylation and force are complex in smooth muscle (Murphy, 1976; Wahl, 1985; Hai & Murphy, 1988).

In conclusion, we suggest that, under physiological conditions, the pacemaker activity of the ureter will generate action potentials that govern the characteristics of the fast Ca²⁺ transients, which always result in contraction. This contraction is not maximal because the myofilaments do not have time to reach a steady state with the peak [Ca²⁺]_i. If, however, contraction needs to be increased, then a mechanism for quickly modifying the force-Ca²⁺ relationship exists which does not change the sensitivity or the kinetics of the Ca²⁺ rise but increases its duration. This is achieved by prolongation of the plateau phase of the action potential. This increases both the duration and amplitude of the contraction and therefore increases the peristaltic force on the urine bolus passing into the bladder. It is accepted that force development in smooth muscle is dependent upon the amount of free [Ca²⁺]_i and the sensitivity of the myofilaments to [Ca²⁺]_i. From our data we would draw attention to a third important determinant in phasic smooth muscle: the duration of the [Ca²⁺]_i signal and thus the presence or absence of steady-state conditions.

We are grateful to Emily Wray for secretarial help and the Wellcome Trust and NKRF for financial support.