After the concentration of potassium in the haemolymph of Helix pomatia has been raised by the infusion of KCl, it falls approximately exponentially for a time and then tends to rise. The accompanying rise and fall of calcium concentration can be fitted to a simple mathematical model.
The mobilization of calcium is accompanied by the generation of bicarbonate in equivalent amounts, without much change in pH or .
There is probably an increased production or retention of carbon dioxide at this time, but the main cause of the changes in calcium and bicarbonate is not respiratory acidosis.
The concentration of potassium rises in snalis that have been infused with CaCl2.
The adverse responses visible in snails infused with KCl are largely prevented when CaCl2 is infused at the same time.
Homeostasis seems to involve the maintenance of a proper balance of calcium and potassium concentrations.
When the concentration of potassium in the haemolymph of a snail is naturally or artificially raised, the concentration of calcium tends also to rise. The effect was first seen in Helix pomatia as a response to 1 ml injections of 228 mm-KCl (Jullien, Ripplinger & Cardot, 1958). In H. aspersa, the concentrations of both ions are raised after feeding, in aestivation, and also in snails injected with 100 mm-KCl or made to crawl in 85 mm-KCl (Burton, 1968, 1970). In H. aspersa the converse effect, of calcium on potassium, is small and not always evident. This paper is mainly concerned with the mechanism and timing of the effect of potassium on calcium and on bicarbonate, but discusses also the role of the effect in homeostasis.
Calcium is mobilized not only by potassium, but also by raised tensions of carbon dioxide (Burton, 1970, 1975; Burton & Mathie, 1975). When snails are exposed to 5−10% CO2 the concentration of bicarbonate rises along with that of calcium and in approximately equivalent amounts. The pH therefore falls less than it otherwise would. The extent to which the haemolymph is supersaturated with calcium carbonate, definable in terms of the ionic product , is necessarily reduced by a fall in pH, per se, but is restored by the rise in calcium and bicarbonate ; it may thus be tha state of supersaturation that governs calcium mobilization (Burton & Mathie, 1975). The sources of the calcium and bicarbonate are not known.
Snails (Helix pomatia) were obtained from T. Gerrard and Co. Ltd, Sussex, mostly weighing between 15 and 30 g. Cannulae were inserted into the optic tentacles of hydrated snails the day before use and used both for infusions and for the sampling of haemolymph (Burton, 1975). Infusions were made at a rate of 0·11 ml/min by means of a motor-driven syringe. Haemolymph samples were centrifuged and pre-pared for analysis immediately after collection. Calcium was estimated using an atomic absorption flame spectrophotometer (Burton, 1975) and potassium with a flame photometer. Duplicate analyses were made whenever possible, usually on 60 μl samples. pH was measured in a Radiometer glass microelectrode filled 3−4 times with uncentrifuged, anaerobically collected samples each of 30−40 μl. Concentrations of ionized bicarbonate were calculated from the pH and carbon dioxide tensions of samples equilibrated at 20 °C with 5·2% CO2 in O2. For this purpose it was assumed that = 7·500, where , is in mm Hg and [HCO3−] is in mm (Burton, 1969, 1970). Total bicarbonate (i.e. [HCO3−] + [CaHCO3+] + [MgHCO3+]) was calculated using a dissociation constant of 160 mm for both CaHCO3+ and MgHCOs+ (Greenwald, 1941), and assuming that the haemolymph contained 10 mm of magnesium and 1 mm of calcium bound to haemocyanin.
Model used in analysis of results
As shown below, potassium leaves the haemolymph following the infusion of KC1, while the concentration of calcium rises at first and then falls. The first set of results is analysed in terms of the following simple model.
The parameters for each snail were calculated as follows :
(1) To find [K]0 and γ, data were fitted to equation (4) by the method of least squares, with [K]a chosen to maximize the correlation coefficient. Since potassium concentration fell exponentially only for a limited period (‘exponential phase’), only data for this period were used here.
(2) Values of α/ β and c were estimated from a graph of calcium against potassium (equation 9). The line was taken as passing through the point for [Ca]1 and [K]1 Data obtained after the exponential phase were also used here.
(4) The constant βwas found by trial and error so that equation (8) gave a reason-able fit to the calcium data of the exponential phase. The curve was always taken as passing through [Ca]0 at time zero.
Time course of changes in potassium and calcium
Changes in haemolymph concentrations of calcium and potassium occurring after the infusion of 1 ml of 100 mm-KCl over 9 min were followed in each of nine snails. The first sample in each case was collected about 30 min from the start of the infusion and the last of each series was collected 2 h 55 min to 7 h 40 min later (Fig. 1). In each snail potassium concentration fell approximately exponentially over 2−7 h to a value 0·7−2·0 mm above that before the infusion and then usually rose by 0·3−1·0 HIM (six snails), as illustrated by snail 8 in Fig. 1, or at least steadied prematurely (two snails).
The calcium concentration must initially have been lowered by dilution of the haemolymph with infusate (as found with snails infused with 100 mm-NaCl). However, this was never apparent from the results, because of the prompt rise in concentration that followed. The calcium concentration rose to a peak 2·6−5·5 mm above the pre-infusion value at 40 min to 3 h 30 min. It then fell again, but never, during the period of the experiment, back to the pre-infusion value.
The data for the periods in which potassium seemed to fall exponentially (‘exponential phase’) may conveniently be summarized with reference to the model described above. For simplicity, the infusion is regarded for this purpose as occurring instantaneously at time zero (t = 0), which is 6 min after the start of the actual 9 min infusion period.
Table 1 summarizes the various parameters, except V, [Ca]0 and c which can be obtained from the others using equations 1, 2 and 9. V averaged 7·9 ±3·0 (S.D.) ml, which is consistent with other estimates (Burton, 1964). The fit of the curves to the potassium and calcium data during the exponential phase is indicated by values of . D is the difference between the calculated and measured concentrations. As expected, [K]a usually exceeds [K]1 For the one exception, snail 9, a second set of parameters is therefore tabulated, and this is based on the lowest reasonable value of [K]a (i.e. [K]a = [K]1) ; this set was used in the calculation of the above average for V and of the correlation coefficients (r) given below.
There are a number of correlations amongst the various parameters. Thus, y in-creases with ([K]a – [K]1 (r = 0·91) and decreases with V (r = −0·77), which is itself necessarily correlated closely, but inversely, with [K]o, ([K]o − [K]1) and ([K]o − [K]a) (equation 1). The other rate constants α and β do not correlate with V or [K]o, but are closely correlated with each other (r = 0·85), so that a/f only varies between 0·9 and 2·3 (average 1·6). Both α and βcorrelate with γ/([K]0 − (K]a) (r = 0·91 for a and r = 0·89 for β). Values of r corresponding to 5 % and 1 % probability levels are respectively 0·67 and 0·80.
Fig. 2 shows for each snail the time, tCa-min, at which the calcium concentration is maximum (calculated from equation 4), the time, tK.-min, at which the potassium concentration is minimum and the half time, , for the exponential fall in potassium concentration, where . All three are correlated.
Fig. 3 shows results obtained with a snail that was sampled through one cannula and periodically infused with 0·105 ml of 100 mm-KCl through a second. Infusions clearly need not be large to affect calcium.
Changes in bicarbonate, pH, [Ca2+][CO32−] and
Changes in calcium and bicarbonate were followed in nine snails that were given single infusions of 1 ml of 100 mm-KCl. Samples were collected before the infusions and, with the exception of the first 30 min, at intervals over the next 1 h 25 min to 4 h 30 min. Changes during and just after the infusions were calculated on the assumption that both ions were diluted with infusate by a factor of 8/9 (i.e. V was taken as 8 ml). Bicarbonate tended to rise to a peak along with calcium, and in general, as in respiratory acidosis, total bicarbonate and calcium increased or decreased in roughly 2:1 ratio, though with some irregularity (Fig. 4). The average concentrations of total calcium, total bicarbonate and ionized bicarbonate before the infusions were respectively 7·8 ± 0·8 (S.D.) mm, 31 ± 5 (S.D.) mm and 29 ± 5 (s.D.) mm.
Given the possibility that the mobilization of calcium and bicarbonate is a result of a potassium-induced acidosis, it was necessary to see what happened to the pH of the haemolymph following the usual 1 ml infusion of 100 mm-KCl. Since the period of increasing calcium concentration was especially important, the first post-infusion samples were collected only 20 min after the infusion started. Fig. 5 shows that when calcium reached its peak later than 80 min from the start of the infusion (five snails), then the pH before the peak was usually lowered. However, when the peak occurred within 80 min of the start of the infusion (eight snails), then the pH both before and at the peak was almost always slightly raised. One snail gave results too aberrant to be included in Fig. 5 : calcium rose only 0·3 mm in the first hour and a further 1·1 mm in the second, while the pH fell from 7·79 to 7·38 over the first hour and to 7·08 by the end of the second.
For four of the above snails, data were obtained on both bicarbonate and pH and this allowed changes to be followed in the ionic product [Ca2+][CO32−], or rather in the more convenient product [free Ca2+] × [free HCO32−] × (antilog pH), which is proportional to it. The values of this were found to increase following the infusions and to exceed the pre-infusion values by 51−88% at tCa-max three samples the product was raised even though pH was lowered.
Though mostly for different snails, the data on bicarbonate and pH together indicate that , changed little. The pH values at the calcium peak on average exceeded the pre-infusion values by only 0·005 unit (Fig. 5b), whereas ionized bi-carbonate rose by 19 %. On average, therefore, probably rose by about 19% also, though it could sometimes have fallen a little. A typical pre-infusion value for , calculated from the average pH (7·774) and the average concentration of ionized bicarbonate (29 HIM) would be 15·4 mmHg.
The influence of calcium on potassium
Five snails were each infused over 9 min with 1 ml of a solution containing 100 mm-CaCl2 and 2 mm-KCl. Fig. 6 shows the effects on calcium and potassium. The concentration of potassium always rose.
Responses to infusions: the protective action of calcium
The infusion of 100 mm-KCl into an active snail always caused rapid retraction into the shell. About 0·005−0·02 ml over 3−11 s was enough to cause a response. In con-trast, the effect of infusing even 1 ml of 100 mm-CaCl2 was never pronounced and was often barely visible.
The responses to potassium were greatly reduced when calcium was infused at the same time. This point was tested by infusing, at the usual rate, solutions containing 100 mm-KCl2 plus either i5omm-NaCl or 100 mm-CaCl2. The inclusion of the NaCl made no noticeable difference to the responses of the snails. The solution containing calcium was infused into 10 snails (0·3−1·0 ml), starting when their uncannulated tentacles were protruded. Two snails did not visibly respond. Others retracted the foot, or just the tentacles. Even as the infusions continued, the retracted foot and tentacles were sometimes protruded again and the overall response was more like that to a tactile stimulus than to potassium alone. The same protective effect of calcium was found when the two solutions were tested by injection into H. aspersa.
The fate of the potassium leaving the haemolymph was not investigated, but much of it probably entered the cells with chloride. Since the increasing intracellular concentrations would tend to oppose further entry, it is not surprising that haemo-lymph potassium never returned to its pre-infusion level. Why it sometimes rose a little after its initial fall is not known. It is unlikely that renal excretion could account for the rapid loss of infused potassium from the haemolymph, although potassium can become slightly concentrated in the urine (Skelding, 1973; Burton, unpublished).
The principle mechanism by which calcium is mobilized is one that involves the generation of approximately equivalent amounts of bicarbonate at the same time. This is clearly shown in Fig. 4, though the scatter suggests that other processes sometimes affect calcium or bicarbonate separately. Perhaps these, and the lack of serial sampling, account for the fact that bicarbonate generation was not detected in H. aspersa (Burton, 1970).
Even on the assumption that the calcium is derived from calcium carbonate, about half of the bicarbonate appearing with it must be formed from carbon dioxide.
Although the concentration of this in normal haemolymph is about 0·7 mm, the bi-carbonate levels generally rose in response to hyperkalaemia by much more than twice this amount, with little change in . It follows that the conversion of carbon dioxide to bicarbonate was balanced by an increased production or retention of carbon dioxide. Since seemed on average even to rise a little, we must consider now whether the mobilization of bicarbonate and calcium is simply the result of a potassium-induced respiratory acidosis.
A tendency to respiratory acidosis could well be brought about both by impaired gas exchange and by increased metabolism, the first due to a general loss of neuro-muscular coordination and the second to contraction of muscle induced either by its own depolarization or by increased neural activity. (Potassium stimulates metabolism independently of contraction in frog muscle, while calcium reduces this effect - Solandt, 1936.) Although the haemolymph pH is sometimes slightly lowered when the concentration of calcium is rising (Fig. 5 a), acidosis can hardly have been respon-sible for the rapid rise in those other snails in which the peak was attained soonest (i.e. within 80 min). In them the pH was generally raised. Whether the pH rises or falls at first presumably depends on the rate at which free CO2 accumulates relative to the rate at which it is converted to bicarbonate, so that a more rapid release of calcium and bicarbonate tends to give a higher pH. The one ‘aberrant’ snail, in which the pH fell 0·7 unit, underlines this point since the calcium level rose so little.
Although hydrogen ions can leave the cells of hyperkalaemic mammals in exchange for potassium, there is no evidence that this exchange occurs in snails since in these the concentration of bicarbonate rises after KC1 infusion. If both respiratory and metabolic acidosis are ruled out as important stimuli to calcium mobilization in these experiments, so too must be the fall in [Ca2+][CO32−] through which acidosis might have acted. Indeed [Ca2+][CO32−] was found to rise well above pre-infusion values.
The average volume of extracellular fluid in nine snails prior to their infusions (V) was estimated from potassium data as 7·9 ml. This volume was increased by the infu-sion of 1 ml of KC1 solution and was then reduced by the withdrawal of samples totalling about 1–3 ml. Water may also have moved into or out of the tissues as a result of the electrolyte disturbances. It is not known how these volume changes may have affected the experimental results, but snails tolerate three-to fourfold changes in haemolymph volume in normal life (Burton, 1964).
Infusion of KC1 causes the haemolymph potassium level to be raised and then to fall approximately exponentially for a time, while the concentration of calcium rises to a peak and then falls. The mathematical model fits the data for this exponential phase fairly well and is useful in summarizing them. However, the model is based for sim-plicity on linear relationships (equations 2 and 5), ignores the multicompartmental nature of the body, and fails to account for the delayed rise in potassium. It also disregards calcium binding in the haemolymph, the changes in acid-base parameters and intracellular potassium, and the demonstrated influence of calcium levels on extra-cellular potassium. Nevertheless, it serves as a vehicle for discussion, and present data do not seem to justify more complex modelling.
Some of the correlations between the numerical values of the various parameters of the model may reflect deficiencies in the model, including perhaps that between γ and ([K]a − (K]1). Others could in principle reflect deficiencies in the data, in that a wrong choice of one parameter leads to the wrong choice of others (e.g. snail 9 in Table 1). Yet the correlations shown in Fig. 2 are real and could be expressed without reference to the model, though less conveniently. It is natural that γ should vary inversely with V, if V happens to reflect, not just the absolute volume of extracellular fluid, but also its volume relative to the exchanging surface. However, it is then curious that neither α nor β correlate with V. The correlation between α and β themselves suggests, as is likely, that the two are partly determined by common factors.
Another way of looking at the model is to regard equation (6) as more basic than equation (5) − i.e. to postulate that there exists an ‘ideal’ linear relationship between [Ca] and [K], as represented by equation (9), and that d[Ca]/dt is proportional to the deviation of [Ca] from its ‘ideal’ value of (α/ β [K] + c). The relative constancy of the ratio α/ β (i.e. 0·9−2·3)is consistent with this idea.
Whether calcium movements are governed by the levels of potassium and calcium acting independently (equation 5) or together (equation 6), the outcome is a positive correlation between the concentrations of the two ions. It therefore seems that homeo-stasis is directed more to preserving ionic balance in this situation than to maintaining individual concentrations. Not only does the correlation apply in normal H. aspersa (Burton, 1968), but also in normal Planorbarius corneus, as is evident from the data of Sorokina & Zelenskaya (1967). The effectiveness of calcium in counteracting some of the effects of potassium in whole snails has been clearly shown and is reminiscent of the clinical use of calcium when the human heart is endangered by hyperkalaemia (e.g. Hazard, 1954). Calcium and potassium have antagonistic actions on the snail heart too (Krijgsman & Divaris, 1955; Burton & Loudon, 1972), but the nervous system is probably much more significant in this context. There, as in other animals, the effects of potassium, acting through membrane potential, are to some extent counteracted by calcium (Christoffersen, 1973: Kostyuk, Krishtal & Doroshenko, 1974; Standen, 1975). Total spontaneous activity in the palliai nerve of Lymnaea stagnalis is increased when the concentration of potassium is raised, though some units stop firing, and is decreased when the concentration of calcium or magnesium is raised (Duncan, 1961).