Evolutionary determinants of normal arterial plasma pH in ectothermic vertebrates

The regulation of extracellular pH implies that this has an optimum range. Normal arterial plasma pH (pHa) varies from one species to another, even when allowance is made for the important effect of temperature (see below), but the significance of the differences is unclear. Although pHa affects plasma proteins, it presumably matters most for its influence, through interstitial and cell-surface pH, on the ionization, and hence biological properties, of cell-surface molecules. The aim of the present study is to explore the possibility that the optimum pH at particular regions of the cell surface is similar (at any given temperature) in all heterothermic vertebrates. An alternative view might be that extracellular pH is more relevant to the homeostasis of intracellular pH, but the two are not rigidly linked, either in evolution or as acid–base balance changes in individual animals. Indeed, the cells in a single body may show diverse patterns of intracellular pH homeostasis (e.g. Heisler, 1986). Independent treatment of extracellular homeostasis is therefore appropriate.

That pH matters for its effects on ionization has long been orthodoxy, especially since the waning of the notion of relative alkalinity, or [OH^–]/[H⁺] ratio (Rahn, 1967); this ratio is no easier to define in terms of activities than is pH (Covington et al., 1985), its use does not eliminate the difficulties inherent in comparing pH values at different temperatures, as suggested by Howell et al. (1970), and it has no known functional significance.

This paper is little concerned with temperature effects, but it is helpful to consider these briefly here – and temperature differences must be allowed for when comparing pH data. The ionization of any one chemical group varies with (pH–pK), where K is its dissociation constant and pK=–logK. The condition for constant ionization with varying temperature, T, is that ΔpH/ΔT=ΔpK/ΔT. In individual heterothermic vertebrates, pHa (as operationally defined) typically decreases in vivo with increasing temperature, with ΔpHa/ΔT usually in the range –0.005 to –0.02°C^–1 (e.g. Robin, 1962; Howell et al., 1970; Reeves, 1972; Heisler, 1986; Ultsch and Jackson, 1996). This suggests that extracellular pH homeostasis relates to key ionizing groups with matching temperature-sensitivity, the most obvious candidates being protein imidazole groups since ΔpK/ΔT values in these fall mostly in a similar range. Thus, ΔpK/ΔT values for imidazoles in myoglobin are –0.01 to –0.02°C^–1 (Bhattacharya and Lecomte, 1997). Therefore, the temperature-dependence of pHa characteristic of a species may be largely such as to preserve the ionization state of key imidazole groups at cell surfaces.

This idea is suggestive of the much debated ‘imidazole alphastat hypothesis’ of Reeves (1972), but this does not refer specifically to cell-surface molecules other than those involved as sensors in pH homeostasis. An important issue here is whether the wide range of ΔpHa/ΔT found in different species is compatible with a single optimum value of ΔpH/ΔT at the hypothetical cell-surface sites. Regarding this, two points may be made. First, it is an important implication of this paper (see also Burton, 2001) that cell-surface pH is not uniquely related to pHa. Second, different studies on given species have sometimes yielded very diverse values for ΔpHa/ΔT, so that not all can be fully representative; Heisler (1986) discusses possible errors.

Just as temperature and pH may affect protein function, so too may salt concentration. Specific binding of Na⁺ or Cl^– is sometimes involved, but more often relevant is screening of the protein fixed charges (Kao et al., 2000). A constant functional state of the protein may therefore be achieved, not only by matching pH to temperature, but by balancing pH and salt concentration. At given temperatures, negative correlations have been found between normal pHa and plasma [Na⁺] in both tetrapods and teleosts, but with pH generally higher in the fish for any given [Na⁺] (Burton, 1994, 1996). The proposed explanation for the correlations within either group (Burton, 1994) involves the maintenance of an optimum pH within a diffuse double layer that is associated with an excess of fixed negative charges on important, but unidentified, regions of cell membrane; these would attract protons, but be screened by other cations. If Na⁺ and H⁺ were the only significant cations involved, then the condition for surface pH to be invariant with bulk-phase extracellular [Na⁺] would be that local bulk-phase pH decreases with increasing [Na⁺], with ΔpH/Δlog[Na⁺]=–1. The relationships between pHa and plasma [Na⁺] within the tetrapods and within the teleosts each conform roughly to this value of –1, but need to be better quantified. The little-studied effects of salt concentration on the ionization equilibria of dissolved proteins, hence enzyme activity etc., can be much smaller (e.g. Burton, 1969; Kao et al., 2000), but proteins at the hypothetical sites may lie amongst separate fixed anionic groups such as phosphate. We return to the possible role of other cations in the Discussion.

Another reason for re-examining the pHa/[Na⁺] relationships is that Ultsch and Jackson (1996) failed to confirm them, although this was mainly because they were not then aware of the need to treat teleosts and tetrapods separately. What they did find is that pHa in freshwater teleosts and freshwater amphibians does tend to be higher, at a given temperature, than in marine or terrestrial species, which include teleosts, elasmobranchs and reptiles (in which [Na⁺] is generally higher). This suggested that a pHa/[Na⁺] relationship might at least apply to teleosts.

For a given temperature and [Na⁺], pHa seems to be approximately 0.2 unit higher in water-breathing teleosts, on average, than in air-breathing tetrapods (Burton, 1996). However, most cells are bathed by an interstitial fluid that should generally be more acid than arterial plasma. Thus, if the latter difference happens to be greater in water-breathers, the interstitial pH could actually be more nearly similar in the two groups than is pHa. In water-breathers, arterial and tissue CO₂ tensions (P_CO2) tend to be much lower than in air-breathers (Rahn, 1966) (see below), so that CO₂ from the cells (or released from extracellular HCO₃^– by secreted acid) would have a larger proportionate effect on interstitial P_CO2, thus enhancing the pH difference.

Thus put, the argument is simplistic, but more detailed modelling (Burton, 2001) suggests that the difference between interstitial and arterial pH for the whole body on average (DpH) could typically be approximately 0.1–0.2 unit more in water-breathing fish than in air-breathing tetrapods. Given certain assumptions, DpH may be estimated by relating CO₂ diffusion in one direction with O₂ diffusion in the other. The ratio of these diffusion rates, equal to the respiratory exchange ratio or respiratory quotient (R), depends on the relative solubilities (S) and diffusion coefficients (D) of the two gases and also on the tension differences between capillary blood and interstitial fluid. Relevant tensions are estimated from arterial and venous values (denoted by a and v respectively), with arbitrary low values assigned to the unknown mean interstitial P_O2. For simplicity, P_CO2 and P_O2 are taken as changing uniformly along the capillaries. The model yields an estimate of mean interstitial P_CO2 and, hence, if the interstitial [HCO₃^–] is modelled as being that of the arterial plasma, an estimate of mean DpH. This estimate, denoted D′pH, is given by:

where A is [1+(Pv_CO2/Pa_CO2)]/2, K is (S_O2/S_CO2)×(D_O2/D_CO2) and G is the mean difference in P_O2 between interstitial fluid and capillary blood. For the data collated by Burton (2001), A is 1.01–1.40 and (Pa_O2+Pv_O2)/2 varies from 16 to 81 mmHg with a mean of 51 mmHg (1 mmHg=0.133 kPa). How far the latter values match those for typical mean capillary P_O2, as assumed for simplicity by Burton (2001), must depend on the oxygen dissociation curves, which are unavailable for most species. With interstitial fluid treated as a solution of NaCl, K is 0.036 at 15°C and 0.040 at 25°C (Burton, 2001). For plausible values of R and of mean capillary and interstitial P_O2, representative values of KRG are thus likely to be approximately 1–3 mmHg. For any given value of KRG, equation 1 implies an inverse relationship between D′pH and Pa_CO2 that is steepest when Pa_CO2 is low, as it in water-breathers; DpH in air-breathing tetrapods should be generally lower than in water-breathers and less dependent on Pa_CO2.

The assumption that [HCO₃^–] is identical in interstitial fluid and arterial plasma implies that there is no net loss of acid or base equivalents from all the cells treated collectively. Net acid secretion, releasing CO₂ from interstitial HCO₃^–, would raise R and, hence, DpH. Then [HCO₃^–] would become a factor in determining DpH, but the reduction in [HCO₃^–] by the acid from the cells would be proportionately much less than the resulting elevation in P_CO2. (In human extracellular fluid, for example, a 4 % reduction in [HCO₃^–] from 25 to 24 mmol l^–1 would nearly double P_CO2.) Most tissues produce very much more CO₂ than titratable acid.

Adequate data on all the relevant variables in the model are available for few species (Burton, 2001), but the main determinant of D′pH is Pa_CO2, and for this there are many more data. It is therefore appropriate to explore here the dependence of normal pHa, not just on [Na⁺], but on Pa_CO2 as well, without reference to variables for which data are scarce.

A correlation between pHa and Pa_CO2 is not demanded by the Henderson–Hasselbalch equation, for this relates pH not just to P_CO2 but to the [HCO₃^–]/P_CO2 ratio. To consider data for 15°C in Table 1 of Ultsch and Jackson (1996), in seven species of obligate water-breathing fish, Pa_CO2, [HCO₃^–] and pHa average 2.7±1.5 mmHg, 8.3±5.0 mmol l^–1 and 7.91±0.06 respectively. In eight species of obligate air-breathing anphibians and reptiles, the respective means are 13.6±5.1 mmHg, 25.2±7.6 mmol l^–1 and 7.80±0.14 (means ± s.d.). Given the variation in Pa_CO2 and [HCO₃^–] within each group, it is not obvious, from these considerations alone, why these variables could not be matched to give the same pHa in every species.

There are several elements to the thesis of this paper: the existence of correlations amongst pHa, [Na⁺] and Pa_CO2; the undoubted effect of [Na⁺] on pH in regions of fixed negative charge; the inevitable pH gradients between most interstitial fluid and arterial plasma that probably vary with Pa_CO2; and the possibility that particular cell-surface structures require a similar local pH in all vertebrates. Although these ideas are integrated in a single quantitative thesis, they, like the multicomponent imidazole alphastat hypothesis, are not a single theory to be judged only as a whole.

In many vertebrates, pHa varies much more than in ourselves, even at constant temperature, and variability may increase in the context of particular normal activities and conditions. According to species, these might include, for example, diving, vigorous activity, hibernation and dehydration. Intermittent breathing, as in the turtle Chelonia mydas, causes pHa to fluctuate (Kraus and Jackson, 1980). Whether extracellular pH is usually more nearly optimal under non-stressful resting conditions or when special activity is called for is not known. Here, however, the pragmatic approach is adopted of using mean values obtained either in studies on the effect of temperature or for groups of animals used as experimental controls (not all of which actually purport to characterize normality). Two representative temperatures are emphasized here, 15°C and 25°C. For some species, pHa and Pa_CO2 at one or other temperature were obtained by linear interpolation between measurements at other temperatures or from published regression equations. In other cases, data are used that were obtained within 3°C of those two temperatures. Some data were read from graphs. All blood had been sampled from chronically implanted arterial cannulae.

The data vary in their suitability. Where several studies have been published, the most representative values were generally selected. Nevertheless, preference was usually given to sets in which all three variables were measured in the same study. In other cases, mean [Na⁺] had to be taken from separate studies. Effects of temperature on [Na⁺] are perforce largely ignored; in the steady state, these are generally small and inconsistent (Burton, 1986) so that uncertainties in this regard are unlikely to be of overriding importance here. (Errors in [Na⁺] of 10 % result in errors of 0.04 in log[Na⁺].) All species are represented for which full data were found; exclusion on the basis of too-strict criteria would increase both the risk of biased selection and the impact of any grossly inappropriate data that are included.

According to arguments in the Introduction, regulation of cell-surface pH implies regulation of pHa+N–DpH, where N is some function of [Na⁺] (and possibly other cations also; see Discussion) and DpH is largely dependent on Pa_CO2. The expression pHa+N–DpH should differ from the cell-surface pH by a constant amount which, with [Na⁺] expressed in mmol l^–1, is likely to approach 4 units (see Discussion). On the assumption that the expression has a similar optimum in each species, analysis of the data on pHa, [Na⁺] and Pa_CO2 involves finding parameters relating to N and DpH that minimize variations in that expression. For N, a convenient function is log([Na⁺]+n), where n is the parameter in question. This function was chosen because it is simple and because it can be interpreted in terms of screening by other cations (see Discussion). Since data on Pa_CO2 alone do not suffice to calculate either DpH or D′pH, DpH is replaced by a new variable, D′′pH. Like D′pH, this is based on equation 1, but it is a function only of Pa_CO2 with all the other variables subsumed within three empirical parameters. Of these, m replaces KRG, so that D′′pH is defined as log[A+(m/Pa_CO2)]. The other two parameters relate A to Pa_CO2 (see Results).

Since the parameters to be estimated are contained within log([Na⁺]+n) and D′′pH, multiple regression analysis cannot be used. In any case, no one variable is clearly ‘dependent’ in this evolutionary context: D′′pH and pHa together determine surface pH (at a given [Na⁺]) and need to be matched one to the other.

Irrespective of any basis in theory, log([Na⁺]+n) and D′′pH may be seen as convenient functions of [Na⁺] and Pa_CO2 that yield approximately linear relationships in the exploration of correlations. Analysis of the data in terms of these therefore obviates the need for more straightforward correlational analysis of untransformed data.

Because the heterogeneous data are unsuited to the calculation of statistical significance, correlation coefficients (r), of 0.6 or higher, are stated just for their descriptive value. Within some classes, e.g. the Amphibia, the small numbers of data and narrow ranges of [Na⁺] and Pa_CO2 make significant correlations unlikely.

Mean values taken from the literature are presented without indications of scatter. Other means are given ± 1 s.d.

Tables 1 and 2 show mean values of pHa and plasma [Na⁺], and in most cases Pa_CO2, at approximately 25°C (34 data sets) and approximately 15°C (30 data sets). Some data need special comment. Of those on [Na⁺] in reptiles taken from the compilation of Minnich (1979), five are means of two or more of his tabulated values. For Oncorhynchus mykiss (Table 2), pHa and Pa_CO2 are means based on 34 studies (Ultsch and Jackson, 1996), while [Na⁺] is a mean based on five studies (Burton, 1996). The pHa of 7.82 given for Bufo marinus at 25°C (Boutilier et al., 1987) is much higher than the 7.54 plotted by Ultsch and Jackson (1996), but close to their tabulated mean of 7.814 based on 11 studies.

For Dipsosaurus dorsalis at 25°C, Burton (1994) inappropriately plotted a mean venous pH (7.53) instead of the arterial mean of 7.69 (Bickler, 1981). Ultsch and Jackson (1996) used a much higher pHa of 7.87, since a value for [Na⁺] (164 mmol l^–1), typical of normal values tabulated previously (Minnich, 1979), was available from the same source (Bickler, 1984). The most appropriate of those means is probably 7.69 (P. E. Bickler, personal communication), and that is the value in Table 1. There is some diurnal variation in this species (Bickler, 1986).

For ‘Varanus spp.’, the pHa and Pa_CO2 are means for V. niloticus (Ishimatsu et al., 1988), V. salvator (Mitchell and Gleeson, 1985) and V. exanthematicus (Wood et al., 1981), all individually similar, and the value for [Na⁺] is the mean of five separate means for V. griseus and V. gouldii (Minnich, 1979). In four other cases, [Na⁺] is again taken as the mean for one or more related species. Thus, for the sea snake Lapemis hardwickii in Table 1, [Na⁺] is for the closely related Pelamis platurus. Here, the combination of low pHa (7.41) and high [Na⁺] (237 mmol l^–1, the mean of two means given previously) (Minnich, 1979) would be especially worth confirming for either of the species. Seymour and Webster (1975) give data on Pa_CO2 in Lapemis hardwickii, but no mean for use here. For Lepisosteus oculatus (Table 1), [Na⁺] is the mean for four other species of Lepisosteus (Urist et al., 1972; Sulya et al., 1960). For Myoxocephalus octodecimspinosus (Table 2), [Na⁺] is for the related M. spinosus (Oikari, 1975). For Scyliorhinus stellaris in both tables, there are separate entries for juveniles and adults (Heisler et al., 1976) since they differ markedly in their patterns of acid–base regulation; [Na⁺] for both is taken as that for S. canicula. The Amia calva of Table 1 rarely breathed air at 24.5°C (Randall et al., 1981).

Fig. 1 confirms the existence of the disputed negative correlation between pHa and [Na⁺] (plotted as log[Na⁺]) in tetrapods at approximately 25°C. Two air-breathing fish (Protopterus aethiopicus and Electrophorus electricus), both with high Pa_CO2, can be seen as conforming to the same relationship, but for most of the other fish pHa is higher for a given log[Na⁺]. For water-breathing fish, Fig. 1 shows no correlation between pHa and log[Na⁺] at approximately 25°C; as shown below, this relates to the large variation in Pa_CO2. Data for approximately 15°C (Table 2) confirm the negative correlations between pHa and log[Na⁺] in teleosts (r=–0.61) as well as in the ectothermic tetrapods (r=–0.86). However, these data are not presented here as in Fig. 1 because the separate correlations are better unified by taking Pa_CO2 into account.

The next stage in the analysis concerns A in equation 1. Eptatretus cirrhatus (Wells et al., 1986) is of special interest for its high [Na⁺] and low Pa_CO2 (Table 2). The data for this species yield unusually high values of A (1.36) and of D′pH (0.52, with interstitial P_O2 taken as 7 mmHg). With data for E. cirrhatus included with those for the 22 species tabulated by Burton (2001), the regression of A on logPa_CO2 (r=–0.54) is given by the equation:

This relationship is assumed in the subsequent data analysis. That it is inexact is unimportant because A has much less influence on D′′pH than does m/Pa_CO2.

With A thus calculated, the parameters n and m were obtained by trial and error so as to minimize the standard deviation of pHa+log([Na⁺]+n)–D′′pH at each temperature. This process suggested that m should be 2.3 mmHg at 25°C and 1.2 mmHg at 15°C, with n at the two temperatures being respectively 94 and 70 mmol l^–1. Since an intermediate n of 80 mmol l^–1 raises the standard deviation only beyond the third decimal place, D′′pH is hereafter as calculated using that single value of n, together with the two values of m. The expression pHa+log([Na⁺]+80)–D′′pH then averages 9.89±0.08 at 25°C and 10.00±0.08 at 15°C, a difference of –0.01°C^–1. As already noted, the relevant surface pH is probably lower than these means by nearly 4 units.

The expression pHa–D′′pH may be seen as an estimate of mean interstitial pH. Fig. 2 shows this plotted against log[Na⁺]. The curves conform to the results of the previous paragraph. At 25°C, r=–0.65 in the tetrapods and r=–0.72 in the fish. At 15°C, the corresponding values are r=–0.84 and r=–0.74, respectively, with these correlations discernible in both the reptiles alone (r=–0.70) and the teleosts alone (r=–0.65). Thus, the overall correlations seem not to result merely from the merging of disparate data sets.

Fig. 3 shows pHa+log([Na⁺]+80) plotted against D′′pH, the line through the points being of gradient +1. Since D′′pH is an inverse function of Pa_CO2, Fig. 3 shows that pHa, adjusted for variations in [Na⁺], is negatively correlated with Pa_CO2. For all fish, r=0.82 at 25°C and r=0.72 at 15°C. For the tetrapods at 15°C, r=0.60.

Figs 2 and 3 show that pHa depends separately on both [Na⁺] and D′′pH. In Fig. 4, these two variables are combined as log([Na⁺]+80)–D′′pH. The negative correlation between pHa and that expression is evident within the reptiles (r=–0.61 at 25°C; r=–0.77 at 15°C) as well as in the tetrapods collectively (r=–0.75 at 25°C; r=–0.87 at 15°C). At 25°C, r=–0.84 for the teleosts and –0.64 for all the fish. (Eptatretus cirrhatus is a notable outlier at 15°C.) For all data taken together, r=–0.74 at 25°C and r=–0.65 at 15°C.

The analysis has been in terms of equations 1 and 2, but the correlations amongst pHa, Pa_CO2 and [Na⁺] may also be expressed using functions other than D′′pH and log([Na⁺]+n). It would be surprising if multiple regression analysis, coupled with a free choice of such functions, did not yield enhanced correlations. One expression correlating better with pHa than does log([Na⁺]+80)–D′′pH is log[Na⁺]+klogPa_CO2, where k is 0.51 at 25°C and 0.58 at 15°C. The correlation coefficients are –0.77 at 25°C and –0.76 at 15°C (compare the values of –0.74 and –0.65 in the previous paragraph). The expression klogPa_CO2 has no obvious functional meaning here.

The analysis of all these correlations is simplified by the fact that there is little correlation between Pa_CO2 and [Na⁺] at either temperature, except that Pa_CO2 is low and [Na⁺] high in elasmobranchs and Eptatretus cirrhatus.

The correlations accord with the hypothesis that the pH at particular cell surface sites is normally more nearly similar in different species (at a given temperature) than is pHa. It is a noteworthy test of the hypothesis both that the two estimates of m, i.e. 2.3 mmHg and 1.2 mmHg, correspond to the likely values for KRG of 1–3 mmHg given in the Introduction and that the data points in Fig. 3 are compatible with a straight line of gradient 1.0. Within their limitations, the data therefore accord also with the model of Burton (2001). That model was originally formulated in terms of whole-body mean interstitial pH, since most venous data on gas tensions are for mixed venous blood. In this paper, venous gas tensions are relevant only to A, which is a minor determinant of D′′pH. It is therefore permissible to interpret R and G in terms of particular tissues, e.g. those deemed most likely to require good extracellular pH homeostasis.

Although the scatter of points in Figs 2–4 must be due largely to inadequacies in the data, it is also required by the theoretical model. Thus, there are other variables in equation 1, notably G, that, for lack of sufficient data, have not been considered here.

If the cell-surface sites bear a constant density of fixed negative charges, then surface pH would be raised by the screening effect of cations in the bulk interstitial fluid. If Na⁺ were the only cation present other than H⁺, the effect would be proportional to log[Na⁺] (see Introduction). In fact, K⁺, Ca²⁺ and Mg²⁺ would contribute to screening too, to an extent that depends on the concentrations of their free ions and on the fixed charge density at the cell surface (Burton, 1973a,b). That interspecific variations in [Ca²⁺] and [Mg²⁺] do not obscure the supposed effect of [Na⁺] could result from a sufficiently low fixed charge density together with the known interspecific correlation between [Ca²⁺] and [Na⁺] in vertebrate plasma (Burton, 1973a). However, screening by [Ca²⁺] and [Mg²⁺] might explain why n in the expression log([Na⁺]+n) is not zero, but approximately 80 mmol l^–1. Only an approximate treatment is possible here, since the geometry of the supposed structures is unknown and full data on free [K⁺], [Ca²⁺] and [Mg²⁺] in plasma are lacking. However, we may apply diffuse double-layer (Gouy–Chapman) theory to other data. Burton (1973a) gives an approximate form of the Grahame equation relating the surface potential in volts, Ψ, to the molar concentrations of the four cations and to σ, the density of fixed electronic charges per nm² on the cell surface. In terms appropriate to the present context, it may be re-written as:

where F is the Faraday constant and R is now the gas constant, and where:

and

Table 1 of Burton (1973a) gives data for 10 species in which mean plasma [Na⁺] is 0.087–0.544 mol l^–1, and for these it is possible to find a value of σ that makes ([Na⁺]+0.08) (in mol l^–1) a good approximation on average for Q/2. The data used in these calculations are for diffusible [Ca²⁺] or, where possible, free [Ca²⁺], with concentrations of free Mg²⁺ taken as 70 % of the total concentrations (this being the mean percentage for Ca²⁺). The required value of σ is approximately 0.8 electronic charges nm^–2. This is plausible (Burton, 1973a). For the 10 species in question, the corresponding surface potentials are –56 to –86 mV. With estimates of logS being 1.00–1.08, with log(2/[1000 mmol mol^–1]) being 2.70 and with the mean of pHa+log([Na⁺]+80)–D′′pH being 9.89 at 25°C and 10.00 at 15°C (see above), the Boltzmann equation (Burton, 1973b) implies surface pH values near 6.2.

It now seems at least plausible that there exists a common determinant of optimum pHa in ectothermic vertebrates, namely a cell-surface structure with a conserved requirement for surface pH. Minor variations in the optimum cannot be ruled out, but there is no evidence in the present data for consistent differences amongst reptiles, amphibians and fish. Regarding mammals, our own pHa is typical of reptiles at the same temperature that share our plasma [Na⁺] of approximately 145 mmol l^–1 (Burton, 1994). The human Pa_CO2 of 40 mmHg is higher than that typical of reptiles at 37°C, namely approximately 29 mmHg as calculated from a regression equation for reptiles given by Ultsch and Jackson (1996). Accordingly, D′′pH would be approximately 0.02 higher in reptiles than in man. This is small enough not to belie our own conformity to reptilian data.

According to this conserved determinant hypothesis, optimal (and normal) pHa has evolved and diversified in such a way as to maintain constant the pH-dependent functional properties of key molecular structures (probably proteins or protein complexes). These are sited on cell surfaces bathed by an interstitial fluid that is more acid than arterial plasma – and especially so in species with low Pa_CO2. The pH-dependent functional properties are also affected by temperature and by the screening action of other cations in the extracellular fluid. The plasma [Na⁺] typical of each species seems to be determined independently; it is generally close to the concentration needed to minimize the work of Na⁺ transport while remaining compatible, so it seems, with an optimum range of cell [K⁺] (Burton, 1973b). Because DpH may be temperature-dependent, the hypothesis does not require ΔpHa/ΔT to be the same in all species.

The cells bearing the relevant molecular structures are probably not the same as those acting as pH sensors in extracellular pH homeostasis. The latter would presumably evolve in such a way as to regulate pH appropriately, but both their evolution and their moment-to-moment efficacy would be aided if they showed similar sensitivities to temperature and salt concentration. How far the interspecific pHa/[Na⁺] relationship is maintained in individuals when [Na⁺] varies has yet to be properly explored (Burton, 1996); there may be an advantage to this, but no logical necessity.

The pH must generally be lower in interstitial fluid than in arterial blood, and lower still in those diffuse double layers that are associated with excesses of fixed negative charge. Nevertheless, it is important to seek alternative explanations for the correlations explored here. Thus, the apparent antagonism between H⁺ and Na⁺ might involve, not screening, but a straightforward competition for binding to specific protein sites. If only those two ionic species were involved, the proportion of protonated sites might be expected to be proportional to the ratio of [H⁺] to [Na⁺] in the interstitial fluid; Δ(pHa–D′′pH)/Δlog[Na⁺] should then be –1.0. Since n is not zero, it would seem necessary to postulate binding of one or more other ionic species. A quite different possibility is that Cl^–, not Na⁺, is relevant. Since Cl^– is the main anion balancing the charge on Na⁺ in plasma, the concentrations of the two ions in plasma are strongly correlated within the vertebrates.

It should also be questioned whether attention is correctly focused on P_CO2, rather than on [HCO₃^–] or [CO₃^2–] (or even on ion pairs involving one or other of these). Since [HCO₃^–] and [CO₃^2–], at a given temperature and salt concentration, may be calculated from pH and P_CO2 (with appropriate equilibrium constants and CO₂ solubility coefficient), correlations must exist amongst other sets of these variables than the trio investigated (e.g. [Na⁺] and [HCO₃^–] with either pHa or Pa_CO2). Whether a more direct functional basis exists for any of these is an open question.

Since the validity of some data sets in Tables 1 and 2 may be questioned (especially when [Na⁺] and acid–base variables are from separate sources), one may hope that more and better data will be obtained, especially for species in which the variables have extreme values. Ideally, all variables relevant to the model should be measured, including R and both arterial and venous gas tensions. This could prove revealing in relation to the changes in maturing Scyliorhinus stellaris (Heisler et al., 1976). The possibility of acid–base disequilibrium and variations in D_O2/D_CO2 should be considered (Burton, 2001). Since all animals should ideally be studied unstressed and under conditions corresponding as far as possible to their typical habitats and preferred temperature ranges, a unified survey of many species would be ambitious. More realistically, one may urge that plasma [Na⁺] and P_O2 be more routinely measured in acid–base studies.

Equation 1 was originally formulated in terms of mixed venous blood and whole-body mean D′pH. However, if extracellular pH homeostasis is assumed to be more important to particular tissues, it may be preferable to calculate D′pH just for these.

One component of the overall conserved determinant hypothesis may be tested more directly than through correlational studies. This is the predicted greater DpH in species with low Pa_CO2, i.e. in water-breathers. Most studies so far have been on mammals (Burton, 2001). The most decisive insight could emerge, however, through the identification of a conserved cell-surface structure with appropriate local charge density and appropriate sensitivites to pH and temperature.