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Perspective |
Temperature and acid—base balance in ectothermic vertebrates: the imidazole alphastat hypotheses and beyond
Institute of Biomedical and Life Sciences, Thomson Building, University of Glasgow, Glasgow G12 8QQ, UK
e-mail: R.F.Burton{at}bio.gla.ac.uk
Accepted 22 August 2002
Summary
The `imidazole alphastat hypothesis' states that intracellular and extracellular pH, partly via buffering by imidazole groups, change with temperature in a way that keeps imidazole and protein ionization constant, thus maintaining cell function and minimizing shifts of base equivalents and total CO2, while adjustment of PCO2 involves imidazole-based receptors. `The hypothesis', which is actually several hypotheses, has been variously perceived and judged, but its underlying conceptual framework remains largely valid, and is reformulated using differential equations requiring less information input than their integral equivalents. Their usefulness is illustrated with published data on temperature responses in fish cells and whole tetrapods. Mathematical modelling allows general principles to be explored with less immediate concern for uncertainties in experimental data and other information. In tetrapods, it suggests that warming is followed by a loss of base equivalents from the body, and that this loss is due to metabolic adjustments that are not part of pH homeostasis. Uncertainties include intracellular buffer values, local variations in PCO2 within the body, the possible role of buffering by bone mineral, and the temperature dependence of pK values for CO2/HCO3- and imidazole groups. The equations utilize a single, notional, temperature-dependent pK value for all non-bicarbonate buffers in a given body compartment. This approximates to the `passive component' of pH adjustment to temperature change as measured by the homogenate technique. Also discussed are the diversity of cell responses within individual animals, relevant aspects of the control of ventilation, metabolism and transmembrane transport, and the basis of optimum pH—temperature relationships.
Key words: acid—base balance, alphastat, imidazole alphastat, temperature, pH, carbon dioxide tension, vertebrate, fish, amphibian, reptiles, cell pH
Introduction
The `imidazole alphastat hypothesis' of Reeves
(1972
) has inspired many
studies on the effects of temperature on acid—base balance. Some writers
accept it without question, while others (e.g.
Heisler, 1986c) are
dismissive. However, it is not one hypothesis, but several, and some of these
may apply to varying degrees in different species and tissues. It should be
judged accordingly. The purpose of this paper is not to review the extensive
literature, but more to analyze and comment on the constituent hypotheses. To
help in this, a simple mathematical model is presented. Its use is
illustrated, sometimes with new light shed on old data. Discussion of the
model's limitations raises other issues that are equally relevant to some
published experimental studies. This paper is not concerned with effects of
temperature beyond critical limits, where steady-state function is
disturbed.
What Reeves (1972)
describes as a "general conceptual framework" was put
forward mainly as a basis for computing relationships between pH,
CO2 tension (PCO2) and total
CO2 content (CCO2). It can be
regarded as having the following components, of which those marked with
asterisks are highlighted by Reeves himself as conclusions. Components (1) and
(2) are not so much proposals of `the hypothesis' as fundamental facts
underlying it. (12) is a natural addition
(Reeves, 1985).
pH/T is close to
pKIm/T, where T is temperature. pH/T is close to
pKIm/T). Equality implies constant imidazole
alpha, and thus the preservation of protein net charge.
Underlying the whole scheme is an attractive idea that is implied rather than stated: to the extent that protein properties are all similarly affected by pH and temperature through the dominant role of imidazole groups, each imidazole group facilitates pH homeostasis for all others.
Reeves (1972) did not
propose that all conditions apply exactly. Thus item (7) refers to changes
that are "small" or "minimized"; in
bullfrogs he found no dependence of CO2 content on temperature in
blood and cardiac muscle, but an increase with warming in liver, and possibly
(0.05<P<0.1) in striated muscle. He acknowledged that inorganic
phosphate, and to a small extent N-terminal 
-amino groups, contribute
to intracellular buffering (item 2). He did not refer to the small imidazole
compounds, e.g. carnosine, that abound in some cells
(Crush, 1970;
Burton, 1983).
Items (4) or (9) are most often singled out as `the hypothesis'. Reeves
(1976a) put the focus more
clearly on preservation of protein net charge (Z), as had Stadie et
al. (1925) and Austin et al.
(1927) in relation to serum and
blood. Many authors have since done the same. Indeed, Cameron
(1989) suggested that a
`Z-stat' model might be more appropriate than an imidazole alphastat
model. But is Z exactly the key variable? Where buffering is the
issue, i.e. in relation to changes in [HCO3-], it is the
ionization and net charge of all the non-bicarbonate buffers that
matters. The properties of enzymes may depend largely on the states of
specific imidazole, and other, groups, but enzyme properties are also much
affected by the crowding effect of other proteins present, and that may itself
be affected by net charge (Garner and
Burg, 1994; Elcock and
McCammon, 2001).
The temperature dependence of pK values
Individually, imidazole groups on proteins have diverse values of
pKIm/T, ranging from -0.01 to
-0.02°C-1 in myoglobin
(Bhattacharya and Lecomte,
1997). The value for one histidine in ribonuclease even changes,
in vitro, from -0.01 to -0.05°C-1 above 32°C
(Roberts et al., 1969).
Therefore values of pKIm/T can hardly match
those of pH/T in every instance (item 4). Despite this
variation, one may define a single quantity,
pKprot/T, that characterizes the temperature
dependence of protein net charge. This is not a simple mean of individual
values, but, for proteins with net charge Z and combined buffer value
ßprot, is such as to satisfy the equation:
 | (1) |
pK/T is calculable from the standard enthalpy change,
H°, as
H°/(2.303RT2), where
R is the gas constant (1.99 cal °C-1
mol-1; 1 cal=4.186J) and T is the absolute
temperature.
As discussed by Heisler
(1986c), various values of
pKprot/T have been assumed in the
interpretation of experimental results, notably -0.018°C-1 as
calculated for histidine at 15°C
(Edsall and Wyman, 1958), and
-0.021°C-1, which lies between values for imidazole and
4-methylimidazole (i.e. -0.020 and -0.022°C-1, respectively),
from the same source and again at 15°C. Measurements on actual proteins
are preferable, but few are available, not all of these representative. For
plasma proteins near pH7, Reeves
(1976b) found H° to
be 6940 cal mol-1, corresponding to a value of
pKprot/T of -0.018°C-1 at
20°C. For oxyhaemoglobin near pH7, he found respective values of 7300 cal
mol-1 and -0.019°C-1. For oxyhaemoglobin at pH
6.8-8.0, Wyman had found H° to be near 6000-7000 cal
mol-1 (Edsall and Wyman,
1958). For proteins extracted from white skeletal muscle of the
eelpout Zoarces viviparus, van Dijk et al.
(1997) obtained a less
negative value of -0.013°C-1.
Some vertebrate tissues are also buffered by substantial amounts of low
molecular mass imidazole compounds, such as L-histidine itself and the
dipeptides carnosine, anserine and balenine (=ophidine)
(Crush, 1970;
Burton, 1983;
Abe, 2000). In fish white
muscle, containing amounts between 0 and 148 mmol kg-1 wet mass,
these compounds may be more concentrated than in red muscle, be responsible
for much of the buffer capacity, and show a strong correlation with lactic
dehydrogenase activity (Abe,
2000). As calculated from figure 2 of Abe and Okuma
(1991), the value of
pKIm/T for carnosine is
-0.018°C-1, while values for anserine and balenine are both
-0.013°C-1. From the same figure, the value for histidine is
about -0.020°C-1 (compared with -0.018°C-1 as
given above). Hitzig et al.
(1994) obtained values of
-0.0166°C-1 for imidazole (compared with
-0.02°C-1 as given above) and -0.0154°C-1 for
carnosine. For several of these compounds there is thus significant
disagreement.
Although buffering is dominated by imidazole groups, and concentrations of
inorganic phosphate are often very low (e.g.
Marjanovic et al., 1998), the
latter may sometimes contribute significantly to intracellular buffering (but
note that concentrations are sometimes artefactually raised in tissue samples
by hydrolysis of organic phosphates;
Heisler and Neumann, 1980).
Values of pK/T for inorganic phosphate are small, i.e.
-0.006°C-1 for 0-5°C and -0.001 for
35-40°C-1 (Seo et al.,
1983), or -0.003°C-1 overall, as also found by
Alberty (1972). Adenosine
triphosphate (ATP), because it is present mainly as MgATP, contributes little
to buffering. Phosphocreatine, with its pK of 4.6
(Edsall and Wyman, 1958), is
not a significant buffer at cell pH. Although taurine has a high pK (8.8 at
37°C), some cells contain enough to make this a significant buffer, and
pK/T is probably strongly negative
(Bevans and Harris, 1999).
Temperature effects are modelled below in terms of a single, notional,
non-bicarbonate buffer with a temperature-dependent pK denoted pK*.
It stands for all the different non-bicarbonate buffers and buffer groups that
might be present. With these denoted by subscripts A, B etc.,
pK*/T is in principle calculable as follows
(Burton, 1973):
 | (2) |
In general, data now available give only approximate values in this way,
but estimates have been obtained more directly from the effects of temperature
on tissue homogenates. Thus, data of Heisler and Neumann
(1980) for the dogfish,
Scyliorhinus stellaris, imply mean values for
pK*/T of -0.017°C-1 in white
skeletal muscle, -0.012°C-1 in red skeletal muscle and
-0.016°C-1 in heart muscle. (I have derived these by
recombining separate estimates for phosphate-like and imidazole-like buffers,
themselves originally calculated using assumed values for
pK/T of -0.002°C-1 and
-0.021°C-1, respectively.) The concentrations of inorganic
phosphate in the homogenates used could have been raised by hydrolysis of ATP
and phosphocreatine, leading to underestimates of
pK*/T. Heisler and Neumann argued against
that and it is also possible that some inorganic phosphate was precipitated by
the added calcium (approximately 3.3 mmol l-1).
In a simple solution of non-bicarbonate buffers, free of
HCO3-,
pH/T=pK*/T. Therefore
pK*/T may be estimated by measuring
pH/T. A similar method has been applied to tissue
homogenates, with the value of pH/T described as the
`passive component' of the pH adjustment to temperature change
(Pörtner, 1990;
Pörtner et al., 1990;
Pörtner and Sartoris,
1999). In fact the original CO2 and
HCO3- are retained in the closed system, but this has
little effect on pH/T
(Burton, 1973;
van Dijk et al., 1997), so
that this should still provide a good estimate of
pK*/T (see item 3 of the hypothesis). An
important aspect of this method is that continuing metabolism and the
hydrolysis of organic phosphates are prevented by rapid dissection and
freeze-clamping of the tissue, followed by homogenization in a solution
containing KF and nitrilotriacetic acid that precipitate and chelate
Mg2+ and Ca2+. The method is also used for measuring
non-bicarbonate buffer values and in vivo pH.
For skeletal muscle of the black racer snake, Coluber constrictor,
the value for pK*/T thus found averages
-0.013°C-1 (Stinner et al.,
1998). Corresponding values in both the cane toad Bufo
marinus and the bullfrog Rana catesbeiana average
-0.011°C-1 (Stinner and
Hartzler, 2000), and a similar value applies in tissues of the
eelpout Pachycara brachycephalum
(Pörtner and Sartoris,
1999). For white skeletal muscle of Z. viviparus the
value of pK*/T is about
-0.006°C-1 (van Dijk et
al., 1997). It is not known what component makes this value so
much less negative than that of pKprot in the same muscle
(-0.013°C-1). All these estimates of
pK*/T could have been made slightly less
negative by the conversion of MgATP, a poor buffer at intracellular pH, to
ATP, which is more like inorganic phosphate in its buffer properties
(Alberty, 1972), but the
concentration in Z. viviparus averages only 3.6 mmol kg-1
fresh mass (van Dijk et al.,
1997).
There is evidently variation amongst tissues and species, but, for
modelling of hypothetical, generalized cells, it seems that representative
values of pK*/T, at least for muscle, may be
taken as about -0.011 to -0.018°C-1. Muscle containing much
carnosine may be expected to yield values in the more negative part of this
range. Values need to be more accurately known for calculations on real
experimental data.
Other background information
It is a general finding that arterial blood pH falls with increasing
temperature. According to the compilation of Heisler
(1986c), values of
pH/T in plasma are mostly -0.005 to
-0.018°C-1 in reptiles, -0.011 to -0.018°C-1 in
amphibians and -0.007 to -0.014°C-1 in fish, with respective
mean values of approximately -0.011, -0.015 and -0.012°C-1.
Separate studies on a given species have sometimes yielded very disparate
results. Intracellular values of pH/T, again as
compiled by Heisler (1986c),
have been found to vary between 0 and -0.029°C-1, with a mean
of approximately -0.012°C-1. Again there are marked differences
amongst tissues and species, and values may vary with temperature range
(Boutilier et al., 1987;
Stinner and Hartzler, 2000).
Heisler (1986c) discusses
sources of error. The compilation of Ultsch and Jackson
(1996) includes more recent
data on both plasma and cells.
Within cells, there is thus some similarity between values of
pH/T and overall
pKIm/T, but exact comparisons are not yet
generally possible. Despite this, it is evident that overall imidazole
ionization, dependent on the difference, must increase with cooling in some
cells and decrease in others. In the case of white skeletal muscle of Z.
viviparus, values of both pKprot/T for
dialyzed homogenates and intracellular pH/T have been
measured, averaging -0.013°C-1 (as already noted) and
-0.016°C-1, respectively, a difference that is not
statistically significant. Thus the net charge on these proteins, and the
dissociation state of their histidine residues, hardly varies with temperature
(van Dijk et al., 1997). The
fractional dissociation of carnosine imidazole has been measured directly, by
proton NMR, in tail muscle of intact unanaesthetized newts (Notophthalmus
viridescens); it was independent of temperature between 10 and 30°C,
thus showing alphastat regulation for carnosine
(Hitzig et al., 1994).
Concentrations of HCO3- in arterial plasma are
typically 14-40 mmol l-1 in reptiles, with the higher values mostly
occurring in chelonians, 10-30 mmol l-1 in amphibians, and 3-15
mmol l-1 in water-breathing fish
(Toews and Boutilier, 1986;
Heisler, 1986b;
Ultsch and Jackson, 1996). The
generally lower concentrations in water breathers relate to the fact that
PCO2 in these is typically lower than in air
breathers (Rahn, 1967). There
is a general tendency for plasma [HCO3-] to fall with
warming, especially in fish, but as discussed more fully below, the trend is
usually small or absent in tetrapods (Heisler,
1986b,c;
Ultsch and Jackson, 1996). It
is reversed in adults, but not juveniles, of S. stellaris
(Heisler et al., 1980).
It is harder to generalize about intracellular HCO3-,
especially since absolute concentrations and temperature effects both differ
amongst tissues. For modelling, however, reasonable representative values may
often suffice. Figures 3-7 of Ultsch and Jackson
(1996) suggest that the
cytoplasmic pH of muscle and liver is commonly about 0.3-0.6 unit lower than
arterial plasma pH. If PCO2 is assumed to be
not much higher in the cells than in arterial plasma (but see below), then the
Henderson—Hasselbalch equation suggests that
[HCO3-] in cells should often be about a quarter or half
that in plasma.
Intracellular non-bicarbonate buffer values vary with tissue and species,
with measurements in skeletal and cardiac muscle of ectothermic vertebrates
being typically 25-110 mequiv l-1 cell water pH unit-1
(Castellini and Somero, 1981;
Heisler, 1986a;
Milligan and Wood, 1986;
Abe, 2000). Many such values
must have been significantly raised artefactually by the release of inorganic
phosphate from phosphocreatine and ATP (Pörtner,
1989,
1990). With the homogenate
technique (Pörtner et al.,
1990), this hydrolysis is avoided (see above) and in gastrocnemius
muscle of B. marinus the non-bicarbonate buffer value has been found
in that way to be 29.8 mequiv l-1 cell water pH unit-1
(Pörtner, 1990). Measured
similarly, values in white muscle of Z. viviparus average 31 mequiv
l-1 cell water pH unit-1, being slightly higher at
12°C than at 0°C (van Dijk et al.,
1997). A small positive error results from the conversion of MgATP
to ATP (see above) but, in Z. viviparus, the ATP concentration of 3.6
mmol kg-1 fresh mass (van Dijk
et al., 1997) implies a maximum contribution to the buffer value
of 2.1 mequiv l-1 fresh mass pH unit-1 (i.e.
3.6x0.575; Burton,
1973).
Buffer values in separated plasma, about 6-8 mequiv l-1 pH
unit-1 in mammals, are usually lower in plasma of ectothermic
vertebrates and lower still in their interstitial fluid
(Cameron and Kormanik, 1982;
Heisler, 1986a;
Tufts and Perry, 1998).
Other general findings are discussed below. These include the tendency for PCO2 to rise with increasing temperature and, in many tetrapod species, for whole-body CO2 content to fall.
Modelling the effects of temperature
In thinking generally about the effects of temperature on acid—base
balance, as opposed to fully analyzing experimental data, it is helpful to
start with a single-compartment model described mainly in terms of
differential equations expressing changes per degree rise in temperature. This
reduces the number of variables and allows easy exploration of the effects of
changing them, but the equations are strictly valid only for small temperature
changes. The equations are based on well-established principles (e.g.
Edsall and Wyman, 1958;
Reeves, 1972;
Burton, 1973;
Heisler and Neumann, 1980;
Heisler, 1986a), but some may
be novel. The model is in line with the general conceptual framework of Reeves
(1972), but lacks a
restrictive focus on imidazole buffering (item 2 of the hypothesis).
This model of what could be cells or extracellular fluid has a constant
volume and contains a single, notional, non-bicarbonate buffer having a buffer
value ß* and a temperature-dependent pK, denoted
pK* as above. Also present is HCO3-, for
which the buffer value in open system, ßbic, is
2.303[HCO3-]. For simplicity, the small amounts of
CO32- included by Reeves
(1972) are ignored here. With
the principle of electroneutrality in mind, we may define a quantity
N, reflecting the concentrations and net charge of all other
(non-buffer) ions present, such that, in terms of equivalents:
 | (3) |
N, when positive, can, for example, match
movements of HCO3- out of the compartment or the
production of dissociating lactic acid within it (see below). Effectively,
HCO3- movements in one direction are equivalent to
movements of CO32- or OH- in the same
direction or of H+ in the opposite direction. All are conveniently
described as movements of `base equivalents', so that an increase in
N can equate to a loss of base equivalents. Such changes may be part
of the acid—base adjustment or unrelated responses to temperature
change. In accordance with the definition of buffer value, buffer ionization
depends on the difference between pK* and pH
(Heisler, 1986a), such that:
 | (4) |
 | (5) |
 | (6) |
 | (7) |
 | (8) |
log[HCO3-] is
[HCO3-]/(2.303[HCO3-]) and
2.303[HCO3-] is ßbic,
 | (9) |
pK1'/T-logS/T
as a single term. It happens to be nearly constant at
0.0053°C-1 between 0 and 40°C (as calculated from data on
S and pK1' given by
Reeves, 1976b) and this value
is assumed in all calculations below. Two equations follow from Equations 5
and 9:
 | (10) |
 | (11) |
 | (12) |
[CO2]/T is often a minor
term in Equation 7.
The equations may be adapted to a model of several compartments, each of
fractional water volume (or mass) V, such that 
V=1.
Then both N/T and
[HCO3-]/T may be averaged for the
whole, as {VN/T} and
{V[HCO3-]/T},
respectively. While the terms ß*, ßbic,
pK*/T and pH/T may
differ from one compartment to another, the terms
pK1'/T-logS/T
and logPCO2/T, in the
absence of information to the contrary, may be taken as identical in each.
Equations 5 and 9 become:
 | (13) |
 | (14) |
Initial exploration of the model
Given the set of model equations, what general conclusions may be drawn,
using a minimum of specific experimental data and applying other postulates of
the alphastat hypotheses? Let us start by modelling either particular cells,
or all cells collectively, as a single compartment. The alphastat hypotheses
(items 7, 9 and 10) suggest that we consider the special case in which values
of both N/T and
CCO2/T are zero. With
the value of [HCO3-]/T taken as
similar to that of
CCO2/T (i.e. zero) in
accordance with Equation 12, Equation 11 then reduces to the approximation:
 | (15) |
pH/T equals
pK*/T. This accords with the imidazole
hypotheses provided that pK*/T reflects only
imidazole buffering. From Equation 15, with
pK*/T lying, say, between -0.011 and
-0.018°C-1 (see Introduction),
logPCO2/T is
0.016-0.023°C-1. Inasmuch as losses and gains of CO2
or base equivalents are best minimized, the model thus suggests an appropriate
relationship between PCO2 and temperature.
These values of
logPCO2/T can also be
expressed as Q10 values of 1.45-1.70. These lie within the
much wider range for arterial blood tabulated by Heisler
(1986c), namely 1.17-1.63 in
reptiles, 1.08-1.89 in amphibians and 1.04-1.95 in fish. (This overall range
corresponds to values of
logPCO2/T of
0.0017-0.029°C-1.) Matches between model and reality cannot
establish the correctness of the assumptions for any species, but they do
suggest that these could sometimes be about right.
The possibility that water breathers can increase
PCO2 as temperature rises has sometimes been
dismissed, and muscle PCO2 in Z.
viviparus may actually fall with rising temperature
(van Dijk et al., 1997). In
any case, the characteristic fall in plasma pH is partly due, in most fish
species studied, to a fall in plasma [HCO3-]. This is
discussed below, as also the temperature dependence of
PCO2 in reptiles and amphibians.
Item (6) of the hypothesis, reworded in model terms, states that regulation
of PCO2 to maintain constant buffer ionization
in one compartment maintains buffer ionization in all others. In the imidazole
alphastat scheme all values of NT are zero,
while the value of pH/T in each compartment equals that
of pK*/T. Equation 10 then reduces to
Equation 15 (not now an approximation). If values of
logPCO2/T are to be the
same in each compartment, so must those of
pK*/T; they are so in the idealized
alphastat model since all buffering is due there to similar imidazole
compounds. It is noteworthy that buffer values, i.e. bic and
ß*, do not appear in Equation 15, and are thus irrelevant. In
reality, the stated conditions do not generally apply. Nevertheless,
regulation of blood PCO2 may well help to
regulate pH appropriately in different cell types. Indeed, each type is likely
to be adapted — whether in evolution or from day to day — to the
characteristic temperature dependence of PCO2
to which it is exposed.
The model suggests an advantage, unrelated to pH optima, for the general
fall in intracellular pH with rising temperature: were it not to happen,
shifts of base equivalents amongst compartments (N) could
often be excessive. Modelling cells of a hypothetical fish as a single
compartment, suppose that pH/T were actually zero.
Suppose also that
logPCO2/T were
0-0.03°C-1 (encompassing the range of actual averages given
above), that intracellular ß* and ßbic were,
say, 50 and 4 mequiv kg-1 water pH unit-1, respectively,
and that the value of pK*/T were, say,
-0.015°C-1. Then, from Equation 10,
N/T would lie between -0.73 and -0.85 mequiv
kg-1 water °C-1, implying a movement of base
equivalents into the cells. (The most influential term is
ß*pK*/T.) Suppose now that
this shift applied to all cells in the body, that the ratio of extracellular
to intracellular water were 0.4 as in the channel catfish Ictalurus
punctatus (Cameron, 1980)
and that the extracellular [HCO3-] were initially, say,
7 mmol kg-1 water. A temperature rise of 4°C would then suffice
to deplete the extracellular fluid of all its HCO3-.
This is so unrealistic that the postulated constancy of cell pH has to be
wrong and the mean intracellular value of pH/T must be
negative. As discussed below, the lesser reduction in plasma
[HCO3-] that occurs with increasing temperature in many
fish is a separate issue. The argument applies less forcefully to
air-breathing vertebrates, in which extracellular
[HCO3-] is higher, but, as already noted, values of
pH/T within cells are typically negative even in these
animals. As to individual tissues, these may gain or lose base equivalents on
warming (e.g. Reeves, 1972;
Heisler and Neumann, 1980;
Heisler, 1986c;
Stinner and Hartzler,
2000).
Equation 10 may be rearranged as:
 | (16) |
pH/T
through adjustments in PCO2 and in N,
but it is the passive mechanism of non-bicarbonate buffering that acts more
promptly. This is represented by the term
(ß*/ßbic)(pK*/T-pH/T),
which may be positive or negative. In the special case that
pH/T equals pK*/T in
the steady state, non-bicarbonate buffering makes no ultimate contribution to
homeostasis, regardless of how much buffer is present. This contrasts with the
determination of pH/T by
pK*/T in CO2-free buffer
solutions.
In extracellular fluids, including cerebrospinal fluid, the buffer value,
ß*, is often much less than ßbic (see
Introduction). Then, regardless of the value of
pK*/T-pH/T, the
temperature dependence of pH is governed mainly by the values of
logPCO2/T and
(N/T)/ßbic. Further modelling
of the extracellular compartment in isolation is unrewarding, especially when
compared with previous treatments of true plasma (e.g.
Reeves, 1972;
Rodeau and Malan, 1979).
Applying the one-compartment model to fish cells
In its ideal form, the alphastat scheme has proved particularly
inappropriate to the water-breathing fish that have been studied, for
temperature changes in these produce substantial shifts of base equivalents
into and out of both cells and body, as well as changes in plasma
[HCO3-]. Here we start by modelling all the cells of the
body as a single compartment. As in the source papers, it is assumed that
N/T relates only to shifts of base equivalents
across cell membranes, and not to metabolic changes within cells. The first
two examples illustrate how old data may be usefully approached in new
ways.
The adult dogfish, S. stellaris, is notable for its high value of
logPCO2/T in arterial
blood, i.e. 0.029°C-1 on average as compared with
0.0017°C-1 in juveniles
(Heisler et al., 1980).
Warming leads to net loss of base equivalents from the cells collectively, and
also from the whole body. Unusually, extracellular
[HCO3-] rises
(Heisler et al., 1980;
Heisler, 1984). In modelling
the cells, we may take the following representative values:
logPCO2/T,
0.029°C-1; ß*, 45 mequiv kg-1 cell
water pH unit-1; N/T, 0.105 mequiv
kg-1 cell water °C-1
(Heisler and Neumann, 1980;
Heisler, 1984). Based on an
intracellular [HCO3-] of "about 1 mmol
l-1" (Heisler and
Neumann, 1980), ßbic is 2.3 mequiv kg-1
cell water pH unit-1. The value of
pK*/T-pH/T may now be
estimated from Equation 10. If the value of
pK*/T is taken to be between -0.011 and
-0.018°C-1 (see Introduction), that of
pK*/T-pH/T must be
0.0025-0.0028°C-1. For white muscle, which makes up most of the
fish, the corresponding difference is also positive, approximately
0.001°C-1, since pK*/T is
approx. -0.017°C-1 (see Introduction) and
pH/T is approx. -0.018°C-1
(Heisler et al., 1980). The
estimated difference of 0.0025-0.0028°C-1 for all cells
collectively, multiplied by ß*, implies that non-bicarbonate
buffering generates base equivalents at 0.11-0.13 mequiv kg-1 cell
water °C-1. The value chosen for whole-body ß*
is based somewhat arbitrarily on measurements on white, red and cardiac
muscle, all possibly raised artefactually by inorganic phosphate (see
Introduction). If a lower value is used, say 30 mequiv kg-1 cell
water pH unit-1, the estimate of
pK*/T-pH/T becomes
0.0037-0.0042°C-1 and the quantities of base equivalents
generated on warming are 2.4% lower.
The mean value of
pK*/T-pH/T may also
be estimated for the intracellular compartment of I. punctatus. Data
of Cameron and Kormanik (1982)
suggest the following representative values. For the whole body:
logPCO2/T,
0.0164°C-1;
{VN/T}, 0.056 mequiv
kg-1 cell water °C-1. For all cells: V,
0.726; pH/T, -0.0148°C-1;
[HCO3-]/T, -0.028 mmol
kg-1 water °C-1; ß*, 35 mequiv
kg-1 water pH unit-1. For the extracellular fluid:
V, 0.274; pH/T, -0.0141°C-1;
[HCO3-]/T, -0.097 mmol
kg-1 water °C-1; ß*, say 4 mequiv
kg-1 water pH unit-1 (chosen as slightly below the value
of approximately 5.8 for blood with zero haematocrit). The extracellular value
of pK*/T is unknown, but not very critical.
If it is taken as, say, -0.013 to -0.019°C-1 (see
Introduction), then, from Equation 13, the intracellular value of
pK*/T-pH/T is
0.0003-0.0006°C-1, again positive. This seems small enough to
suggest item (4) of the alphastat scheme and implies very little generation of
HCO3- by buffering. From Equation 5, the value of
N/T for the cells is 0.039-0.048 mequiv
kg-1 water °C-1.
With increasing temperature, there is a net loss of base equivalents from
the cells of both these species, and a rise in
PCO2. These effects can be seen as alternative
ways of lowering cell pH. According to Equation 10, for constant intracellular
values of ßbic, ß*,
pK*/T and pH/T,
reduction in the value of N/T from x
to zero in a model fish would require that the value of
logPCO2/T be raised by
x/ßbic. In S. stellaris the value of
logPCO2/T would thus
need to be approximately 0.075°C-1. Such a high, perhaps
unattainable, value does not explain why the shifts in base equivalents occur
in the real fish, since, with only minor changes in
pK*/T or pH/T,
N/T could be zero even at constant
PCO2.
The air-breathing swamp eel Synbranchus marmoratus contrasts with
these two species in that, collectively, the cells take up base equivalents on
warming, i.e. about 0.25 mequiv kg-1 cell water °C-1
(Heisler, 1984). Here,
therefore, the value of pK*/T must be more
negative than that of pH/T. Indeed, values of
pH/T are only -0.009 and -0.003°C-1,
respectively, in white skeletal muscle and heart.
White skeletal muscle of Z. viviparus is of interest for its high
value of N/T
(van Dijk et al., 1997). From
the mean value of [HCO3-]/T, i.e.
-0.27 mmol kg-1 cell water °C-1, and from estimates,
already noted, of pH/T in vivo and of
pK*/T and ß*, the value of
N/T is calculated from Equation 5 as 0.58
mequiv kg-1 cell water °C-1. If all the cells were
like this, large temperature changes would have major implications for
extracellular homeostasis.
Applying the model to tetrapods: the protein titration hypothesis of
Stinner et al. (1998)
In detailed studies of C. constrictor, Stinner and Wardle
(1988) and Stinner et al.
(1998) found an increase in
whole-body CO2 stores with cooling, and with it increases in both
CCO2 and pH in arterial plasma and skeletal
muscle. Little evidence was found for changes in either lactate or the balance
of inorganic anions and cations that would suggest shifts of base equivalents.
It was concluded that changes in whole-body CO2 stores result from
changes in protein ionization coupled with ventilatory regulation of
PCO2, such that the overall value of
pKprot/T is more negative than that of
pH/T. Thus there is titration of proteins by carbonic
acid (along with other non-bicarbonate buffers), rather than a maintenance of
their overall ionization state as in item (4) of the hypothesis.
Stinner et al. (1998)
extended this idea to other reptiles and amphibians. Whole-body CO2
stores increased with cooling in all 13 species studied
(Stinner and Wardle, 1988;
Stinner et al., 1994,
1998). The changes took many
hours. Mean values of
CCO2/T ranged from -0.02
mmol kg-1 body mass °C-1 in R. catesbeiana,
to -0.21 mmol kg-1 body mass °C-1 in the tortoise,
Testudo graeca. Presumably the range would be even greater if
expressed in terms of body water. Only in the bullfrogs do the results seem
close to the alphastat prediction of constant tissue CO2
content.
The further analysis by Stinner et al.
(1998) may be described in
terms of the one-compartment model, in which Equation 7 shows the determinants
of CCO2/T. The term
N/T is regarded as negligible on the basis of
the findings for C. constrictor. As already noted, the term
[CO2]/T is also trivial here. Thus Equation
7 reduces to:
 | (17) |
) took the
whole-body value of pH/T as approximating that for
arterial plasma and found a linear relationship between that and whole-body
CCO2/T (10 species;
r=-0.93). The values of pH/T are mostly taken
from other studies over similar ranges of temperature
(Howell et al., 1970;
Jackson et al., 1974;
Malan et al., 1976;
Bickler, 1981;
Wood et al., 1981;
Nicol et al., 1983). The
equation of the regression line is:
 | (18) |
pK*/T of -0.022°C-1.
As Stinner et al. (1998)
pointed out, this value of pK*/T is
reasonable for some small imidazole compounds. However, the real value is
probably no more negative than -0.018°C-1 (see Introduction).
As for that whole-body value of ß*, it may be re-expressed in
terms of body water using a representative body water content of, say, 76%
(Deyrup, 1964;
Bentley, 1976); it then becomes
10.8 mequiv kg-1 water pH unit-1. This is little above
the 8.1 mequiv l-1 pH unit-1 calculated for plasma of
C. constrictor, despite the greater contribution of the cells, where
ß* is presumably much higher (see Introduction). It therefore
seems improbably low. Next, the assumption that the whole-body value of
pH/T approximates that for arterial plasma may be
inappropriate, since values of pH/T in C.
constrictor averaged -0.009°C-1 in muscle and
-0.0028°C-1 in arterial plasma. (Modelling of the sort to be
described next, but starting with Equations 13 and 18, also shows the
assumption to be implausible.)
The data may be better modelled by treating the body water as two
compartments, intracellular and extracellular, and taking account of data on
PCO2. Values of
logPCO2/T are assumed to
be the same in both compartments, both for simplicity and because the average
differences in PCO2 between blood and cells in
these air breathers are likely to be small
(Burton, 2001). Again
{V[HCO3-]/T} is
taken as approximating
CCO2/T. Equation 18 is
assumed to apply exactly. Plausible values, representing all species
collectively, are allotted to other parameters. The water content of the body
is again taken as 76%.
Fig. 1 shows the
correlations between pH/T and
logPCO2/T in arterial
plasma and between
CCO2/T and
logPCO2/T for the whole
body. The nine species fall into two groups and the mean values for each group
of pH/T and
logPCO2/T are shown by
crosses marked A and B. For group A they are, respectively,
-0.015°C-1 and 0.018°C-1. For group B they are,
respectively, -0.004°C-1 and 0.008°C-1. Values
of CCO2/T corresponding
to groups A and B, calculated from Equation 18, are -0.058 and -0.148 mmol
kg-1 body mass °C-1, or -0.076 and -0.195 mmol
kg-1 water °C-1, respectively.
|
For the extracellular and intracellular fluids, respectively, the values of
V are taken as 0.4 and 0.6 and the bicarbonate buffer values,
ßbic, are taken as 60 and 24 mequiv kg-1 water pH
unit-1. From these parameters and the data of the previous
paragraph, the value of pH/T for the cells is
calculated using Equation 14. For both sets of data it is
-0.0141°C-1. The important point here is not its exact value,
which depends on the chosen parameters, but the fact that the mean values for
the two groups of species are plausibly modelled as similar. This seems a
reasonable postulate (despite differences within groups) if optimum cell
function depends on the relationship between intracellular pH and
temperature.
The parameters ß* and
pK*/T for extracellular fluid are now
allotted plausible values, say 5 mequiv kg-1 water pH
unit-1 and -0.018°C-1, respectively (see
Introduction). Then the extracellular values of
N/T, calculated from Equation 10, are 0.123
mequiv kg-1 water °C-1 for group A and 0.008 mequiv
kg-1 water °C-1 for group B. Warming therefore leads
to a loss of base equivalents from the extracellular fluid. These calculations
may be repeated for the whole body using Equation 13, with values for
ß* and pK*/T in the
intracellular fluid taken, say, as 25 mequiv kg-1 water pH
unit-1 and -0.0130°C-1, respectively. Then the
whole-body value of N/T, i.e.
{VN/T}, is 0.087 mequiv
kg-1 water °C-1 for group A and 0.183 mequiv
kg-1 water °C-1 for group B. These are almost equal,
but opposite in sign, to the respective values of
CCO2/T given above.
(That this is about equally true of the two group means was arbitrarily
achieved by adjusting the value of pK*/T.)
For groups A and B, the sums
{VN/T}+CCO2/T
are, respectively, +0.011 and -0.012 mequiv kg-1 water
°C-1. These small differences correspond to the titration of
proteins and other buffers (Equation 13).
The model compares and integrates data from two groups of species, but the
diagnoal lines in Fig. 1 can
also represent the changes in a single hypothetical individual as the value of
{VN} alters after temperature changes. After warming, there is
a loss of gaseous CO2 from its body and, as modelled, this loss is
nearly matched by a loss of base equivalents. These come partly from the
cells, with the CO2 generated from HCO3- and
H+ ions (and almost entirely so in the case of group B). The
reduction in [HCO3-] in the cells is matched by a fall
in PCO2 that keeps the value of
pH/T constant. (For the
PCO2 to fall even as CO2 is
generated from HCO3-, ventilatory adjustments to
PCO2 would have to be rapid; the many hours
needed to achieve a steady state would thus reflect slow changes in N
rather than slow gas exchange.) If the value of
{VN/T} were zero,
CCO2/T would be positive
instead of negative, i.e. 0.036 mmol kg-1 water °C-1
(calculated from Equations 13 and 18).
No one set of parameters can be right for all species, and each species or
individual should ideally be modelled with its own set. Moreover, data for
real cells are generally for particular muscle tissue rather than for the
whole intracellular compartment. The chosen parameters are broadly in line
with data given in the Introduction, but the constant intracellular value of
pH/T in the model (-0.0141°C-1) is more
negative than the values of -0.009, -0.012 and -0.007°C-1
measured in skeletal muscle of C. constrictor, R. catesbeiana and
B. marinus, respectively (Stinner
et al., 1998; Stinner and
Hartzler, 2000). It is closer to the mean whole-body intracellular
value (-0.0151°C-1) obtained by Bickler
(1982) in the lizard
Dipsosaurus dorsalis, itself more negative than his values for
skeletal and cardiac muscle (-0.0098 and -0.0104°C-1,
respectively).
According to the model,
[HCO3-]/T for the extracellular
fluid is negative, having values of -0.14 and -0.08 mmol l-1
°C-1, respectively, for groups A and B (calculated from
Equations 5 or 9). Some values determined for real arterial plasma in these
tetrapods are similar in sign and magnitude
(Wood et al., 1981;
Stinner and Wardle, 1988;
Stinner et al., 1998), but
others do not differ significantly from zero
(Jackson et al., 1974;
Bickler, 1981;
Nicol et al., 1983;
Stinner et al., 1994). Shifts
of base equivalents (N/T) between compartments
are hard to quantify experimentally, because accurate analyses are needed for
all ions present. The shifts seem insignificant in D. dorsalis
(Bickler, 1984) and, although
they do occur in B. marinus and R. catesbeiana, a consistent
trend is not evident (Stinner and
Hartzler, 2000). Neither these discrepancies and uncertainties,
nor the arbitrariness of some model parameters, invalidate the
semi-quantitative conclusions summarized next.
Two important conclusions have emerged. Firstly, it is shown that mean
intracellular values of pH/T could be similar in the
two groups of species. Secondly, the net loss of gaseous CO2
following a rise in temperature could be due largely to titration of
HCO3- as base equivalents are lost from cells and body
(or proton equivalents gained). The latter idea is absent from the model of
Stinner et al. (1998), but was
originally suggested by Stinner
(1982) for the snake
Pituophis melanoleucus. Bickler
(1984) did not find evidence
for a major role of excretion in the acid—base responses of D.
dorsalis to temperature. Moreover, in none of the species can the loss of
base equivalents be due mainly to excretion of HCO3-
since the accompanying reduction in whole-body CO2 stores is
measured as gaseous CO2. It is therefore more likely that the
whole-body gains and losses of base equivalents involve metabolic adjustments
to intracellular concentrations of organic ions (see below). Because
pH/T does not alter, these would not be homeostatic for
pH. A major temperature-dependent process modifying N, and best
developed in species where CCO2 changes most,
should now be sought. Although the model is made consistent with the
relationship of Equation 18, that remains unexplained.
Discussion
The equations provide a convenient approach to the effects of temperature on pH, PCO2, [HCO3-] and buffer ionization. They can be used both to explore the effects of varying buffer properties etc. in hypothetical animals and to complement previous analyses of experimental data. The tetrapod model unites various facts, ideas and uncertainties in what may be less a true description than a step towards better understanding. Indeed there are yet more uncertainties involved and some of these are discussed under the next heading. Also discussed below are other parts of the imidazole alphastat scheme (items 5, 11 and 12) that do not relate directly to the model, and three phenomena that are excluded from the strict alphastat scheme. These are metabolic adjustments to non-buffer ions within cells, and movements of base equivalents both amongst cells of different types and between body and environment.
Some limitations of the model in interpreting measurements on real
animals
In the model `total CO2' consists just of the dissolved gas and
HCO3- ions, and their reactions are treated in terms of
a straightforward apparent equilibrium constant, pK1'.
However, this has been found in many studies to decrease with increasing pH
(e.g. Dill et al., 1937;
Boutilier et al., 1985;
Heisler, 1986a). This effect
can markedly influence estimates of intracellular
[HCO3-] when this is calculated from
PCO2 and pH
(Reeves, 1976a).
Unfortunately, the influence of pH on pK1' varies from study
to study and a relationship quantified for arterial plasma may be wrong for
cells, especially when some of the cell water is `bound'
(Garner and Burg, 1994).
Uncertainties regarding pK1'/T and
[HCO3-]/T are much less. This
effect of pH is not fully understood. `CO2' as measured
gasometrically exists not only as free HCO3- and
dissolved gas (plus minute amounts of carbonic acid), but as
CO32- (generally in small amounts), as carbamate (barely
studied outside of erythrocytes), possibly as the compound
H2CO3.HCO3-
(Covington et al., 1981) and
as ion pairs of HCO3- with cations such as
Na+, Mg2+ and Ca2+. Boutilier et al.
(1985) and Burton
(1987) discuss these and other
uncertainties in calculating `[HCO3-]' from pH and
PCO2. According to formulae given by Heisler
(1986a), values of
pK1'/T-logS/T
for solutions resembling protein-free plasma are about
0.0053°C-1 for 0-25°C, as above, and about
0.0069°C-1 for 25-35°C. As discussed in the next paragraph,
the intracellular PCO2 cannot be assumed to be
exactly that of accessible extracellular fluids.
The single-compartment model is homogeneous, unlike both real extracellular
space and real cells. Regarding PCO2, this is
generally higher in venous than arterial plasma and higher still in
interstitial fluid (Pörtner and
Sartoris, 1999), and cells vary in their relationships to blood
vessels. As modelled by Burton
(2001), the discrepancy
between arterial and mean whole-body interstitial or cellular
PCO2 varies inversely with arterial
PCO2 and is therefore greatest in
water-breathing fish. How far the discrepancy varies with temperature is
unclear, because it depends also on respiratory quotient, oxygen tensions, the
relative solubilities of the two gases, and the possible disequilibrium of
CO2 in blood. As modelled for the whole body, average interstitial
and cellular PCO2 in some fish can be more than
twice the arterial PCO2. For real cells
CCO2 has sometimes been calculated from cell pH
and arterial PCO2 by the method of Cameron
(1980); for fish especially,
the results could be much too low. Equation 14 is based on the assumption that
logPCO2/T, but not
necessarily PCO2, is the same in all
compartments.
Cytoplasm is heterogeneous too. Much of a cell may be taken up with acidic
organelles or the very alkaline mitochondrial matrix. In addition, local
variations in net fixed charge density on proteins and membranes must cause
inhomogeneities of pH and [HCO3-]. Estimates of cell pH
made using DMO (5,5-dimethyloxazolidine-2,4-dione) yield values that
approximate to averages for the whole cell contents, but, more exactly, what
is averaged is 10-pH (Waddell
and Bates, 1969). There is little quantitative information on
mitochondrial pH in vivo and on its temperature sensitivity in
ectotherms. However, Moyes et al.
(1988) have studied
mitochondria isolated from red muscle of the carp, Cyprinus carpio:
provided extramitochondrial pH varied as in vivo, the transmembrane
pH gradient remained constant. If this gradient is generally insensitive to
temperature in ectothermic vertebrates, then values of
pH/T in cells obtained with DMO should reflect
cytosolic values. Cell [HCO3-] may be calculated from pH
and PCO2. With pH values obtained by the DMO
method, the resulting [HCO3-] averaged over all
subcompartments, each with its fractional volume V and concentration
[HCO3-], equals
1/{(V/[HCO3-])}, where
V=1. Given, for example, two subcompartments of equal volume
differing in pH by 0.3, the true mean [HCO3-] is 12%
higher than that calculated from the pH measured by DMO. Pörtner and
Sartoris (1999) give a
detailed analysis of the effects of cytoplasmic heterogeneity on pH
measurements and calculations of [HCO3-].
The model compartments are of constant vol
