Clinical Science (1990) 78,247-254
247
Editorial Review
Methods for expressing the characteristics of transmembrane
ion transport systems
J. K. ARONSON
MRC Unit and University Department of Clinical Pharmacology, Radcliffe Infirmary, Oxford, U.K.
INTRODUCTION
In recent years, many groups of clinical scientists have
become interested in measuring transmembrane ion
fluxes of various kinds in patients with different diseases.
The ion fluxes of interest have included the ouabainsensitive Na+/K+ pump, the loop-diuretic-sensitive Na+/
K+ co-transport system, the phloretin-sensitive Na+/Na+
(or Na+/Li+) countertransport system, and the amiloridesensitive Na+/H+ antiport. The diseases of interest have
included chronic renal failure, essential hypertension,
affective disorders, endocrine disorders, haemolytic
anaemias, neuromuscular disorders, cystic fibrosis and
obesity, in studies too numerous to refer to individually
here (for a general review of some of these see [ 11).
In studies of this kind it has become common for
workers to measure the intracellular o r extracellular concentration of the ion in which they are interested, the rate
at which that ion is transported across the cell membrane
in one direction or another, and the so-called 'rate
constant' of the transport. T h e 'rate constant' is taken to
be a function of the rate of transport and the concentration from which the transport is occurring.
It is my purpose in this review to suggest that this 'rate
constant' is not an appropriate way of delineating the
characteristics of a transmembrane ion transport system. I
shall lay the theoretical foundation by discussing the
glycoside-sensitive K + influx and Na+ efflux, i.e. the
transmembrane inward transport of K + and the outward
transport of Na+ mediated by the action of the Mg2+dependent, Na+,K+-activated adenosine triphosphatase
(Na+/K -ATPase, EC 3.6.3.37).
+
RELATIONSHIP BETWEEN THE CONCENTRATION OF AN ION AND THE RATE OF FLUX OF
THAT ION
For simplicity in this section I shall discuss the theoretical
arguments in relation to the ouabain-sensitive K + influx.
Correspondence: Dr J. K. Aronson, MRC Clinical Pharmacology Unit, University Department of Clinical Pharmacology,
Radcliffe Infirmary, Woodstock Road, Oxford OX2 6HE, U.K.
However, the arguments apply equally well to the
ouabain-sensitive Na+ efflux and to other fluxes, such as
the Na+/K+/Cl- co-transport.
The relationship between the extracellular K + concentration and the rate of K + influx into a cell would be given
by those who express their results in terms of a 'rate
constant' in the following way:
where v is the rate of K + influx, [K+],, is the external K +
concentration, and k is the 'rate constant'. Thus, the
concept of a 'rate constant' involves the assumption that
the relationship between the influx of K + and its external
concentration is linear, as shown in Fig. 1 (broken line).
However, it has long been known that this is not the
case, and that the relationship between the influx of K +
and its external concentration is, at the very simplest,
hyperbolic [2]and described by the following relationship
[rearranged from eqn (2) of [3] and substituting K+ for
Na+]:
where v is the rate of K + influx and [K+], is the external
K + concentration, both as before. However, their relationship is governed by two new constants, the v,,,
which is the maximal rate of K+ influx that the Na+/K+ATPase can support and which occurs at high values of
[K+],, and the K,, which is the external K + concentration
at which the rate of influx is half-maximal. The form of
this equation will be recognized by enzymologists as being
the same as that used for describing enzyme kinetics (the
Michaelis-Menten equation) and by pharmacologists as
being the same as that used for describing the binding of a
ligand to its receptor (Langmuir's adsorption isotherm). A
relationship of this sort is shown in Fig. 1 (continuous
line).
It is clear that eqn (1)and eqn (2) are not the same (cf.
the two curves in Fig. l),and that the 'rate constant' as I
have defined it here cannot be an adequate description of
J. K. Aronson
248
same arguments apply) which is low enough to satisfy the
definition of a true rate constant. How should we interpret
the observation of a change, or of no change, in the true
rate constant of K+ influx or of Na+ efflux in such an
experiment? In Figs. 2 and 3 I have shown theoretical
activation curves which illustrate several different cases
for interpretation.
Case 1: a decrease in the true rate constant
I/
’“:
0
0
10
20
[K+I,, (mmol/l)
Fig. 1. Relationship of K + influx in human erythrocytes
to [K+],,.The broken line is the tangent to the curve at the
origin. (Redrawn and adapted from [2], with permission.)
the characteristics of the influx of K + via the N a + /
K+-ATPase if eqn (2) is the correct way to describe that
influx (1 shall discuss more complicated models below).
However, at concentrations of [K+], substantially lower
than the K , the value of ( K , + [K],) [the denominator in
eqn (2)]becomes approximately equal to K,, and in these
circumstances eqn (2)becomes:
(3)
It can be seen that eqn (3)is the same as eqn ( l ) , with k,
the ‘rate constant’, equal to the ratio V,,/K,. Thus, the
correct interpretation of the ‘rate constant’ for K + influx
as I have defined it above is that it is the ratio of the rate of
K + influx to the external K + concentration only when the
influx is measured at concentrations of external K + which
are low by comparison with the K,. Another way of
putting this is that the ‘rate constant’ is the slope of the
tangent at the origin to the hyperbolic curve (the activation curve) of influx (Fig. 1). I shall call this rate constant a
‘true rate constant’, since it is constant over the relevant
range of concentrations (i.e. at concentrations below the
Km).
However, the ‘rate constant’ is often measured at concentrations of the ion which are above the K,, and in
these circumstances the ‘rate constant’, v/[K+],, becomes
equal not to V m a X / K ,[see eqn (3)] but to Vmm/
( K , + [K+],) [see eqn (2)]. In these circumstances the ‘rate
constant’ is not a constant and I shall therefore call the
rate constant measured under these circumstances a
‘quasi rate constant’.
INTERPRETATION OF CHANGES IN THE TRUE
RATE CONSTANT
Let us then assume that an experiment is carried out at a
concentration of external K+ o r of internal Na+ (since the
Under the defined conditions the true rate constant
k = Vmm/K,.This means that a decrease in k could come
about as a result of any one of five different combinations
of changes in V,,,, and K,: case la, a decrease in Vmm,;
case 1b, an increase in K,; case lc, a decrease in V,,,
with a concomitant increase in K,; case Id, an increase in
V,,, with a larger increase in K,; case le, a decrease in
K , with a larger decrease in V,,,. These are not simply
theoretical possibilities. Most, if not all, of these patterns
of change have been demonstrated in different circumstances, itemized below. As well as illustrating these
changes schematically in Fig. 2 (a-e, corresponding to
cases la-le) I have illustrated two of the cases in Figs.
4(a) and 4(b), using real examples taken from the
published literature.
Case l a (Fig. 2 4 . Partial depletion of human erythrocyte membrane cholesterol by incubation with phosphatidylcholine vesicles causes a decrease in the Vmm,of K +
influx without altering the K , (Fig. 4 a taken from [4]).
Case l b (Fig.. 2b). When human erythrocytes are
exposed to ions such as T1+, Rb+ or Cs+, there is a pure
increase in the K , of transport, provided the conditions
are right. For example, TI+ (0.1 mmol/l) causes a doubling
of the K , of K + influx in human erythrocytes in the
presence of a low external concentration of Na+ (Fig. 46,
taken from [5]).
Case l c (Fig. 2 4 . When purified Na+/K+-ATPase is
trypsinized and incorporated inside-out into phospholipid vesicles, the V,,,, of Na+ flux is decreased and its K,,,
is increased [6].
Case Id (Fig. 2 4 . At the time of writing, I have found
no example of this pattern of change in the N a + /
K+-ATPase. However, as I shall discuss below, a change
of this kind is found in the co-transport of Na+/K+/CIin the erythrocytes of patients with essential hypertension.
Case l e (Fig. 2 4 . When human erythrocytes are
exposed to a reduced temperature, both the K , and the
Vmm,of K+ influx are reduced. However, the extent of
reduction in the V,,, is much greater than the extent of
reduction in the K,. For example, reducing the temperature from 37°C to 27°C causes a 29% decrease in K , and
a 60% decrease in Vmm,[7].
Case 2: no change in the true rate constant
Superficially it might appear that no change in the true
rate constant of a transport system under particular
circumstances must imply that in those circumstances the
characteristics of the transport system are not altered.
However, that is not the case. Under the conditions
Characterizingion transport systems
l01
Case la
1°1
249
Case Ib
Km t
0
10
Ion concn.
15
0
5
10
Ion concn.
15
0
5
15
0
'5
10
Ion concn.
15
X
2
c
.-0
CCI
0
Q
4-
2
1°1
10
Ion concn.
Case l e
X
ac
.-0
G I
0
0
4-
Vmax.
2
0 ,
0
I
I
5
10
Ion concn.
Km
1
i
15
Fig. 2. Schematic representations of the five cases of changes in V , = , and/or K, which may
result in a decrease in the true rate constant. In each case a schematic normal activation curve
(-)
is compared with the curve which would occur in the changed circumstances specified
(----). Note that the quasi rate constant at a specified ion concentration decreases in cases la,
lb, l c and le. The possible changes in quasi rate constant in case Id are discussed in detail in the
text. The following values (arbitrary units) have been used to construct these curves:
Normal
Case l a
Case l b
Case lc
Case Id
Case l e
10
5
10
5
15
4
-
2
2
4
4
8
1.5
J. K. Aronson
250
Case 2b
Case 2a
151
x 10E
C
.-0
LI
0
Ion concn.
Ion concn.
Fig. 3. Schematic representations of the two cases of changes in V,,, and K , which may result in
no change in the true rate constant. In each case a schematic normal activation curve (-)
is
compared with the curve which would occur in the changed circumstances specified (----). Note
that the quasi rate constant at a specified ion concentration increases in case 2a and decreases in
case 2b. The following values (arbitrary units) have been used,to construct these curves:
Normal
Case 2a
Case 2b
defined above, the true rate constant k = VmaX/K,,and
there are thus two possible combinations of changes in
Vma. and K , which would lead to no change in the true
rate constant: case 2a, an equal increase in both V,,, and
K,; case 2b, an equal decrease in both V,=. and K,.
As in case 1, these possibilities are not purely theoretical. Both of these patterns of change have been demonstrated in different circumstances, itemized below. As well
as illustrating these changes schematically in Fig. 3, I have
presented one of the cases in Fig. 4(c) using a real
example taken from the published literature.
Case 2a (Fig. 3 4 . Partial depletion of human erythrocyte membrane cholesterol by incubation with phosphatidylcholine vesicles causes symmetrical increases in the
Vma,and K , of Na+ efflux (Fig. 4c, taken from [4]).
Case 2b (Fig. 3b). The exposure of human erythrocytes to increased hydrostatic pressure causes symmetrical decreases in the Vma,and K , of K + influx [7].
Case 3: an increase in the true rate constant
It is obvious that the respective converses of the five
cases outlined above under case 1 will cause increases
rather than decreases in the true rate constant. I have not
presented schematic illustrations of these cases, since they
would simply be the same as those in Fig. 2 with the key
reversed. However, in Fig. 4(d) I have given a real
example taken from work done in our own laboratory.
Vmm
Knl
10
15
2
3
5
1
Case 3a. Incubation of human lymphocytes with Li+ (8
mmol/l) for 3 days causes an increase in the V,,, of Rb+
influx without a change in K , (i.e. the converse of case l a )
(R. J. Jenkins & J. K. Aronson, unpublished work, shown
in Fig. 4 4 .
Case 3b. The exposure of the erythrocytes of LK sheep
or goats to anti-L antibody causes a decrease in the K , of
K+ influx without a change in the Vma,(i.e. the converse
of case l b ) [8].
Case 3d. Reducing the internal concentration of K + in
human erythrocytes from normal to below 30 mmol/l
causes a reduction in the K , of Na+ efflux and a proportionately smaller reduction in the V,,, (i.e. the converse of case I d ) [3].
I have not found published examples of circumstances
affecting the Na+/K+-ATPase which are associated with
the other two patterns of change from normal (i.e. the
converses of cases l c and le).
In all these three cases the examples given are not
necessarily unique. For example, case 3a (here exemplified by the effect of Li+) also describes what happens to
Rb+ influx in human erythrocytes when the intracellular
Na+ concentration is increased above normal, in which
case the V,,, increases without a change in K , [3]. However, the effect of Li+ is due to an increase in the absolute
number of pump sites in the cell membrane without a
change in turnover number, whereas the effect of increasing the intracellular Na+ concentration is likely to be due
25 1
Characterizing ion transport systems
0.81 (a) Case l a
(c)Case 2a
0.5
/
P
A
0
Vmw.
-
( d ) Case 3a
x
t Krn t
10
i0
"a+], (mmol/l)
30
[Rb+], (mmol/l)
Fig. 4. Real examples of the ways in which changes in the V,,, or K , of ion transport may result
in changes in the true rate constant. In each part of the Figure the normal case is illustrated by
filled symbols and the changed case by open symbols. In cases l a and l b ( a and b) the true rate
constant decreases; in case 2a (c) the true rate constant is unchanged; in case 3a ( d )the true rate
constant increases. Note that in cases la, l b and 3a, the quasi rate constant at a specified ion
concentration changes in the same direction as the true rate constant; however, in case 2a the
quasi rate constant increases while the true rate constant remains unchanged.
( a )Change in the activation curve for ouabain-sensitive K + influx (measured in the presence of
a non-saturating concentration of external Na') when human erythrocyte membranes are
partially (35%) depleted of cholesterol. Vmm,and K, were calculated from the data in the Figure
using eqn (3)and JZ = 2. (Redrawn from [4], with permission.)
Vmm.
Normal
35% depleted
Km
(mmol h-I I - ! )
(mmol/l)
0.91
0.48
1.6
1.7
(b) Change in the activation curve for ouabain-sensitive K + influx when human erythrocytes are
incubated with thallium'(a,0.10 mmol/l; 0,0.15 mmol/l) in a low external concentration of Na'.
(Redrawn from [5],with permission.)
Normal
0.10 mmol/l TI+
0.15 mmol/l TI+
2.56
2.41
2.58
0.17
0.37
0.60
J. K. Aronson
252
Fig. 4 (contd.) (c) Change in the activation curve for ouabain-sensitive Na+ efflux when human
erythrocytes are partially depleted of cholesterol ( A , 15% depletion; 0, 35% depletion).
with permission.)
(Redrawn from [4],
Vmm.
(mmol h - ' I - ' )
2.4
7.0
19.0
Normal
15% depleted
35% depleted
Kln
(mmol/l)
3.2
5.3
11.5
(d)Change in the activation curve for ouabain-sensitive Rb+ influx when human lymphocytes are
incubated with Li+ (8 mmol/l) for 3 days (R. J. Jenkins & J. K. Aronson, unpublished work).
Vmax.
Kln
(fmoI/min per cell)
(mmol/l)
0.36
0.50
0.67
0.54
Normal
Li +
to an increase in turnover number without an increase in
the numbcr of pump sites. This last point illustrates the
fact that the demonstration of a change in the V,,, or K,
of transport is merely the first step in the characterization
of the underlying changes in pump function which result
in changes in these kinetic parameters.
MEASUREMENT OF THE 'RATE CONSTANT' AT
ION CONCENTRATIONS AT OR ABOVE THE K,,,
In the discussion so far I have assumed that the 'rate
constant' would be a true rate constant as I have defined
it, i.e. measured at an ion concentration low enough to
justify the assumption that the denominator of eqn (2),
(K, + [K+],), was approximately equal to the K,. However, this cannot be so for Na+ efflux in human erythrocytes, in which the K, for ouabain-sensitive Na+ efflux is
around 1.S mmol/l at the normal internal K+ concentration (about SO mmol/l) [3],while the normal internal Na+
concentration is about 8 mmol/l cells [9]. Similarly, for K+
influx the K, is about 1 mmol/l, and measurements made
in human erythrocytes at the physiological concentration
of external K + (4 mmol/l) will violate the assumption.
Thus, published 'rate constants' are usually quasi rate
constants, as defined above, rather than true rate
constants. I shall discuss the implications of this when I
come to consider the interpretation of published values of
'rate constants'.
MORE COMPLEX MODELS OF ION TRANSPORT
So far I have been considering the simplest type of activation curve, the rectangular hyperbola, whose function is
given by eqn (2). Eqn (2) is a particular case of a more
general function with the following equation:
(4)
If n is taken to be unity, eqn (2)results (with K, = K,,,,, as
explained below). However, for transport systems which
do not have one-for-one stoichiometry, eqn (2) is inadequate. For example, the stoichiometry of the transport
of K + and Na+ ions by the Na+/K+-ATPase is such that
two K+ ions are transported in for every three Na+ ions
transported out. If one assumes that transport will not
take place unless these numbers of ions are bound to the
transporter, eqn (4) is a more accurate expression of the
activation curves, with n = 2 for K+ influx and n = 3 for
Na+ efflux [3, 101. This is shown clearly in Fig. 4(c), in
which the activation curve for Na+ efflux in cells depleted
of cholesterol is sigmoid in shape rather than hyperbolic.
Note also that the curve shown in Fig. 1 as a rectangular
hyperbola would have taken on a sigmoidicity had more
data points been measured at the lowest concentrations.
Curves of this shape can be linearized by the use of square
root or cube root semi-reciprocal plots, from which the
values of V,=, and K,,,, may be derived.
[I have used the symbol K,,,, in eqn (4) rather than K,,
because the nature of the K,,,, changes when n changes.
When n = 1, K,,,, is the concentration of ion at which the
rate of transport is half-maximal, and this is how K, is
defined. However, Km9,,
# K, when n is other than unity.
For example, when n = 2, Km9,,
is equal to the ion concentration at which the rate of transport is equal to onequarter of the V,,.]
However, there is a further complication, since the
apparent K,.,, of the transport of one ion may be
influenced by the concentration of the other ion on the
same side of the membrane. For example, the apparent
K,,,, of the ouabain-sensitive Na+ efflux in human
erythrocytes is linearly related to the intracellular K+ concentration: at an intracellular K+ concentration of 150
mmol/l the K,,,, for Na+ efflux is 3.2 mmol/l, whereas in
the absence of internal K + it is 0.2 mmol/l [3]. For this
reason the following, more complex, function has been
suggested for the description of the ouabain-sensitiveNa+
and K+ exchange in human erythrocytes (rearranged from
eqn [ 111in [3]):
Characterizing ion transport systems
Even in this more complicated model the values assigned
to Km,,,(Na+)
and Km,rr(K+)
depend on the internal K+ and
external Na+ concentrations.
Other possible models are discussed in [lo] and [ll],
and all these additional complexities make the use of the
true and quasi rate constants as described above even
more tenuous as descriptors of the Na+/K+ pump.
METHODS FOR MEASURING THE Vma.AND K, OF
ION TRANSPORT SYSTEMS
The methods for measuring the V,,, and K, of transport
systems are well described. For example, the activation
curve for ouabain-sensitive K+ influx can be simply constructed by measuring the rate of influx of K+ (or of Rb+
as a substitute) into cells incubated in varying concentrations of K+ in the presence and absence of a cardiac
glycoside, such as ouabain or digoxin [12]. The
measurement of ouabain-sensitive Na+ efflux in this way
is more difficult, and requires pre-loading of the cells with
different concentrations of Na+, for example using
nystatin [ 131. Comparable techniques have been
described for other transport systems (for example, for
references on Na+/K+/CI- co-transport see [ 141).
Instead of measuring the efflux rate itself, one can
measure the quasi rate constant by measuring the concentration of ion inside the cell at various times during efflux
and then calculating the slope of the plot of log concentration with time, which equals the quasi rate constant.
Knowing the starting concentration, the rate of efflux can
then be calculated from eqn (1).This is a legitimate use of
the quasi rate constant and is discussed by Sachs & Welt
[lo].
If it is found too difficult to construct complete activation curves, then at a minimum one should measure the
V,,. of transport by measuring the rate of flux at a
saturating concentration of the ion, remembering that no
change in the V,,, does not necessarily mean that there is
no change in the K,,,,]. The Na+ and K+ concentrations
required to produce saturation of the ouabain-sensitive
transport can be calculated from eqn (5),taking the values
for Krn.n(Nat) and Krn.n(K+) from [3i.
INTERPRETATION OF PUBLISHED VALUES OF
'RATE CONSTANTS'
Changes in the true rate constant
If the rate constant for the flux of an ion has been
measured at a sufficiently low ion concentration to justify
the assumption that it is a true rate constant, i.e. is equivalent to the ratio V,,/K,,
changes in the rate constant can
be taken to be evidence of changes in the physiology of
the transport system involved. However, in such cases the
nature of the underlying changes in pump physiology
cannot be deduced (i.e. whether there are changes in V,,,
or in K,, or in both).
253
However, the observation of no change in a true rate
constant is strictly uninterpretable. It could mean that
there really is no change in the physiology of the transport
system, or it could mean that there are symmetrical
changes (increases or decreases) in both V,,. and K,.
Changes in the quasi rate constant
The usual problem in the interpretation of published
literature arises when one has to compare different groups
of subjects in regard to quasi rate constants rather than
true rate constants. Here there are two separate cases.
The quasi rate constants are measured at the same
concentration of the ion. In all such cases a difference in
quasi rate constants between groups is evidence of a
difference in the physiology of the transport system,
although, as in the case of the true rate constant, it will not
be possible to say whether the difference is due to a
change in V,,,, or in K,, or in both.
In this context, case Id (Fig. 2d) provides an instructive
example of the importance of characterizing the complete
range of transport functions rather than simply measuring
the rate of flux at a single ion concentration. In 1980,
Garay et al. [15] measured Na+/K+/CI- co-transport in
the erythrocytes of patients with essential hypertension.
They found a large reduction. Subsequently, Adragna et
al. [16] did the same. They found an increase. Both of
these results have been reproduced by others (see [l]and
~41).
The reason for this discrepancy becomes clear when
one examines the methods used. Garay et al. [15]
measured co-transport by measuring Na+ efflux at an
intracellular Na+ concentration of 20-30 mmol/l- I ,
whereas Adragna et al. [16] did it at a concentration of 50
mmol/l. Since the K, for Na+ efflux via the co-transporter system is around 13 mmol/l, the experiments in
which co-transport was found to be increased in hypertension were carried out at a concentration at which the
transport is about 80% saturated, i.e. near the V,,. In
contrast, the experiments in which co-transport was found
to be reduced in hypertension were carried out at a much
lower level of saturation (about 60%).
These results can be explained by case I d (Fig. 2 4 , in
which there is an increase in both V,,, and K,, the
increase in the latter being proportionately greater. This
results in reduced flux at low concentrations and
increased flux at high concentrations. Furthermore, if one
were to measure the rate of Na+ efflux via co-transport at
an intracellular Na+ concentration of around 30-40
mmol/l one would hit the spot where the two curves cross
and find no change in the rate of transport or quasi rate
constant, adding a third apparently discrepant result to
the two already described.
Interindividual differences in activation curves may
also explain the apparent differences which have been
found among sub-groups of hypertensive subjects, even
when co-transport is measured at a high ion concentration
[ 171. Even though one may measure the rate of transport
at an ion concentration which is near the V,,,, by SO
doing one obtains only an estimate of the true V,,,, since
254
J. K. Aronson
saturation is not complete and the extent of saturation at a
given ion concentration will vary from individual to individual. Only by completely characterizing the activation
curve in each individual can one determine whether or
not the true V,,, is altered, with the added bonus of finding out about the K,.
The quasi rate constants are measured at different concentrations of the ion. In this case it is possible to get any
result at all, an increase, a decrease, or no change in the
rate constant, no matter which of the cases illustrated in
Figs. 2 and 3 applies. The difficulties in interpretation
which can arise when this is done are demonstrated in
relation to erythrocyte ion fluxes in hypertension in [ 181.
CONCLUSIONS
Much interesting information about abnormalities of ion
transport systems has come in recent years from the study
of how those systems function in health and disease. However, many such studies are inadequate, in that they have
failed to define as precisely as is possible the exact nature
of the abnormalities in the physiology of those ion transport systems. Furthermore, the results of such studies are
not comparable with those of studies in which the K ,
and/or V,,,. of transport have been measured, and a
direct comparison of such results may lead to apparent
discrepancies in interpretation.
If the abnormalities in ion transport in various diseases,
such as renal failure and essential hypertension, are to be
described precisely it is important that investigators
attempt to delineate as complete a range of functions of
the transport systems they are studying as possible.
Furthermore, the example of the different effects of
erythrocyte membrane cholesterol depletion on K + influx
and Na+ efflux (cf. Figs. 4 a and 46) shows that at least as
far as the Na+/K+ pump is concerned both these
functions should be determined separately.
To argue that to d o this is to subject cells to unphysiological conditions is not relevant. The discoveries that the
Na+/K+ pump of erythrocytes could run backwards (i.e.
transport Na+ in and K + out) with the synthesis of adenosine 5'-triphosphate, and that it could support ouabainsensitive Na+/Na+ exchange, were made by studying cells
under unphysiological conditions [ 191. Nonetheless, these
observations, and others of a comparable nature, have
contributed enormously to our understanding of how the
Na+/K+ pump works in physiological circumstances [20].
Enzyrno~ogists characterize enzyme function by
measuring V,,, and K,; so d o clinical scientists [21].
Pharmacologists characterize ligand-receptor binding
interactions by measuring BmU,and K,; so d o clinical
scientists [22]. Physiologists characterize ion transport
systems by measuring V,,, and K,; so should clinical
scientists.
ACKNOWLEDGMENTS
I am grateful to Dr Clive Ellory for much helpful discussion during the preparation of this paper, and to the
Wellcome Trust for financial support.
REFERENCES
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3. Garay, R.P. & Garrahan, P.J. The interaction of sodium and
potassium with the sodium pump in red cells. J. Physiol.
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4. Claret, M.,Garay, R. & Giraud, F. The effect of membrane
cholesterol on the sodium pump in red blood cells. J.
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5. Cavieres, J.D. & Ellory, J.C. Thallium and the sodium pump
in human red cells. J. Physiol. (London) 1974;242,243-66.
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