489

J. Physiol. (1977), 273, pp. 489-514 With 10 text-figurem Printed in Great Britain

KINETIC EVALUATION OF THE NA-K PUMP REACTION MECHANISM BY J. R. SACHS From the Department of Medicine, State Univereity of New York at Stony Brook, Stony Brook, New York 11794 and the Department of Phy8iology, Yale Univer8ity School of Medicine, New Haven, Connecticut 06510, U.S.A.

(Received 16 March 1977) SUMMARY

1. The ouabain-sensitive K influx was measured at varying external K concentrations ([K]0) and at several fixed internal Na concentrations ([Na],). The cells were nominally K-free and the solutions Na-free. Both the apparent maximal velocity (VM) and the apparent Michaelis constant for K (KK) increased as Nac increased. The ratio app. VM/app. KK increased with increasing Nac. 2. The ouabain-sensitive Cs influx was measured at varying external Cs concentrations and at several fixed Nac in K-free cells and Na-free solutions. Both app. VM and app. Kr. increased as Na, increased and the ratio app. Vm/app. Kcs increased with increasing Nac. 3. The data were evaluated in terms of a ping-pong model and a simultaneous model for the pump reaction mechanism. The simultaneous model described the data adequately and the ping-pong models did not. 4. The K influx was measured at varying external K concentrations in solutions containing Na and at a low and high Na,; the cells contained K. The relation between the pump rate and the external K concentration was sigmoid. A Hill equation was fitted to the data. KK was higher in the high Nac cells, but the Hill coefficient (n) was not altered as Nac increased. 5. The K influx was measured at varying internal Na concentrations and two fixed external K concentrations; the cells contained K. The relation between the pump rate and Na, was sigmoid. When a Hill equation was fitted to the data, it was found that KNha was higher at the high external K concentration, but n was the same at both K concentrations. INTRODUCTION

The coupled movement of Na and K across cell membranes is accomplished by a protein which in broken membrane preparations demonstrates Na +K dependent ATP-ase activity. If both Mg and ATP are held at

490

J. B. SACHS

constant concentration and if Na and K are considered as substrates and varied in concentration, then the enzyme can be considered as catalysing a bisubstrate reaction. For such reactions there are two general mechanisms which are kinetically distinguishable: the ping-pong mechanism and the simultaneous mechanism (Cleland, 1963). (In this paper the term simultaneous is used to refer to mechanisms which Cleland (1963) refers to as sequential. This is to avoid confusion since the term sequential has been applied to mechanisms which Cleland (1963) refers to as ping-pong by previous authors discussing pump mechanisms.) As applied to the pump, the ping-pong mechanism requires that one of the ions (Na or K) first binds to the enzyme, is translocated, and released as product before the second ion binds. Following the release of the first ion, the second ion binds in turn, is translocated, and released; the pump is then ready for a second cycle. This mechanism implies that the pump can exist in two conformations, one with a high affinity for Na and the other with a high affinity for K, which occur in order during a pump cycle. The simultaneous model, on the other hand, requires that both ions bind to the enzyme before either ion is released as product at the opposite membrane surface. There is an extensive body of evidence obtained from the study of the Na + K dependent ATPase reaction and of the phosphorylated intermediates of the reaction which is most readily interpreted in terms of the ping-pong mechanism. It is clear that Na promotes phosphorylation of the enzyme (Post, Sen & Rosenthal, 1965) and K promotes dephosphorylation (Post, Kume, Tobin, Orcutt & Sen, 1969). In addition, under certain circumstances, it is possible to demonstrate that the enzyme catalyses an Na dependent ATP-ADP exchange (Fahn, Koval & Albers, 1966; Fahn, Hurley, Koval & Albers, 1966) and a K stimulated phosphate-water exchange (Dahms & Boyer, 1973). These findings suggest that there are two conformations of the phosphorylated intermediate which occur during the pump cycle, one induced by Na (E1P) and the other dephosphorylated by K (E2P). Evidence for two distinct conformations ofthe phosphorylated intermediate has also been obtained from the results of studies of the inhibition of the pump by N-ethylmaleimide (NEM) (Bannerjee, Wong, Khanna & Sen, 1972; Bannerjee, Wong & Sen, 1972). Support for the pingpong mechanism is also provided by evidence that under certain circumstances the pump is capable of carrying out a Na-Na exchange (Garrahan & Glynn, 1967a) and a K-K exchange (Glynn et al. 1970). The simplest explanation of these exchanges is that they represent the two half reactions of a ping-pong pump cycle and that they are carried out by two pump conformations which occur during a pump cycle. The earliest explicit model of the pump was formally a ping-pong mechanism in which a single site changed from high Na affinity to high K

Na-K PUMP REACTION MECHANISM 491 affinity during the pump cycle (Shaw, 1955). Recently studies of the effect of Na, K and the combination of Na and K on the interaction of inhibitors with the pump have been described which strongly suggest that high affinity sites for Na and K probably exist on the pump at the same time (Robinson, 1973, 1974; Skou, 1974). A similar conclusion can be drawn from the observation that Na increases the activity of the K-dependent phosphatase (Nagai, Izumi & Yoshida, 1966). This observation seems to require that pump sites for Na and K coexist at some point during a transport cycle. The simultaneous presence of Na and K sites is not, of course, inconsistent with a ping-pong mechanism, but it is also consistent with a simultaneous mechanism. Kinetic distinction between the ping-pong and simultaneous mechanism of bisubstrate reactions requires that the apparent Michaelis constant (KRa) and the apparent maximum velocity (VM) for one of the substrates be determined at several fixed concentrations of the other substrate in the absence of products of the reaction (Cleland, 1963). From the relation between the apparent Ks and the apparent VM as a function of the concentration of the second substrate, distinction between the two mechanisms can be made. Baker & Stone (1966) have discussed early experimental measurements in terms of the two models and several such measurements in red cells have been reported. Hoffman & Tosteson (1971) using sheep red cells found that the apparent Ks for intracellular Na did not vary with the extracellular K concentration; the cells contained K. Similarly, Garay & Garrahan (1973) reported that in human red cells the apparent Ks for Rb did not vary with intracellular Na; the cells apparently contained K. On the other hand, Chipperfield & Whittam (1974, 1976) reported that the apparent Ks for K increased as intracellular Na increased; the ratio VMIKs decreased. In these experiments both extracellular Na and intracellular K were kept low. In all three cases the results were interpreted as inconsistent with a ping-pong mechanism. In view of the importance of the conclusion and the apparent disagreement about the findings, it seemed desirable to pursue the matter further. METHODS Venous blood was obtained from healthy donors and anticoagulated with heparin. The cells were separated from the plasma by centrifugation and the plasma and buffy coat removed by aspiration. The cells were then washed thrice in unbuffered isosmotic (107 mm) MgCl2 solution and used as appropriate. Alteration of intracellular cation content was accomplished by a modification of the PCMBS (p-chloromercuribenzenesulphonic acid) method described by Garrahan & Rega (1967); details of the procedure have recently been described (Sachs, 1977; Kropp & Sachs, 1977). Unidirectional influx measurements were made as previously described (Sachs, 1977). Cells were distributed to centrifuge tubes containing the appropriate ice-cold

J. R. SACHS

492

solutions with 42K or 137Cs; the final haematocrit was about 1 %. The influx was begun by placing the tubes in a 37 0C water-bath and the suspensions were mixed as necessary to keep the cells suspended. After 0-5 hr the fluxes were terminated by immersing the tubes in an ice-cold water-bath. The cells were then separated from the suspensions and washed thrice in isosmotic MgCl, solution. The washed cells were haemolysed in distilled water and counted. The influx was calculated from the amount of 4"K or 1i7Cs taken up by the cells over the 0-5 hr period and the specific activity of the solution. No correction was made for backflux since the ouabain insensitive fluxes were small and measurements were of short duration; backilux estimated from the total influx and the ouabain insensitive influx was always less than 2 % of the ouabain sensitive influx. Measurement of the supernatant K or Cs concentration was made by flame photometry at the begining and end of the influx measurement and the average of the values taken. The method for the measurement of the unidirectional 4"K or 2"Na outflux has also been recently described (Kropp & Sachs, 1977). Cells were loaded with 4"K or "2Na while the cells were being exposed to the PCMBS solution. When "SK outfilux was measured, the cells were suspended at about a 20 % haematocrit in a Tris P0O solution (295 m-osmole/kg HO, pH 7-4 at 37 00) and incubated at 37 0C for 0-5 hr. The cells were then separated from the solution and washed 3 times in isosmotic MgCl, solution. The isotope loaded cells were suspended in the appropriate solutions at about 2 % haematocrit and incubated at 37 0C. Samples were taken at 0, 30, 60, and 90 min and the supernatants saved and counted. The outflux rate constant was calculated as previously described (Sachs & Welt, 1967). The solutions used for the measurements were all made up to 295 m-osmole/kg water. Glycylglycine-MgCO3 buffer (glycylglycine 273 mM, MgCO, 54 m , 295 mosmolelkg water, pH 7-4 at 37 0C) made up 10% by volume of all solutions. The remaining 90 % was made up of appropriate volumes of 160 mm solutions of choline chloride, NaCl, KlC and CsCl. Bovine serum albumin was present at a concentration of 20 mg/100 ml. solution and glucose at 10 mm. Ouabain when present was 10'4 m. Ouabain sensitive fluxes were calculated as the difference between measurements made in the absence and presence of ouabain. Intracellular Na and K concentrations were estimated as previously described (Sachs & Welt, 1967). Determinations-were usually made in duplicate, although occasionally quadruplicate determinations were made. The curves were fitted to the data points by a nonlinear least-squares programme using a Hewlett-Packard 98-20 calculator. Points were weighted by using their variances. In the Figures, unless otherwise noted, each point is the mean of duplicate determinations and the range is given as a measure of variability. RESULTS

For a simple bisubstrate reaction in which intracellular Na (Nac) and extracellular K (K.) are substrates and extracellular Na (Nao) and intracellularK (Kc) are products, the distinction between a ping-pong mechanism Nac Nao Ko Kc

41

1

1I

and a simultaneous mechanism

Nac

4

Ko

Nao

Kc

1

1

T

493 Na-K PUMP REACTION MECHANISM is easily accomplished (Cleland, 1963). If one measures the reaction rate at several fixed concentrations of one substrate (Na0) and at varying concentrations of the other substrate (Ko), one can calculate values of the apparent maximal velocity (app. VM) and the apparent Michaelis constant for Ko (app. KK) as a function of the concentration of Na0. The determination requires that the concentration of the products (Kc and Nao) be kept at zero. For both the ping-pong mechanism and the simultaneous mechanism, the app. VM is related to the true VM (the velocity at saturating concentrations of Na0 and Ko) by app. VM - VM 1 + KNa Na0

where KNa is the true Michaelis constant for Na,. For the ping-pong mechanism app. KK is related to the true KK (KK in the presence of a saturating concentration of Na0) by KK app. KK 1+ N

Na. VM/app. KK is constant at all concentrations of Nac. For the simultaneous mechanism, the relation is more complex and is so that the ratio app.

given by app. KK

K(1 +Kj KN&a Nan K

Nas where K1 is a combination of kinetic constants. For this mechanism app.

VM/app. KR will, in general, vary with Na0.

Although the relation between the pump rate and the external K concentration is sigmoid when measured in solutions containing Na (Garrahan & Glynn, 1967b; Sachs & Welt, 1967), in Na-free solutions the relation is approximately a rectangular hyperbola (Garrahan & Glynn, 1967b, Sachs, 1967; Priestland & Whittam, 1968) so that it is tempting to fit the data to a Michaelis-Menten equation (1) V= mKKo

KK+ Ko

Fig. 1. is an Eadie plot of an experiment in which the active K influx was measured at varying external K concentrations; the solutions were Nafree and the cells were approximately free of K. The curves are drawn to the appropriate rearrangement of eqn. (1) V = VM-K K 0

(2)

494 J. R. SACHS with values of VM and IK obtained from a least-squares fit of eqn. (1) to the data; the values so obtained are listed in Table 1. The ratio app. VMJ app. KK at each intracellular Na concentration is also listed in Table 1. The ratio is far from constant. Similar findings have been reported by

02

0-1 x C

a) .0

2

1

TO

3

2

4

6

(a

a

a) .0

or 1*00 075 050 0-25 2

4

6

8 2 4 K influx/external K concentration

Fig. 1. Ouabain-sensitive K influx (m-molefl. R.B.C. per hr) v8. ouabainsensitive K influx/external K concentration (mM). The ouabain-sensitive K influx was measured at nine concentrations of external K (00102--2*860 m ) and eight fixed concentrations of Na0 (m-molefl. R.B.C.). The average intracellular K concentration was 1-06 m-molefl. R.B.C. and the average extracellular Na concentration 0 03 mM. The lines are plots of eqn. (2) with values of V., and KK listed in Table 1.

Chipperfield & Whittam (1974, 1976) although in their experiments app. VM/app. KK decreased as intracellular Na increased. If the simple bisubstrate model applies to the Na-K pump, this would be clear evidence that the pump mechanism is simultaneous rather than ping-pong. Unfortunately, the pump mechanism is far more complicated than a simple bisubstrate reaction; it seems likely that three Na ions and two K ions bind to the pump and are transported during each pump cycle

495 Na-K PUMP REACTION MECHANISM (Post & Jolly, 1957; Post, Albright & Dayani, 1967; Sachs & Welt, 1967; Garrahan & Glynn, 1967b, d; Sachs, 1970; Sachs, 1972; Garay & Garrahan, 1973). A ping-pong mechanism with multiple binding sites can be represented as Na0 Na0 Na0 3Nao Ko Ko 2Kc

1T

I

I

l

1

1

1

For such a mechanism the relation between the pump rate and the external K concentration at any fixed intracellular Na concentration is given by

Kg+K1K0+K2'

(3)

TARLE 1. Values of V., and K8 obtained by fitting eqn. (1) to the data presented in Figs. 1 and 2 Cs influx experiment K influx experiment

Nas

VE

KK

VlIKK

Nae

VK

K0,

VxIK0.

1-07 1-24 1-76 2-45

0-112 0-223 0-440 0*690

0-034 0-052 0'071 0-085

3-28 4-30

1-20 1-79 2-65

8-11

3-86

0-174 0-220 0-296 0-330

0-65

6-20

0-113 0-220 0-395 0*554

3-26 3-95

0-926 1-195

0-093

7-33

0-803

0*442

12-81

1*039

0-492

1-82 2-11

5-60 7-96

1-496

0-135

1-722

0-143

9-96 10-66 11-06 12-08

0-112

1-00 1-34

1-68

Eqn. (1) was fitted to the values of v and S from the experiments presented in Figs. 1 and 2 and values of V. and K. which best fit the data at each intracellular Na concentration (Na0; m-mole/i. R.B.C.) are listed. The units are: VK, m-mole/I. R.B.C. per hr; KK and Kc, mm.

where K1 and K2 are constants. If the measurements are made at several fixed intracellular Na concentrations, it can be shown that app. VM/app. K1 and app. VM/app. K2 should not vary with Nac. Eqn. (3) fits the data reasonably well when measurements are made in solutions containing Na (Sachs & Welt, 1967). It has been reported that eqn. (3) also fits the results of measurements made in Na-free solutions if it is assumed that the dissociation constants for the two K sites are 100 and 4 #M so that the value of K2 would be very small (0-4 /SM) (Lew, Hardy & Ellory, 1973). Recently we have reported (Sachs, 1977) that least-squares fits of eqn. (3) to measurements made in Na-free solutions, and especially at high intracellular Na concentrations, result in negative values of K2; that is, at low external K concentrations a plot of pump rate against external K concentration at first rises more rapidly than a rectangular hyperbola. This is

J. R. SACHST 496 seen in Fig. 1 since the data would obviously be better fitted by a curved line with the concavity directed upward than by a straight line. Cs is known to be capable of replacing K as a substrate for the pump, and is transported inward in exchange for intracellular Na (Love & Burch, 1953). However, the Michaelis constant for Cs (Kc5) is considerably higher than that for K so that it is possible to make accurate measurements of the active Cs influx at Cs concentrations much below Kcy. Fig. 2 gives the

' C

Nac

0 tN

1.79

\ Nac12081

a

0-2 Nac~~~~ 2. 'ubi-estv Fig.120 o ~~~1.

'0-4-

I'~ ~~Na 'Nc~

Nac 2-65

7.33

sifu

...prh)V.oaa -1mmlel 0 -

Cs influx/external Cs concentration

Fig. 2. Ouabain-sensitive Cs influx (m-molefl. R.B.c. per hr) V8. ouabaim. sensitive Cs inflxl/external Cs concentration (mm). The ouabain-sensitive Cs influx was measured at twelve concentrations of external Cs (0.00504 7770 mA) and six fixed concentrations of Na0 (m-molefl. R.B.C.). The average intracellular K concentration was 0-62 m-molefl. R.B.C. and the average extracellular Na concentration was 0 03 mm. The dashed lines are plots of eqn. (4) with values of V.t amd K.. listed in Table 1. The continuous lines are plots of v from eqn. (5) using values of VK, Kc, and Kc,' listed under experimental values in Table 3 V8. v/external Cs concentration.

results of an experiment, again presented as an Eadie plot, in which the ouabain sensitive Cs influx was measured as a function of the external Cs concentration; the solutions were Na free and the intracellular K concentration very low. The deviation from linearity is pronounced, and the concavity is directed upward, which indicates that at low Cs concentrations the curve rises more rapidly than a rectangular hyperbola; that is, the curve is anti-sigmoid. The straight lines in Fig. 2 are plots of V =

VM-KcbVC0

(4)

where Cs. is the extracellular Cs concentration and the values of VM and

Kc. were obtained by fitting an equation of the form of eqn. (1) to the data. The values of VM and

Kc. so obtained are listed in Table 1.

Na-K PUMP REACTION MECHANISM 497 The anti-sigmoid activation curve can be accounted for by assuming that both the pump loaded with two K or Cs ions and the pump loaded with a single K or Cs ion is capable of transport (Sachs, 1977):

E+Soo +

K8

SO E +Sc 16

' ES-÷ E+Se +

SO

kSE +So Ks'E2S kPE+2Sc A,~~~~~C

A.

B 0

0

12

11,02

l

l

l

4 8 4 8 Intracellular Na concentration (rn-mole/I. R.B.C.)

I 12

Fig. 3. The points represent VJJK, V8. the intracellular Na concentration from the fit of eqn. (5) to the experimental points for both (A) the K influx experiment (Table 2) and (B) the Cs influx experiment (Table 3). The continuous lines represent the ratio of the calculated parameters from the simultaneous model and the broken lines the ratio of the calculated parameters from the ping-pong model.

where S is either K or Cs and Ks, KS' and kp are constants. This results in the rate equation =

VM (Ks1S + S2)

KS KS + 2Ks'S + S2

5

(5) Eqn. (5) was fitted both to the data from the K experiment and from the Cs experiment; the values of VM, KS and KS' so obtained are listed in Tables 2 and 3. The curved lines in Fig. 2 are plots of v V8. v/Cso using values of v obtained from eqn. (5) with the values of VM, KS and KS' listed in Table 3.

J. B. SACHS

498

P

M

,

_

u9 eo 0

'P.

O

ec

MN M 10 w ON

.

,o

ko

*_ C.) o o o o o o o*

O~~~1 o _

C0=

o0

=

0 0 M

A wK00 oo o. _ co _

0

-o

.

co

o o o o o __

*P

;-1~ ~ ~ooo

v

v _ e0 r0

1~~0

0000

10

aqj

t-

0

CO

P

X

o+>Xeq "

*

4 _q

'LIat 0~ c4 Qc

o

Na-K PUMP REACTION MECHANISM o

10 m m 14*t-CO 0 00 o

cq

bO

.5 *rZ

0

.0

oooeqo

*1 *i

m ~10 CO

Co v c 10

00

0~

SCD"X>

6

101 o c4100 CO ~ 0'-ooo0ooo 0CO10 0~

wQ 0 ~ 0

F

CDO v .

*

O

b'I

*

-

O 10 .

*

4 .

Q

*l

.~

_

aq t- r- e

%

-s

o

o

e co

10eq01M* 1w0e 0 oooooo

I

V

qD

0

eq

V

cooeq

O

co

CO

t.-

0

o

A

ko 0

.0

4

4

_ _ cs N

.$-

cO um a ua0 0 o

O

.s

P

0 a

P. 0

.0

.5co

.*

"O

-,

~

_-

0

'D .a

0

s

0 '

0

0O

eq

,0i

00

CO

I ? e 1O

v

Ez a

1-

5

-

10

eq

-4

S

0

10

0 _

*o30

r

0

C4o x

m 0 o N m I* **

.

.

.

.

0100

0

of

eq

100w

V-_

t.0co ~~~~~~~~~-

CQ 4.

~e q7 >

499

J. R. SACHS Although the fit is not perfect, especially at the lowest Cs concentrations, it is much better than that obtained from the Michaelis-Menten equation. Several unlikely assumptions have been made in the derivation of eqn. (5) including the assumption that kP is the same for both the singly and doubly loaded pump; it is possible that a better fit could be obtained if the value of kP were allowed to differ for the singly and doubly loaded pump. In Fig. 3 VMIKK and VMIKc. obtained from eqn. (5) is plotted as a function of the intracellular Na concentration. The ratio rises as intracellular Na 500

increases. Ping-pong

K

k6

K E'

(E 'R

ENa3)

'E'

S

KS

~Na(>EK