Ca2+ antiporter and the Ca2+ channel in smooth muscle cells

175

Bioeiectrochemistry and Bioenergetics, 22 (1989) 175-186 A section of J. Ek:roana/. Chem., and constituting Vol. 276 (1989) Elscvier Sequoia 8%. Lausanne - Printed in The Netherlands

IIpteractiombetween the Na’/Ca’+ clmnuel in smooth muscllecells * and SM.

K.V. Kazarian Orbeli Institute

NJ.

of Physiology,

antiporter and the Ca2+

Martimsov

Academy

of Sciences of rhe &x.i.Gan

SSR,

375028

Yerevan

(U.S.S.R.)

Markevich

Znstifute of Biologicaf Physics Moscow Region (U.S.S.R.) (Received

25 November

of the Academy

1988; in revised

of Sciences

of the USSR,

142292

Z’uschino,

form 8 July 1989)

A basic model of the interaction becrveen membrane ion-transferring systems in smooth muscle cells is developed i;i this work. The permanent ion exchange through a cell membrane is proposed to be maintained by the interplay between a potential-dependent Ca”+ channel, an electrogenic 3 Na+/Ca*+ antiporter, a Na+ K+ pump and a K+ channel. It is shown that the 3 Na+/Ca’+ exchange mechanism can play a major role in the steady self-oscillation of the membrane potential in smooth muscles.

INTRODUCTION

It has long been known that the electrical activity of smooth muscle cells is produced by inward Ca 2-t fluxes [1,2]. Accumulated calcium ions must be extruded against a high concentration gradient. Smooth muscle cells need a system for active extrusion of Ca2+. Such work could be performed by a special Ca2+ pump or a Na “/Ca2+ antiporter. Over the past two decades, Na+/Ca’+ exchanging systems in excitab!e tissues have been studied [3,4]. It has been proposed that Na+/Ca2+ exchange serves as a reserve mechanisms for lthe elitination of extra Na+ in smooth muscle cells when the NaC K+ pump is inoperative [5]. This means that Na+‘/Ca2+ exchange has. no meaning for active Ca*+ extrusion and, moreover, the Ca2+ gradient directed into a cell is used for the extrusion of extra Na+. Hence, a Ca2+ pump is assumed to operate in smooth muscle membrane because a cell has to * To whom

correspondence

should

be addressed.

176

extrude extra internal Ca2+ to maintain its &cttical activity. Data on the presence of a Ca2+ pump in the membrane of smooth muscle cells arc. rather inconsistent [6-8]. At the same time, the electrical self-oscillation of smooth mu&e is terminated after inhibition of the Na+K+ pump’s operation [9,10]. Thus t.‘neelectrical activity of- smooth muscle is blocked by the inhibition of both a poten?&&dependent Ca2+ ciiannel and the sodium pump. ‘We have shown in previous work [ll] that a cell is capable of Iproducing ekctrical self-oscillations using only two membrane mech::misms: a potentiaLdepenl2ent ionic channel and an ionic pump, respectively. However, here we have no possibility to use this model, because a CazC channel and a Na’K+ pump transfer different ions. Therefore, a special intermediate mechanism has to be involved to provide the extrusion of Ca2+ from a cell. The experimentally best-founded transport system for such an aim is an electrogenic 3 Na+/Ca2+ antiporter, in spite of the above opinion of some authors [5]. I[n this case Ca” ions enter a cell via C;r”+ channels and are antiporter that uses the electrochemical potential difextruded by a Na+/Ca’* ference for Na+ to extrude Ca2+‘, The sodium pump expels sodium ions to maintain steady state conXtions inside the cell. A’general theory of the interplay between m?rrbrane mechanisms for creating self-oscillations in smooth muscles is developed in this work. MODEL

The membrane mechanisms represented in Fig. l are supported to act separately without direct structural conPact [12]. Ttte ion-exchanging, stoichiometry of the wa -rK” pump and the Nac/Ca2+ antiporter serves to close Ithe total ionic cycle via the membrane (Fig. 1). For the sake of simplicity, some possible connections between transport systems, namely the different modes of electro- and chemoexcitable channels or the regulation of transport phencmen.a by chemical compounds, are not considered in this work. These restrictions affect only on the shape of the oscillations.

in

Fig. 1. The proposed arrangement

of the ionic ..ycle through the membrane of smooth muscle cells. Ca2+ channels serve as the 014y electro-excitabfc ml.%hanism and Na+ K+ pumps are the only energy-depenandporters connect these two main transport systems. dent system, while the Na+/Ca2+

177 BASIC

ASSUMPTIONS

(1) The outward current considered negative on the (2) The conductance of K”) is a linear function of I,, =&&%,

is taken as positive and the memhisne potential At&, is intracellular side. the K+ channel (Xx) is co:nstant and IK (the current of A&,:

-A&!

(0

where A@K = (RT/F)

ln([K+lout/[K+lin)

0)

is the potassium equilibrium potential; R, T and F have their -usual n~eaning; and are the concentrations of K.+ in a cell and in the medium, ]K’]i” and EK+],,, respectively. (3) There is presently no generally accepted dec~rochemical model of voltagegated channels, though in the opinion of most researchers the change in conductance is determined by intrinsic conformational changes inside the channels. For example, the charge-dependent dissociation of subunits of oligomeric channels leading to the opening of a channel 1131or the potential-dependent interconversion of subunits opening and closing a charmel [14] can be attributed to such a rebuilding of channels, Since the aim of this work is to study the interaction between membrane systems rather than an analysis of proposed molecular mechanisms of voltage-gated processes, we shall use one of the simplest mathe.matical schemes that is in good agreement with the experimentally observed-data. We assume that a channel has two types of gate (m- and h-gates) which monitor the passage of Ca*+ via the channels. Opening and closing of these gates occur as a result of conformational transitions of m- and h-subunits (gate particles) between two positions. Let us designate by m and h the positions of channels for which the m- and h-subunits, respectively, Lre in the opened state. The following equations will be true for m and h: dm

-

dt

= a,m

dh = c,h ‘dt

-- flm(l - m)

&,(l -

“..

h)

where a,, I$.,,,(Yh and

Ph are the rate constants of the appropriate

conformational

transitions. The conductance of Ca*+ channds (X,) is determined by the number of m- and h-chanrjels opened at any one time. This means that x Ca =X,,mh

(5)

where xc- is the maximum conductance. Since the activation of channels observed experimentally take place with a certain delay, a channel is assumed to have several

178

m-subunits opened simultaneous&. We shall consider the simplest case when a channel involves two m-subunits which accomplish transitions independently. Then x Ca

= x (-.an12h

(6)

it is also assumed that ihese confolmational transitions of subunits lead to a dislocation of the charges associated with these particles, the valency of the charges being Z, and Z,, respectively. According IO ref. 15, the link of am, &,, ah and &, with the potential may be represented as follows:

a0.m exp( &,Z,

a,= Nh = &I

aO.h

=

& =

rS0.m fl0.h

exp(

ehzh

)

A+:)

exP[Uk exp[teh

AS

- ‘lIZan A+% ] 7

ljzh

&Cl

where A+; = Akl(F/RT)

01)

is the dimensionless membrane potential; ao,mr /30.,, &h and (Yg,hare rate constants at A+” = 0; and @,,, and @h are factors related to the profile of free energy of the conformational transitions and range from 0 to 1. For the sake of simplicity, wr,: shaii assume that &,.,Z,=i)

(6,~i)Z,=

-1,

@hZh=

-1,

(&,-i)Zh=l

The electtic current along the potcntizl-dependent I ca =&,m2h

(A&,

02)

Caz+ ch?Lmefs is

- AC, )

0%

where Aka = (R7”/2F)

ln~{Ca2+],,J[Ca2’

Iin)

(14)

is the calcium equilibrium potential; and [Ca2+Iou, and tCa2+]i, are the extracellular and intracellular concentrations of CJ2+, respectively. (4) The values of [K“‘],,,, [Na+],,, and [Ca2+],,, are maintained stable. The are recognized to be neg&ible. HeXe, u,& and uNaCa are changa in [K+]i, changed only with variations in [Na+ Ii, and /Ca2’li,. BI:sides, uFtaCadepends on the membrane potential. The expressions for the determination of these rates can be presented as: is the coefficient of the pump operation. K, is in9 where K, (a) UNaK = K,fW measured in cm s-‘, UN& in mol s-l cma2_ jbI

UNaCa=kiCa2+Iin

exp(-A#W)

--z[Na+I~i,exdMW2)

(9

where k, and k, are the coefficients of the antiporter operation and A+2 is the dimensionless value of the membrane potential. k, and k, are measured in cm s-l, oNaCa in mol s-l cmD2_ (5) The Na+K+ pump and the Na+/Ca’+ antiporter are electrogenic mechanisms. Both transport systems translocate one positive chm,ge (Na+) through the

179

membrane (Fig. 1). The electrical current densities produced by these syskms are I NaK = F”NeK 06) and I NaCa = - FUNaCa (17) (6) Calcium ions inside the cell can be partially bound by some internal structures. THE SYSTEM

OF EQUATIONS

Taking into account the ak~e assumptions, the whole equation system can be writtel2 as: d A*.$ - -lK - I,, - &I& + p”NaCa =mdl.= = dm =ar,,,(exp A++$)(~ 4 dt dh --+I - &.,(exp A#% dt = %,h [exp(-A+m)](l

P~.J~~P(-A+,z)I~

d[Ca2+]i, dt d[Na]i,

=

Ff

(-vNaCa

Sm . = l/i(-3UNaK

d.,

-

+

1Ca/2F)

3uN~Cn)

where C,.,,is the specific capacity of the membrane; S, is the membrane area; and Vi is the cell volume. Aaording to ref. 16 the dimensionless parameter f shows the influence of the Ca2+ binding buffer in a cell on the rate of change in the concentration of free CZ2+ . f is the ratio of the dissociation constant of @a2+ to the capacity of the buffer. The first equation of system (18) shows the hnlc between the membrane potential and the transmembrane ionic current. The second and third equation describe the activation and inactivation of Ca2+ channels. Finally, the.fourth’and fifth equation reflect the changes in the concentrations of free Ca2+ and Na+. For convenience of operation, the equation system (18) is reduced to a dimensionless form: d A:: = -” K - “Ca - UNnK + UNnCn dr

2 = p,[(exp

A#!,)(1

- ni) -x,.&p

dh x = ~.r,[(exp - A+:)(1

- h) - x&xp

d(cCa dr

vcz&P)

)in

=C(k-%Wa-

- A+z>m] AG)h]

(l?j

where 11~= x(Aqf); - A&) v,, = m2rk{ A+: - *ln[ ( ‘ca )0”!/( cca Iin]

) m)

‘VNZIK v NaCa

=

Xp(CN*

)in

=xI[(cc~)~~

exd--&G/:~)

-~(Cca)in

exP(A@z/2)1

are the dimensionless rates of ion transport through the K+ channel, the Ca2+ channel, the Na+K+ pump and the Na+/Ca’+ antiporter, respectively. The dimensional and dimensionless values are connected through the following relations: ( cca)in = jCa2+]in/Az,

(~c~)~,~, = [Ca2+]I,,,/&

4

= IO-’

M,

(cNa)in Z [Na*Iin/A1, 4

= 1O-3 M, I=

xp = K,F2Al/RT&,,

CURRENT-VOLTAGE

&/C,,

xk = AK/xc,.

x, = klF2AJRTS;,,,

A#lt, = ln([K+L/[K+I;,J, x2 = k2A,/klA2,

(21)

CHARACTERISTICS

The time behaviour of system (19) is determined mainly by the current-voltage characteristics, the typical shapes of which are presented in Fig. 2. The current-voltage characteristics for the separate transport systems (except VN~K = const) and for the whole membrane ( vt = UK i- vca f VN~K - vNaCa) are depicted in Fig. 2a. The behaviour of the Ca2+ channel is of special concern. Its characteristic was derived from the conditions ~.r-‘(dm/dr) = 0 and p;‘(dh/dr) = 0, i.e. for steady state values of $I

[l +x,(exp

- 2A&)I

and

& = [ 1 + x,(exp

2A#,)]

-r

(22)

It has the same form as the stationary current-voltage characteristics of potentialdependent Na+ and Ca2+ channels. The curve involves a section with negative resistance. Due to this feature of the Ca 2+ channel the characteristic for the overall L-J ~{a stationL:,y current (&) is N-sll,,, ,_ _ 2bj, as for all exci*Able membranes. The presented characteristics were obtained for different values of the intracellular Ca2+ concentration. As follows from Fig. 2b, some curves cross the line of zero current at three points. This means that three different voltages correspond to zem current at the same value of the intracellular Ca2+ concentration. Such an equivocal result is observed as a hysteresis in the curve of the potential at zero current (v, = 0) plotted against the internal Cat+ concentration (Fig. 3a).

181

-1.25

-4

-3

-2

-1

0 a&

FvI 1.0

b

Fig. 2. The current-voltage characteristics (eqns. 16 and 17) at x1 = 0.001. x2 - 100. x,, = 0.01. xK = 1.5. = 0.005, xh = 50, A+k = - 3.4, (C&out =lo4. (Qa)in =10 (see equation system 21). uc-. uNaCa and uK are the rates of ion tknsfer via .the Ca2* channel, the Na+/Ca*+ antiporter and the K+ channel. respectively; u, is the total membrane current. (a) (cca)i, = 1; (b) (CCa)in is variable.

X,

Na+/Ca2+

ANTIPORTER

Another essential feature of these characteristics is the depolarization of the membrane at sufficiently high internal Ca2+ concentrations. This phenomenon arises due to the increase of Na+ influx via the Na+/Ca2+ antiporter at high _

W2+li,-

The complicated characteristic of the potential at zero current creates two interesting singulariltk in the overall quasi-stationary rate of Ca2+ transp,ort (6,&j when the intracellular Ca’+ concentration changes (Fig. 3b). We accept Gj&= u,-,/2 + uNeCaas the quasi-stationary rate. This value can be calculated when the variables *AiT_-? AZ.* ;m .z, .L. vrcv -y-m II. -8%c 1”“. (‘-9) assume qttasi-stationary values and satisfy the equation system:. d &#P -.= = 0, p;*(dm/d.r) = 0, &‘(dh/dT) = 0 (23) dr The term C‘quasi-stationary values” is used because the parameters (cCcr)in and ( CNa) i* change SlOWl_V.

Ad&*0

-

a

I

I

-1.25

0

I

-2.5

&

b

zs -

-2

I

1.25 logC+Jn

4

0.75 O-

-0.75

-1.5

4

1 -2.9

3

2 1

2

I -125

v0 * e&J,

Fig. 3. The quasi-stationary potential at zero cxrrent (a) and the total rate of Ca2+ transport (b) plotted agziifst the intracellular Ca2+ concentration. The curves reflect diFFerent activities of the Na+/Ca’+ an&porter (x,). The values of x, are: 0 (1); 0.001 (2); 0.01 (3); and 0.05 (4). The values OF the other parameters are: x2 = 1. ?P = 0.05, xk = 2, x, = 0.005. xh = 50, AQE = - 3.4, ( c’=~),,“~ ==104. ( cNa)in = 15..

The first feature of the function &(Cca)i, is a hysteresis at low (CCa)in. The second important feature is an increase in the Ca2+ influx rather than the Ca2+ efflux after an increase in the internal Ca2+ concentration within a certain interval Of [Ca”+]i,. Furthermore, as follows from Fig. 3b, this effect becomes more pronounced with an increase in the Na+/Ca2+ antiporter activity. The order of events leading to this phenomenon could be described as follows. An increase in the intracellular Ca2+ concentration leads to intensification of the exchange and, hence, to membrane depolarization. The Ca2+ channels Na+/Ca’+ are opened and the membrane conductance for Ca2” is increased drastically. On the whole, the Ca2+ influx via the Ca 2+ channels becomes higher than the Ca2+ efflux via the Na+/Ca’+ antiporters. Further depolarization of the membrane inactivates the Ca2+ channels, leading to the expected extrusion of Ca2+ through the Na+/Ca2+ exchanging system.

183

Fig. 4. The family of quasi-stationav characteristics U&(CCa)in. Curves 1 to 5 were obtained for [Na+ Iin - 5.0; 7.5; 10.0; 12.5 and 15.0, respectively. Tht other parameters have the same values as in Fig. 3, except XK =I.5 and x1 = 0.~5.

This non-monotonic beh&our OF i&,(c,) in is of particular importance in rendering mode: system (19) unstable. 6& becomes zero at three different points for a given internal Ca2+ concentration, as follows from the family of curves presented in Fig. 4 for [Na+]i,, = const. As in Fig. 3a, the curve for (cc& derived from the condition d(C,-,)&dT = CL&, = 0 must involve a hysteris. This fact results in a quasi-stationary rate of Na+/Ca’+ exchange fiNeCn,showing a hysteresis depending

exchange and Na+ K+ pump operation Fig. 5. The stable rates of Na’*/Ca2+ intracellular Nu* concentration. The parameter values are the same as in Fig. 4.

plotted

against

the

a

T

b

1.0

0.5 c

Fig. 6. The sclCo.scillations of (a) the parameters A+$, ( ccm)in. (cN~)~” ad numerical dution of system (19) at pr - 1, p2 * 1. cc3 - 0.1, CL4= 0.01.

(b) the rates UC-. ON&-* after

on INa%, (Fig. 5), cNpCa also being derived from the solution of the equation system d A+vdd = 0, dh/dT s 0, d(cca)iJdT = 0, dm/dT = 0. The unstable quasi-stationary values of [Ca’+]i, are denoted by the dottetj, line. It should be noted that all the points of the BNaCa curve represent steady state values of the variables in system (19) except the Na+ concentration. I?he last equation shows that the stationary value of (CNe)in is attained at uNaK= UINe’;-ar i.e. the stationary state of equation system (19) is expressed graphically in terms of the intersection df the curve for &&, and the straight line for U”N,,. Figure 5 indicates that the intersection of the unstable region of the cNaca curve with the straight line for uNRKcorrespondings to a certain slope of the straight line, i.e. to a definite activity of the Na+K+ pump. The intersection reflects both the unstable stationary state in s/stern (19) and the origin of the steady self-oscillation. The: undamped oscillations of the membrane potential, the internal Ca2.+ and Na+ concentrations as well as u,, and uNaCeare given in Fig. 6. The rate of operation of the Na+K* pump is not shown here because the pump’s activity is directly proportional to the internal Na+ concentration.

Comparison of the oscillation phases of the membrane potential with the oscillations of the other parameters allows us to arrive at the following conclusion. The phases of fast depolarization and hyperpolarization of the membrane (A+z) are caused by the activation and inactivation of the Ca*+ channels (v,,). The phases of slow depolarization coincide with the onset of Ca2+ channel activation, when the Ca2+ influx is increased again. The fast accumulation of Ca2+ through the Ca2+ channels (Cc, ) in leads to activation of ?Tre Na+/Ca’+ exchanger (vNaclr) and a subsequent decrease of internal Ca2+ (CCa)in and an increase of internal Na+ (cNn)in. The slow hypelpolarization reflects the complicated process of Na+/K+ pump and Na+/Ca2+ I.:xchanger activities. Quantitative estimates show that the The Na+/K+ pump’s contribution to the common result is hyplxpolarization. electrogenic effect is nc t essential when the Ca2+ channel is openect. That is why a slow depolarization is observed despite the intense extrusion of Na+ (cf. A+; and (CNa)in curves in Fig. 6). Sakamoto and Tomita [17] also noted that the interaction between the different ion transport systems can lead to unexpected shifts in the membrane potential. This effet depends on the rate of ion transfer through the separate systems. DlSCUSSlON

A peculiar feature of smooth muscle tissues is the distribution of cells between separate functional populations: a small part of the cells is capable of producing spontaneous self-oscillations, while the other 41s are electro-excitable. The so-called pace-maker zones, in which the oscillations of the membrane potential arise, manifest most commonly slow-wave depolarizaticsns lasting seconds or even minutes, whereas spike activity in the electro-excitable region is observed in response to a depolarizing signal arriving from the pace-maker zor.e. Nevertheless, we cannot exclude that the general mode of interplay between membrane mechanisms transiocating Ca 2+ Na+ and K+ remains the same for both cell popuL n*:ons. The main distincticn be&een them seems to consist in the rates of Ca2+ channel operation [2] and in the ability to respond to chemical or/and electrical signals. There are good reasons to assume that this point is correct for ureter tissue, in which the division into functional zones is pronounced [Ml. The model presented (Fig. 1) is appropriate for slow-wave processes (Fig. 6). Further improvements of the theory must involve regulation of the activity of the separate mechanisms by chemical oompounds and/or Ca2+ as well as an increase in the number of interacting transport pathways. The same membrane mechanisms are supposed to operate in electro-excitable cells, or general in spike-generating formations, e.g., the electrogenic 3 Na+/Ca’+ antiporter can contribute to the transmembrane current flow, perhaps even leading, to the oscillatory behaviour of heart Purkinje fibres [19]. It stands to reason that the fast Ca2+ channels, lacking as a rule in the pace-maker membranes, serve as the main mechanism for excitation of these ells.

186

Therefore, the value of the electrical threshold of the Ca2+ channel rises in importance as a trigger factor [20]. We hope that this model (Fig. I) is a basic system for describing the ionic cycle in smooth muscle cell membranes. Most of all, it is necessary to note that the system contains calcium channels without appropriate Ca2+ pumps. The metabolic, energy-dependent regulation of the intracellular Ca2+ concentration is accomplished indirectly through a Na+K+ pump which operates in absolute stoichiometric antiporter. Thus, the Na+/Ca2+exchanging mechaaccordance with a Na+/Ca2+ nism extrudes Ca2+ from the cell and serves as a mediator between the Ca2+ channel and the Na”K+ pump. REFERENCES 1 E. BUlbring and T. Tomita in A.W. Cuthbrxt (Ed.), Calcium and CelIuIar Function, Macmilian. London, 1970, p. 249. 2 M.F. Shuba, Fiziol. Zh. Akad. Nauk Ukr. SSR, 27 (1981) 533. 3 M.P. Blaustein, Am. J. Physiol., 232 (1977) C165. 4 D.A. Eisner and W.J. Lederer, Am. J. Physiol., 248 (1985) C189. 5 C.C. Aickin, A.F. Brading and Th.V. Burdyga, J. Physiol. (London), 347 (1984) 411. 6 R Casteels and C. van Brecman, Pfliigers Arch., 359 (1975) 197. 7 A.K. Grover, S.Y. Kwan and P.J. Oakes, Am. J. Physiol., 248 (1985) C449. 8 K.V. Kazarian. A.S. Howanissyan, A.S. Tirayan, R.R. Hakopian and SM. Martirosov, Fhiol. Zh. SSSR, 75 (1989) 845. 9 J-A. Connor, C.L. Presser and W.A. Weems. J. Physiol. (London), 240 (1974) 671. . 10 K.V. Kazarian, A.S. Tirayan, V.Ts, Vantsiam and S.M. Martirosov, Fisiol. Zh. SSSR, 73 (1987) 738. 11 N.I. Markevich, K.V. Kazuian and SM. Martirosov, Bioclectrochem. Bkoenerg., 17 (1987) 559. 12 G.I. Bourd and S.M. Martirosov, Bioelectrochem. Bioenerg., 10 (1983) 315. 13 M. Blank, Bioelectrochem. Bioenerg., 13 (1984) 93. 14 B. Hiile, Biophys., J., 22 (1978) 283. 15 T.L. Hill and Y. Chcn, Proc. Nat]. Acad. Sci. USA, 69 (1972) 1723. 16 T.R. Chay. Biol. Cybem., 52 (1983) 339. 17 Y. Sakamoto and T. Tomita, J. Physiol. (‘London), 326 (1982) 329. 18 S-A. Bakuntz and V.Ts. Vantsian in E. Billbring and M.F. Shuba (Eds.), Physiology of Smooth Muscle, Raven Press, New York, 1976, p. 121. 19 S.R. Fischmeister and G. Vassort, J. Physiol. (Paris)* 77 (1981) 705. 20 Y. Hara and J.H. Szurszewski, J. Physiol. (London), 372 (1986) 521.