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Mechanisms of the tetrahydroaminoacridine effect on action potential and ion currents in myelinated axons
European Journal of Pharmacology - Molecular Pharmacology Section. 2f~'~( 199 ~) 1-8 © 1991 Elsevier Science Publishers B.V. All rights reserve t 0922-4106/:~I/$03.50
ADONIS 09224106910015~5
E J P M O L 90211
Mechani'~ms of the tetrahydroaminoacridine effect on action ?etential and io~ curre~]ts in myelir, a t e d axons o
Fredrik Elinder and ?eter Arhem Nobel Institute ]'or Neurophysiology, Karolinska Instituter, S-104 O1 Stockhobn, Sweden Received 23 April 1991, accep ed 14 May 1991
9-Amino-l,2,3,4-tetrahydroacridine (THA) in the range of 10-3~9 /.tM was shown to prolong the action potential in myelinated nerve fibres of Xenopus laevis. Voltage-clamp experiments showed that THA. besides reducing the Na ~ and the K* current, modified the Na + current it~activation and the K + current activation. The effects were frequency dependent. Quantitative models were developed and used in computer simulations of the THA effect on the action potential. "Yhe computations showed that the observed effects on the ion currents were sufficient to explain the observed prolongation of t ae action potential. The models further suggest that THA binds to Na + channels in an open state and from the a×oplasmic side while it binds to K + channels in a closed state. The findings suggest an explanation to some aspects of the clinical effects of T H ~ on Alzheimer patients. 9-Amino-l,2,3,4-tetrahydroacridine (THA); Ion channels; Myelinatcd nerve fiber; Voltage-clamp cxpcrinieat; Computer simulations; AIzheimcr's disease
1. Introduction 9-Amino-l,2,3,4-tetrahydroacridine ( T H A ) has been shown to improve cognitive functions in patients with A l z h e i m e r ' s disease ( S u m m e r s et al., 1986). Since T H A is a p o t e n t acetylcholinesterase ( A C h ) inhibitor it has been s u g g e s t e d that its main effect is to e n h a n c e the levels of A C h , thereby c o m p e n s a t i n g for the effect of d e g e n e r a t e d cholinergic neurons. However, since o t h e r inhibitors, e.g. physostigmine, were f o u n d not to show this effect ( M o h s et al., 1985) T H A h a s also been proposed to have o t h e r effects in order to explain its effects on Alzheinte.r patients. D u e to the structural similarity between the central aromatic ring of T H A and the K + c h a n n e l blocker 4-aminopyridine (4-AP) (Yeh et al., 1976) it has been suggested that the clinical effects of T H A d e p e n d on K + c h a n n e l blocking, thereby prolongating the action potential and e n h a n c i n g the release of A C h ( S u m m e r s et a l , 1986). T H A also has structural similarities to 9-aminoacridine (9-/~,), a blocker of open Na + channels (Yeh, 1979; Y a m a m o t o and Yeh, 1984). Several studies have c e n f i r m e d that T H A influences voltage-gated K + c h a n n e l s as well as Na ÷ and Ca z+ c h a n n e l s ( D r u k a r c h et al., 1987; Elinder et al., 1989;
Correspondence to: Peter Arhem, Nobel Institute for Neurephysiology, Karo[inska Instinaet, Box 60 400, S-104 01 Stockholm, Sweden.
Osterrieder, 1987; Rogawski, 1987; Schauf and Sattino 1987). It has also been shown that t':e action potential in s o m e cells is prolonged by T H A (Dra~:arch et al., 1987; Osterrieder, 1987; Reiner and McGeer, i988). In a previous study (Elinder et al., 1989) we investigated the effects of T H A on the node of Ranvier in axons from the clawed toad. Xenopus laevis. It was f o u n d that T H A blocks Na + a n d K ~ channels, that the steady-state inactivation curve is shifted in a negative direction along the potential axis and that the Na + current inactivation b e c o m e s biphasic. T h e effect could quantitatively be described as decreased permeability c o n s t a n t s (PN, and P~,) and a modified potential dep e n d e n c e of the Na + inactivation. T h e purpose of the present investigation was to examine these effects in further detail and their relation to the effect on the action potential. We expressed the effects on the ion currents in mathematical models that were used to calculate the effects on the action potentials by c o m p u t e r simulations.
Z Materials and methods Large myelinated fibres were isolated from the sciatic nerve of the clawed toad, Xenopus laevis. A single fibre was m o u n t e d in a recording c h a m b e r and cut at half-internodal lengths on both sides of the node u n d e r investigation, q h e c h a m b e r was connected by salt
bridges to the voltage-clamp apparatus (Frankenhaeuser, 1957; see also Huxley and StLmpfli, 1949). The circuitry and balancing procedt:res were essentially the same as described by Dodg~- and Frankenhaeuser (1958), with the modifications described by Arhem e t a l . (1973). Pulse generation and sampling were made using a TL-I DMA interface (Labmaster, U.S.A.) and the pCLAMP software tAxon Instruments, U.S.A.). In order to obtain good feedback cov_~rol and recording situations, all experiments were performed at a relatively low temperature (8°C). Since only relative current values were essential in the present investigation and since there is some uncertainty in the estimation of the nodal area and the axoplasmic resistance (see Dodge and Frankenhaeuser, 1958), no attempt to calibrate the currents in absolute values was made. The test solution was applied to the pool with the node. The control Ringer solution contained (in raM): NaCt 115.5. KCI 2.5, CaCl 2 2.0 and Tris buffer (adjusted to pH 7.2) 5.0. The solution used in the end pools consisted of (in raM): KC1 120, and Tris buffer (pH 7.2) 5.0. THA was obtained from Nobel Chemicals, Sollentuna, Sweden, and was added to the Ringer solution. The computations were performed on an IBM-compatible personal computer (80286 CPU). The software was written in BASIC. For the computational procedures, see the Appendix.
time course and ~mplitudc of the action potential. At about 1000 ,u.i',~ the action potential was completely blocg,:d. At lower concentrations the time to reach a steau state was about 3 rain (fig. 1, left panel). The duranon of the action potential increased with increased concentration. M e a s u e d at the base, and at steady state, it doubled at a o mcentration between 30 and !00 ,aM. In parallel with the prolongation the slope of the initial falling phase became steeper (at concentrations above 30/xM; consequently not seen in fig. 1, left aan,A). Effects on the amplitude were ob~ served only in the highest concentration range studied (> 100 ,aM). The reversibility was not complete within the times for the washout in the present investigation (5-10 min). The time to reach steady-state recovery was about 3 rain. 3.2. Effects on the t,m currents
As previously shown (Elinder et al., 1989) THA reduces both the Na ~- and the K + currcnts. In order to quantify the dose-response relation we measured the effects on the peak Na + current and the steady-state K ÷ current. Complications due to effects on the Na + inactivation were avoided by keeping the membrane at a potential of - 1 3 0 to - 1 2 0 mV between the test pulses. The dose-response curve for both the Na + and the K + current effects could approximately be described by the equation I~'~,×/Im,~ = 1(1 + CTHA/Kd)
3. Results 3.1. Effects on tl, e action potenlial
THA was found, in conce,;tra:ions from 10 # M and upwards, to reversibly and non-linearily affect both
(1)
where I,,,~ and Im,× are the maximum peak Na + currents or the steady-state K* currents in control and test solutions, respectively, CTHa the concentration of THA in ,aM and K a the dissociation constant in p.M. The geometrical mean value of K d for the peak Na + current measured at - 10 mV was 220 p.M (n = 5; the 4t)
+41)
13 A
+2(~
20
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> E ~"
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-20
E ~. -40
-411 -
g -6()
-
-60
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-
-8(I ,
0
-
~
.....
¢'
4 "1 im
ms)
, ~2
.
. 16
.
.
1(10
'
~
'
~ ' Time. (ms)
l~
'
l'~;
'
Fig. I. The effect of 30 ,aM THA ~,r. the action potential. Left panel: Time course of the effect. Time in minutes after change to test solutioe, indicated. Holding potential - 9 0 inV. Right panel: Computed action potentials at different THA concentrations (in ,aM) as indicated. The computations are described in f,he Appendix. Note that the values used do not refer to the fibre in the left panel.
~"
0.8 0.6
~
0.4
0.2
0 10
1C0
1000
10 000
(,M) Fig. 2. Dose-response curves for ~.he effects on maximum peak Na ~ (o) and maximum steady-state K ÷ ( ~ ) currents. Measurements of peak Na + currents at test steps to - 10 mV from a holding potential Concentration
of - 120 mV and measurementsof steady-state K~ currents at steps to +50 mV from a ho!ding potential of -70 inV. Continuous lines are solut' as of Eqn. 1 with dissociation constants of 200 and 540 .~M, respectively. The deviating experimental values for the steadystate current at 1000 p.M may be explained by an induced inacti,~ation at high concentrations of THA (see text and fig. 6).
corresponding arithmetical mean _ :..D. was 270 + 170) and for the steady-state K + cv" ~t measured at + 4 0 or + 5 0 mV was 540 p,M (n = s; arithmetical mean + S.D. was 570__+ 180). As a measure of the relation between the effect on the K + system and the Na + system we calculated the quotient between the dissociation constants for the two s :terns. By using the geometrical means above, the ~ ometrical mean for this quotient w~ o directly o b r :ned. The value was 2.5 (n = 5; the individual va|ues ed between 1.3 and 4.6).
1 - - I
....
~"~000 aM
Time (ms) 2 3 P
I
Fig. 2 shows the typical dose-response curves for one fibre. As shown in the figure, Eqn. 1 describes the T H A effects on the Na + system better than on the K ~ system. At high conzentrations (1000 g M ) T H A reduced the steady-state K + current more than predicted. This was presumably related to the THA-induced inactivation described below. No systematic T H A effect on the leak current was noted. At high concentrations (1000 IzM), however, an irreversible increase in leak current sometimes was observed. In accordance with the effects on the action potential, the T H A effect on the ion currents was only partially revergibie. The time course of both the onset of the effect arid the recovery varied fo~ different parameters (peak N a - current, time course of inactivatien, etc.) but a steady state was systematica!ly reached within 1-2 rain. 3.2.1. N a + c u r r e n t
Besides the amplitude reduction of the Na ÷ current T H A also modified the time course of the N a " inactivation. The monoexponential time course in control solution became biphasic (fig. 3, left panel). The effect was more pronounced at higher concentrations; the slope of the initial phase was increased while that of the late phase decreased. As previously shown (Elinder et al., 1989), the T H A effect on the Na + inactivation was also seen as a negative shift of the steady-state Na + inactivation curve along the voltage axis. Fig. 4 shows the steady-state inactivation for a prepulse duration of 1 s for three concentrations (open symbols) and one fibre. In order to obtain initial values for the mathematical models
Time (ms) 4
5
I
p
I)
l
2
3
4
5
ii
o
°'lb/ Fig. 3. Effects of THA on the Na* current associated v,,ith a potential step to - 10 mV from a holding potential of - 7 0 mV. Left panel: Recorded currents at indicated concentrations. Right panel: Computed currents based on Model I (see lextL Ordinat.: indicates the quotient between open and total number of channels.
The shift, ..1U]/2(= U ~ 2 - UI/2), along the voltage axis was related to the blocked maximum peak current by the equation: 0.8
1~=
(I,*,,~/I ..... ) / 2 = 1/(1 + exp(...1U,/2/k,/2) )
£ 0(,-
(1.2
-110
-90
-70 -50 Potential (mV)
-31~
Fig. 4. Effects on steady-state Na* current inactivation measured for a test step to - l0 mV from prepulscs of ! s duration. Concentrations were 0 ( v ), 3(I (D), 100 ( A ) and 390 ~ M (+). Continuous lines are the solutions of Eqn. 2. Midpoi!'m, (as shown in the inset) for the calculated curves are indicated (filled squ&res). Also included are midpoints (filled circles) for three other fibres assuming a control midpoint potential of - 6 0 mV, Continuous line is the solution of Eqn. 3.
described in the Discussion, the curves were quantified. The following equation was found to describe the curves well: I*m,~/1 ....
I * / 1 .... =
(2)
1 + exp((U,/, - Upv)/kl/2) ,,g
where Im,,x d;.d |ma~ have the same meanings as in Eqn. 1, I* is t>,e peak current in test solution, U~/: the potential at half-steady-state inactivation, Upv the prepulse potential and kl/2 the slope value of the steadystate inactivation curve (see Hodgkin and Huxley, 1952). kl/2 was found to be independent of THA concentration. In fig. 4, kl/2 was assumed to be - 7 . 0 mV.
I
~
(3)
The equation is shown graphically in fig. 4 where midpoint values (potential at half-steady-state inactivation) from three different fibres (gilled symbols) are also shown. The described T H A effects on the Na + current showed frequency dependence. The block increased with increased pulse frequency (above 2 Hz). The time course and the steady-state level of the increase depended on the holding potential. The time course of the peak Na + current decrease was exponential and had a ~ime constant that depended on the holding potential but not on concentration. At 5 Hz and - 7 0 mV the time constant was 1.6 s (fig. 5, right pane..) and at - 9 0 mV it was 0.6 s (fig. 5, left panel). At - 7 0 mV 300 p.M caused a steady-state reduction of about 30% and at - 9 0 mV about 10%.
3.2.2. K + cunent Besides the reduction of the steady-state K + current T H A also affected the activation time course (fig. 6, left panel). It caused a dose-dependent delay of the activation. As seen from the figure, the dose dependence was complex. The effect appeared to be saturated at 10 p.M and did not increase at higher concentrations. The induced delay measured at half-steadystate current was 1.4 + 0.1 (mean _+ S.D.; n = 8; five fibres; concentration range: 10-1000 /.tM) times the control. At high concentrations (1000 p.M) and high potential steps (above 50 mV) T H A also induced a slow inactivation (steady-state values not reached within 20
_ Control
~ 7~'~" ~
":'7";" ~
~. ..........
100 ~M
300 ~M
.
0.8
"
0r8
30 uM
" .'7,,V'V'----" 10/) *'M 300 ~M
g
0.6
-~ o.6
0.4
E L~ 0.4
0.2
0.2
ca
A
B
0 4 Time (s)
8
0
2
4 Time (s)
6
8
Fig. 5. The frequency dependence of the T H A block at a step to - l0 mV from a holding potential of - 9 0 mV (]eft panel) and - 7 0 mV (righ~ panel). Frequency 5 Hz and concentrations as indicated in the figure. Continuous lines are fitted monoexpo~mntial curves with time constants o~ 0.6 s (left panel) and 1.6 s (right panel).
0.8
0.8 .
"~" 0.6
0.6" .
"6 0.4-
°2t20
0.2-,
,
,
~ a 1~ Time (ms)
'
II2 1 0 6'
0
i
i
4
i
i
16
8 12 Time (ms)
2{)
Fig 6. Effects on the K + current associated with a potential step to + 6 0 mV from a holdint.' potential of - 7 0 mV, The step was chosen to minimize the complications caused by Na + currents. Left panel: Recorded currenf.s at indicated concentrations. Note the induced inactivation at 1000 t t M T H A . Right panel: C o m 0 u t e d currents based on Model 2 (see text).
ms). Since it only occurred at unphysiological values, no detailed analysis was performed.
4. Discussion In a previous study (E, inder et al., 1989) we analysed the effects of THA on the ion currents. In the present investigation we have examined these effects in further detail and tried to relate these effects to the effects on the action potential. We found that THA caused a dose-dependent prolongation. A THA-induced prolongation has also been reported for mammalian heart muscle (Osterrieder, 1987), central histamine neurons (Reiner and McGcer, 1988) and immunopositive ACTH cells (Drukarch et al., 1987). Some features of the effects not described in our previous study were also found. Thus (i) the effect on the Na + system was frequency dependent, (ii) the activation of the K * current was modified, and (iii) a voltage-dependent slow inactivation of the K + current was induced. A modified K + current activation has been described for Myxicola axons (Schauf and Sattin, 1987). The frequency-dependent Na + current effect and the voltage-dependent K + channel effect, however, seem not to have been described before. In order to quantify the effects of THA on the ionic currents, mathematical models were developed. These models were found to deviate from ~he description of the THA effect used in our previous study (Elinder et al., 1989).
4.1. A model for the Na * channel effects The model used for the Na + system assumed a blocked state couFled to the open state in addition to the inactivated state. As basis we used the model proposed by Bezanilla and Armstrong (1977) to explain
gating current measurements and pronase effects on the Na + system of the squid giant axon. This model deviates from the classical Hodgkin-Huxley description (1952) and consequently from the FrankenhaeuserHuxley (1964) description in several respects: (i) the inactivated state is reached exclusively from the open state, (ii) the rate constants descrJbing the transition to the inactivated state are voltage-independent, and (iii) the activation rate constants between the different closed states are equal as are the deactivation rate constants (see below). Applying the model proposed by Bezanilla and Armstrong to the node and introducinl; the THAblocked state, the following 5-state diagram is obtained: a,..,, ( U )
c1,~, •
7,,,,u~
c2N~,
a...~ ( U )
K...,, to)
, ..... - oN~
----,"
B,~
x~.,
'
~..,
~ul
ii'
8 ,,,,, [[ gx., I
Na
(Model 1) where CIN~, and C2N~, are closed states, ON~ the open state, IN~ the inactivated state and BN~ the introduced blocked state; aN~,, /~N~, YN,,, 6rq~ are activation and inactivation rate constants, while ~:N~ and aN~ are blocking and deblocking rate constants. (U) indicates voltage and (c) concentration dependence. Fig; 3 (right panel) shows computed currents based on the modci above for varying concentrations of THA. The computational procedure used is described in the Appendix. It is clear that both the biphasic time course and the peak amplitude are well predicted by the model. It should be noted, however, that the model does not explain effects on a longer time scale such as the frequency depende::ce of the block or refractoriness
after the ac'.iop, poter~tSai. T,"'s may be accounted for by introdu~ :~g a direct pathv, ay between resting and blocked s!a'ies. Such a scheme has been proposed by Armstror~,~,,. ;.rid Bezanilta (1977). Neither does the model predict a dose-res~9onse relationship of Eqn. 1 type. At high concentrations the model predicts a smaller reduction of the peak current than observed. However, this discrepancy may easily be explained by assuming an .~ndependent THA effect with a higher dissociation constant than 220/.tM. We also made computations of a model of the THA effects based directly on the description of the Na + system given by Frankenhaeuser and Huxley (1964) and with an added blocked state as above. Assuming the same values for KN~ and Ar~a as in Model 1, the computed o:rrents were found to be ahnost identical to those of Model 1. Thus, there was no possibility to distinguish between the two models in the present investigation. However, due to the arguments of Armstrong (1970), Goldman and Schauf (1972), Armstrong and Bezanilla (1977), Bezanilla and Armstrong (1977) and Armstrong (1981), we chose Model 1 for the calculations of the THA effects on the action potential below.
4.2. A model for the K ~ channel effects For the description of the effects on the K + current we used a m tet which in many respects differs from that described above. It is similar to the model used to describe the slow effects of aminopyridincs on squid axons (Yeh et al., ~976). It assumes a block~'d state coupled to the open state. In addition it assume ~,-sta*~es that are both blocked and closed. In accordance with Model 1 it assumes that the activation rate cons~'ants between the different closed states are equal z~,sare the deactivation rate constants. THA is asst, med to have a higher affinity to ttv~ closed channel than to the open: a K (U) C I K = C 2
aK(U) K .
~ O K
"~, #K (c)
XK ~K(c) aK(U)
C1B K , - - C 2 B Bk (U)
(Model 2)
aK(U)
K.
~K (U)
BK
where C1K, C2K, O K and B n have the same meanings as in Model 1. C1B K and C2B n are the closed aqd blocked states. Fig. 6 (right panel) shows computed currents based on this model for varying concentrations of THA. The eq'~ations and the constants used are described in the Appendix. As shown in Fig. 6 (right panel) this model explains both the modified activation and the reduction of the K + current. However, it does not explain the THA-induced inactivation at high concentrations and high
voltage steps. This did not constitute a problem for the compv*,ation of the effects on the action potential since it wa~ obse~ed exclusively at unphysiological potentials, it may be accounted for by introducing an extra blocked state coupled to the open state.
4.3. Computation of the effects on the action potential In order to investigate whether the observed effects 6n the ion currents were sufficient to explain the effects on the action potential we computed action potentials for different assumed concentrations based on the models above and the mathematical description for the node by Frankenhaeuser and Huxley (1964). The details of the zomputationai procedure are described in the Appel,'dix. Fig. 1 (right panel) shows a computed family of action potentials for different concentrations of THA. It is clear that the models predict the essential features of the experimentally observed effects. Thu~, we conclude that the effect on the action potential may be explained by the described effects on the Na + and the K + currents.
4. 4. Molecular mechanisms The models discussed above may be interpreted in molecular terms. Both models assume that one T H A molecule binds to a single binding site. The measured dose-response curves are approximately described by Eqn. 1. Model 2 exactly predicts a dose response of this type, while Model 1 predicts a slight deviation. This, as mentioned above, may be accounte~ for by another THA effect mediated by another binding site. The dose-re,'~oonse curves we found were consistent with th,~se of Schauf and Sattin (1987) for the effect on Myxicota axons. The action of T H A on the Na ÷ channel (Model 1) may be envisaged as the molecule entering and obstructing the channel when open. Inactivation is prevented by the T H A molecule and will not occur until it is removed. Such a 'foot-in-the-door' mechanism was first proposed by Armstrong (1969) for the effect of TEA on K + channels, and has later been proposed to explain the action of other substances (quaternary ammonium io_rs in general, Armstrong, 1971 and French and Shoukimas, 1981; crown ethers, ,~rhem et al., 1982). Since there are indications from different experimental approaches (pronase treatment, Armstrong et al., 1973; channel protein primary structure, Noda et al., 1984; site-directed mutagenesis, Stiihmer et al., 1989; site-directed antibodies, Vasilev et al., 1988) that the inactivation mechanism is located at the axoplasmic side of the membrane, the model implies that the disc,,ssed THA receptor is accessible exclusively from thi~ side. This supports the conclusions of Schauf and
Sattin (1987) from experiments with direct application of THA on both sides of the membrane. Model 2 suggests that T H A mainly binds to the K + channel in a closed state and unbinds when the channel is opened. In contrast to the case of the Na + system this does not indicate where the THA receptor of the K + system is located, The induced inactivation at high potentials, however, indicates another T H A receptor on the axoplasmic side.
4.5. Relecance of the findings for the THA effect on Alz.heimer's disease Most earlier discussions on the relation between clinical effects of THA on Alzheimer patients and effects on vo!tage-gated channels have focused on effects on the K + channel, and a consequent proior~gation of the action potential. However, the present and our previous study (Elinder et al., 1989) indicate that the main effect is on the Na ~- channels, which at first may seem to contradict the observed effect on the action potential. However, the presented analysis shows that the specific effects of TH ~, on the Na + inactivation system in fact predict the o;zserved prolongation. It should be noted that the pr, Jongation is enhanced by the T H A effects on the K + s" .m. At lower concentrations ( < 10 # M ) the delayed K ÷ current activation may even be the dominating effect. The thus induced prolongation is likely to modify the synaptic processing in certai~ ~ystems (LliMs and Heuser, 19.7). Hence the described findings may be of relevance for understanding the mechanism of T H A action on Alzheimer patients.
6Na = 0.0014 KNa = CTItA//50
3 >!2 = 1.2 The values of :'~ and /3m were calculated from Eqns. 13 and 14 and table i b.~ Frankenhaeuser and Huxley (1964) and modified for a temperature of 7°C as described by Frankenhaeuser and Moore (1963). The value of 3Na was assvmed to be : / 5 0 0 of y in accordance with the assumptions of the model of Bezanilla and Armstrong (1977). K was assumed to be concentration dependent (cT. A in/~M) and voltage independent and A both concentration and voltage independent, in similarity to the assumptions of Yamamoto and Yeh (1984) for the effect of 9-AA (where A, however, showed a slight potential dependence). Model 2 was computed from the differential equations derived from the state diagram shown in Model 2. The following values of the rate constants (in ms - t ) were chosen to fit the currents in fig. 6 (left panel): otK = 1.4 a~ /3K = 1.4/3 n KK = CTttA/540 AK=I /.zK = KK t, K = 0.001 The values of a~ and /3n were taken from Frankenhaeuser and Huxley (1964). The initial conditions were assumed to be the following, in accordance with Eqns. 1, 2 and 3 (U~= resting potential): C1N~ = 1/(1 + (1 + 2CTttA/Kd) e x p ( U , / = - U ~ ) / k , , 2 )
Acknowledgeraents These studies were financed by research granzs from Gun och Bertil Stohnes S~iP.else. Stiftdsen f6r Gamla Tjiinarinnor and the Swedish Medical Research Cot_ncil.
INs = C 1 N a e x p ( U I / 2
- Ur)//kl/2
qN~, = 1 -- C1Na -- IN~ C2Na = O N A = 0 C1K = UK/(/xi< + ut: ) = 1/( 1000 CTttA/K d + 1)
Appendix Constants and procedures for the computer simulations A.1. Computation of THA effects on ion currents Model 1 was computed from a system of parallel differential equations derived from the state diagram shown in Model 1. The following values of the rate constants (in ms - j ) were chosen to fit the currents in fig. 3 (left panel): O/Na = 1.40~ m ]~Na = 1.4 J~m
YN~,= 0.7
C1BK= ! - - C I K = # K / ( # K +
UK)
= 1/(KM'(1000 CTHA) + 1) C2 K = O K = C2B K = B K = 0 The eqnation systems were solved by a simple Euler integration procedure (Wilson ard Bower, 1989). An integration step duration of 0.01 ms was found to be sufficient in b•th cases.
A.2. Computations of THA effects on the action potential In order to compute THA effects on the action potential the Na + and K + currents were calculated from the equations and iniqal conditions above and the
c o n s t a n t - f i e l d e q u a t i o n ( G o l d m a n , 1943; H o d g k i n a n d Kats, 1949; D o d g e a n d F r a n k e n h a e u s e r , 1958). T h e value o f the p e r m e a b i l i t y c o n s t a n t PN~ u s e d w a s 0.7 of t h a t u s e d by F r a n k e n h a e u s e r a n d H u x l e y ¢1964); P~, w a s identical. T h e leak a n d capacitive c u r r e n t s w e r e c a l c u l a t e d f r o m E q n s . 1 5 - 1 7 in the p a p e r by F r a n k e n h a e u s e r a n d H u x l e y (1964). A s above, a s i m p l e E u l e r i n t e g r a t i o n p r o c e d u r e w a s used. A n i n t e g r a t i o n s t e p d u r a t i o n o f 0.005 ms w a s f o u n d sufficient.
References .Arhem. P., B. Frankenhaeuser and L.E. Moore, 1973, Ionic currents at resting potential in nerve fibres from Xenopus hwtis. Potential clamp experiments, Acta Physiol. Scand. 88, 446. fitrhem, P,, B. Frankenhaeuser and H. Kristbjarnarsom 1982, Inactivation of the potassium transport system of myelinated nerve in the presence of a cyclic ionophore, Acta Physiol. Scand. 114, 593. Armstrong, C.M., 1969, Inactivation of the potassium conductance and related penomena caused by quaternary ammonium ion injection in squid axons, J. Gen. Physiol. 54, 553. Armstrong, C.M., 1970, Comparison of gK inactiw~tion caused by quaternary ammonium ion with gN,, inactivation, Biophys. J. 11~ (2, P" rt 2), 185a (abstract). Armsh~ng, C.M., 1971, Interaction of tetraethylammonium ion derivatives with the potassium channels of giant axons, J. Gen. Physiol. 58, 413. Armstrong, C.M., 1981, Sodium channels and gating currents, Physiol, Rev. 61,644. Armstrong, C.M. and F. Bezanilla, 1977, Inactivation of the sodium channel. If. Gating current experiments. J. Gen. Physiol. 70, 567. Armstrong, C.M., F. Bezanilla and E. Rojas, 1973, Destruction of sodium conductance inactivation in ,,,quid axons perfused with pronase, J. Gen. Physiol. 62, 375. Bezanilla. F. and C.M. Armstrong, 1977, Inactivation of the sodium channel. I. Sodium current experiments, J. Gen. Physiol. 70, 549. Dodge, F,A. and B. Frankenhaeuser, 1958, Membrane currenls in isolated frog nerve fibre under voltage damp conditions, J. Physiol. (London) 143, 76. Drukarch, B., K.S. Kits, E.G. Van der Meer, J.C, Lodder and J,C. Stool 1987, 9-Amino-l,2,3,4-tetrahydroacridine (THA), an alleged drug for the treatment of Alzheimer's diseasc, inhibits acetylcholinesterase activity and slow outward K-current, ~:ur. J. Pharmacol. 141, 153. Elinder, F., A.K. Mohammed, B. Winblad and P. ,~.rhem, 1989, Effects of THA on ionic currents in mych~ated axons of X~nopus laet'is, Eur. J. Pharmacol. 164, 599. Frankenhaeuser, B., 1957. A method for recording resting and action potentials in the isolated myelinated nerve fibre of the f;og, J. Physiol, (London) 135, 550. Frankenhaeuser, B. and A. Huxley, 1964, The action potential in the myelinated nerve fibre of Xenopus laeHs as computed on the basis of voltage clamp data, J. Physiol. (London) 171, 3112. Frankenhaeuser, B, and L.E, Moore, 1963, The effect of temperature on the sodium and potassium permeability changes in myelihated nerve fibres of Setloptls It'el'is, J. Physiol. (London) 169, 431.
French. R.J. and J.J. Shoukimas, 1981. Blockage of squid axon potassium conductance by Mtern,,I tetra-N-alkylammonium ion'~ of various sizes, Biophys. J. 34, 271. Goldman, D.E., 1043, Potential, impedance, and rectification in membranes, J. Gen. Physiol. 27, 37. Goldman, L. and C.L SchauL 1972, Inactication of the sodium current in Myxk'ola giant axons. Evidence for coupling to the actiwation process, J. Gen. Physiol. 59, 659. Hodgkin. A.I_ and A.F. Huxley, 1952, Quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London) 117, 500. Hodgkin, A L and B. Katz, 1949, The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. (London) 108, 37. Huxley, A.F. and R. Stiimpfli, 1949, Evidence for saltatory conduction in peripheral myelinated nerve fibres, J. Physiol. (London) 108. 315. Llinfis, R,R. and J.E. Heuser, 1977, Depolarization-release coupling systems in neurons, Neurosci. Res. Program Bull. 15, 555. Mohs, R.C,, B.M. Dav!es. C.A. Johns, A.A. Math~, B.S. Greenwald, T.B. Horvath an(~ K.L. Davies, 1985, Oral physostigmine treatment of patients with Alzheimer's disease, Am. J. Psychiatry 142, 28. Noda, M.. S. Shimizu, T, Tanabc, T. Takai, T. Kayano, T. lkeda, H. Takahashi, H. Nakayama, Y. Kanaoka, N. Minamino, K. Kangawa, H. Matsuo, M.A. Raftery, T. Hirose, S. Inayama, H. Hayashida, T. Miyata and S. Numa, 1984, Primary structure of Electrophorus electricus sodium channel deduced from eDNA sequence, Nature 312, 121. Osterrieder, W.; 1987, 9-Amino-l,2,3A-tetrahydroacridine (THA) is a potent blocker of cardiac potassium channels, Br. J. Pharmacol. 92, 521. Reiner, P,B. and E.G. McGeer, 1988, THA increases action potential duration of central histamine neurons in vitro, Eur. J. Pharmacol. 155, 265. Rogawski, M.A., 1987, Tetrahydroaminoacridine blocks voltage dependent ion channels in hippocampal neurones, Eur. J. Pharmacol. 142, 169. Schauf, C.L and A. Sattin, 1987, Tetrahydroaminoacridine blocks potassium channels and inhibits sodium inactivation in M~,xicola, J. Pharmacol. Exp. Ther. 243, 609. Stiihmer, W., F. Conti, H. Suzuki, X. Wang, M. Noda, N. Yahagi, H. Kubo and S. Numa, 1989, Structural parWs involved in activation and inactivation of the sodium channel, Nature 339, 597. Summers, W.K., L.V. Majovsky, G.M. Marsh, K. Tachiki and A. Kling, 1986, Oral tetrahydroaminoacridine in long-term treatment of senile dementia, Alzheimer type, New Engl. J. Med. 315, i241. Vassilev. P.M., T. Scheuer and W.A. Catteral!, 1988, Identification of an intracellular peptide segment involved in the sodium channel inactivation, Science 241. 1658. Wilson, M.A. and J.M. Bower, 1989, The simulation of large-scale neural networks, in: Methods in Neuronal Modeling, eds, C. Koch and 1. Segev (MIT Press, Cambridge, MA - London) p. 291. Yamamoto, D. and J.Z. Yeh, 1984, Kinetics of 9-aminoacridine block of single Na + channels, J. Gen. Physiol, 84, 361. Yeh, J.Z.. 1979, Dynamics of 9-aminoacridine block of sodium channels in squid axons, J. Gen. Physiol. 73, 1. Yeh, J.Z., G.S. Oxford, C.H. Wu and T. Narahashi, 1976, Dynamics o1' aminopyridine block of potassium channels in squid axon membrane. J. Gen. Physiol. 68, 519.
ADONIS 09224106910015~5
E J P M O L 90211
Mechani'~ms of the tetrahydroaminoacridine effect on action ?etential and io~ curre~]ts in myelir, a t e d axons o
Fredrik Elinder and ?eter Arhem Nobel Institute ]'or Neurophysiology, Karolinska Instituter, S-104 O1 Stockhobn, Sweden Received 23 April 1991, accep ed 14 May 1991
9-Amino-l,2,3,4-tetrahydroacridine (THA) in the range of 10-3~9 /.tM was shown to prolong the action potential in myelinated nerve fibres of Xenopus laevis. Voltage-clamp experiments showed that THA. besides reducing the Na ~ and the K* current, modified the Na + current it~activation and the K + current activation. The effects were frequency dependent. Quantitative models were developed and used in computer simulations of the THA effect on the action potential. "Yhe computations showed that the observed effects on the ion currents were sufficient to explain the observed prolongation of t ae action potential. The models further suggest that THA binds to Na + channels in an open state and from the a×oplasmic side while it binds to K + channels in a closed state. The findings suggest an explanation to some aspects of the clinical effects of T H ~ on Alzheimer patients. 9-Amino-l,2,3,4-tetrahydroacridine (THA); Ion channels; Myelinatcd nerve fiber; Voltage-clamp cxpcrinieat; Computer simulations; AIzheimcr's disease
1. Introduction 9-Amino-l,2,3,4-tetrahydroacridine ( T H A ) has been shown to improve cognitive functions in patients with A l z h e i m e r ' s disease ( S u m m e r s et al., 1986). Since T H A is a p o t e n t acetylcholinesterase ( A C h ) inhibitor it has been s u g g e s t e d that its main effect is to e n h a n c e the levels of A C h , thereby c o m p e n s a t i n g for the effect of d e g e n e r a t e d cholinergic neurons. However, since o t h e r inhibitors, e.g. physostigmine, were f o u n d not to show this effect ( M o h s et al., 1985) T H A h a s also been proposed to have o t h e r effects in order to explain its effects on Alzheinte.r patients. D u e to the structural similarity between the central aromatic ring of T H A and the K + c h a n n e l blocker 4-aminopyridine (4-AP) (Yeh et al., 1976) it has been suggested that the clinical effects of T H A d e p e n d on K + c h a n n e l blocking, thereby prolongating the action potential and e n h a n c i n g the release of A C h ( S u m m e r s et a l , 1986). T H A also has structural similarities to 9-aminoacridine (9-/~,), a blocker of open Na + channels (Yeh, 1979; Y a m a m o t o and Yeh, 1984). Several studies have c e n f i r m e d that T H A influences voltage-gated K + c h a n n e l s as well as Na ÷ and Ca z+ c h a n n e l s ( D r u k a r c h et al., 1987; Elinder et al., 1989;
Correspondence to: Peter Arhem, Nobel Institute for Neurephysiology, Karo[inska Instinaet, Box 60 400, S-104 01 Stockholm, Sweden.
Osterrieder, 1987; Rogawski, 1987; Schauf and Sattino 1987). It has also been shown that t':e action potential in s o m e cells is prolonged by T H A (Dra~:arch et al., 1987; Osterrieder, 1987; Reiner and McGeer, i988). In a previous study (Elinder et al., 1989) we investigated the effects of T H A on the node of Ranvier in axons from the clawed toad. Xenopus laevis. It was f o u n d that T H A blocks Na + a n d K ~ channels, that the steady-state inactivation curve is shifted in a negative direction along the potential axis and that the Na + current inactivation b e c o m e s biphasic. T h e effect could quantitatively be described as decreased permeability c o n s t a n t s (PN, and P~,) and a modified potential dep e n d e n c e of the Na + inactivation. T h e purpose of the present investigation was to examine these effects in further detail and their relation to the effect on the action potential. We expressed the effects on the ion currents in mathematical models that were used to calculate the effects on the action potentials by c o m p u t e r simulations.
Z Materials and methods Large myelinated fibres were isolated from the sciatic nerve of the clawed toad, Xenopus laevis. A single fibre was m o u n t e d in a recording c h a m b e r and cut at half-internodal lengths on both sides of the node u n d e r investigation, q h e c h a m b e r was connected by salt
bridges to the voltage-clamp apparatus (Frankenhaeuser, 1957; see also Huxley and StLmpfli, 1949). The circuitry and balancing procedt:res were essentially the same as described by Dodg~- and Frankenhaeuser (1958), with the modifications described by Arhem e t a l . (1973). Pulse generation and sampling were made using a TL-I DMA interface (Labmaster, U.S.A.) and the pCLAMP software tAxon Instruments, U.S.A.). In order to obtain good feedback cov_~rol and recording situations, all experiments were performed at a relatively low temperature (8°C). Since only relative current values were essential in the present investigation and since there is some uncertainty in the estimation of the nodal area and the axoplasmic resistance (see Dodge and Frankenhaeuser, 1958), no attempt to calibrate the currents in absolute values was made. The test solution was applied to the pool with the node. The control Ringer solution contained (in raM): NaCt 115.5. KCI 2.5, CaCl 2 2.0 and Tris buffer (adjusted to pH 7.2) 5.0. The solution used in the end pools consisted of (in raM): KC1 120, and Tris buffer (pH 7.2) 5.0. THA was obtained from Nobel Chemicals, Sollentuna, Sweden, and was added to the Ringer solution. The computations were performed on an IBM-compatible personal computer (80286 CPU). The software was written in BASIC. For the computational procedures, see the Appendix.
time course and ~mplitudc of the action potential. At about 1000 ,u.i',~ the action potential was completely blocg,:d. At lower concentrations the time to reach a steau state was about 3 rain (fig. 1, left panel). The duranon of the action potential increased with increased concentration. M e a s u e d at the base, and at steady state, it doubled at a o mcentration between 30 and !00 ,aM. In parallel with the prolongation the slope of the initial falling phase became steeper (at concentrations above 30/xM; consequently not seen in fig. 1, left aan,A). Effects on the amplitude were ob~ served only in the highest concentration range studied (> 100 ,aM). The reversibility was not complete within the times for the washout in the present investigation (5-10 min). The time to reach steady-state recovery was about 3 rain. 3.2. Effects on the t,m currents
As previously shown (Elinder et al., 1989) THA reduces both the Na ~- and the K + currcnts. In order to quantify the dose-response relation we measured the effects on the peak Na + current and the steady-state K ÷ current. Complications due to effects on the Na + inactivation were avoided by keeping the membrane at a potential of - 1 3 0 to - 1 2 0 mV between the test pulses. The dose-response curve for both the Na + and the K + current effects could approximately be described by the equation I~'~,×/Im,~ = 1(1 + CTHA/Kd)
3. Results 3.1. Effects on tl, e action potenlial
THA was found, in conce,;tra:ions from 10 # M and upwards, to reversibly and non-linearily affect both
(1)
where I,,,~ and Im,× are the maximum peak Na + currents or the steady-state K* currents in control and test solutions, respectively, CTHa the concentration of THA in ,aM and K a the dissociation constant in p.M. The geometrical mean value of K d for the peak Na + current measured at - 10 mV was 220 p.M (n = 5; the 4t)
+41)
13 A
+2(~
20
0
> E ~"
-2o E u
-20
E ~. -40
-411 -
g -6()
-
-60
-80
-
-8(I ,
0
-
~
.....
¢'
4 "1 im
ms)
, ~2
.
. 16
.
.
1(10
'
~
'
~ ' Time. (ms)
l~
'
l'~;
'
Fig. I. The effect of 30 ,aM THA ~,r. the action potential. Left panel: Time course of the effect. Time in minutes after change to test solutioe, indicated. Holding potential - 9 0 inV. Right panel: Computed action potentials at different THA concentrations (in ,aM) as indicated. The computations are described in f,he Appendix. Note that the values used do not refer to the fibre in the left panel.
~"
0.8 0.6
~
0.4
0.2
0 10
1C0
1000
10 000
(,M) Fig. 2. Dose-response curves for ~.he effects on maximum peak Na ~ (o) and maximum steady-state K ÷ ( ~ ) currents. Measurements of peak Na + currents at test steps to - 10 mV from a holding potential Concentration
of - 120 mV and measurementsof steady-state K~ currents at steps to +50 mV from a ho!ding potential of -70 inV. Continuous lines are solut' as of Eqn. 1 with dissociation constants of 200 and 540 .~M, respectively. The deviating experimental values for the steadystate current at 1000 p.M may be explained by an induced inacti,~ation at high concentrations of THA (see text and fig. 6).
corresponding arithmetical mean _ :..D. was 270 + 170) and for the steady-state K + cv" ~t measured at + 4 0 or + 5 0 mV was 540 p,M (n = s; arithmetical mean + S.D. was 570__+ 180). As a measure of the relation between the effect on the K + system and the Na + system we calculated the quotient between the dissociation constants for the two s :terns. By using the geometrical means above, the ~ ometrical mean for this quotient w~ o directly o b r :ned. The value was 2.5 (n = 5; the individual va|ues ed between 1.3 and 4.6).
1 - - I
....
~"~000 aM
Time (ms) 2 3 P
I
Fig. 2 shows the typical dose-response curves for one fibre. As shown in the figure, Eqn. 1 describes the T H A effects on the Na + system better than on the K ~ system. At high conzentrations (1000 g M ) T H A reduced the steady-state K + current more than predicted. This was presumably related to the THA-induced inactivation described below. No systematic T H A effect on the leak current was noted. At high concentrations (1000 IzM), however, an irreversible increase in leak current sometimes was observed. In accordance with the effects on the action potential, the T H A effect on the ion currents was only partially revergibie. The time course of both the onset of the effect arid the recovery varied fo~ different parameters (peak N a - current, time course of inactivatien, etc.) but a steady state was systematica!ly reached within 1-2 rain. 3.2.1. N a + c u r r e n t
Besides the amplitude reduction of the Na ÷ current T H A also modified the time course of the N a " inactivation. The monoexponential time course in control solution became biphasic (fig. 3, left panel). The effect was more pronounced at higher concentrations; the slope of the initial phase was increased while that of the late phase decreased. As previously shown (Elinder et al., 1989), the T H A effect on the Na + inactivation was also seen as a negative shift of the steady-state Na + inactivation curve along the voltage axis. Fig. 4 shows the steady-state inactivation for a prepulse duration of 1 s for three concentrations (open symbols) and one fibre. In order to obtain initial values for the mathematical models
Time (ms) 4
5
I
p
I)
l
2
3
4
5
ii
o
°'lb/ Fig. 3. Effects of THA on the Na* current associated v,,ith a potential step to - 10 mV from a holding potential of - 7 0 mV. Left panel: Recorded currents at indicated concentrations. Right panel: Computed currents based on Model I (see lextL Ordinat.: indicates the quotient between open and total number of channels.
The shift, ..1U]/2(= U ~ 2 - UI/2), along the voltage axis was related to the blocked maximum peak current by the equation: 0.8
1~=
(I,*,,~/I ..... ) / 2 = 1/(1 + exp(...1U,/2/k,/2) )
£ 0(,-
(1.2
-110
-90
-70 -50 Potential (mV)
-31~
Fig. 4. Effects on steady-state Na* current inactivation measured for a test step to - l0 mV from prepulscs of ! s duration. Concentrations were 0 ( v ), 3(I (D), 100 ( A ) and 390 ~ M (+). Continuous lines are the solutions of Eqn. 2. Midpoi!'m, (as shown in the inset) for the calculated curves are indicated (filled squ&res). Also included are midpoints (filled circles) for three other fibres assuming a control midpoint potential of - 6 0 mV, Continuous line is the solution of Eqn. 3.
described in the Discussion, the curves were quantified. The following equation was found to describe the curves well: I*m,~/1 ....
I * / 1 .... =
(2)
1 + exp((U,/, - Upv)/kl/2) ,,g
where Im,,x d;.d |ma~ have the same meanings as in Eqn. 1, I* is t>,e peak current in test solution, U~/: the potential at half-steady-state inactivation, Upv the prepulse potential and kl/2 the slope value of the steadystate inactivation curve (see Hodgkin and Huxley, 1952). kl/2 was found to be independent of THA concentration. In fig. 4, kl/2 was assumed to be - 7 . 0 mV.
I
~
(3)
The equation is shown graphically in fig. 4 where midpoint values (potential at half-steady-state inactivation) from three different fibres (gilled symbols) are also shown. The described T H A effects on the Na + current showed frequency dependence. The block increased with increased pulse frequency (above 2 Hz). The time course and the steady-state level of the increase depended on the holding potential. The time course of the peak Na + current decrease was exponential and had a ~ime constant that depended on the holding potential but not on concentration. At 5 Hz and - 7 0 mV the time constant was 1.6 s (fig. 5, right pane..) and at - 9 0 mV it was 0.6 s (fig. 5, left panel). At - 7 0 mV 300 p.M caused a steady-state reduction of about 30% and at - 9 0 mV about 10%.
3.2.2. K + cunent Besides the reduction of the steady-state K + current T H A also affected the activation time course (fig. 6, left panel). It caused a dose-dependent delay of the activation. As seen from the figure, the dose dependence was complex. The effect appeared to be saturated at 10 p.M and did not increase at higher concentrations. The induced delay measured at half-steadystate current was 1.4 + 0.1 (mean _+ S.D.; n = 8; five fibres; concentration range: 10-1000 /.tM) times the control. At high concentrations (1000 p.M) and high potential steps (above 50 mV) T H A also induced a slow inactivation (steady-state values not reached within 20
_ Control
~ 7~'~" ~
":'7";" ~
~. ..........
100 ~M
300 ~M
.
0.8
"
0r8
30 uM
" .'7,,V'V'----" 10/) *'M 300 ~M
g
0.6
-~ o.6
0.4
E L~ 0.4
0.2
0.2
ca
A
B
0 4 Time (s)
8
0
2
4 Time (s)
6
8
Fig. 5. The frequency dependence of the T H A block at a step to - l0 mV from a holding potential of - 9 0 mV (]eft panel) and - 7 0 mV (righ~ panel). Frequency 5 Hz and concentrations as indicated in the figure. Continuous lines are fitted monoexpo~mntial curves with time constants o~ 0.6 s (left panel) and 1.6 s (right panel).
0.8
0.8 .
"~" 0.6
0.6" .
"6 0.4-
°2t20
0.2-,
,
,
~ a 1~ Time (ms)
'
II2 1 0 6'
0
i
i
4
i
i
16
8 12 Time (ms)
2{)
Fig 6. Effects on the K + current associated with a potential step to + 6 0 mV from a holdint.' potential of - 7 0 mV, The step was chosen to minimize the complications caused by Na + currents. Left panel: Recorded currenf.s at indicated concentrations. Note the induced inactivation at 1000 t t M T H A . Right panel: C o m 0 u t e d currents based on Model 2 (see text).
ms). Since it only occurred at unphysiological values, no detailed analysis was performed.
4. Discussion In a previous study (E, inder et al., 1989) we analysed the effects of THA on the ion currents. In the present investigation we have examined these effects in further detail and tried to relate these effects to the effects on the action potential. We found that THA caused a dose-dependent prolongation. A THA-induced prolongation has also been reported for mammalian heart muscle (Osterrieder, 1987), central histamine neurons (Reiner and McGcer, 1988) and immunopositive ACTH cells (Drukarch et al., 1987). Some features of the effects not described in our previous study were also found. Thus (i) the effect on the Na + system was frequency dependent, (ii) the activation of the K * current was modified, and (iii) a voltage-dependent slow inactivation of the K + current was induced. A modified K + current activation has been described for Myxicola axons (Schauf and Sattin, 1987). The frequency-dependent Na + current effect and the voltage-dependent K + channel effect, however, seem not to have been described before. In order to quantify the effects of THA on the ionic currents, mathematical models were developed. These models were found to deviate from ~he description of the THA effect used in our previous study (Elinder et al., 1989).
4.1. A model for the Na * channel effects The model used for the Na + system assumed a blocked state couFled to the open state in addition to the inactivated state. As basis we used the model proposed by Bezanilla and Armstrong (1977) to explain
gating current measurements and pronase effects on the Na + system of the squid giant axon. This model deviates from the classical Hodgkin-Huxley description (1952) and consequently from the FrankenhaeuserHuxley (1964) description in several respects: (i) the inactivated state is reached exclusively from the open state, (ii) the rate constants descrJbing the transition to the inactivated state are voltage-independent, and (iii) the activation rate constants between the different closed states are equal as are the deactivation rate constants (see below). Applying the model proposed by Bezanilla and Armstrong to the node and introducinl; the THAblocked state, the following 5-state diagram is obtained: a,..,, ( U )
c1,~, •
7,,,,u~
c2N~,
a...~ ( U )
K...,, to)
, ..... - oN~
----,"
B,~
x~.,
'
~..,
~ul
ii'
8 ,,,,, [[ gx., I
Na
(Model 1) where CIN~, and C2N~, are closed states, ON~ the open state, IN~ the inactivated state and BN~ the introduced blocked state; aN~,, /~N~, YN,,, 6rq~ are activation and inactivation rate constants, while ~:N~ and aN~ are blocking and deblocking rate constants. (U) indicates voltage and (c) concentration dependence. Fig; 3 (right panel) shows computed currents based on the modci above for varying concentrations of THA. The computational procedure used is described in the Appendix. It is clear that both the biphasic time course and the peak amplitude are well predicted by the model. It should be noted, however, that the model does not explain effects on a longer time scale such as the frequency depende::ce of the block or refractoriness
after the ac'.iop, poter~tSai. T,"'s may be accounted for by introdu~ :~g a direct pathv, ay between resting and blocked s!a'ies. Such a scheme has been proposed by Armstror~,~,,. ;.rid Bezanilta (1977). Neither does the model predict a dose-res~9onse relationship of Eqn. 1 type. At high concentrations the model predicts a smaller reduction of the peak current than observed. However, this discrepancy may easily be explained by assuming an .~ndependent THA effect with a higher dissociation constant than 220/.tM. We also made computations of a model of the THA effects based directly on the description of the Na + system given by Frankenhaeuser and Huxley (1964) and with an added blocked state as above. Assuming the same values for KN~ and Ar~a as in Model 1, the computed o:rrents were found to be ahnost identical to those of Model 1. Thus, there was no possibility to distinguish between the two models in the present investigation. However, due to the arguments of Armstrong (1970), Goldman and Schauf (1972), Armstrong and Bezanilla (1977), Bezanilla and Armstrong (1977) and Armstrong (1981), we chose Model 1 for the calculations of the THA effects on the action potential below.
4.2. A model for the K ~ channel effects For the description of the effects on the K + current we used a m tet which in many respects differs from that described above. It is similar to the model used to describe the slow effects of aminopyridincs on squid axons (Yeh et al., ~976). It assumes a block~'d state coupled to the open state. In addition it assume ~,-sta*~es that are both blocked and closed. In accordance with Model 1 it assumes that the activation rate cons~'ants between the different closed states are equal z~,sare the deactivation rate constants. THA is asst, med to have a higher affinity to ttv~ closed channel than to the open: a K (U) C I K = C 2
aK(U) K .
~ O K
"~, #K (c)
XK ~K(c) aK(U)
C1B K , - - C 2 B Bk (U)
(Model 2)
aK(U)
K.
~K (U)
BK
where C1K, C2K, O K and B n have the same meanings as in Model 1. C1B K and C2B n are the closed aqd blocked states. Fig. 6 (right panel) shows computed currents based on this model for varying concentrations of THA. The eq'~ations and the constants used are described in the Appendix. As shown in Fig. 6 (right panel) this model explains both the modified activation and the reduction of the K + current. However, it does not explain the THA-induced inactivation at high concentrations and high
voltage steps. This did not constitute a problem for the compv*,ation of the effects on the action potential since it wa~ obse~ed exclusively at unphysiological potentials, it may be accounted for by introducing an extra blocked state coupled to the open state.
4.3. Computation of the effects on the action potential In order to investigate whether the observed effects 6n the ion currents were sufficient to explain the effects on the action potential we computed action potentials for different assumed concentrations based on the models above and the mathematical description for the node by Frankenhaeuser and Huxley (1964). The details of the zomputationai procedure are described in the Appel,'dix. Fig. 1 (right panel) shows a computed family of action potentials for different concentrations of THA. It is clear that the models predict the essential features of the experimentally observed effects. Thu~, we conclude that the effect on the action potential may be explained by the described effects on the Na + and the K + currents.
4. 4. Molecular mechanisms The models discussed above may be interpreted in molecular terms. Both models assume that one T H A molecule binds to a single binding site. The measured dose-response curves are approximately described by Eqn. 1. Model 2 exactly predicts a dose response of this type, while Model 1 predicts a slight deviation. This, as mentioned above, may be accounte~ for by another THA effect mediated by another binding site. The dose-re,'~oonse curves we found were consistent with th,~se of Schauf and Sattin (1987) for the effect on Myxicota axons. The action of T H A on the Na ÷ channel (Model 1) may be envisaged as the molecule entering and obstructing the channel when open. Inactivation is prevented by the T H A molecule and will not occur until it is removed. Such a 'foot-in-the-door' mechanism was first proposed by Armstrong (1969) for the effect of TEA on K + channels, and has later been proposed to explain the action of other substances (quaternary ammonium io_rs in general, Armstrong, 1971 and French and Shoukimas, 1981; crown ethers, ,~rhem et al., 1982). Since there are indications from different experimental approaches (pronase treatment, Armstrong et al., 1973; channel protein primary structure, Noda et al., 1984; site-directed mutagenesis, Stiihmer et al., 1989; site-directed antibodies, Vasilev et al., 1988) that the inactivation mechanism is located at the axoplasmic side of the membrane, the model implies that the disc,,ssed THA receptor is accessible exclusively from thi~ side. This supports the conclusions of Schauf and
Sattin (1987) from experiments with direct application of THA on both sides of the membrane. Model 2 suggests that T H A mainly binds to the K + channel in a closed state and unbinds when the channel is opened. In contrast to the case of the Na + system this does not indicate where the THA receptor of the K + system is located, The induced inactivation at high potentials, however, indicates another T H A receptor on the axoplasmic side.
4.5. Relecance of the findings for the THA effect on Alz.heimer's disease Most earlier discussions on the relation between clinical effects of THA on Alzheimer patients and effects on vo!tage-gated channels have focused on effects on the K + channel, and a consequent proior~gation of the action potential. However, the present and our previous study (Elinder et al., 1989) indicate that the main effect is on the Na ~- channels, which at first may seem to contradict the observed effect on the action potential. However, the presented analysis shows that the specific effects of TH ~, on the Na + inactivation system in fact predict the o;zserved prolongation. It should be noted that the pr, Jongation is enhanced by the T H A effects on the K + s" .m. At lower concentrations ( < 10 # M ) the delayed K ÷ current activation may even be the dominating effect. The thus induced prolongation is likely to modify the synaptic processing in certai~ ~ystems (LliMs and Heuser, 19.7). Hence the described findings may be of relevance for understanding the mechanism of T H A action on Alzheimer patients.
6Na = 0.0014 KNa = CTItA//50
3 >!2 = 1.2 The values of :'~ and /3m were calculated from Eqns. 13 and 14 and table i b.~ Frankenhaeuser and Huxley (1964) and modified for a temperature of 7°C as described by Frankenhaeuser and Moore (1963). The value of 3Na was assvmed to be : / 5 0 0 of y in accordance with the assumptions of the model of Bezanilla and Armstrong (1977). K was assumed to be concentration dependent (cT. A in/~M) and voltage independent and A both concentration and voltage independent, in similarity to the assumptions of Yamamoto and Yeh (1984) for the effect of 9-AA (where A, however, showed a slight potential dependence). Model 2 was computed from the differential equations derived from the state diagram shown in Model 2. The following values of the rate constants (in ms - t ) were chosen to fit the currents in fig. 6 (left panel): otK = 1.4 a~ /3K = 1.4/3 n KK = CTttA/540 AK=I /.zK = KK t, K = 0.001 The values of a~ and /3n were taken from Frankenhaeuser and Huxley (1964). The initial conditions were assumed to be the following, in accordance with Eqns. 1, 2 and 3 (U~= resting potential): C1N~ = 1/(1 + (1 + 2CTttA/Kd) e x p ( U , / = - U ~ ) / k , , 2 )
Acknowledgeraents These studies were financed by research granzs from Gun och Bertil Stohnes S~iP.else. Stiftdsen f6r Gamla Tjiinarinnor and the Swedish Medical Research Cot_ncil.
INs = C 1 N a e x p ( U I / 2
- Ur)//kl/2
qN~, = 1 -- C1Na -- IN~ C2Na = O N A = 0 C1K = UK/(/xi< + ut: ) = 1/( 1000 CTttA/K d + 1)
Appendix Constants and procedures for the computer simulations A.1. Computation of THA effects on ion currents Model 1 was computed from a system of parallel differential equations derived from the state diagram shown in Model 1. The following values of the rate constants (in ms - j ) were chosen to fit the currents in fig. 3 (left panel): O/Na = 1.40~ m ]~Na = 1.4 J~m
YN~,= 0.7
C1BK= ! - - C I K = # K / ( # K +
UK)
= 1/(KM'(1000 CTHA) + 1) C2 K = O K = C2B K = B K = 0 The eqnation systems were solved by a simple Euler integration procedure (Wilson ard Bower, 1989). An integration step duration of 0.01 ms was found to be sufficient in b•th cases.
A.2. Computations of THA effects on the action potential In order to compute THA effects on the action potential the Na + and K + currents were calculated from the equations and iniqal conditions above and the
c o n s t a n t - f i e l d e q u a t i o n ( G o l d m a n , 1943; H o d g k i n a n d Kats, 1949; D o d g e a n d F r a n k e n h a e u s e r , 1958). T h e value o f the p e r m e a b i l i t y c o n s t a n t PN~ u s e d w a s 0.7 of t h a t u s e d by F r a n k e n h a e u s e r a n d H u x l e y ¢1964); P~, w a s identical. T h e leak a n d capacitive c u r r e n t s w e r e c a l c u l a t e d f r o m E q n s . 1 5 - 1 7 in the p a p e r by F r a n k e n h a e u s e r a n d H u x l e y (1964). A s above, a s i m p l e E u l e r i n t e g r a t i o n p r o c e d u r e w a s used. A n i n t e g r a t i o n s t e p d u r a t i o n o f 0.005 ms w a s f o u n d sufficient.
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