Neurotransmission parameters estimated from miniature endplate current growth phase

Brain Research, 402 (1987) 387-392 Elsevier

387

BRE 220117

Neurotransmission parameters estimated from miniature endplate current growth phase

Barry W. Madsen

Robert O. Edeson 2 and Robin K. Milne 3

1Department of Pharmacology, University of Western Australia, Nedlands (Australia), 2Department of Anaesthesia and Intensive Care, Sir Charles Gairdner Hospital, Nedlands (Australia) and 3Department of Mathematics, University of Western Australia, Nedlands (Australia) (Accepted 16 September 1986) Ker words: Neuromuscular junction; Miniature endplate current; Rising phase; Kinetic parameter:

Non-linear regression; Estimation

A numerical model of miniature endplate current (mepc) generation was fitted to the rising phase of individual mepcs recorded at the frog neuromuscular junction, and estimates of 6 transmission parameters were obtained. Model fitting was enabled by assuming literature values for geometric parameters and determining single channel current by noise analysis, the channel closing rate constant from the mepc decay, and acetylcholine hydrolysis parameters from mepcs recorded in esterase-blocked endplates. Under control conditions, mean estimates were: number of molecules in a quantum = 29,000, diffusion coefficient = 2.8 x 1()-~ cm2s 1 endplate receptor density = 85001¢m -', forward binding rate constant = 7.6 x 10s M-Is ~, equilibrium dissociation constant - 581LM and channel opening rate constant = 8100 s-~.

Classical analysis of the time course of m i n i a t u r e endplate currents (mepcs) has focussed on the decay phase, providing data on channel relaxation kinetics. However, the growth phase also contains information on the transmission process but is harder to study b e c a u s e it is faster and requires more complex modelling for analysis. The feasibility of recovering certain model quantities related to diffusion, receptor binding, and channel kinetics from the mepc growth ,phase has been d e m o n s t r a t e d in work Ih12 based on summary data ( 2 0 - 8 0 % rise time). The aim of the present study was to obtain reliable estimates of selected neurotransmission p a r a m e t e r s by utilizing all the information contained in the precise curvature of the growth phase. To avoid the problems of time and amplitude alignment involved in waveform averaging, individual mepcs were studied. A quantitative model of mepc generation was d e v e l o p e d 15 and used with numerical optimization techniques to e s t i m a t e

several p a r a m e t e r s . The validity of the method w a s

then examined using two pharmacological probes with known properties. Mepcs were recorded in frog (Litoria moorei) sartorius muscle using a two-electrode voltage clamp as described previously j6. Muscles were maintained in carbogenated Ringer solution (mM: NaC1 115, KCI 2.5, CaC12 1.8, phosphate buffer 3; pH 7.2) at 20 _+ 0.2 °C. M e m b r a n e potential was held at - 9 0 mV and clamp performance was optimized so that the res p o n s e to a 1 mV c o m m a n d step had a total rise time of less than 25 Ks. Mepcs w e r e filtered at 3 kHz ( - 3 dB, 4 pole Butterworth), digitized at 5(] kHz and stored on c o m p u t e r disk for off-line analysis. Model p a r a m e t e r s requiring assumption or e s t i m a tion are listed in Table I. Single channel current (i) w a s d e t e r m i n e d by noise analysis using ionophoretically applied acetylcholine ( A C h ) . A C h spectra w e r e computed and the variance obtained from the zero-

Correspondence." B.W. Madsen, Department of Pharmacology, University of Western Australia, Nedlands, WA 60(19, Australia. 1100~-8993/87/$03.50 © lC)87Elsevier Science Publishers B.V. (Biomedical Division)

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Fig. 1. Estimation of transmission parameters from mepc growth phase. The continuous trace is an mepc which has been digitized at 20kcs intervals. The broken trace is the optimized or predicted waveform given the freedom to vary 6 transmission parameters; for this mepc the parameter set pj-p~ was 24,500. 2.95, 10,100, 7.11, 56.1 and 8,240 respectively (dimensions given in Table I), with a = 538 s I The error S.D. for this regression was _ 0.19 nA, whereas for the baseline alone it was + 0.32 nA. In only 4 out of 34 control mepcs from 3 endplates was the error variance significantly greater than the corresponding baseline variance; two of these had prolonged 20-80% rise times (280 ,us) and were probably non-focal. The left inset shows the complete mepc (calibration: vertical 1 nA, horizontal 4 ms) with the region enclosed by the arrows being the 600 ,us segment used in the regression. The right inset provides partial information on the relationship of the sum of squares to parameter estimates, namely the independent parameter dependencies. Data generated by taking the best fit parameters for this mepc and computing a new sum of squares (nA2) after incrementing each parameter in turn by 21)%. Bars represent from the left, Pl-P6; the dotted line shows the best fit. Four of the parameters (Pl,P>P3,P6) are well defined whereas more uncertainty would be expected in the two binding terms. Possible correlations between parameters complicate this interpretation, and the usual method of establishing reliability of estimates is to rerun regressions from several different starting points.

frequency asymptote of a best-fit, least-squares Lorentzian. The value of i was 1.72 + 0.21 p A (mean + S.E.M., n = 19 from 12 endplates, - 9 0 m V membrane potential). The channel closing rate constant was determined from the decay phase of each mepct6; waveforms requiring two exponentials for this fit were excluded from subsequent analysis~ Six transmission parameters (denoted P~-P6, see Table I) were estimated by non-linear least squares regression. In addition, for each mepc, the initial time point (t0) was determined; A n o n - g r a d i e n t adaptive simplex method of function minimizationl* was

III computer with a typical regression taking - h central processing unit-time. To estimate the M i c h a e l i s - M e n t e n hydrolysis parameters 1/'m~,~and K m, mepcs from a single endplate were examined under control cortditions and where acetylcholinesterase was blocked by diisopropyltluorophosphate I DFP. 1 raM. muscle bathed for 50 min followed by washout with fresh Ringer and equilibration for 60 rain 1o eliminate the direct, non-anticholinesterase effects of DFP"~ Parameter sets determined for mepcs recorded in D F P ~ith hydrolysis excluded from the model provided average values of

Pe-P~,, which were then used as fixed paratneter.s in redticed regressions I estimating t;1. V~,~,,~and K ml on the control series, where hvdrolx si~ was modelled. Fig. l shows the growth phase of an individual mepc on an expanded time scale, together with the curve predicted by optimization of the 6 parameters. Best estimates for these parameters (mean m S.E.M. I from 34 control mepcs from 3 endplates are given in Table I. While the estimate of quantal size is larger than a w i d e n quoted value of 10.000 ~ret. t0), the present mepcs were on average larger than those in that studv and other models l-'''> would predict at least 15-20.()00 molecules u n d e r our conditions. If we accept a simple correspondence between the quantal event and a single vesicle t there is some evidence suggesting this may not be the case31 it would appear that frog synaptic vesicles, with a diameter of 40-70 nm 5 iv are large enough to contain 30.000 molecules at a concentration of ca. 400 mM: in comparison, fish electric organ vesicles contain 47.000260.000 molecules at concentrations approaching 1 M 19'22. Best estimates for the other 5 parameters are in substantial agreement witt~ those from other studies, though in the case of fl there is a wide range

389 TABLE I Model parameters in mepc growth phase optimization Details of the model are given in ref. 15. Rate constants are defined by the kinetic scheme: 2k k~ ~ 2A + R ~ 1 AI R + A ~_ A~R A~R* k~ 2k 4 c~ where A = A C h , R = free receptor, AiR = bound receptor and * denotes conducting state;/3 = p~. To contain the numerical estimation problem, k I was put equal to k 3 (= p.,), and k j k I = k4/k ~ (=Ps). V...... and K m are Michaelis-Menten parameters for A C h hydrolysis. For each inept, the parameters Pl-P~, were estimated by non-linear regression of the growth phase and (t was independently obtained from the decay phase. Reference n u m b e r s are noted in parentheses.

A s s u m e d class parameters cleft height cleft radius vesicle height and radius receptor distribution parameter esterase distribution p a r a m e t e r

60 nm 1.25/tin 5 nm 2001~m 501/m

Estimated class parameters single channel current ( 90 V...... Km

1.72 pA 8.2 Ms I I 1.9,uM

mV)

(20) (13) i I

Estimated individual parameters quantal size (Pl) diffusion coefficient (Pc, × 10 6cm2s i) endplate receptor density (P3, u m :) forward binding ratc constant (Pa, x l0 s M-is i) equilibrium dissociation constant (/?5, ,uM) channel opening rate constant (P6, s 1)

Best estimates (mean + S. E. M. )

Some literature values

29.00(I _+ 1300 2.78 + 0.12 8470 _+ 40

10.000 (10) 4 112,131 10.000 (20)

7.56_+0.19 58.4 _+ 2.0 8150 _+ 190

I 10(8) 30-80 (1,2) 1200 30,600 12,14)

channel closing rate constant ((~, s ~)

of literature values (see Table I). The validity of the technique was examined by studying mepcs recorded in the presence of a-bungarotoxin (c~-BTX) and hemicholinium (HC-3). The toxin caused a significant (P < 0.001) reduction in effective receptor density, as expected from its known properties; no other parameter was altered (Fig. 2a). HC-3 is a classic high-affinity choline uptake inhibitor, and the decrease in quantal size shown in Fig. 2b was therefore expected. However, effective receptor density was also decreased, a property not as widely discussed but nonetheless documented 21. In addition, HC-3 increased the apparent diffusivity of ACh, a new finding which needs further investigation. All 3 changes due to HC-3 were reversible on choline washout. Analysis of 20 control mepcs from a single endplate showed that mepc amplitude (/max) was strongly correlated with the number of molecules (P0 in a quantum (Fig. 3a), with 73% of the variation in/max explained by pj. There was also a significant (P < 0.05) but lesser correlation of/max with endplate receptor density (Fig. 3b), and together these two parameters explained 94% of the variation. Hence,

while the traditional viewpoint attributing variation in mepc peak amplitude to quantal size is largely correct, the data suggest that ca. 21% is due to a postsynaptic component, receptor density. This is supported by another study 6, where it was concluded that variation in receptor density could be greater than 14%. A significant negative correlation was also observed between diffusivity and the forward binding rate constant, probably indicating that for the data and model considered, these two parameters could not be completely distinguished. Another finding, in agreement with others ~1'~2, was that there are multiple determinants of 20-80% rise time (t,.); in this study t r w a s correlated with the channel opening rate constant (r = -0.66) and the equilibrium dissociation constant (r = 0.63). In summary, the present technique enables simultaneous estimation of several fundamental neurotransmission parameters. Furthermore, drug activity at the neuromuscular junction can be described succinctly and quantitatively in terms of a specified parameter set. We believe the method will be applicable, with appropriate model design, to synaptic physiology and pharmacology at other sites.

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Fig. 2. Pharmacological testing of the model with a-BTX and HC-3. Because of the considerable computation involved in the regression for each mepc, representative waveforms (n = 5-8. within _+ 1 S.D. of the mean amplitude (l~,~xl a n d 2 0 - 8 0 % rise time (q)) from larger samples (n - 100) were chosen for analysis. Traces are averages (aligned on the peak) of the mepcs selected for optimization under each condition; calibration: vertical 2 nA. horizontal 4 ms. Histograms show changes m parameters exp~'essed as percentage of control in the order Pl-P~. Error bars show standard errors of the differences: significance (t-test): *P < 0.05. **P < 0.01, ~**P < 0.001. a: effect of a-BTX (32 n M incubated 22 rain followed by 16 min washout and equilibration). For control mepcs-(n = 117) Ira,~ = 5.03 _+ 0,12 nA (mean + S.E.M.), tr = 159 _+ 11 us and the decay time constant (rD) -----1.87 _+ 0.029 ms, while for a-BTX (n = 153) Ira,~ = 2.65 + 0.044 hA. t~ = 235 _+ 13k~s and rt~ = 1.69 + 0.022 ms. Upper trace, control (n = 5); lower trace, a-BTX (n = 5). O n t y t h e third parameter, endplate receptor density, was significantly altered, b: effect of HC-3. Mepcs were recorded under control conditions, following 140 rain incubation in 10/~M HC-3 including 70 rain exposure to 20 mM K + to stimulate quantal release, and following washout of HC-3 with 300 rain incubation in 10uM choline. For control In = 98) lm, x = 4.70 + 0.08 nA. t r = 169 +_ 10 us, r D = 1.80 _+0.039 ms: for 10,uM HC-3 after high K + (n = 95) l,~x = 3.5I _+_+0 . 0 6 n A . tr = 158 + 11 us. r D = 1.12 --+ 0.026 ms; following HC-3 washout 'n = 136) lm,x = 4.46 + 0.08 nA, tr = 146 + 8/~s, rl~ = 1.85 -~ 0.032 ms. These changes are reflected in the traces on the right; upper, control (n = 6); centre, HC-3 (n = 8); lower, choline washout (n = 5). The effect on r D indicates that HC-3 has a direct postsynapuc blocking action and at least part of the reduction in 1,,,~ is due to this. The upper histogram shows the effects of HC-3 on the p a r a m e t e r set P~-P6, with a significant decrease in quantal size. It also shows an effective decrease in receptor density which is compatible with the change in r D, and an increase in the apparent diffusion coefficient of ACh in the synaptic cleft. The latter effect has not to our knowledge been reported, though ouabain-induced depletion of transmitter stores is associated with substantial changes in cleft geometry 7. The lower histogram shows that all effects of HC-3 were completely reversible with choline

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Fig. 3. Relationship between mepc amplitude (lmax) and (a) the number of molecules in a quantum (Pl), and (b) endplate receptor density (P3). Results for 20 mepcs from a single endplate under control conditions. Correlation coefficients (r) were (a) 0.85, P < 0.001 and (b) 0.51, P < 0.05. The regression of/max on Pl andp3 had a multiple correlation coefficient of 0.97 (P < 0.001 ).

S u p p o r t e d by grants f r o m the Sir C h a r l e s G a i r d n e r Hospital

Research

Anaesthetists,

Foundation,

the

Faculty

of

R o y a l A u s t r a l a s i a n C o l l e g e of Sur-

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geons, and the V e t e r a n s Affairs D e p a r t m e n t .

We

thank the W e s t e r n A u s t r a l i a n R e g i o n a l C o m p u t i n g C e n t r e for p r o v i d i n g subsidised c o m p u t i n g .

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14 15

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