Synaptic depression at a synapse inAplysia californica: Analysis in terms of a material flow model of neurotransmitter

Brain Research, 109 (1976) 41-59 © ElsevierScientificPublishingCompany,Amsterdam- Printed in The Netherlands

41

SYNAPTIC DEPRESSION AT A SYNAPSE IN APLYSIA CALIFORNICA: ANALYSIS IN TERMS OF A MATERIAL FLOW MODEL OF NEUROTRANSMITTER

PAUL B. J. WOODSON, WERNER T. SCHLAPFER, JACQUES P. TREMBLAY* AND SAMUEL H. BARONDES

Departments of Neuroscience and Psychiatry, University of California, San Diego, School of Medicine, La Jolla, Calif. 92037 and Department of Psychiatry, Veterans Administration Hospital, San Diego, Calif. 92161 (U.S.A.) (Accepted October 20th, 1975)

SUMMARY

When a pair of stimuli separated by an appropriate interval is given to the right visceropleural connective of Aplysia californica the amplitude of the second EPSP elicited in cell R15 is usually smaller than the amplitude of the first EPSP. In the present paper we show that this phenomenon, synaptic depression, can be analyzed in terms of the material flow model of neurotransmitter economics developed in our preceding publications. We specifically show how changes in the 4 model parameters: A, the available pool of transmitter; F, the fraction of the available pool released by a presynaptic action potential; M, the rate of transmitter mobilization into the available pool; and D, the rate constant of demobilization of transmitter from the available pool, all affect synaptic depression. In addition, we show how transient changes in F and M, that are observed immediately and for seconds after a stimulus, influence the time course of synaptic depression. Using this analysis we then tested our previous inferences about changes in the model parameters produced either by pharmacological manipulations or repetitive stimulation, by comparing the observed effects of these manipulations on synaptic depression with the theoretical predictions. The theoretical and experimental findings agreed, thereby strengthening both our previous conclusions of the mode of action of these manipulations and the model itself.

INTRODUCTION

In the previous paper of this series 18 we showed that it is possible to determine * Present address: Department of Anatomy,Laval University,Quebec, P.Q., Canada.

42 the values of the parameters of a material flow model of synaptic transmission at a synapse in the abdominal ganglion of Aplysia californica both at equilibrium and after repetitive stimulation. In the present investigation we sought to determine how synaptic depression is affected by changes in these model variables. This was prompted by experimental findings in previous studies7,12 and also in the succeeding two papers 11, 14, which indicated that repetitive stimulation and/or the administration of various pharmacological agents affected synaptic depression. From an analysis of effects of repetitive stimulation and pharmacological agents we have drawn some tentative inferences about changes they produce in the model variables. If a theory could be developed which related changes in each of the model variables to depression it should be possible to experimentally test our inferences about the effects of repetitive stimulation and pharmacological agents on these model variables. In the present paper we analyze the effects of changes in each of the model variables on synaptic depression. We then show that changes in the model variables with repetitive stimulation or pharmacological agents, inferred from other considerations, are associated with changes in synaptic depression like those predicted from this theoretical treatment. This analysis will prove to be of particular importance for an understanding of the effects of dopamine, serotonin and other biogenic amines on synaptic transmission to be considered in the next paper in this series 11. In previous studies6,7, evidence has been presented that synaptic depression, under the experimental conditions which we use, is due exclusively to a presynaptic mechanism. Although it is possible to change synaptic depression by postsynaptic mechanisms4, these have been avoided and excluded in all the cases under consideration. We have also argued, as have others z,5,8,9 that synaptic depression of the type seen here, is due to depletion of neurotransmitter from the readily available pool. We will continue to maintain this assumption throughout the course of the present work; and strengthen it further by showing that predictions based on this assumption are fulfilled. METHODS

The basic methods were described previously6,7,1°,12,13. Unitary and monosynaptic EPSPs were evoked in cell R15 of the abdominal ganglion of Aplysia californica by stimulation of the visceropleural connective. This identified synapse is referred to as RC1-R15. The time course of synaptic depression between isolated pairs of EPSPs was assayed by giving a pair of stimuli separated by a variable interval (0.5-30 sec). Such pairs were repeated every 4-5 min to obtain sufficient data for statistical analysis. The assay of the pattern sensitivity of synaptic depression was performed as follows: a train of stimuli, usually 100, was given at a stimulus frequency of 1/sec, and this train was followed at various intervals by a pair of test pulses, separated from each other by 1 sec. By repeating this sequence every 40 min (the wait is necessary to allow the PTP generated by a run to decay) and varying the interval between the first pulse of the post-train pair and the termination of the train, we built up a trajectory

43 for the amplitude of PTP (i.e., the size of first pulse of post-train pair) after the train. At the same time the magnitude of synaptic depression was assayed at different times after the train. Since the train frequency was 1/sec, the same frequency as used to assay synaptic depression, depression during the train was automatically assayed as the ratio of one pulse to another. The depression between the first two pulses of such a train served to assay synaptic depression between an isolated pair. RESULTS AND DISCUSSION

Changes in the EPSP amplitude after an isolated EPSP When an isolated EPSP (EPSPr) is evoked at RC1-R15, and followed at various intervals by a second EPSP (EPSPII), the amplitude of EPSPII varies with time after EPSPI. At short intervals (less than 0.5 sec) between two stimuli, the amplitude of EPSPII is elevated above that of EPSPI (short-term facilitation). At longer intervals (0.5-30 sec) the second EPSP is usually smaller than the first EPSP (synaptic depression) 7. The time course of the amplitude of EPSPIr after EPSPI is given for a typical animal in Fig. 1A. Six of the 21 animals examined differed from the typical animal shown in Fig. 1A in that they showed no synaptic depression, i.e., the amplitude of EPSPII was never less than that of EPSPI. These 6 preparations all exhibited shortterm facilitation and could be made to show synaptic depression by increasing the Ca 2+ concentration in the bathing medium. Since we are concerned at present with synaptic depression at normal divalent cation concentrations (11 mM Ca 2+ and 55 mM Mg2+), a detailed analysis of this latter type of preparation shall be reserved for a future communication. As will be considered below, preparations of this type are compatible with the analysis to be presented. We have previously argued 7 that the phase of synaptic depression at RC1-R15 is due to a transient depletion of the pool of available transmitter. The present work will lend additional support to this assumption. The flow model of transmitter economics which has been developed in the previous publications6, la assumes that, in the absence of spike evoked release of transmitter, the pool, A, behaves accordingto : dA(t)/dt = Meq - - (Deq) (A(t))

(1)

where A(t) is the size of the pool A at any time t, Meq is the 'equilibrium' or resting value of the rate of mobilization of transmitter into the available pool A, and Deq is the equilibrium value of the rate constant of demobilization of transmitter out of A. At the time EPSPI is evoked, and at long times after EPSPI, dA/dt = 0. The size of the pool A is then at its equilibrium value, Aeq, and is given by: Aeq = Meq/Deq

(2)

The size of EPSPI is EPSPI = q • Feq • Aeq

(3)

where Feq is the equilibrium value of the fractional releaseS,13, i.e., a number between 0 and 1 giving the fraction of A released by an isolated action potential and q is the

44 postsynaptic conversion factor in mY/raM6,13. The size of A immediately after EPSP1 is therefore: A(O) = Aeq - - Feq "Aeq

(4)

Integration of equation 1 with constant coefficients (Meq and Deq) from t = 0 to t = c~ describes the refilling trajectory followed by A as it returns to equilibrium after a release event has depleted it. Thus, A(t) ---- Aeq -~ [A(0) - - Aeq] • e-Deq " t

(5)

Equation 5 may be rewritten using equation 4: A(t)/Aeq -- 1 - - Feq • e-Deq • t

(6)

and rearranged to give: In {[Aeq - - A(t)]/Aeq} :

(In Feq) - - Deq" t

(7)

For the moment, let us also assume that, after EPSPI, F remains constant at its equilibrium value, Feq. The amplitude of EPSPn under this assumption is EPSPn :

q • Feq • A(t)

(8)

Combining equation 7 with equations 3 and 8 then gives in [1.0 - - (EPSPn/EPSPr)] :

(In F e q ) - - D e q " t

(9)

Therefore plots of - - l n [ l . 0 - - (EPSPn/EPSPI)] versus time should be straight lines with slope Deq and intercepts o f - - I n Feq.

Deviation from the depletion-refilling hypothesis As in the previous paper la the plots o f - - l n [ 1 . 0 - - (EPSPn/EPSPI)] versus time are straight lines (Fig. 1B) at long intervals after EPSPI (10-20 sec or longer), in confirmation of the prediction of equation 9. However, at intervals of less than 10 sec there is deviation from the straight line, as shown for a typical animal in Fig. lB. At intervals of less than about 1 sec the size of EPSPn is larger than expected according to the depletion-refilling hypothesis, and therefore shows an upward deviation from the dashed extrapolated line of Fig. lB. At intervals between 1 and 10 sec, EPSPn is smaller than predicted according to the depletion-refilling hypothesis, and therefore shows a downward deviation from the dashed extrapolated line of Fig. lB. The exact time course of the deviations varied somewhat from preparation to preparation and in some animals the straight portion of the curve was not reached until 20 sec after EPSPI. Fig. 1B was typical for 10 out of 15 animals which showed a phase of synaptic depression while 5 preparations had depression curves which had no downward deviations. These latter preparations will be considered separately below. The deviations from the straight refilling trajectory at intervals of less than 10 sec forces us to conclude that at these early times the assumptions underlying equation 9 are wrong. These assumptions were that M, D and F were constants and equal to their equilibrium values. We would now like to propose that after a stimulus

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Fig. 1. A: two successive EPSPs designated EPSPx and EPSPzI respectively, were evoked with various intervals at RC1-R15. The amplitude of EPSPIr is plotted as a function of the interval between EPSPI and EPSPH. At intervals of less than 0.5 see EPSPtz is larger than EPSPz (short-term facilitation), while at intervals greater than 0.5 see EPSPI] is smaller than EPSPt (synaptic depression). Each data point represents the average of 4 measurements in a single animal. B: the data of part A is replotted in the coordinates specified by equation 9, Le., the coordinates which linearize the parts of the depression trajectory which are characterized by a single exponential function. For time points greater than 10 see a straight line is obtained. The slope of this line is Deq, while the extrapolated intercept is In Feq.

there is a transient elevation o f F lasting about 5 sec and a transient elevation o f M lasting 10-20 sec.

Basis for the F- and M-wave hypothesis We have previously shown la that both F and M rise above their equilibrium values u p o n repetitive stimulation. Furthermore, the a m o u n t o f increase in these parameters is dependent u p o n both the frequency and n u m b e r o f stimuli in a train. Thus, at a given frequency, these parameters rise over a n u m b e r o f pulses to reach a steady state, the amplitude o f which is larger for higher frequencies6, 7,18. This m a n n e r o f rise suggests the possibility o f post-stimulus transients in F and M, which summate to produce frequency-dependent plateaus. The duration o f the proposed transients (waves) is necessarily less than 10-20 sec, since after this time the trajectory predicted for constant F and M is followed (i.e., the late points in Fig. 1B follow a straight line). Further knowledge a b o u t the

46 postulated transients may be gained from an inspection of Fig. l A. The correct expression for the amplitude of EPSPn is EPSPII ~-- q • F(t) • A(t)

(10)

where F(t) and A(t) now include the hypothesized transients in F and M, respectively. Since EPSPn is larger than EPSPI at short intervals (short-term facilitation), and since by the depletion hypothesis, A(t) is less than Aeq at these times, F(t) must be larger than Feq at short intervals. The F-transient appears to be over by 5 sec since EPSPH is no longer facilitated and reaches a minimum by this time. This F-wave provides a ready explanation for the rise in F during a train. An apparent problem with this hypothesis is that summation of a 5-sec wave cannot give rise to a long-lasting elevation of F 6 (the elevated F after a train decays with a single exponential time course over 30 min). However, the observation ~ that the rate constant of decay of F after a train is also a function of the stimulus frequency and number during a train, suggests that another wave-like summation controls the rate of decay of F. Thus, we would like to postulate that isolated F waves decay with 5 sec time constants but that after a large number of stimuli the rate of decay of F transients is slower. The manner in which the mechanism controlling the F-wave decay rate can relax after a train so as to not affect the ongoing decay of an elevated F is not clear but it may be a challenging clue as to the physical basis of F, which we cannot pursue further at present. While the postulated isolated F-wave may last only 5 sec, the M-wave may last longer (10-20 sec) since the plots of Fig. 1A do not become straight until that time. Such an M-wave is supported by the observation ~3 recalled above, that M rises upon repetitive stimulation in a fashion highly suggestive of post-stimulus transients in M. We observed 6,13 that the elevated M decayed to Meq within 30-45 sec of the end of a train. This rate of decay is compatible with the hypothesis that isolated M-waves of 10 sec duration after each stimulus summed to produce the elevated M observed at the end of a train. There is also the possibility that there is a post-stimulus transient in the value of D. Because of the observed small size of D, a frequency-dependent elevation of M, independent of the stimulus-dependent behavior of D, is required to account for the observation of frequency facilitation ~3. This necessitates the existence of an M-wave. We shall show below that F- and M-waves are adequate to account for the observed trajectory of EPSPII (Fig. IA). The effects of a possible D-wave shall be considered below, after the necessary M- and F-waves have been treated. Post-stimulus transient of the rate of transmitter mobilization. "We first treat the M-wave. In Fig. 2A a hypothetical rectangular M-wave of 10 sec duration following a stimulus at t = 0 is illustrated. The recovery of the pool A is shown in Fig. 2B. The open circles in Fig. 2B demonstrate the trajectory according to equation 5, i.e., in the absence of an M-wave. The filled circles in Fig. 2B illustrate the trajectory that would be followed if the value of M were permanently increased immediately after the occurrence of EPSPx. Inspection of equation 5 reveals that the effect of a change in M is not to change the rate constant Deq, but rather to change the value of Aeq (A2)

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Fig. 2. Effect of a hypothetical post-stimulus transient in the rate of transmitter mobilization (M) on the refilling of the pool of available transmitter, A (t). A: open circles, constant rate of transmitter mobilization, M(t), = Meq = Mz; filled circles, hypothetical post-stimulus increase in the rate of mobilization to M(t) = Ms; heavy solid line, normalized hypothetical rectangular post-stimulus wave of transmitter mobilization (M-wave) lasting 10 see after a stimulus. B: normalized theoretical refilling trajectories after depletion of pool A by a stimulus. Trajectories were generated using the average model parameters determined in the previous publication la. Open circles, refilling toward Az; filled circles, refilling toward A~; heavy solid line, refilling toward A~ for the first 10 sec and then toward A~. C: theoretical refilling trajectories in the coordinates of equation 7. All trajectories have the same slope, Deq. Open circles, refilling toward An = A1; filled circles, refilling toward An = A2; heavy solid line, refilling toward Az for the first 10 sec and then toward A~. Note that while all trajectories have the same slope, the intercept is different for every case.

which the pool is attempting to approach exponentially. The heavy solid line in Fig. 2B shows the effect of the M-transient illustrated by the heavy solid line in Fig. 2A. In this case M is elevated for 10 sec then returns abruptly to normal. The trajectory of the filled circles in Fig. 2B is followed for the first 10 sec in the presence of the transiently elevated M, and thereafter recovery is towards the normal meq (A1) with the same rate constant. The result of the M-wave has therefore been to produce a period of faster refilling with respect to thefinally realized goal. The fine dashed line in Fig. 2B is the extrapolation of the late part of the solid line, which corresponds to the equilibrium refilling after termination of the M-wave. It is this late part which leads to the straight line of Fig. 1B and hence the part which we extrapolated in our previous work 13 to obtain the values of A(0) and hence Feq. It is obvious that the M-wave can only lead to overestimation of A(0) and hence to an underestimation of Feq. This conclusion will be dealt with further below. In Fig. 2C we have replotted the data of Fig. 2B according to equation 7, an operation which linearizes the refilling trajectory. Fig. 2C illustrates that Deq (slope of the lines of Fig. 2C), the rate constant of return of A to its equilibrium value, is the same for all trajectories shown in Fig. 2B. The accelerated refilling during the M-wave is really refilling the pool A with the same rate constant but toward a higher target. Post-stimulus transient of fractional release. In Fig. 3A we plot a hypothetical F-wave, and in Fig. 3B we show the effect that such a wave has upon the trajectory of

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Fig. 3. Effect of the addition of a post-stimulus transient in the fraction of transmitter release (Fwave) to the theoretical refilling trajectory. A: hypothetical F-wave following EPSPI. B: theoretical depression trajectory of the amplitude of EPSPH at various intervals after EPSP~. Open circles, theoretical trajectory in the absence of an M-wave. This curve was obtained by assuming the refilling trajectory of Fig. 2B (open circles) and multiplying by F(t) (equation I0). Solid line, theoretical depression trajectory in the presence of the hypothetical M-wave of Fig. 2A. C: curve of part B replotted in the coordinates of equation 9, Note the similarity of the theoretical trajectory (heavy solid line) to the experimental data (Fig. 1B). The upward deviation from the extrapolated late part of the heavy solid line is due to the F-wave (short-term facilitation). The downward deviation between 2 and 10 sec is due to the M-wave. The presence of an M-wave decreases synaptic depression and changes the extrapolated intercept. This leads to an underestimate of the value of Feq.

EPSPr~. The open circles of Fig. 3B illustrate the effect of an F-wave like that in Fig. 2A, when it is multiplied (equation 10) by the refilling trajectory of Fig. 2B, in which there is no M-wave (open circles, Fig. 2B). The solid line of Fig. 3B illustrates the case which includes both F- and M-waves during the refilling of the pool. Note the similarity between this theoretical plot and the data of the typical preparation (Fig. 1B). The fine lines in Fig. 3B show the various extrapolations possible to estimate the value of A(0) relative to Aeq. In practice it is not possible to extrapolate the segment of the solid line between 5 and 10 see since the true shape of the M-wave is unknown. The only realistic extrapolation is the latter part of the solid line, which leads to an overestimate of A(0). In Fig. 3C the data of Fig. 3B is replotted in the coordinates of Fig. 1B (equation 9). This is the plot normally used to obtain the resting values of the model parameters 1~. From equation 9 the intercept of this plot is --ln Feq, and it is clear that we underestimate Feq in the presence of an M-Wave. The F-wave on the other hand, has no effect on the intercept. The shapes of the hypothetical post-stimulus transients. At this point it is appropriate to discuss the choice of shapes of the F- and M-waves and the effect that these decisions have on the above conclusions. A rectangular M-wave (Fig, 2A) is mathematically convenient but of course is biologically unrealistic. To investigate the effect of the shape of the M-wave we have tried two other idealized wave shapes. (1) A triangular wave of equal area to the rectangular wave of Fig. 2A, with a

49 value of 1.2 × Meq at t = 0, decreasing linearly with time to a value of Meqat t/> 10 sec. Such a wave decreased the area of the downward deviation in Fig. 3B. (2) A triangular wave of increasing M, from Meq at t = 0 to 1.2 × Meq at t ---- 10 sec, with M = Meq for t /> 10 see. This wave increased the area of the downward deviation in Fig. 3B compared to the rectangular wave of equal area. Thus, the amplitude of the downward deviation at 5-10 sec intervals depends mostly on the magnitude of the integral of the M-wave over the time after the termination of the F-wave. In addition to these conclusions about the shape of the M-wave, it is possible to estimate the maximum amplitude of a rectangular M-wave of 10 sec duration which is compatible with the observation of synaptic depression. With the average values of the model parameters according to the previous publication la, we found that such a wave cannot be larger than 1.2 times the value of Meq, if depression is required at a 5-sec interval. Larger M-waves result in the obliteration of synaptic depression. Based on the observation of the time course of short-term facilitation (Fig. 1A) we infer that the F-wave has a shape similar to that illustrated in Fig. 3A. Increasing the amplitude and/or duration of the F-wave can obscure the deviance produced by the M-wave. In an extreme case, an F-wave of large amplitude and/or long duration could even obliterate synaptic depression, as is indicated by equation 10. These conceivable variations in the shape of the F- and M-waves give a variety of predicted trajectories of EPSPII which are actually observable in different preparations. (1) Preparations with EPSPn trajectories exhibiting downward deviation. Ten of the 21 preparations where the time course of synaptic depression was studied systematically had a behavior similar to that shown in Fig. 1B. This suggests that they had Fand M-waves similar to those used to construct the solid line of Fig. 3B. (2) Preparations with EPSPH trajectories without downward deviation. Five of the 21 preparations studied had synaptic depression but their EPSPn trajectory did not deviate below the extrapolated straight line analogous to that of Fig. I B. Their EPSPr~ trajectories were similar to that illustrated by the open circles in Fig. 3B and C. Like these theoretical trajectories (open circles in Fig. 3B and C) these preparations may have had little or no M-wave. Alternatively, the F-waves could have outlasted the M-waves and thereby obscured the deviation-producing effect of the M-waves as discussed above. (3) Preparations exhibiting no synaptic depression. Six of the 21 preparations had no synaptic depression. As is evident from the above considerations, this situation can arise in a number of different ways. However, these 6 animals had smaller than average EPSPIs. This observation, taken with the correlations among the model parameters described earlier la, indicate the value of Feq in these preparations is below average, while their capability to increase F and M during repetitive stimulation is greater than normal. These latter observations suggest that the F- and M-waves are both larger in such animals, therefore obscuring synaptic depression. Possible post-stimulus transients in D. While transients in the values of F and M are adequate to explain the time course of EPSPn, it is possible that the parameter D also undergoes a post-stimulus transient. However, a transient elevation of D after a

50 stimulus was found to result in an upward deviation from the extrapolated refilling trajectory (dashed line Fig. 1B). This was found by substituting equation 2 into equation 5 and plotting A(t) versus t with an elevated value of Deq for the first 10 sec, then returning to a value of Deq for the remaining time course. Therefore, a post-stimulus transient of D above Deq would require the existence of an even larger M-wave to explain the observed downward deviation from the refilling trajectory. On the other hand, a transient decrease in D after a stimulus could by itself give the observed refilling trajectory. Such a negative D-wave would therefore contribute to the downward deviation produced by the M-wave. Since F- and M-waves are adequate to explain the trajectory of EPSPII and since an M-wave is necessary to explain our observations concerning frequency facilitation lz there is no need to postulate a D-wave. This is certainly not excluded; but will not be considered further because such a consideration is not parsimonious.

Comparison of this proposal to others There are some important conclusions which may be drawn from this analysis at this point. The theoretical analysis of the depression trajectory (Fig. 3B) provides a simple explanation for the observed deviation of the depression trajectory from an exponential return to the size of the control EPSP. To explain similar observations in vertebrate neuromuscular junctions, other authors 2,3 have postulated that synaptic depression cannot be due solely to transmitter depletion and have suggested a phase of depressed F following the elevated F at short intervals. However, we have shown above that in the presence of an M-wave such a phase of depression of F below its equilibrium value need not be postulated to account for the observed deviation from an exponential trajectory (Fig. 3B). Furthermore, arguments against the transmitter depletion hypothesis of synaptic depression, based upon variation of the Ca 2+ concentration 3, wrongly assume that Ca 2+ does not affect the statistical parameter n, the analog of A. We, as others 1, have found that Ca 2 ~ affects A, such that elevation of external Ca '~ raises A (to be published). Another argument against the depletion hypothesis of synaptic depression is based upon the deviation of the magnitude of end-plate potential size upon repetitive stimulation from the size expected solely by assuming depletion of n (see ref. 3). We and others1,13 have shown that repetitive stimulation not only depletes A (and by analogy n), but that it also elevates both F and M. The rates of stimulation may be quite low to still effect a rise in these parameters 6,7. Thus, i f p and n are changing, one would expect incorrect values of F and/or p to emerge. A very important conclusion of the present work is that care must always be taken to account for stimulus pattern sensitivity of the rate of supply and the efficiency of release. This analysis of synaptic depression provides a framework which allows the interpretation of changes in the synaptic depression upon pharmacological and physiological manipulations. With the proposed model of transmitter economics 13 we shall be able to show below that the plastic phenomena at RC1-R15, and their modification by pharmacological agents, may be integrated into a single paradigm.

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Fig. 4. Theoretical trajectories (dashed lines) in depression-release space (EPSPI/EPSPlz versus EPSPI). In A, B and D agreement between experimental data and theoretical predictions are also illustrated. The average model parameter values are: Feq = 0.209, q A e q = 5 3 . 8 m V , q M e q = 3.45 mV/sec, Deq = 0.65 sec -z (see ref. 13). The interval between EPSPx and EPSPI; is 1 sec. A: qMeq is varied from 1.0 to 5.0 mV/sec to generate the dashed line with all other parameters at their average values. The M-wave was kept a constant proportion of the value of Meq. Points are for 3 different animals at various times after administration of morphine (5 × 10 -5 M) (see ref. 10). B: Feq is varied from 0.15 to 0.45 with the other parameters constant at their average values. The amplitude of the F-wave was kept a constant proportion of the value of Feq. Data points are for 3 animals at different times during the decay of PTP produced by 300 pulses at 1/sec6. Two typical preparations and the most aberrant preparation are shown. C: Deq is varied from 0.03 to 0.13 sec -z with all other parameters at their average values. D: the amplitude of the F-wave is varied with all other parameters at their average values. Data is from 4 animals before (solid points) and after (open points) administration of trimethidinium at 10 -4 M (see ref. 12).

Effect of changes in the model parameters on synaptic depression T h e effects o f variations in the m o d e l p a r a m e t e r s on the m a g n i t u d e o f synaptic depression m a y be conveniently illustrated by plots o f the m a g n i t u d e o f synaptic depression versus the a m o u n t o f t r a n s m i t t e r which was released to p r o d u c e the depression. A m e a s u r e o f the m a g n i t u d e o f synaptic depression is the r a t i o EPSPz/EPSPzI at a fixed interval (always 1 sec in the following discussion). A m e a s u r e o f the a m o u n t o f t r a n s m i t t e r released is the a m p l i t u d e o f EPSPI. Thus we shall analyze the effects o f changes in the m o d e l p a r a m e t e r s on synaptic depression in ' d e p r e s s i o n - r e l e a s e ' space, the c o o r d i n a t e s o f which are E P S P z / E P S P I I a n d EPSPz. The theoretical curves in d e p r e s s i o n - r e l e a s e space for variations in the m o d e l p a r a m e t e r s were o b t a i n e d b y the following general m e t h o d : (1) F a m i l i e s o f curves in the c o o r d i n a t e s o f Fig. 3B were generated by v a r y i n g one m o d e l p a r a m e t e r at a time while keeping all others c o n s t a n t at the average value f o u n d in o u r p r i o r w o r k 13. The M - a n d F - w a v e s illustrated in Figs. 2 A a n d 3 A were used in all cases where the wave p a r a m e t e r s were k e p t constant. (It s h o u l d be n o t e d t h a t c o n s t a n t wave p a r a m e t e r s m e a n s a c o n s t a n t f a c t o r b y which the e q u i l i b r i u m value o f the p a r a m e t e r in question changes. The a r e a u n d e r the F - a n d / o r M - w a v e thus v a r i e d when Feq o r Meq were changed. The effect o f u n c o u p l i n g the a b s o l u t e m a g n i tude o f the wave f r o m its e q u i l i b r i u m value will be discussed when a p p r o p r i a t e . ) (2) H a v i n g o b t a i n e d a family o f curves in the space o f Fig. 3B b y v a r i a t i o n o f a

52 single model parameter, we then measured the various values of EPSPI and EPSPI corresponding to the one second point on each curve. The pairs of EPSPI and EPSPrI so obtained, each pair coming from a curve obtained with a certain value of the variable model parameter, were then plotted as points in depression-release space. i.e., Fig. 4. Variations of Meq. The dashed line in Fig. 4A represents the effect of varying Meq, with a proportional change in the M-wave, i.e., the amplitude of the rectangular M-wave of Fig. 2A was always 1.1 times the particular value of Meq. It is evident from equations 2 and 3 that variation of Meq produces a strictly proportional change in EPSPI. However, the amplitude of EPSPI/EPSPI~ is unaffected as shown in Fig. 4A. F r o m equations 3 and l0 we have: EPSPI/EPSPII = Feq " Aeq/F(t) • A(t)

(11)

A change in Meq will not change the ratio Feq/F(t). The ratio Aeq/A(t) is similarly invariant upon changing Meq provided that the M-wave remains a constant proportion of Meq. This can be demonstrated as follows: Let Al(t) = (a" Meq/Deq) + [ ( M e q / O e q ) - (Feq" Meq/Deq) - - (a • Meq/Deq)]e-Deq • t

(12)

where A1 (t) is the size of A at any time t after EPSP1, when the equilibrium size of A is given by M eq/Deq, a is the factor corresponding to 1.1 for the M-wave, which produces a temporary change in the target value of A(t) as illustrated in Fig. 2A and B, and [(Meq/Oeq) - - (Feq " Meq/Oeq)] is A(0). I f Aeq is changed by a factor b then we have for this case A2(t) ~ (a • b • Meq/Deq) -~- [(b • Meq/Deq) - - (b • Feq " Meq/Deq) - - - (a" b • Meq/Deq)]e-Oeq " t

(13)

where Az(t) is the size of A at any time t after EPSP~, for another value of Aeq, namely b • Meq/Deq. Therefore, Al(t)/Aeq = a + (1 - - Feq - - a)e-Deq • t

(14)

A2(t)/(b • Aeq) -- a + (l - - Feq - - a)e-Deq • t

(15)

and

and consequently Al(t)/Aeq -~ A2(t)/(b • Aeq)

(16)

Hence A(t)/Aeq is invariant upon changes in Meq, provided that the M-wave remains a constant fraction of Meq. We therefore conclude that EPSPI/EPSPr~ is invariant upon changes in Meq with proportional changes in the M-wave. If the M-wave has a constant integral rather than a constant proportional size (i.e., a in equation 15 is less than a in equation 14) then the synaptic depression was found to become larger when M eq was increased. Fig. 4A also contains the data from 3 animals in which 5 × 10-4 M morphine

53 was administered in the perfusate. We found previously1° that chronically applied morphine progressively reduces the amplitude of EPSPz without changing the synaptic depression. This action was established to be presynaptic, and we proposed that morphine acted to inhibit all forms of transmitter mobilization, both resting and stimulus-dependent, hence lowering Meq and the M-wave. The agreement of that hypothesis, based on much less formal arguments, and the predicted behavior for such an action in depression-release space, strengthens both the conjecture as to the mode of action of morphine at this synapse and the model being used. Variations of Feq. Fig. 4B illustrates (dashed line) the effect of varying Feq and allowing the F-wave to change by a constant proportion, in this case by the same factor as that shown in Fig. 3A. Variation of Feq produces a linear change in EPSP~, as can be seen from equation 3. On the other hand, raising Feq was found to raise EPSPz more than it raised EPSPII, so that synaptic depression increased upon elevation of Feq. Arguments similar to those represented by equations 11-16 demonstrate that if EPSPz is changed by changing Feq by a factor a, then EPSPI/EPS PH changes by a factor of (1.0 - - Feq

" e-Deq

•

t)/(1.0 - - a • Feq

• e-Deq

• t)

(17)

which gives the non-linear relationship demonstrated in Fig. 4B. Uncoupling the magnitude of the F-wave from the size of Feq, that is allowing the F-wave to have a constant absolute size rather than a constant size relative to Feq, produces even more synaptic depression at larger Feqs, i.e., a steeper curve. Fig. 4B also contains data points for synaptic depression determined by giving pairs of pulses at 1/see at a number of times during PTP in 3 animals. We have previously shown 6 that PTP is exclusively due to an elevation and slow decay of F. Since the F decays very slowly (over 30 min), the behavior of synaptic depression during the PTP period should be described well by a variation of Feq, i.e., F will not change significantly over the 1-see period used to assay synaptic depression during the PTP period. We show in Fig. 4B data obtained for the amplitude of synaptic depression at various times during the decay of PTP. The observed agreement between the theoretical curve and the experimental points is further evidence for the hypothesis that PTP is due to an elevated and decaying F alone, as well as for the depletion hypothesis of synaptic depression. Variation of Deq. Fig. 4C depicts the effects of changing Deq. From equations 2 and 3 it is evident that a change in Deq by a factor a will produce a linear change in EPSPr by a factor of 1/a. Again, by using similar arguments as used in equations 11-16 it can be shown that when Deq is changed by a factor of a, EPSPI/EPSP~ changes by a factor of (1.0 - - Feq e-Deq : t)/(1.0 - - Feq e-a- Deq" t)

(18)

This results in the relationship depicted by the dashed line in Fig. 4C. It is important to note that the dependence of EPSPI/EPSPzI on the size of Deq is very slight; this is because Deq was found to have an average value of only 0.064 see-I (see ref. 13), which when varied by even a factor of 10 and then raised to the negative power of e, results in a small number. Therefore, we note that Deq affects EPSPz very much but

54 depression very little. As of yet we have found no pharmacological agent or stimulus schedule which appears to act on Den only. Simultaneous variation of Meq and Deq Changing both Meq and Deq by the same factor, so as to leave Aeq untouched, has no effect upon EPSPI. It is further easy to show that the effect of this manipulation on EPSPI/EPSPII is exactly the same as that seen above in the case of Deq variation, i.e., EPSPI/EPSPII changes by the same factor as equation 18. Again, because of the small size of Deq, the change in EPSPI/EPSPII is very small; e.g., lowering both Deq and Meq by a factor of 100 produces only a 2 ~ larger depression at a 1-sec interval. Further lowering Deq produces very little change in synaptic depression since e-Deq •t approaches 1.0. We have found no agent or stimulus schedule which leaves EPSPr untouched while systematically producing a small change in synaptic depression, and a large change in the slope of the straight line segments of Fig. 1B. Variation in the M-wave. We turn now to changes in the postulated poststimulus transients without changes in the corresponding equilibrium values. First we treat the M-wave. Fig. 3B illustrates the effect of an M-wave on synaptic depression. Note that at an interval of 1 see the decrease in synaptic depression due to the M-wave is very slight; at later time points the difference in depression is greater. We found that a change in the M-wave over larger limits produces very little changes in synaptic depression at a 1-sec interval. Of course a change in the M-wave has no effect upon the amplitude of EPSPt. Thus, a plot in depression-release space for this possibility would be short vertical lines. Variation in F-wave. In Fig. 4D we illustrate (dashed line) the effect of changing the amplitude of the F-wave. Inspection of Fig. 3A and B shows that this operation should produce a very large change in synaptic depression at a l-sec interval. Of course EPSPI remains unaffected. A large increase in the synaptic depression without much change in EPSPI can be produced by the addition of trimethidiniumlk Data from 4 preparations treated with 10-4 M trimethidinium is shown in Fig. 4C. Because of effects of trimethidinium upon frequency facilitation we have previously proposed 12 that trimethidinium decreases the M-wave. The present analysis indicates that the decrease in the M-wave is not of sufficient magnitude to explain the change in synaptic depression observed with this agent. Therefore it seems that trimethidinium should also affect the F-wave. We are currently analyzing the actions of trimethidinium in terms of the model parameters developed in the previous paperlL At the present we point out that the action oftrimethidinium is certainly not upon Aeq or Feq, nor can it be explained by an action on the F-wave alone, although it appears that trimethidinium must affect the F-wave in order to have the observed effect upon synaptic depression. From the relationship between the predictions and the experimental data, it should be clear that this method of analysis is useful. In particular, it should be pointed out that the relationship between the magnitude of EPSPI and synaptic depression varies as a function of specific manipulations. The nature of this relationship permits inferences about the underlying mechanism of action of the specific manipula-

55

i lOmv i I0 sec.

30 sec.

6min.

Fig. 5. EPSPs recorded intracellularly in R15 (hyperpolarized to --100 mV) during and after a train of 100 stimuli at 1/sec. Single pairs of EPSPs, 1 sec apart, were given 5 sec, 30 sec and 6 min after trains similar to the one shown to assay the magnitude of synaptie depression during the PTP period. The magnitudes of both the first EPSP of each test pair and the synaptic depression (ratio of the first EPSP of each test pair to the second EPSP of the pair) first increase after the train and then decay slowly. Note that the magnitudes of the first EPSPs of the test pairs given at 5 sec and 6 rain are the same, but the synaptic depression is greater at 6 min than at 5 sec.

tion. This type of analysis will therefore prove useful in determining the mechanism of action of dopamine, serotonin and heterosynaptic inhibition at this synapse, to be discussed in the succeeding papers in this series 11,14. In the next section of this paper we will show that the model can also be used to predict changes in depression by repetitive stimulation.

Changes in synaptic depression during and after repetitive stimulation We have previously presented evidence that a number of changes in the parameters that control transmitter release occur at RC 1-R 15 with repetitive stimulation6, 7, 13. Based on our theoretical treatment we would therefore predict that there are changes in synaptic depression during the course of repetitive stimulation at this synapse. The successful prediction of the detailed changes in synaptic depression during the PTP period, to be reported below, constitutes an example of the predictive utility of the transmitter economics approach to synaptic pattern sensitivity. To study this we determined EPSPI/EPSPII at a number of times during and after a train of stimuli at 1/sec. By comparing the amplitude of any pulse during this train with a succeeding pulse an index of synaptic depression at any point in the train is obtained. By testing with pairs of pulses separated by a 1-sec interval at one of a number of times after the train synaptic depression at various times after the train can also be determined. An example of an experiment of this type is shown in Fig. 5. It should be noted that early in the train we observe conventional synaptic depression in that the second EPSP in the train was smaller than the first. During the period of the facilitated plateau, EPSPI/ EPSPII was approximately 1. When pairs of pulses were given at one of a number of times after the train clear synaptic depression was again observed in that the second of the pair was smaller than the first. The data from these experiments can be plotted in depression-release space, i.e., using EPSPI/EPSPII and EPSPI as coordinates. Such plots for 3 different animals are shown in Fig. 6. Fig. 6B is the typical relationship found with most animals. Variations are shown in Fig. 6A and C. The figures show a decrease in EPSPI/EPSPza early in the train and a subsequent rise in EPSPI/EPSPn to approximately 1.0 later in the train. With continued stimulation the relationship EPSPI/EPSPII versus E P S P j

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Fig. 6. EPSPI/EPSPzz plotted as a function of EPSPz during (dashed lines) and after (solid lines) repetitive stimulation of RC1-R15. A plot of this type is referred to as a plot in depression-release space. The experiment is exactly the same as in Fig. 5. The numbers on the dashed portions designate the EPSPs of the train used as EPSPz and EPSPzz to generate the point in question, e . g . , the third and fourth EPSPs of a train at 1/see give one point in depression-release space. The times indicated on the solid line give the time at which a test pair of EPSPs I sec apart, was evoked a f t e r the train of t00 pulses at 1/sec. All curves were built up by giving single pairs of test pulses at the indicated times after repeated trains. The data shown is for 3 different animals. In C standard errors of each point are indicated. Note that the minimum and maximum synaptic depression are reached after the minimum and maximum EPSPt. At the frequency facilitated plateau there is no synaptic depression, i.e., every EPSP is of the same size.

57 becomes constant for each preparation. This is usually approximated after about 100 pulses. Slight changes (data not plotted) are observed if stimulation is continued for 300 pulses and there are essentially no further changes with continued stimulation. This is as would be expected from previous findings that the facilitated plateau is approximated with 100 stimuli at 1/sec and shows no detectable change after about 300 stimuli at 1/see6. This indicates that with continued stimulation a new stable state is arrived at where each EPSP is identical in amplitude with the one that precedes and succeeds it. However, with cessation of stimulation there is a striking transient increase in depression which gradually returns to the resting value by a new trajectory. After a number of minutes (between 20 and 40 min in Fig. 6) the initial equilibrium value (i.e., the value before the train of stimulation) is reached. Although the precise shapes of the curves vary from animal to animal, their general form is like that demonstrated with the 3 examples. A closed loop is always found with the pathway returning to the 0 frequency equilibrium being different than the pathway describing the movement away from the 0 frequency equilibrium. It should be noted that during repetitive stimulation, the smallest value of depression usually lags behind the smallest value of EPSPI. During the PTP period, the largest depression value lags behind the largest value of EPSPI (Fig. 6). The significance of the lags will be considered below.

Analysis of the changes in synaptic depression during and after repetitive stimulation The changes in depression during the early part of a train are a direct consequence of the sequence of changes in the EPSP size during the initial period of stimulation. Depression falls during the first part of the train (Fig. 6) because the net rate of transmitter mobilization gradually increases and hence, increasingly counteracts transmitter depletion caused by any one pulse. After a lag, depression rises to 1.0 as a new steady state (frequency facilitation) is achieved in which net mobilization balances release. During the lag period there is a transition to this new steady state where the rate of increase in net mobilization is decreasing. The cessation of a train of pulses produces PTP at RC1-R156. The early rising phase of PTP has been attributed to a refilling of A to its equilibrium value6. Thus, the size of EPSPI will grow after the cessation of the train. However, the rapid decay of net mobilization after the train leads to a rapid increase in synaptic depression (Fig. 6). As net mobilization decreases after the train the amount put into A over a 1-sec interval (the interval used to test EPSPI/EPSPII) becomes less and less so that depression increases. The late PTP period (after the peak) is characterized by an elevated and falling F with A and M being back to their equilibrium valueslL Since F is falling very slowly (over 30 min) we may treat the F at any moment as if it were in a steady state like Feq. The effect of change in Feq on EPSPI/EPSPII is shown in Fig. 4B. This is the same sort of behavior seen in the falling arms of the plots in Fig. 6 for the period after the peak of the PTP. Thus, the behavior of synaptic depression during the PTP period is consistent with our inference that the decline in PTP after the peak is due to a decay of an elevated F, with A and M now being constant and back to resting equilibrium values.

58 We have already discussed the lag in synaptic depression seen early in a train (Fig. 6). There is also a lag after the train (Fig. 6) as a new steady state in M and A are reached. The maximum EPSPI occurs when the product F . A is maximum. We believe, however, that the maximum depression is observed when M and A have reached their resting values such that (M - - DA) is 0. Therefore A and M have reached their resting values after the maximum EPSP~ is achieved. Thus the lag suggests that F is at its maximum before M and A have reached their resting steady state.

The possible role of synaptic depression It is evident that the phenomenon of synaptic depression serves to limit the effects of short bursts of EPSPs in the integration produced by RI 5. Furthermore, the system scales the degree of limitation to the amplitude of EPSPI (EPSPI/EPSPH increases with increasing EPSPI). In addition, the system has been shown to possess a method for overruling the limitation subsystem, namely, frequency facilitation; thus, if a burst is prolonged it grows again to be restored to a greater weight in the postsynaptic integration in RI 5. In addition to this homosynaptic overrule system, it will be shown in a subsequent paper of this series 14 that heterosynaptic stimulation can also block the action of the depressing mechanism. As has been seen in many neuronal control systems, the presynaptic limiting system at RC1-R15 is only one way of accomplishing the same end. Daut 4 has described a postsynaptic system which, at normal membrane potential, acts to limit the size of closely spaced large EPSPs. Again, this latter system attenuates successive EPSPs in proportion to the size of EPSPI and is overriden upon repetitive stimulation ~, The occurrence of redundant limiting systems, and the provision of both pre- and postsynaptic overrides make it seem that it is very 'important' to R I5 to be able to 'ignore' short bursts of large EPSPs at RC1-R15; but to override this damping influence with sustained stimulation. ACKNOWLEDGEMENTS

This work was sponsored by the Veterans Administration Hospital, San Diego, under M.R.I.S. Nos. 7734(01) and 0818(01) and by a grant from the U.S.P.H.S., N.I.M.H. 18282. P.B.J.W. was supported by a U.S.P.H.S. Predoctoral Traineeship in Neurosciences, U.S.P.H.S. 5-T01-NS-05628-05 and by the Scottish Rite Benevolent Foundation and J.P.T. by the Canadian Medical Research Council. We are grateful to Sea World, San Diego, foc providing excellent storage facilities for the experimental animals.

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59 3 CrmIST~NSEN,B. N., AND MAR~N, A. R., Estimates of probability of transmitter release at the mammalian neuromuscular junction, J. Physiol. (Lond.), 210 (1970) 933-945. 4 DAUT, J., Modulation of the excitatory synaptic response by fast transient K + current in snail neurones, Nature New Biol., 246 (1973) 193-196. 50TSUKA, M., ENDO, M., AND NONOMURA,Y., Presynaptic nature of neuromuscular depression, Jap. J. Physiol., 12 (1962) 573-584. 6 SCHLAPFER,W. T., TREMBLAY,J. P., WOODSON,P. B. J., AND BARONDES,S. H., Frequency facilitation and post-tetanic potentiation of a unitary synaptic potential in Aplysia californica are limited by different processes, Brain Research, 109 (1976) 1-20. 7 SCHLAP~R, W. T., WOODSON, P. B. J., TREMBLAY,J. P., ANO BAROND~, S. H., Depression and frequency facilitation at a synapse in Aplysia californica: evidence for regulation by availability of transmitter, Brain Research, 76 (1974) 267-280. 8 TAr~UCHI, A., The long-lasting depression in neuromuscular transmission of frog, Jap. J. Physiol., 8 (1958) 102-113. 9 TmF.s, R. E., Neuromuscular depression and the apparent depletion of transmitter in mammalian muscle, J. NeurophysioL, 28 (1965) 427-442. 10 TREMBLAY,J. P., SCHLAPFER,W. T., WOODSON,P. B. J., AND BARONDES,S. H., Morphine and related compounds: evidence that they decrease available neurotransmitter in Aplysia californica, Brain Research, 81 (1974) 107-118. 11 TREMBLAY,J. P., WOODSON,P. B. J., SCHLAPFER,W. T., AND BARONDES,S. H., Dopamine, serotonin and related compounds: presynaptic effects on synaptic depression, frequency facilitation and post-tetanic potentiation at a synapse in Aplysia californica, Brain Research, 109 (1976) 61-81. 12 WOODSON,P. B. J., SCHLAPFER,W. T., TREMBLAY,J. P., AND BARONDES,S. H., Cholinergic agents affect two receptors that modulate transmitter release at a central synapse in Aplysia californica, Brain Research, 88 (1975) 455-474. 13 WOODSON,P. B. J., SCHLAPFER,W. T., TREMBLAY,J. P., AND BARONDES,S. H., Resting and stimulated values of model parameters governing transmitter release at a synapse in Aplysia californica, Brain Research, 109 (1976) 21-40. 14 WOODSON,P. B. J., TREMBLAY,J. P., SCHLAPFER,W. T., AND BARONDES,S. H., Heterosynaptic inhibition modifies the presynaptic plasticities of the transmission process at a synapse in Aplysia ealifornica, Brain Research, 109 (1976) 83-95.