- Email: [email protected]
Quantal analysis and synaptic efficacy in the CNS
perspectives
Quantalanalysisandsynapticefficacyin the CNS Henri Korn and Donald S. Faber of release of each quantum. The amplitude distributions of evoked responses, which had distinct peaks, then matched Poisson predictions. However, as this statistic involves only one term, i.e. the mean quantal content, the two critical parameters, n and p, remain hidden in this formulation (see Box 1 for definitions and different models with their restraints). The initial proposal was that since n is supposed to be large in the Poisson theorem and nerve terminals contain numerous synaptic vesicles, these vesicles therefore represent 'the population of units capable of responding to a nerve impulse', p being their average probability of responding 2. Subsequent studies suggested that under more Until recently, attempts to gain insight into the physiological conditions (see references contained in Ref. 3) n is actually small, and p is large, so that question of the mechanism by which neurotransmitters are released and detected in the CNS have been binomial statistics (simple and compound) are more confronted by a number of technical difficulties appropriate for the description of fluctuating postspecific to central neurons and networks. However, synaptic potentials. This forced a revision of ideas the advent of patch-clamp techniques that consider- about what might be the correlates of n, although ably improve the signal-to-noise ratio has resulted in direct information about its physical meaning was a renewed interest in how synapses work at the still unavailable. At the same time, EM studies microscopic level. The expectation is that it may be showed that a synaptic vesicle fuses with the possible to resolve elementary problems such as: is presynaptic terminal membrane, and undergoes release quantal in a given system, and according to exocytosis (rupture and release of ACh) at a what model does it occur? A focus on quantal specialized site called an 'active zone '4'5. analysis has also been prompted by the fact that it It is interesting that a morphological definition of is an irreplaceable tool for identifying the pre- or n was finally reached by studies of synaptic transpostsynaptic locus of changes in synaptic efficacy, mission in central neurons rather than at the NMJ, the most dramatic being long-term potentiation with simultaneous recordings from pairs of ident(LTP). ified pre- and postsynaptic cells, followed by stainThese two questions are interconnected, because ing and reconstruction of the investigated neurons. the uncertainties associated with quantal analysis in At inhibitory synapses on the Mauthner (M) cell, the CNS can lead to contradictory conclusions about the simple binomial model provides a statistically the transmission process and, hence, the mechan- significant description of the quantal release of the isms underlying the nature of plasticity. This issue is transmitter glycine, and it was found that the als,o complicated by the fact that the quantal theory number of active zones established on this neuron itself has evolved from observations of single by the afferent cell equals binomial n computed central connections using classical methods of re- from statistical analysis of inhibitory postsynaptic cording, complemented by light and electron potential (IPSP) amplitudes 3'°. This striking identity microscopy (EM). A background to this evolution is implies that each releasing unit, which at these necessary because it emphasizes the pitfalls and terminals 7 exhibits the typical structure of active misinterpretations that can still be encountered, zones in the CNS 8, functions in an independent, allparticularly when addressing statistical results in the or-none manner. absence of structural guidelines - which have beBecause the size of the derived quantum was come the touchstone for assessing the validity of relatively small, resulting from the opening of about such results. 1000 postsynaptic CI channels, the more parsimonious explanation was that one quantum correThe quantal releasehypothesistoday sponds to the amount of transmitter released by a The quantal notion is derived from the neuromus- given active zone. Thus, the 'one vesicle hypothesis' cular junction (NMJ) 1, where (1) spontaneously was coined, which states that one vesicle, rather occurring miniature synaptic potentials, or quanta, than many, is released in a binary manner after an were first discovered, and (2) evoked end-plate impulse, with a probability p. This view is now potentials correspond to integral multiples of the generally accepted for most synaptic connections, quantal unit. These observations were made poss- including the NMJ, despite the general lack of ible by reducing extracellular Ca2+ in order to further evidence. It has received indirect support decrease the average number of quanta released by from studies of excitatory inputs onto cat dorsal an action potential, i.e. by lowering the probability spinocerebellar neurons 9, and from investigations
Quanta/analysls of synapti~:transmission at connections between neuronstn the CNS has provided mslghtsconcerningthe structural constraintson transmitter releaseand postsynaptic responsiveness. However, it hasproven difhcultin manycasesto resolvethe sizeand variabihty of a single quantum or to distinguish clear peaks in amphtude histograms of evoked responses,due m part to the superp0sitionof background tnstrumentaland biological notse. These /imitations raise questions about recent attempts to use direct or indirect methods of quanta/analysism orderto distinEuish between pre- andpostsynaptic/oct of the modifications underlyinE lonE-term potenttat/on, particularly since the interpretations are mode/dependentand the statisticaltreatmentsandexperimentaltechniques employed incorporate stmplifyinB assumptions not yet proven.
TINS, Vol. 14, No. 10, 1991
© 1991.ElsevieSci r encePublishersI td, (UK) 0166-2236/91/$O200
Henri Komis at the Laboratoirede Neurobio/oBie CelMaire, D~partementdes Biotechnologies, INSERMU261, InstitutPasteur, 75724PartsCedex15, Franceand DonaldS. Faberis at the Neurobiology Laboratory, Departmentof Physiology,University of Buffalo,Buffalo, NY 14214,USA.
439
Box 1. Statistics of quantal analysis in the CNS Measurements of synaptic responses elicited by single presynaptic spikes in the brain include two main sources of variability, the release process itself and background noise. The analytical approaches used have addressed the complications differently. However all are directed towards extracting an appropriate mathematical description of neurotransmission. The most general model assumes release follows compound binomial statistics. In this formulation, there are n potential sites for exocytosis with their own probabilities of release, p~. The chance that a postsynaptic cell receives x packets of neurotransmitter after a presynaptic impulse is, Px = PlP2 ... px(1--Px+l) --. (1--Pn) + PlP3 ... Px+l (1--p2) (1--px+2) ... (1--p,) Jr
.
.
,
+ (1-Pl) ... (1-Pn-x) (Pn-x+l) ..- P. In concrete terms, once discrete peaks are identified, or derived from amplitude distribution histograms of evoked responses, their measured probabilities can be used to calculate each p~. This procedure has most often been used in conjunction with the two-step deconvolution. The simple binomial is the special case where the average release probability, p, is assumed to be the same at all release sites. Then Px =
x (1 --p) n - x
x
where (n) x
n, (n-x)!xf
represents the number of combinations by which n sites can emit x quanta. Again, once quantal size, q, is known, n and p can be determined from response histograms. An apparent advantage in this case is that the coefficient of variation, CV, is independent of q. Specifically, CV = ~/(1-p)/np This relationship provides the basisof the coefficient of variation method, whereby CV values are compared before and after synaptic strength is modified, to identify the locus of the change. The potential problems with this method are that (1) the value of CV is subject to measurement error and (2) q may influence CV if it varies from site to site or has intrinsic variability. The Poisson distribution is an extreme case of the simple binomial, which applies when n is large and p is small; then the two parameters are not defined since the critical variable is the np product m, called mean quantal content (or average number of quanta released). In this case, e-m m x P(x)
-- -
X!
The Poisson has been used extensively for historical reasons (i.e. at the neuromuscular junction) and because m can be easily calculated from the failure rate (method of failures), since Po ----e-m It is generally not adequate for central connections. 440
of other M-cell connections1°; such studies confirm that when there are several active zones in a single bouton 11, they function as independent release sites (Fig. 1). In other words, this provides a unifying framework for quantal release, where the synaptic unit, including the active zone (rather than the terminal bouton) and its postsynaptic complement, represents the building block of the connection between two cells. To recognize that this also holds for the NMJ it is sufficient to note that there are 300-1000 active zones on one junction, and the estimated mean quantal content, under normal conditions, is only about 200 (see references contained in Ref. 12). A number of issues emerged subsequently. The first is whether there is a control of exocytosis and the probability of it occurring at the level of one active zone 13. The second is what determines p at the macroscopic level and the extent to which it varies from site to site. Others call for caution when interpreting pharmacological treatments that produce multiquantal release in a non-physiological manner [for example, 2-amino-4-phosphobutanoate (Ref. 14)], or when activating a single bouton that may in fact contain more than one active zone. For example, in hippocampal cultures, hyperosmotic solutions were applied to very restricted areas, including to only one presynaptic knob, to enhance spontaneous release. The results were interpreted on the understanding that one release site per ending was involved. However, in some cases, the number of peaks in the histogram exceeded the number of boutons activated 15 Ultrastructural data are needed to resolve this apparent contradiction. Problems in the CNS: quantal release versus quantal response It is fair to say that most if not all difficulties associated with quantal analysis at central synapses revolve around uncertainties about the size and variance of single quanta, which are often small, and involve the opening of 10-250 channels 15-19. Thus, they generally cannot be distinguished within a synaptic bombardment generated by diverse inputs distributed on the cell. In addition, when single pairs of neurons are studied, discrete multiquantal peaks may be obscured by instrumental noise (but see below). This situation is exemplified in the spinal motoneuron (at la and inhibitory synapses) where Kuno made the first attempts to determine if release is quantal in the CNS; both Poisson and binomial statistics were applied, but with limited success2°'21. The unfavourable signal-to-noise ratio for synaptic events in motoneurons prompted the development of the deconvolution technique 22. This procedure considers the statistical properties of background noise normally superimposed upon the fluctuations of the synaptic potentials and attempts to 'extract' the distribution of synaptic responses from the resulting composite amplitude histograms. (In practice, the amplitude of an event is the sum of its true size plus that of the instrumental and biological noise.) Although this method is not constrained by the postulate of a specific release TINS, Vol. 14, No. 10, 1991
perspectives model, e.g. Poisson or binomial, it still assumes that the fluctuations of the synaptic potential are discrete. Unfortunately, while it represented an interesting and important technical advance, its results allow for multiple, if not contradictory, interpretations. For instance, the size and number of the derived peaks are sensitive to the measurement protocol and to the signal-to-noise ratio 23'24, and thus this strategy may not reveal the 'true' quantal size, q25. In fact, a retrospective analysis of results from la motoneuron connections has demonstrated that the magnitude of the derived q is directly proportional to the standard deviation of the background noise, a conclusion also obtained with simulated data even when the actual value of q was smaller than that derived with deconvolution 26. In addition, the separation between the discrete components extracted from a single connection shifts with changes in ongoing synaptic noise, suggesting non-linear interactions between such noise and evoked postsynaptic potentials 27. Indeed, when deconvolution was constrained to include specific release models and incorporating for the first time the maximum likelihood criterion 3'6, it was also found that the success was limited by the signal-tonoise ratio. Is there postsynaptic saturation? An apparent outcome of this method has been the proposal that the quantal size is invariant at a given synapse 23, although this assumption was embedded in the deconvolution model 24, with at most a 5% coefficient of variation 28. This postulated quantal invariance has been taken as reflecting saturation of the postsynaptic receptors. Alternative explanations for events generated at sites distant from the recording electrode could be (1) local saturation at spine synapses, where, because of the high input impedance, opening of a few channels may bring membrane potential to the equilibrium level for excitatory responses, and (2) activation of voltage-dependent conductances. In these cases the postsynaptic membrane would no longer be a reliable detector of release events. That is, quantal analysis would be precluded, or could lead to nonquantal conclusions 22,23,29, since quantization of amplitudes of synaptic signals would be a postsynaptic phenomenon 3°. However, when the quantal unit is isolated by blocking presynaptic impulses with tetrodotoxin, leaving only true spontaneous exocytoses, its size varies more than the background noise (Fig. 2); there is a net coefficient of variation (CV) of - 1 0 - 1 5 % for inhibitory postsynaptic currents (IPSCs) recorded in the M cell 31 and in rat hippocampal slices18. Thus, the CV is surprisingly the same for quanta opening about 1000 M-cell CIchannels and less than 30 hippocampal CI- channels, respectively (interestingly, these values are inversely proportional to the input impedance of the cells18,32). These results suggest that, unless they are nonstationary 33, quanta can (at least in some cases) be distinguished in the CNS, even when small. Furthermore, in the case of the M cell, saturation does not occur, as demonstrated by physiological TINS, Vol. 14, No. 10, 1991
1 connection -- n release sites Motor nerve terminal End-plate
o ,o,. ~ ° " ~ °
,~. cO ,~._ °°
^ o
°°'~' ~° °°~
Y Prej\ Post
/o OOoO "~ Statistical n=l
Statistical n = number of release sites (4)
Fig. 1. Release sites of the neuromuscular junction and presynaptic vesicular grids of the central synapses are functionally equivalent. (Upper diagram) Longitudinal section through a terminal branch of a frog neuromuscular junction. On the presynaptic side (motor nerve terminal) synaptic vesicles duster around a dense cytoplasmic formation (hatched) that forms parallel bands facing muscular folds, each density and its adjacent vesicles thus defining an active zone. A dense material (dark areas) represents the receptive complex of the postsynaptic element (end-plate). (Lower diagram) Drawings of terminal boutons (pre-) and their synaptic complexes (post-); here the active zones are composed of arrays of presynaptic dense projections (dark triangles), which delineate the presynaptic vesicular grid, with synaptic vesicles nestling between them. Note that the statistical term, n, is equivalent to 1 for a synaptic bouton bearing only one synaptic grid (on the left), but is greater, and equal to the total number of active zones, for boutons containing several such release sites (middle) or for more complicated connections (on the right). (Modified from Ref. 11 .) recordings and readily explained by modelling the quantal response 34. Regardless of this, the issue raises the question of what determines the size and variance of the quantal conductance? Again, ultrastructural data might be helpful in ascertaining if the limiting factor is related to the dimensions of the postsynaptic receptor clusters, as postulated recently 3°. Receptor matrices studied so far can stretch beyond the synaptic contact zone in the M cell 35'~6 and at synapses mediating responses to GABA 37, [3adrenaline 38, neurotensin 39 or opioids 4°, as they do at the NMJ. If receptor number is not limiting, other postsynaptic properties [for example, probability of opening of single channels, extension and structure (Fig. 3) of the receptor matrix 41 and functional versus non-functional receptors, as controlled intracellularly] could be critical. Method of failures and silent synapses A small q, with few channels being opened, introduces two additional problems related to the inability to detect a response when repeatedly stimulating a presynaptic cell. One is whether failures can be clearly distinguished from quanta buried in background noise; this can be particularly critical for studies of variations in synaptic efficacy 42, since an increase in quantal amplitude alone may appear to reduce the failure rate. Also, even in unambiguous cases, a failure could have a post441
A
After TTX
B o"N= 0.37 nA
~s
\ 56 \
14 2
5msec
4 nA
C
I.= 5msec
Fig. 2. Extraction of miniature inhibitory postsynaptic currents OPSCs) from the background synaptic noise, and their variance, in the Mauthner cell. (A,B) Sample voltage clamp recordings, monitored from a tetrodotoxin-treated preparation (after TTX), showing quanta (arrows) of inverted polarity, due to spontaneous exocytosis (A) and their unimodal amplitude distribution, which is best fit by a single gaussian curve with a standard deviation of 0.42 nA (B), which is greater than that of instrumental noise [ON in (A)]. (C) Superimposed a verages of composite inhibitory postsynaptic potentials (IPSPs) selected according to their amplitude classes; the smallest one is from (B), and the two largest are from a multi-peaked histogram obtained before tetrodotoxin application, i.e. when presynaptic action potentials could evoke simultaneous release from several terminals. As indicated, their sizes are consistent with the notion that they represent responses produced by 1, 2 and 3 q, respectively. (Modified from Ref. 31.)
i
lOO
20
30 40 Max. intensity / cluster
Fig. 3. Evidence that the amount of clustered postsynaptic receptors fluctuates from one synapse to another. (Left panel) Variability of the size and shape of receptor domains on the Mauthner cell lateral dendrite. Pseudo-color image of glycine receptor matrices, each of which faces an active zone, stained with a fluorescently labelled specific monodonal antibody provided by H. Betz. The fluorescence emitted was coded with a linear 'look-up' table that decreases progressively from a maximum at red to a minimum at blue. Scale bar: 3 l~m. (Right panel) Histogram of the maximum intensity per cluster (abscissa) measured on one dendrite and expressed in arbitrary units, versus the number of observations (ordinate), with indicated mean and standard deviation. This histogram was constructed using direct measurements of the emitted fluoresence (Triller et al., unpublished data).
442
synaptic origin 43 with receptors being unresponsive. This need for caution has been noted 44 for the case when statistical data suggest that the parameter n is altered. In a more general context, quantal analysis has sometimes suggested that some synapses within a connection are silent, because the incidence of structural release sites is superior to the number identified statistically 4~-48. This criterion alone is not sufficient to locate the site of their ineffectiveness; rather, direct use of specific pharmacological tools to enhance the probability of release 1° or postsynaptic responsiveness43 may be helpful. Perspective on quantal analysis in the CNS
There are two distinct objectives associated with quantal analyses at central connections. The first is to determine accurately the parameters n, p and q, and to provide an appropriate description of the release mechanisms; as discussed above, this might not be easily achieved 26,33. The second is to ask where a synaptic modification is expressed. Here, indirect methods that may ignore parametric values are often used for a first approximation. It is important to recognize that the results are modeldependent and may be misleading. Ideally, the most neutral approach would be a sequential (two-step) deconvolution where (I) the superimposed noise is 'removed' from the amplitude histogram, revealing the true synaptic steps, and (2) the deconvolved histograms are fitted with different models, such as a Poisson, and simple or compound binomials. The first step requires large samples of events, and is most reliable when q is at least twice as large as the standard deviation of the added noise 25'49. Results of the fits may vary, since at la motoneuron 24 or hippocampal connections 33 simple or compound binomials could be adequate, compound binomials being more successful- although sometimes neither model fits the data satisfactorily. In the case of the dorsal spinocerebellar tract neurons, the compound model was better, with the requirement that quantal sizes were the same for all contacts, regardless of where they were generated on the dendritic tree 28. The initial principle of deconvolution was modified by deliberately adding constraints corresponding to different statistical models, so that the optimization technique generates their best sets of parameters for comparison 3'6. Estimated values could then be obtained with smaller sample sizes or a lower signal-to-noise ratio or both, and in one system this method has detected a reduction of quantal size produced by a specific receptor antagonist 32. As with all fitting procedures it works best when discrete components are already manifest in the histograms, but these components are not absolutely required 6,5°. At M-cell inhibitory synapses the strong correlation between structure (number of release sites) and function (binomial n) provided the experimental basis for the now-generalized one vesicle hypothesis. Thus far, this constrained deconvolution has not been used to weigh simple and compound models, but it has been compared with the 'two-step' TINS, Vo/. 14, No. 10, 199I
........................................................................................................................................... ............... methods for the same data. One important controversy was addressed there, namely whether adjusting data in order to obtain a 'better fit' could lead to erroneous conclusions, since the sequential deconvolution re-distributes event amplitudes having low frequencies of occurrence to adjacent classes24. That approach was found to overestimate q and to underestimate n relative to both the constrained binomial and the structural correlate of n 51. The conclusion would have been that n is impossible to define, because 'silent' release sites (or ones with very low p) were involved 24. Subsequently, however, quantal events were measured in synaptic noise from the same experiments, and this independent test showed that their size matched those of the simple binomial predictions 12, stressing once more the danger of accepting biological conclusions on the basis of statistics alone. Validation of any quantal model is obtained when the predicted q can be verified with direct observations of spontaneous miniature events. This has the best chance of success when recordings are made close to the release sites. Tetrodotoxin or other pharmacological treatments have been used to isolate single quanta in the CNS (see references contained in Ref. 12) and to demonstrate that their distributions match those of the first peaks in composite histograms of evoked excitatory 52 and inhibitory 3~ synaptic responses (see also Figs 2 and 4). This may not be so obvious when the miniature distribution is skewed ~5J9 or has a large variance, or both. Quantal variance may have an impact on the interpretation of data subjected to the coefficient of variation analysis, which, when applied, is typically based on equations pertaining to a simple binomial (or its limiting case, the Poisson) 42'44,53 and ignores possible variances in any of the quantal parameters. In this case no change in the CV implies that modulation is purely postsynaptic, while a shift in its value implicates a presynaptic site, at least in part 54. However, it was found that postsynaptic modifications alone can alter the CV 5s,56 by including quantal variances regardless of whether one or several input cells are involved. Thus, the only remaining unambiguous outcome that can be used is that an invariant CV must reflect a change in q when synaptic efficacy is modified 56. Quantal approaches to LTP Despite the difficulties mentioned above, shortterm modifications of synaptic efficacy, such as depression 33'57 and paired pulse potentiation 5°, have been assigned a presynaptic locus using both deconvolution techniques. Quantal analysis has also been successful in cases of long-term changes when quanta could be compared before and after modifications of synaptic efficacy 58,59. However, the question of where LTP, or enhancement, is expressed in hippocampus is still open 5° and will remain so until quanta at hippocampal synapses are also resolved in experiments with single pairs (see Box 2). This may be difficult to achieve with a patch electrode, which precludes extended periods of control recordings before LTP induction. It is relTINS, Vol. 14, No. 10, 1991
~ ~ P ~ ~: ~ ~ ~ ~V ~ ~
evant here that statistical methods used so far without this information, especially the CV technique and the method of failure 53,6° have required excessive simplifications, particularly when using extracellular minimal stimulation 42,44,50,61, which does not guarantee reliable activation of a single cell. Studies of LTP in the hippocampal slice using the CV method (Box 1) have suggested that its maintenance is due to enhanced release. Yet, data in one report were interpreted on the assumption that any change in the CV is indicative of a presynaptic locus 44, while the same results would have been understood by others 15 to signify the opposite, since the mean increased more than the square of (I/CV). This discrepancy illustrates the fact that any conclusion from indirect methods is model dependent; namely, the different postulates were (I) no quantal variation and single cell stimulation 42 versus (2) homogenous quantal variance and multiple inputs 44. As discussed elsewhere, the CV is independent of q only if the latter is the same for all contributing afferent cells; if all inputs are not stimulated reliably, the classical pre- and postsynaptic domains become indistinguishable. This holds even in the case of one celP6; for example, if changes in q and its variance are correlated (see also Ref. 33). It is also interesting that despite the high resolution provided by patch-clamp techniques the magnitude of the apparent quantum differed by a factor of three in the two studies (i.e. - 0 . 0 7 ns in Ref. 42 versus 0.21 ns in Ref. 15). Recently, recordings were obtained during LTP from pairs with a postsynaptic patch-clamp electrode °2, and shifts in both the amplitude histograms and the apparent rate of failures were reported. These changes were interpreted as signalling a presynaptic locus although there was also a relatively smaller increased quantal size (in comparison with an unusual 1000-2000% enhancement of synaptic strength) and, in addition, there were large oscillations in transmission. The latter, taken as pre-
Box 2. Recipe for a 'proper' quantal analysis 1 Presynaptic spike to ensure only one cell is firing reliably. 2 Noise level sufficiently low to isolate miniature events (quanta) and first peak of the histogram, with no overlap. 3 Resolution of single quantum amplitude, preferably by recording sufficiently close to postsynaptic site to eliminate 'cable filtering' (particularly dendritic cable filtering). 4 Direct data on possible variations in quantal amplitude at a single site.* 5 Morphological identification of number of potential release sites. 6 Independent evidence on whether p is similar or different at multiple release sites comprising a single connection.
*Saturation of postsynaptic receptor clusters may compromise interpretation of the data.
443
perspectives Concluding remarks Despite the recent interest in central synapses, the major concepts used still depend upon guidelines provided by early studies at the NMJ, with the main additions and perhaps differences being dependent upon structural features, which have not been fully investigated. Data reviewed here nevertheless indicate that divergence from this model 3° cannot be generalized to all central junctions, but may rather indicate specializations at given connections.
2 mM-Ca 2+ 1 mM-Mg 2+
A 15-
.~ z
lO
5
0
i
0
°°t 0
--
,
100 lf~
I
200
B. (1969) The Release of Neural Transmitter Substances, Charles C. Thomas 2 del Castillo, J. and Katz, B. (1954) J. Physiol. 124, 560-573 1 Katz,
0.5 raM-Ca 2.
100
200
Amplitude (pA)
Fig. 4. Evidence that inhibitory postsynaptic currents (IPSCs) are multiquantal in rat hippocampal slices. (A) Amplitude distributions of stimulus-evoked inhibitory currents obtained by whole cell patch-clamp recording in physiological saline. Several peaks, regularly spaced by about 21 pA, and fit by a sum of gaussian functions, stand out. (B) Only the first class of events, which represents single mlPSCs, remains when the probability of release, but not the quantal size, is lowered by high M g 2÷ and low Ca 2+. (Data from Ref. 18.)
synaptic in origin, again based on the CV method, in fact precluded quantal analysis. An opposing postsynaptic explanation was deduced 5° in other experiments where the CV, the method of failures, and a deconvolution constrained with a simple binomial model were compared. Minimal stimulation and cell pairs both yielded an apparent increase in q, the exact value of which differed, however, with the analysis used. Although the data were obtained with standard microelectrodes, there were peaks in the amplitude histograms of the evoked responses, lending credibility to the use of the constrained deconvolution. The intriguing fact is that, despite reservations about any one methodological approach, all the studies considered above were substantiated by independent internal checks that reinforced their primary, albeit opposing conclusions. This paradox may reflect differences in experimental conditions (such as the age of the material, protocols for producing LTP and recording methods), LTP expression then becoming a combination of preand postsynaptic determinants. As noted in Ref. 55, this notion is inherently attractive, as it would reinforce the unity of a synapse. 444
Selected references
3 Korn, H., Mallet, A., Triller, A. and Faber, D. S. (1982) J. Neurophysiol. 48, 679-707 4 Couteaux, R. and Pecot-Dechavassine, M. (1970) C.R. Acad. Sci. 271, 2346-2349 5 Heuser, J. E. and Reese, T. S. (1977) in Handbook of Physiology: The Nervous System (Sect. I, Vol. I, Part I), pp. 261-294, American Physiological Society 6 Korn, H., Triller, A., Mallet, A. and Faber, D. S. (1981) Science 213, 898-901 7 Triller, A. and Korn, H. (1982)J. NeurophysioL 48, 708-736 8 Akert, K., Pfenninger, K., Sandri, C. and Moor, H. (1972) in Structure and Function of Synapses (Papas, G. D. and Purpura, D. P., eds), pp. 67-86, Raven Press 9 Walmsley, B., Wienawa-Narkiewicz, E. and Nicol, M. J. (1985) J. Neurosci. 5, 2095-2106 10 Lin, J. W. and Faber, D. S. (1988) J. NeuroscL 8, 1313-1325 11 Korn, H. (1984) Exp. Brain Res. (Suppl. 9), 201-224 12 Korn, H. and Faber, D. S. (1990) J. Neurophysiol. 63, 198-222 13 Triller, A. and Korn, H. (1985) J. Neurocytol. 14, 177-192 14 Heuser, J. E. etal. (1979)J. CellBioL 81,275-300 15 Bekkers, J. M., Richerson, G. B. and Stevens, C. F. (1990) Proc. Nail Acad. Sci. USA 87, 5359-5362 16 Rang, H. P. (1981)J. Physiol. 311, 23-55 17 Collingridge, G. L., Gage, P. W. and Robertson, B. (1984) J. Physiol. 356, 551-564 18 Edwards, F. A., Konnerth, A. and Sakmann, B. (1990) J. Physiol. 430, 213-249 19 Ropert, N., Miles, R. and Korn, H. (1990) J. Physiol. 428, 707-722 20 Kuno, M. (1964) J. PhysioL 175, 81-99 21 Kuno, M. and Weakly, J. N. (1972) J. Physiol. 224, 287-303 22 Edwards, F. R., Redman, S. J. and Walmsley, B. (1976) J. Physiol. 259, 665-688 23 Jack, J. J. B., Redman, S. J. and Wong, K. (1981) J. Physiol. 321, 65-96 24 Redman, S. J. (1990) PhysioL Rev. 70, 165-198 25 Kullmann, D. M. (1989) J. Neurosci. Methods 30, 231-245 26 Clamann, H. P., Rioult-Pedotti, M. S. and LLischer, H. R. (1991) J. Neurophysiol. 65, 67-75 27 Solodkin, M., JimEnez, I., Collins, W. F., Mendell, L. M. and Rudomin, P. (1991) J. Neurophysiol. 65, 927-945 28 Walmsley, B., Edwards, F. R. and Tracey, D. J. (1988) J. NeurophysioL 60, 889-908 29 Edwards, F. R., Redman, S. J. and Walmsley, B. (1976) J. Physiol. 259, 689-704 30 Edwards, F. (1991) Nature 350, 271-272 31 Korn, H., Burnod, H. and Faber, D. S. (1987) Proc. NatlAcad. Sci. USA 84, 5981-5985 32 Faber, D. S. and Korn, H. (1988) J. Neurophysiol. 60, 1982-1999 33 Larkmann, A., Stratford, K. and Jack, J. (1991) Nature 350, 344-347 34 Faber, D. S. and Korn, H. (1988) Proc. NatlAcad. Sci. USA 85, 8708-8712 35 Faber, D. S., Funch, P. G. and Korn, H. (1985) Proc. Natl Acad. Sci. USA 82, 3504-3508 36 Seitanidou, T., Triller, A. and Korn, H. (1988) J. Neurosci. 8, 4319-4333 37 Somogyi, P., Takagi, H., Richards, J, G. and Mohler, H.
TINS, VoL 14, No. 10, 1991
Acknowledgement
79-91 (1989) J. Neurosci. 9, 2197-2209 38 Stader, C. B. et al. (1983) Proc. Natl Acad. Sci. USA 80, 51 Korn, H. and Faber, D. S. (1987)in NewlnsightsintoSynaptic Function (Edelman, G. M., Gall, W. E. and Cowan, W. M., 1840-1844 eds), pp. 57-108, Neurosciences Research Foundation, Wiley 39 Dana, E. etal. (1989)J. Neurosci. 9, 2247-2257 & Sons 40 Hamel, E. and Beaudet, A. (1984) Nature 312, 155-157 41 Triller, A., Seintanidou, T., Franksson, O. and Korn, H. (1990) 52 Blankenship, J. E. and Kuno, M. (1968) J. Neurophysiol. 31, 195-209 The New Biologist 2,637-641 53 MacLachlan, E. M. (1978) Int. Rev. Physiol. Neurophysiol. 17, 42 Malinow, R. and Tsien, R. W. (1990) Nature 346, 859-861 49-117 43 Korn, H. and Faber, D. S. (1990) in Glycine Neurotransmission (Ottersen, O. P. and Storm-Mathisen, J., eds), pp. 54 Clements, J. D. (1990) J, Neurosci. Methods 31, 75-88 55 Korn, H., Fassnacht, C. and Faber, D. S. (1991) Nature 350, 139-170, Wiley & Sons 282 44 Bekkers, J. M. and Stevens, C. F. (1990) Nature 346, 56 Faber, D. S. and Korn, H. Biophys. J. (in press) 724-729 45 Neale, E. A., Nelson, P. G., MacDonald, R. L., Christian, C. N. 57 Korn, H., Faber, D. S., Burnod, Y. and Triller, A. (1984) J. Neurosci. 4, 125-130 and Bowers, C. M. (1983)J. Neurophysiol. 49, 1459-1468 46 Redman, S. and Walmsley, B. (1983) J. Physiol. 343, 58 Mintz, I., Gotow, T., Triller, A. and Korn, H. (1989) Science 245, 190-192 135-145 59 Dale, N. and Kandel, E. R. (1990) J. Physiol. 421,203-222 47 Wojtowicz, J. M. and Atwood, H. L. (1986) J. Neurophysiol. 60 Martin, A. R. (1977) in Handbook of Physiology: The 55, 484-498 Nervous System, (Sect. I, Vol. I, Part I), pp. 329-355, 48 Wojtowicz, J. M., Smith, B. R. and Atwood, H. L. Ann. N.Y. American Physiological Society Acad. Sci. (in press) 49 Sayer, R. J., Redman, S. J. and Andersen, P. (1989) 61 MacNaughton, B. L., Barnes, C. A. and Andersen, P. (1981) J. Neurophysiol. 46, 952-966 J. Neurosci. 9, 840-850 50 Foster, T. C. and MacNaughton, B. L. (1991) Hippocampus 1, 62 Malinow, R. (1991)Science 252, 722-724
. . . .
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r
e
We thank R. Miles for critical reading of the manuscriptand help with Box2.
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s
Neuralmodelsof stereoscopicvision Randolph
B l a k e a n d H u g h R. W i l s o n
Human stereopsis remains an enigma: how does the brain match features between the left and right eye images and compute disparity between these matched features? Developments in computational neuroscience and machine vision have led to several models of human stereopsis that provide insight into possible mechanisms underlying this phenomenon. These models, reviewed in this paper, adopt one of three general strategies. One class of models employs cooperative interactions, whereby a unique solution to the matching problem emerges from excitatory and inhibitory interactions among binocular neural elements. A second class of models implements matching and disparity computation serially over multiple spatial scales. A third class relies on local, non-interacting computations performed in parallel to overcome speed limitations inherent in the other models. Considered together, these theoretical developments offer fresh insights concerning the actual neural concomitants of binocular stereopsis. Looking about the visual world, we see objects from two slightly different perspectives owing to the lateral separation of the eyes in the head. Evidently the brain is remarkably adept at combining these two monocular views, for binocular single vision and stereopsis occur effortlessly even when the two monocular views contain no discernible form information to guide the matching of the left and right eye images 1. Moreover, the brain is incredibly accurate in registering slight positional differences of image features from the left and right eyes, as evidenced by our keen sense of stereoscopic depth perception. How does the binocular visual system identify corresponding monocular features, measure positional disparities between those features and transform those measurements into a description of the three-dimensional layout of objects in the visual scene? TINS, Vol. 14, No. 10, 1991
A first glimpse of the actual neural hardware underlying binocular vision was provided in the late 1960s when physiologists began recording from individual neurons in the visual cortex of mammals with frontally placed eyes. Shortly after Hubel and Wiesel2 described the existence of binocularly innervated cortical cells, several laboratories 3'4 reported that many of these binocular cells in fact possessed receptive fields on non-corresponding areas of the two eyes. In other words, the optimum stimulus for activating these neurons would be an edge or surface marking located somewhere in depth other than the plane of fixation. By virtue of their disparity selectivity, these binocular neurons provided a plausible neural basis for stereopsis. This idea received further support from behavioral experiments demonstrating deficits in stereopsis in animals that lacked the normal complement of binocular cortical neurons 5'6 Following these initial exciting discoveries, other laboratories concentrated on measuring the degree of disparity selectivity among single binocular neurons 7, correlating those measures with cortical cell types 8 and searching for disparity-selective cells in extrastriate areas 9. Much of that work is reviewed elsewhere 1°. Despite this enduring interest in disparity processing by the brain, however, real progress in our understanding of the neural bases of stereopsis has come slowly, partly because of the absence of a theoretical context in which to frame physiological questions. Recent developments in computational neuroscience and machine vision have provided new theoretical insights into the nature of stereoscopic vision, in turn leading to important psychophysical discoveries concerning human stereopsis. This article reviews those theoretical and empirical developments, in the hope of stimulating a refined assault on the actual neural concomitants of stereopsis.
© 1991, EPsevierScience Publishers Lid, (UK) 0166- 2236/91/$0200
Randolph Blakeis at the Dept of Psychology, Vanderbilt University, Nashville, TN.77240, USA, and Hugh R. Wilson is at the Dept of Ophthalmology and VisualScience, Universityof Chicago, 939 E. 57th Street, Chicago, IL 60637, USA.
445
Quantalanalysisandsynapticefficacyin the CNS Henri Korn and Donald S. Faber of release of each quantum. The amplitude distributions of evoked responses, which had distinct peaks, then matched Poisson predictions. However, as this statistic involves only one term, i.e. the mean quantal content, the two critical parameters, n and p, remain hidden in this formulation (see Box 1 for definitions and different models with their restraints). The initial proposal was that since n is supposed to be large in the Poisson theorem and nerve terminals contain numerous synaptic vesicles, these vesicles therefore represent 'the population of units capable of responding to a nerve impulse', p being their average probability of responding 2. Subsequent studies suggested that under more Until recently, attempts to gain insight into the physiological conditions (see references contained in Ref. 3) n is actually small, and p is large, so that question of the mechanism by which neurotransmitters are released and detected in the CNS have been binomial statistics (simple and compound) are more confronted by a number of technical difficulties appropriate for the description of fluctuating postspecific to central neurons and networks. However, synaptic potentials. This forced a revision of ideas the advent of patch-clamp techniques that consider- about what might be the correlates of n, although ably improve the signal-to-noise ratio has resulted in direct information about its physical meaning was a renewed interest in how synapses work at the still unavailable. At the same time, EM studies microscopic level. The expectation is that it may be showed that a synaptic vesicle fuses with the possible to resolve elementary problems such as: is presynaptic terminal membrane, and undergoes release quantal in a given system, and according to exocytosis (rupture and release of ACh) at a what model does it occur? A focus on quantal specialized site called an 'active zone '4'5. analysis has also been prompted by the fact that it It is interesting that a morphological definition of is an irreplaceable tool for identifying the pre- or n was finally reached by studies of synaptic transpostsynaptic locus of changes in synaptic efficacy, mission in central neurons rather than at the NMJ, the most dramatic being long-term potentiation with simultaneous recordings from pairs of ident(LTP). ified pre- and postsynaptic cells, followed by stainThese two questions are interconnected, because ing and reconstruction of the investigated neurons. the uncertainties associated with quantal analysis in At inhibitory synapses on the Mauthner (M) cell, the CNS can lead to contradictory conclusions about the simple binomial model provides a statistically the transmission process and, hence, the mechan- significant description of the quantal release of the isms underlying the nature of plasticity. This issue is transmitter glycine, and it was found that the als,o complicated by the fact that the quantal theory number of active zones established on this neuron itself has evolved from observations of single by the afferent cell equals binomial n computed central connections using classical methods of re- from statistical analysis of inhibitory postsynaptic cording, complemented by light and electron potential (IPSP) amplitudes 3'°. This striking identity microscopy (EM). A background to this evolution is implies that each releasing unit, which at these necessary because it emphasizes the pitfalls and terminals 7 exhibits the typical structure of active misinterpretations that can still be encountered, zones in the CNS 8, functions in an independent, allparticularly when addressing statistical results in the or-none manner. absence of structural guidelines - which have beBecause the size of the derived quantum was come the touchstone for assessing the validity of relatively small, resulting from the opening of about such results. 1000 postsynaptic CI channels, the more parsimonious explanation was that one quantum correThe quantal releasehypothesistoday sponds to the amount of transmitter released by a The quantal notion is derived from the neuromus- given active zone. Thus, the 'one vesicle hypothesis' cular junction (NMJ) 1, where (1) spontaneously was coined, which states that one vesicle, rather occurring miniature synaptic potentials, or quanta, than many, is released in a binary manner after an were first discovered, and (2) evoked end-plate impulse, with a probability p. This view is now potentials correspond to integral multiples of the generally accepted for most synaptic connections, quantal unit. These observations were made poss- including the NMJ, despite the general lack of ible by reducing extracellular Ca2+ in order to further evidence. It has received indirect support decrease the average number of quanta released by from studies of excitatory inputs onto cat dorsal an action potential, i.e. by lowering the probability spinocerebellar neurons 9, and from investigations
Quanta/analysls of synapti~:transmission at connections between neuronstn the CNS has provided mslghtsconcerningthe structural constraintson transmitter releaseand postsynaptic responsiveness. However, it hasproven difhcultin manycasesto resolvethe sizeand variabihty of a single quantum or to distinguish clear peaks in amphtude histograms of evoked responses,due m part to the superp0sitionof background tnstrumentaland biological notse. These /imitations raise questions about recent attempts to use direct or indirect methods of quanta/analysism orderto distinEuish between pre- andpostsynaptic/oct of the modifications underlyinE lonE-term potenttat/on, particularly since the interpretations are mode/dependentand the statisticaltreatmentsandexperimentaltechniques employed incorporate stmplifyinB assumptions not yet proven.
TINS, Vol. 14, No. 10, 1991
© 1991.ElsevieSci r encePublishersI td, (UK) 0166-2236/91/$O200
Henri Komis at the Laboratoirede Neurobio/oBie CelMaire, D~partementdes Biotechnologies, INSERMU261, InstitutPasteur, 75724PartsCedex15, Franceand DonaldS. Faberis at the Neurobiology Laboratory, Departmentof Physiology,University of Buffalo,Buffalo, NY 14214,USA.
439
Box 1. Statistics of quantal analysis in the CNS Measurements of synaptic responses elicited by single presynaptic spikes in the brain include two main sources of variability, the release process itself and background noise. The analytical approaches used have addressed the complications differently. However all are directed towards extracting an appropriate mathematical description of neurotransmission. The most general model assumes release follows compound binomial statistics. In this formulation, there are n potential sites for exocytosis with their own probabilities of release, p~. The chance that a postsynaptic cell receives x packets of neurotransmitter after a presynaptic impulse is, Px = PlP2 ... px(1--Px+l) --. (1--Pn) + PlP3 ... Px+l (1--p2) (1--px+2) ... (1--p,) Jr
.
.
,
+ (1-Pl) ... (1-Pn-x) (Pn-x+l) ..- P. In concrete terms, once discrete peaks are identified, or derived from amplitude distribution histograms of evoked responses, their measured probabilities can be used to calculate each p~. This procedure has most often been used in conjunction with the two-step deconvolution. The simple binomial is the special case where the average release probability, p, is assumed to be the same at all release sites. Then Px =
x (1 --p) n - x
x
where (n) x
n, (n-x)!xf
represents the number of combinations by which n sites can emit x quanta. Again, once quantal size, q, is known, n and p can be determined from response histograms. An apparent advantage in this case is that the coefficient of variation, CV, is independent of q. Specifically, CV = ~/(1-p)/np This relationship provides the basisof the coefficient of variation method, whereby CV values are compared before and after synaptic strength is modified, to identify the locus of the change. The potential problems with this method are that (1) the value of CV is subject to measurement error and (2) q may influence CV if it varies from site to site or has intrinsic variability. The Poisson distribution is an extreme case of the simple binomial, which applies when n is large and p is small; then the two parameters are not defined since the critical variable is the np product m, called mean quantal content (or average number of quanta released). In this case, e-m m x P(x)
-- -
X!
The Poisson has been used extensively for historical reasons (i.e. at the neuromuscular junction) and because m can be easily calculated from the failure rate (method of failures), since Po ----e-m It is generally not adequate for central connections. 440
of other M-cell connections1°; such studies confirm that when there are several active zones in a single bouton 11, they function as independent release sites (Fig. 1). In other words, this provides a unifying framework for quantal release, where the synaptic unit, including the active zone (rather than the terminal bouton) and its postsynaptic complement, represents the building block of the connection between two cells. To recognize that this also holds for the NMJ it is sufficient to note that there are 300-1000 active zones on one junction, and the estimated mean quantal content, under normal conditions, is only about 200 (see references contained in Ref. 12). A number of issues emerged subsequently. The first is whether there is a control of exocytosis and the probability of it occurring at the level of one active zone 13. The second is what determines p at the macroscopic level and the extent to which it varies from site to site. Others call for caution when interpreting pharmacological treatments that produce multiquantal release in a non-physiological manner [for example, 2-amino-4-phosphobutanoate (Ref. 14)], or when activating a single bouton that may in fact contain more than one active zone. For example, in hippocampal cultures, hyperosmotic solutions were applied to very restricted areas, including to only one presynaptic knob, to enhance spontaneous release. The results were interpreted on the understanding that one release site per ending was involved. However, in some cases, the number of peaks in the histogram exceeded the number of boutons activated 15 Ultrastructural data are needed to resolve this apparent contradiction. Problems in the CNS: quantal release versus quantal response It is fair to say that most if not all difficulties associated with quantal analysis at central synapses revolve around uncertainties about the size and variance of single quanta, which are often small, and involve the opening of 10-250 channels 15-19. Thus, they generally cannot be distinguished within a synaptic bombardment generated by diverse inputs distributed on the cell. In addition, when single pairs of neurons are studied, discrete multiquantal peaks may be obscured by instrumental noise (but see below). This situation is exemplified in the spinal motoneuron (at la and inhibitory synapses) where Kuno made the first attempts to determine if release is quantal in the CNS; both Poisson and binomial statistics were applied, but with limited success2°'21. The unfavourable signal-to-noise ratio for synaptic events in motoneurons prompted the development of the deconvolution technique 22. This procedure considers the statistical properties of background noise normally superimposed upon the fluctuations of the synaptic potentials and attempts to 'extract' the distribution of synaptic responses from the resulting composite amplitude histograms. (In practice, the amplitude of an event is the sum of its true size plus that of the instrumental and biological noise.) Although this method is not constrained by the postulate of a specific release TINS, Vol. 14, No. 10, 1991
perspectives model, e.g. Poisson or binomial, it still assumes that the fluctuations of the synaptic potential are discrete. Unfortunately, while it represented an interesting and important technical advance, its results allow for multiple, if not contradictory, interpretations. For instance, the size and number of the derived peaks are sensitive to the measurement protocol and to the signal-to-noise ratio 23'24, and thus this strategy may not reveal the 'true' quantal size, q25. In fact, a retrospective analysis of results from la motoneuron connections has demonstrated that the magnitude of the derived q is directly proportional to the standard deviation of the background noise, a conclusion also obtained with simulated data even when the actual value of q was smaller than that derived with deconvolution 26. In addition, the separation between the discrete components extracted from a single connection shifts with changes in ongoing synaptic noise, suggesting non-linear interactions between such noise and evoked postsynaptic potentials 27. Indeed, when deconvolution was constrained to include specific release models and incorporating for the first time the maximum likelihood criterion 3'6, it was also found that the success was limited by the signal-tonoise ratio. Is there postsynaptic saturation? An apparent outcome of this method has been the proposal that the quantal size is invariant at a given synapse 23, although this assumption was embedded in the deconvolution model 24, with at most a 5% coefficient of variation 28. This postulated quantal invariance has been taken as reflecting saturation of the postsynaptic receptors. Alternative explanations for events generated at sites distant from the recording electrode could be (1) local saturation at spine synapses, where, because of the high input impedance, opening of a few channels may bring membrane potential to the equilibrium level for excitatory responses, and (2) activation of voltage-dependent conductances. In these cases the postsynaptic membrane would no longer be a reliable detector of release events. That is, quantal analysis would be precluded, or could lead to nonquantal conclusions 22,23,29, since quantization of amplitudes of synaptic signals would be a postsynaptic phenomenon 3°. However, when the quantal unit is isolated by blocking presynaptic impulses with tetrodotoxin, leaving only true spontaneous exocytoses, its size varies more than the background noise (Fig. 2); there is a net coefficient of variation (CV) of - 1 0 - 1 5 % for inhibitory postsynaptic currents (IPSCs) recorded in the M cell 31 and in rat hippocampal slices18. Thus, the CV is surprisingly the same for quanta opening about 1000 M-cell CIchannels and less than 30 hippocampal CI- channels, respectively (interestingly, these values are inversely proportional to the input impedance of the cells18,32). These results suggest that, unless they are nonstationary 33, quanta can (at least in some cases) be distinguished in the CNS, even when small. Furthermore, in the case of the M cell, saturation does not occur, as demonstrated by physiological TINS, Vol. 14, No. 10, 1991
1 connection -- n release sites Motor nerve terminal End-plate
o ,o,. ~ ° " ~ °
,~. cO ,~._ °°
^ o
°°'~' ~° °°~
Y Prej\ Post
/o OOoO "~ Statistical n=l
Statistical n = number of release sites (4)
Fig. 1. Release sites of the neuromuscular junction and presynaptic vesicular grids of the central synapses are functionally equivalent. (Upper diagram) Longitudinal section through a terminal branch of a frog neuromuscular junction. On the presynaptic side (motor nerve terminal) synaptic vesicles duster around a dense cytoplasmic formation (hatched) that forms parallel bands facing muscular folds, each density and its adjacent vesicles thus defining an active zone. A dense material (dark areas) represents the receptive complex of the postsynaptic element (end-plate). (Lower diagram) Drawings of terminal boutons (pre-) and their synaptic complexes (post-); here the active zones are composed of arrays of presynaptic dense projections (dark triangles), which delineate the presynaptic vesicular grid, with synaptic vesicles nestling between them. Note that the statistical term, n, is equivalent to 1 for a synaptic bouton bearing only one synaptic grid (on the left), but is greater, and equal to the total number of active zones, for boutons containing several such release sites (middle) or for more complicated connections (on the right). (Modified from Ref. 11 .) recordings and readily explained by modelling the quantal response 34. Regardless of this, the issue raises the question of what determines the size and variance of the quantal conductance? Again, ultrastructural data might be helpful in ascertaining if the limiting factor is related to the dimensions of the postsynaptic receptor clusters, as postulated recently 3°. Receptor matrices studied so far can stretch beyond the synaptic contact zone in the M cell 35'~6 and at synapses mediating responses to GABA 37, [3adrenaline 38, neurotensin 39 or opioids 4°, as they do at the NMJ. If receptor number is not limiting, other postsynaptic properties [for example, probability of opening of single channels, extension and structure (Fig. 3) of the receptor matrix 41 and functional versus non-functional receptors, as controlled intracellularly] could be critical. Method of failures and silent synapses A small q, with few channels being opened, introduces two additional problems related to the inability to detect a response when repeatedly stimulating a presynaptic cell. One is whether failures can be clearly distinguished from quanta buried in background noise; this can be particularly critical for studies of variations in synaptic efficacy 42, since an increase in quantal amplitude alone may appear to reduce the failure rate. Also, even in unambiguous cases, a failure could have a post441
A
After TTX
B o"N= 0.37 nA
~s
\ 56 \
14 2
5msec
4 nA
C
I.= 5msec
Fig. 2. Extraction of miniature inhibitory postsynaptic currents OPSCs) from the background synaptic noise, and their variance, in the Mauthner cell. (A,B) Sample voltage clamp recordings, monitored from a tetrodotoxin-treated preparation (after TTX), showing quanta (arrows) of inverted polarity, due to spontaneous exocytosis (A) and their unimodal amplitude distribution, which is best fit by a single gaussian curve with a standard deviation of 0.42 nA (B), which is greater than that of instrumental noise [ON in (A)]. (C) Superimposed a verages of composite inhibitory postsynaptic potentials (IPSPs) selected according to their amplitude classes; the smallest one is from (B), and the two largest are from a multi-peaked histogram obtained before tetrodotoxin application, i.e. when presynaptic action potentials could evoke simultaneous release from several terminals. As indicated, their sizes are consistent with the notion that they represent responses produced by 1, 2 and 3 q, respectively. (Modified from Ref. 31.)
i
lOO
20
30 40 Max. intensity / cluster
Fig. 3. Evidence that the amount of clustered postsynaptic receptors fluctuates from one synapse to another. (Left panel) Variability of the size and shape of receptor domains on the Mauthner cell lateral dendrite. Pseudo-color image of glycine receptor matrices, each of which faces an active zone, stained with a fluorescently labelled specific monodonal antibody provided by H. Betz. The fluorescence emitted was coded with a linear 'look-up' table that decreases progressively from a maximum at red to a minimum at blue. Scale bar: 3 l~m. (Right panel) Histogram of the maximum intensity per cluster (abscissa) measured on one dendrite and expressed in arbitrary units, versus the number of observations (ordinate), with indicated mean and standard deviation. This histogram was constructed using direct measurements of the emitted fluoresence (Triller et al., unpublished data).
442
synaptic origin 43 with receptors being unresponsive. This need for caution has been noted 44 for the case when statistical data suggest that the parameter n is altered. In a more general context, quantal analysis has sometimes suggested that some synapses within a connection are silent, because the incidence of structural release sites is superior to the number identified statistically 4~-48. This criterion alone is not sufficient to locate the site of their ineffectiveness; rather, direct use of specific pharmacological tools to enhance the probability of release 1° or postsynaptic responsiveness43 may be helpful. Perspective on quantal analysis in the CNS
There are two distinct objectives associated with quantal analyses at central connections. The first is to determine accurately the parameters n, p and q, and to provide an appropriate description of the release mechanisms; as discussed above, this might not be easily achieved 26,33. The second is to ask where a synaptic modification is expressed. Here, indirect methods that may ignore parametric values are often used for a first approximation. It is important to recognize that the results are modeldependent and may be misleading. Ideally, the most neutral approach would be a sequential (two-step) deconvolution where (I) the superimposed noise is 'removed' from the amplitude histogram, revealing the true synaptic steps, and (2) the deconvolved histograms are fitted with different models, such as a Poisson, and simple or compound binomials. The first step requires large samples of events, and is most reliable when q is at least twice as large as the standard deviation of the added noise 25'49. Results of the fits may vary, since at la motoneuron 24 or hippocampal connections 33 simple or compound binomials could be adequate, compound binomials being more successful- although sometimes neither model fits the data satisfactorily. In the case of the dorsal spinocerebellar tract neurons, the compound model was better, with the requirement that quantal sizes were the same for all contacts, regardless of where they were generated on the dendritic tree 28. The initial principle of deconvolution was modified by deliberately adding constraints corresponding to different statistical models, so that the optimization technique generates their best sets of parameters for comparison 3'6. Estimated values could then be obtained with smaller sample sizes or a lower signal-to-noise ratio or both, and in one system this method has detected a reduction of quantal size produced by a specific receptor antagonist 32. As with all fitting procedures it works best when discrete components are already manifest in the histograms, but these components are not absolutely required 6,5°. At M-cell inhibitory synapses the strong correlation between structure (number of release sites) and function (binomial n) provided the experimental basis for the now-generalized one vesicle hypothesis. Thus far, this constrained deconvolution has not been used to weigh simple and compound models, but it has been compared with the 'two-step' TINS, Vo/. 14, No. 10, 199I
........................................................................................................................................... ............... methods for the same data. One important controversy was addressed there, namely whether adjusting data in order to obtain a 'better fit' could lead to erroneous conclusions, since the sequential deconvolution re-distributes event amplitudes having low frequencies of occurrence to adjacent classes24. That approach was found to overestimate q and to underestimate n relative to both the constrained binomial and the structural correlate of n 51. The conclusion would have been that n is impossible to define, because 'silent' release sites (or ones with very low p) were involved 24. Subsequently, however, quantal events were measured in synaptic noise from the same experiments, and this independent test showed that their size matched those of the simple binomial predictions 12, stressing once more the danger of accepting biological conclusions on the basis of statistics alone. Validation of any quantal model is obtained when the predicted q can be verified with direct observations of spontaneous miniature events. This has the best chance of success when recordings are made close to the release sites. Tetrodotoxin or other pharmacological treatments have been used to isolate single quanta in the CNS (see references contained in Ref. 12) and to demonstrate that their distributions match those of the first peaks in composite histograms of evoked excitatory 52 and inhibitory 3~ synaptic responses (see also Figs 2 and 4). This may not be so obvious when the miniature distribution is skewed ~5J9 or has a large variance, or both. Quantal variance may have an impact on the interpretation of data subjected to the coefficient of variation analysis, which, when applied, is typically based on equations pertaining to a simple binomial (or its limiting case, the Poisson) 42'44,53 and ignores possible variances in any of the quantal parameters. In this case no change in the CV implies that modulation is purely postsynaptic, while a shift in its value implicates a presynaptic site, at least in part 54. However, it was found that postsynaptic modifications alone can alter the CV 5s,56 by including quantal variances regardless of whether one or several input cells are involved. Thus, the only remaining unambiguous outcome that can be used is that an invariant CV must reflect a change in q when synaptic efficacy is modified 56. Quantal approaches to LTP Despite the difficulties mentioned above, shortterm modifications of synaptic efficacy, such as depression 33'57 and paired pulse potentiation 5°, have been assigned a presynaptic locus using both deconvolution techniques. Quantal analysis has also been successful in cases of long-term changes when quanta could be compared before and after modifications of synaptic efficacy 58,59. However, the question of where LTP, or enhancement, is expressed in hippocampus is still open 5° and will remain so until quanta at hippocampal synapses are also resolved in experiments with single pairs (see Box 2). This may be difficult to achieve with a patch electrode, which precludes extended periods of control recordings before LTP induction. It is relTINS, Vol. 14, No. 10, 1991
~ ~ P ~ ~: ~ ~ ~ ~V ~ ~
evant here that statistical methods used so far without this information, especially the CV technique and the method of failure 53,6° have required excessive simplifications, particularly when using extracellular minimal stimulation 42,44,50,61, which does not guarantee reliable activation of a single cell. Studies of LTP in the hippocampal slice using the CV method (Box 1) have suggested that its maintenance is due to enhanced release. Yet, data in one report were interpreted on the assumption that any change in the CV is indicative of a presynaptic locus 44, while the same results would have been understood by others 15 to signify the opposite, since the mean increased more than the square of (I/CV). This discrepancy illustrates the fact that any conclusion from indirect methods is model dependent; namely, the different postulates were (I) no quantal variation and single cell stimulation 42 versus (2) homogenous quantal variance and multiple inputs 44. As discussed elsewhere, the CV is independent of q only if the latter is the same for all contributing afferent cells; if all inputs are not stimulated reliably, the classical pre- and postsynaptic domains become indistinguishable. This holds even in the case of one celP6; for example, if changes in q and its variance are correlated (see also Ref. 33). It is also interesting that despite the high resolution provided by patch-clamp techniques the magnitude of the apparent quantum differed by a factor of three in the two studies (i.e. - 0 . 0 7 ns in Ref. 42 versus 0.21 ns in Ref. 15). Recently, recordings were obtained during LTP from pairs with a postsynaptic patch-clamp electrode °2, and shifts in both the amplitude histograms and the apparent rate of failures were reported. These changes were interpreted as signalling a presynaptic locus although there was also a relatively smaller increased quantal size (in comparison with an unusual 1000-2000% enhancement of synaptic strength) and, in addition, there were large oscillations in transmission. The latter, taken as pre-
Box 2. Recipe for a 'proper' quantal analysis 1 Presynaptic spike to ensure only one cell is firing reliably. 2 Noise level sufficiently low to isolate miniature events (quanta) and first peak of the histogram, with no overlap. 3 Resolution of single quantum amplitude, preferably by recording sufficiently close to postsynaptic site to eliminate 'cable filtering' (particularly dendritic cable filtering). 4 Direct data on possible variations in quantal amplitude at a single site.* 5 Morphological identification of number of potential release sites. 6 Independent evidence on whether p is similar or different at multiple release sites comprising a single connection.
*Saturation of postsynaptic receptor clusters may compromise interpretation of the data.
443
perspectives Concluding remarks Despite the recent interest in central synapses, the major concepts used still depend upon guidelines provided by early studies at the NMJ, with the main additions and perhaps differences being dependent upon structural features, which have not been fully investigated. Data reviewed here nevertheless indicate that divergence from this model 3° cannot be generalized to all central junctions, but may rather indicate specializations at given connections.
2 mM-Ca 2+ 1 mM-Mg 2+
A 15-
.~ z
lO
5
0
i
0
°°t 0
--
,
100 lf~
I
200
B. (1969) The Release of Neural Transmitter Substances, Charles C. Thomas 2 del Castillo, J. and Katz, B. (1954) J. Physiol. 124, 560-573 1 Katz,
0.5 raM-Ca 2.
100
200
Amplitude (pA)
Fig. 4. Evidence that inhibitory postsynaptic currents (IPSCs) are multiquantal in rat hippocampal slices. (A) Amplitude distributions of stimulus-evoked inhibitory currents obtained by whole cell patch-clamp recording in physiological saline. Several peaks, regularly spaced by about 21 pA, and fit by a sum of gaussian functions, stand out. (B) Only the first class of events, which represents single mlPSCs, remains when the probability of release, but not the quantal size, is lowered by high M g 2÷ and low Ca 2+. (Data from Ref. 18.)
synaptic in origin, again based on the CV method, in fact precluded quantal analysis. An opposing postsynaptic explanation was deduced 5° in other experiments where the CV, the method of failures, and a deconvolution constrained with a simple binomial model were compared. Minimal stimulation and cell pairs both yielded an apparent increase in q, the exact value of which differed, however, with the analysis used. Although the data were obtained with standard microelectrodes, there were peaks in the amplitude histograms of the evoked responses, lending credibility to the use of the constrained deconvolution. The intriguing fact is that, despite reservations about any one methodological approach, all the studies considered above were substantiated by independent internal checks that reinforced their primary, albeit opposing conclusions. This paradox may reflect differences in experimental conditions (such as the age of the material, protocols for producing LTP and recording methods), LTP expression then becoming a combination of preand postsynaptic determinants. As noted in Ref. 55, this notion is inherently attractive, as it would reinforce the unity of a synapse. 444
Selected references
3 Korn, H., Mallet, A., Triller, A. and Faber, D. S. (1982) J. Neurophysiol. 48, 679-707 4 Couteaux, R. and Pecot-Dechavassine, M. (1970) C.R. Acad. Sci. 271, 2346-2349 5 Heuser, J. E. and Reese, T. S. (1977) in Handbook of Physiology: The Nervous System (Sect. I, Vol. I, Part I), pp. 261-294, American Physiological Society 6 Korn, H., Triller, A., Mallet, A. and Faber, D. S. (1981) Science 213, 898-901 7 Triller, A. and Korn, H. (1982)J. NeurophysioL 48, 708-736 8 Akert, K., Pfenninger, K., Sandri, C. and Moor, H. (1972) in Structure and Function of Synapses (Papas, G. D. and Purpura, D. P., eds), pp. 67-86, Raven Press 9 Walmsley, B., Wienawa-Narkiewicz, E. and Nicol, M. J. (1985) J. Neurosci. 5, 2095-2106 10 Lin, J. W. and Faber, D. S. (1988) J. NeuroscL 8, 1313-1325 11 Korn, H. (1984) Exp. Brain Res. (Suppl. 9), 201-224 12 Korn, H. and Faber, D. S. (1990) J. Neurophysiol. 63, 198-222 13 Triller, A. and Korn, H. (1985) J. Neurocytol. 14, 177-192 14 Heuser, J. E. etal. (1979)J. CellBioL 81,275-300 15 Bekkers, J. M., Richerson, G. B. and Stevens, C. F. (1990) Proc. Nail Acad. Sci. USA 87, 5359-5362 16 Rang, H. P. (1981)J. Physiol. 311, 23-55 17 Collingridge, G. L., Gage, P. W. and Robertson, B. (1984) J. Physiol. 356, 551-564 18 Edwards, F. A., Konnerth, A. and Sakmann, B. (1990) J. Physiol. 430, 213-249 19 Ropert, N., Miles, R. and Korn, H. (1990) J. Physiol. 428, 707-722 20 Kuno, M. (1964) J. PhysioL 175, 81-99 21 Kuno, M. and Weakly, J. N. (1972) J. Physiol. 224, 287-303 22 Edwards, F. R., Redman, S. J. and Walmsley, B. (1976) J. Physiol. 259, 665-688 23 Jack, J. J. B., Redman, S. J. and Wong, K. (1981) J. Physiol. 321, 65-96 24 Redman, S. J. (1990) PhysioL Rev. 70, 165-198 25 Kullmann, D. M. (1989) J. Neurosci. Methods 30, 231-245 26 Clamann, H. P., Rioult-Pedotti, M. S. and LLischer, H. R. (1991) J. Neurophysiol. 65, 67-75 27 Solodkin, M., JimEnez, I., Collins, W. F., Mendell, L. M. and Rudomin, P. (1991) J. Neurophysiol. 65, 927-945 28 Walmsley, B., Edwards, F. R. and Tracey, D. J. (1988) J. NeurophysioL 60, 889-908 29 Edwards, F. R., Redman, S. J. and Walmsley, B. (1976) J. Physiol. 259, 689-704 30 Edwards, F. (1991) Nature 350, 271-272 31 Korn, H., Burnod, H. and Faber, D. S. (1987) Proc. NatlAcad. Sci. USA 84, 5981-5985 32 Faber, D. S. and Korn, H. (1988) J. Neurophysiol. 60, 1982-1999 33 Larkmann, A., Stratford, K. and Jack, J. (1991) Nature 350, 344-347 34 Faber, D. S. and Korn, H. (1988) Proc. NatlAcad. Sci. USA 85, 8708-8712 35 Faber, D. S., Funch, P. G. and Korn, H. (1985) Proc. Natl Acad. Sci. USA 82, 3504-3508 36 Seitanidou, T., Triller, A. and Korn, H. (1988) J. Neurosci. 8, 4319-4333 37 Somogyi, P., Takagi, H., Richards, J, G. and Mohler, H.
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Neuralmodelsof stereoscopicvision Randolph
B l a k e a n d H u g h R. W i l s o n
Human stereopsis remains an enigma: how does the brain match features between the left and right eye images and compute disparity between these matched features? Developments in computational neuroscience and machine vision have led to several models of human stereopsis that provide insight into possible mechanisms underlying this phenomenon. These models, reviewed in this paper, adopt one of three general strategies. One class of models employs cooperative interactions, whereby a unique solution to the matching problem emerges from excitatory and inhibitory interactions among binocular neural elements. A second class of models implements matching and disparity computation serially over multiple spatial scales. A third class relies on local, non-interacting computations performed in parallel to overcome speed limitations inherent in the other models. Considered together, these theoretical developments offer fresh insights concerning the actual neural concomitants of binocular stereopsis. Looking about the visual world, we see objects from two slightly different perspectives owing to the lateral separation of the eyes in the head. Evidently the brain is remarkably adept at combining these two monocular views, for binocular single vision and stereopsis occur effortlessly even when the two monocular views contain no discernible form information to guide the matching of the left and right eye images 1. Moreover, the brain is incredibly accurate in registering slight positional differences of image features from the left and right eyes, as evidenced by our keen sense of stereoscopic depth perception. How does the binocular visual system identify corresponding monocular features, measure positional disparities between those features and transform those measurements into a description of the three-dimensional layout of objects in the visual scene? TINS, Vol. 14, No. 10, 1991
A first glimpse of the actual neural hardware underlying binocular vision was provided in the late 1960s when physiologists began recording from individual neurons in the visual cortex of mammals with frontally placed eyes. Shortly after Hubel and Wiesel2 described the existence of binocularly innervated cortical cells, several laboratories 3'4 reported that many of these binocular cells in fact possessed receptive fields on non-corresponding areas of the two eyes. In other words, the optimum stimulus for activating these neurons would be an edge or surface marking located somewhere in depth other than the plane of fixation. By virtue of their disparity selectivity, these binocular neurons provided a plausible neural basis for stereopsis. This idea received further support from behavioral experiments demonstrating deficits in stereopsis in animals that lacked the normal complement of binocular cortical neurons 5'6 Following these initial exciting discoveries, other laboratories concentrated on measuring the degree of disparity selectivity among single binocular neurons 7, correlating those measures with cortical cell types 8 and searching for disparity-selective cells in extrastriate areas 9. Much of that work is reviewed elsewhere 1°. Despite this enduring interest in disparity processing by the brain, however, real progress in our understanding of the neural bases of stereopsis has come slowly, partly because of the absence of a theoretical context in which to frame physiological questions. Recent developments in computational neuroscience and machine vision have provided new theoretical insights into the nature of stereoscopic vision, in turn leading to important psychophysical discoveries concerning human stereopsis. This article reviews those theoretical and empirical developments, in the hope of stimulating a refined assault on the actual neural concomitants of stereopsis.
© 1991, EPsevierScience Publishers Lid, (UK) 0166- 2236/91/$0200
Randolph Blakeis at the Dept of Psychology, Vanderbilt University, Nashville, TN.77240, USA, and Hugh R. Wilson is at the Dept of Ophthalmology and VisualScience, Universityof Chicago, 939 E. 57th Street, Chicago, IL 60637, USA.
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