Unveiling synaptic plasticity: a new graphical and analytical approach

E.C. Gilmore et al. – DNA breaks in the developing CNS

in the central nervous system of transgenic mice. Science 257, 404–408 27 Abeliovich, A. et al. (1992) On somatic recombination in the central nervous system of transgenic mice. Science 257, 404–410 28 Kerr, J.F. et al. (1972) Apoptosis: a basic biological phenomenon

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with wide-ranging implications in tissue kinetics. Br. J. Cancer 26, 239–257 29 Wyllie, A.H. (1980) Glucocorticoid-induced thymocyte apoptosis is associated with endogenous endonuclease activation. Nature 284, 555–556

TECHNIQUES Unveiling synaptic plasticity: a new graphical and analytical approach John D. Clements and R. Angus Silver Short-term synaptic plasticity has a key role in information processing in the CNS, whereas memories can be formed through long-lasting changes in synaptic strength.Despite the importance of these phenomena, it remains difficult to determine whether a synaptic modulation is expressed at a presynaptic or postsynaptic site. This article describes a new approach that, in its simplest form, can identify the site of expression by direct graphical means.A more-sophisticated form of the technique can quantify functional synaptic properties and determine which of these properties is altered following a modulation of synaptic strength. Trends Neurosci. (2000) 23, 105–113

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LUCTUATIONS in the amplitude of a synaptic response were first reported at the neuromuscular junction (NMJ)1. The similarity between the incremental amplitude of these fluctuations and the amplitude of spontaneous miniature synaptic events2, led to the development of the ‘quantal’ hypothesis of transmitter release1. Quantal theory was subsequently extended to synapses in the CNS, and has been used in many studies of synaptic function and plasticity (reviewed in Refs 3–6). A generalized version of quantal theory7,8 underlies the simple experimental, graphical and analytical techniques described in this article. Three parameters describe transmission at a typical synapse: the average amplitude of the postsynaptic re– sponse to a packet of transmitter (Q), the number of independent transmitter release sites that make up the synaptic contact (N) and the average probability of – transmitter release across sites (Pr). Together these three parameters define the strength of a synaptic connection. – – Pr summarizes presynaptic efficacy and Q summarizes postsynaptic efficacy. A modulation of synaptic strength must alter one or more of these parameters, and the mechanism that produces the modulation will determine which of the parameters is altered. For example, an antagonist that binds to postsynaptic receptors will – – reduce Q without altering N or Pr. The mechanism underlying a synaptic modulation can therefore be investigated by monitoring changes in these parameters. In principle, it is possible to extract the three synaptic – – parameters, Q , Pr and N from the pattern of synaptic amplitude fluctuations, but this has proved difficult in practice. Several fluctuation-analysis techniques have been developed (reviewed in Refs 3–6), but they all require restrictive assumptions about the synaptic con– nection and tend to break down when Q is small relative to the recording noise. The technical difficulties 0166-2236/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved.

associated with existing techniques have been discussed extensively9–16. The experimental, graphical and analytical approach described in this article simplifies the investigation of synaptic behaviour by using a recently developed7,8 synthesis and extension of existing techniques1,15,17–24. It requires fewer assumptions and is less sensitive to recording noise than previous techniques. A key feature of this new approach is that it explores the synaptic amplitude fluctuations at several different release probability settings, thereby providing useful additional information about synaptic function. Another important characteristic is that the analysis incorporates nonuniform presynaptic and postsynaptic properties. This permits the analysis to be applied with confidence, both to single-fibre synaptic inputs and to compound inputs where several presynaptic axons are stimulated. The general approach is very simple and can be implemented as a purely graphical technique using commercially available software.

Construction and visual interpretation of a variance–mean plot Postsynaptic currents (PSCs) are recorded under several different release probability conditions (typically – 20–200 PSCs under each condition; Box 1). Pr can be 21 21 adjusted by altering the Ca to Mg ratio or by adding cadmium (Cd21) to the extracellular solution. The variance and the mean of the PSCs are calculated during a stable recording epoch after wash-in of each solution, and the variance is plotted against the mean (Box 1). The general form of the variance–mean (V–M) plot is para– bolic. Its initial slope is related to Q , its degree of cur– vature is related to Pr and its size is related to N. A postsynaptic modulation of synaptic strength will change the initial slope of the V–M parabola, a presynaptic PII: S0166-2236(99)01520-9

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John D. Clements is at the Division of Biochemistry and Molecular Biology, Australian National University, Canberra, ACT 0200, Australia, and R. Angus Silver is at the Dept of Physiology, University College London, London, UK WC1E 6BT.

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Box 1. Construction and analysis of a variance–mean plot In order to construct a variance–mean (V–M) plot, synaptic responses are recorded at several different average release – probability (Pr) settings (Fig. Ia). At each setting, 20–200 responses are recorded, their amplitudes are measured and the mean and variance of the amplitudes are calculated. The baseline noise variance is subtracted from the synaptic variance and the synaptic variance is then plotted against – the mean at each Pr setting (Fig. Ib). The general form of the V–M relationship can be understood as follows. When – Pr is low (,0.1), most sites do not release transmitter and the trial-to-trial variance of postsynaptic current (PSC) – amplitude is low (Fig. Ia, blue). When Pr is around 0.5, the number of sites that release transmitter varies widely from trial-to-trial, and the variance is high (Fig. Ia, black). When – Pr is close to 1.0, almost all sites release transmitter after every stimulus, the PSC amplitude approaches its maximum level, and the variance is again low (Fig. Ia, red). Thus, the

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where y is the PSC variance, and x– is the PSC mean amplitude. The free parameters, A and B, are adjusted to fit the parabola to the V–M plot optimally, and are then used to calculate the average synaptic parameters, – Qw 5 A/(1 1 CVI2) (2)

Slope = Qw

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V–M relationship plotted over a range of release probabilities is approximately parabolic (Fig. Ib). Useful information can be obtained by visual inspection of the V–M – plot. The degree of curvature is related to the maximum Pr setting, as outlined above. In addition, the initial slope of the parabola is related to postsynaptic responsiveness, and the size of the parabola is related to the number of active release sites or terminals. Thus, the V–M plot can be used as a simple graphical tool for investigating synaptic function and modulation. The exact form of the V–M relationship can be determined from theoretical considerations. The development of the equations that predict its shape will not be presented in this article (see Refs a,b for details). These equations are remarkably simple, and they permit a quantitative inves– tigation of synaptic behaviour. When Pr is varied over a low range (,0.3) the V–M relationship is approximately linear, with a slope that is equal to the average amplitude – of the synaptic response to a packet of transmitter (Qw). If – Pr is increased to a moderate level (<0.7), the V–M relationship can be approximated by a simple parabola. Thus, a V–M plot can be analysed either by fitting a straight line or by fitting a simple parabola over the low-to-moderate – – Pr rangea. When Pr is increased towards 1.0 and release probabilities are nonuniform, the V–M relationship will deviate from the parabolic form and become skewed (the simulated V–M plot in Fig. Ib is not skewed because the release probabilities were chosen to be uniform). Under these conditions, the skewed plot can be analysed by fitting a more-complex equation (Box 2)b. For many synaptic pre– parations, Pr will be restricted to the low-to-moderate range and a simple linear or parabolic fit will be appropriatea. The equation for a parabola is y 5 A x– – B x–2 (1)

– Prw 5 x– (B/A) (1 1 CVI2)

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Fig. I. Simulated EPSC data demonstrating the variance–mean analysis technique. (a) EPSC peak amplitudes are plotted against event number. The simulation assumed release probabilities were uniform across 50 independent release sites, and quantal amplitude was 20 pA at each site. Moderate quantal variability was included – (CVI 5 0.2). Average release probability (Pr) was set to three different values during three separate epochs, each of 190 events. The release – – probability values were low P r (0.02; blue), mod P r (0.5; black) and – high Pr (1.0; red). (b) The variance of the EPSC amplitudes was plotted against mean amplitude for each epoch. The variance–mean plot was then fitted with a simple parabola. The initial slope of the fitted – curve provides an estimate of the average quantal amplitude (Qw).

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CVI is the coefficient of variation of the PSC amplitude at an individual release site (typically 0.2–0.4). It appears in these equations as a minor (5–15%) adjustment term. The – – ‘w’ subscript indicates that Qw and Prw are weighted averages that emphasize terminals with higher release probabilities and larger postsynaptic amplitudes. The rate of curvature of the variance–mean plot can be used to place a lower limit (Nmin) on the number of independent release sites, Nmin 5 1/B

(4) – If the V–M plot is approximately linear, then Prw is low (,0.3) and the plot can be analysed by fitting the equation for a line, y 5 A x– (5) – – This permits an estimate of Qw from Eqn 2, but Prw and Nmin cannot be estimated under these conditions. References a Reid, C.A. and Clements, J.D. (1999) Postsynaptic expression of long-term potentiation in the rat dentate demonstrated by variance-mean analysis. J. Physiol. 518, 121–130 b Silver, R.A. et al. (1998) Locus of frequency-dependent depression identified with multiple-probability fluctuation analysis at rat climbing fibre-Purkinje cell synapses. J. Physiol. 510, 881–902

J.D. Clements and R.A. Silver – Variance–mean analysis

Quantitative analysis of a V–M plot The graphical approach outlined above can be made more quantitative by fitting a V–M plot with an equation that incorporates one or more of the synaptic – – parameters, Q , Pr and N (Boxes 1 and 2). The locus of expression of a modulation can be determined by comparing synaptic parameters obtained before and after the modulation. This quantitative approach also permits a comparison to be made between the functional and morphological parameters of a particular synapse, or between the functional characteristics of different synapses. A V–M plot can be analysed by fitting either a line or – a simple parabola over the low-to-moderate Pr range8, or by fitting a more-complex equation when data are – also available at higher Pr values7. Analysis of V–M plots

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modulation will change the degree of curvature, whereas a change in the number of release sites will alter the size of the parabola. Thus, the locus of expression can be determined by visual comparison of two V–M plots recorded before and after the modulation. Figure 1 shows a simulation of the three standard forms of synaptic modulation. Each produces a distinctive change in the shape of the V–M curve. A purely postsynaptic modulation is the easiest to identify, because it alters – the V–M plot at all Pr settings. The V–M plots for a purely presynaptic modulation, and for an increase in – functional sites, are similar at lower Pr settings. – However, when Pr is increased above 0.5, the two V–M plots diverge, which makes it possible to identify the modulatory mechanism (Fig. 1). Experimental case studies, which demonstrate V–M analysis of the three standard forms of synaptic modulation, are presented in later sections. Visual inspection of a V–M plot can also be used to investigate short-term plasticity even when several different modulatory mechanisms are involved. When two presynaptic stimuli are delivered within a few milliseconds of one another, the response to the second stimulus is often smaller than the response to the first stimulus. This phenomenon is known as paired-pulse depression (PPD), and could be due to a presynaptic mechanism such as vesicle depletion, a postsynaptic mechanism such as receptor desensitization, or a combination of these factors. Both of these hypothetical – mechanisms will be activated progressively as Pr is increased. They will be superimposed on paired-pulse facilitation (PPF), which acts at a presynaptic site. In Fig. 2, a V–M plot is constructed for both the first and second response to a paired-pulse stimulus paradigm. Three different models, which incorporate PPF and PPD, were used to simulate the fluctuating paired-pulse responses. In the first model, the mechanism of PPD was postsynaptic receptor desensitization; in the second model, presynaptic and postsynaptic mechanisms contributed equally to PPD; and in the third model, the mechanism of PPD was presynaptic vesicle depletion. The V–M plot for the first pulse followed the standard parabolic trajectory, but the plot for the second response followed a characteristic trajectory depending on the mechanism(s) underlying PPD (Fig. 2). A recent study of the giant calyceal synapse in the rat cochlear nucleus, produced a paired-pulse V–M plot that was consistent with a mixed presynaptic and postsynaptic mechanism of PPD (S. Oleskevich, J.D. Clements and B. Walmsley, unpublished observations).

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Fig. 1. The locus of expression of a synaptic modulation can be determined using V–M analysis. The shape of a V–M (variance–mean) plot changes in a characteristic way depending on the site of modulation. V–M plots were simulated, before (black diamonds) and after three different types of modulation: 50% presynaptic potentiation (red circles); 50% postsynaptic potentiation (black circles); or 50% potentiation via an increase in the number of release sites (blue circles). A nonuniform presynaptic mechanism was simulated by doubling Pr (the probability of transmitter release) at half the release sites. A nonuniform postsynaptic mechanism was simulated by doubling Q (the amplitude of the postsynaptic response to a packet of transmitter) at half the sites. Modulation via an increase in N (the number of independent transmitter release sites that make up the synaptic contact) was simulated by a 50% increase in the number of release sites. Each V–M point was calculated from an epoch of 100 simulated postsynaptic currents (PSCs). A single simulation run consisted of four epochs, each with a different Pr setting. V–M plots represent the ensemble average of plots from 20 simulation runs. The standard errors of the variance are so small that the bars are obscured by the symbols.

can be implemented using any scientific graphics software that incorporates a general curve-fitting feature. The two different equations for fitting the V–M plot were developed separately and independently. The technique was termed ‘variance–mean analysis’ in one report8 and ‘multiple-probability fluctuation analysis’ in the other7. It will be referred to as V–M analysis in this article. This analysis represents an extension and generalization of several previously reported methods for analysing synaptic amplitude fluctuations1,11,15,19,22–24, but with several important experimental and theoretical TINS Vol. 23, No. 3, 2000

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Synaptic connections with nonuniform release probabilities (Pr) and quantal amplitudes (Q) behave differently from those with uniform parameters. For example, they have a variance–mean (V–M) relationship with a shape that deviates from the parabolic when the average release probability – (Pr) is in the moderate to high range. The simplest model that describes transmitter release at N independent sites and incorporates nonuniform Pr is the compound binomial. This model assumes uniform Q, and can be defined in terms of the variance of the synaptic amplitude (y), the mean synaptic amplitude (x–) and the coefficient of variation of the Pr distribution (CVPr): y = Qx −

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Fig. 2. V–M plots can distinguish between different mechanisms of PPD. EPSC amplitudes were simulated under a range of release probability conditions, and the variance–mean (V–M) relationship was plotted for both the first response (black circles) and second response (coloured circles) to a paired-pulse stimulus paradigm. Three different models were used in the simulations. All three models incorporated both PPF (paired pulse facilitation) and PPD (paired pulse depression). PPD dominated – under high P r conditions (the average probability of transmitter release across sites) and reached a maximum of 70% in all three models. In the first model, the mechanism of PPD was purely postsynaptic (receptor desensitization, blue circles); in the second model, presynaptic and postsynaptic mechanisms contributed equally to PPD (purple circles); and in the third model, the mechanism of PPD was purely presynaptic (vesicle depletion, red circles). The V–M plot for the second response followed a characteristic trajectory, depending on the mechanism underlying PPD.

innovations. The mathematical foundations of the V–M method are closely related to non-stationary noise analysis of ion-channel function20 (reviewed in Ref. 25).

– is low or moderate Analysis of V–M when P r – When a V–M plot is approximately linear, Pr is in the low range (,0.3) and the plot can be analysed by fitting the equation for a straight line8 (Box 1). This per– mits an estimate of average quantal amplitude, Qw, but – Pr and N cannot be estimated under these conditions. – The ‘w’ subscript indicates that Qw is a weighted average that emphasizes terminals with higher release probabilities and larger postsynaptic amplitudes. The weighted average will be slightly larger than the arithmetic – average, Q. When a V–M plot curves over and approaches or reaches a plateau but does not descend back towards 108

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As CVPr has not been defined experimentally, nonuniform Pr was incorporated into the model by making use of a family of continuous functions. These functions mimic the distribution of Pr across release sites, and describe how the – distribution might change when Pr is varied. The beta funca tion was chosen because it is very flexible and can take a wide range of different shapes (Fig. Ib). In addition, the shape of the simulated Pr distributions can be defined with just two parameters, a and b. With this approach, CVPr can be – expressed simply as a function of Pr, and a (Fig. Ic): CV Pr =

0

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By substituting for CVPr in Eqn 1 and expressing in terms of – x– rather than Pr (see Eqn 5) we have: y = Qx −

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The level of dispersion in Pr is thus reduced to a single parameter, a. This model includes the simple binomial as one of its solutions (a→`). Synaptic behaviour and the V–M relationship are also affected by nonuniform quantal size. Quantal variance that arises from individual release sites (intrasite or type I) – increases linearly with Pr (and thus x–), whereas variance arising from differences in Q at different sites (intersite or type II) has the same shape as the V–M relationship (Fig. Id). These two types of quantal variability, can be incorporated into the model by adding two coefficient of variation terms (CVI and CVII) to Eqn 3:  Qx 2 (1 + a)  y = Qx −  1 + CV II2 + QxCV I2 x + NQa  

(

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The advantage of this approach is that it allows estimation of the mean quantal parameters and describes the full V–M relationship for synapses with nonuniform parameters (Fig. Id). Although it has a more-complex form than the simple parabola, it has only one additional free parameter (a), because CVI and CVII can be determined indepen-

– the x-axis, the maximum Pr is likely to be in the moderate range (0.3 to 0.7, for example; see Fig. 1). The plot can then be analysed by fitting it with a parabola8. The – – average synaptic parameters, Qw and Prw can be determined from the fitted parabola using the equations in Box 1. In addition, the rate of curvature of the variance– mean parabola can be used to place a lower limit (Nmin) on the number of independent release sites. When a V–M plot passes through a maximum and – descends back towards the x-axis, the maximum Pr is

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Fig. I. Effect of nonuniform synaptic parameters on the variance–mean relationship. (a) Upper trace shows the theoretical V–M relationship for a synaptic connection with a uniform quantal size (Q) of 210 pA, and uniform release probability (Pr) at ten independent release sites (N). The lower trace shows the V–M relationship for the same synaptic parameters when Pr is nonuniform (calculated with Eqn 3). Note the rela– tionships are only similar when the mean release probability (Pr) is low. (b) Beta distributions were used to approximate nonuniform Pr. Solid lines show three examples from a family of beta distributions with the same a value. The dotted line shows the gamma distribution (scaled by two) that described the Pr distri– bution at cultured hippocampal synapses d. The beta function with P r 5 0.17 (a 5 1.76, b 5 8.52) approximates this distribution well. (c) The relationship between the coefficient of variation of the beta-function– generated Pr distributions and Pr for three different levels of dispersion in Pr. Note that the CVPr (the coefficient – of variation of the Pr distribution) is always constrained to zero when Pr 5 1. (d) The solid line shows the full – V–M relationship for a synaptic connection with nonuniform Q and nonuniform Pr [from Eqn 4; Q , N and a as in part (a)]. The variance contributed from intrasite (CVI 5 0.35) and intersite (CVII 5 0.35) quantal variation are indicated by the dotted and broken lines below. Note the initial slope and maximum variance – is larger than the uniform case shown in (a) and there is a substantial variance remaining at P r 5 1.

dentlyb,c. The parameter a is inversely related to the dispersion in Pr and thus to the skew of the V–M plotc: when a .10 the V–M relation– ship is not skewed. The parameters Q and N are estimated by optimally fitting Eqn 4 to the V–M data. Release probability is then calculated as Pr =

Pr = 0.68

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This approach requires two assumptions that are not discussed in the main text. The first is that real Pr distributions can be approximated with a family of beta functions. We believe this is a useful approximation because beta functions make plausible predictions about how – the Pr distribution might change as Pr is varied. In particular, these functions are bound by 0 and 1, as are release probabilities. CVPr will – therefore be constrained to zero at Pr 5 1. Furthermore, a beta distribution closely approximates a real Pr distribution measured with FM1–43 (Ref. d; Fig. Ib). This assumption can be tested by comparing – – Q with the initial slope, and NQ with the maximal synaptic response – estimated from linear extrapolation of the high Pr region. The second – – assumption is that Q does not change with Pr. This could occur if there was a strong correlation between Q and Pr (Ref. c), or if postsynaptic – receptor occupancy increased with Pr, owing to transmitter spilloverb,e f or multiquantal release . At the climbing fibre, worst-case simulations show a positive correlation can result in an underestimation of N of – – up to 40%, an estimate of Q that reflects the low Pr values and an – underestimate of a (Ref. c). However, Pr is relatively insensitive to the presence of correlation. In reality these errors are likely to be small, especially at synaptic connections where intersite variability is smaller

likely to be in the high range (.0.7). If the release probabilities are relatively uniform across release sites, then a simple parabola will fit the V–M plot well, and the equations in Box 1 remain valid. However, if the V–M plot deviates from a simple parabola then a more-complex equation (introduced in Box 2) should be used. The ability of V–M analysis to extract synaptic parameters and to distinguish between different mechanisms of synaptic modulation is demonstrated in Figs 1 and 3.

than intrasite variationg,h,i, because the correlation between Pr and Q – will be weak. Changes in Q that are due to changes in receptor occub pancy can be tested directly with low-affinity receptor antagonistsi,j. – If the level of antagonism is similar at low and high Pr then changes in receptor occupancy should be small.

a Bennett, M.R. and Lavidis, N.A. (1979) The effect of calcium ions on the secretion of quanta evoked by an impulse at nerve terminal release sites. J. Gen. Physiol. 74, 429–456 b Silver, R.A. et al. (1996) Non-NMDA glutamate receptor occupancy and open probability at a rat cerebellar synapse with single and multiple release sites. J. Physiol. 494, 231–250 c Silver, R.A. et al. (1998) Locus of frequency-dependent depression identified with multiple-probability fluctuation analysis at rat climbing fibre-Purkinje cell synapses. J. Physiol. 510, 881–902 d Murthy, V.N. et al. (1997) Heterogeneous release properties of visualized individual hippocampal synapses. Neuron 18, 599–612 e Barbour, B. and Hausser, M. (1997) Intersynaptic diffusion of neurotransmitter. Trends Neurosci. 20, 377–384 f Tong, G. and Jahr, C.E. (1994) Multivesicular release from excitatory synapses of cultured hippocampal neurons. Neuron 12, 51–59 g Forti, L. et al. (1997) Loose-patch recordings of single quanta at individual hippocampal synapses. Nature 388, 874–878 h Frerking, M. et al. (1995) Variation in GABA mini amplitude is the consequence of variation in transmitter concentration. Neuron 15, 885–895 i Liu, G. et al. (1999) Variability of neurotransmitter concentration and nonsaturation of postsynaptic AMPA receptors at synapses in hippocampal cultures and slices. Neuron 22, 395–409 j Diamond, J.S. and Jahr, C.E. (1997) Transporters buffer synaptically released glutamate on a submillisecond time scale. J. Neurosci. 17, 4672–4687

A realistic model synapse that incorporates non-uniform release probabilities and quantal amplitudes was used to generate fluctuating synaptic currents. Three types of modulation were modelled: an increase in release probability, an increase in postsynaptic responsiveness and an increase in the number of active terminals. The – – parameters, Q w and Prw were estimated by fitting a parabola to the V–M plots from each of the simulated experiments (n 5 20). Figure 3 shows the average values – – for Q w and Prw that were obtained before and after the TINS Vol. 23, No. 3, 2000

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three different types of modulation (same data as Fig. 1). – As expected, postsynaptic modulation increased Qw – whereas presynaptic modulation increased Prw. It is relatively easy to use V–M analysis to test for a purely postsynaptic modulation. Only two or three epochs are required under low-release-probability con– ditions (Pr,0.3). The V–M plot is linear under these – conditions and its slope provides an estimate of Qw. A postsynaptic modulation should alter the slope of the V–M plot, whereas other types of modulation should not. This was confirmed in a series of experiments in the rat hippocampal-slice preparation8. EPSCs were recorded in dentate granule neurones before and after applying each of three different synaptic modulators: (1) 6-cyano7-nitroquinoxaline-2,3-dione (CNQX, 0.4 mM), a competitive antagonist at postsynaptic AMPA receptors; (2) baclofen (4 mM), a presynaptic modulator that acts via GABAB receptors; and (3) an increase in the stimulus strength to activate additional presynaptic terminals. As expected, CNQX reduced the slope of the V–M plot – (and hence Qw) to the same extent that it reduced aver– age EPSC amplitude (Fig. 4a). By contrast, Qw was not affected by baclofen or by increased stimulus strength (Fig. 4b,c,d).

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Fig. 3. Synaptic parameters reveal the locus of expression of a modulation. A realistic model synapse incorporating nonuniform release probabilities and quantal amplitudes was used to generate fluctuating synaptic currents. Postsynaptic currents (PSCs) were generated in four separate epochs, each with a different Pr (the probability of transmitter release) setting, and the variance and mean were calculated for each epoch (100 events per epoch). Twenty experiments were simulated for – each type of modulation. The parameters, Qw (weighted average quantal – amplitude) and P rw (weighted average probability of transmitter release across sites) were estimated by fitting a simple parabola to each variance– mean plot resulting from a single simulation run. This produced 20 estimates for each parameter under each simulated recording condition. The – – graphs show the average estimates for Qw and P rw that were obtained before and after the three different types of modulation (same data as in Fig. 1). The broken line shows the true values of these parameters before – – modulation. A 50% presynaptic potentiation (increased Pr) increased Prw – without affecting Qw , whereas a 50% postsynaptic potentiation (increased – – Q) increased Q w without affecting P rw.

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Further insights into synaptic behaviour are possible if data are available over a wider range of mean release probabilities. A full description of the synaptic behaviour can be made at nonuniform synaptic connections, – – with mean quantal parameters (Q, Pr and N) being estimated, rather than (a) (b) the weighted means. This estimation Baclofen CNQX 100 can be achieved by fitting the V–M 400 plot with an equation for a modified parabola (Box 2). However, a larger 50 200 number of experimental observations are required to estimate quantal parameters reliably with this ap0 0 proach. This is because the modified 30 100 0 200 parabola equation has an additional 0 60 Mean amplitude (pA) Mean amplitude (pA) free parameter and will produce nonunique or unrealistic solutions when the V–M plot is too noisy. The presence of nonuniform re(c) (d) lease probability (Pr) tends to reduce Increased 1 50 synaptic variance, having a minimal stimulus – effect at low Pr but becoming more pronounced at higher probabilities 25 (Box 2). This causes the V–M relationship to become skewed, with the 0 degree of distortion depending on 0 the level of dispersion in Pr. Al0 10 20 30 though nonuniform Pr is a compliMean amplitude (pA) cated property because it changes with mean release probability, it can trends in Neurosciences be represented by a single paramFig. 4. V–M analysis can identify the locus of synaptic modulation when applied to EPSCs recorded from dentate eter (a; Box 2), and this can be estigranule cells. (a) V–M (variance–mean) plot before (black circles) and after (grey circles) the application of 6-cyano- mated from the V–M plot. Non7-nitroquinoxaline-2,3-dione (CNQX) (0.4 mM), a competitive antagonist at postsynaptic AMPA receptors. CNQX uniformity in Q can occur as vari– reduced the slope of the plot and hence Q w (weighted average quantal amplitude), which is consistent with a postsy- ability at an individual site (intrasite) naptic modulation. (b) V–M plot before (black circles) and after (grey circles) the application of baclofen (4 mM), which or variation across sites (intersite) or – reduces the probability of vesicle release from the presynaptic terminals. There was no change in Q w , which is consisboth14. Although these two comtent with a presynaptic modulation. (c) V–M plot before (black circles) and after (grey circles) an increase in the strength – of the stimulus to the presynaptic axons. There was no change in Qw, which is consistent with a presynaptic modulation. ponents affect the V–M relationship – (d) Average change in Q w after the application of CNQX (n 5 5), baclofen (n 5 5) and an increase in stimulus strength differently (Box 2), they both in(n 5 5). Error bars indicate SEM and the broken line indicates the true value of this parameter before modulation. Only crease the initial slope of the V–M – relationship and must therefore be CNQX produced a significant change in Q w. Modified, with permission, from Ref. 8.

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– taken into account if Q is to be determined. Virtually the whole range of release probability can be studied at the cerebellar climbing-fibre synapse by recording EPSCs at low frequency (0.033–0.2 Hz) and by using a range of extracellular Ca21, Mg21 or Cd21 – concentrations to raise or depress Pr (Fig. 5a). Typically, about 50 climbing-fibre EPSCs were recorded under – each of 6–8 Pr conditions. Plots of V–M were then constructed for each individual synaptic connection, and quantal parameters were extracted from the plots. Direct measurement of climbing-fibre quanta elicited in the presence of Sr21 (Fig. 5b) gave a peak conductance of (0.55 nS), simi– lar to the value of Q estimated by fitting the V–M data (0.5 nS). Analysis at the climbing-fibre input also showed the presence 500 release sites – with a Pr close to unity at low frequencies (0.9 at 0.033Hz). This number of release sites is similar to the readily releasable pool at the giant Fig. 5. V–M analysis reveals functional synaptic properties and identifies the locus of synaptic modulation at the calyx synapse, when estimated using climbing-fibre–Purkinje-cell synapse. (a) The upper trace shows the average climbing fibre EPSC recorded at 230 mV different methods26,27. Some fibres in 2 mM Ca21 at 0.2 Hz and 3 Hz. The lower trace shows the variance–mean (V–M) plot for the same cell. The solid had nonuniform Pr (Box 2) with a circles show data recorded at 0.2 Hz and triangles show data recorded at 3 Hz. Each data point was calculated from 21 21 that set the mean probability of release. The open circle coefficient of variation7 comparable a series of EPSCs recorded in different Ca and Mg solutions shows the maximal release probability (0.033 Hz in high Ca21). The fit of the equation for a skewed parabola (Box 2), with that measured in hippocampal when the variation of the PSC (postsynaptic current) amplitude at an individual release site (CVI ) is zero (solid lines), neurones with FM1–43 (Ref. 28). gave similar parameter estimates at 0.2 Hz (Q 5 0.56 nS, N 5 313, a 5 10.7; 0.033 Hz point included) and 3 Hz The ability of the V–M technique (Q 5 0.53 nS, N 5 348; a constrained to be same as 0.2 Hz fit), which indicated that the frequency-dependent depression to detect changes in quantal param- of the EPSC was due to a reduction in P– (the average probability of transmitter release across sites). (b) The upper panel r eters was tested by changing the post- shows the EPSC elicited in the presence of Sr21, which causes desynchronization of the release of quanta. The solid horisynaptic responsiveness using a sub- zontal bar shows the analysis window, and the histogram shows the amplitude distribution of miniature EPSCs (open maximal concentration of CNQX. bars) and the background noise (filled bars) collected from the same cell. The mean miniature EPSC amplitude was 0.56 nS – Similar estimates of N and Pr were and the CV of the distribution was 0.39, which represents the total quantal variation at this connection. (c) V–M data obtained from V–M data in control expressed in terms of CV for control experiements and experiments carried out in the presence of 6-cyano-7-nitro(CNQX; 1 mM). CNQX reduced the synaptic amplitude but did not alter the CV at several different experiments and in experiments quinoxaline-2,3-dione – – for N in control experiements and experiments carried out in carried out with CNQX, but Q was Pr values. Fitting a multinomial model gave similar estimates – the presence of CNQX. The fractional reduction of Q was similar to the fractional reduction of EPSC amplitude indicating substantially reduced, as expected a purely postsynaptic locus of action of CNQX. (d) Relationship between Pr and steady-state stimulation frequency for (Fig. 5c). The fractional reduction in climbing fibres in 2 mM Ca21 at room temperature. Abbreviations: a, an inverse measure of the dispersion in Pr across sites – – Q matched the reduction in EPSC (see Box 2); N, number of independent release sites; Q , the average response to a packet of transmitter. Modified, with amplitude, which indicates a purely permission, from Ref. 7. postsynaptic locus for the action of CNQX. Analysis of V–M was used to investigate the locus of vation of active dendritic conductances and the octhe profound frequency-dependent depression observed casional failure of the stimulus to excite a presynaptic at the climbing fibre. Comparison of the V–M plots axon. Standard precautions can be taken to guard obtained at 0.2 Hz and 3 Hz shows that they overlie each against these possibilities. Series resistance should be other, have a similar initial slope but a reduced maximal monitored throughout the experiment, the stimulus current at 3 Hz (Fig. 5a). Fitting each plot gave similar intensity should be set well above threshold for acti– estimates for Q and N. Thus, the frequency-dependent vation of the input fibres and the threshold should be – depression is caused by a reduction in Pr. Examination of rechecked periodically. Stability of the PSC amplitude depression at other frequencies (10 Hz) also showed a can be tested statistically (for example, with the presynaptic locus and allowed the relationship between Spearman rank correlation test) with commercial soft– stimulation frequency and Pr to be quantified (Fig. 5d). ware packages. Active conductances can be inhibited by including caesium ions and QX314 in the pipette Practical considerations solution. Progressive depression of the synaptic reWhen constructing a V–M plot, the variance and sponse can be difficult to avoid, especially under high mean must be calculated over an epoch where the re- release probability conditions8,29. If the depression during cording conditions are stable. Unfortunately, a number an epoch is gradual, it is possible to estimate the variof processes can cause the synaptic variance to be over- ance after subtracting a regression line (S. Oleskevich, estimated. These include depression or rundown of the J.D. Clements and B. Walmsley, unpublished obsersynaptic response, a change in the series resistance, acti- vations). However, if irreversible rundown of more than TINS Vol. 23, No. 3, 2000

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Acknowledgements The authors’ research is supported by an ARC Senior Fellowship from the Australian Research Council (J.D.C.) and an RCDF from the Wellcome Trust, UK (R.A.S.). The authors thank Mark Farrant and Sharon Oleskevich for useful comments on the manuscript.

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20% occurs, this could complicate interpretation of the resulting V–M plot. A relatively long stable recording is required to collect the data for a V–M plot. The length of time that is needed will depend on the synapse and the goals of the experi– ment. If the low-to-moderate Pr analysis is to be used, then 3–4 epochs before and 3–4 epochs after a modulation of synaptic strength are sufficient (Figs 1 and 3). The simulations in Fig. 3 revealed that an epoch length of 100 events gave reliable results, so a total of 800 events would be required for a complete experiment. This corresponds to about 35 min of stable recording, assuming a stimulus frequency of 0.5 Hz and assuming the solution can be completely exchanged in 1 min. Experiments would take longer than this at the lower frequencies (0.1–0.5 Hz), which are necessary at some synapses to prevent rundown. Additional stable epochs (6–8) are required to define a more-complete V–M plot – – for estimating Q , Pr and N (Box 2). The reliability of each point on the plot depends on the number of events per epoch. The V–M method will be severely compromised if fewer than 20 events per epoch are collected. Although collecting data at higher frequencies is possible at some synapses, it might complicate the analysis because it could introduce temporal correlations in the synaptic amplitudes. At synapses with – intrinsically low Pr, raising release probability above 0.5 might be difficult, and paired or multi-pulse protocols could be necessary to facilitate the synapse. The equations that estimate the functional synaptic parameters contain correction terms for the variation of the PSC amplitude at an individual release site (CVI) and the variation between release sites (CVII) (Boxes 1 and 2). Total quantal variability (that is, intrasite and intersite) can be measured at a single synaptic input from asynchronous events elicited in the presence of Sr21 (Fig. 5b)7,30. If measurements from single release sites are available, CVI can be determined directly31–34. Alternatively, an upper limit of CVI can be estimated from – the variance remaining at the maximal Pr for the elicited EPSC (Fig. 5a; Box 2). Typical values of CVI and CVII produce only minor corrections. For example, a value of 0.3 could be assumed for both parameters without introducing a large systematic error. Some assumptions and simplifications are required to describe the functional properties of a synaptic input using a small number of parameters. The most basic of these are that quanta are independent and sum linearly, – – and that Q , N and Pr are stable with time. For analysis – of moderate and high Pr ranges it is also assumed that – Q does not change as a function of Pr, which could occur if these two parameters were strongly correlated7 or if multi-vesicular release occurs at a single site (Box 2). However, this is not a problem if a uniform presynaptic modulation is achieved, as has been shown at hippocampal synapses where Cd21 acts uniformly at – all terminals in the low Pr range29. (Software modules that assist with V–M analysis have been written by the authors and can be downloaded from http://jcsmr. anu.edu.au/neurophys/variance_mean.sit. In addition, see http://www.axon.com/CN_AxoGraph4.html.)

Concluding remarks A new method for identifying the locus of expression of synaptic plasticity and for estimating functional synaptic parameters has been developed. The method is easy to apply, because it requires little or no mathTINS Vol. 23, No. 3, 2000

ematical analysis and will work even when synaptic properties are nonuniform. It is hoped that V–M analysis will prove to be a useful tool for understanding the functional basis of synaptic behaviour and diversity. Selected references 1 del Castillo, J. and Katz, B. (1954) Quantal components of the end plate potential. J. Physiol. 124, 560–573 2 Fatt, P. and Katz, B. (1952) Spontaneous subthreshold activity at motor nerve endings. J. Physiol. 117, 109–128 3 Redman, S.J. (1990) Quantal analysis of synaptic potentials in neurons of the central nervous system. Physiol. Rev. 70, 165–198 4 Voronin, L.L. (1994) Quantal analysis of hippocampal long-term potentiation. Rev. Neurosci. 5, 141–170 5 Jack, J.J. et al. (1994) Quantal analysis of the synaptic excitation of CA1 hippocampal pyramidal cells. In Molecular and Cellular Mechanisms of Neurotransmitter Release (Stjärne, L. et al., eds), pp. 275–299, Raven Press 6 McLachlan, E.M. (1978) The statistics of transmitter release at chemical synapses. In International Review of Physiology (Porter, R. ed.), University Park Press 7 Silver, R.A. et al. (1998) Locus of frequency-dependent depression identified with multiple-probability fluctuation analysis at rat climbing fibre–Purkinje cell synapses. J. Physiol. 510, 881–902 8 Reid, C.A. and Clements, J.D. (1999) Postsynaptic expression of long-term potentiation in the rat dentate demonstrated by variance– mean analysis. J. Physiol. 518, 121–130 9 Barton, S.B. and Cohen, I.S. (1977) Are transmitter release statistics meaningful? Nature 268, 267–268 10 Korn, H. et al. (1991) Is maintenance of LTP presynaptic? Nature 350, 282 11 Faber, D.S. and Korn, H. (1991) Applicability of the coefficient of variation method for analysing synaptic plasticity. Biophys. J. 60, 1288–1294 12 Faber, D.S. et al. (1992) Intrinsic quantal variability due to stochastic properties of receptor-transmitter interactions. Science 258, 1494–1498 13 Bekkers, J.M. (1994) Quantal analysis of synaptic transmission in the central nervous system. Curr. Opin. Neurobiol. 4, 360–365 14 Walmsley, B. (1995) Interpretation of ‘quantal’ peaks in distributions of evoked synaptic transmission at central synapses. Proc. R. Soc. London B Biol. Sci. 261, 245–250 15 Frerking, M. and Wilson, M. (1996) Effects of variance in mini amplitude on stimulus-evoked release: a comparison of two models. Biophys. J. 70, 2078–2091 16 Korn, H. and Faber, D.S. (1998) Quantal analysis and long-term potentiation. C. R. Acad. Sci. Ser. III 321, 125–130 17 Miyamoto, M.D. (1975) Binomial analysis of quantal transmitter release at glycerol treated frog neuromuscular junctions. J. Physiol. 250, 121–142 18 Brown, T.H. et al. (1976) Evoked neurotransmitter release: statistical effects of nonuniformity and nonstationarity. Proc. Natl. Acad. Sci. U. S. A. 73, 2913–2917 19 Bennett, M.R. and Lavidis, N.A. (1979) The effect of calcium ions on the secretion of quanta evoked by an impulse at nerve terminal release sites. J. Gen. Physiol. 74, 429–456 20 Sigworth, F.J. (1980) The variance of sodium current fluctuations at the node of Ranvier. J. Physiol. 307, 97–129 21 Clamann, H.P. et al. (1989) Variance analysis of excitatory postsynaptic potentials in cat spinal motoneurons during posttetanic potentiation. J. Neurophysiol. 61, 403–416 22 Bekkers, J.M. and Stevens, C.F. (1990) Presynaptic mechanism for long-term potentiation in the hippocampus. Nature 346, 724–729 23 Malinow, R. and Tsien, R.W. (1990) Presynaptic enhancement shown by whole-cell recordings of long-term potentiation in hippocampal slices. Nature 346, 177–180 24 Quastel, D.M. (1997) The binomial model in fluctuation analysis of quantal neurotransmitter release. Biophys. J. 72, 728–753 25 Traynelis, S.F. and Jaramillo, F. (1998) Getting the most out of noise in the central nervous system. Trends Neurosci. 21, 137–145 26 Schneggenburger, R. et al. (1999) Released fraction and total size of a pool of immediately available transmitter quanta at a calyx synapse. Neuron 23, 399–409 27 Wu, L.G. et al. (1999) Calcium channel types with distinct presynaptic localization couple differentially to transmitter release in single calyx-type synapses. J. Neurosci. 19, 726–736 28 Murthy, V.N. et al. (1997) Heterogeneous release properties of visualized individual hippocampal synapses. Neuron 18, 599–612 29 Reid, C.A. et al. (1997) Nonuniform distribution of Ca21 channel subtypes on presynaptic terminals of excitatory synapses in hippocampal cultures. J. Neurosci. 17, 2738–2745 30 Bekkers, J.M. and Clements, J.D. (1999) Quantal amplitude and quantal variance of strontium-induced asynchronous EPSCs in rat dentate granule neurons. J. Physiol. 516, 227–248 31 Silver, R.A. et al. (1996) Non-NMDA glutamate receptor occupancy

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and open probability at a rat cerebellar synapse with single and multiple release sites. J. Physiol. 494, 231–250 32 Forti, L. et al. (1997) Loose-patch recordings of single quanta at individual hippocampal synapses. Nature 388, 874–878 33 Gulyas, A.I. et al. (1993) Hippocampal pyramidal cells excite

inhibitory neurons through a single release site. Nature 366, 683–687 34 Auger, C. et al. (1998) Multivesicular release at single functional synaptic sites in cerebellar stellate and basket cells. J. Neurosci. 18, 4532–4547

LETTERS Peptide hormones and neuropeptides: birds of a feather In his review of Neuropeptides: Regulators of Physiological Processes, Leslie Iversen defines a neuropeptide as a peptide secreted from a neuron1. He finds it confusing that adrenocorticotrophic hormone (ACTH) and other hormones are classified as neuropeptides, because such classification would include almost every peptide hormone, even those that originate from the gut, kidney, heart, parathyroid and thyroid. This is true, given that almost all of the hormones found in these organs are also produced by neurons. Peptides exert many different functions: ACTH acts as a hormone in order to regulate the activity of the adrenal cortex. In the brain, secreted by pro-opiomelanocortin-containing neurons, ACTH or fragments thereof, such as melanocyte-stimulating hormone (MSH) and other smaller fragments, regulate nervous-system functions, as explained in Neuropeptides. In the 1960s, I found pituitary hormones such as ACTH, MSH and vasopressin, and their fragments to have behavioral properties, even though they are devoid of peripheral endocrine activities. I, therefore, suggested that the pituitary might manufacture peptides with neurogenic activities, as reviewed in Ref. 2. The term ‘neuropeptide’ was coined by my colleagues and I: it was used for the first time in 1971 in a Dutch journal and subsequently in 1974 (Ref. 3). During the first ten years of our studies, it was not known that nerve cells did secrete peptides, except for substance P and the neurohypophyseal hormones. The central distribution of the latter hormones, however, still remained to be discovered. The brilliant studies that led to the isolation of the enkephalins by Kosterlitz et al. in 1975, highlighted the beginning of the search for other peptides in the brain. Peter Burbach and I defined neuropeptides as endogenous substances synthesized in nerve cells and involved in nervous-system functions. However, because, as we know, other cells might now have the same property, the definition had to be extended (as we explained recently in Elsevier’s Encyclopedia of Neuroscience4). Not only is pro-opiomelanocortin synthesized in nerve cells, but

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various melanocyte receptors, which also recognize ACTH, have been found in the brain. Whether or not ACTH acts as a melanocyte-receptor agonist or is processed before it produces its actions is not known. Similarly, the same can be said for many other hormones that are found in the brain. Besides, the nervous system, the gut and the skin, which also produces peptide hormones, have a similar embryological origin. Indeed, the versatility of peptide hormones reflects their evolutionary signifance as regulators of physiological processes. I do not think that students will be confused to see all the endocrine peptides mixed together with neuropeptides. They should be taught that the first transmitters of information in living organisms were the precursors of neuropeptides.

TO THE EDITOR

They should marvel about it and understand that endocrinology and neurophysiology are overlapping fields that for too long have been separated because of our ignorance. David de Wied Dept of Pharmacology, Rudolf Magnus Institute for Neurosciences, University of Utrecht, 3508 TA Utrecht, The Netherlands. References 1 Iversen, L. (1999) Neuropeptides: regulators of physiological processes. Trends Neurosci. 22, 482 2 de Wied, D. (1969) Effects of peptide hormones on behavior. Front. Neuroendocrinol. 1, 97–140 3 de Wied, D. et al. (1974) Pituitary peptides and behavior: influence on motivational, learning and memory processes. Excerpta Med. Int. Congr. Ser. 359, 653–658 4 Adelman, G. and Smith, B.H., eds (1998) Elsevier’s Encyclopedia of Neuroscience, Elsevier

What is a neuropeptide? Iversen considers it an idiosyncracy of Strand to define a neuropeptide as any peptide that has direct effects on the nervous system1. His preferred definition limits a neuropeptide to one that is secreted from a neuron: this older definition was superseded many years ago. Currently, a neuropeptide is defined as such, regardless of whether it is secreted by neurons or nonneural cells, if it expresses the same genetic information and undergoes identical processes of synthesis and transport, and of binding to similar families of receptors, in order to act on neural processes. For example, somatostatin is found in the hypothalamus and extraneural somatostatin is localized widely in the gastrointestinal system, including the pancreas. Yet the inhibitory effects of somatostatin on a wide variety of neural functions are independent of its neural or non-neural source. It would be difficult to justify classifying hypothalamic somatostatin as a neuropeptide, while ignoring the profound neural effects of nonneural somatostatin. Similarly, galanin, bombesin, calcitonin-gene-related peptide, vasoactive intestinal polypeptide and many

other neuropeptides have both neural and non-neural origins. This broader definition of a neuropeptide has been adopted at most neuroendocrine meetings and by The International Neuropeptide Society. It is similarly regrettable that Iversen overlooked the extensive discussion of the NO synthase knockout mouse, complete with illustrations. Other sections of the book are similarly up to date. Personally, I find Neuropeptides very comprehensive, yet concise and easy to read. Owing to its superb organization and integration, it already is being used with great success as the basis of a course directed by Richard D. Olson at the University of New Orleans. It constitutes an outstanding contribution to the peptide field. Abba J. Kastin VA Medical Center and Tulane University School of Medicine, New Orleans, LA 70146, USA. Reference 1 Iversen, L. (1999) Neuropeptides: regulators of physiological processes. Trends Neurosci. 22, 482

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