Cerebral Cortex, Vol. 9, No. 7, 722-732,
October 1999
© 1999 Oxford University Press
Estimation of the Number of Synapses in the Cerebral Cortex: Methodological Considerations
1 Instituto Cajal (CSIC), 28002 Madrid and , 2 Universidad Europea de Madrid, Villaviciosa de Odón, 28670 Madrid, Spain
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Abstract |
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 Top Abstract IntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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In the present work we discuss several sampling procedures commonly used for counting synapses in the cerebral cortex. We compare, within the same tissue, two frequently used sterereological methods for determining the numerical density of synapses per unit volume, using as an example the estimation of the number of types of synapses by layers in the neuropil of the adult human temporal neocortex. These two methods are a size–frequency method (formula NA/d) and the disector method (
Q–/a x h). Since the size–frequency method is assumption-based and the disector method is considered to be an unbiased method, the latter is often recommended for the quantification of synapses and other objects. We obtained, however, similar estimates for the numerical density of the different types of synapses using both methods, although they presented different technical difficulties and statistical properties. In addition, we show that the size–frequency method is more efficient and easier to apply than the disector method. Nevertheless, there are other methods for quantification which may also be valid, depending on the aim of the research; but the data reported in many articles are often complicated, which makes it very difficult for the reader to follow all the steps of the calculation. If certain basic information were given, this would facilitate the interpretation and sharing of important information with other laboratories, regardless of the method used for quantification. Finally, based on our present results and previous literature, we propose a simple general protocol for estimating the numerical synaptic density by volume in the neuropil of the cerebral cortex. |
Introduction |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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It is well known that the number of synapses in the brain changes during the course of normal life and under certain pathological or experimental circumstances [reviewed by Rakic et al. (Rakic et al., 1994
) and Bourgeois (Bourgeois, 1997)]. One of the main goals of numerous researchers has been to find simple and accurate methods for estimating the magnitude of these changes. The number of synapses has been estimated for surface areas and volumes using a variety of methods. Since these numbers depend not only on the density, but also on the size and shape of the synaptic junctions (Coggeshall, 1992), and these factors may vary, it is preferable to estimate the number of synapses present in a unit volume using stereological methods (Anker and Cragg, 1974; Mayhew, 1979). These methods allow us to deduce three-dimensional characteristics of synaptic junctions observed two-dimensionally, and to relate their sizes and numbers to a given volume of tissue (Mayhew, 1979).
A number of papers have dealt with the theoretical background of stereological principles and the formulae for estimating the number of synapses per volume (Mayhew, 1979; Sterio, 1984; Gundersen et al., 1988a,b; Royet, 1991; Coggeshall, 1992; Mayhew and Gundersen, 1996; Coggeshall and Lekan, 1996). There are two common methods used: the formula NV = NA/d (where NA is the number of synaptic profiles per unit area and d is the average length of synaptic junctions) (Colonnier and Beaulieu, 1985); and the disector method, using the formula NV= Q–/a x h (where Q– is the number of synaptic profiles that are present in the reference sections, but disappear in the look-up sections, a is the sampled area and h is the mean thickness of ultrathin sections used for each disector) (Sterio, 1984). The formula NV = NA/d is an assumption-based method, because it is assumed that synaptic membrane densities form a polydispersed population of disk-shaped particles, whereas the disector method is not dependent on size, shape or distribution. Since the disector method is considered to be unbiased (there is only one count per particle), easy to use and more reliable than those based on shape and size, it has been recommended by numerous authors as the method of choice for counting synapses [see recent reviews by Mayhew (Mayhew, 1996) and Coggeshall and Lekan (Coggeshall and Lekan, 1996); see also Geinisman et al. (Geinisman et al., 1996)].
Additionally, in most methodological studies, synapses are considered simply as test objects, without considering that a variety of morphological types of synapses, with different functional significance, exist in the brain, and that some types are relatively scarce, whereas others are very numerous. In the cerebral cortex there are two major morphological types of synapses, type I and type II of Gray (Gray, 1959), which correspond, respectively, to the asymmetrical and symmetrical types of Colonnier (Colonnier, 1968) [see also Colonnier (Colonnier, 1981) and Peters and co-workers (Peters, 1987; Peters et al., 1991; Peters and Palay, 1996)]. In general, asymmetrical synapses are considered to be excitatory and symmetrical synapses inhibitory, asymmetrical synapses being much more abundant than symmetrical synapses [reviewed by Houser et al. (Houser et al., 1984), White (White, 1989) and DeFelipe and Fariñas (DeFelipe and Fariñas, 1992)]. These differences are not trivial since they may be of great importance in determining the procedure to be used for estimating their numbers. Furthermore, the protocols used by different laboratories to estimate numerical synaptic density are highly variable because there is no general consensus in several of the various steps followed for electron microscopic analysis of the cerebral cortex, such as sampling procedures and identification of synapses. Therefore, in the present study we have reviewed some of these issues that are particularly relevant for counting synapses.
Another main objective of the present work was to compare in detail the estimations obtained with the formula NV = NA/d with those of the disector method within the same tissue, using as an example the estimation of the number of types of synapses by layers in the neuropil of the normal adult human temporal neocortex. We used portions of normal brain tissue from the anterolateral middle temporal cortex that had been removed from a 34 year old neurologically and psychiatrically normal patient in order to gain access to a dysembryoplastic neuroepithelial tumour located near the hippocampus. Part of this tissue was used in a previous study (del Río and DeFelipe, 1997), and was prepared for electron microscopy using a correlative light and electron microscope technique (Fig. 1) described previously (DeFelipe and Fairén, 1993). Finally, the following comments and discussion refer mainly to studies using tissue prepared for conventional electron microscopy that has been fixed with aldehydes and treated with osmium tetroxide.
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Identification, Classification and Counting of Synapses |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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A synapse is recognized according to well-established criteria (Colonnier, 1981
; Peters et al., 1991; Peters and Palay, 1996). Strictly, a structure is identified as a synapse when the following elements are clearly recognized: synaptic vesicles in the presynaptic axon terminal adjacent to the presynaptic density, a synaptic cleft (with electron-dense material in the cleft) and densities on the cytoplasmic faces in the preand postsynaptic membranes. There is a general consensus for classifying cortical synapses into asymmetrical (or type I) and symmetrical (or type II) synapses. The main characteristic distinguishing these synapses is either a prominent (Fig. 2A) or a thin postsynaptic density (Fig. 2B) respectively (Gray, 1959; Colonnier, 1968, 1981; Peters, 1987; Peters et al., 1991; Peters and Palay, 1996). Asymmetrical synapses constitute 75–95% of all synapses, whereas the remaining 5–25% are symmetrical synapses [reviewed by DeFelipe and Fariñas (DeFelipe and Fariñas, 1992)].
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However, in single sections the cleft and densities in the preand postsynaptic membranes are blurred in a large proportion of synaptic junctions (Figs 3, 4
), varying between 40 and 60% (Bourgeois and Rakic, 1993; DeFelipe et al., 1997; Marco and DeFelipe, 1997). This is because the planes of section in these cases are not passing at right angles to the synaptic junctions, with the extreme case being the en face view (plane of section parallel to the plane of synaptic junction) (Peters and Kaiserman-Abramof, 1969). Examination of the same section, but viewed with various tilt angles using the goniometer stage of the electron microscope, or examination of serial sections have confirmed in numerous studies the synaptic nature of these junctional complexes (Figs 3, 4). Thus, the presence of synaptic vesicles in the presynaptic axon terminal, together with the characteristic synaptic membrane specializations, regardless of their orientation with respect to the plane of section, should be sufficient criteria for identifying synapses. Since synaptic junctions viewed at different angles of plane of section are easily recognizable, we disagree with the assertion made by Geinisman et al. (Geinisman et al., 1996) that an unambiguous identification of synapses can only be performed after examination of consecutive serial sections. Therefore, we have classified as ‘uncharacterized' those synapses with no visible synaptic clefts or whose postsynaptic densities could not be clearly identified as symmetrical or asymmetrical (Bourgeois and Rakic, 1993; Bourgeois et al., 1994).
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Counting Units for Synapses
In general, three structural units have been used as counting units for synapses [reviewed by Mayhew (Mayhew, 1996)]: the boutons, the total apposition zones and the synaptic membrane densities, whose identification are commonly associated with other structural characteristics. Membrane densities are, by far, the most commonly used units. However, different investigators have used different criteria for identifying these elements as counting units, which can be grouped into two main criteria (see Figs 3, 4
):
Criterion 1
The counting units are those structures in which there is a clearly recognized synaptic cleft with preand postsynaptic membrane specializations and synaptic vesicles (with or without an arbitrary minimum number) (Mayhew, 1996) in the pre-synaptic element.
Criterion 2
The counting units are those structures in which can be observed synaptic vesicles in the presynaptic element and synaptic membrane specializations, regardless of the angle of section at which the synaptic junctions are viewed (i.e. whether showing a synaptic cleft or not).
Furthermore, it is well known that a single bouton may form more than one synaptic junction and that some synaptic junctions show two or more separated postsynaptic densities with the same postsynaptic element (perforated synapses) (Peters and Kaiserman-Abramof, 1969). Thus, a single bouton may account for as many synaptic units as there are synaptic junctions formed with different postsynaptic elements.
Since, in a large proportion of synaptic junctions, the cleft and the densities in the preand postsynaptic membranes are blurred (see above), those investigators applying criterion 1 to single sections will systematically obtain an underestimate of the numerical synaptic density. However, this problem could be solved if all the possible synaptic junctions are followed through consecutive serial sections until the morphological characteristics for fulfilling criterion 1 are met (or not). Nevertheless, as pointed out above, synaptic junctions viewed at different plane-of-section angles are easily identifiable in single sections. Certainly some structures are difficult to recognize as synaptic junctions in single sections, particularly at low magnification. But, using relatively high-power electron micrographs (at a final magnification of around x30 000), the number of structures that cannot be unambiguously identified as synaptic junctions by an experienced electron microscopist are so few that we consider the use of time-consuming serial section analysis unnecessary. Thus, the application of criterion 2 for identifying counting units in single sections should be enough.
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Sampling Procedures |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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There are several procedures for obtaining samples in order to estimate synaptic density by layers. Commonly, a large semithin plastic section (1–2 µm thick) of the surface of the selected block of tissue is first cut with an ultramicrotome and stained to determine the boundaries of the layers. Then the block is trimmed and a series of ultrathin sections of silver/grey interference color is cut and examined in the electron microscope (Bourgeois and Rakic, 1993
; Granger et al., 1995). Currently, we use a simple sampling procedure method (DeFelipe and Fairén, 1993) that consists of resectioning into ultrathin sections the same semithin sections used for determining cortical layers, instead of obtaining ultrathin sections adjacent to these semithin sections. The main advantage of this method is that it allows us to accurately study light-microscope-selected neuropil regions within any given layer (Fig. 1). Sampling of Cortical Tissue
In the cerebral cortex, synapses are formed between axon terminals and the cell somata and dendrites of both pyramidal and nonpyramidal cells, and with the axon initial segments of pyramidal cells and of some nonpyramidal cells. Therefore, any estimation of the total numerical synaptic density of the cerebral cortex should include these synaptic regions. A uniform sampling procedure from equally spaced regions, starting with a randomly chosen position, may not be efficiently applicable for the following main reasons:
(1) The vast majority of synapses are formed with dendrites, the dendritic spines of pyramidal cells being the most numerous synaptic targets (Beaulieu and Colonnier, 1985; Beaulieu et al., 1992) [reviewed by DeFelipe and Fariñas (DeFelipe and Fariñas, 1992)]. However, the cortex is richly vascularized with a non-random distribution of blood vessels (Duvernoy et al., 1981). Furthermore, there are a large number of neuronal somata and glial cells, and the pyramidal cells (which are the predominant type of neuron in layers II–III and V–VI) and spiny nonpyramidal cells (the predominant type in layer IV) often form small clusters (Peters, 1994) (see Fig. 1A). Since the sizes of blood vessels and cell somata are large, or very large, in relation to the high magnification of electron micrographs necessary for identifying synapses (see below), if a blood vessel or soma is included in a given electron micrograph, a portion or all of the electron micrograph might be occupied by the lumen of the blood vessel or by the cytoplasm of the soma, and the number of synapses obviously will be few or none. Consequently, the number of synapses sampled in a given layer may vary considerably, depending on the extent of neuropil sampled, and the efficacy of sampling will depend on the number and extent of electron micrographs that include blood vessels and cell somata, the number of these electron micrographs also being variable, depending on the packing density of blood vessels and somata of the region examined (see Fig. 1B,C).
(2) The structure and amount of neuropil varies considerably, depending not only on the layer and cortical area, but also in any given area (e.g. between the fundus of a sulcus and the crown of a gyrus). In all areas, the neuropil of layer I is made up mainly of small-caliber axonal, dendritic and glial processes. However, in the other cortical layers there are numerous large dendrites (mainly apical dendrites) and myelinated axons that are embedded in a fine network of axonal, dendritic and glial processes with a morphological appearence similar to the neuropil of layer I. Furthermore, apical dendrites and myelinated axons of pyramidal cells form bundles in some regions of the neuropil in certain layers, whose disposition may also vary, depending on the cortical areas and species (Peters et al., 1997). Within these regions, the number of synapses sampled will be relatively low (for the above reasons) as compared to those sampled regions not containing large processes. Thus, we refer to such neuropil as ‘thin' neuropil, to distinguish it from neuropil containing large dendrites and myelinated axons.
(3) The probability of including a postsynaptic axon initial segment in a given sampled region is very low, because these structures are very small [the mean diameter and length of axon initial segments of corticothalamic pyramidal cells in the cat visual cortex, for example, is approximately 1 and 22 µm respectively (Fariñas and DeFelipe, 1991)] and relatively few (one per neuron).
Therefore, estimating the number of synapses formed with cell somata, axon initial segments, large (apical) dendrites and thin neuropil should be carried out separately, layer by layer and using different sampling procedures to make a more meaningful and efficient estimate. For example, given the large sizes of cell somata, each electron micrograph should be taken so as to cover the maximum surface area of the soma, with the whole perimeter being sampled [for axon initial segments, see, for instance Fariñas and DeFelipe (Fariñas and DeFelipe 1991)]. The following discussion will refer to estimating synapses found in the thin neuropil.
Electron Micrographs: Sampled Area and Magnification
Electron micrographs are taken from each cortical layer, usually in three different ways: first, from whole cortical tissue, i.e. from areas including the neuropil, cell bodies and blood vessels; second, from areas excluding cell bodies and blood vessels; third, from thin neuropil, i.e. excluding large dendrites and myelinated axons.
Electron micrographs are taken at an initial magnification that varies, depending on the investigator, between approximately x5000 and x15 000. These pictures are printed at a final magnification that also varies, between approximately x12 000 and x30 000. The lower the magnification of the initial electron micrograph, the larger would be the sampled neuropil area, but this would result in a more difficult identification of synaptic junctions. In the present study, we tested four initial magnifications (x5000, x8000, x10 000 and x12 000), which were printed at a final magnification of x30 000 (a photomicrograph of a cross-grating replica containing 2160 lines/mm was used to print all pictures at the same magnification), to see how accurately the various types of synapses could be identifed and classified. Although the four initial magnifications yielded similar results, the higher the initial magnification was, the greater the accuracy, particularly in identifying small synaptic junctions. However, an initial x10 000 was sufficient and, therefore, this has been the magnification used by a number of investigators (including ourselves) to estimate synaptic density.
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Estimation of Numerical Density of Synapses |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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We used selected areas of thin neuropil (i.e. excluding large dendrites and myelinated axons) from normal adult human temporal neocortex as representative material to provide examples of numerical synaptic densities obtained by the two commonly used formulae NV = NA/d and NV =
Q–/a x h. We first examined certain key parameters for each method to obtain the estimates and then we compared the values obtained with the two formulae. Size–Frequency Method (NV = NA/d)
The sampling procedure consisted of electron microscope samples of neuropil (excluding large dendrites and myelinated axons) from each cortical layer (layers I, II, IIIA, IIIB, IV, V and VI). These samples were non-overlapping electron micrographs at an initial magnification of x10 000 that were taken with at least a 50 µm distance between them. These electron micrographs were printed at a final magnification of x30 000. All synapses were counted in each print within an unbiased counting frame (Gundersen, 1977), which represented ~35 µm2 of tissue. Synaptic profiles touching the exclusion lines were not counted. The lengths of synaptic junctions (length of paired membrane densities at each junction) of all synapses were measured directly from the prints using a magnetic tablet (SummaSketch III) and the NIH Image analysis program.
Number of Samples (Electron Micrographs)
In a first approach, we tried to find the minimum number of photomicrographs per layer that yielded reliable results. Of course, the higher the number of samples, the better; but, for obvious practical reasons, one cannot increase the number of samples arbitrarily. The final decision about the number of photographs (samples) that should be used to make an estimation depends on the precision the researcher needs for the aim of the study (Guillery and Herrup, 1997). In the cases of estimating the number of synapses per surface area, or per volume using stereological methods other than the disector, the number of electron micrographs used by investigators is usually 10, or a few more, per layer, the pictures being either contiguous or non-contiguous. Granger et al. studied the changes in estimates of the density of synapses per surface area as a function of the number and distribution of electron micrographs sampled in the monkey cerebral cortex (Granger et al., 1995). They found that with only 13 noncontiguous electron micrographs regularly distributed at a horizontal distance of 700 µm, the mean synaptic density values obtained were within the 95% confidence level obtained with 25 electron micrographs. However, when the 13 electron micrographs were contiguous, this percentage decreased to 82%.
We thus decided to compare the measurements obtained from 5, 10 and 15 randomly chosen noncontiguous electron micrographs per layer taken at an initial magnification of x10 000 (in total, 35, 70 and 105 micrographs for the whole cortex; each micrograph represents a sample area of ~35 µm2). The mean number of synapses per unit volume and 95% confidence intervals for the whole cortex, were similar using 5, 10 or 15 photographs per layer. Nevertheless, when the different kinds of synapses were compared independently, or when data were considered layer by layer, the results obtained from the group of five photographs were significantly different from the other two groups (particularly for symmetrical synapses). Moreover, standard deviations and 95% confidence intervals were much wider than with the estimates obtained with 10 and 15 photo-micrographs. However, the estimates obtained with 10 and 15 photomicrographs per layer yielded similar results, although confidence intervals were, in general, slightly narrower when 15 photographs were used for the calculations (Fig. 5). Therefore, our results basically confirmed the results of Granger et al. (Granger et al., 1995). We conclude that 10 noncontiguous electron micrographs per layer (i.e. a sampling area of ~350 µm2) are sufficient for obtaining a good estimate of the density of any type of synapse found in thin neuropil in all layers, since the estimates obtained with 15 photomicrographs were only slightly better, in spite of the 50% increase in the number of samples.
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Disector Method (NV =
Q–/a x h)
There is great variability in the number of disectors used by different investigators to estimate the density of the different types of synapses in a given layer. For example, Keller et al., DeFelipe et al., and Micheva and Beaulieu used 15, 5 and 3 disectors respectively (Keller et al., 1992; DeFelipe et al., 1997; Micheva and Beaulieu, 1996). In the present study, in order to use a comparable set of samples for the disector method with respect to the size–frequency method, we took 10 pairs of serial non-overlapping electron micrographs at an initial magnification of x10 000 per layer (layers I, II, IIIA, IIIB, IV, V and VI). These electron micrographs were printed at a final magnification of x30 000. The number of synaptic profiles that were present in the reference sections, but disappeared in the look-up sections (Q–), were counted in each pair of prints within an unbiased counting frame (Gundersen, 1977), which represented ~35 µm2. From each pair of photographs, we performed two disectors, since the top and bottom photographs can be used alternatively as the reference and look-up sections (Gundersen et al., 1988b). Thus, 20 disectors were obtained from each cortical layer (a total of 140 for the whole cortex).
The mean thickness h of ultrathin sections was calculated by the small fold method (Weibel, 1979); this value ranged from 33 to 42 nm (mean 40). In practice, the estimate of object numbers with the disector method is not influenced by section thickness, provided that this does not exceed one-quarter to one-third the mean particle height (Gundersen et al., 1988b). In the case of synapses, the mean length of synaptic junctions measured in several areas of the neocortex of various species is ~0.2–0.35 µm in most studies (Beaulieu and Colonnier, 1987; Schüz and Palm, 1989; Peters and Harriman, 1990; Beaulieu et al., 1992; Keller et al., 1992; Bourgeois et al., 1994; Marco and DeFelipe, 1997; DeFelipe et al., 1997); thus, the thickness of the ultrathin sections should not be greater than 116.0 nm. Since the thickness of ultrathin sections more commonly used is between 40 and 60 nm (silver–gray or silver–gold interference color), this constraint may be neglected.
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Comparison Between the Size–Frequency and Disector Methods |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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Colonnier and Beaulieu (Colonnier and Beaulieu, 1985
) compared the estimates of a known number of test objects using several stereological formulae [procedures based on a number of formulae (DeHoff and Rhines, 1961; Weibel, 1979; Anker and Cragg, 1974; O'Kuski and Colonnier, 1982)], which had commonly been used to estimate numerical synaptic density per unit of volume and which were based on the observation that synaptic membrane specializations have the form of a disk. The test objects were carrot slices and tangerine and grapefruit rinds, chosen so that they approximated the curvatures, size distributions and sizes (relative to the thickness of the sections) found in cortical synapses. These objects were embedded in a known volume of gelatine and then sectioned at an appropriate thickness. These investigators found that the application of the NA/d formula produced an accurate estimate, with an error of only ~5 %.
A number of investigators have used this formula to estimate synaptic density by volume in the cerebral cortex (Zecevic et al., 1989; Zecevic and Rakic, 1991; Keller et al., 1992; Beaulieu et al., 1992; Bourgeois and Rakic, 1993; Bourgeois et al., 1994; Granger et al., 1995; DeFelipe et al., 1997). However, after the introduction of the disector method in 1984 by Sterio, some investigators have claimed that the method of choice must be the disector because it is said to yield an unbiased and efficient estimate of the numerical synaptic density, and that the stereological formulae based on the shape and size of synaptic membrane specializations have mainly historical interest (Mayhew, 1996). Therefore, one of the main aims in the present study was to compare in detail the estimates obtained with the size–frequency and disector methods.
Statistical Comparisons
Data obtained with both methods were compared in several different ways. We compared the numerical density of all synapses and the different morphological types (asymmetrical, symmetrical and uncharacterized) in the whole cortex (all layers). All these items were also compared layer by layer.
Statistical comparisons of the means were performed by an unpaired Student's t-test; standard deviations and 95% confidence intervals were also calculated. For each of the two methods, the possible differences in the density of synapses between different layers were analyzed by a one-way ANOVA. All these studies were performed with the aid of the SPSS statistical package.
Asymmetrical, Symmetrical and Uncharacterized Synapses
The mean numbers of different morphological types of synapses obtained with the two methods, considering all layers, were similar. However, standard deviations were higher and 95% confidence intervals wider with the disector method than with size–frequency method (Table 1).
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When the different cortical layers were compared independently, the greatest differences between the two methods were found in layers I and II, although in only one case (asymmetrical synapses of layer I) were these differences statistically significant for P
0.005 (Fig. 6). The main discrepancies were found in symmetrical synapses, since the disector method failed to identify any symmetrical synapses in layers II and VI. In addition, as occurred when considering all layers, standard deviations were higher and 95% confidence intervals wider with the disector method than with the size–frequency method in each cortical layer (Fig. 6).
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Total Synapses
Estimates of the numerical density of all synapses (asymmetrical, symmetrical and uncharacterized synapses) in the whole cortical neuropil were similar for both methods. Means were 16.26 for the size–frequency method and 15.08 for the disector method (expressed as number of synapses x 108/mm3). They were not significantly different when compared with Student's t-test. There were differences, however, in both the standard deviations and 95% confidence intervals, which were greater for the disector method (Table 1).
Layer-by-layer comparisons between the two methods were similar; the greatest differences were found in layers I and II. Again, standard deviations and 95% confidence intervals were higher for the disector method than for the size–frequency method (Fig. 6).
Comparisons Between Layers Within the Same Group
When the total numbers of synapses in each layer were compared with the total numbers of synapses in the other layers, the size–frequency method detected statistically significant differences between layers I and VI (P 0.001), II and VI (P 0.001) and I and V (P 0.005). However, with the disector method, no statistically significant differences between layers were found.
In summary, the present results indicate that the NA/d and Q–/a x h formulae produce, in general, similar estimates of the density of synapses in the neuropil. Similar conclusions have been reached in previous studies in which a comparison of the two formulae have been performed in several cortical areas (somatosensory, motor, visual and temporal cortex) and species (mouse, cat, monkey and human) (Keller et al., 1992; Beaulieu et al., 1992; Marco and DeFelipe, 1997; DeFelipe et al., 1997). Therefore, either of the two methods could be used for this estimation.
As shown in Table 1, the number of electron micrographs (surface area) that should be analyzed in order to get comparable values from applying the formulae NA/d and Q–/a x h is greater for the disector method. In addition, the coefficient of variation was 77.46 for the total density of synapses using the disector method, whereas for the size–frequency method it was 39.21. This was mainly due to the high variability of the Q– number with the disector, whose coefficient of variation was 77.76, whereas for the number of synaptic profiles counted with the size—frequency method, this coefficient was only 34.07. Thus, if we use the coefficient of variation as a measure of variability, then the size–frequency method shows less variability than the disector method. Since the coefficients of variation and 95% confidence intervals were greater with the disector method than with the size–frequency method, it can be concluded that the NA/d formula is more efficient and shows less variability than the disector method.
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How to Compare and Interpret Data from Other Studies Regardless of the Method Used for Quantification |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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Obviously, the use of exactly the same protocols by all investigators would give a straightforward comparison of data. But in practice this is very difficult because, as discussed above, there is no general consensus for several of the steps followed for counting synapses. Unfortunately, in many articles the data commonly reported are often complicated, making it very difficult, if not impossible, to follow every step of the calculation. However, if certain basic information is given, it would facilitate the interpretation and sharing of important information with other laboratories, independent of the method used for quantification. This information is as follows:
- Initial and final (printing) magnifications.
- Extent of thin neuropil examined.
- Definition of the counting units for synapses and their classification.
- Number of synaptic profiles per surface area of thin neuropil (e.g. synapses per 100 µm2).
- Average length of synaptic junctions of the different types of synapses.
Without at all undervaluing other procedures, we propose the following general protocol for estimating numerical synaptic density by volume in the cerebral cortex:
- Initial and final magnifications: x10 000 and x30 000.
- Sampling of 10 electron micrographs of thin neuropil per cortical layer.
- Using as counting units those structures in which the synaptic vesicles in the presynaptic element and the synaptic membrane specializations can be observed, regardless of the angle of section at which the synaptic junctions are viewed.
- Classifying synapses showing a synaptic cleft as either asymmetrical or symmetrical on the basis of the appearance of the postsynaptic density, and classifying those synaptic junctions which have been cut obliquely or tangentially as uncharacterized synapses.
- Using the formula NV = NA/d.
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Concluding Remarks |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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Recently, it has been proposed by some investigators that the disector method should be the only method used for making an accurate estimate of particle numbers. This idea has been so strong that some investigators have stated that the validity of conclusions drawn from quantitative studies using other methods have little or no interest. However, as pointed out by Guillery and Herrup, the goal of quantification in most cases is to make comparisons (Guillery and Herrup, 1997
); for example, in evaluating the impact of a particular experimental condition on the number of neurons or synapses in a given region, rather than estimating absolute numerical densities of neurons or synapses. Furthermore, the method chosen for quantification depends on many factors, such as the level of accuracy necessary for the aim of the research and characteristics of the element to be counted (frequency, distribution, size, etc.) (Guillery and Herrup, 1997). In addition, we, as well as other authors, have shown that applying the formulae NA/d and Q–/a x h yields similar results and, thus, either of the two methods can be applied. We have also shown that the formula NA/d is more efficient and presents less variability than the disector method. Therefore, the above general assertion that the disector method is intrinsically more accurate and that it should be the method used for quantification of synapses is not justified, at least in the cerebral cortex. We also conclude that in order to fully evaluate quantitative electron microscopic data, it is very important to report certain basic information that is usually omitted, regardless of the method used for quantification. |
Notes |
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This work was supported by FIS grant 98/0933 and Comunidad de Madrid grant 08.5/ 0014/ 1997.
Address correspondence to Dr J. DeFelipe, Instituto Cajal (CSIC), Avenida Dr Arce 37, 28002 Madrid, Spain. Email: defelipe{at}cajal.csic.es.
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References |
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TopAbstractIntroductionIdentification, Classification...Sampling ProceduresEstimation of Numerical Density...Comparison Between the Size...How to Compare and...Concluding RemarksReferences |
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