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. 2011 Oct 17;219(6):647–660. doi: 10.1111/j.1469-7580.2011.01438.x

Mapping the distributions and quantifying the labelling intensities of cell compartments by immunoelectron microscopy: progress towards a coherent set of methods

Terry M Mayhew 1
PMCID: PMC3237875  PMID: 21999926

Abstract

An important tool in cell biology is the combination of immunogold labelling and transmission electron microscopy (TEM) by which target molecules (e.g. antigens) are bound specifically to affinity markers (primary antibodies) and then detected and localised with visualisation probes (e.g. colloidal gold particles bound to protein A). Gold particles are electron-dense, punctate and available in different sizes whilst TEM provides high-resolution images of particles and cell compartments. By virtue of these properties, the combination can be used also to quantify one or more defined targets in cell compartments. During the past decade, new ways of quantifying gold labelling within cells have been devised. Their efficiency and validity rely on sound principles of specimen sampling, event counting and inferential statistics. These include random selection of items at each sampling stage (e.g. specimen blocks, thin sections, microscopical fields), stereological analysis of cell ultrastructure, unbiased particle counting and statistical evaluation of a suitable null hypothesis (no difference in the intensity or pattern of labelling between compartments or groups of cells). The following approaches are possible: (i) A target molecule can be tested for preferential labelling by mapping the localisation of gold particles across a set of compartments. (ii) Data from wild-type and knockdown/knockout control cells can be used to correct raw gold particle counts, estimate specific labelling densities and then test for preferential labeling. (iii) The same antigen can be mapped in two or more groups of cells to test whether there are experimental shifts in compartment labelling patterns. (iv) A variant of this approach uses more than one size of gold particle to test whether or not different antigens colocalise in one or more compartments. (v) In studies involving antigen translocation, absolute numbers of gold particles can be mapped over compartments at specific positions within polarised, oriented or dividing cells. Here, the current state of the art is reviewed and approaches are illustrated with virtual datasets.

Keywords: cell compartments, immunogold electron microscopy, labelling density, membranes, multilabelling, organelles, relative labelling index, specific labelling

Introduction

Indirect immunolabelling of structural compartments within biological systems involves locating one or more target molecules (e.g. protein or peptide antigens) using specifically bound affinity markers (usually primary antibodies). Attempts are made to reduce non-specific binding by means of blocking agents such as bovine serum albumin, gelatine or skimmed milk. The resolution obtainable by confocal optical microscopy is in the order of 250 nm. Depending on the fluorescent probe, so-called super-resolution optical microscopes, not yet widely available, can provide resolution of about 50 nm (Elsaesser et al. 2010; Toomre & Bewersdorf, 2010). However, with immunogold transmission electron microscopy (TEM) (Griffiths, 1993; Koster & Klumperman, 2003), target-marker complexes are detected and localised at high resolution with visualisation probes, of which the most commonly employed are colloidal gold particles bound to protein A. Detection and localisation depend on the target-recognition specificity of the affinity markers and the ability of TEM to resolve different compartments and gold particles. The ability to quantify is facilitated by the fact that colloidal gold particles are electron-dense, punctuate, countable and available in different sizes (usually 5–20 nm; Griffiths, 1993).

The principal aims of quantitative immunoTEM are to describe numerically the labelling distributions (or, in the case of multiple labelling, codistributions) across different structural compartments and/or the labelling intensities of those compartments. Depending on whether the compartments are volume- or surface-occupying, labelling intensities on the cut surfaces of TEM thin sections may be expressed as numbers of gold particles per profile area or per length of membrane trace (Griffiths, 1993). The precision and validity of quantification require the application of random sampling procedures and estimation tools which yield unbiased (or minimally biased) estimates of the numbers of gold particles and sizes of compartments. During the past decade, attempts have been made to improve quantitative methods for achieving these objectives (Mayhew et al. 2002, 2003, 2004; Lucocq et al. 2004; Mayhew & Desoye, 2004; Mayhew & Lucocq, 2008a, 2011; Lucocq & Gawden-Bone, 2009, 2010).

This review summarises these innovations and provides a progress report on developing a coherent set of methods for quantifying immunogold particles following post-embedding or on-section labelling.

Materials and methods

Sectioning and sampling

To achieve the high resolution that permits ultrastructural localisation, TEM requires the cutting of ultrathin (50–90 nm thick) sections through specimens or sampled parts thereof. Two important outcomes of this process are loss of dimensional information about the specimen and the fact that only tiny fractions of the specimen can be examined. Consequently, TEM images (fields of view) of specimens must be selected carefully and appropriately. This is important also because biological specimens are not, in general, homogeneous or isotropic. Their appearance varies with both position and orientation in space.

When cells and their compartments are physically sectioned, their images on the cut surface of the thin slice do not display, in general, their real sizes and shapes. Usually, there is some loss of dimensionality. For example, a nucleus (with a volume, μm3) appears on a section plane as a profile of a certain size (a sectional area, μm2) and its outer envelope (with a surface area, μm2) as a membrane trace (with a certain length, μm). The position and orientation of section planes also determine the areas, lengths or numbers of structures observed on TEM images. Cutting a sphere generates a circular profile, the area of which depends on whether the sphere was sectioned near its equator or pole. However, circular profiles can arise also by slicing through ellipsoids, cones and cylinders. The important point is that images on independent sections can be misleading in terms of the size, shape and number of real structures, hence the importance of taking multiple sampling items which cover a range of locations and orientations within the specimen.

As fields of view on TEM thin sections account for so little of the specimen, the final sample of fields should represent an unbiased selection of all parts of the specimen. This can be achieved with a multistage sampling scheme via which each specimen provides a number of tissue blocks. These are sampled further by cutting sections from which microscopical fields of view are chosen. By randomly sampling at every stage, an unbiased sample of the specimen is obtainable. This is important regardless of the nature of the compartments being examined. In addition, random sampling can accord all orientations of the specimen an equal chance of being selected. Indeed, combining random location and random orientation is essential when dealing with compartments which include membranes or filaments (Baddeley et al. 1986; Gundersen & Jensen, 1987; Mattfeldt et al. 1990; Nyengaard & Gundersen, 1992; Lucocq et al. 2004; Howard & Reed, 2005; Mayhew, 2008).

All varieties of random sampling share the property of unbiasedness but they are not equally efficient. In independent random (equal to simple random) sampling, the position and orientation of each sampling item is randomised. In contrast, with systematic uniform random (SUR) sampling, the position and orientation of the first item are randomised and then a pre-determined pattern, based on a constant sampling interval, governs the positions and orientations of other items. SUR sampling gives more even coverage of the specimen and, provided the sampling interval does not correspond to some repeating pattern in the specimen, this usually makes SUR sampling more efficient than independent random sampling (Mayhew, 2008). All the methods here are based on SUR sampling but the method of testing for colabelling of structural profiles in dual-labelling experiments requires an additional level of unbiased sampling (see below and Mayhew & Lucocq, 2011).

Defining cell compartments

Compartments can be volume-, surface- or length-occupying and, for descriptive convenience, may be thought of as corresponding to organelles, membranes and filaments, respectively (Mayhew et al. 2002). They may also be heterogeneous or homogeneous. For example, the sum total of all rough endoplasmic reticulum (RER) cisternae forms a homogeneous volume-occupying compartment. By contrast, the different plasma membrane domains of a polarised cell constitute a heterogeneous surface-occupying compartment.

Having sampled randomly and selected optimal operating magnifications (the lowest sufficient to be able to identify compartments and gold particles), compartments to be included in the analysis must be identified. The final choice will be governed largely by the aims of the study but, for certain analyses, it should include both the labelled compartments of interest and other (‘unlabelled’ or ‘background-labelled’) compartments. The latter can be lumped together for convenience as a composite ‘residual’ compartment (Mayhew et al. 2002).

The number of compartments should be limited to 3–12. Having too few compartments is likely to compromise functional interpretation. Generally speaking, increasing the number of compartments will improve the precision of topological localisation but also reduce the estimation precision (determined by variation of gold counts within a compartment). If the latter is so low that it compromises the statistical evaluations, it will be necessary to reduce the number of compartments (by omission or conflation) or to count more gold particles.

Counting gold particles and relating them to compartments

Gold particles are counted and assigned to the compartments with which they are associated. Because colloidal gold is available in various particle sizes, this allows multilabelling experiments in which different antigens are localised simultaneously (Geuze et al. 1981; Bendayan, 1982; Slot & Geuze, 1985). Whereas the smallest gold particles more closely resemble ‘points’, larger particles may appear to lie on more than one compartment. In order to count the latter, it is necessary to adopt an unbiased counting rule, the simplest of which is to count a particle as belonging to a compartment if its centre lies on that compartment. A reasonable workload for counting gold particles is about 200 per cell (= experimental replication) spread across the selected microscopic fields and compartments. This number should also be based on at least two ultrathin sections per replication (Lucocq et al. 2004).

Estimating the numerical or percentage frequency distributions of gold particles across a set of compartments provides a quick and simple way of showing where target molecules reside but these frequencies are size-dependent because larger compartments occur, and are sampled by section planes, more often than smaller compartments. Even though two compartments might share the same antigen concentration and label equally efficiently (Lucocq, 1992; Griffiths, 1993), more gold particles will be seen on the larger compartment. An alternative way of expressing gold particle counts involves estimating a labelling intensity for each compartment. This can take the form of a labelling density (LD) or relative labelling index (RLI).

Labelling density

Labelling density values relate numbers of gold particles to the sizes of compartments which can be obtained efficiently and unbiasedly by applying design-based stereological methods (Mayhew, 1991; Lucocq, 1994; Howard & Reed, 2005). With these tools, lattices of test probes (points and lines) are randomly superimposed on sectional images and used to identify and count chance encounters with compartments. Unbiased estimation depends crucially on randomised sampling (Gundersen & Jensen, 1987; Gundersen et al. 1999; Mayhew, 2008) because LD estimation depends on sampling compartments according to their relative sizes and, as already indicated, random sampling for the position and orientation of section planes meets these sampling conditions.

Labelling density values have been expressed as numbers of gold particles per μm2 (organelle profiles) or per μm (membrane traces and filament transections) on the section plane, or, less often, per μm3 of compartment (Lucocq, 1992; Griffiths, 1993). As a consequence, calibration of instrument magnification is required to convert areas and lengths on the magnified image into real dimensions on the scale of the specimen. However, stereology can provide more efficient estimators of LD which do not require knowledge of the magnification or of the lattice constants used to convert test point counts into organelle profile areas or line intersections into membrane trace lengths (see below and Mayhew et al. 2003).

Relative labelling index

A useful alternative approach is to compare the LD of a given compartment (LDcomp) with that of the entire cell (LDcell). If compartments label randomly, we predict that they would all share the same LD value as that of the cell as a whole. Therefore, the ratio LDcomp/LDcell provides a useful measure of the degree to which the observed labelling of a compartment departs from a predicted (random) pattern. This measure is known as the RLI (Mayhew et al. 2002) and it can be calculated from LD values or from raw gold counts and counts of chance encounters between stereological test probes (points, lines) and sectional images of compartments (whether profile areas or membrane trace lengths).

A portfolio of quantitative methods

Over the past decade, a portfolio of different methods for rigorously comparing labelling intensities and patterns in different compartments and groups has been devised (Mayhew et al. 2002, 2003, 2004; Lucocq et al. 2004; Mayhew & Desoye, 2004; Lucocq & Gawden-Bone, 2009, 2010; Mayhew & Lucocq, 2011). All rely on multistage random sampling (from specimens to fields), unbiased counting or morphometry and statistical evaluation of a null hypothesis (no difference in labelling intensity or pattern between compartments or groups). The latter is tested by chi-square (χ2) analysis or Fisher's exact probability test and with or without contingency table analysis. A useful site for undertaking calculations is offered by Graphpad Software Inc. (http://www.graphpad.com/quickcalcs/contingency1.cfm) and levels of significance (P-values) can be obtained from statistical tables in appropriate texts (e.g. Petrie & Sabin, 2000). Inferential statistical testing involves comparing observed and expected distributions of gold particles and, in the case of comparing compartments within a group of cells, the expected distribution can be calculated by randomly superimposing lattices of stereological test probes (points or lines). For statistical testing by chi-square analysis to be valid, preferably no expected value should be < 1 and no more than 20% should be < 5 (Daly & Bourke, 2000; Petrie & Sabin, 2000). For Fisher's exact test, preferably no expected value should be < 5 (Fisher, 1922).

Approach 1 – comparing different compartments in a cell

The aim is to test whether the observed distribution of gold particles between compartments within a given cell type is random or non-random (Mayhew et al. 2002). A convenient way of simulating a random distribution on the cut surface of a TEM thin section is to take advantage of fundamental stereological principles (Fig. 1). For example, if all compartments are volume-occupying (i.e. organelles rather than membranes or filaments), test points randomly superimposed on randomly located section planes will hit compartments with probabilities determined by their relative volumes (Howard & Reed, 2005). By summing the points that hit each compartment, the resulting distribution represents the expected spread of randomly positioned points and can be used to compare randomly distributed gold particles with the actual distribution of gold particles (Fig. 1A).

Fig. 1.

Fig. 1

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Testing for preferential labelling of compartments within a cell (Approach 1). Gold particles (yellow circles) lying on compartments of interest are counted and provide an observed distribution. If compartments are volume-occupying (A), the expected distribution of random label is obtained by superimposing a lattice of test points (P) and counting those which fall on profiles of the chosen compartments. If compartments are surface-occupying (B), the expected distribution is obtained by superimposing a lattice of test lines and counting intersections (I) which lines make, with the traces of membrane surfaces. After normalising point or intersection totals for the gold particle total, observed and expected distributions are compared by chi-square analysis. Refinements are available for dealing with mixtures of volume- and surface-occupying compartments.

In an analogous way, expected distributions can be calculated for compartments which are surface-occupying (membranes). This is achieved by another stereological principle involving application of test line probes (Fig. 1B). If such lines are randomly distributed and oriented on random section planes, they intersect membranes with probabilities determined by their relative surface areas. Again, resulting distributions can be used to compare expected and observed distributions of gold particles.

Direct estimates of RLI.

This entails simulating the random (expected) distribution and then testing whether actual gold particles are distributed in the same fashion. As an illustration, consider the example in Table 1 where the data might represent counts made on a sample of labelled cells of the same type or from the same study group. The cell is divided into four volume-occupying compartments.

Table 1.

Approach 1 – testing for differences in the observed distributions of gold particles between compartments in a single group of cells, estimating RLI from observed and expected numbers of gold particles and undertaking a chi-square analysis

Compartments Ngo P Nge RLI (= Ngo/Nge) χ2 χ2 as %
RER + Golgi 81 10 10.556 7.67 470.10 55.1
Granules 79 14 14.778 5.35 279.09 32.7
Mitochondria 15 18 19.000 0.79 0.84 0.1
Residuum 34 156 164.667 0.21 103.69 12.1
Column total 209 198 209 1.00 853.72 100
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For total χ2 = 853.72 and df = 3, P < 0.001. The distribution of gold particles is not random. There is preferential labelling of the RER + Golgi (RLI > 1 and partial chi-square accounts for ∼ 55% of total) and granules (RLI > 1 and chi-square accounts for ∼ 33% of total).

The total number of random test points falling on the whole cell (ΣP = 198) and the observed number of gold particles (ΣNgo = 209) are used to calculate the expected gold particles (Nge) for each compartment. For example, if 209 gold particles were randomly distributed on the sections, we would expect Nge for the granule compartment to be 14 × 209/198 = 14.778. Furthermore, this step offers the opportunity to derive a measure of the degree to which a particular compartment is labelled in comparison with random labelling. In fact, RLI is calculated by dividing Ngo by Nge for each compartment. So, for granules, RLI = 79/14.778 = 5.35. It seems that granules are at least five times more intensely labelled than might be expected for a purely random scatter of gold particles. The corresponding partial chi-square value for any compartment is calculated from observed and expected gold counts as (Ngo − Nge)2/Nge. For granules, the partial chi-square value is (79 − 14.778)2/ 14.778 = 279.09.

For the full dataset in Table 1, the total chi-square value is 853.72 and, for 3 degrees of freedom (df, determined by 2–1 groups × 4–1 compartments), the probability level is P < 0.001. This means that the null hypothesis (the labelling pattern is essentially random) must be rejected.

Where observed and expected distributions are shown to be significantly different, criteria for deciding on preferential labelling of a compartment are invoked. There are two criteria: (i) the RLI value for the compartment must be > 1 and (ii) the partial chi-square value must account for a significant proportion (say 10% or more) of total chi-square. On these grounds, the cells display preferential labelling of two compartments, that is RER + Golgi and granules (Table 1).

For statistical testing by chi-square analysis, a mix of labelled and unlabelled compartments should be included, especially if the labelled compartments have similar RLI values (Mayhew et al. 2002). The test also imposes conditions on the numbers of expected gold particles on individual compartments (Mayhew et al. 2004). No more than 20%, and preferably none, of the compartments should have < 5 expected gold particles and this may influence the choice of compartments and numbers of gold particles to count. For instance, if it is necessary to include a compartment which is small, rare or poorly labelled, extra effort will be required in counting gold particles associated with it. If the compartment is not of primary interest, it can be subsumed into some larger compartment (e.g. ‘residuum’ or ‘rest of cell’).

RLI estimated via LD

An alternative way to test for non-random labelling of compartments within a cell is to compare LDcomp of each compartment with LDcell. This can be performed simply and efficiently by expressing the LD of a volume-occupying compartment with the estimator LDcomp = Ngo/Pcomp, where Pcomp is the sum of test points falling on that compartment (Mayhew et al. 2003). The RLI value for any compartment is calculated as RLIcomp = LDcomp/LDcell.

Table 2 provides LD values for each compartment in a cell. For example, the LD for granules is estimated as 79/14 = 5.643 gold particles per test point and LDcell as 209/198 = 1.056 gold particles per point. It follows that the RLI for granules is 5.643/1.056 = 5.35 and the partial chi-square is 279.09 (as in Table 1). Again, it is clear that there is preferential labelling of granules and RER + Golgi.

Table 2.

Approach 1 – testing for differences in the observed distributions of gold particles between compartments in a single group of cells, estimating RLI from LD and undertaking a chi-square analysis

Compartments Ngo P LD (= Ngo/P) RLI (= LD/LDcell) χ2 χ2 as %
RER + Golgi 81 10 8.100 7.67 470.10 55.1
Granules 79 14 5.643 5.35 279.09 32.7
Mitochondria 15 18 0.833 0.79 0.84 0.1
Residuum 34 156 0.218 0.21 103.69 12.1
Column total 209 198 1.056 1.00 853.72 100
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Again, total χ2 = 853.72 and df = 3, P < 0.001. There is preferential labelling of the RER + Golgi and granule compartments.

As originally presented, Approach 1 catered for compartments belonging to the same category, that is, they are all either volume-occupying or surface-occupying. However, it is now possible to deal with target antigens associated with different categories of compartment or translocating from one to another, for example from plasma membrane to interiorised vesicles (Mayhew & Lucocq, 2008a). The more general approach attempts to treat all compartments in a similar manner by recognising that surface-occupying compartments appear on TEM thin sections as membrane trace lengths, whereas volume-occupying compartments appear as profile areas. As a result of this, there is a dichotomy: profiles can be hit by randomly superimposed test point probes but membrane traces cannot (the probability of this occurring is zero).

To overcome this dichotomy, linear membrane traces are converted to profile areas (Mayhew & Lucocq, 2008a). In practice, this involves defining an ‘acceptance zone’ on both sides of the membrane trace. A convenient width for this zone is twice the diameter of the gold particles used for labelling. The profile area of the acceptance zone is calculated by multiplying its overall width by its trace length estimated by intersection counting. Alternatively, the number of equivalent test points can be counted after randomly superimposing a lattice of test points (Mayhew & Lucocq, 2008a,b;).

An additional issue is that, although most membrane traces are clearly visible on TEM thin sections, some are indistinct or vague because the parent membrane was not cut orthogonally by the section plane. The observed numbers of gold particles falling on membranes are obtained by confining counts to membrane traces which are clearly visible because their parent membranes were sectioned orthogonally. These numbers must then be corrected for image loss to calculate corresponding Nge values. Appropriate correction factors can be estimated by goniometry or stereology (Mayhew & Reith, 1988; Mayhew & Lucocq, 2008a,b;).

Table 3 provides a virtual dataset for a mixture of volumeoccupying compartments (RER cisternae, mitochondria, residuum) and a surface-occupying compartment (granule membranes). Compartments were labelled with 10-nm gold particles so the overall width (w) of the membrane acceptance zone was taken to be 40 nm, or 0.04 μm (0.02 μm on each side of the membrane trace) and the correction factor for membrane loss was 9.03. This would be appropriate for roughly orthogonally sectioned membranes with a critical angle of tilt from the electron axis of up to 5° (Mayhew & Reith, 1988; Mayhew & Lucocq, 2008a,b). A total of 10 gold particles were counted on clear membrane images of granules and so the number corrected for image loss was 10 × 9.03 = 90.3. By the same argument, 45 test line intersections (I) were counted with clear (orthogonally sectioned) images of granule membranes so the figure corrected for image loss is 45 × 9.3 = 406.35 intersections. Using a square lattice of ‘vertical’ and ‘horizontal’ test lines with a line spacing of d = 0.5 μm on the scale of the specimen (equivalent to an area of 0.25 μm2 per test point), this corresponds to a point count of (π/4 × I × d × w)/ 0.25 = (3.1416/4 × 406.35 × 0.5 × 0.04)/0.25 = 25.53 falling on the acceptance zone of granule membranes.

Table 3.

Approach 1 – testing for differences in the observed distributions of gold particles in cells with a mixture of volume-occupying (RER cisternae, mitochondria, residuum) and surface-occupying (granule membrane) compartments. The orthogonally sectioned membranes are treated as profiles, correcting for membrane image loss and RLI is then estimated from LD and a chi-square analysis undertaken

Compartments Ngo P or I Corrected P Nge LD RLI χ2 χ2 as %
RER cisternae 30 28 28 42.84 1.071 0.70 3.85 4.5
Granule membrane (10) 90.3 (45) 406.35 25.53 39.06 3.537 2.31 67.22 79.5
Mitochondria 21 15 15 22.95 1.400 0.92 0.17 0.2
Residuum 63 65 65 99.45 0.969 0.63 13.36 15.8
Column total 204.3 133.53 204.3 1.530 1.00 84.59 100
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For total χ2 = 84.59 and df = 3, P < 0.001. The distribution of gold particles is not random. Granule membranes are preferentially labelled (RLI > 1 and partial chi-square accounts for ∼ 79% of total).

Nge values for each compartment were calculated from the corrected point totals and Ngo values and then the corresponding LD and RLI values were computed. For the final dataset, the total chi-square value of 84.59 for df = 3 gives P < 0.001. The RLI value (2.31) and partial chi-square value (79.5% of total) indicate preferential labelling of granule membranes.

Approach 2 – producing distributions of specific labelling

A limitation of Approach 1 is that it does not distinguish between gold particles which represent specific rather than non-specific labelling. An effective way of controlling for specificity is to alter the expression or location of the target antigen (e.g. by using gene deletion, siRNA, mutation, microinjection, chemical modification). This has been referred to as specimen-based control (Lucocq & Gawden-Bone, 2010) and these authors have devised an approach for abstracting specific labelling distributions by using separate groups of cells which show normal and reduced expression (Fig. 2). The description below is a variation on their approach.

Fig. 2.

Fig. 2

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Estimating specificity of labelling (Approach 2). Here, two groups of cells are compared: those showing normal expression (A) and those with reduced or absent expression (B). The observed gold particle distributions across compartments are determined for each group and used to correct the observed distribution for the effects of non-specific labelling. To confirm preferential specific labelling of compartments, the corrected observed distribution may be compared with an expected distribution by chi-square analysis.

To begin, two groups of cells are selected: one to represent normal expression (e.g. wild-type), given the symbol +, and the second to represent reduced or absent expression (e.g. knockout), given the symbol −. Next, the observed numbers of gold particles found on selected compartments (say, volume occupiers) are counted in each group, Ngo+ and Ngo−. By superimposing lattices of test points on randomly sampled microscopical fields from each group, the observed gold counts can be converted into labelling densities, LD+ and LD−, expressed as gold particles per test point. The specific labelling density for each compartment, LDsp, is estimated as LDsp = LD+ − LD−.

In addition, the fraction of observed labelling that is specific (Fsp) for a given compartment can be estimated as Fsp = LDsp/LD+.

A worked example is provided in Table 4. This uses the dataset in Table 1 and treats the cells therein as belonging to the normal expression group. For instance, LD+ for the granule compartment in normal expression cells is estimated to be 5.643 gold particles per test point, whereas LD− in the reduced expression cells is only 1.077. Therefore, LDsp for this compartment is equal to 4.566 gold particles per test point and Fsp is 4.566/5.643 = 0.809. In other words, almost 81% of the labelling of granules is specific.

Table 4.

Approach 2 – calculating specific labelling densities (LDsp) and fractions of labelling that are specific (Fsp) in two cell groups representing normal (+) and reduced (−) expression. The normal expression cell is the same as that in Tables 1 and 2

Compartments Ngo+ P+ LD+ Ngo− P− LD− LDsp Fsp
RER + Golgi 81 10 8.100 17 12 1.417 6.683 0.825
Granules 79 14 5.643 14 13 1.077 4.566 0.809
Mitochondria 15 18 0.833 12 15 0.800 0.033 0.040
Residuum 34 156 0.218 29 175 0.166 0.052 0.239
Column total 209 198 1.056 72 215 0.335 0.721 0.683
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By back calculation, it is now possible to estimate the number of gold particles on each compartment which represents specific labelling. For example (see Table 5), LDsp for granules is 4.566 gold particles per test point but this compartment in the LD+ group contained 14 test points. Therefore, Ngosp for granules is predicted to be 4.566 × 14 = 63.92. The total points falling on the cell (Σ = 198) and the total number of specific gold particles (Σ = 139.46) can now be used to calculate the expected number of specific gold particles for each compartment, Ngesp. In this way, the expected number of gold particles falling on granules is calculated to be 14 × 139.46/198 = 9.86. The specific RLI for granules is equal to 63.92/9.86 = 6.48. The granules appear to exhibit more than six-fold greater labelling than that predicted for a random scatter of gold particles. The corresponding partial chi-square for granules amounts to 296.40 and the total chi-square for the entire dataset is 909.96. For 3 degrees of freedom, the P-value is < 0.001. Overall, the data confirm that two compartments, granules and RER + Golgi, show preferential specific labelling.

Table 5.

Approach 2 – testing for differences in the specific-labelling distributions of gold particles between compartments in a cell, estimating RLI from observed and expected numbers of gold particles and undertaking a chi-square analysis

Compartments LDsp P+ Ngosp Ngesp RLIsp (= Ngosp/Ngesp) χ2 χ2 as %
RER + Golgi 6.683 10 66.83 7.04 9.49 507.79 55.8
Granules 4.566 14 63.92 9.86 6.48 296.40 32.6
Mitochondria 0.033 18 0.60 12.68 0.05 11.51 1.3
Residuum 0.052 156 8.11 109.88 0.07 94.26 10.4
Column total 0.721 198 139.46 139.46 1.00 909.96 100
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For total χ2 = 909.96 and df = 3, P < 0.001. The specific-labelling distribution of gold particles is not random. There is preferential labelling of the RER + Golgi (RLI > 1 and partial chi-square accounts for ∼ 56% of total) and granules (RLI > 1 and chi-square accounts for ∼ 33% of total).

Approach 3 – testing for shifts in compartment labelling in different groups of cells

This approach is used to test whether the distribution of gold particles across compartments alters in different groups of cells. The observed numerical frequency distributions of raw gold counts in different groups of cells are compared directly by contingency table analysis (Mayhew et al. 2002, 2003; Mayhew & Desoye, 2004).

For a particular compartment in a given cell, the number of expected gold particles is calculated by multiplying the corresponding column sum by the corresponding row sum and then dividing by the grand row sum. For example (Table 6), in Group A, the expected gold particles on the plasma membrane is given by 228 × 286/855 = 76.27. With an observed gold count of 63, partial chi-square amounts to (63 − 76.27)2/76.27 = 2.31.

Table 6.

Approach 3 – testing for differences in the observed distributions of the same membrane antigen (labelled by gold particles) between three groups of cells, estimating observed (expected) numbers of gold particles by contingency table analysis

Compartments Group A Group B Group C Row total χ2 χ2 as %
Plasma membrane 63 (76.27) 105 (101.35) 118 (108.38) 286 2.31, 0.13, 0.85 14.1, 0.8, 5.23
Endosomal membrane 7 (15.47) 21 (20.55) 30 (21.98) 58 4.63, 0.01, 2.93 28.4, 0.1, 17.9
Golgi membrane 29 (24.80) 31 (32.96) 33 (35.24) 93 0.71, 0.12, 0.14 4.4, 0.7, 0.9
Mitochondrial (outer) 40 (33.60) 42 (44.65) 44 (47.75) 126 1.22, 0.16, 0.29 7.5, 1.0, 1.8
Residuum 89 (77.87) 104 (103.48) 99 (110.65) 292 1.59, 0.00, 1.23 9.7, 0.0, 7.5
Column total 228 303 324 855 16.33 100
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For total χ2 = 16.33 and df = 8, P < 0.05. The distributions differ because cells in Group A have fewer gold particles than expected on plasma membrane (chi-square is ∼ 14% of total) and endosomal membrane (chi-square is ∼ 28% of total). Cells in Group C have more gold particles than expected on endosomal membrane (chi-square is ∼ 18% of total).

Total chi-square for these three groups is 16.33 and, for df = 8 (3–1 groups × 5–1 compartments), P < 0.05. Therefore, the null hypothesis of no difference in distributions between groups can be rejected. Inspection of partial chi-square values reveals that the plasma membrane and endosomal membrane compartments are responsible for the difference. Cells in Group A have fewer gold particles than expected on these membranes. In contrast, cells in Group C have more gold particles than expected on endosomal membranes (Table 6).

For this approach, magnification need not be known or standardised between groups. For statistical evaluation by contingency table analysis, it is advisable that expected numbers of gold particles should not be < 5. It is also sensible to aim for similar column sums for total gold counts in each group of cells so that statistical analysis is not distorted by large discrepancies between groups.

A potential disadvantage of Approach 3 is that it may not suffice to permit mechanistic interpretations of shifts in labelling patterns. For example, a shift of labelling away from the plasma membrane and into the cell could reflect changes in membrane LD (resulting from a change in antigen concentration) or membrane extent (resulting from a change in surface area). In such situations, it would be wise to support analysis by estimating LD or RLI values (e.g. Schmiedl et al. 2005).

Approach 4 – testing for colocalisation of different-sized gold particles

Sometimes, the study aim is to test whether different antigens (labelled with different sizes of gold marker) colocalise in a chosen set of compartments. It is worth noting that the LD and RLI methods described above could be used to test for such differences. An alternative version can be applied to test directly for colabelling in individual profiles which make up a given compartment (Mayhew & Lucocq, 2011).

Version 4a – dealing with compartments

This version is appropriate when testing for colocalisation in a multilabelling experiment using different sizes of gold particle to label two or more target molecules in a set of compartments (Fig. 3). Evidence for colocalisation can be adduced if the distribution of gold label between compartments, or the labelling of a given compartment, does not change significantly for the different sizes of gold particle. By way of illustration, imagine a triple-labelling experiment (using three sizes of gold particle to localise three distinct antigens) in which the aim is to test for colocalisation in membrane compartments (Table 7). The calculations are performed as for Approach 3.

Fig. 3.

Fig. 3

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Testing for colocalisation of different-sized gold particles in a multilabelling study (Approach 4a). Small gold particles lying on compartments of interest are counted and provide an observed distribution. Another observed distribution is obtained by counting large gold particles across the same set of compartments. The two numerical frequency distributions are compared by a combination of chi-square and contingency table analysis. The same basic principle may be used to test for shifts in labelling distributions between two groups of cells in a single-label study (Approach 3).

Table 7.

Approach 4a – testing for membrane colocalization of three different antigens labelled by 5, 10 and 15 nm gold particles, estimating observed (expected) numbers of gold particles by contingency table analysis

Compartments 5 nm gold 10 nm gold 15 nm gold Row total χ2 χ2 as %
Plasma membrane 17 (18.04) 13 (13.33) 15 (13.63) 45 0.06, 0.01, 0.14 3.5, 0.5, 7.9
Secretory granule membrane 121 (117.89) 85 (87.08) 88 (89.03) 294 0.08, 0.05, 0.01 4.7, 2.8, 0.7
Golgi membrane 60 (63.76) 47 (47.09) 52 (48.14) 159 0.22, 0.00, 0.31 12.7, 0.0, 17.6
Mitochondrial (outer) 12 (11.23) 9 (8.29) 7 (8.48) 28 0.05, 0.06, 0.26 3.0, 3.5, 14.8
Residuum 31 (30.08) 24 (22.21) 20 (22.72) 75 0.03, 0.14, 0.32 1.6, 8.2, 18.5
Column total 241 178 182 601 1.75 100
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For total χ2 = 1.75 and df = 8, P = 0.99. The distributions do not differ significantly. It appears that the three antigens colocalise.

With 5-nm gold particles, Σ = 241 were counted, of which 17 were associated with plasma membrane, 121 with the membrane of secretion granules, 60 with Golgi membranes, 12 with outer mitochondrial membrane and 31 with other membranes. Corresponding totals for 10- and 15-nm gold particles were 13, 85, 47, 9, 24 and 15, 88, 52, 7, 20, respectively. Total chi-square amounted to 1.75 for which, with df = 8 (3–1 groups × 5–1 compartments), P = 0.99. The distributions do not differ significantly and the data seem to indicate that antigens colocalise. Further analysis to calculate LD or RLI values (Approach 1) would help to identify the main sites of colocalisation.

Version 4b – dealing with individual organelle profiles

It is may be of interest to know whether individual organelles that make up a volume-occupying compartment are dual-labelled. The procedure here (Mayhew & Lucocq, 2011) is to examine whether an organelle profile (identified as containing a given antigen by labeling with one size of gold particle) also labels for a second antigen (identified by another size of gold particle). This can be tackled by selecting individual organelle profiles using an SUR set of unbiased counting frames such as forbidden line frames (Gundersen, 1977; Sterio, 1984). With such frames, profiles are selected if they are entirely within the frame or if they touch its acceptable borders but do not touch its forbidden borders and their extensions. Selected profiles are counted and divided into four classes: double positive, positive only for the first antigen, positive only for the second antigen, and double negative (Fig. 4). So far, this approach has been developed to deal with dual labelling of volume-occupying compartments such as small vesicles (Mayhew & Lucocq, 2011). Alternative sampling strategies will be required to deal with large surface-occupying compartments (e.g. plasma membrane, RER membranes) that are not associated with small vesicles.

Fig. 4.

Fig. 4

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Testing for colabelling of structural profiles in a dual-labelling study (Approach 4b). An unbiased counting frame is superimposed at a random location on a cell in which target molecules have been labelled separately with small and large gold particles. Secretory granule profiles (black) are selected and counted if they fall completely within the frame or touch its allowable edges (green). Profiles cannot be counted if they touch the forbidden lines or their extensions (red). On these criteria, 10 profiles are counted. Of these, two are dual-labelled, one is labelled by small gold particles alone, three are labelled by large gold particles alone and four are unlabelled. The numbers of profiles in the different classes are compared by contingency table analysis coupled with either a chi-square test or Fisher's exact test.

In the example provided (Table 8), 38 organelle profiles were selected by the counting frames. Of these, seven were labelled for both antigens, one was labelled for the first antigen (5-nm gold particles) only, five for the second antigen (10-nm gold particles) only, and 25 were double negative. Again, the numbers of organelle profiles in each labelling class are analysed using a 2 × 2 contingency table. Consequently, if some of the frequencies are low (i.e. some expected values are < 5), use of the chi-square test will not be admissible but, fortunately, Fisher's exact probability test suits data classified in two ways. With this test, a probability value of P < 0.05 signifies that labelling of profiles by the two sizes of gold particle is not independent. In other words, dual labelling occurs more (or less) often than would be expected for a random process. To help interpret outcomes, an odds ratio is calculated. For example, the ratio of labelled : unlabelled profiles for 10-nm gold particles is calculated separately for each of the groups that are positive and negative for 5-nm gold particles. The odds ratio is then the ratio of these two ratios. The magnitude of the odds ratio indicates whether there is a higher proportion of labelling by 10-nm particles on profiles that are also labelled by 5-nm gold particles (Mayhew & Lucocq, 2011).

Table 8.

Approach 4b – testing for colabelling of individual organelle profiles containing antigens labelled by 5-nm (first antigen) or 10-nm (second antigen) gold particles by contingency table analysis

10 nm+ 10 nm− Row total Ratios 10 nm+ : 10 nm−
5 nm+ 7 1 8 7
5 nm− 5 25 30 0.2
Column total 12 26 38 Odds ratio = 35
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Values represent observed numbers of variously labelled profiles selected with unbiased counting frames. The Fisher exact test yields P < 0.001. The two labelling patterns are not independent. The odds ratio (7/0.2 = 35) indicates that this is attributable to dual-labelling.

For the data in Table 8, Fisher's exact test gives a probability value of P < 0.001. The labelling patterns are not independent and the odds ratio [(7/1)/(5/25) = 35)] indicates dual labelling of these organelles.

Approach 5 –mapping the positions of gold particles relative to a fixed cell axis

The approaches described so far serve the needs of those interested in labelling intensities and compartmental distributions. However, they are not designed to map labelling in a three-dimensional sense. To achieve this, a stereological tool known as the rotator can be applied. As originally presented (Vedel-Jensen & Gundersen, 1993), the rotator is a two-step local estimator existing in isotropic and vertical versions. The vertical version begins by uniformly sampling cells according to their number using physical disectors (Sterio, 1984) applied at light microscopic or TEM levels. The disector section planes are randomly rotated around an identifiable axis of sampled cells in order to estimate certain structural quantities, principally volumes (e.g. Mironov & Mironov, 1998). The second step involves measuring or classifying distances of cellular structures from the vertical axis passing through an identifiable feature within cells such as the centrosome/centrioles or nucleolus. Interestingly, the vertical rotator can be modified to derive efficient local estimates of numbers of structures at specific locations with respect to this vertical axis (Nyengaard & Gundersen, 2006). Recently, Lucocq & Gawden-Bone (2009) have exploited the latter to map numbers of gold particles within cells relative to the position of the nuclear equator.

An efficient sampling procedure is to generate random sections orthogonal to a convenient reference plane which might be intrinsic to the cells or external to them. As an example of the former, consider the equatorial plate of mitotic cells and, of the latter, the underlying basal lamina of epithelial cells or the medium or dish of cultured cells. Having chosen randomised section orientations orthogonal to the reference plane, cells are selected by means of physical disectors so as to identify those with a single point-like feature such as the nucleolus within the nucleus or the centrosome within the cytoplasm. A short series of sections spanning the chosen feature is now taken and labelled as appropriate with immunogold. Cells with profiles of the chosen feature are selected when they appear on one section plane (the reference section) but not on a parallel section (the look-up section). The reference and look-up sections of the disector pair are separated by a known distance, t, equivalent to section thickness. TEM fields are recorded and a vertical axis identified on them which passes through the chosen feature of the selected cells (Fig. 5).

Fig. 5.

Fig. 5

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Estimating spatial distributions of label using the rotator (Approach 5). The cell lies on an external horizontal reference plane (the culture medium substratum) and has been cut by a section vertical to this plane. On the cut surface, a vertical axis (blue arrow) is indicated and passes through the centrosome situated near the centre of the cell profile in the nuclear hof. A lattice of equally spaced lines with five distance classes is superimposed. Gold particles are classified according to both the compartment on which they lie and their distances from the vertical axis. The black arrow indicates a gold particle lying on a mitochondrial profile in distance class 5. From such data, three-dimensional spatial distributions of gold particles can be established.

On the sampled TEM fields, gold particles lying on compartments of interest are identified and the distances (dv) from these particles to the vertical axis are classified. This can be performed with the aid of a test lattice of systematic points (Nyengaard & Gundersen, 2006) or lines (Lucocq & Gawden-Bone, 2010) aligned parallel to the vertical axis (Fig. 5). Alternatively, a ruler graduated into classes with equal intervals can be used. The numbers of gold particles falling on each compartment are summed for each class and then multiplied by the corresponding class mid-points. The sum of all these values (Σdv), multiplied by π/t, provides an estimator of the number of gold particles in the cell (Lucocq & Gawden-Bone, 2010). The factor π/t is appropriate for gold particles applied on section (post-embedding) because, clearly, these cannot be present on both the reference and look-up sections.

For a worked example, refer to the data in Table 9. Here, a set of 10 epithelial cells has been sampled using physical disector planes randomly rotated about the epithelial basal lamina and orthogonal to it. The section thickness is 70 nm (= 0.07 μm). The vertical axis passed through nucleoli appearing on the reference but not the look-up section. A ruler with seven size classes and a class interval equivalent to 0.6 μm on the specimen scale was applied and distances from gold particles to the vertical axis were classified for those lying on RER, the Golgi complex and secretion granules.

Table 9.

Approach 5 – calculating spatial distribution of gold particles in 10 epithelial cells sampled using the rotator

Observed gold particles, Ngo Sum of distances, Σdv
Class Mid-class point (μm) RER Golgi complex Granules RER Golgi complex Granules
1 0.3 11 78 53 3.3 23.4 15.9
2 0.9 29 22 31 26.1 19.8 27.9
3 1.5 19 31 2 28.5 46.5 3.0
4 2.1 1 34 17 2.1 71.4 35.7
5 2.7 0 1 0 0 2.7 0
6 3.3 21 29 0 69.3 95.7 0
7 3.9 25 8 3 97.5 31.2 11.7
Column total 106 203 106 226.8 290.7 94.2
Ng = Σdv × π/0.07 10178.8 13046.6 4227.7
Ng/cell = Ng/10 ∼ 1018 ∼ 1305 ∼ 423
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Distances in μm from a vertical axis (orthogonal to epithelial basal lamina and passing through the nucleolus) were classified using equidistant (0.6-μm) intervals. Section thickness was 0.07 μm.

For the granules, 53 gold particles were found within class 1, the mid-point for which was 0.3 μm. The sum of these distances was therefore 53 × 0.3 = 15.9 μm. For class 2, the corresponding values were 31 gold particles, mid-point 0.9 μm and Σ = 27.9 μm. Summing all class values, the cumulative distances for granules amounted to Σdv = 94.2 μm. The number of gold particles in this set of cells is now estimated as Ng = Σdv × π/t = 94.2 × (3.1416/0.07) = 4227.7. As a total of 10 epithelial cells were sampled, the approximate number of gold particles within the granule compartment was 423. Corresponding totals for RER and Golgi were 1018 and 1305 gold particles, respectively.

Discussion

The approaches reviewed here have the potential to advance quantitative immunoEM by virtue of their rigour in terms of efficiency and minimal bias and the fact that they form a coherent set based on sound principles of sampling, estimation and inferential statistics. All the worked examples presented were based on synthetic rather than real experimental data. However, except for the most recently published approaches (for colocalisation, specificity evaluation and three-dimensional spatial analysis), they have been applied in a wide variety of studies involving animal cells, plant cells, bacteria and viruses. Hitherto, correlation functions and other tools have been used to quantify colocalisation (Philimonenko et al. 2000; Anderson et al. 2003; Wilson et al. 2004; D'Amico & Skarmoutsou, 2008).

Since Approach 1 was introduced (Mayhew et al. 2002, 2003), its LD and RLI variants have been applied to localise antigens in diverse cells and tissues (Ochs et al. 2002; Cernadas et al. 2003; Fujii et al. 2003; Mironov et al. 2003; Bennett et al. 2004; Kweon et al. 2004; Mayhew & Desoye, 2004; Mazzone et al. 2004; Wu et al. 2004; Fehrenbach et al. 2005; Potolicchio et al. 2005; Schmiedl et al. 2005; Signoret et al. 2005; Touret et al. 2005; Vancova et al. 2005; Young et al. 2005, 2008; Zhang et al. 2005; Li et al. 2006; Lopes et al. 2006; Vasile et al. 2006; Welsch et al. 2006; Davey et al. 2007; Driskell et al. 2007; Jacob et al. 2007; Southworth et al. 2007; Tomas et al. 2007; Abdallah et al. 2008; Godsave et al. 2008; Holst et al. 2008; Oberley et al. 2008; Piwonska et al. 2008; Portolani et al. 2008; Swanlund et al. 2008; Francolini et al. 2009; Ruel et al. 2009; Vigliano et al. 2009; Chevalier et al. 2010; Habermann et al. 2010; Heinz et al. 2010; La Rosa et al. 2010; Segretain et al. 2010; Ueda et al. 2010; Zhou et al. 2010; Keel & Songer, 2011; Ridsdale et al. 2011; Smeele et al. 2011). Similarly, Approach 3 (Mayhew et al. 2002, 2004; Mayhew & Desoye, 2004) has been used to follow shifts in antigen distributions in several different groups of cells (Potolicchio et al. 2005; Santambrogio et al. 2005; Mühlfeld & Richter, 2006; Nithipongvanitch et al. 2007; Godsave et al. 2008).

Specificity is an important potential source of bias in labelling studies because the observed labelling by gold particles may be both specific and non-specific for the target antigens. Non-specific labelling can arise in various ways and influence any compartment but it seems to affect mostly mitochondria and nuclei. It is influenced by such factors as primary antibody dilution, salt concentration, use of detergents and addition of blocking agent proteins (Griffiths, 1993). The approach to quantifying specific labelling proposed by Lucocq & Gawden-Bone (2010) represents a real advance and will be a valuable addition to the growing portfolio of immunoEM methods. Future refinements might include an iterative approach to test the impact of different levels of reduced expression, for example by assuming that this represents levels between 100% (equivalent to knockout) and some arbitrary minimum of, say, 20% knockdown.

Apart from specificity, another factor influencing the labelling of target antigens is labelling efficiency (LE). This is a measure of the number of gold particles per target molecule. However, on-section labelling does not guarantee that all of the target molecules are labelled by gold particles and, occasionally, a given molecule might be associated with more than one gold particle. In practice, LE is influenced by several technical factors including fixation, embedding and labelling protocols and gold particle size (as size increases, so LE declines). Even when these factors are controlled, LE may still vary between compartments, mainly because of differential penetration of labelling reagents into the section. Methods for estimating LE require reference to some external standard and are discussed more fully elsewhere (Lucocq, 1992; Griffiths, 1993; Mayhew & Lucocq, 2008b; Mayhew et al. 2009). They usually involve preparing reference gels with known amounts of antigen or biochemical estimates of the total amounts of antigen. Interestingly, a further potential development of the specificity correction procedure (Approach 2) is to apply resulting correction factors to apparent LE estimates.

Application of the rotator sampling and estimation tools has obvious benefits for mapping labelling in three-dimensional space. With vertical sectioning, there is the potential for applying the approach to study polarised, oriented or dividing cells and cells (or syncytia) exhibiting movement of organelle compartments from one region to another (Lucocq & Gawden-Bone, 2009). One potential disadvantage acknowledged by the authors themselves is the extra effort involved in sampling and estimation. However, there is currently no alternative or more efficient way of obtaining this sort of detailed numerical and spatial information. The authors have suggested the combination of gold counting with other stereological tools as a future development to estimate labelling densities as gold particles per μm3 of a compartment. However, another possibility would be to combine stereological analysis with electron tomography (Vanhecke et al. 2007). With electron tomography, stacks of sampled thick sections (200–400 nm thickness) can be used to estimate compartment volumes, surface areas and numbers. Moreover, section thickness can be reduced to a few nanometres, thereby reducing sources of bias which are otherwise difficult to correct. Application to pre-embedded immunogold-labelled sections (Griffiths, 1993) would be required to determine absolute numbers of gold particles and express labelling densities per μm3 of organelle volume or per μm2 of membrane surface.

Acknowledgments

As ever, I am grateful for the friendship, collegiality, humour, advice and collaboration of my fellow teachers on international courses of stereology, electron microscopy and cell and molecular biology.

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