A Stereological Approach for Estimation of Cellular ... · stereology rotator immuno-EM gold labeling quantification ... Pappus theorem (Howard and Reed 1998) and utilizes random

Volume 57(8): 709–719, 2009Journal of Histochemistry & Cytochemistry

http://www.jhc.org

ARTICLE

A Stereological Approach for Estimation of CellularImmunogold Labeling and Its Spatial Distribution in OrientedSections Using the Rotator

John Milton Lucocq and Christian Gawden-Bone

Division of Cell Biology and Immunology, School of Life Sciences, University of Dundee, Dundee, Scotland,United Kingdom

SUMMARY Particulate gold labeling applied to ultrathin sections is a powerful approachfor locating cellular proteins and lipids on thin sections of cellular structures and compart-ments. Effective quantitative methods now allow estimation of both density and distribu-tion of gold labeling across aggregate organelles or compartment profiles. However, currentmethods generally use random sections of cells and tissues, and these do not readily presentthe information needed for spatial mapping of cellular quantities of gold label. Yet spatialmapping of gold particle labeling becomes important when cells are polarized or showinternal organization or spatial shifts in protein/lipid localization. Here we have applied astereological approach called the rotator to estimate cellular gold label and proportions oflabeling over cellular compartments at specific locations related to a chosen cell axis or cho-sen cellular structures. This method could be used in cell biology for mapping cell compo-nents in studies of protein translocation, cell polarity, cell cycle stages, or component celltypes in tissues. (J Histochem Cytochem 57:709–719, 2009)

KEY WORDS

stereology

rotator

immuno-EM

gold labeling

quantification

polarity

FOR A NUMBER OF DECADES, immunogold labeling onultrathin sections has been used as a method for local-izing proteins and lipids. The method relies on affin-ity probes such as antibodies, which associate withtarget molecules in the section. The antibodies are “con-trasted” using colloidal gold particle reagents and af-ford an easily counted digital readout (Griffiths 1993;Skepper 2000; Bendayan 2001). The quantity of thesediscrete events reflects the number of target molecules(Griffiths 1993; Mayhew and Lucocq 2008) and pro-vides a means for mapping of cellular components.

The standard approaches for quantifying gold la-beling estimate the density or the distribution of goldin relation to compartment profiles (D’Amico andSkarmoutsou 2008). Typically, the gold density is es-timated by combining gold counts with stereological es-timators of profile areas or length, and the distribution

is estimated by counting gold labeling across appropri-ately sampled cellular compartments (Lucocq 1994,2008). For such analyses, recent studies have empha-sized the usefulness of x2 statistics for comparison oflabeling intensities/distributions between compartmentsor experiments (Mayhew and Lucocq 2008).

But these methods are not well suited to mappingcell components in three-dimensional (3D) space. Thereason is that they often employ random sections thatcan intersect parts of a cell that cannot be identified asbelonging to the cell of interest, and may lack preciseinformation about the spatial arrangements of labelingor structures. And yet it could be of interest to map thelocation of antigens relative to a cell axis or a centrallocation in the cell, for example, in polarized cells inwhich membrane domains are organized relative tothe cell axis, or in polarized cells that contain gradientsof organelles through their cytoplasm. Even in cellswithout obvious polarization, there may be regionalvariation in the distribution of cell components, forexample, when the endoplasmic reticulum (ER) is dis-persed and the Golgi is central, or when movement ofendocytic organelles from the periphery toward the cellcenter occurs. One way of mapping gold particles in

Correspondence to: Dr. John Lucocq, Division of Cell Biologyand Immunology, School of Life Sciences, University of Dundee,Dundee, DD1 5EH, Scotland, United Kingdom. E-mail: [email protected]

Received for publication September 3, 2008; accepted December 19,2008 [DOI: 10.1369/jhc.2008.952671].

C The Histochemical Society, Inc. 0022-1554/09/$3.30 709

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individual cells would be to carry out serial sectioning,but this is labor intensive, and it would be preferable touse a method that requires analysis of only a single sec-tion. Such a technique could be a useful tool in cell andtissue biology.

The solution presented here is to use the rotator(Vedel-Jensen and Gundersen 1993; Tandrup et al.1997; Mironov and Mironov 1998). This is a stereo-logical probe that represents an application of thePappus theorem (Howard and Reed 1998) and utilizesrandom rotation of a section plane around an identi-fiable axis to estimate aggregate parameters (such asvolume) within appropriately sampled cells. Becausethe axis may be chosen along a recognizable directionin the cell, this approach is well-adapted for use in po-larized cells, and stereological estimates can be adaptedto obtain local estimates of organelle/structure at spe-cific cell regions relative to the axis or other identifiablestructures (Nyengaard and Gundersen 2006).

However, it has been pointed out recently that therotator can be used in combination with a probe calledthe disector to estimate numbers of cell components/organelles (Nyengaard and Gundersen 2006), and thisprinciple is adapted here for the estimation of gold par-ticle labeling. The method uses a single section throughthe central portions of a cell and allows estimation ofrelative proportions of gold label over different com-partments, estimation of the total amount of gold la-bel per cell in 3D if needed (Lucocq 1992,1994,2008;Griffiths 1993), and importantly, the mapping of quan-tities of labeling relative to a unique reference axis, a cellcenter, or any identifiable structure or set of structures.This adaptation of the rotator for number estimation ofgold particle labeling should be particularly useful forassessing the distribution, amounts, and gradients oflabeling in polarized cells or in specific cell types/cellstages in culture or tissues.

Materials and Methods

Cell Preparation

MDCK cells were grown on polycarbonate filters witha pore size of 1 mm (Sterlitech; Kent, WA). The cellswere fixed in 0.5% glutaraldehyde in 0.2 M PIPES,pH 7.2, at room temperature for 30 min, washed inPBS (155 mM NaCl, 4 mM phosphate buffer, pH 7.4),filters rolled and then embedded using progressive lower-ing of temperature (PLT). Dehydration of the samplewas done in progressive steps of ethanol comprising30%, 50%, 70%, 100%, and 100% v/v in water at0C, 210C, 225C, 240C, and 250C, respectively for30 min at each step, followed by HM23 resin-ethanolat 250C in volume ratios of 25:75, 50:50, and 75:25,each for 1 hr, followed by an hour in 100%HM23 witha final change to 100%HM23 and infiltration for 16 hr.The resin was polymerized using a 15-Wultraviolet lamp

for 24 hr at 250C followed by a 48-hr polymerizationstep at 25C. All PLT steps were done using a Leica AFSfreeze substitution machine (Leica Systems; Vienna,Austria). Sections were made with a Diatome diamondknife (Biel, Switzerland) and collected on 1-mm 3 2-mmslot copper support grids coated with pioloform (AgarScientific; Stansted, Essex, UK). Ultrathin sections werecut orthogonal to the monolayer.

Immunogold Labeling and Rotator Sampling

Sections were preincubated on blocking buffer, whichcontained 1% BSA and 0.5% cold-water fish skin gelatin(Sigma; Poole, Dorset, UK) in PBS. This was followedby incubation on anti-actin antibody polyclonal anti-body raised in rabbit (a kind gift from Giulio Gabbiani,Geneva, Switzerland) diluted in the blocking buffer andthen, after washes in PBS, by gold labeling using 10 nmgold 1:100 in PBS (prepared as described in Lucocq1993). Sections were contrasted in 3% uranyl acetatefollowed by lead citrate.

To sample the central region of MDCK cells, a stackof sections was randomly positioned, with approxi-mate intervals of 1 mm between the sections. At eachlocation, a 300-nm section and an adjacent 80-nm sec-tion were mounted separately on slot grids. Images ofthe whole filter were recorded from 300-nm sectionsat low magnification (3300). Cell nuclei with profilesthat appeared in the second (so-called reference) sec-tion and disappeared in the first look-up section wereselected and followed through the series to identifythe section with a nuclear profile of largest diameter.Eighty-nm sections immediately adjacent to this sec-tion were then labeled for actin as described aboveand imaged at higher magnification (37500). Goldparticles located over homogeneous fibrillar materialin contact with the plasma membrane (actin cortex) wereconsidered for quantitation.

Results

Rationale and Overview of the Approach

The rotator was originally used as an approach to es-timate volume and is an application of the Pappustheorem, which states that “If a planar figure revolvesabout an external axis in its plane, the volume of thesolid thus generated is equal to the product of the areaof the figure and the distance travelled by the centre ofthe gravity of the figure” (Vedel-Jensen and Gundersen1993). In electron microscopy, the rotator can be usedto estimate organelle and cell volume (Mironov andMironov 1998; Nyengaard and Gundersen 2006). First,an axis of rotation needs to be defined, and one way todo this is to use sections that are allowed freedom to“rotate” (during processing) around a constant direc-tion. This direction could be “vertical,” passing throughcells orthogonal to a defined horizontal plane, e.g., the

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surface of a culture dish or a plane inside a tissue, suchas an epithelial surface. Sections passing through anappropriately sampled, centrally located structure, suchas a nucleolus, centrosome, or nucleus, can then be usedfor rotator estimates (see below). Another way to allowfreedom of rotation around an axis is to first ensure un-restricted freedom of rotation in all directions duringprocessing. The axis might then be defined after section-ing by an appropriately sampled (and aligned) set ofstructures within the cell. These structures could betwo centrosomes at either end of the mitotic spindle(McCullough and Lucocq 2005) or the long axis passingthrough the apical dendrite and axon of a neuronal cell.Formal ways of ensuring uniform random rotation havebeen described (see Howard and Reed 1998).

For rotator estimates to be unbiased, the cells, orthe centrally located structure within them, must besampled with equal probability. This can be done usingthe disector, which selects individual structures accord-ing to their number rather than their size (Sterio 1984).It may be advantageous in the present approach tosample a central structure such as the centrosome or anucleolus (if solitary) so that the axis of rotation is lo-cated as near to the center of the cells as possible. Analternative is to sample the edge of the cell nucleus firstand then scan through subsequent sections at intervalsuntil the nucleus reaches a maximum size. These pro-cedures tend to position the sections used for estimationfairly reproducibly from cell to cell and aid their identi-fication. They also preserve aspects of cellular organiza-tion that may be present in relation to this axis.

A simple published method for volume estimation inelectron microscopy with the rotator utilizes randompoint hits on organelles, combined with distances ofthese hits from the axis, to estimate global volumes(Mironov and Mironov 1998). But the application ofthe rotator is not limited to the estimation of volume.Number can also be estimated by applying the physicaldisector, in which objects found in one section planeare counted if they disappear in a second section planeparallel to the first (Sterio 1984; Gundersen 1986). Asimple equation (Nyengaard and Gundersen 2006)then combines, the height of the disector, h(dis), andthe distance, d, from the object/structure (str) countedto the axis to estimate the number per cell:

Nstr(cell) 5p

h(dis)?Sd (1)

This forms the basis of a rather straightforwardway of estimating the number of gold particles in 3D(Figures 1B and 2). In immunocytochemical labeling,the gold-labeled epitopes/determinants are unique tothe section, and the gold particles themselves are addedafter sectioning and cannot be present in the adjacentsection(s). Therefore, the height of the disector used

for counting the gold particles is equal to the thickness(t) of the section that has been labeled. So in a rotator:

Ng(cell) 5pt?Sd (2)

Thus, it is only necessary to know the sectionthickness, t, to find the total number of gold parti-cles, Ng(cell), that would label the cell under theconditions of sectioning and labeling. The sum of dis-tances (Sd) can be rather quickly obtained for anygold-labeled section to obtain an estimate of the totalnumber of gold particles per cell. The speed of summa-tion of distances can be further increased by classifyingparticles in bands or zones of equal and known width,located at defined distances from the axis (see Figure 3).It is important to point out that in equations 1 and 2,the denominators h or t are used here because thedisector is used to count gold particles in only one di-rection (i.e., only one labeled section of a pair is usedto sample the structures of interest). In the equationpresented in the report of Nyengaard and Gundersen(2006), the denominator 2h refers to the more con-ventional use, in which both sections of the disectorpair are used for sampling structures of interest ( JensNyengaard, personal communication; see also Sterio1984; Gundersen 1986).

Notice that it is only in rather special circumstancesthat the absolute value of Ng per cell is needed. Oneexample would be the estimation of labeling efficiency,where the number of gold particles per cell is comparedwith the number of molecules estimated biochemically(Lucocq 1992,1994,2008; Griffiths 1993), an issue notdiscussed further here. Section thickness determina-tion can be achieved for resin sections using publishedmethods (Small 1968; Gunning and Hardham 1977),and has also been achieved for thawed frozen sectionsprior to contrasting (Griffiths et al. 1984). Alternatively,labeling may be expressed in terms of a labeling index,in which the section thickness is kept constant fromexperiment to experiment and ignored along with theconstant p (section thickness may influence the labelingsignal if there is penetration into the section; see below).In this case, the sum of distances from the axis for goldparticles in each organelle/compartment/location for allcells, Sd(cells), is related to the number of cells examined:

Mean labeling index 5Sd(cells)Ncells

(3)

In everyday usage, however, it is the proportion oftotal golds over different compartments that is often ofinterest, and this can also be determined in the rotator.Importantly, this proportion cannot be obtained hereby simply counting the numbers of particles over eachcompartment. This is because gold particles furthestfrom the axis have a greater weighting than those close

Immunogold Quantification Using the Rotator 711

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to it. To obtain an estimate of the proportion of totallabeling that would label a compartment in 3D, therotator estimate of the number of particles over theorganelle/compartment per cell is divided by the esti-mate of total particles. Here, the section thickness term t,as well as the constant p, cancel in the equation. There-fore, the fraction of gold particles over an organelle/compartment (comp) compared with the total (tot) isgiven simply by the ratio of sums of distances of goldparticles to the axis:

Ng(comp)Ng(cell)

5Sd(comp)Sd(tot)

(4)

The advantage of the rotator for mapping gold par-ticle location is that the axis of rotation may be defined

according to the cell structure/organization. For exam-ple, in a polarized cell, the axis might be chosen in adirection through the center of a basal nucleus to theapex, through an apical dendrite and basal axon of aneuronal cell, or the centrosome and apex/basolateralaspect of a polarized epithelial cell. Alternatively, the axismay be defined by a vertical section oriented orthogonalto a culture dish or an epithelial surface and may passthrough an appropriately sampled structure such as thecentrosome. The gold labeling can be assigned accordingto its compartment or organelle location or even its posi-tion in space relative to some visible structures, say theplasma membrane or the centrosome or the axis itself.In fact, gold labeling can be grouped/assigned in anyway that allows better understanding of relative quantitiesin different regions/structures of the sampled cell or cells.

Figure 1 Sampling central cell regionsof nuclei and application of the rotatorfor quantifying gold particles. (A) Sam-pling of central regions of nuclei inoriented sections. A stack of semithinsections with an appropriate orienta-tion for rotator analysis (see text) iscut with a constant spacing betweenthe sections, say 1 mm for nuclei of5-mm diameter. At each location, anadjacent thin section is mounted ona single EM support grid. Selectionmay be done using a two-sectionprobe called the physical disector(Sterio 1984). The second section ofthe series (the reference section,dotted line) is used to locate cell nu-cleus profiles (such as the one illus-trated here) that disappear in thefirst, so-called look-up section. If nec-essary cell nuclei profiles can be sam-pled unbiasedly using quadrats placedsystematically with a random startbefore examination in the look-up(see Gundersen 1977; Sterio 1984). Thesemithin sections passing through se-lected nuclei are then examined toidentify the nuclei profiles with thelargest diameter (red arrow and check-mark in figure) or the largest area. Ifnuclei are complex in form, it may beeasier to simply select the middle nu-clear section. The thin section adjacentto the selectedmost “central” semithinsection is then immunogold labeled,and images are recorded at a magnifi-cation that allows gold and structuresof interest to be identified clearly. (B)A cell in a vertical section is sampledby unbiased selection of a centrallylocated structure/feature (in this casethe centrosome). This defines an axis

of rotation. The axis may be selected according to the organization of the cell in question, e.g., its polarity. Images are recorded and viewedat a magnification suitable for identifying both the gold particle labeling and the compartments of interest. Gold particles in the organelle orregion of interest are then located and their distance from the axis (d) determined and the distances summed. Further processing of thesedata allows estimation of the proportion of cellular gold label in a compartment within a cell or experiment, or changes in the proportion ofcellular gold between experiments (see text). If required, estimates of total gold labeling per cell can be obtained by using the sectionthickness, as described in equation 2. Under these conditions of sectioning and labeling, the total gold per cell may be combined with label-ing efficiency estimates to obtain direct measures of the number of molecules per cell.


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Basic Procedure for Data Acquisition

1. Embed cells in suitable medium for labeling andstructural display. It may be necessary to identifya vertical direction perpendicular to an identifiablehorizontal plane such as the surface of a culturedish or the surface of an epithelium. Embedding isthen carried out so that sections may be cut per-pendicular (vertical) to this axis. Orientation ofthe specimen (or section) around the vertical axisshould be randomized during embedding, and thesection(s) should be placed at a random locationwithin the specimen. In some cases, say for cellsin suspension, an alternative strategy might be toensure random orientation and position (isotropicuniform random) (Nyengaard and Gundersen1992) and then consider cells that are sectionedalong a chosen axis. Here the axis might be definedby apical and basal structures that can been sam-pled appropriately. If a vertical direction is used,this does not have to pass along any preferred axisof the cell structures. However the precise and re-producible location of the vertical axis central tothe cell(s) will reduce variation in the estimatesand allows greater precision, especially if spatialmapping is carried out (see below for details).

2. Select cells appropriate for the study. One possi-bility is to use disectors to select the edge of uniqueorganelles/structures within the cell such as the cen-triole or nucleus (Sterio 1984). Once the cell has beenselected in this way, a short series of sections may benecessary to identify a section that is more centrallylocated in the sampled organelle (Figure 1A). Thiscould be the middle section of a series through the

centriole or nucleus, or the section with the maximalprofile size (diameter or area). Selection can be donewith semithin sections using light microscopy or ultra-thin sections mounted on slot grids using electron mi-croscopy. Selection of section locations and cells usingdisectors should form part of a multistage samplingscheme, as detailed in Lucocq (2008) and Mayhewand Lucocq (2008).

3. Carry out immunogold labeling of sections contain-ing central regions of selected cells/organelles andrecord images at the lowest magnification that al-lows visualization of both gold and the structuresof interest. If ultrathin sections mounted on delicateslot grid support films are to be used for sampling aswell as gold counting, it may be useful to immuno-label the whole set of sections prior to selection ofcells. As with any quantitative study, the sectionsshould be of highest possible quality, with good dis-play of structures/compartments and minimal arti-facts such as folds.

4. Take images covering the whole of each selectedcell (it may be necessary to overlap images and tomake a collage of these). Next, draw an axis bi-secting any structures that define the axis to whichthe gold labeling will be referred. As already noted,the precision of the placement and orientation ofthis axis on the 2D image, and in 3D space, willdetermine the precision of the estimations of goldper cell and also the precision of any local esti-mates of gold labeling relative to cell structuresor to the axis.

5. Identify gold labeling of interest and measure thedistance between gold particles and the selected axis

Figure 2 Theoretical example of goldlabeling for a protein that translocatesthrough the secretory pathway. Cellsexpressing a viral glycoprotein wereinvestigated under conditions inwhichthe glycoprotein first accumulates inthe endoplasmic reticulum (ER; experi-ment 1). The glycoprotein is thenallowed to move by vesicular transportinto the secretory pathway (experi-ment 2), during which time furtherprotein synthesis is inhibited. In experi-ment 2, gold particle labeling increasesin the Golgi and plasma membrane(PM), reflecting intracellular transportthrough the secretory pathway. Afterfixation and embedding, vertical ultra-thin sections passing through the cen-tral regions of cell nuclei were selectedas described in the text and labeledfor the viral glycoprotein. Detailedanalysis of data is given in the textand in Table 1.


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Figure 3 Example of gold labeling for actin analyzed using the rotator in an MDCK cell. The MDCK cells were embedded in Lowicryl HM23and immunogold labeled for actin. Cells were selected using the procedure described in the text and illustrated in Figure 1. (A) Low magni-fication. Gold particles located over apical, basal, and lateral plasma membranes were counted in bands of 0.540-mm width situated aroundthe vertical axis (V), which was placed to bisect the nuclear profile. The rotator estimates are displayed and their calculation explained in Tables 2and 3 and their legends. (B) High-magnification micrograph of the cell apex to illustrate gold labeling (arrows) situated over electron-densematerial in contact with the plasma membrane (cortical actin). Bar 5 100 nm.


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(d). As required by the aims of the study, assignpopulations of particles to regions/structures (see Fig-ures 1B and 2). Then calculate the sum of d for eachcell, or for each compartment or location of interestwithin each cell. To speed up this procedure, it is use-ful to classify gold particles into bands of knownwidth that are oriented along the axis (see Figure 3).The number of gold particles in each band multipliedby the distance of the center of the band to the axis isan estimate of the Sd for that band.

Data Processing

The sum of distances of gold particles from the axisfor each compartment (Sd) is an index of total goldlabeling on that compartment for that cell (labelingindex). This is because the estimate of the total goldlabeling on that compartment for that cell is obtainedby multiplying Sd by a constant (p/t), when mean sec-tion thickness does not vary. The index can be expressedas a mean labeling index by summing distances over anumber of cells and dividing by the number of cellsexamined: Sd(comp)/Ncell. Also, in any one cell-section,Sd for gold labeling on one organelle or location can beused to calculate the proportion of a total pool of goldlabeling (tot) that is associated with that particularorganelle/compartment/location. Sd(comp)/Sd(tot) isan estimator of the fraction of gold labeling over thatcompartment (equation 4 above). Note that becausethese estimates depend on the length of the circles ofrotation, the proportion cannot be found by simplycounting the gold particles (unless the golds are equi-distant from the axis). It is then also possible to com-pare gold labeling of a compartment(s)/location (orindeed whole cell) between two experimental condi-tions (Figure 2; Table 1). The values of Sd(comp) orSd(cell) can be compared as a ratio; for example, asSd(compexp2)/Sd(compexp1), or as (Sd(compexp2) 2 Sd(compexp1))/Sd(compexp1), which reveals the relativechange in labeling in the compartment/cell from onetreatment to the next. Interestingly, under conditionswhere the amount of target molecule per cell is constant,such ratios, e.g., Sd(cellexp2)/Sd(cellexp1), inform aboutany change in the relationship between gold label andtarget molecule (labeling efficiency). Thus, if labelingefficiency decreases, say because of movement betweencompartments or posttranslational modifications, thenthe total labeling per cell will fall.

To estimate the number of golds per cell, it is nec-essary to multiply Sd by p/t, where the section thick-ness t can be found by measurement of section folds(Small 1968), or by changes in the size of a truncatedspecimen block (Gunning and Hardham 1977). Thisestimate is equivalent to the total gold that wouldbe located over that compartment if the cell were seri-ally sectioned entirely at that particular section thick-

ness (see discussion below on labeling penetration intothe section).

Statistical Considerations

For the estimate to reflect the population from which itis drawn, it is important to obtain data from more thanone cell as part of a multistage sampling design (seeMayhew and Lucocq 2008). Data might be obtainedfrom ?10–20 cells in the first instance (see Tables 2and 3), and the variation in any estimate will dependon a number of factors, which include: (1) the intensityof labeling, (2) heterogeneity in distribution of labeling,(3) reproducibility in axis position/orientation, and (4)inherent differences in the cells. If the intensity of label-ing is high, it may be necessary to sub-sample, and thiscan be easily done using systematically spaced quadratsto which unbiased 2D counting rules can be applied(see Real Example below and also Lucocq 2008). Inthis case, the rotator estimates will tend to be more pre-cise if the labeling distribution is more dispersed in thecell volume and will be more imprecise if the labeling isspatially restricted.

Theoretical Example

To illustrate application of the rotator to gold label-ing, we present a theoretical example, which examines

Table 1 Theoretical example

Experiment 1 Experiment 2

dER dGolgi dPM dER dGolgi dPM

1.6 0.24 2.08 0.25 0.532.01 0.21 2.962.09 0.56 2.852.19

Sdorg (cm) 7.89 0.24 0 2.08 1.02 6.34Sdtot (cm) 8.13 9.44Sdorg/Sdtot 0.970 0.030 0 0.220 0.108 0.672Ng/cell 496 15 0 131 64 398Ng/cell (tot) 511 593

Polarized cells from two experiments (described in the text and illustratedin Figure 2) were grown on a substratum, fixed, and embedded in resin. Cellnuclei were sampled unbiasedly using the disector in sections oriented orthog-onal (vertical) to the substratum but with random rotation around the verticaldirection. Centrally located nuclear sections were immunogold labeled, andimages were recorded. An axis bisecting the nuclear profile in a vertical direc-tion was drawn, and the apparent distance (d ) of each gold particle to theaxis was recorded. Then d was summed for gold particles labeling endoplasmicreticulum (ER), Golgi apparatus (Golgi) and plasma membrane (PM) to providea labeling index applicable to these conditions of labeling and magnification.An estimate of the fraction of golds over each organelle (org), compared tothe total (tot) for each experiment, is given by Sdorg /Sdtot. Whereas in experi-ment 1, most (97%) of the gold labeling is present over the ER, this drops to22% in experiment 2, and now 67% of label is found at the plasma mem-brane, indicating movement of the protein from the ER through the Golgi tothe plasma membrane. Total golds (Ng) per cell can be calculated using themagnification of 35000 and section thickness, t, of 0.1 mm. The real Sd 5apparent Sd (mm) /5000, and according to equation 2, would be multiplied bythe factor p/0.1 to give the total golds. So for the ER in experiment 1, Ng/cellwould be (78,900/5000) 3 p /0.1 mm 5 496 golds per cell over the ER. Becauseprotein synthesis was inhibited, a consistent small increase in the total goldsper cell in experiment 2 could suggest a small increase in the overall labelingefficiency when the protein resides in the Golgi and/or the plasma membrane.dER signifies the distance of this particular ER-related gold label to the axis.


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the distribution of gold labeling across membrane-bound compartments in cells labeled under two differ-ent experimental conditions (Figure 2; Table 1). In thissystem, the gold labeling is located over three compart-ments for simplicity. The labeled protein is a viral gly-coprotein that is made in the ER. After synthesis, theprotein passes by vesicular transport through the Golgien route to the plasma membrane. In this cell type,the ER and plasma membrane are widely dispersed,whereas the Golgi is centrally located close to thenucleus. The cells examined here come from a pulse-chase-type study in which the protein was accumulatedin the ER (experiment 1) and was then released into thesecretory pathway in the presence of a protein synthe-sis inhibitor (experiment 2). The protein passes first intoand then through the Golgi apparatus and then to theplasma membrane. This cell type is grown on culturedishes and polarizes with a brush border situated at itsapex. To sample the cells, vertical sections were pre-pared at a random location with random orientation

allowed around the vertical direction. The cells wereselected using combined light and electron microscopyas follows. A stack of section pairs composed of adjacentsemithin (500-nm) and ultrathin (100-nm) sections wereprepared with 1 mm between each pair. Using the semi-thin sections viewed by light microscopy, cells that ex-hibited a nucleus profile in one section but not in thepreceding section (the “look-up” section; Sterio 1984)were selected, and subsequent semithin sections wereexamined to find the sections containing the largestnuclear profile (diameter; see Figure 1). Next the EMsection(s) adjacent to these semithin sections wereimmunogold labeled for the viral protein of interestand contrasted. Cells were located and photographedat a magnification large enough to locate the gold andto identify the compartments of interest (35000).

On images of complete cell profiles assembled fromoverlapping fields, an axis was drawn in a vertical di-rection central to the nucleus profile (orthogonal to theculture dish). Then, for gold particles in the ER, Golgi,and plasma membrane, the distances of gold particlesto the axis were measured and summed for each organ-elle. The data were then processed and interpreted asshown in Table 1. In this hypothetical example, label-ing and cell number has been kept low for reasons ofclarity, but in a real experiment, there would be muchmore. In experiment 1, the sums of d for each organelle(Sdorg) and the overall total (Sdtot) were calculatedusing apparent distances without correction for magni-fication. Each of these sums represents a labeling index,which can be used to estimate the proportion of label-ing over the cell in 3D, given by Sdorg/Sdtot. For the ERin experiment 1, the proportion was 7.89/8.13 5 0.97.Thus, expressed as a percentage, there was an estimated97% of the gold labeling associated with the ER in thiscell. The estimate for the Golgi was 3%. Note that onthe basis of gold counts, the apparent proportion was80% and 20% over the ER and Golgi, respectively,which is not correct for the 3D estimates for this cell.This shows that in sections oriented along this axis, la-beling proportions in 2D do not report on 3D quantities.The reason is that the ER is more dispersed and is dis-tributed more peripherally so that the circles of rotationfor ER elements are much larger than for the Golgi, and,therefore, each gold particle over the ER will represent alarger amount of label in 3D. Using the magnification50003, the real Sd would be apparent Sd(mm)/5000,and at the section thickness of 0.1 mm, the Sd wouldbe multiplied by the factor p/0.1. So for ER in experi-ment 1, Ng/cell would be (78,900/5000) 3 p/0.1) 5496 golds per cell over the ER.

Notice that it is also possible to assess the changesfrom experiment to experiment over individual organ-elles. Thus, the number of gold particles over the ERdecreases by (7.89–2.08)/7.89 5 0.74 or 74% fromone experiment to the next, which is roughly reflected

Table 2 Real example: rotator estimates of actin labeling inMDCK cells (data from a single cell)

Raw gold counts Sum of distances (Sd mm)

Band Apical Basal Lateral d Apical Basal Lateral

1 1 8 0 0.270 0.270 2.16 02 3 3 0 0.809 2.43 2.43 03 2 4 0 1.35 2.70 5.40 04 0 4 0 1.89 0 7.55 05 0 1 0 2.43 0 2.43 06 3 3 0 2.97 8.90 8.90 07 1 1 0 3.51 3.51 3.51 08 3 1 1 4.05 12.1 4.05 4.059 2 0 2 4.59 9.17 0 9.1710 1 0 1 5.13 5.13 0 5.13Sum 16 25 4 44.2 36.4 18.4% 35.55 55.55 8.9 44.7 36.8 18.5Ng/cell 1,737 1,430 720

Summary data for all nine cells analyzed in this experiment are presented inTable 3. MDCK cells grown on polycarbonate filters were fixed, embedded,and sectioned vertically. Sections passing through central portions of nucleiwere identified using the sampling scheme described in the text and shownin Figure 1. These sections were immunogold labeled and recorded at thelowest magnification that allowed gold and compartments of interest to beidentified. As shown in Figure 3, an axis was placed at the midpoint of thenuclear profile, and approximately 12–15 equal-sized bands were superim-posed on the image on each side of the midpoint. In this case, these measured0.540 mm in width. The central points of each band are therefore located atd1 5 0.270 mm, d2 5 0.809 mm, d3 5 1.35 mm, etc. For each cell, the gold par-ticles in each location of interest (apical, basal, and lateral plasma membrane)were counted for each band (apical is at the top in this micrograph). The esti-mate of the sum of distances of gold particles from the axis (Sd) for each bandwas calculated from number of gold counted (Ng) 3 d. The first band containsone gold counted over the apical membrane, and so Sd1 5 1 3 0.270 mm 50.270, and the second band contains three golds, so Sd2 5 3 3 0.809 mm 52.43. Note that golds on both sides of the axis are counted and summed. Thesum for the apical compartment for this cell (Sdap,cell1) would be Sd1 1 Sd2 1Sd3 1… Sdn 5 44.2, which is a labeling index that can be used in calculationsof labeling proportions. The total golds for the cell are calculated using a sec-tion thickness of 0.08 mm. Notice that there is a marked difference between thepercentages of gold label over each compartment based on the raw counts(biased), compared to the percentages based on the rotator estimates (un-biased). In this case, the sums of distances for the individual bands containspatial information and could be analyzed further, e.g., to test for potentialgradients of actin labeling in the apical or basal plasma membrane domains.


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in the observable label, because the compartment hasnot changed its distribution. (If the ER had changedits distribution, then the rotator estimates would stillbe unbiased and the 2D counts would not!) This reduc-tion corresponds to a change from 496 gold particlesper cell to 131 over the ER (365 gold particles). In thecase that the labeling efficiency (golds per antigen) forthe ER under these conditions is known, which mightbe say 0.01, then these 365 gold particles would repre-sent 36,500 molecules of viral protein per cell leavingthe ER in the time between experiments. Such conclu-sions may help the interpretation of such experimentsin which protein translocation occurs. For this system,therefore, the results show that during the time of re-lease from the ER, substantial labeling has appeared atthe plasma membrane, even though a substantial frac-tion of the total particles on the section appear to bein the Golgi. However, because of its central location,the particles over the Golgi represent only a minorityof the total. The plasma membrane pool predominatesbecause that compartment is a dispersed structure andis relatively distant from the axis of rotation.

This experimental system also illustrates additionalpossibilities for spatial mapping. For example, move-ment from the base to the apex of the cell could bedetected if gold particles were categorized accordingto their distance from the cell base or from the centerof the nucleus; or movement from the centrally locatedGolgi to the plasma membrane might also be detectableby mapping the distance of gold labeling in relation-ship to the point at which the axis crosses the most api-cal aspect of the nuclear envelope.

Real Example

Cells grown on a substratum can be sampled easilyusing vertical sectioning for rotator estimates. MDCKcells are polarized and display an apical domain ex-posed free to the culture medium, a lateral domain con-

tacting adjacent cells, and a basal domain contactingthe substratum (Figure 3). This example estimates thetotal cellular labeling for the cytoskeletal protein actinat each of these locations.

MDCK cells were cultured on polycarbonate filtersand embedded using the PLT method in HM23. Theywere then sectioned at random locations, but in anorientation perpendicular to the culture dish. Adjacent300-nm and 80-nm sections were taken at intervals of1 mm, and cells were sampled with the semithin sec-tions using the disector principle (as described aboveand in Figure 1). Nuclei profiles found in the samplingsemithin section but not in the previous section wereselected for examination. For each sampled cell, thesuccessive semithin sections were then examined toidentify the cell nucleus with the largest diameter. Theadjacent thin section was then immunogold labeled foractin. Micrographs of selected cells (n59) were takenat 37500, and an axis was drawn passing throughthe midpoint of the nuclear profile and vertical to thefilter surface (Figure 3A). Gold particles labeling areasof homogeneous material in contact with the plasmamembrane (cortical actin) were then classified accord-ing to their distance from the axis and according to theircategory of “apical,” “basal,” or “lateral.” In this case,class widths were 0.540 mm. The data obtained fromsampled cells are displayed in Tables 2 and 3, and pro-cessing is described in the legend to these tables. The datafrom this single experiment suggest that coefficients oferror may be acceptable from this level of sampling.

In this example, the labeling density was such thatall gold particle labeling could be counted easily. Butwhat strategy might be employed if labeling were moreintense? One solution would be to sample a knownfraction of the gold particles unbiasedly. This can bedone using a systematic array of quadrats, together rep-resenting a known fraction of the total area (f ). Byrandom placement of the array and applying unbiased

Table 3 Real example: rotator estimates of actin labeling in MDCK cells (summary of data from nine cells)

Cell Apical Basal Lateral Total Apical % Basal % Lateral %

1 1,388 635.6 672.7 2,696 51.5 23.6 24.92 1,737 1,430 720.4 3,888 44.7 36.8 18.53 1,621 1,420 974.7 4,015 40.4 35.4 24.34 784.0 1,409 805.2 2,998 26.1 47.0 26.95 1,727 1,271 646.3 3,644 47.4 34.9 17.76 1,080 836.9 577.4 2,495 43.3 33.5 23.17 2,564 2,045 598.6 5,207 49.2 39.2 11.58 2,829 858.1 1,541 5,228 54.1 16.4 29.59 1,133 1,430 429.1 2,993 37.9 47.8 14.3Mean 1,651 1,259 774 3,685 43.8 35.0 21.2SD 675.3 425.9 325.6 1,012 8.42 10.0 6.00CE 0.136 0.113 0.140 0.092 0.064 0.096 0.094Gold counts 127 130 41 298

Summary of results obtained from the same experiment as reported in Table 2. Results were obtained from nine cells and are expressed as the number of goldparticles per cell for apical, basal, and lateral domains of the plasma membrane. Results are also presented as percentages, means, standard deviations (SD), andcoefficients of error (CE = standard error of the mean expressed as a fraction of the mean value).


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counting rules to these quadrats (Gundersen 1977;Lucocq 1994) gold particles would be selected unbi-asedly. They could be analyzed by direct measurementof d or by the banding method illustrated in Figure 3.It would be prudent to make the quadrats small rela-tive to the cell and therefore at high density, so as topreserve the resolution of any spatial information. Theproportion of golds over different organelles could thenbe computed directly from equation 4, and if neces-sary, the total golds for each compartment computedfor each d or band by multiplying the counts by 1/f.

Labeling Specificity, Labeling Penetration,Section-compression, and Shrinkage

The method described here assesses the quantity andrelative proportions of labeling signal in the rotator anddoes not address questions of specificity. This issue can-not be answered by mapping of gold labeling per se andneeds to be addressed with the use of appropriate con-trol conditions (Lucocq 2008). One of the best controlsis experimental or genetic manipulation that leads to areduction in expression of the protein/component of in-terest. Diminution of the signal then signifies its speci-ficity. Signals that are generated by such controls couldbe compared with experimental values using the presentmethods. For example, after knockdown of expressionof a specific protein, rotator estimates expressed as totalgold signal per cell or as a mean labeling index could becompared with the experimental value.

Penetration of labeling into the section occurs to avariable degree depending on the technique and thecompartments of interest (see Lucocq 1994 for discus-sion). In methacrylate and epoxy resin sections, label-ing is essentially limited to the section surface, whereasin thawed cryosections, labeling penetration dependson the matrix density of the cellular compartment inquestion. The penetration can have an impact on howthe rotator estimates of labeling will vary when thesection thickness is changed. If labeling is located onlyat the section surface, then as the section thicknessincreases, the number of gold particles per cell willdecrease because the total signal in each section willremain the same. However, if the labeling is locatedthroughout the section, then the number of gold par-ticles in each section will increase in proportion to thesection thickness, and the number of golds per cell in3D will remain constant. Therefore, even though full-thickness penetration of gold particles is likely to be rare,it may be advisable to perform experiments at constantnominal section thickness irrespective of whether thefinal readout used is gold particles per cell, mean label-ing index, or labeling proportions.

Finally, shrinkage and section compression are im-portant effects generated during section preparation(Lucocq 1994). Both of these factors will tend to re-

duce the overall apparent size of cells and their profiles,and will tend to increase the concentration of antigensand therefore increase the labeling density. However,unless the antigens become so crowded that the label-ing efficiency starts to drop, the total number of goldparticles is likely to remain constant. Therefore, rotatorestimates are likely to be robust to such changes be-cause they are sensitive to the total amount of goldlabeling and not its concentration. Consequently, thisis an advantage over methods that use local density/concentration of gold label as their readouts.

DiscussionThe application of the rotator to gold labeling esti-mates has a number of advantages. The first is that itallows individual cells with a particular characteristicto be selected for analysis with a degree of surety. Eachselected cell is sectioned through its central portionalong a defined axis, thereby increasing the probabilitythat characteristic structures will be visible. By com-parison, random sections (even if they are orientatedalong the cell axes) will inevitably slice some cells inregions where identification of cell type or its compo-nent structures will be harder or where spatial relation-ships between labeled cell components are not as clearas in centrally located oriented sections. The methoddescribed here now allows the investigator to performtargeted studies on cells that may form the minority ofa total cell population, as is the case in many tissues.Cells can be selected (unbiasedly) using light micros-copy sections first and the final estimates providedby immuno-EM analysis of selected and immunogold-labeled sections.

A second advantage of this “golden” rotator is thepreservation of spatial information, which can be orga-nized according to any convenient spatial marker(s).Thus, if the axis of rotation is biologically significant,as in a polarized cell, the axis itself could be used as areference. In this case, labeling quantities can be mappedaccording to distance along the axis from the cell base orfrom a central cell structure, or according to the distancefrom the axis to the cell periphery in a horizontal direc-tion. Preserving spatial information could be very usefulin strongly polarized cells such as neurons, in motile orepithelial cells, or in cells where transport of organellesfrom one region of the cell to another occurs. A furtheradvantage is that internal organization of organelles isnow accessible, and gradients of molecules in widespreadorganelles such as nucleus, ER and Golgi, or plasmamembrane can now be studied without recourse to serialsection analysis.

One apparent disadvantage of these rotator estimatesmay be the amount of effort needed to obtain them.This is in part due to the sampling procedure, whichwould normally require a stack of sections to be made


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for disector sampling and selection of “central” sec-tions. However, compared with serial sectioning, thisis a rather minor investment in effort to obtain spatialinformation. Furthermore the work load can be signifi-cantly reduced by judicious use of light microscopyat the cell sampling stage, thereby restricting the EManalysis to a limited number of gold-labeled sections.Importantly, our study suggests that once cells have beenidentified, it may be possible to get reasonably preciseand unbiased estimates of spatial distributions with arather modest amount of work, say from 10–20 cellsand a total count of 200–300 particles. Our experiencesuggests that like most stereological approaches, thespecimen preparation for these rotator estimates formsa major portion of the total effort, with the measurement/estimations comprising a relatively minor fraction of thetotal work load.

Finally, there are a number of related strategies thathave not been explored in the present report. One ofthese would be to combine gold particle estimates withvolume estimates to assess the 3D density of gold label-ing inside organelles or cell space. Another is to use therelated spatial estimator, the nucleator (Gundersen1988), to map the spatial arrangement of gold particlesin relation to a central point in the cell. This could beespecially useful in structures organized around thecentrosome, such as the Golgi, elements of the endo-some system, or secretory vesicles. Further work willnow be required to refine and extend the usefulness ofthe rotator and related stereological approaches in gold-labeling studies.

Acknowledgments

C.G.B. was a recipient of a Capacity-building Studentshipfrom the Medical Research Council.

We thank Alan Prescott for advice and John James forhelp with the electron microscopy.

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