JOURNAL OF ELECTRON MICROSCOPY TECHNIQUE 18:291-295 (1991)
A Study of Protein A-Gold Resolution for Immunoelectron ~icroscopy HISATO SHIDA Department of Biology, University of Yamanashi Medical School, Tamaho, Yamanashi 40938, Japan
KEY WORDS
Quantitative analysis, Post-embedding, Actin, JB-4, Ultrathin sections
For the purpose of investigating a topographical correlation between antigen molABSTRACT ecules and protein A-gold(PAG1 particles which localized a s a n immunocytochemical probe, the simplest model on a localization pattern of antigen molecules, which were arranged two-dimensionally on a plane surface of the resin, was used. Ultrathin sections of a G-actin layer, which was adsorbed on epoxy resin and was re-embedded subsequently in JB-4 resin, was stained indirectly with rabbit anti-actin antibody and subsequently by PAG. From this immunoelectron microscopy, a histogram (relative frequency, denoted by y vs. relative length, denoted by x) was obtained using a computer-assisted method. For this histogram, a fitting curve was calculated by a least squares optimization and three parameters (H, U, and W) of the curve which could be useful for a study on the topographical organization of antigen molecules were estimated. Parameter H (maximum y of the curve) would reflect the maximum amount of epitopes at x = U. Half width W, which is the width of the curve at y = H/2, would reflect a breath of epitope masses. This fitting curve was separated into two overlapping curves whose Ws were different from each other. The one constituent curve of which value W was smaller than the other was regarded as a unit curve and the other constituent curve could be resolved into many unit curves whose W values are the same. From these unit curves, the resolution power of the immunoelectron micrbscopy, using a post-embedding procedure of ultrathin sections, was estimated as 58-66 A".
INTRODUCTION
jugates, for ultrathin sections of G-actin layers which were arranged linearly. On the basis of the fitting analIn the field of immunoelectron microscopy, such dig- ysis, three parameters of the curve were calculated. ital markers as ferritin (Singer and Mclean, 1963) or These three parameters suggested useful tools to decolloidal gold particles (Faulk and Tayler, 19711, which termine the strict position and the extent of the conare conjugated with IgG or protein A, have provided centrated area of epitopes. Furthermore, the resolution information on the structural organization of antigens power of this new quantitative analysis in immunoby describing the correlation between the number of electron microscopy was estimated as 58-66 A" on the particles and the explored ultrastructure. However, basis of the constituent curve. most labeling results using immunogold or immunoferritin electron microscopy have been analyzed qualPreparation of Antigen Arrangement Formed itatively rather than quantitatively. For the purpose of Into Line in the Ultrathin Sections applying immunoelectron microscopy to the molecular Experimental procedure was published elsewhere organization of antigens, a new analytical methodology (Shida et al., 1987). Briefly, a polymerized block of epof data processing is needed. oxy resin which contained fixed epidermis of bovine Recently, we have successfully obtained histograms muzzle was trimmed with a glass knife on a n ultramifrom the immunoelectron microscopy of desmosomal antigens using a post-embedding procedure with pro- crotome to obtain accurate flat surface. This plane surtein A-gold (PAG) (Shida et al., 1983; Shida and Stein- face was immersed in a 0.1% solution of G-actin from berg, 1984). In these histograms, the localization pat- rabbit muscle (Sigma Co., St. Louis, MO). The resin terns of PAG have been expressed as a frequency of block whose surface was covered with a layer of G-actin was then embedded in a JB-4 resin mixture (20 part PAG vs. the relative position of PAG from the reference JB-4A containing 0.9% catalyst, 1part divinylbenzene, line drawn along the center of the cytoplasmic plaque 1part methyl methacrylate, and 1 part JB-4B) for the at desmosomes. According to these histograms, several immunoelectron microscopy. The sample which was peaks were identified within 150 nm. However, we transferred to a mixture of JB-4 was polymerized in have no data and no theory specific to the correlation between the profile of the histogram and its cytochemical meaning at the molecular level. In the present study, a fitting analysis of curve was applied to the histogram obtained from immunoelecReceived May 28, 1990; accepted in revised form September 28, 1990. tron microscopy using post-embedding labeling with a n Address reprint requests to Hisato Shida, Department of Biology, University anti-actin antibody, and subsequently with PAG con- of Yamanashi Medical School, Tamaho, Yamanashi 409-38, Japan.
0 1991 WILEY-LISS, INC.
292
H. SHIDA
BEEM capsules (Chemisciences Inc., Tokyo, Japan) at - 18°C overnight. After hardening, the polymerization was completed by ultraviolet (UV) light in a curing chamber (Ladd Research Industries, Burlington, VT) a t room temperature for several hours. Cutting was carried out a t right angle to the plane of the adsorbed layer of G-actin.
Immunoelectron Microscopic Labeling An indirect immunoelectron microscopic labeling was carried out with PAG conjugates (average diameter:12 nm) a s a second antibody, according to methods described elsewhere (Shida e t al., 1987). The ultrathin sections of materials embedded in JB-4 resin were incubated in phosphate-buffered saline (PBS) and 1%bovine serum albumin (BSA) in PBS for 30 minutes, respectively, to block the nonspecific adsorption of antibodies to the resin surface. The sections were then incubated in the first antibody or preimmune serum diluted in PBS containing 1% BSA. To obtain maximum intensity of specific labeling and minimum intensity of nonspecific adsorption, suitable dilution and incubation periods were checked. After having been washed three times for 30 minutes in PBS, the sections were incubated again in 1% BSA in PBS for 30 minutes and were then labeled for 1hour with a solution of PAG containing 1%BSA. The labeled grids were washed twice with PBS for 30 minutes and then with distilled water for 30 minutes. Finally, the labeled sections were stained with 1%aqueous solution of uranyl acetate for 15 minutes and with Reynold’s lead citrate solution for 5 minutes. The samples were examined with a Hitachi H-600 transmission electron microscope a t a n acceleration voltage of 100 kV.
RESULTS Between the two plastic, epoxy resin and JB-4 resin, a n electron-dense line was observed a t high magnification (Fig. 1). Though this line generally had a constant width, wider parts were caused randomly. The specific standing was localized only along the dark line, which should reflect the site of the G-actin layer adsorbed on the plastic surface. As shown in Figure 2, a least square line which was calculated from the localization of PAG fit closely to the adsorbed line of Gactin. A histogram obtained from the 500 data points superficially reveals a unimodal distribution. As the histogram is a kind of probability profile a t the given position expressed in a frequency of PAG particles, we could use a Gaussian distribution as a mathematical model. When we tried a fitting analysis using least square optimization, the curve of a single Gaussian distribution did not fit well with the data (Fig. 3A). Several points of data around the mode and sleeves deviated from the single curve which was calculated by the least square method. When we combined two single Gaussian distributions with the different values of half width W and the same values of peak position U, this mathematical model agreed better with data than the single Gaussian model as shown in Figure 3B.
DISCUSSION The combined curve of two Gaussian distributions whose values W are different from each other appears to represent a better mathematical model than the single Gaussian distribution. For the purpose of explaining this cause, a deformation of the adsorption layer forming a single “line” of the antigen should be disImmunochemical Reagents cussed. One has to keep in mind that the arrangement The anti-actin used was rabbit antibody purchased of antigens is far from a n ideal line. In some parts, the from Miles Scientific Co. (Nihonbashi, Tokyo). The layer of the antigen molecules formed a n irregular netPAG complex was prepared in our laboratory according work whose average diameter was variable from fine to thick. Though we exclude the extremely thick parts of to the method of Slot and Geuze (1981). the layer, it was impossible to unify the localization of Immunoelectron Microscopy Measurements antigens into a n ideal line from the image of electron The position of each PAG particle, denoted by a pair micrographs. In other words, the arrangement of antiof x, and y, (in cm a t magnification x 300,000; Fig. 1) gens could be deformed partially from the first adfrom the corrdinates given, was projected on a cathode sorbed surface in the process of the re-embedding. The ray tube. The guesstimate region which would give us histogram obtained from the immunocytochemical laa n approximate image of the actin layer was selected beling of the region a t the point where antigens formed and the least square line was calculated on the basis of a sharp and fine adsorbed line, could be a unit distrithe above data with a microcomputer system (NEC bution like curve A. Curve B, whose half width was PC8801 MKII). The distance (D,) between the least thicker than the first one, would be explained as a comsquare line and the center of each PAG particle was bination of many unit Gaussian curves caused by the calculated according to the following formula: D, = [y, deformed layer of antigens making the thicker distri- f(x,)] coslatn(jf(l)/)}; where f(x) is the linear regres- bution (Fig. 4). From a mathematical point of view, the sion function. The one-dimensional data of D, were combined curve from many unit curves is able to be stored, processed, and printed out by the microcom- expressed a s a single Gaussian function whose half puter system to obtain histograms. All histograms (rel- width is larger than a unit Gaussian one if the peak ative frequency vs. distance from the reference line ex- positions of each unit curve are close enough, i.e., less pressed in A”) were processed by a simple five-point than 0.7 x Wa. As stated above, the resolution power of this analytmoving average to decrease noise (Savitzky and Goray, 1964) and three parameters; the peak value(H), the ical method could be estimated on the basis of curve A position of peak(U), and the half width of curve(W), which might reflect correctly its linear array. When we were calculated from the fitting curves by a least combine two unit curves into a curve 1 apart from one U to the other U, which could be decomposed into two square optimization (Maddams, 1980).
PROTEIN A-GOLD RESOLUTION
293
Fig. 1. Immunoelectron micrographs of G-actin layer (arrow mark) which was linearly arrayed between epoxy resin and JB-4 resin. PAG particles are observed specifically in the restricted region.
single curves, the minimum value of 1 should be the resolution power. According to the second differential curve, 0.7 0.8 x W gives us a practical value of resolution power. Figure 5 shows a second differential curve obtained from a combination of two curves A whose peak positions are separated by 0.8 x W. We could recognize the positions of peaks easily from this differential curve. Another convenient aspect of the parameter W is that from it, we can estimate a stretch of antigen. As shown in Figure 4,the curve whose half width is the same value a s curve B is able to be constituted numer-
-
ically from 9 unit curves. In the constituent curves, each of those height parameters Hs is different from that of curve A and each of those half width parameters Ws is the same a s that of curve A. I n this case, the length from the peak position of curve #1 to that of curve #9 would give us a n expansion of the epitopes which would deviate from the reference line. Recently, several studies which have dealt with the quantitative analysis of the molecular organization of proteins, using ultrastructural cytochemistry, combined a digital marker with post-embedding staining, have been reported (Geiger et al., 1981; Shida et al.,
294
H. SHIDA
Fig. 2. A-F. Comparison between the least sauare line (dotted line) and G-actin layer (solid line). Solid circle, PAG.
..... ..-.. w
-
3 C
10T
k
-
. . . . .. ., .. .. ... ... . . .-... .,... .... ... . . . ..: B ':::. zh ---._._.. .--...- . -..i .. . .-.-. ... .. ... ... .... ......... ... .... -. ...... ...... .. .- -.-. -..- . .. ... .._ -. . . - - .. . .,.., --,,
-
3
W
2Y
+ 4
:
Y
1 W CT
- -- . . . - ._ .............................................. I._..
-
@
200
100
0
100
200
ABSOLUTE LENGTH ( X I
@
i
7
200
'
100
0
100
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200
ABSOLUTE LENGTH ( X )
Fig. 3. A,B: A fitting analysis using the least square method. As a mathematical model, a single Gaussian function which is expressed in F(x) = H,Exp;-4ln2(~-U,)~/W,~i (Fig. 3A), or a combined curve of two Gaussian functions (curve C ) which is expressed in F(x) = H,Exp( - 41n2(x-U,)2/W,2: + H,Exp/ -41n2(x- U,)'/WB2/ (Fig. 3B), was adopted. Dotted squares indicate the data. The zero value of
the absolute length means the position of a reference line. Estimated values of each parameter are summarized in the following. H,(peak value):13.0216; U, (position of peak):O; W, (half widthk132.6465; sum of square error:27.0604; H,:8.70519; U,:O; W,:82.666; H,:5.4275; U,:O); W,:212.3745; sum of square error:2.8183. Note improved fitting by curve C to the data.
1982,1983, 1987; Shida and Steinberg, 1984; Volk and Geiger, 1986). Though histograms (frequency of markers vs. distance from a reference line) have been reported in these studies, the geometrical meaning of the distribution pattern, which should reflect a correlation between a receptor and a marker bound specifically with binding sites, have been insufficiently analyzed.
The present study would develop a new field of quantitative immunoelectron microscopy for the purpose of analyzing the correlation between the antigen arrangement and the histogram. In conclusion, three parameters of each curve which could be estimated from the fitting analysis using the least square method could give us extremely useful in-
295
PROTEIN A-GOLD RESOLUTION
. .... ..... .. .. ... I
.
formation on a molecular organization of antigens, e.g., H would reflect the maximum concentration of epitopes a t the given position, W could give us a n extent of expansion on epitopes, and U could give u s a position at which the concentration of epitopes would be the rnaximum value.
. .. ..... ..:..
... ... .. .L. ... .. .. :. i
.
I
Ic W
w M
I--
4 -1 W LT
. . . . . . . . . . . . . . . . . . . . .
@
250
0
250
ABSOLUTE LENGTH ( X )
Fig. 4. Nine curves of A which have different values of H and U are combined into a single Gaussian curve whose half width is the same one as curve B.
Fig. 5. A second differential curve (DC) obtained from a combined one (C,,) of two curves A whose peaks are positioned 0.8 x W, apart from each other.
ACKNOWLEDGMENTS I would like to express my thanks to M. Shida and R. Ohga for their constant encouragement to pursue this work. I also wish to thank N. Sugi for her helpful discussions concerning the mathematical calculations. This work was supported in part by Grants-in-Aid for Scientific Research from the Japan Ministry of Education, Science and Culture (No. 02670474 and No. 02305016). REFERENCES Faulk, W.P., and Tayler, G.M. (1971) An immunocolloid method for the electron microscope. Immunochemistry, 8:1081-1083. Geiger, B., Dutton, A.H., Tokuyasu, K.T., and Singer, S.J. (1981) Immunoelectron microscope studies of membrane-microfilament interacti0ns:distributionsof actinin, tropomyosin, and vinculin in intestinal epithelial brush border and chicken gizzard smooth muscle cells. J . Cell Biol., 91:614-628. Maddams, W.F. (1980) The scope and limitations of curve fitting. Appl. Spectroscopy, 34:245-267. Savitzky, A., and Goray, M.J.E. (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem., 36: 1627-1639. Shida, H., Gorbsky, G., Shida, M., and Steinberg, M.S. (1982) Ultrastructural and biochemical identification of Con A receptors in the desmosome. J. Cell. Biochem., 20:113-126. Shida, H., Cohen, S.M., Guidice, G.J., and Steinberg, M.S. (1983) Quantitative electronmicroscopic immunocytochemistry of desmosoma1 antigens. J. Cell Biol., 97:85a. Shida, H. (1984) A new quantitative high resolving power immunoelectron microscopy. Acta Histochem. Cytochem., 17:736. Shida, H., and Steinberg, M.S. (1984) Domain organization of the desmosomal glycoproteins. Zool. Sci., 1:890. Shida, H., Shida, M., and Ohga, R. (1987) A model experiment to develop a high resolving power analysis of immunoelectron microscopy. J . Electron Microsc., 36:361-367. Singer, S.J., and McLean, J.D. (1963) Ferritin-antibody conjugates as stains for electron microscopy. Lab. Invest., 12:1002-1008. Slot, J.W., and Geuze, H.J. 11981) Sizing of protein A-colloidal gold probes for immunoelectron microscopy. J . Cell Biol., 90:533-536. Volk, T., Geiger, B. (1986) A-CAM:a 135-KD receptor of intercellular adherens junctions. I. Immunoelectron microscopic and biochemical studies. J . Cell Biol., 103:1441-1450.
A Study of Protein A-Gold Resolution for Immunoelectron ~icroscopy HISATO SHIDA Department of Biology, University of Yamanashi Medical School, Tamaho, Yamanashi 40938, Japan
KEY WORDS
Quantitative analysis, Post-embedding, Actin, JB-4, Ultrathin sections
For the purpose of investigating a topographical correlation between antigen molABSTRACT ecules and protein A-gold(PAG1 particles which localized a s a n immunocytochemical probe, the simplest model on a localization pattern of antigen molecules, which were arranged two-dimensionally on a plane surface of the resin, was used. Ultrathin sections of a G-actin layer, which was adsorbed on epoxy resin and was re-embedded subsequently in JB-4 resin, was stained indirectly with rabbit anti-actin antibody and subsequently by PAG. From this immunoelectron microscopy, a histogram (relative frequency, denoted by y vs. relative length, denoted by x) was obtained using a computer-assisted method. For this histogram, a fitting curve was calculated by a least squares optimization and three parameters (H, U, and W) of the curve which could be useful for a study on the topographical organization of antigen molecules were estimated. Parameter H (maximum y of the curve) would reflect the maximum amount of epitopes at x = U. Half width W, which is the width of the curve at y = H/2, would reflect a breath of epitope masses. This fitting curve was separated into two overlapping curves whose Ws were different from each other. The one constituent curve of which value W was smaller than the other was regarded as a unit curve and the other constituent curve could be resolved into many unit curves whose W values are the same. From these unit curves, the resolution power of the immunoelectron micrbscopy, using a post-embedding procedure of ultrathin sections, was estimated as 58-66 A".
INTRODUCTION
jugates, for ultrathin sections of G-actin layers which were arranged linearly. On the basis of the fitting analIn the field of immunoelectron microscopy, such dig- ysis, three parameters of the curve were calculated. ital markers as ferritin (Singer and Mclean, 1963) or These three parameters suggested useful tools to decolloidal gold particles (Faulk and Tayler, 19711, which termine the strict position and the extent of the conare conjugated with IgG or protein A, have provided centrated area of epitopes. Furthermore, the resolution information on the structural organization of antigens power of this new quantitative analysis in immunoby describing the correlation between the number of electron microscopy was estimated as 58-66 A" on the particles and the explored ultrastructure. However, basis of the constituent curve. most labeling results using immunogold or immunoferritin electron microscopy have been analyzed qualPreparation of Antigen Arrangement Formed itatively rather than quantitatively. For the purpose of Into Line in the Ultrathin Sections applying immunoelectron microscopy to the molecular Experimental procedure was published elsewhere organization of antigens, a new analytical methodology (Shida et al., 1987). Briefly, a polymerized block of epof data processing is needed. oxy resin which contained fixed epidermis of bovine Recently, we have successfully obtained histograms muzzle was trimmed with a glass knife on a n ultramifrom the immunoelectron microscopy of desmosomal antigens using a post-embedding procedure with pro- crotome to obtain accurate flat surface. This plane surtein A-gold (PAG) (Shida et al., 1983; Shida and Stein- face was immersed in a 0.1% solution of G-actin from berg, 1984). In these histograms, the localization pat- rabbit muscle (Sigma Co., St. Louis, MO). The resin terns of PAG have been expressed as a frequency of block whose surface was covered with a layer of G-actin was then embedded in a JB-4 resin mixture (20 part PAG vs. the relative position of PAG from the reference JB-4A containing 0.9% catalyst, 1part divinylbenzene, line drawn along the center of the cytoplasmic plaque 1part methyl methacrylate, and 1 part JB-4B) for the at desmosomes. According to these histograms, several immunoelectron microscopy. The sample which was peaks were identified within 150 nm. However, we transferred to a mixture of JB-4 was polymerized in have no data and no theory specific to the correlation between the profile of the histogram and its cytochemical meaning at the molecular level. In the present study, a fitting analysis of curve was applied to the histogram obtained from immunoelecReceived May 28, 1990; accepted in revised form September 28, 1990. tron microscopy using post-embedding labeling with a n Address reprint requests to Hisato Shida, Department of Biology, University anti-actin antibody, and subsequently with PAG con- of Yamanashi Medical School, Tamaho, Yamanashi 409-38, Japan.
0 1991 WILEY-LISS, INC.
292
H. SHIDA
BEEM capsules (Chemisciences Inc., Tokyo, Japan) at - 18°C overnight. After hardening, the polymerization was completed by ultraviolet (UV) light in a curing chamber (Ladd Research Industries, Burlington, VT) a t room temperature for several hours. Cutting was carried out a t right angle to the plane of the adsorbed layer of G-actin.
Immunoelectron Microscopic Labeling An indirect immunoelectron microscopic labeling was carried out with PAG conjugates (average diameter:12 nm) a s a second antibody, according to methods described elsewhere (Shida e t al., 1987). The ultrathin sections of materials embedded in JB-4 resin were incubated in phosphate-buffered saline (PBS) and 1%bovine serum albumin (BSA) in PBS for 30 minutes, respectively, to block the nonspecific adsorption of antibodies to the resin surface. The sections were then incubated in the first antibody or preimmune serum diluted in PBS containing 1% BSA. To obtain maximum intensity of specific labeling and minimum intensity of nonspecific adsorption, suitable dilution and incubation periods were checked. After having been washed three times for 30 minutes in PBS, the sections were incubated again in 1% BSA in PBS for 30 minutes and were then labeled for 1hour with a solution of PAG containing 1%BSA. The labeled grids were washed twice with PBS for 30 minutes and then with distilled water for 30 minutes. Finally, the labeled sections were stained with 1%aqueous solution of uranyl acetate for 15 minutes and with Reynold’s lead citrate solution for 5 minutes. The samples were examined with a Hitachi H-600 transmission electron microscope a t a n acceleration voltage of 100 kV.
RESULTS Between the two plastic, epoxy resin and JB-4 resin, a n electron-dense line was observed a t high magnification (Fig. 1). Though this line generally had a constant width, wider parts were caused randomly. The specific standing was localized only along the dark line, which should reflect the site of the G-actin layer adsorbed on the plastic surface. As shown in Figure 2, a least square line which was calculated from the localization of PAG fit closely to the adsorbed line of Gactin. A histogram obtained from the 500 data points superficially reveals a unimodal distribution. As the histogram is a kind of probability profile a t the given position expressed in a frequency of PAG particles, we could use a Gaussian distribution as a mathematical model. When we tried a fitting analysis using least square optimization, the curve of a single Gaussian distribution did not fit well with the data (Fig. 3A). Several points of data around the mode and sleeves deviated from the single curve which was calculated by the least square method. When we combined two single Gaussian distributions with the different values of half width W and the same values of peak position U, this mathematical model agreed better with data than the single Gaussian model as shown in Figure 3B.
DISCUSSION The combined curve of two Gaussian distributions whose values W are different from each other appears to represent a better mathematical model than the single Gaussian distribution. For the purpose of explaining this cause, a deformation of the adsorption layer forming a single “line” of the antigen should be disImmunochemical Reagents cussed. One has to keep in mind that the arrangement The anti-actin used was rabbit antibody purchased of antigens is far from a n ideal line. In some parts, the from Miles Scientific Co. (Nihonbashi, Tokyo). The layer of the antigen molecules formed a n irregular netPAG complex was prepared in our laboratory according work whose average diameter was variable from fine to thick. Though we exclude the extremely thick parts of to the method of Slot and Geuze (1981). the layer, it was impossible to unify the localization of Immunoelectron Microscopy Measurements antigens into a n ideal line from the image of electron The position of each PAG particle, denoted by a pair micrographs. In other words, the arrangement of antiof x, and y, (in cm a t magnification x 300,000; Fig. 1) gens could be deformed partially from the first adfrom the corrdinates given, was projected on a cathode sorbed surface in the process of the re-embedding. The ray tube. The guesstimate region which would give us histogram obtained from the immunocytochemical laa n approximate image of the actin layer was selected beling of the region a t the point where antigens formed and the least square line was calculated on the basis of a sharp and fine adsorbed line, could be a unit distrithe above data with a microcomputer system (NEC bution like curve A. Curve B, whose half width was PC8801 MKII). The distance (D,) between the least thicker than the first one, would be explained as a comsquare line and the center of each PAG particle was bination of many unit Gaussian curves caused by the calculated according to the following formula: D, = [y, deformed layer of antigens making the thicker distri- f(x,)] coslatn(jf(l)/)}; where f(x) is the linear regres- bution (Fig. 4). From a mathematical point of view, the sion function. The one-dimensional data of D, were combined curve from many unit curves is able to be stored, processed, and printed out by the microcom- expressed a s a single Gaussian function whose half puter system to obtain histograms. All histograms (rel- width is larger than a unit Gaussian one if the peak ative frequency vs. distance from the reference line ex- positions of each unit curve are close enough, i.e., less pressed in A”) were processed by a simple five-point than 0.7 x Wa. As stated above, the resolution power of this analytmoving average to decrease noise (Savitzky and Goray, 1964) and three parameters; the peak value(H), the ical method could be estimated on the basis of curve A position of peak(U), and the half width of curve(W), which might reflect correctly its linear array. When we were calculated from the fitting curves by a least combine two unit curves into a curve 1 apart from one U to the other U, which could be decomposed into two square optimization (Maddams, 1980).
PROTEIN A-GOLD RESOLUTION
293
Fig. 1. Immunoelectron micrographs of G-actin layer (arrow mark) which was linearly arrayed between epoxy resin and JB-4 resin. PAG particles are observed specifically in the restricted region.
single curves, the minimum value of 1 should be the resolution power. According to the second differential curve, 0.7 0.8 x W gives us a practical value of resolution power. Figure 5 shows a second differential curve obtained from a combination of two curves A whose peak positions are separated by 0.8 x W. We could recognize the positions of peaks easily from this differential curve. Another convenient aspect of the parameter W is that from it, we can estimate a stretch of antigen. As shown in Figure 4,the curve whose half width is the same value a s curve B is able to be constituted numer-
-
ically from 9 unit curves. In the constituent curves, each of those height parameters Hs is different from that of curve A and each of those half width parameters Ws is the same a s that of curve A. I n this case, the length from the peak position of curve #1 to that of curve #9 would give us a n expansion of the epitopes which would deviate from the reference line. Recently, several studies which have dealt with the quantitative analysis of the molecular organization of proteins, using ultrastructural cytochemistry, combined a digital marker with post-embedding staining, have been reported (Geiger et al., 1981; Shida et al.,
294
H. SHIDA
Fig. 2. A-F. Comparison between the least sauare line (dotted line) and G-actin layer (solid line). Solid circle, PAG.
..... ..-.. w
-
3 C
10T
k
-
. . . . .. ., .. .. ... ... . . .-... .,... .... ... . . . ..: B ':::. zh ---._._.. .--...- . -..i .. . .-.-. ... .. ... ... .... ......... ... .... -. ...... ...... .. .- -.-. -..- . .. ... .._ -. . . - - .. . .,.., --,,
-
3
W
2Y
+ 4
:
Y
1 W CT
- -- . . . - ._ .............................................. I._..
-
@
200
100
0
100
200
ABSOLUTE LENGTH ( X I
@
i
7
200
'
100
0
100
'
200
ABSOLUTE LENGTH ( X )
Fig. 3. A,B: A fitting analysis using the least square method. As a mathematical model, a single Gaussian function which is expressed in F(x) = H,Exp;-4ln2(~-U,)~/W,~i (Fig. 3A), or a combined curve of two Gaussian functions (curve C ) which is expressed in F(x) = H,Exp( - 41n2(x-U,)2/W,2: + H,Exp/ -41n2(x- U,)'/WB2/ (Fig. 3B), was adopted. Dotted squares indicate the data. The zero value of
the absolute length means the position of a reference line. Estimated values of each parameter are summarized in the following. H,(peak value):13.0216; U, (position of peak):O; W, (half widthk132.6465; sum of square error:27.0604; H,:8.70519; U,:O; W,:82.666; H,:5.4275; U,:O); W,:212.3745; sum of square error:2.8183. Note improved fitting by curve C to the data.
1982,1983, 1987; Shida and Steinberg, 1984; Volk and Geiger, 1986). Though histograms (frequency of markers vs. distance from a reference line) have been reported in these studies, the geometrical meaning of the distribution pattern, which should reflect a correlation between a receptor and a marker bound specifically with binding sites, have been insufficiently analyzed.
The present study would develop a new field of quantitative immunoelectron microscopy for the purpose of analyzing the correlation between the antigen arrangement and the histogram. In conclusion, three parameters of each curve which could be estimated from the fitting analysis using the least square method could give us extremely useful in-
295
PROTEIN A-GOLD RESOLUTION
. .... ..... .. .. ... I
.
formation on a molecular organization of antigens, e.g., H would reflect the maximum concentration of epitopes a t the given position, W could give us a n extent of expansion on epitopes, and U could give u s a position at which the concentration of epitopes would be the rnaximum value.
. .. ..... ..:..
... ... .. .L. ... .. .. :. i
.
I
Ic W
w M
I--
4 -1 W LT
. . . . . . . . . . . . . . . . . . . . .
@
250
0
250
ABSOLUTE LENGTH ( X )
Fig. 4. Nine curves of A which have different values of H and U are combined into a single Gaussian curve whose half width is the same one as curve B.
Fig. 5. A second differential curve (DC) obtained from a combined one (C,,) of two curves A whose peaks are positioned 0.8 x W, apart from each other.
ACKNOWLEDGMENTS I would like to express my thanks to M. Shida and R. Ohga for their constant encouragement to pursue this work. I also wish to thank N. Sugi for her helpful discussions concerning the mathematical calculations. This work was supported in part by Grants-in-Aid for Scientific Research from the Japan Ministry of Education, Science and Culture (No. 02670474 and No. 02305016). REFERENCES Faulk, W.P., and Tayler, G.M. (1971) An immunocolloid method for the electron microscope. Immunochemistry, 8:1081-1083. Geiger, B., Dutton, A.H., Tokuyasu, K.T., and Singer, S.J. (1981) Immunoelectron microscope studies of membrane-microfilament interacti0ns:distributionsof actinin, tropomyosin, and vinculin in intestinal epithelial brush border and chicken gizzard smooth muscle cells. J . Cell Biol., 91:614-628. Maddams, W.F. (1980) The scope and limitations of curve fitting. Appl. Spectroscopy, 34:245-267. Savitzky, A., and Goray, M.J.E. (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem., 36: 1627-1639. Shida, H., Gorbsky, G., Shida, M., and Steinberg, M.S. (1982) Ultrastructural and biochemical identification of Con A receptors in the desmosome. J. Cell. Biochem., 20:113-126. Shida, H., Cohen, S.M., Guidice, G.J., and Steinberg, M.S. (1983) Quantitative electronmicroscopic immunocytochemistry of desmosoma1 antigens. J. Cell Biol., 97:85a. Shida, H. (1984) A new quantitative high resolving power immunoelectron microscopy. Acta Histochem. Cytochem., 17:736. Shida, H., and Steinberg, M.S. (1984) Domain organization of the desmosomal glycoproteins. Zool. Sci., 1:890. Shida, H., Shida, M., and Ohga, R. (1987) A model experiment to develop a high resolving power analysis of immunoelectron microscopy. J . Electron Microsc., 36:361-367. Singer, S.J., and McLean, J.D. (1963) Ferritin-antibody conjugates as stains for electron microscopy. Lab. Invest., 12:1002-1008. Slot, J.W., and Geuze, H.J. 11981) Sizing of protein A-colloidal gold probes for immunoelectron microscopy. J . Cell Biol., 90:533-536. Volk, T., Geiger, B. (1986) A-CAM:a 135-KD receptor of intercellular adherens junctions. I. Immunoelectron microscopic and biochemical studies. J . Cell Biol., 103:1441-1450.
