- Email: [email protected]
Stereology: a working tool for cell biologists
184
T I B S - May 1985
workers who had no malignancy did have high concentrations of markers, but in some instances the markers disappeared. We found essentially the same thing in our laboratory. This implies the possibility of reversal of the path to a devastating malignancy. The animal system studied by Nass would be ideal for examining the reversibility of the aberrant metabolism which leads to malignancy. In collaboration with John Brewer, a distinguished gynecologist, we followed six women with choriocarcinoma by determining the nucleoside markers before therapy and then 7-8 days after therapy. We determined the nucleoside markers whereas Brewer determined the standard marker, human chorionic gonadotrophin (HCG). The nucleoside markers returned to normal in seven days; yet HCG concentrations remained high. Normally, gynecologists continue to feed methotrexate to patients until the HCG values return to normal or near normal - this may take weeks, if not months. Brewer decided that, according to the nucleoside markers, the women's malignancies had been eliminated and, therefore, stopped feeding methotrexate but followed the clinical progress of the women for two years. They remained
normal; two of them had normal deliveries, one had an elective abortion and the others were normal. Therefore, if our colleagues in gynecology are willing to try this new method of following effectiveness of therapy, we may be able to spare women the debilitating exposure to the hepatoxic agent, methotrexate n.
more workers are needed in this field, because a great many questions remain to be answered. If one-tenth of the effort which has been expended on the protein markers is devoted to these two nonprotein markers in the coming years, we will reap far greater benefits for our patients.
Neopterin The other nonprotein marker, which has been introduced by colleagues from the University of Innsbruck, is neopterin. Neopterin is derived from guanosine triphosphate and appears in the urine of the cancer patient as a result of some abnormal metabolism of malig: nant tissue. Unfortunately, data on the various malignancies in which this marker is useful are sparse, but it is very interesting that the concentrations of both nucleoside markers and neopterin are high in subjects with AIDS who, as it is well known, are on the way to various malignancies. I hope that our colleagues and perhaps even more importantly, the funding agencies, will slowly become convinced that more effort and resources should be directed to work on the nonprotein tumor markers. Many
References 1 Pohl, A. L. et al. (1983) Cancer Detection and Prevention 6, 7-20 2 Fuks, A., Shuster, J. and Gold, P. (1980) Cancer Markers (Sell. S., ed.), p. 315, Humana Press 3 Klavins, J. V. (1983) Ann. Clin. Lab. Sci. 13 4 Borek, E. and Kerr, S. J. (1972) Adv. Cancer Res. 15, 163-192 5 Magee, P. N. and Father, E. (1962) Biochem. J. 83, 114 6 Kuchino, Y., Borek, E., Grunberger, D. et al. (1982) Nucleic Acids Res. 10, 6421-6432 7 Borek, E. (1984) Tumour Biol. 5, 1-14 8 Rasmuson, T., Bjork, G. R., Damber, L. etal. (1983) Recent Results Cancer Res. 84, 331-343 9 Muller, J., Erb, N., HeUer-SchOchet al. Recent Results Cancer Res. 84, 317-330 10 Thomale, J. and Nass, G. (1982) Cancer Left. 15, 149-159 11 Borek, E., Sharma, O. K. and Brewer, J. I. (1983) Am. J. Obst. Gynecol. 146, 906-910 12 Hausen, A. et al. (1981) Clin. Chim. Acta 117, 297-305
EmergingTechniques Stereology: a working tool for cell biologists
relevant data relating the structure of cellular components to biochemical functions, and to describe the molecular structure of these components.
K. Schwerzmann and H. Hoppeler What is stereology? Stereology estimates three-dimensional parameters of biological structures from twodimensional pictures obtained in the electron microscope. The structural data can be combined with biochemical measurements to relate quantitatively cellular structures with their biochemical functions in vivo, or to describe the molecular architecture of cellular compartments. At first glance, biochemistry and stereology seem to have little in common. Biochemistry is the science dealing with chemical compounds and products of biological processes, stereology deals with the quantitation of three-dimensional objects from information contained in two-dimensional pictures. Stereology is of no use to the biochemist who studies reactions in a test-tube. If he wants to know what
K. Schwerzmann and H. Hoppeler are at the Anatomisches lnstitut, University o f Berne, CH-3000 Berne 9, Switzerland.
happens in a cell, however, he has to take structural features into account. The cell is a highly ordered structure divided into numerous compartments by intracellular membranes which limit reaction spaces and availability of substrates, and probably affect the sequential order of metabolic processes. Hence, quantitative information concerning, for instance, volume, surface area, and distribution of a given structure in a cell may assist in the elucidation of biochemical processes at the cellular level. Stereology applied to images of cell ultrastructure can be combined with biochemical measurements to obtain
~) 1985.ElsevierSciencePublishersB.V.. Amsterdam 0376- 5067/85/$ff2.f10
Stereology has been described as 'a body of mathematical methods relating three-dimensional parameters of a structure to two-dimensional measurements obtainable on sections of the structure'1. A life scientist uses micrographs, obtained from sections through biological material usually with an electronmicroscope, for measurements which yield the real dimensions of the structure of interest. The principle of stereology is demonstrated in Fig. 1. On a section, the volume V of an object is represented by an area a. Intuitively, the size of the area a is related to the volume V of the object. Likewise, the surface A of an object is represented by the boundary lines l on the section. Stereology defines the relationship between object and profile parameters using mathematical and statistical methods. However, stereology only
TIBS-
185
M a y 1985
describes the dimensions of objects as densities, i.e. the volume of the object is. given as a fraction of the reference space and the surface area of the object is calculated as surface density (surface area of object/volume of reference space). Stereological estimates are hence derived from the ratio of two measurements: namely estimates of the size of the object and of the size of the reference space. The absolute values for stereological parameters are calculated by multiplying the stereological ratios with the absolute volume of the reference space determined by an independent method. For example, stereology provides the volume density of mitochondria in the liver, while the total mitochondrial volume in liver is calculated by multiplying the mitochondrial volume density with the total volume of the liver measured by fluid displacement2. Sampling for stereology
The methods of stereology are statistical and a fundamental postulate is that the sections are oriented randomly with respect to the object. To avoid bias, the sections must be cut at random and not selected for 'nice' pictures. Also, a sufficient number of sections has to be analysed to meet a specified precision for the final data. (For a detailed discussion of the statistical problems of stereology see Refs 1-4.) The design of an appropriate sampling scheme for a specific biological problem is crucial in any stereological study and deserves careful planning. In most cases, stereological parameters are derived from several samples of the same section (micrographs) as well as from several samples of a specimen. It has been shown that at all stages of sampling, systematic sampling with a random starting point yields good results (i.e. low statistical error) if the specimen does not show periodicities. However, since many biological materials are highly organized structures (e.g. the cristae of muscle mitochondria or the thylakoids in chloroplasts) sampling for stereology is not trivial, if unbiased stereological parameters ar~ to be obtained. (Examples for sampling designs are given in Refs. 1-4.) Estimation procedures in stereology In 1847, the French geologist Delesse was the first to show that volume densities of objects can be estimated by areal densities on representative sections of a solid. To estimate areal densities, he cut out and weighed the profiles. It was realized later5 that this can be
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Fig. 1. (a) The polyhedron serves as a model object with the parameters V (volume), A (surface), L (length o f the edges) and P (comer points). The reference space is a cube with side-length d. (b) Sectioning o f the reference space with a plane produces a profile with the parameters a (area), 1 (side ler~gth) and p (corner points) while the corner points P are lost (adapted from Ref. 1). Reproducedby courtesyof
AcademicPress. achieved more efficiently by super- present the situation in vivo. A stereoimposing sections with test points and logical analysis of the ultrastructure in lines, as shown in Fig. 2. The estimating tissue sections and in the corresponding procedure consists of a simple differ- subcellular fractions can overcome some ential count of points and lines falling of the problems related to recovery onto the objects and reference space. and sample representativeness8. For For the specimen given in Fig. 2, the example, Massey and Butler 9 found that ratio of test points (end-points of lines) phenobarbitone treatment of rats infalling on mitochondria to the total creased endoplasmic membrane area, number of points falling in the reference but only in particular regions of the space (the cell) represents the volume liver. However, the activities of marker fraction of mitochondria in the cell. enzymes for the endoplasmic reticulum Likewise, the surface density of inner were not significantly greater than the membranes is calculated by the ratio of control values when measured for liver number of intersections of test lines with homogenates or isolated fractions. They inner membranes to the square of the concluded that, as a consequence of the points falling on mitochondrial profiles. Such point counting methods are often faster and more cost-effective than semi- or even fully-automatic image analysing systems6. Stereology and biochemistry
Stereology has often been used to study quantitatively the alterations in the ultrastructure of cells or tissues which are induced by some type of treatment, such as drugs, chemicals, exercise or disease. The structural modifications can then be related to changes in biochemical activities observed in the tissue homogenate or in subcellular fractions. This complementary approach of biochemical and stereological measurements is superior to individual biochemical techniques alone. Since tissue homogenization and fractionation can cause substantial losses of subcellular membranes and compartments7'8, the activity measured in the homogenate or in isolated fractions may, in many cases, not re-
Fig. 2. High-power micrograph o f a hepatocyte with a stereological test-grid superimposed. The end points of the test lines are used to estimate volume densities, while the intersections with membrane traces are used to estimate surface densities.
186 drug treatment, the newly synthesized membranes had a lower density of marker enzymes than the control membranes. Since the drug treatment did not detectably increase total or specific activities measured, such local changes would have been missed with simple biochemical measurements. Stereology can also be used to study the biosynthesis and structure of biological membranes since they are well recognized on electronmicrographs of ultrathin sections. The different types of cellular membranes are easy to identify and estimates of total membrane areas may be obtained by established stereological procedures. An excellent example is given in the work of Steinman et al. 1° who used stereological methods to quantitate the incorporation of fluid and plasma membrane during pinocytosis in cultured macrophages. These events have been studied previously by following the concentration of macromolecular markers in the different cellular compartments participating in pinocytosis, but biochemical experiments can only provide a qualitative description of the pinocytic process. Steiranan et al. obtained quantitative information by measuring the volume and surface area of pinocytic and lysosomal vesicles and of the whole cell. The different cellular compartments were previously labeled with horseradish peroxidase, a cytochemical marker for pinocytosis. The results of these studies show that macrophages engulf the equivalent of twice their plasma membrane and one fourth of their internal volume in about one hour. To gain the relevant quantitative information on the volume and membrane flows during endocytosis, stereology is, obviously, the method of choice. When structural measurements on membrane areas can be combined with biochemical assays of the concentration of components within the respective membrane, one may derive quantitative parameters of the molecular structure of the membrane. This is demonstrated in recent studies by Griffiths and coworkers lz'12 on the transport of plasma membrane proteins from their site of synthesis in the endoplasmic reticulum (ER) to their final insertion in the plasma membrane. To understand how these proteins are sorted and concentrated during the passage from ER to Golgi complex, the magnitude of the sorting process must be described in quantitative terms, e.g. as a change in density of newly synthesized proteins in the different membranes. These densities
TIBS-
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total protein density in both membranes was estimated to be 30 000 molecules/ pJn2 (Ref. 12). This sort of quantitative data gives a clear perception of the magnitude of the sorting processes in intracellular protein traffic and of the packing of proteins in cellular membr.anes. The approach of combining biochemistry with stereology may become a very powerful tool for elucidating membrane structure, when the concentration of all the macromolecular components, e.g. proteins, of the membrane can be measured individually. We chose this approach to estimate structural parameters of the inner mitochondrial membrane t3 which are relevant for evaluating the role of lateral diffusion of enzyme complexes in electron transport and energy transduction 14, namely the density of each of the five multi-subunit complexes involved in oxidative phosphorylation and the distances between them. For this purpose, we estimated the total surface area of inner membrane in aliquots of purified mitochondrial suspensions (Fig. 3) by stereology. In the same suspension, the concentration of the five complexes was determined by difference spectroscopy of their intrinsic heme groups or by measuring their specific activity. Since stereological and biochemical data were obtained from the same preparation, they could be used to derive the densities for the various complexes in the membrane, and to calculate the mean nearest distance between reaction partners (Table I). In addition, from the published molecular data the approximate fraction of the membrane area covered by each complex can be calculated. The results in Table I support the notion that the inner membrane is closely packed with proteins, but also suggest that lateral diffusion p e r se of individual complexes may not be a limiting factor in oxidative phosphorylation.
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M a y 1985
Fig. 3, Low-power micrograph of a section through a mitochondrial preparation sedimented on a millipore fdter (the ~lter disk has been dissolved). The reference space is the volume of the sediment, a disk of lO mm diameter and the height indicated in the micrograph (d=lO tam).
could be calculated by Caifliths and coworkers for model proteins, the spike proteins of Semliki Forest virus in infected baby hamster kidney cells. Upon infection, the cells produce high concentrations of the viral proteins which follow the same route to the plasma membrane as the cell's own proteins. To obtain the protein densities in the membranes, they first measured the absolute surface areas of ER, Golgi and plasma membrane of an 'average' cell by stereological proceduresn. Then, the concentration of the viral spike proteins in the respective membranes was determined biochemically from their synthesis rate and the mean time spent in each membrane 12. From the two sets of data it was possible to calculate that the viral proteins had a density of only 90 molecules/~rn2 in the ER membrane, and were concentrated nine-fold to 750 molecules/ixm 2, after insertion into the Golgi membrane. The
Table L Molecular architecture of the inner mitochondrial membrane of rat liver
Globular diameter
(~T1-2)
Mean nearest distanceto reaction partner" (.~)
(A)
Area of inner membrane (%)
Complex I Complex II bcl-complex cyt. c aa3-complex
430 860 900 2750 2610
140 119 83 68 -
80 14 I00 20 88
2.2 O. 1 7.1 0.9 15.9
F:Fo-ATPase
2570
-
90
16.3
Component
Density
"Based on a random-distribution(Poisson pattern) of the reaction partners, calculatedfrom their densities(0.5/V~'~----).
TIBS-
187
M a y 1985
two
These last examples show how routine biochemical measurements can be combined with stereology to solve problems related to the molecular structure of complex membrane systems which, so far, could not be attacked with biochemical techniques alone. The limits for using stereology are set primarily by electronmicroscopy which produces the raw material, i.e. the micrographs. Keeping this in mind, stereology may prove to be useful in solving other structural problems in cell biology.
R d m 1 Weib¢l, E. R. (1979) Stereological Methods, Vol. I, AcademicPress 2 Bolender, R. P. (1978) Int. Rev. Cytol. 247-289 3 Miles,R. E. and Davy, P. (1976)J. Microsc. 107, 211-226 4 Mayhew,T. M. and Cruz-Orive,L. M. (1974) J. Microsc. 102, 195-207 5 Chalkley,H. W. (1943)J. Nad Cancer Inst. 4, 47 6 Mathieu,O., Hoppeler,H. and Weibel,E. R. (1980) Mikroskopie 37, 413-414 7 Bandhuin, P. (1974) Methods Enzymol. 32, 3-20 8 Bolander,R. P., Paumgartner,D., Losa, G.,
Muellener, D. and Weib¢l, E.R. (1978) J. Cell Biol. 77, 56%589
55,
9 Massey, E. D. and Butler, W. H. (1981) Chem. Biot Interact. 34, 31-38 10 Steinman, R. H., Brodie, S. E. and Cohn, Z. A. (1976) J. Cell Biol. 68, 665-687 11 Grifliths, G., Warren, G., Quirm, P., Mathieu-Costello, O. and Hoppeler, H. (1984) J. Cell Biol. 98, 2133-2141 12 Quinn, P., Griffiths, G. and Warren, G. (1984) ]. Cell Biol. 98, 2142-2147 13 Schwerzmann, K. and Weibel, E. R. in EBEC Short Reports, ICSU Press Short Report Series, Miami, in press 14 Hackenbrock, C. R. (1981) Trends Biochem. Sci. 6, 151-154
Letters to the Editor =,
More on metabolic control Does fructose 1,6-bisphosphate reflect phosphofmctokinase
acUvity?
In a recent artide in T1BS 1 Drs Bosefi and Corredor questioned the concept of phosphofructokinase (PFK) as the major regulatory enzyme of the glycolytic pathway. They reasoned that while most cells have a low fructose 1,6bisphosphate content, others accumulate it to such extents that the ratio fructose 6-phosphate/fructose 1,6-bisphosphate (F6P/FBP) is far below 0.1. Since PFK is strongly activated by FBP, a slight rise in this product would maximally activate the enzyme thereby switching off control at the PFK step. The fact that FBP accumulates reflects a rate-limiting step further down the pathway. In some cells, PFK can shift from a regulatory to a non-regulatory role and the authors take the blood platelet as an example where the F6P/FBP ratio shifts from 1 in unstimulated cells to far below 1 during aggregation and secretion. Although the F6P/FBP ratio already shows great variations in unstimulated platelets (0.5-2.7, depending on the suspending medium2), a 2-3 fold decrease is seen during stimulation with thrombin3. Interestingly, these changes greatly depend on the glucose content of the medium. Platelets do not contain detectable quantities of glucose, whereas glycogen, although abundantly present, can only be slowly degraded. Hence, the glycolytic flux responds to changes in extracellular glucose content in the range 1-1000 IxM glucose 4. In the presence of glucose (1 mM), the three-fold decrease in F6P/FBP ratio is accompanied by a two-fold increase in the flux
ations of FBP and dihydroxyacetonephosphate during flux activationL More importantly, they suggest a massive accumulation of FBP, relatively independent of the degree of flux activation. The relevance of this in cellular energy metabolism must be sought in the fact that FBP contains two energy-rich phosphate groups and represents a considerable amount of metabolic energy. Under normal conditions, the FBP content in platelets (350 nmol (1011 cells)-') represents 1 ixmol ATP equivalents~, which is about 10% of the cell's energy content stored in ATP and ADP. This energy remains rapidly accessible to the energy consuming processes (via ADP phosphorylation-ATP dephosphoryla-
(from 3 to 6 i~mol lactate formed min -] (1011 cells)-1). But in the absence of glucose, thrombin induces a three-fold increase in the flux (from 1 to 3 p.mol lactate rain-1 (1011 cells)-1), without appreciable changes in the F6P/FBP ratios. In the concept of Bosc~ and Corredor, these findings indicate that PFK shifts from a non-regulatory to a regulatory role as the extracellular glucose concentration decreases and the actual flux slows down. These differences are even more striking when flux activation by CN- is conlabelled FBP sidered (Pasteur effect). As illustrated in 800--32P[% of control) Fig. 1, the changes in FBP vary from a decrease in the absence of glucose to a 700 seven-fold rise with 1 mM glucose. With 40-100 I~Mglucose, flux activation is not 600 accompanied by any significant change in FBP concentration. Since the F6P concentration remains constant, the 500 F6P/FBP ratio varies as much as 150fold 5. The relative flux activation 400 remains similar over the whole range of glucose concentrations (1.4-1.7-fold) 300 although the actual fluxes increase with extracellular glucose (from 1.7 to 3.6 Ixmol lactate rain -I ( 1 0 1 1 cells)-1). Simi- 200 lar findings are obtained when platelets are treated with H20 2. This leads to a 1 0 0 . . . . . . . . . . . . . . . . . . . . . . six-fold increase in FBP while the glycolytic flux remains constant6,7. ., These data illustrate the dual role of PFK in glycolysis. When flux control is switched off, other enzymes in the lower Fig. 1. Influence of extracellular glucose on the part of the pathway take over and in CN-induced variations in fructose 1,6-bisphosplatelets aldolase may play such a role, phate concentration in platelets (for details see Ref. as indicated by the independent vari- 5).
/
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t ~ 1985, Elsevier Science Pubtishels B.V.. Anuterdam
(B76 - 5067/85/$02.1)0
T I B S - May 1985
workers who had no malignancy did have high concentrations of markers, but in some instances the markers disappeared. We found essentially the same thing in our laboratory. This implies the possibility of reversal of the path to a devastating malignancy. The animal system studied by Nass would be ideal for examining the reversibility of the aberrant metabolism which leads to malignancy. In collaboration with John Brewer, a distinguished gynecologist, we followed six women with choriocarcinoma by determining the nucleoside markers before therapy and then 7-8 days after therapy. We determined the nucleoside markers whereas Brewer determined the standard marker, human chorionic gonadotrophin (HCG). The nucleoside markers returned to normal in seven days; yet HCG concentrations remained high. Normally, gynecologists continue to feed methotrexate to patients until the HCG values return to normal or near normal - this may take weeks, if not months. Brewer decided that, according to the nucleoside markers, the women's malignancies had been eliminated and, therefore, stopped feeding methotrexate but followed the clinical progress of the women for two years. They remained
normal; two of them had normal deliveries, one had an elective abortion and the others were normal. Therefore, if our colleagues in gynecology are willing to try this new method of following effectiveness of therapy, we may be able to spare women the debilitating exposure to the hepatoxic agent, methotrexate n.
more workers are needed in this field, because a great many questions remain to be answered. If one-tenth of the effort which has been expended on the protein markers is devoted to these two nonprotein markers in the coming years, we will reap far greater benefits for our patients.
Neopterin The other nonprotein marker, which has been introduced by colleagues from the University of Innsbruck, is neopterin. Neopterin is derived from guanosine triphosphate and appears in the urine of the cancer patient as a result of some abnormal metabolism of malig: nant tissue. Unfortunately, data on the various malignancies in which this marker is useful are sparse, but it is very interesting that the concentrations of both nucleoside markers and neopterin are high in subjects with AIDS who, as it is well known, are on the way to various malignancies. I hope that our colleagues and perhaps even more importantly, the funding agencies, will slowly become convinced that more effort and resources should be directed to work on the nonprotein tumor markers. Many
References 1 Pohl, A. L. et al. (1983) Cancer Detection and Prevention 6, 7-20 2 Fuks, A., Shuster, J. and Gold, P. (1980) Cancer Markers (Sell. S., ed.), p. 315, Humana Press 3 Klavins, J. V. (1983) Ann. Clin. Lab. Sci. 13 4 Borek, E. and Kerr, S. J. (1972) Adv. Cancer Res. 15, 163-192 5 Magee, P. N. and Father, E. (1962) Biochem. J. 83, 114 6 Kuchino, Y., Borek, E., Grunberger, D. et al. (1982) Nucleic Acids Res. 10, 6421-6432 7 Borek, E. (1984) Tumour Biol. 5, 1-14 8 Rasmuson, T., Bjork, G. R., Damber, L. etal. (1983) Recent Results Cancer Res. 84, 331-343 9 Muller, J., Erb, N., HeUer-SchOchet al. Recent Results Cancer Res. 84, 317-330 10 Thomale, J. and Nass, G. (1982) Cancer Left. 15, 149-159 11 Borek, E., Sharma, O. K. and Brewer, J. I. (1983) Am. J. Obst. Gynecol. 146, 906-910 12 Hausen, A. et al. (1981) Clin. Chim. Acta 117, 297-305
EmergingTechniques Stereology: a working tool for cell biologists
relevant data relating the structure of cellular components to biochemical functions, and to describe the molecular structure of these components.
K. Schwerzmann and H. Hoppeler What is stereology? Stereology estimates three-dimensional parameters of biological structures from twodimensional pictures obtained in the electron microscope. The structural data can be combined with biochemical measurements to relate quantitatively cellular structures with their biochemical functions in vivo, or to describe the molecular architecture of cellular compartments. At first glance, biochemistry and stereology seem to have little in common. Biochemistry is the science dealing with chemical compounds and products of biological processes, stereology deals with the quantitation of three-dimensional objects from information contained in two-dimensional pictures. Stereology is of no use to the biochemist who studies reactions in a test-tube. If he wants to know what
K. Schwerzmann and H. Hoppeler are at the Anatomisches lnstitut, University o f Berne, CH-3000 Berne 9, Switzerland.
happens in a cell, however, he has to take structural features into account. The cell is a highly ordered structure divided into numerous compartments by intracellular membranes which limit reaction spaces and availability of substrates, and probably affect the sequential order of metabolic processes. Hence, quantitative information concerning, for instance, volume, surface area, and distribution of a given structure in a cell may assist in the elucidation of biochemical processes at the cellular level. Stereology applied to images of cell ultrastructure can be combined with biochemical measurements to obtain
~) 1985.ElsevierSciencePublishersB.V.. Amsterdam 0376- 5067/85/$ff2.f10
Stereology has been described as 'a body of mathematical methods relating three-dimensional parameters of a structure to two-dimensional measurements obtainable on sections of the structure'1. A life scientist uses micrographs, obtained from sections through biological material usually with an electronmicroscope, for measurements which yield the real dimensions of the structure of interest. The principle of stereology is demonstrated in Fig. 1. On a section, the volume V of an object is represented by an area a. Intuitively, the size of the area a is related to the volume V of the object. Likewise, the surface A of an object is represented by the boundary lines l on the section. Stereology defines the relationship between object and profile parameters using mathematical and statistical methods. However, stereology only
TIBS-
185
M a y 1985
describes the dimensions of objects as densities, i.e. the volume of the object is. given as a fraction of the reference space and the surface area of the object is calculated as surface density (surface area of object/volume of reference space). Stereological estimates are hence derived from the ratio of two measurements: namely estimates of the size of the object and of the size of the reference space. The absolute values for stereological parameters are calculated by multiplying the stereological ratios with the absolute volume of the reference space determined by an independent method. For example, stereology provides the volume density of mitochondria in the liver, while the total mitochondrial volume in liver is calculated by multiplying the mitochondrial volume density with the total volume of the liver measured by fluid displacement2. Sampling for stereology
The methods of stereology are statistical and a fundamental postulate is that the sections are oriented randomly with respect to the object. To avoid bias, the sections must be cut at random and not selected for 'nice' pictures. Also, a sufficient number of sections has to be analysed to meet a specified precision for the final data. (For a detailed discussion of the statistical problems of stereology see Refs 1-4.) The design of an appropriate sampling scheme for a specific biological problem is crucial in any stereological study and deserves careful planning. In most cases, stereological parameters are derived from several samples of the same section (micrographs) as well as from several samples of a specimen. It has been shown that at all stages of sampling, systematic sampling with a random starting point yields good results (i.e. low statistical error) if the specimen does not show periodicities. However, since many biological materials are highly organized structures (e.g. the cristae of muscle mitochondria or the thylakoids in chloroplasts) sampling for stereology is not trivial, if unbiased stereological parameters ar~ to be obtained. (Examples for sampling designs are given in Refs. 1-4.) Estimation procedures in stereology In 1847, the French geologist Delesse was the first to show that volume densities of objects can be estimated by areal densities on representative sections of a solid. To estimate areal densities, he cut out and weighed the profiles. It was realized later5 that this can be
V A d
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'
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Fig. 1. (a) The polyhedron serves as a model object with the parameters V (volume), A (surface), L (length o f the edges) and P (comer points). The reference space is a cube with side-length d. (b) Sectioning o f the reference space with a plane produces a profile with the parameters a (area), 1 (side ler~gth) and p (corner points) while the corner points P are lost (adapted from Ref. 1). Reproducedby courtesyof
AcademicPress. achieved more efficiently by super- present the situation in vivo. A stereoimposing sections with test points and logical analysis of the ultrastructure in lines, as shown in Fig. 2. The estimating tissue sections and in the corresponding procedure consists of a simple differ- subcellular fractions can overcome some ential count of points and lines falling of the problems related to recovery onto the objects and reference space. and sample representativeness8. For For the specimen given in Fig. 2, the example, Massey and Butler 9 found that ratio of test points (end-points of lines) phenobarbitone treatment of rats infalling on mitochondria to the total creased endoplasmic membrane area, number of points falling in the reference but only in particular regions of the space (the cell) represents the volume liver. However, the activities of marker fraction of mitochondria in the cell. enzymes for the endoplasmic reticulum Likewise, the surface density of inner were not significantly greater than the membranes is calculated by the ratio of control values when measured for liver number of intersections of test lines with homogenates or isolated fractions. They inner membranes to the square of the concluded that, as a consequence of the points falling on mitochondrial profiles. Such point counting methods are often faster and more cost-effective than semi- or even fully-automatic image analysing systems6. Stereology and biochemistry
Stereology has often been used to study quantitatively the alterations in the ultrastructure of cells or tissues which are induced by some type of treatment, such as drugs, chemicals, exercise or disease. The structural modifications can then be related to changes in biochemical activities observed in the tissue homogenate or in subcellular fractions. This complementary approach of biochemical and stereological measurements is superior to individual biochemical techniques alone. Since tissue homogenization and fractionation can cause substantial losses of subcellular membranes and compartments7'8, the activity measured in the homogenate or in isolated fractions may, in many cases, not re-
Fig. 2. High-power micrograph o f a hepatocyte with a stereological test-grid superimposed. The end points of the test lines are used to estimate volume densities, while the intersections with membrane traces are used to estimate surface densities.
186 drug treatment, the newly synthesized membranes had a lower density of marker enzymes than the control membranes. Since the drug treatment did not detectably increase total or specific activities measured, such local changes would have been missed with simple biochemical measurements. Stereology can also be used to study the biosynthesis and structure of biological membranes since they are well recognized on electronmicrographs of ultrathin sections. The different types of cellular membranes are easy to identify and estimates of total membrane areas may be obtained by established stereological procedures. An excellent example is given in the work of Steinman et al. 1° who used stereological methods to quantitate the incorporation of fluid and plasma membrane during pinocytosis in cultured macrophages. These events have been studied previously by following the concentration of macromolecular markers in the different cellular compartments participating in pinocytosis, but biochemical experiments can only provide a qualitative description of the pinocytic process. Steiranan et al. obtained quantitative information by measuring the volume and surface area of pinocytic and lysosomal vesicles and of the whole cell. The different cellular compartments were previously labeled with horseradish peroxidase, a cytochemical marker for pinocytosis. The results of these studies show that macrophages engulf the equivalent of twice their plasma membrane and one fourth of their internal volume in about one hour. To gain the relevant quantitative information on the volume and membrane flows during endocytosis, stereology is, obviously, the method of choice. When structural measurements on membrane areas can be combined with biochemical assays of the concentration of components within the respective membrane, one may derive quantitative parameters of the molecular structure of the membrane. This is demonstrated in recent studies by Griffiths and coworkers lz'12 on the transport of plasma membrane proteins from their site of synthesis in the endoplasmic reticulum (ER) to their final insertion in the plasma membrane. To understand how these proteins are sorted and concentrated during the passage from ER to Golgi complex, the magnitude of the sorting process must be described in quantitative terms, e.g. as a change in density of newly synthesized proteins in the different membranes. These densities
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total protein density in both membranes was estimated to be 30 000 molecules/ pJn2 (Ref. 12). This sort of quantitative data gives a clear perception of the magnitude of the sorting processes in intracellular protein traffic and of the packing of proteins in cellular membr.anes. The approach of combining biochemistry with stereology may become a very powerful tool for elucidating membrane structure, when the concentration of all the macromolecular components, e.g. proteins, of the membrane can be measured individually. We chose this approach to estimate structural parameters of the inner mitochondrial membrane t3 which are relevant for evaluating the role of lateral diffusion of enzyme complexes in electron transport and energy transduction 14, namely the density of each of the five multi-subunit complexes involved in oxidative phosphorylation and the distances between them. For this purpose, we estimated the total surface area of inner membrane in aliquots of purified mitochondrial suspensions (Fig. 3) by stereology. In the same suspension, the concentration of the five complexes was determined by difference spectroscopy of their intrinsic heme groups or by measuring their specific activity. Since stereological and biochemical data were obtained from the same preparation, they could be used to derive the densities for the various complexes in the membrane, and to calculate the mean nearest distance between reaction partners (Table I). In addition, from the published molecular data the approximate fraction of the membrane area covered by each complex can be calculated. The results in Table I support the notion that the inner membrane is closely packed with proteins, but also suggest that lateral diffusion p e r se of individual complexes may not be a limiting factor in oxidative phosphorylation.
,llzm,
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Fig. 3, Low-power micrograph of a section through a mitochondrial preparation sedimented on a millipore fdter (the ~lter disk has been dissolved). The reference space is the volume of the sediment, a disk of lO mm diameter and the height indicated in the micrograph (d=lO tam).
could be calculated by Caifliths and coworkers for model proteins, the spike proteins of Semliki Forest virus in infected baby hamster kidney cells. Upon infection, the cells produce high concentrations of the viral proteins which follow the same route to the plasma membrane as the cell's own proteins. To obtain the protein densities in the membranes, they first measured the absolute surface areas of ER, Golgi and plasma membrane of an 'average' cell by stereological proceduresn. Then, the concentration of the viral spike proteins in the respective membranes was determined biochemically from their synthesis rate and the mean time spent in each membrane 12. From the two sets of data it was possible to calculate that the viral proteins had a density of only 90 molecules/~rn2 in the ER membrane, and were concentrated nine-fold to 750 molecules/ixm 2, after insertion into the Golgi membrane. The
Table L Molecular architecture of the inner mitochondrial membrane of rat liver
Globular diameter
(~T1-2)
Mean nearest distanceto reaction partner" (.~)
(A)
Area of inner membrane (%)
Complex I Complex II bcl-complex cyt. c aa3-complex
430 860 900 2750 2610
140 119 83 68 -
80 14 I00 20 88
2.2 O. 1 7.1 0.9 15.9
F:Fo-ATPase
2570
-
90
16.3
Component
Density
"Based on a random-distribution(Poisson pattern) of the reaction partners, calculatedfrom their densities(0.5/V~'~----).
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two
These last examples show how routine biochemical measurements can be combined with stereology to solve problems related to the molecular structure of complex membrane systems which, so far, could not be attacked with biochemical techniques alone. The limits for using stereology are set primarily by electronmicroscopy which produces the raw material, i.e. the micrographs. Keeping this in mind, stereology may prove to be useful in solving other structural problems in cell biology.
R d m 1 Weib¢l, E. R. (1979) Stereological Methods, Vol. I, AcademicPress 2 Bolender, R. P. (1978) Int. Rev. Cytol. 247-289 3 Miles,R. E. and Davy, P. (1976)J. Microsc. 107, 211-226 4 Mayhew,T. M. and Cruz-Orive,L. M. (1974) J. Microsc. 102, 195-207 5 Chalkley,H. W. (1943)J. Nad Cancer Inst. 4, 47 6 Mathieu,O., Hoppeler,H. and Weibel,E. R. (1980) Mikroskopie 37, 413-414 7 Bandhuin, P. (1974) Methods Enzymol. 32, 3-20 8 Bolander,R. P., Paumgartner,D., Losa, G.,
Muellener, D. and Weib¢l, E.R. (1978) J. Cell Biol. 77, 56%589
55,
9 Massey, E. D. and Butler, W. H. (1981) Chem. Biot Interact. 34, 31-38 10 Steinman, R. H., Brodie, S. E. and Cohn, Z. A. (1976) J. Cell Biol. 68, 665-687 11 Grifliths, G., Warren, G., Quirm, P., Mathieu-Costello, O. and Hoppeler, H. (1984) J. Cell Biol. 98, 2133-2141 12 Quinn, P., Griffiths, G. and Warren, G. (1984) ]. Cell Biol. 98, 2142-2147 13 Schwerzmann, K. and Weibel, E. R. in EBEC Short Reports, ICSU Press Short Report Series, Miami, in press 14 Hackenbrock, C. R. (1981) Trends Biochem. Sci. 6, 151-154
Letters to the Editor =,
More on metabolic control Does fructose 1,6-bisphosphate reflect phosphofmctokinase
acUvity?
In a recent artide in T1BS 1 Drs Bosefi and Corredor questioned the concept of phosphofructokinase (PFK) as the major regulatory enzyme of the glycolytic pathway. They reasoned that while most cells have a low fructose 1,6bisphosphate content, others accumulate it to such extents that the ratio fructose 6-phosphate/fructose 1,6-bisphosphate (F6P/FBP) is far below 0.1. Since PFK is strongly activated by FBP, a slight rise in this product would maximally activate the enzyme thereby switching off control at the PFK step. The fact that FBP accumulates reflects a rate-limiting step further down the pathway. In some cells, PFK can shift from a regulatory to a non-regulatory role and the authors take the blood platelet as an example where the F6P/FBP ratio shifts from 1 in unstimulated cells to far below 1 during aggregation and secretion. Although the F6P/FBP ratio already shows great variations in unstimulated platelets (0.5-2.7, depending on the suspending medium2), a 2-3 fold decrease is seen during stimulation with thrombin3. Interestingly, these changes greatly depend on the glucose content of the medium. Platelets do not contain detectable quantities of glucose, whereas glycogen, although abundantly present, can only be slowly degraded. Hence, the glycolytic flux responds to changes in extracellular glucose content in the range 1-1000 IxM glucose 4. In the presence of glucose (1 mM), the three-fold decrease in F6P/FBP ratio is accompanied by a two-fold increase in the flux
ations of FBP and dihydroxyacetonephosphate during flux activationL More importantly, they suggest a massive accumulation of FBP, relatively independent of the degree of flux activation. The relevance of this in cellular energy metabolism must be sought in the fact that FBP contains two energy-rich phosphate groups and represents a considerable amount of metabolic energy. Under normal conditions, the FBP content in platelets (350 nmol (1011 cells)-') represents 1 ixmol ATP equivalents~, which is about 10% of the cell's energy content stored in ATP and ADP. This energy remains rapidly accessible to the energy consuming processes (via ADP phosphorylation-ATP dephosphoryla-
(from 3 to 6 i~mol lactate formed min -] (1011 cells)-1). But in the absence of glucose, thrombin induces a three-fold increase in the flux (from 1 to 3 p.mol lactate rain-1 (1011 cells)-1), without appreciable changes in the F6P/FBP ratios. In the concept of Bosc~ and Corredor, these findings indicate that PFK shifts from a non-regulatory to a regulatory role as the extracellular glucose concentration decreases and the actual flux slows down. These differences are even more striking when flux activation by CN- is conlabelled FBP sidered (Pasteur effect). As illustrated in 800--32P[% of control) Fig. 1, the changes in FBP vary from a decrease in the absence of glucose to a 700 seven-fold rise with 1 mM glucose. With 40-100 I~Mglucose, flux activation is not 600 accompanied by any significant change in FBP concentration. Since the F6P concentration remains constant, the 500 F6P/FBP ratio varies as much as 150fold 5. The relative flux activation 400 remains similar over the whole range of glucose concentrations (1.4-1.7-fold) 300 although the actual fluxes increase with extracellular glucose (from 1.7 to 3.6 Ixmol lactate rain -I ( 1 0 1 1 cells)-1). Simi- 200 lar findings are obtained when platelets are treated with H20 2. This leads to a 1 0 0 . . . . . . . . . . . . . . . . . . . . . . six-fold increase in FBP while the glycolytic flux remains constant6,7. ., These data illustrate the dual role of PFK in glycolysis. When flux control is switched off, other enzymes in the lower Fig. 1. Influence of extracellular glucose on the part of the pathway take over and in CN-induced variations in fructose 1,6-bisphosplatelets aldolase may play such a role, phate concentration in platelets (for details see Ref. as indicated by the independent vari- 5).
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t ~ 1985, Elsevier Science Pubtishels B.V.. Anuterdam
(B76 - 5067/85/$02.1)0