ARTICLE |
Correspondence to: Karoly Gulya, Dept. of Zoology and Cell Biology, University of Szeged, 2 Egyetem St., POB 659, Szeged H-6722, Hungary..
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Summary |
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We developed and tested a novel quantitative method for the quantification of film autoradiographs, involving a mathematical model and a dot-blot-based membrane standard scale. The exponential model introduced here, ROD = p1(1 - exp[p2x]), appropriately (r2>0.999), describes the relation between relative optical density (ROD) and radioactivity (x) in the range between 0 and 240 gray scale values (using a 256-gray scale level digitizer). By means of this model, standard curves with distinct quenching properties can be exactly interconverted, permitting the tissue-equivalent calibration of different standard scales. The membrane standard scale employed here has several advantages, including the flexible radioactivity range, the facile and rapid preparation technique, and the compact size. The feasibility of the quantification procedure is exemplified by the comparative quantification of multiple calmodulin mRNAs in the rat brain by in situ hybridization with [35S]-cRNA probes. The procedure for quantification provides a significant improvement in that the direct and exact comparison of radiolabeled species, even from different experiments, can be reliably performed. Further, the procedure can be adapted to the quantification of autoradiographs produced by other methods. (J Histochem Cytochem 46:11411149, 1998)
Key Words: quantitative autoradiography, in situ hybridization, image analysis, computer-assisted, microdensitometry, mathematical model, calibration procedure, exponential function, 35S standards, calmodulin mRNAs, Hyperfilm-ßmax
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Introduction |
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Autoradiography is a powerful method for revealing the spatial distribution of radiolabeled substances in biological materials. The choices for the high-resolution quantitative tracing of radioactivity in biological specimens are the grain counting of emulsion-coated sections (
Although the fundamentals of the quantitative analysis of film autoradiographs have already been described (
The quantification of a radiolabel bound to experimental tissue sections is performed by co-exposing a series of calibrated radioactive standards. The aim of using standards is to relate the signal units (here the OD) accurately to calibrated units of radioactivity and then, on the basis of this relationship, to determine the quantities of radiolabel corresponding to the observed signals of experimental samples. The two currently used radioactive standard scales are the tissue paste- and plastic-based ones. Tissue paste standards are prepared by the investigator by mixing increasing amounts of the radioisotope to be quantified with tissue paste (
With an adequate number of data points on the tissue paste scale, the sensitometric curve of the film can be determined. In the absence of an explicit theory describing the complex relationship between OD and radioactivity, third-order (
The study reported here presents a new quantitative autoradiographic method which involves a novel mathematical model of film autoradiography and a membrane standard scale. The meanings of the parameters in the model are clear and can be associated with the experimental conditions. This model can be used for the approximation and interpolation of data points on different standard scales. In addition, their calibration to tissue-equivalent radioactivity can be performed by means of a simple mathematical operation. A dot-blot-based 35S membrane standard scale, its calibration to 35S brain paste standards (by means of our model), and its subsequent use for the quantification of in situ hybridization involving [35S]-cRNA labeling are also shown. The membrane scale, alternative to tissue paste or plastic standards, has several advantages and can easily be adapted to other radiolabeling systems. The use of our quantification method allows accurate determination of the radiolabel in terms of absolute units (e.g., mRNA copy numbers). Moreover, even the quantitative evaluation of different experiments can be reliably performed, which therefore permits a direct comparison concerning the amounts of labeled molecules. To demonstrate the merits of our method, an example of the comparative determination of the distribution of the mRNA species corresponding to the three bona fide calmodulin (CaM) genes in rat brain is presented.
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Materials and Methods |
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Derivation of the Mathematical Model
The fundamental feature of film autoradiography is that, during exposure, the absorption of radiation by silver halide crystals in the photoemulsion reduces silver ions to silver atoms. In the developer, additional reduction of silver ions takes place preferentially where silver atoms reduced by radiation are already present, finally making the exposed area gray. Therefore, the degree of grayness is determined by the quantity of silver ions reduced during the exposure. The mathematical model reported here describes how the quantity of silver atoms depends on the intensity and duration of the exposing radiation.
Let us expose an autoradiographic film to a homogeneous radiation source (all the following statements correspond to the exposed film area) and presume that the decrease in the concentration of silver ions in unit time at moment t is proportional to the concentration of silver ions and to the intensity of the radiation. Let E(t) denote the concentration of silver ions at moment t of the exposure. In the time interval [t,t + Dt], for small values of t, we then get
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(1) |
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(2) |
Dividing by E(t) and integrating over the interval [0,t'] (where t' is the time of exposure), we get
Raising to the power of the natural base leads to the formula
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(3) |
Therefore, if C denotes the molar concentration of atomic silver at the end of the exposure, we have
As C cannot be measured directly, after the film has been developed, the degree of grayness (presumed to be homogeneous) as a function of light transmission is determined instead by microdensitometry. Grayness is characterized by its opacity (O; O = Li/Lo, where Li is the amount of light incident on the film and Lo is the amount of light transmitted). According to the BeerLambert law, O = 10c1C (c1 is a constant). To linearize the function between grayness and C, the OD as a new measure of grayness is introduced as
When a 256-gray level digitizer is used, the grayness is expressed as a gray value (GV) on the linear scale between 0 (brightest) and 255 (darkest). The GV can be transformed into an OD-like value, the relative optical density (ROD;
The ROD units display the same log-reciprocal relationship to light transmittance as the true OD and are reported to be closely correlated with the true OD values (in the OD range 0.052.4, r2 = 0.997;
where c2 is a constant. Parameter p1 = C2E(0) depends on the film [mostly on the initial concentration E(0) of silver ions] and the conditions of film development; parameter p2 = ct' depends on the radioisotope, the film, the exposure time, and other experimental conditions.
In brief, we use nonlinear regression with the function
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(4) |
Generalization of the Mathematical Model
When the exposure time is not negligible relative to the half-life (T1/2) of the radioisotope, the radioactivity x varies considerably according to x(t) = x(0) exp[-lt], where denotes the radioactive decay parameter (
= ln2/T1/2). If the film exposure starts at t = 0 and x(0) denotes the activity at the beginning of the exposure, then Equation 1 takes the form
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(1a) |
By means of operations identical to those performed in connection with Equation 1Equation 2Equation 3Equation 4, from formula (1a) we get
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(4a) |
Formula (4a) allows determination of the sensitometric curves under general conditions, even when the exposure times are different. However, it should be emphasized that function (4) can be used to establish the relation between ROD and radioactivity, even if the duration of the exposure is comparable to T1/2, provided that all the samples and standards are exposed for the same length of time. Since the exposure time was kept fixed (36 hr) in this study, Equation 4 was applied for regression analysis.
Calibration Procedure of a Membrane Standard Scale for Tissue-equivalent Radioactivity Using a Mathematical Transformation
Let us first determine the relation between the standard curves of tissue paste (b) and membrane (m) standard scales. Let us co-expose standards to and develop the film, evaluate the autoradiographic data, and apply regression analysis with Equation 4. As parameter p1 in Equation 4 is a characteristic of the film and developing conditions, thus independent of quenching in different standards, the corresponding parameters for both scales are equal: p1b = p1m. Furthermore, because the two data sets are obtained under identical conditions, all factors except the different extents of quenching are equal in both parameter p2b and p2m. Thus, the relation between the different quenching factors of the standards can readily be determined by introducing the transformation quotient as follows:
Now, through use of the predetermined value (characteristic of a particular fixed set of experimental conditions), the regression function (ROD = p1z(1 - exp[-p2zx]) of each of the subsequent membrane standard scales (z), processed with the fixed experimental conditions, can be simply transformed to that of the corresponding tissue paste scale by setting p2b =
p2z, i.e., ROD = p1z(1 - exp[-g p2zx]). An example for the calibration procedure is provided in the Results section.
Experimental Animals and Tissue Preparation
Male SpragueDawley rats (200250 g) maintained under standard housing conditions were decapitated and the brains were quickly removed for either brain paste preparation or in situ hybridization. All animal experiments were carried out in strict compliance with the European Communities Council Directive (86/609/EEC) regarding the care and use of laboratory animals for experimental procedures.
Twelve brain paste standards with halving radioactivity levels were prepared as described by
For in situ hybridization, brains were embedded in Cryomatrix and frozen immediately at -70C. Serial coronal cryostat sections (15 µm) from selected brain areas were cut and thaw-mounted onto CrAlgelatin-coated glass slides. Sections were air-dried and stored at -70C until further processing.
cRNA Probes
Rat genomic DNA was isolated by standard procedures (S (1100 µCi/nmol; Isotope Institute, Budapest, Hungary) was incorporated, using Riboprobe System-T7 and Riboprobe System-SP6 (Promega; Madison, WI) according to the manufacturer's instructions. Labeled probes were purified by size exclusion chromatography on a ProbeQuant G-50 Sephadex microcolumn (Pharmacia Biotech; Uppsala, Sweden) and the probe-specific activities were determined to be 3.56.5 x 108 cpm/µg.
Membrane Standard Scale
A scale consisting of 16 halving dilutions was prepared with a size exclusion chromatography-purified [35S]-cRNA probe (final activity range 0.51.64 x 104 cpm/mm2). The radioactive probe was diluted in RNase-free water and the radioactivity was counted by liquid scintillation counting. Fifty µl from each dilution was dot-blotted onto a Duralon-UV nylon membrane (Stratagene; La Jolla, CA) by vacuum filtration (Minifold; Schleicher & Schuell, Keene, NH) and fixed by UV crosslinking (120,000 µJ/cm2; Stratalinker, Stratagene). Membranes were subsequently dried at 37C for 30 min and co-exposed with tissue paste standards or brain sections to autoradiographic film. The retention of radiolabel by the membrane during vacuum filtration was determined. Known amounts of radioactive probe dilutions were vacuum-filtered or soaked into the membrane. After crosslinking and drying, radioactivities bound to membranes were determined. Because no significant differences were found between filtered and soaked membranes, the retention was accepted as being 100%.
In Situ Hybridization
The protocol for hybridization with [35S]-cRNA probe was that of
Autoradiography
Tissue sections, tissue paste and membrane standards were apposed to Hyperfilm-ßmax autoradiographic film (Amersham, Arlington Heights, IL) at 4C for 36 hr. Films were developed in Kodak D19 developer (Eastman Kodak; Rochester, NY) at 19C for 3.5 min and fixed in Kodak Fixer at 19C for 10 min.
Densitometry
Autoradiographic data were quantified by computer-assisted microdensitometry. The image analysis system consisted of a high-resolution, 24-bit flatbed color scanner (Mikrotec IIHR; Mikrotec International, Taiwan, ROC) attached to a Power Macintosh 8100/80 AV. Video images of the autoradiographs were captured at 600 x 600 dpi resolution (pixel size ~42 µm) and analyzed by the public domain computer program NIH Image 1.59 (
The autoradiographic images of both tissue paste and membrane standards were delineated on the computer screen, and their areas and the corresponding GVs were determined. Data were corrected for film background and expressed in ROD, and averages of three or four measurements were calculated. Radioactivity/pixel ± SD vs ROD ± SD was plotted and nonlinear regression analysis with function (4) was applied (Statgraphics 6.0; Statistical Graphics Corp. and Manugistic Inc., Rockville, MD). Membrane standards were calibrated to tissue paste standards and their activity was calculated in tissue-equivalent radioactivity. In situ hybridization autoradiographs were quantified by use of calibrated membrane scales. Film background-corrected RODs (nonspecific hybridization was indistinguishable from the film background) of brain areas anatomically defined according to toluidine blue-counterstained sections (
where the Avogadro no. = 6.0225 x 1023 and f = 37792.9 is a correction factor to scale up a pixel volume (42 µ x 42 µ x 15 µ) to 1 mm3. Final results were expressed in mRNA copy number ± SD.
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Results |
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Calibration of the 35S Membrane Scale to Tissue-equivalent Radioactivity
Typical autoradiographic images of a series of radioactive brain paste and membrane standards are shown in Figure 1. RODs and areas corresponding to each member of the standards were determined, and regression analysis with function (4) was applied to both series. For both scales, values of r20.999 were observed in the ROD range 00.85 (0240 total GV; Figure 2). Data points corresponding to this range were used to determine parameter values: p1m = 0.8657 and p2m = 3.0252 for the membrane scale, and p1b = 0.8590 and p2b = 5.0702 for the brain paste scale. In support of the model, the p1 values differed from each other by less than 1%. Transformation quotient
= p2b/p2m = 1.676 indicates that the absorption of ß-emission was higher in the membrane than in the brain paste. The determination of
was repeated with different pairs of standard scales, and almost identical values were obtained.
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CaM In Situ Hybridization Autoradiography
To demonstrate the method, we performed a comparative determination of the distribution of multiple CaM mRNA species in the hypothalamic and adjacent areas at the level of bregma1.3 mm in the rat brain. Coronal brain sections hybridized with the CaM I, CaM II, and CaM III cRNA probes were co-exposed with membrane standard scales (18 films with their own scales were used in this study). Regression parameters (p1m and p2m) corresponding to membrane standard curves were determined for each scale (r2>0.9995), p2m values were transformed according to p2b = p2m (b, brain paste) into tissue-equivalent form, and the resulting equations, ROD = p1m(1 - exp[-g p2mx]), were utilized for the interpolation and approximation of radioactivity in defined areas of the co-exposed brain sections. The correctness of the method is demonstrated by the fact that the parameter values of the 18 standard scales exhibited low variance: p1m = 0.8528 ± 0.0188 (mean ± SD) and p2m = 3.3414 ± 0.2227 (mean ± SD). The autoradiographic images of the brain sections revealed a widespread and differential localization of CaM mRNAs (Figure 3). No measurable images were observed when the sense probe was hybridized to tissue sections (data not shown). Table 1 lists the determined CaM mRNA copy numbers of selected brain areas at the level of bregma1.3 mm.
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Summary of the Quantitative Method
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Discussion |
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The response of the film to radioactive exposure was found to be similar to that reported by other authors (0.999) between 0 and 240 (out of 255) GVs with Hyperfilm-ßmax. For higher GVs, regression analyses result in poorer fits (r2
0.992). The first parameter (p1) is determined by the autoradiographic film and developing conditions, which were kept fixed during our experiments. The second parameter (p2) depends on the experimental conditions, which were kept fixed, but also involves the quenching of radioactivity which, in contrast, varies with the different tissue sections and standard scales. The main novel features of this model are (a) the clear theoretical basis, yielding parameter values with low variance even when different experiments are compared, and thus more accurate quantification, and (b) the determination of the transformation quotient
for a particular experimental set and standard scales makes it possible to perform exact transformations of sensitometric curves and thereby accurately calibrate different standard scales to tissue-equivalent radioactivity.
Earlier attempts at tissue-equivalent calibration (e.g.,
A dot-blot-based 35S membrane standard scale was also introduced in this study. The preparation of this standard scale is fast and simple. Series of dilutions are prepared from the same probe as used for hybridization, dot-blotted, and fixed to a nylon membrane and then dried. The entire procedure takes less than an hour and requires little effort compared to the difficulties of preparing tissue paste standards (
To demonstrate the feasibility of our quantification procedure, the distribution of CaM mRNAs belonging to the three bona fide CaM genes was determined in certain hypothalamic and adjacent areas in the rat brain by in situ hybridization. Quantification was performed by use of the calibrated membrane standard scales. Our results indicate a widespread, area-specific and differential CaM gene expression in the rat brain. To the best of our knowledge, this is the first copy number determination for the multiple CaM mRNA species. In general, these results are in agreement with the findings of other authors on rodent brains (
To summarize, we have developed and tested a novel quantitative method with a new mathematical model and a membrane standard scale. This exponential model makes it possible to approximate, interpolate, and (on the basis of their different quenching properties) also differentiate, transform, and calibrate between autoradiographic images of specimens. This highly advantageous model has been applied to calibrate our dot-blot-based membrane standard scales to tissue paste standards and to quantify and compare the amounts of the multiple CaM mRNA species in the rat brain. The model, the calibration procedure, and the membrane scale can be used for the quantification of film autoradiographs of in situ hybridization or of other applications, such as receptor binding studies.
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Acknowledgments |
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Supported by the Hungarian Science Foundation (OTKA No. T 22822 to KG and OTKA No. F 22658 to AP) and by the National Council on Technical Development (OMFB No. 97-20-MU-0028 to KG).
The skillful technical assistance of Ms Susan Ambrus and Ms Maria Kosztka is greatly appreciated.
Received for publication March 31, 1998; accepted June 9, 1998.
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