The liver is thought to consist of lobules, numerous repeating, randomly oriented units. Within these lobules, genes are expressed in gradients along the porto-central axis, which spans the distance between portal and central veins. We have developed a robust stereological method to map all points in an image to their position on this porto-central axis. This approach is based on the distribution of well-characterized periportal and pericentral enzymes, which are visualized on sections preceding and following the section of interest. Because expression of the model genes phosphoenolpyruvate carboxykinase and ornithine aminotransferase declines gradually with increasing distance from the portal vein and central vein, respectively, these genes can be used to prepare images with topographical information without any assumption about the shape of the hepatic unit, or about the direction or shape of the gradient to be determined. The “relative distance” image is a 2-dimensional image that accurately maps the relative position of hepatocytes on the porto-central axis in 3-dimensional space. It is superimposed on the serial section under investigation to relate local staining density to position on the porto-central axis and obtain the gene expression gradient. The method was used to determine the expression gradient of 2 periportal and 2 pericentral enzymes and their response to fasting. The “total distance” image was used to measure the length of the porto-central axis, which was approximately 210 μm in mice and found to decrease 13% after 1 day of starvation. The method can be applied to any tissue component that can be stained quantitatively. (HEPATOLOGY 2004;39:343–352.)
Using the cellular concentration of enzymes as a parameter, 2 populations of hepatocytes can be recognized: those around the terminal branches of the portal vein (periportal hepatocytes) and those around the terminal branches of the hepatic vein (pericentral hepatocytes). In this concept, the liver consists of a collection of interdigitating, functionally distinct periportal (or upstream) and pericentral (or downstream) domains: “metabolic zonation.”1 The concept of upstream and downstream populations of hepatocytes further predicts a direct relationship between the enzymic phenotype of a hepatocyte and its position on the porto-central axis (Fig. 1). The abundance of phenotypically similar cells in relatively fixed positions makes the liver the organ of choice for studying the molecular mechanisms underlying metabolic regulation. Nevertheless, it is well established that the actual shape of porto-central gradients in gene expression differs among genes. We have attributed this to differences in affinity between transcription factors and their ligands, the gene-specific, highly degenerate DNA-response elements.2 The mathematical description and characterization of such gradients, which is needed to test this hypothesis, requires a reliable, accurate method to measure these gene expression gradients in histological sections.
Several approaches for establishing structure-function relationships within the liver have been reported. First, tissue sampling for functional assays can be carried out according to topographical guidelines. This approach has been perfected—from sampling around portal and central veins3 by means of strips of tissue4, 5 to a comprehensive, 2-dimensional sample isolation procedure.6 In all these procedures, a histochemically stained adjacent section is used as a guide to assign topographical information to the sample. A major drawback of these methods is their laboriousness. As the sampling and analytical procedures for cytometry became more comprehensive, quantification of the final reaction product of histochemical methods became the preferred approach. Initially, when only integrating cytophotometers were available, spot measurements were taken either individually in periportal or pericentral regions7 or radially away from a vessel.8 With the advent of sensitive analog and digital cameras, sampling was extended to linear profiles between central and portal veins.9, 10 However, for unbiased measurement of the density information in the histochemical image, the image has to be sampled according to a positional reference image based on the porto-central axis.
To solve this topological problem, we initially described an approach that assumed that the shape of the smallest structural unit of the liver was the cylindrical lobule.11 Although the approach has been applied successfully,2 we felt uncomfortable with the a priori shape assumption. Furthermore, the approach could deal only indirectly with bidirectional gradients and not at all with discrete elements such as nonparenchymal cells. For these reasons, we developed a new method to map all points in an image to their position on the porto-central axis. The approach is based on the distribution of well-characterized periportal and pericentral enzymes, which are visualized on sections preceding and following the section of interest. These sections are used to extract the positional information that is then superimposed on the section under investigation and used to relate local density information to position on the porto-central axis. The present method does not make any assumptions about the shape of the hepatic unit, nor does it depend on the direction or shape of the gradient studied.
Liver from fed mice or 24-hour-starved mice was fixed in 4% freshly prepared formaldehyde for 4 hours at 4°C and overnight at room temperature. After histological processing and embedding in Paraplast (Tyco Healthcare Group, Mansfield, MA), each liver was cut into serial sections (7 μm). Adjacent series of 4 sections were stained by in situ hybridization with S-labeled complementary RNA probes of glutamine synthetase (GS),12 phosphoenolpyruvate carboxykinase (PEPCK),13 ornithine aminotransferase (OAT),14 or carbamoylphosphate synthetase (CPS),15 exactly as described.16 The sections were simultaneously processed under well-defined conditions to ensure that the optical density (OD) of the autoradiography signals linearly reflected the cellular messenger RNA levels (mRNA).16, 17 The maximum OD did not exceed 0.7.
Images of liver sections were recorded as described.18 Briefly, a Photometrics cooled CCD camera (Tucson, AZ) with a 12-bit dynamic range (1317 × 1035 pixels) attached to an Axioplan microscope (Zeiss, Oberkochen, Germany) with a 5× objective (numerical aperature 0.15), a stabilized power supply, a 580 nm bandpass filter, and an infrared-blocking filter were used. The low-power objective was used to assure the sampling of several lobules in an image. Tissue-mRNA content (silver staining) was recorded using white light.17 The digital transmission images were converted to OD images by calculating the negative logarithm of the transmission image divided by an image of the light source: OD = −10log(I/I0) for each pixel. This conversion implicitly corrects background shading. The OD images were stored as 8-bit images (pixel value is 250 × OD value) with a final format of 658 × 517 pixels, representing 1.8 × 1.4 mm2 of the liver section.
The image processing procedure started with a serial pair of OD images stained for a periportally expressed gene (PEPCK or CPS) and a pericentrally expressed gene (OAT or GS). This pair of images was used to generate a third image in which the value of each pixel represented the relative position of that pixel on the porto-central axis. This relative position was defined as the distance of the pixel to the nearest portal vein, divided by the sum of the distances to the nearest portal and nearest central vein. Because this relative position on the porto-central axis is independent of sectioning direction (Fig. 1), OD measurements based on this relative position can be used to determine porto-central gradients in gene expression.
The periportal (PEPCK) and pericentral (OAT) OD images (Fig. 2A and B) were divided into segments of similar OD using an iterative algorithm that defines segments on the basis of minimizing the pooled pixel-value variation within a segmented image.19 Briefly, this procedure uses a decision tree approach to split an image into 2 density segments. After correction for spatial noise, the pixel-value variation in these segments is determined. This procedure is repeated for each of the resulting daughter segments until the decision to stop the segmentation is reached. This decision is based on two criteria: (1) a decrease of 5% to10% in pooled variation has to be reached by a division, and (2) the difference in mean pixel value that has to exist between daughter segments has to be more than the sum of their standard deviations. Both criteria resulted in 7 to 9 segments (Fig. 2C and D). The lumens of the portal or central veins, which have an OD value close to the tissue background, were interactively marked in their segmented images. A comparison of the marked vessels with those in adjacent sections of the stack ensured consistency. The segmented image was then converted into a binary image by accumulating segments, starting with the blood vessels and the segments with the highest OD, until approximately 35% of the image area was selected. Next, the contours of the periportal and pericentral areas were smoothed by a series of binary “open” and “close” operations in which the number of erosion and dilatation steps increased from 1 to 5. Erosions and dilatations are carried out in an 8-connected neighborhood with an octagonal structural element (Fig. 2E and F).
Skeletonization of the resulting periportal and pericentral areas yielded images with 1-pixel thick portal (Fig. 2G) or central (Fig. 2H) skeletons, on which the blood vessels were superimposed.
The portal and central skeletons can be used to construct an image depicting the position of each hepatocyte on the porto-central axis. To this end, a distance transformation with respect to the skeletons was performed. This resulted in portal (Fig. 2I) and central (Fig. 2J) distance images, in which the value of each pixel represented the distance of that pixel to the nearest portal or central skeleton or vessel. Using image arithmetic (total distance image = portal distance image + central distance image; relative distance image = portal distance image/total distance image), the portal and central distance images were combined to obtain a total distance image (Fig. 2K) and a relative distance image (Fig. 2L). The pixel values in the relative distance image (Fig. 2L) range from 0 (for pixels on the portal skeleton) to 1 (for pixels on the central skeleton). Portal, central, total, and relative distance images were created as 16-bit images (pixel value is 1,000 × relative distance). For image segmentation, the image processing package NIH-Image (version 1.61, NIH, Bethesda, MD) and a customized macro program were used. Further image processing and analysis were carried out with macro programs written for the Optimas image analysis software (version 6.5, Media Cybernetics, Silver Spring, MD). Three-dimensional reconstructions were generated in Amira (Template Graphics Software version 3.0, San Diego, CA).
For each mouse, the expression gradients of the 4 enzymes were determined using 8 pairs of aligned images. The gene expression gradients in an OD image were measured with the help of the corresponding relative distance image (Fig. 2L). The pixel values in the relative distance image were grouped into 20 distance zones (0.05 relative distance per zone; Fig. 3A). Each of these 20 zones (starting at the portal skeleton) was used to mask the corresponding OD image by means of a binary AND operation (Fig. 3B and C), and the frequency histogram of the OD values in that zone was recorded. The 90th-percentile value of the histogram was taken to represent the OD value of that zone, because it both corrects for the large contribution of nonstaining sinusoids in the tissue and avoids the inclusion of high-density staining artifacts. A comparison of this value with the mean OD showed a high correlation between the 2 parameters, but the 90th percentile was less sensitive to outliers (data not shown). The outer one sixth of each image was excluded from measurements to avoid artifacts introduced by the image margins. At the magnification used, the width of this excluded region in mouse sections represents the length of approximately 1 porto-central axis (250 μm).
Choice of Binarization Threshold and Reference Enzymes.
The length of the skeletons depends on the threshold level used for the binarization of the segmented images and on the enzymes used as references for the periportal and pericentral areas. The binarization threshold is determined by comparing these areas at different thresholds using a dissimilarity index (ratio of the differing area to the common area) as parameter (Fig. 4A–D). The dissimilarity index is low and constant at each threshold for the pericentral enzymes GS and OAT; it is low and similar to that of the pericentral enzymes only at a threshold of 35% or 40% for the periportal enzymes PEPCK and CPS (Fig. 4E). Apparently, the most constant periportal and pericentral areas were obtained by using a binarization threshold between 35% and 40%; at this threshold, the dissimilarity between enzymes is low (Fig. 4F). In addition, genes with a wide or narrow zonal distribution—or with a shallow or a steep gradient in expression—generate similar skeletons at this binarization threshold. Nevertheless, it was deemed most appropriate to choose enzymes with a shallow gradient because this would result in concentric segments and, therefore, less abrupt transitions in the binarization step.
Validation of the Determination of Relative Distance in 2-Dimensional Images.
A 3-dimensional reconstruction of the periportal and pericentral areas, together with the enclosed blood vessels, showed that, in 3-dimensional space, these areas have a cylindrical shape, with the blood vessels located in the center (Fig. 5). The skeletonization step in the image processing procedure led to skeletons of periportal and pericentral areas that closely fit the structural details of the corresponding areas in the original OD images (Fig. 2G and H). This shows that the portal and central skeletons identified by image processing can be interpreted as projections of the portal and central vessels on the plane of sectioning.
The relative position of a pixel on the porto-central axis was defined as the distance to the nearest portal vein divided by the sum of the distance to the nearest portal vein and the distance to the nearest central vein. When a portal or central vessel is not detected in a part of the image, a very long total distance is assigned to the pixels in that region. In the case of a portal vessel going unnoticed, the relative distance values in that part of the image increase; in the case of a missed central vessel, the relative distance values decrease (Fig. 6A and B). It can be reasoned that relative distances of 0.5 will only occur when all nearby vessels are detected and that a reliable estimate of the maximum total distance can be found by recording the total distance for all pixels with a relative distance of 0.5 (Fig. 6C). All parts of the image with a total distance that is longer than the real maximum total distance can be considered regions in which image processing failed to detect a portal or central skeleton (Fig. 6D–G). Portal or central vessels could be detected above or below these regions in a 3-dimensional reconstruction (Fig. 6H). On average, only about 1.5% of the pixels in the total distance images have such a long total distance; this indicates that only a very small fraction of the vessel projections is missed by the procedure. To avoid bias caused by missed vessels, these regions were excluded from further measurements. In the remaining parts of the images, the portal and central skeletons are considered projections of the 3-dimensional distribution of the corresponding vessels, so that the relative distance image that is derived from these skeletons accurately estimates the relative position of each pixel on the porto-central axis.
Differences Between Gradients Measured on Absolute and Relative Distance Axes.
The use of the relative distance image to measure gradients in gene expression assumes that the level of expression of a gene depends on its relative distance rather than on its absolute distance from a portal or central vein. To address this issue, we measured gradients based on both absolute or relative distance and compared the results. If the length of the porto-central axis varies widely and gene expression declines proportionally with the absolute distance, variation should be high when the expression gradient is based on the relative distance but low when based on the absolute distance. Alternately, if gene expression declines proportionally with the relative distance, the variation of the gradient based on the absolute distance should show the highest variability. To compare gradients measured on absolute and relative axes, distance values and OD values were determined with a rectangular matrix of 300 equally spaced square regions. The measurements were carried out in a series of 6 corresponding images comprising relative distance, absolute distance, and OD (Fig. 7A–C). The resulting set of 1800 correlated data points could be used to draw graphs of gene expression gradients on absolute and relative axes (Fig. 7D and E). After the binning of density measurements and the calculation of the variation in distance values within these bins, graphs of the resulting OD gradients with the variation in relative and absolute distance were constructed (Fig. 7D and E). The size of the error bars shows that the variation in the distance of the pericentral gradient (OAT) as well as the periportal gradient (PEPCK) is similar in both graphs. By the above reasoning, the length of the porto-central axis is fairly constant and independent of the direction of sectioning. Indeed, a frequency distribution of the length of the porto-central axis derived from the total distance image (Fig. 2K) showed a narrow distribution (SD is 25%-30% of mean; Fig. 7F) in both control and starved mice. Starvation for 1 day leads to a significant 13% decrease in the length of the porto-central axis. For the length of the porto-central axis to be independent of sectioning direction, the liver lobule has to be maximally bent. In a 3-dimensional reconstruction of a 200 μm-thick stack of images, processed to show periportal and pericentral areas, one actually sees that the same liver unit bends from a perpendicular profile in the top view to a longitudinal profile in the bottom view (Fig. 5A and C).
Number of Images Required for a Reliable Gradient Measurement.
The number of images needed to reach the required measurement precision was determined with a subsampling procedure. The gradients of the pericentral enzyme GS were measured in samples with a decreasing number of images and plotted with the gradient measured in a series of 22 images set to 100% for each position of the gradient (Fig. 8). From the resulting graph it can be inferred that with 11 images per sample the deviation from the standard is less than 5%; however, with 6 images per sample this deviation increased to just over 10% at the steepest part of the gradient. A sample size of 7 images was deemed a reasonable compromise between effort and precision.
Gradients in Gene Expression.
Using the procedures described above, we determined the porto-central gradients in expression of PEPCK, CPS, OAT, and GS in fed and 24-hour-starved mice (Fig. 9A–D). In the fed state, PEPCK was expressed with a uniform, rather steep porto-central gradient. Upon fasting, the level of PEPCK increased by a similar amount in all hepatocytes. CPS, in contrast, was expressed with a uniform—but shallow—porto-central gradient. Its expression decreased slightly in the fasting state, and this effect was most pronounced periportally. OAT was confined to the pericentral hepatocytes in the fed state but increased in all hepatocytes upon fasting. Finally, GS had a distribution similar to that of OAT in the fed state. After 24 hours of fasting, all hepatocytes in the pericentral half of the liver increased their GS mRNA content by a fixed amount. This effect tapered off from the middle of the porto-central axis toward the portal vein.
The observed porto-central gradients were fitted to a model for gene expression2 with the following equation: Expression = [F]n/([F]n + Kn). F is the concentration of a putative signal factor that is assumed to decrease (PEPCK and CPS) or increase (OAT and GS) linearly between 0.1 and 0.2 over the length of the porto-central axis. The effects of starvation on the affinity parameter (K, expressed as “K-pos,” the position on the porto-central axis where the expression gradient reaches its point of inflection to make it independent of a signal-factor gradient) and on the cooperativity parameter (n, which determines the steepness of the gradient) for each gene are shown in Fig. 9. For PEPCK and CPS, only changes in n were observed; for OAT, K-pos moved significantly towards the portal vein. The GS gradient showed a change in steepness and a small change in position to include more pericentral hepatocytes.
We have developed a simple and accurate stereological method to measure porto-central gradients in gene expression. The method uses well-characterized marker genes to identify the terminal branches of the portal and central veins and to generate a 2-dimensional distance map and then applies this map to measure an unknown expression gradient in the intervening section. The skeletons of the areas with highest expression represent the projection of the position of the nearest terminal branches of the portal and the central veins on the plane of the section. They are then used, through distance transformation, to generate a map showing the relative distance of every pixel in the image on the axis between the nearest portal and central veins. This map, in turn, is used to relate the cellular concentration of a gene product to the position of that cell on the porto-central axis. Except for image alignment at acquisition and marking of the large portal and central veins, the procedure is entirely automatic. The application of the method is not limited to tissue mRNA gradients as in the present study, but can be applied to any tissue component that can be stained quantitatively, e.g., proteins and glycogen.
The present approach for quantifying porto-central gradients in gene expression is based on our earlier observation that the zonation of gene expression in the liver is intimately related to, and most likely imposed upon the hepatocytes by, the hepatic microcirculation.20 This finding does not imply that the studied genes have to be expressed according to a unidirectional gradient. If the expression gradient is bidirectional8, 21 or if one wants to assess the zonal distribution of discontinuous units, such as nonparenchymal cells or the inhomogeneous glycogen content of hepatocytes,22 the advised procedure is to sandwich such a section between sections stained for marker genes and use the relative distance map that is based on these marker genes to relate absorbance and topography of the compound under investigation. Obviously, the distance transformation and image arithmetic that are used to assign a relative position on the porto-central axis to a hepatocyte are most accurate if consecutive sections that are stained for the presence of periportal and pericentral enzymes are available. However, acceptable gradients were still obtained when both periportal and pericentral areas were derived from the gradient of a single enzyme with a shallow gradient.
A critical issue was whether our 2-dimensional analysis accurately estimates the gene expression gradient in the third dimension. The standard unit of the hepatic architecture—acinus or lobule—is only infrequently identifiable in sections, suggesting a highly twisted or irregularly shaped unit. This impression of irregularity is confirmed by available reconstructions (Fig. 5).23, 24 Our reconstruction of the distribution of PEPCK and OAT areas also shows that the course of a single lobule is highly tortuous, with a 90° change in orientation within the length of a porto-central axis (Fig. 5). Except for the area just underneath the capsule,24 sections through the liver are random with respect to the direction of the different units in a section and thus fulfill the requirements for this stereological approach. Furthermore, the narrow distribution of the observed lengths of the porto-central axis suggests very little effect of the sectioning direction on the outcome. The absence of a tail of long-axis lengths (Fig. 7F) that would result from longitudinal sections through elongated liver lobules also indicates that the lobular organization is such that it is almost impossible to section through a lobule without including both ends of the porto-central axis. Nevertheless, because the distribution of the length of the porto-central axis is slightly skewed toward longer lengths, we checked adjacent serial sections and were able to demonstrate that the long porto-central distances could be traced to regions in the section with branch points of portal or central veins; that is, areas where the terminus of a central or portal vein would become visible in the next few upward or downward sections (Fig. 6H). This finding confirms that periportal and pericentral zones interdigitate.23, 25, 26 The same regions were identified by the “missing vessel” detection algorithm included in the measuring procedure (Fig. 6).
In addition to these quantitative data on gene expression gradients, our approach also yields information on the average length of the porto-central axis, which is defined as the distance along the hepatic sinusoids between portal and central veins. This distance, the porto-central axis, is usually derived from the shortest distance between a preterminal branch of the portal vein and a preterminal branch of a central vein—that is, the assumption is that the structural unit of the liver is a cylinder. Measured in this way, this distance is reported to be 300 to 350 μm in rat liver.6, 8, 27, 28 Without making this assumption, we now report that this distance amounts to 211 ± 57 μm (mean ± SD) in fed mice, and to 183 ± 53 μm in 24-hour-fasted animals. This decrease corresponds to a 35% decrease in liver volume; the liver weight in a group of 24-hour-fasted mice decreased 25% (from 1.20 ± 0.03 g to 0.90 ± 0.04 g; n = 8). Because the diameter of diploid mouse hepatocytes averages 17 ± 1 μm,29 because hepatocyte volume corresponds with ploidy,30 and because 15%, 65%, and 20% of young adult mouse hepatocytes are diploid, tetraploid, and octoploid, respectively,31 the result is a porto-central axis containing 9 to 10 hepatocytes. Using sophisticated graphical reconstruction, Takahashi26 showed that the porto-central axis in human liver measured 350 to 420 μm. Because diploid human hepatocytes have an average diameter of 22 to 23 μm,32 and because human hepatocytes remain diploid until the age of 5033 the smallest functional unit in humans consists of a linear array of approximately 16 to18 hepatocytes. Similarly, the porto-central axis of rat liver consists of 13 to 15 hepatocytes. Our approach should be very useful for modeling the microcirculatory units of different species more quantitatively.
As an extension of the stereological model used for gradient measurements, a prediction of the section area per relative distance zone can be derived for hepatic units of spherical, cylindrical, or linear shape. Fitting the observed area per zone in the mice used for this study showed that the hepatic unit is close to linear and consists of a slightly greater periportal than pericentral area,34 which is in agreement with the shape of the choleohepaton proposed by Ekataksin et al.35
The observed gradients in expression of PEPCK, CPS, GS, and OAT reveal that changes in phenotype along the porto-central axis are gradual, although the steepness of the gradients varies, with the steepest gradient observed for GS. The data also show that a response to fasting is seen in both periportal and pericentral hepatocytes, and are in agreement with available data for PEPCK, CPS, and OAT.15, 36, 37 Only the observed increase in GS expression upon fasting appears to distinguish the mouse from the rat, in which GS activity decreases after 24 hours of starvation.38, 39 Even though the parameters describing the porto-central gradient in PEPCK are similar in fed and fasted animals, the response of PEPCK to fasting differs qualitatively from the other enzymes in that the absolute increase in mRNA concentration is similar in all hepatocytes. The response of CPS, OAT, and GS to fasting, however, is largely confined to cells that already express the gene at a high level. In addition, the number of hepatocytes along the porto-central axis that express GS and OAT increases by 25% for GS and almost 200% for OAT. In conjunction with the biochemical determination of the tissue concentration of one of the mRNAs, measurement of the gradients in gene expression in the liver can also be used to calculate absolute mRNA concentrations in each of the 10 hepatocytes along the porto-central axis. This stereological approach to gene expression, which is also applicable at the protein level, is therefore an excellent tool to deal with the zonal heterogeneity of the liver in biochemical studies.
The authors thank Dr. Alexandre Soufan for generating the 3-dimensional reconstructions. Drs. Antoon Moorman and Theo Hakvoort are gratefully acknowledged for valuable discussions during the development of this method.