Two-dimensional surface maps of the cortex (neocortex and part of the allocortex) of 6 mice. They are arranged according to the macroscopic location of the injection: central region of the dorsolateral convexity ( a -- c ), lateral ( d ), anterior ( e ), posterior ( f ). Right and left maps correspond to right and left hemispheres, respectively, rostral is at the top. The straight vertical line in each map corresponds to the border between dorsal and medial cortex, the elongated gray field medially corresponds to the corpus callosum (cc), the elongated gray field laterally is the olfactory tract (ot). The pyriform and entorhinal cortex are located laterally of the dotted line (the dotted line marks the dorsal border of the dark layer II of these allocortical areas, except for the most rostral part where it marks the location of the rhinal fissure). The medial piece caudally of the corpus callosum is the transition zone to the subiculum and hippocampus, both of which are not included on the maps. The white spot within the black field indicates the region of uptake. In ( a ) and ( b ), the injection was placed into the left hemisphere, in the other cases into the right hemisphere. The black region indicates the region of highest fiber density, and the regions of dense and wide hatching correspond to middle and low fiber densities, respectively. 

Contexts in source publication

Context 1

... Figure 3 shows a coronal section close to the site of injection in the right hemisphere. Axon collaterals radiate from the injection site within the gray matter, and distant terminal fields can be seen in the cortex of both hemispheres and in the thalamus. The axons are completely filled up to—and probably also within—their terminal fields. Figures 4 and 5 show patterns of anterograde staining on maps of the flattened cortex as described in Methods. For each animal, both hemispheres are shown. In 6 animals, the injection was administered into the right, and in 2 animals into the left hemisphere. The black regions correspond to the highest density of staining, dense and wide hatching to progressively lower densities. The white spot in each figure shows the location of the injection site. Its size indicates the extent of the region of uptake as defined in Methods. In spite of the large variation in projection patterns, some properties are common to the various injections: a large field of stained fibers around the injection and patches or bands at more distant places, numbering between 1 and 8 in the injected hemisphere. In the large field around the injection site, the overall density of stained fibers decreases toward the periphery, although denser patches sometimes appear within regions of lower density. The core of highest density (black on Figs. 4 and 5) extends about 500 l m (sometimes more) from the injection site and is due to the bulk of axon collaterals of the neurons affected by the injection. The adjacent hatched regions are fed by fibers running horizontally over long distances and by other fibers that take a bow-shaped course through layer VI, some of them scratching the white matter. In distant terminal fields, individual axons can ramify such that they contribute fibers to several spots located closely to each other. This is, for example, the case in the 3 densely hatched lateral spots in the right hemisphere in Figure 5 a . It is, of course desirable to have some idea of the cortical areas involved in Figures 4 and 5. Figure 6 a shows the classical map in which Caviness (1975) has adapted the scheme of Brodmann (1909) to the mouse neocortex. On this map, we have marked the locations of the injection sites of the brains in Figures 4 and 5 (Fig. 6 b ). The localization was made by identifying the cortical areas on the Nissl sections according to the cytoarchitectonic criteria used by Caviness (1975). The shape of the map differs from that of the neocortex in our maps by its larger rostrocaudal extent. This is due to the different treatment of the frontal and occipital pole regions: flattening by distortion in the Caviness map, cutting the tip of the poles, and keeping the rest metrically correct as far as possible in our maps. By means of the landmarks indicated in Figure 6 b , it is possible to localize approximately some of the terminal fields. Some observations shall be mentioned. 1) Although the dark field around the injection site can be restricted to the corresponding cortical area, the large terminal field in continuity with it always extends over adjacent areas. 2) There is a striking similarity in the projection patterns in Figure 4b , c . This is obviously due to the fact that these injections were located in the same cytoarchitectonic area. Both injection sites project to a rostromedial region (area 6/8) and laterally to an elongated field comprising the border between area 35 and the adjacent entorhinal cortex and to a shorter elongated field of higher density, which according to the cytoarchitectonic criteria described by Caviness is at least partly contained in area 14. Both injections are located just caudally to the barrel field. 3) The 3 lateral spots in the right hemisphere in Figure 5 a are located in different areas: areas 40 and 14. 4) No fiber stain could be found in the pyriform cortex, and in the entorhinal cortex fiber stain was restricted to its lateral border (e.g., Fig. 4 b , c ). Fiber stain was occasionally found in area 27, the presubiculum (medially posteriorly in Fig. 4 f ). 5) The small hatched field close to the olfactory tract in the right hemisphere of Figure 5 b is located in the orbital region of the frontal pole (area 11). Measurements on the size of the terminal fields in the injected hemisphere were made on the maps shown in Figures 4 and 5. The field in continuity with the injection site was always larger than the sum of the remaining terminal fields (Table 1). In some cases, nearly all projections merged into one large field (Fig. 4 e and 5 b ). Table 1 shows the results of the measurements (not corrected for shrinkage). In column 1, the sum of the areas of all terminal fields in the injected hemisphere is reported for each of the 8 brains. Columns 2 and 3 show separate values for the areal size of the large terminal field in continuity with the injection site and the sum of the distant terminal fields. Columns 4--6 show separate values for the sums of the strong (i.e., black), middle, and weakly stained regions. The table also shows the approximate diameter of the region of uptake, as well as the cytoarchitectonic area in which the injection site was located. The total area of the terminal fields ranges between about 2 2 7 and 22 mm , with an average of 12 mm . The difference in size can largely be explained by the inevitable variation in the strength of the injections and the corresponding variation in the size of the regions of uptake, with their diameters rang- ing between 200 and 400 l m (200 l m is the diameter of the dendritic extension of a large pyramidal cell in the mouse). 2 The region of uptake ranged between about 0.03 and 0.1 mm in area. As can be seen from Table 1, in all injections the main part of the terminal field consisted of weak projections (widely hatched regions in Figs. 4 and 5). If we exclude these, the size of the terminal fields (medium plus strong) ranges between 2.5 and 8.8 mm 2 , with an average of 4.7 mm 2 . The average size of the surface area of the entire neocortex of one hemisphere was 64 mm 2 . Thus, the neurons from a middle-sized column of about 300 l m in diameter can reach about 7% of the total neocortex by projections of high plus middle strength, and even about 19% if the weak projections are included. If we translate the measurements of Table 1 into degrees of divergence by dividing the area of the terminal fields by the area of the region of uptake, we get an average factor of 73 (with individual values between 45 and 122) for the strong plus middle projections and an average factor of 182 (with individual values between 122 and 298) if we include the weak connections. (The large range in the individual values may be partly due to the fact that the values for the size of the region of uptake are approximations only.) In 2 of the brains (Fig. 5) we quantified the densities of stained fibers in distant projections. The contralateral projection in Figure 5 b was one of the densest projections in our material (see micrograph in Fig. 7), whereas the rostral spot in the ipsilateral hemisphere was one of the weakest (see Fig. 8). We therefore took these 2 spots as instances of an upper and a lower limit. The densities of the 2 projections measured in Figure 5 a were in between. The results are shown in Figure 5 and Table 2. For comparison with other data (see Discussion), we express these densities in fiber length per cubic millimeters. Table 2 shows the raw data. The data in Figure 5 indicate the maximum densities measured in each spot because the maximum value may be relevant for the question of how strongly distant places in the cortex can influence each other functionally. These maximum values range 3 between 4.6 and 21 m/mm . The higher value may be an underestimate by some meters per cubic millimeters because in dense regions some intersections with the test line may escape the observer. Thus, the maximum density in the contralateral spot in Figure 5 b may be rounded up to 25 m/mm 3 . We also counted the number of axons entering a terminal field from below. Assuming that each of these axons comes from a different pyramidal cell, this number is a measure of the number of neurons projecting from the injection site to that terminal field. The results of these counts are also reported in Figures 5 a , b . In Figure 5 b , the number of axons entering a terminal field ranged between 14 for the weak spot to about 890 fibers running toward the dense and middle dense region of the callosal spot. The number for the contralateral spot in Figure 5 a was about 230 and for one of the ipsilateral spots 540. We also made an estimate of the number of neurons that had taken up the tracer in the brains in Figure 5. To a first approximation, one can calculate the number of neurons within the region of uptake. This calculation is made on the basis of the diameter of the region of uptake given in Table 1 and the number of neurons under 1 mm 2 of cortical surface area, which is about 10 5 in the mouse (Rockel and others 1980; Schu ̈ z and Palm 1989). However, not all the neurons within the region of uptake defined by the bundles of stained descending axons have necessarily taken up the tracer. In the core region, all neurons appeared to have taken up the tracer because the density of stained cell bodies there was as high as the known cell density in the mouse (Schu ̈ z and Palm 1989). Toward the periphery, the density of stained cells decreases relatively sharply. According to our estimates, an ...

Context 2

... variation in the strength of the injections and the corresponding variation in the size of the regions of uptake, with their diameters rang- ing between 200 and 400 l m (200 l m is the diameter of the dendritic extension of a large pyramidal cell in the mouse). 2 The region of uptake ranged between about 0.03 and 0.1 mm in area. As can be seen from Table 1, in all injections the main part of the terminal field consisted of weak projections (widely hatched regions in Figs. 4 and 5). If we exclude these, the size of the terminal fields (medium plus strong) ranges between 2.5 and 8.8 mm 2 , with an average of 4.7 mm 2 . The average size of the surface area of the entire neocortex of one hemisphere was 64 mm 2 . Thus, the neurons from a middle-sized column of about 300 l m in diameter can reach about 7% of the total neocortex by projections of high plus middle strength, and even about 19% if the weak projections are included. If we translate the measurements of Table 1 into degrees of divergence by dividing the area of the terminal fields by the area of the region of uptake, we get an average factor of 73 (with individual values between 45 and 122) for the strong plus middle projections and an average factor of 182 (with individual values between 122 and 298) if we include the weak connections. (The large range in the individual values may be partly due to the fact that the values for the size of the region of uptake are approximations only.) In 2 of the brains (Fig. 5) we quantified the densities of stained fibers in distant projections. The contralateral projection in Figure 5 b was one of the densest projections in our material (see micrograph in Fig. 7), whereas the rostral spot in the ipsilateral hemisphere was one of the weakest (see Fig. 8). We therefore took these 2 spots as instances of an upper and a lower limit. The densities of the 2 projections measured in Figure 5 a were in between. The results are shown in Figure 5 and Table 2. For comparison with other data (see Discussion), we express these densities in fiber length per cubic millimeters. Table 2 shows the raw data. The data in Figure 5 indicate the maximum densities measured in each spot because the maximum value may be relevant for the question of how strongly distant places in the cortex can influence each other functionally. These maximum values range 3 between 4.6 and 21 m/mm . The higher value may be an underestimate by some meters per cubic millimeters because in dense regions some intersections with the test line may escape the observer. Thus, the maximum density in the contralateral spot in Figure 5 b may be rounded up to 25 m/mm 3 . We also counted the number of axons entering a terminal field from below. Assuming that each of these axons comes from a different pyramidal cell, this number is a measure of the number of neurons projecting from the injection site to that terminal field. The results of these counts are also reported in Figures 5 a , b . In Figure 5 b , the number of axons entering a terminal field ranged between 14 for the weak spot to about 890 fibers running toward the dense and middle dense region of the callosal spot. The number for the contralateral spot in Figure 5 a was about 230 and for one of the ipsilateral spots 540. We also made an estimate of the number of neurons that had taken up the tracer in the brains in Figure 5. To a first approximation, one can calculate the number of neurons within the region of uptake. This calculation is made on the basis of the diameter of the region of uptake given in Table 1 and the number of neurons under 1 mm 2 of cortical surface area, which is about 10 5 in the mouse (Rockel and others 1980; Schu ̈ z and Palm 1989). However, not all the neurons within the region of uptake defined by the bundles of stained descending axons have necessarily taken up the tracer. In the core region, all neurons appeared to have taken up the tracer because the density of stained cell bodies there was as high as the known cell density in the mouse (Schu ̈ z and Palm 1989). Toward the periphery, the density of stained cells decreases relatively sharply. According to our estimates, an equivalent cylinder, containing as many neurons as stained in the core region and its halo of lesser staining, has a diameter about 60 l m lesser than the region of uptake defined by the stained descending axons. With this reduced region of uptake, we end up with a number of about 9074 stained neurons in the brain in Figure 5 b . Because we are concerned with the pyramidal cells that project over larger distances, we subtract from this number 15% nonpyramidal cells (Peters and others 1985; Braak H and Braak E 1986), which leads to an estimate of about 7700 pyramidal cells. The injection in Figure 5 a was smaller, and some of the cortical gray substance was mechanically destroyed by the injection. The number of stained pyramidal cells was about 2900 in this case. In all cases (with the exception of the brain in Fig. 4 f ) fiber stain could also be found in the contralateral hemisphere in a position symmetrical to the place of injection. In some of the injections, additional stain could be found in other (i.e., nonhomotopic) positions on the contralateral side. When such projections were present in the contralateral hemisphere, terminal fields were always found in the corresponding position in the injected hemisphere. This raised the question as to whether these nonhomotopic callosal projections come directly from the injection site or rather are mediated by neurons stained retrogradely through one of their axonal branches and reaching the opposite side through another. In some cases, marked by an asterisk in Figures 4 and 5, the latter possibility could not be excluded entirely because in these cases some retrogradely stained neurons were found on the side of the injection. Nor can we fully exclude that some of the weakly hatched regions around the homotopic contralateral spots are slightly enlarged due to fibers coming from retrogradely stained neurons in the vicinity of the injection site. However, in other cases it was clear that nonhomotopic terminal fields were fed directly from the injection site. For example, in the brain in Figure 5 a , some 230 fibers entered the contralateral terminal field symmetrical to the injection site, whereas at least twice as many crossed the corpus callosum. The rest of the stained fibers bypassed the homotopic site to reach the terminal field located more laterally. Occasionally, an individual axon could be seen to ramify in the other hemisphere to reach 2 closely located contralateral terminal fields (e.g., brain in Fig. 4 e ) or to supply both the symmetrical contralateral field and its weakly stained surround- ings (e.g., brain in Fig. 4 b ). Wherever axons run in the plane of sectioning, they could be followed in their entirety. They showed rich ramifications upon reentering the cortex. This makes it probable that the tracer filled the axonal trees completely. When employing anterograde tracers one should be aware of the possibility of a certain amount of aberrant staining: transneuronal staining, retrograde staining, or staining of fibers passing the injection site. This raises the question of the extent to which the pictures in Figures 4 and 5 are partly the result of such aberrant staining. We scrutinized our whole collection of BDA tracer preparations, which included deep cortical and subcortical injections, but found no evidence for transneuronal staining. However, evidence could be found for staining of fibers passing an injection site in both retrograde and anterograde directions. In our material, this phenomenon seemed to have been restricted to fibers injured by the electrode. The existence of a limited number of Golgi-like retrogradely stained neurons has already been mentioned, a phenomenon that may be activity dependent (Jiang and others 1993). Both the fiber stain due to retrogradely stained neurons and the staining of injured fibers of passage are, however, responsible for a small percentage of stained fibers only. We can exclude that these artifacts had any effects on the size of the middle and densely stained terminal fields. Nor do we believe that they increased the size of the weak projection fields more than slightly because we had taken the precautions described in The Problem of Retrograde Staining. The location of the tip of the electrode varied between layers III/IV and V. This had some influence on the width of the region of uptake in the various layers, but in each case, neurons in all layers had taken up the tracer, as could be gathered from the distribution of darkly stained cell bodies. The existence of nonhomotopic callosal projections in rodents has been debated. For a review see Innocenti (1986). The presence of such projections is evident in our material. The complete lack of contralateral fiber stain in Figure 4 f requires some explanation. This map shows an injection into area 17, the main part of which is known to be ‘‘acallosal’’ (also in the mouse; Yorke and Caviness 1975). In addition, as can be seen on the figure, this brain had an exceptionally small corpus callosum, possibly lacking some of the normal callosal fiber components. The axonal tree of a typical pyramidal cell is divided into local axon collaterals radiating in all directions within the gray matter and a main axon running through the white matter to a selected distant location. In the small brain of the mouse, this neat distinction into gray matter axon collaterals and white matter main axons can only be made with respect to the callosal and subcortical projections. In the large terminal field continuous with the injection site, the 2 systems cannot be separated because the main axons do not enter the white matter and can therefore often not be distinguished from long axon collaterals. Even in more distant projections within the same hemisphere, the main axons tend ...

Context 3

... in Fig. 7), whereas the rostral spot in the ipsilateral hemisphere was one of the weakest (see Fig. 8). We therefore took these 2 spots as instances of an upper and a lower limit. The densities of the 2 projections measured in Figure 5 a were in between. The results are shown in Figure 5 and Table 2. For comparison with other data (see Discussion), we express these densities in fiber length per cubic millimeters. Table 2 shows the raw data. The data in Figure 5 indicate the maximum densities measured in each spot because the maximum value may be relevant for the question of how strongly distant places in the cortex can influence each other functionally. These maximum values range 3 between 4.6 and 21 m/mm . The higher value may be an underestimate by some meters per cubic millimeters because in dense regions some intersections with the test line may escape the observer. Thus, the maximum density in the contralateral spot in Figure 5 b may be rounded up to 25 m/mm 3 . We also counted the number of axons entering a terminal field from below. Assuming that each of these axons comes from a different pyramidal cell, this number is a measure of the number of neurons projecting from the injection site to that terminal field. The results of these counts are also reported in Figures 5 a , b . In Figure 5 b , the number of axons entering a terminal field ranged between 14 for the weak spot to about 890 fibers running toward the dense and middle dense region of the callosal spot. The number for the contralateral spot in Figure 5 a was about 230 and for one of the ipsilateral spots 540. We also made an estimate of the number of neurons that had taken up the tracer in the brains in Figure 5. To a first approximation, one can calculate the number of neurons within the region of uptake. This calculation is made on the basis of the diameter of the region of uptake given in Table 1 and the number of neurons under 1 mm 2 of cortical surface area, which is about 10 5 in the mouse (Rockel and others 1980; Schu ̈ z and Palm 1989). However, not all the neurons within the region of uptake defined by the bundles of stained descending axons have necessarily taken up the tracer. In the core region, all neurons appeared to have taken up the tracer because the density of stained cell bodies there was as high as the known cell density in the mouse (Schu ̈ z and Palm 1989). Toward the periphery, the density of stained cells decreases relatively sharply. According to our estimates, an equivalent cylinder, containing as many neurons as stained in the core region and its halo of lesser staining, has a diameter about 60 l m lesser than the region of uptake defined by the stained descending axons. With this reduced region of uptake, we end up with a number of about 9074 stained neurons in the brain in Figure 5 b . Because we are concerned with the pyramidal cells that project over larger distances, we subtract from this number 15% nonpyramidal cells (Peters and others 1985; Braak H and Braak E 1986), which leads to an estimate of about 7700 pyramidal cells. The injection in Figure 5 a was smaller, and some of the cortical gray substance was mechanically destroyed by the injection. The number of stained pyramidal cells was about 2900 in this case. In all cases (with the exception of the brain in Fig. 4 f ) fiber stain could also be found in the contralateral hemisphere in a position symmetrical to the place of injection. In some of the injections, additional stain could be found in other (i.e., nonhomotopic) positions on the contralateral side. When such projections were present in the contralateral hemisphere, terminal fields were always found in the corresponding position in the injected hemisphere. This raised the question as to whether these nonhomotopic callosal projections come directly from the injection site or rather are mediated by neurons stained retrogradely through one of their axonal branches and reaching the opposite side through another. In some cases, marked by an asterisk in Figures 4 and 5, the latter possibility could not be excluded entirely because in these cases some retrogradely stained neurons were found on the side of the injection. Nor can we fully exclude that some of the weakly hatched regions around the homotopic contralateral spots are slightly enlarged due to fibers coming from retrogradely stained neurons in the vicinity of the injection site. However, in other cases it was clear that nonhomotopic terminal fields were fed directly from the injection site. For example, in the brain in Figure 5 a , some 230 fibers entered the contralateral terminal field symmetrical to the injection site, whereas at least twice as many crossed the corpus callosum. The rest of the stained fibers bypassed the homotopic site to reach the terminal field located more laterally. Occasionally, an individual axon could be seen to ramify in the other hemisphere to reach 2 closely located contralateral terminal fields (e.g., brain in Fig. 4 e ) or to supply both the symmetrical contralateral field and its weakly stained surround- ings (e.g., brain in Fig. 4 b ). Wherever axons run in the plane of sectioning, they could be followed in their entirety. They showed rich ramifications upon reentering the cortex. This makes it probable that the tracer filled the axonal trees completely. When employing anterograde tracers one should be aware of the possibility of a certain amount of aberrant staining: transneuronal staining, retrograde staining, or staining of fibers passing the injection site. This raises the question of the extent to which the pictures in Figures 4 and 5 are partly the result of such aberrant staining. We scrutinized our whole collection of BDA tracer preparations, which included deep cortical and subcortical injections, but found no evidence for transneuronal staining. However, evidence could be found for staining of fibers passing an injection site in both retrograde and anterograde directions. In our material, this phenomenon seemed to have been restricted to fibers injured by the electrode. The existence of a limited number of Golgi-like retrogradely stained neurons has already been mentioned, a phenomenon that may be activity dependent (Jiang and others 1993). Both the fiber stain due to retrogradely stained neurons and the staining of injured fibers of passage are, however, responsible for a small percentage of stained fibers only. We can exclude that these artifacts had any effects on the size of the middle and densely stained terminal fields. Nor do we believe that they increased the size of the weak projection fields more than slightly because we had taken the precautions described in The Problem of Retrograde Staining. The location of the tip of the electrode varied between layers III/IV and V. This had some influence on the width of the region of uptake in the various layers, but in each case, neurons in all layers had taken up the tracer, as could be gathered from the distribution of darkly stained cell bodies. The existence of nonhomotopic callosal projections in rodents has been debated. For a review see Innocenti (1986). The presence of such projections is evident in our material. The complete lack of contralateral fiber stain in Figure 4 f requires some explanation. This map shows an injection into area 17, the main part of which is known to be ‘‘acallosal’’ (also in the mouse; Yorke and Caviness 1975). In addition, as can be seen on the figure, this brain had an exceptionally small corpus callosum, possibly lacking some of the normal callosal fiber components. The axonal tree of a typical pyramidal cell is divided into local axon collaterals radiating in all directions within the gray matter and a main axon running through the white matter to a selected distant location. In the small brain of the mouse, this neat distinction into gray matter axon collaterals and white matter main axons can only be made with respect to the callosal and subcortical projections. In the large terminal field continuous with the injection site, the 2 systems cannot be separated because the main axons do not enter the white matter and can therefore often not be distinguished from long axon collaterals. Even in more distant projections within the same hemisphere, the main axons tend to be reluctant to enter the white matter. In the following discussion, we shall therefore use the terms ‘‘local connections’’ for those fibers constituting the black field around the injection site in Figures 4 and 5 and ‘‘distant connections’’ for all those constituting the hatched regions. The term ‘‘distant spots’’ refers exclusively to the spots of terminal fields disconnected from the large field in continuity with the injection site. Let us assume that a nest of neurons has been activated somewhere in the cortex, for example due to thalamic input. The activity will be relatively strong in the immediate vicinity of the activated neurons because all of them contribute axon collaterals to the local field. A particular distant spot will, however, only be reached by some of the activated neurons because only some of the pyramidal cells at a given place will project to the same distant spot. Most pyramidal cells probably have only one main axon projecting to a distant spot in the cortex. This assumption is supported by double-labeling experiments that show that callosally and intrahemispherically projecting neurons are largely separate populations (Andersen and others 1982; Schwartz and Goldman-Rakic 1982; however, for evidence of ramifying main axons in subcortically projecting pyramidal cells see Cowan and Wilson 1994; Desche ˆ nes and others 1994; Levesque and others 1996). What then are the chances that the activity at a given place A transmitted to a particular distant spot B can activate neurons in B? We leave the final answer to the neurophysiologist or the theoretician modeling cortical activity but will deal with this question below as ...

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... these 2 spots as instances of an upper and a lower limit. The densities of the 2 projections measured in Figure 5 a were in between. The results are shown in Figure 5 and Table 2. For comparison with other data (see Discussion), we express these densities in fiber length per cubic millimeters. Table 2 shows the raw data. The data in Figure 5 indicate the maximum densities measured in each spot because the maximum value may be relevant for the question of how strongly distant places in the cortex can influence each other functionally. These maximum values range 3 between 4.6 and 21 m/mm . The higher value may be an underestimate by some meters per cubic millimeters because in dense regions some intersections with the test line may escape the observer. Thus, the maximum density in the contralateral spot in Figure 5 b may be rounded up to 25 m/mm 3 . We also counted the number of axons entering a terminal field from below. Assuming that each of these axons comes from a different pyramidal cell, this number is a measure of the number of neurons projecting from the injection site to that terminal field. The results of these counts are also reported in Figures 5 a , b . In Figure 5 b , the number of axons entering a terminal field ranged between 14 for the weak spot to about 890 fibers running toward the dense and middle dense region of the callosal spot. The number for the contralateral spot in Figure 5 a was about 230 and for one of the ipsilateral spots 540. We also made an estimate of the number of neurons that had taken up the tracer in the brains in Figure 5. To a first approximation, one can calculate the number of neurons within the region of uptake. This calculation is made on the basis of the diameter of the region of uptake given in Table 1 and the number of neurons under 1 mm 2 of cortical surface area, which is about 10 5 in the mouse (Rockel and others 1980; Schu ̈ z and Palm 1989). However, not all the neurons within the region of uptake defined by the bundles of stained descending axons have necessarily taken up the tracer. In the core region, all neurons appeared to have taken up the tracer because the density of stained cell bodies there was as high as the known cell density in the mouse (Schu ̈ z and Palm 1989). Toward the periphery, the density of stained cells decreases relatively sharply. According to our estimates, an equivalent cylinder, containing as many neurons as stained in the core region and its halo of lesser staining, has a diameter about 60 l m lesser than the region of uptake defined by the stained descending axons. With this reduced region of uptake, we end up with a number of about 9074 stained neurons in the brain in Figure 5 b . Because we are concerned with the pyramidal cells that project over larger distances, we subtract from this number 15% nonpyramidal cells (Peters and others 1985; Braak H and Braak E 1986), which leads to an estimate of about 7700 pyramidal cells. The injection in Figure 5 a was smaller, and some of the cortical gray substance was mechanically destroyed by the injection. The number of stained pyramidal cells was about 2900 in this case. In all cases (with the exception of the brain in Fig. 4 f ) fiber stain could also be found in the contralateral hemisphere in a position symmetrical to the place of injection. In some of the injections, additional stain could be found in other (i.e., nonhomotopic) positions on the contralateral side. When such projections were present in the contralateral hemisphere, terminal fields were always found in the corresponding position in the injected hemisphere. This raised the question as to whether these nonhomotopic callosal projections come directly from the injection site or rather are mediated by neurons stained retrogradely through one of their axonal branches and reaching the opposite side through another. In some cases, marked by an asterisk in Figures 4 and 5, the latter possibility could not be excluded entirely because in these cases some retrogradely stained neurons were found on the side of the injection. Nor can we fully exclude that some of the weakly hatched regions around the homotopic contralateral spots are slightly enlarged due to fibers coming from retrogradely stained neurons in the vicinity of the injection site. However, in other cases it was clear that nonhomotopic terminal fields were fed directly from the injection site. For example, in the brain in Figure 5 a , some 230 fibers entered the contralateral terminal field symmetrical to the injection site, whereas at least twice as many crossed the corpus callosum. The rest of the stained fibers bypassed the homotopic site to reach the terminal field located more laterally. Occasionally, an individual axon could be seen to ramify in the other hemisphere to reach 2 closely located contralateral terminal fields (e.g., brain in Fig. 4 e ) or to supply both the symmetrical contralateral field and its weakly stained surround- ings (e.g., brain in Fig. 4 b ). Wherever axons run in the plane of sectioning, they could be followed in their entirety. They showed rich ramifications upon reentering the cortex. This makes it probable that the tracer filled the axonal trees completely. When employing anterograde tracers one should be aware of the possibility of a certain amount of aberrant staining: transneuronal staining, retrograde staining, or staining of fibers passing the injection site. This raises the question of the extent to which the pictures in Figures 4 and 5 are partly the result of such aberrant staining. We scrutinized our whole collection of BDA tracer preparations, which included deep cortical and subcortical injections, but found no evidence for transneuronal staining. However, evidence could be found for staining of fibers passing an injection site in both retrograde and anterograde directions. In our material, this phenomenon seemed to have been restricted to fibers injured by the electrode. The existence of a limited number of Golgi-like retrogradely stained neurons has already been mentioned, a phenomenon that may be activity dependent (Jiang and others 1993). Both the fiber stain due to retrogradely stained neurons and the staining of injured fibers of passage are, however, responsible for a small percentage of stained fibers only. We can exclude that these artifacts had any effects on the size of the middle and densely stained terminal fields. Nor do we believe that they increased the size of the weak projection fields more than slightly because we had taken the precautions described in The Problem of Retrograde Staining. The location of the tip of the electrode varied between layers III/IV and V. This had some influence on the width of the region of uptake in the various layers, but in each case, neurons in all layers had taken up the tracer, as could be gathered from the distribution of darkly stained cell bodies. The existence of nonhomotopic callosal projections in rodents has been debated. For a review see Innocenti (1986). The presence of such projections is evident in our material. The complete lack of contralateral fiber stain in Figure 4 f requires some explanation. This map shows an injection into area 17, the main part of which is known to be ‘‘acallosal’’ (also in the mouse; Yorke and Caviness 1975). In addition, as can be seen on the figure, this brain had an exceptionally small corpus callosum, possibly lacking some of the normal callosal fiber components. The axonal tree of a typical pyramidal cell is divided into local axon collaterals radiating in all directions within the gray matter and a main axon running through the white matter to a selected distant location. In the small brain of the mouse, this neat distinction into gray matter axon collaterals and white matter main axons can only be made with respect to the callosal and subcortical projections. In the large terminal field continuous with the injection site, the 2 systems cannot be separated because the main axons do not enter the white matter and can therefore often not be distinguished from long axon collaterals. Even in more distant projections within the same hemisphere, the main axons tend to be reluctant to enter the white matter. In the following discussion, we shall therefore use the terms ‘‘local connections’’ for those fibers constituting the black field around the injection site in Figures 4 and 5 and ‘‘distant connections’’ for all those constituting the hatched regions. The term ‘‘distant spots’’ refers exclusively to the spots of terminal fields disconnected from the large field in continuity with the injection site. Let us assume that a nest of neurons has been activated somewhere in the cortex, for example due to thalamic input. The activity will be relatively strong in the immediate vicinity of the activated neurons because all of them contribute axon collaterals to the local field. A particular distant spot will, however, only be reached by some of the activated neurons because only some of the pyramidal cells at a given place will project to the same distant spot. Most pyramidal cells probably have only one main axon projecting to a distant spot in the cortex. This assumption is supported by double-labeling experiments that show that callosally and intrahemispherically projecting neurons are largely separate populations (Andersen and others 1982; Schwartz and Goldman-Rakic 1982; however, for evidence of ramifying main axons in subcortically projecting pyramidal cells see Cowan and Wilson 1994; Desche ˆ nes and others 1994; Levesque and others 1996). What then are the chances that the activity at a given place A transmitted to a particular distant spot B can activate neurons in B? We leave the final answer to the neurophysiologist or the theoretician modeling cortical activity but will deal with this question below as far as possible from an anatomical point of view. The percentage of pyramidal cells that project from a given injection ...

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... the density of stained cell bodies there was as high as the known cell density in the mouse (Schu ̈ z and Palm 1989). Toward the periphery, the density of stained cells decreases relatively sharply. According to our estimates, an equivalent cylinder, containing as many neurons as stained in the core region and its halo of lesser staining, has a diameter about 60 l m lesser than the region of uptake defined by the stained descending axons. With this reduced region of uptake, we end up with a number of about 9074 stained neurons in the brain in Figure 5 b . Because we are concerned with the pyramidal cells that project over larger distances, we subtract from this number 15% nonpyramidal cells (Peters and others 1985; Braak H and Braak E 1986), which leads to an estimate of about 7700 pyramidal cells. The injection in Figure 5 a was smaller, and some of the cortical gray substance was mechanically destroyed by the injection. The number of stained pyramidal cells was about 2900 in this case. In all cases (with the exception of the brain in Fig. 4 f ) fiber stain could also be found in the contralateral hemisphere in a position symmetrical to the place of injection. In some of the injections, additional stain could be found in other (i.e., nonhomotopic) positions on the contralateral side. When such projections were present in the contralateral hemisphere, terminal fields were always found in the corresponding position in the injected hemisphere. This raised the question as to whether these nonhomotopic callosal projections come directly from the injection site or rather are mediated by neurons stained retrogradely through one of their axonal branches and reaching the opposite side through another. In some cases, marked by an asterisk in Figures 4 and 5, the latter possibility could not be excluded entirely because in these cases some retrogradely stained neurons were found on the side of the injection. Nor can we fully exclude that some of the weakly hatched regions around the homotopic contralateral spots are slightly enlarged due to fibers coming from retrogradely stained neurons in the vicinity of the injection site. However, in other cases it was clear that nonhomotopic terminal fields were fed directly from the injection site. For example, in the brain in Figure 5 a , some 230 fibers entered the contralateral terminal field symmetrical to the injection site, whereas at least twice as many crossed the corpus callosum. The rest of the stained fibers bypassed the homotopic site to reach the terminal field located more laterally. Occasionally, an individual axon could be seen to ramify in the other hemisphere to reach 2 closely located contralateral terminal fields (e.g., brain in Fig. 4 e ) or to supply both the symmetrical contralateral field and its weakly stained surround- ings (e.g., brain in Fig. 4 b ). Wherever axons run in the plane of sectioning, they could be followed in their entirety. They showed rich ramifications upon reentering the cortex. This makes it probable that the tracer filled the axonal trees completely. When employing anterograde tracers one should be aware of the possibility of a certain amount of aberrant staining: transneuronal staining, retrograde staining, or staining of fibers passing the injection site. This raises the question of the extent to which the pictures in Figures 4 and 5 are partly the result of such aberrant staining. We scrutinized our whole collection of BDA tracer preparations, which included deep cortical and subcortical injections, but found no evidence for transneuronal staining. However, evidence could be found for staining of fibers passing an injection site in both retrograde and anterograde directions. In our material, this phenomenon seemed to have been restricted to fibers injured by the electrode. The existence of a limited number of Golgi-like retrogradely stained neurons has already been mentioned, a phenomenon that may be activity dependent (Jiang and others 1993). Both the fiber stain due to retrogradely stained neurons and the staining of injured fibers of passage are, however, responsible for a small percentage of stained fibers only. We can exclude that these artifacts had any effects on the size of the middle and densely stained terminal fields. Nor do we believe that they increased the size of the weak projection fields more than slightly because we had taken the precautions described in The Problem of Retrograde Staining. The location of the tip of the electrode varied between layers III/IV and V. This had some influence on the width of the region of uptake in the various layers, but in each case, neurons in all layers had taken up the tracer, as could be gathered from the distribution of darkly stained cell bodies. The existence of nonhomotopic callosal projections in rodents has been debated. For a review see Innocenti (1986). The presence of such projections is evident in our material. The complete lack of contralateral fiber stain in Figure 4 f requires some explanation. This map shows an injection into area 17, the main part of which is known to be ‘‘acallosal’’ (also in the mouse; Yorke and Caviness 1975). In addition, as can be seen on the figure, this brain had an exceptionally small corpus callosum, possibly lacking some of the normal callosal fiber components. The axonal tree of a typical pyramidal cell is divided into local axon collaterals radiating in all directions within the gray matter and a main axon running through the white matter to a selected distant location. In the small brain of the mouse, this neat distinction into gray matter axon collaterals and white matter main axons can only be made with respect to the callosal and subcortical projections. In the large terminal field continuous with the injection site, the 2 systems cannot be separated because the main axons do not enter the white matter and can therefore often not be distinguished from long axon collaterals. Even in more distant projections within the same hemisphere, the main axons tend to be reluctant to enter the white matter. In the following discussion, we shall therefore use the terms ‘‘local connections’’ for those fibers constituting the black field around the injection site in Figures 4 and 5 and ‘‘distant connections’’ for all those constituting the hatched regions. The term ‘‘distant spots’’ refers exclusively to the spots of terminal fields disconnected from the large field in continuity with the injection site. Let us assume that a nest of neurons has been activated somewhere in the cortex, for example due to thalamic input. The activity will be relatively strong in the immediate vicinity of the activated neurons because all of them contribute axon collaterals to the local field. A particular distant spot will, however, only be reached by some of the activated neurons because only some of the pyramidal cells at a given place will project to the same distant spot. Most pyramidal cells probably have only one main axon projecting to a distant spot in the cortex. This assumption is supported by double-labeling experiments that show that callosally and intrahemispherically projecting neurons are largely separate populations (Andersen and others 1982; Schwartz and Goldman-Rakic 1982; however, for evidence of ramifying main axons in subcortically projecting pyramidal cells see Cowan and Wilson 1994; Desche ˆ nes and others 1994; Levesque and others 1996). What then are the chances that the activity at a given place A transmitted to a particular distant spot B can activate neurons in B? We leave the final answer to the neurophysiologist or the theoretician modeling cortical activity but will deal with this question below as far as possible from an anatomical point of view. The percentage of pyramidal cells that project from a given injection site to some distant spot may be taken as an indication of the relative strength of distant connections. In Figure 5 b the number of pyramidal cells projecting to the contralateral spot (ignoring the weak halo) is about 890. This is 12% of the about 7700 pyramidal cells that have taken up the tracer. In the case of Figure 5 a , 540 out of 2900, that is, 19% of the stained pyramidal cells, project to the distant ipsilateral spot investigated. This means that 1/8 to 1/5 of the neurons from a given injection site can contribute fibers to a distant spot. Let us now investigate how this translates in fiber densities. The maximum density of stained fibers measured in a distant spot in the brain in Figure 5 b was about 25 m/mm 3 . This is very 3 little compared with the total axonal length in 1 mm , which is about 4 km in the mouse (Braitenberg and Schu ̈ z 1991; for comparable values in the cat see Foh and others 1973), that is, only about 0.6%. (If we take into account a volume shrinkage to 74% in the BDA preparations [see Methods], the maximum density reduces to 19 m/mm 3 , corresponding to 0.5% of the total axonal population.) In view of the overall arrangement of synapses along axons (Braitenberg 1978 b ; Amir and others 1993; Hellwig and others 1994; Houzel and others 1994; Anderson and others 2002), we take fiber density as a direct indication of synaptic density. Functionally speaking, this implies that of the 8000 postsynaptic sites on a dendritic tree of a pyramidal cell in the mouse (Braitenberg and Schu ̈ z 1991), about 48 synapses can be activated from a distant site of activation (in the event of a strong projection from that site). How do these values compare with the situation in the local terminal field in the vicinity of the injection site? This question cannot be answered by direct measurement because the density of stained fibers in the black regions in Figures 4 and 5 is too high to be measured by stereological methods. However, the density of fibers in the black region can be estimated as follows. In former work we came to the conclusion that individual pyramidal cells in the mouse have a total ...

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... Figure 3 shows a coronal section close to the site of injection in the right hemisphere. Axon collaterals radiate from the injection site within the gray matter, and distant terminal fields can be seen in the cortex of both hemispheres and in the thalamus. The axons are completely filled up to—and probably also within—their terminal fields. Figures 4 and 5 show patterns of anterograde staining on maps of the flattened cortex as described in Methods. For each animal, both hemispheres are shown. In 6 animals, the injection was administered into the right, and in 2 animals into the left hemisphere. The black regions correspond to the highest density of staining, dense and wide hatching to progressively lower densities. The white spot in each figure shows the location of the injection site. Its size indicates the extent of the region of uptake as defined in Methods. In spite of the large variation in projection patterns, some properties are common to the various injections: a large field of stained fibers around the injection and patches or bands at more distant places, numbering between 1 and 8 in the injected hemisphere. In the large field around the injection site, the overall density of stained fibers decreases toward the periphery, although denser patches sometimes appear within regions of lower density. The core of highest density (black on Figs. 4 and 5) extends about 500 l m (sometimes more) from the injection site and is due to the bulk of axon collaterals of the neurons affected by the injection. The adjacent hatched regions are fed by fibers running horizontally over long distances and by other fibers that take a bow-shaped course through layer VI, some of them scratching the white matter. In distant terminal fields, individual axons can ramify such that they contribute fibers to several spots located closely to each other. This is, for example, the case in the 3 densely hatched lateral spots in the right hemisphere in Figure 5 a . It is, of course desirable to have some idea of the cortical areas involved in Figures 4 and 5. Figure 6 a shows the classical map in which Caviness (1975) has adapted the scheme of Brodmann (1909) to the mouse neocortex. On this map, we have marked the locations of the injection sites of the brains in Figures 4 and 5 (Fig. 6 b ). The localization was made by identifying the cortical areas on the Nissl sections according to the cytoarchitectonic criteria used by Caviness (1975). The shape of the map differs from that of the neocortex in our maps by its larger rostrocaudal extent. This is due to the different treatment of the frontal and occipital pole regions: flattening by distortion in the Caviness map, cutting the tip of the poles, and keeping the rest metrically correct as far as possible in our maps. By means of the landmarks indicated in Figure 6 b , it is possible to localize approximately some of the terminal fields. Some observations shall be mentioned. 1) Although the dark field around the injection site can be restricted to the corresponding cortical area, the large terminal field in continuity with it always extends over adjacent areas. 2) There is a striking similarity in the projection patterns in Figure 4b , c . This is obviously due to the fact that these injections were located in the same cytoarchitectonic area. Both injection sites project to a rostromedial region (area 6/8) and laterally to an elongated field comprising the border between area 35 and the adjacent entorhinal cortex and to a shorter elongated field of higher density, which according to the cytoarchitectonic criteria described by Caviness is at least partly contained in area 14. Both injections are located just caudally to the barrel field. 3) The 3 lateral spots in the right hemisphere in Figure 5 a are located in different areas: areas 40 and 14. 4) No fiber stain could be found in the pyriform cortex, and in the entorhinal cortex fiber stain was restricted to its lateral border (e.g., Fig. 4 b , c ). Fiber stain was occasionally found in area 27, the presubiculum (medially posteriorly in Fig. 4 f ). 5) The small hatched field close to the olfactory tract in the right hemisphere of Figure 5 b is located in the orbital region of the frontal pole (area 11). Measurements on the size of the terminal fields in the injected hemisphere were made on the maps shown in Figures 4 and 5. The field in continuity with the injection site was always larger than the sum of the remaining terminal fields (Table 1). In some cases, nearly all projections merged into one large field (Fig. 4 e and 5 b ). Table 1 shows the results of the measurements (not corrected for shrinkage). In column 1, the sum of the areas of all terminal fields in the injected hemisphere is reported for each of the 8 brains. Columns 2 and 3 show separate values for the areal size of the large terminal field in continuity with the injection site and the sum of the distant terminal fields. Columns 4--6 show separate values for the sums of the strong (i.e., black), middle, and weakly stained regions. The table also shows the approximate diameter of the region of uptake, as well as the cytoarchitectonic area in which the injection site was located. The total area of the terminal fields ranges between about 2 2 7 and 22 mm , with an average of 12 mm . The difference in size can largely be explained by the inevitable variation in the strength of the injections and the corresponding variation in the size of the regions of uptake, with their diameters rang- ing between 200 and 400 l m (200 l m is the diameter of the dendritic extension of a large pyramidal cell in the mouse). 2 The region of uptake ranged between about 0.03 and 0.1 mm in area. As can be seen from Table 1, in all injections the main part of the terminal field consisted of weak projections (widely hatched regions in Figs. 4 and 5). If we exclude these, the size of the terminal fields (medium plus strong) ranges between 2.5 and 8.8 mm 2 , with an average of 4.7 mm 2 . The average size of the surface area of the entire neocortex of one hemisphere was 64 mm 2 . Thus, the neurons from a middle-sized column of about 300 l m in diameter can reach about 7% of the total neocortex by projections of high plus middle strength, and even about 19% if the weak projections are included. If we translate the measurements of Table 1 into degrees of divergence by dividing the area of the terminal fields by the area of the region of uptake, we get an average factor of 73 (with individual values between 45 and 122) for the strong plus middle projections and an average factor of 182 (with individual values between 122 and 298) if we include the weak connections. (The large range in the individual values may be partly due to the fact that the values for the size of the region of uptake are approximations only.) In 2 of the brains (Fig. 5) we quantified the densities of stained fibers in distant projections. The contralateral projection in Figure 5 b was one of the densest projections in our material (see micrograph in Fig. 7), whereas the rostral spot in the ipsilateral hemisphere was one of the weakest (see Fig. 8). We therefore took these 2 spots as instances of an upper and a lower limit. The densities of the 2 projections measured in Figure 5 a were in between. The results are shown in Figure 5 and Table 2. For comparison with other data (see Discussion), we express these densities in fiber length per cubic millimeters. Table 2 shows the raw data. The data in Figure 5 indicate the maximum densities measured in each spot because the maximum value may be relevant for the question of how strongly distant places in the cortex can influence each other functionally. These maximum values range 3 between 4.6 and 21 m/mm . The higher value may be an underestimate by some meters per cubic millimeters because in dense regions some intersections with the test line may escape the observer. Thus, the maximum density in the contralateral spot in Figure 5 b may be rounded up to 25 m/mm 3 . We also counted the number of axons entering a terminal field from below. Assuming that each of these axons comes from a different pyramidal cell, this number is a measure of the number of neurons projecting from the injection site to that terminal field. The results of these counts are also reported in Figures 5 a , b . In Figure 5 b , the number of axons entering a terminal field ranged between 14 for the weak spot to about 890 fibers running toward the dense and middle dense region of the callosal spot. The number for the contralateral spot in Figure 5 a was about 230 and for one of the ipsilateral spots 540. We also made an estimate of the number of neurons that had taken up the tracer in the brains in Figure 5. To a first approximation, one can calculate the number of neurons within the region of uptake. This calculation is made on the basis of the diameter of the region of uptake given in Table 1 and the number of neurons under 1 mm 2 of cortical surface area, which is about 10 5 in the mouse (Rockel and others 1980; ...

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... Figure 3 shows a coronal section close to the site of injection in the right hemisphere. Axon collaterals radiate from the injection site within the gray matter, and distant terminal fields can be seen in the cortex of both hemispheres and in the thalamus. The axons are completely filled up to—and probably also within—their terminal fields. Figures 4 and 5 show patterns of anterograde staining on maps of the flattened cortex as described in Methods. For each animal, both hemispheres are shown. In 6 animals, the injection was administered into the right, and in 2 animals into the left hemisphere. The black regions correspond to the highest density of staining, dense and wide hatching to progressively lower densities. The white spot in each figure shows the location of the injection site. Its size indicates the extent of the region of uptake as defined in Methods. In spite of the large variation in projection patterns, some properties are common to the various injections: a large field of stained fibers around the injection and patches or bands at more distant places, numbering between 1 and 8 in the injected hemisphere. In the large field around the injection site, the overall density of stained fibers decreases toward the periphery, although denser patches sometimes appear within regions of lower density. The core of highest density (black on Figs. 4 and 5) extends about 500 l m (sometimes more) from the injection site and is due to the bulk of axon collaterals of the neurons affected by the injection. The adjacent hatched regions are fed by fibers running horizontally over long distances and by other fibers that take a bow-shaped course through layer VI, some of them scratching the white matter. In distant terminal fields, individual axons can ramify such that they contribute fibers to several spots located closely to each other. This is, for example, the case in the 3 densely hatched lateral spots in the right hemisphere in Figure 5 a . It is, of course desirable to have some idea of the cortical areas involved in Figures 4 and 5. Figure 6 a shows the classical map in which Caviness (1975) has adapted the scheme of Brodmann (1909) to the mouse neocortex. On this map, we have marked the locations of the injection sites of the brains in Figures 4 and 5 (Fig. 6 b ). The localization was made by identifying the cortical areas on the Nissl sections according to the cytoarchitectonic criteria used by Caviness (1975). The shape of the map differs from that of the neocortex in our maps by its larger rostrocaudal extent. This is due to the different treatment of the frontal and occipital pole regions: flattening by distortion in the Caviness map, cutting the tip of the poles, and keeping the rest metrically correct as far as possible in our maps. By means of the landmarks indicated in Figure 6 b , it is possible to localize approximately some of the terminal fields. Some observations shall be mentioned. 1) Although the dark field around the injection site can be restricted to the corresponding cortical area, the large terminal field in continuity with it always extends over adjacent areas. 2) There is a striking similarity in the projection patterns in Figure 4b , c . This is obviously due to the fact that these injections were located in the same cytoarchitectonic area. Both injection sites project to a rostromedial region (area 6/8) and laterally to an elongated field comprising the border between area 35 and the adjacent entorhinal cortex and to a shorter elongated field of higher density, which according to the cytoarchitectonic criteria described by Caviness is at least partly contained in area 14. Both injections are located just caudally to the barrel field. 3) The 3 lateral spots in the right hemisphere in Figure 5 a are located in different areas: areas 40 and 14. 4) No fiber stain could be found in the pyriform cortex, and in the entorhinal cortex fiber stain was restricted to its lateral border (e.g., Fig. 4 b , c ). Fiber stain was occasionally found in area 27, the presubiculum (medially posteriorly in Fig. 4 f ). 5) The small hatched field close to the olfactory tract in the right hemisphere of Figure 5 b is located in the orbital region of the frontal pole (area 11). Measurements on the size of the terminal fields in the injected hemisphere were made on the maps shown in Figures 4 and 5. The field in continuity with the injection site was always larger than the sum of the remaining terminal fields (Table 1). In some cases, nearly all projections merged into one large field (Fig. 4 e and 5 b ). Table 1 shows the results of the measurements (not corrected for shrinkage). In column 1, the sum of the areas of all terminal fields in the injected hemisphere is reported for each of the 8 brains. Columns 2 and 3 show separate values for the areal size of the large terminal field in continuity with the injection site and the sum of the distant terminal fields. Columns 4--6 show separate values for the sums of the strong (i.e., black), middle, and weakly stained regions. The table also shows the approximate diameter of the region of uptake, as well as the cytoarchitectonic area in which the injection site was located. The total area of the terminal fields ranges between about 2 2 7 and 22 mm , with an average of 12 mm . The difference in size can largely be explained by the inevitable variation in the strength of the injections and the corresponding variation in the size of the regions of uptake, with their diameters rang- ing between 200 and 400 l m (200 l m is the diameter of the dendritic extension of a large pyramidal cell in the mouse). 2 The region of uptake ranged between about 0.03 and 0.1 mm in area. As can be seen from Table 1, in all injections the main part of the terminal field consisted of weak projections (widely hatched regions in Figs. 4 and 5). If we exclude these, the size of the terminal fields (medium plus strong) ranges between 2.5 and 8.8 mm 2 , with an average of 4.7 mm 2 . The average size of the surface area of the entire neocortex of one hemisphere was 64 mm 2 . Thus, the neurons from a middle-sized column of about 300 l m in diameter can reach about 7% of the total neocortex by projections of high plus middle strength, and even about 19% if the weak projections are included. If we translate the measurements of Table 1 into degrees of divergence by dividing the area of the terminal fields by the area of the region of uptake, we get an average factor of 73 (with individual values between 45 and 122) for the strong plus middle projections and an average factor of 182 (with individual values between 122 and 298) if we include the weak connections. (The large range in the individual values may be partly due to the fact that the values for the size of the region of uptake are approximations only.) In 2 of the brains (Fig. 5) we quantified the densities of stained fibers in distant projections. The contralateral projection in Figure 5 b was one of the densest projections in our material (see micrograph in Fig. 7), whereas the rostral spot in the ipsilateral hemisphere was one of the weakest (see Fig. 8). We therefore took these 2 spots as instances of an upper and a lower limit. The densities of the 2 projections measured in Figure 5 a were in between. The results are shown in Figure 5 and Table 2. For comparison with other data (see Discussion), we express these densities in fiber length per cubic millimeters. Table 2 shows the raw data. The data in Figure 5 indicate the maximum densities measured in each spot because the maximum value may be relevant for the question of how strongly distant places in the cortex can influence each other functionally. These maximum values range 3 between 4.6 and 21 m/mm . The higher value may be an underestimate by some meters per cubic millimeters because in dense regions some intersections with the test line may escape the observer. Thus, the maximum density in the contralateral spot in Figure 5 b may be rounded up to 25 m/mm 3 . We also counted the number of axons entering a terminal field from below. Assuming that each of these axons comes from a different pyramidal cell, this number is a measure of the number of neurons projecting from the injection site to that terminal field. The results of these counts are also reported in Figures 5 a , b . In Figure 5 b , the number of axons entering a terminal field ranged between 14 for the weak spot to about 890 fibers running toward the dense and middle dense region of the callosal spot. The number for the contralateral spot in Figure 5 a was about 230 and for one of the ipsilateral spots 540. We also made an estimate of the number of neurons that had taken up the tracer in the brains in Figure 5. To a first approximation, one can calculate the number of neurons within the region of uptake. This calculation is made on the basis of the diameter of the region of uptake given in Table 1 and the number of ...

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... 5. Two further maps, showing terminal fields as in Figure 4, but containing, in addition, measurements of 1) the number of pyramidal cells that have taken up the tracer (long arrows), 2) the number of stained fibers entering some of the terminal fields, and 3) maximum densities of stained fibers in these terminal fields.  ...