Connectivity and Convergence of Single Corticostriatal Axons

MATERIALS AND METHODS

Axonal arborizations in the neostriatum of rats were stained by intracellular injection of biocytin during intracellular recording of identified corticostriatal neurons of the medial agranular field or by small extracellular injection of biotinylated dextran amine (BDA) in the cingulate, medial agranular cortex, or lateral agranular cortex. When extracellular injections were used, tissue sections were counterstained with calbindin to reveal the calbindin-poor patch (striosome) and calbindin-rich matrix compartments of the neostriatum, and sections were prepared so that they could be used for both light and electron microscopy. Intracellularly stained axons were used for light microscopy only. Estimates of synaptic density were obtained by measuring the spacing between adjacent boutons along individual stained axons. To determine whether these boutons actually represent synapses and whether synapses occur specifically at boutons, the axonal diameters at synaptic and nonsynaptic regions of corticostriatal axons were compared using electron microscopy.

BDA injections. For extracellular tracing, injections of BDA (Molecular Probes, Eugene, OR) were made into the cingulate, medial agranular cortex, or lateral agranular cortex of adult Sprague Dawley rats. Animals were anesthetized intraperitoneally with a mixture of 100 mg/kg ketamine and 20 mg/kg xylazine. A glass micropipette with a tip diameter of 20–40 μm was filled with a solution of 5% BDA in isotonic saline buffered with 0.01 m phosphate buffer, pH 7.4, and placed in the cerebral cortex 1.0–2.0 mm from the surface. The details of injection sites and the macroscopic pattern of axonal arborizations from these injections have been described previously (Kincaid and Wilson, 1996). BDA was ejected using 5 μA current pulses lasting 7 sec and presented every 17 sec for 10–30 min. After a recovery time of 7–12 d to allow for transport of BDA throughout the corticostriatal fibers, the animals were again anesthetized and perfused with 150 ml of isotonic buffered saline followed by 400 ml of a solution of 4% formaldehyde in 0.1 m phosphate buffer. The brains were fixed overnight in the fixative solution and cut in the coronal plane on a vibratome at a thickness of 50 μm. For visualization of BDA, tissue sections were incubated in ABC (1:200; Vector Laboratories, Burlingame, CA) containing 0.2% Triton X-100 for 2 hr, washed in buffered saline, and reacted for 10–20 min in a solution of 0.05% diaminobenzidine, 0.003% hydrogen peroxide, and 0.12% nickel chloride in buffered isotonic saline. The sections were washed thoroughly and incubated in mouse anti-calbindin antibody (1:000; Sigma, St. Louis, MO) with 0.2% Triton X-100 overnight at 4°C. They were then washed thoroughly, treated with biotinylated anti-mouse secondary antibody (1:200; Vector) for 2 hr, and treated again as described above, except for the omission of nickel chloride. The reaction time of this step was shortened to yield a light-brown reaction product in the matrix compartment of the striatum.

Intracellular staining. Corticostriatal neurons were identified in the cortex of adult male Long–Evans rats anesthetized with urethane (1.5 gm/kg) supplemented hourly with a combination of ketamine (30 mg/kg) and xylazine (6 mg/kg, i.m.). Neurons projecting to the neostriatum were impaled using micropipettes containing 4% biocytin in 1 m potassium acetate and identified by antidromic activation from the contralateral neostriatum or the ipsilateral cerebral peduncle. Biocytin was ejected by passing 0.5–1.0 nA current pulses, 300 msec in duration, applied every 600 msec for 15–45 min. At the end of the experiment, animals were perfused intracardially with a fixative containing 4% formaldehyde and 0.1% glutaraldehyde and treated as described above for animals given extracellular BDA injections. Two of the axons analyzed in the study were originally collected in the course of another experiment, as described by Cowan and Wilson (1994). A third axon was also analyzed. This cell was selected because it exhibited the focal pattern but was verified as arborizing exclusively in the matrix using calbindin counterstaining. After drying onto slides, sections prepared for light microscopy shrank 28–44% in thickness, as measured using the focal plane method in the microscope. All measurements were corrected in that dimension using the measured degree of shrinkage, whereas shrinkage in the other dimensions was negligible and was not corrected. Tissue prepared for electron microscopy (see below) showed no measurable shrinkage in any dimension, and no corrections were made. Measurements of the distances between boutons were made using a 100× oil immersion objective (numerical aperture, 1.4), and boutons were plotted in three dimensions using a computer-aided microscope and a video camera. The three-dimensional distances between adjacent boutons were measured automatically using the coordinates for the boutons (without regard to the path of the axon between boutons).

Transmission and high-voltage electron microscopy for measurement of axonal diameters. Neurons used for high-voltage electron microscopy (HVEM) and conventional electron microscopic analysis were collected as described above, except for the addition of 0.1% glutaraldehyde to the fixative and the exclusion of Triton X-100 from all solutions. After processing, the sections were post-fixed in a solution of 0.25% osmium tetroxide in 0.15 m phosphate buffer, infiltrated with epoxy resin, and embedded between slides and coverslips coated with liquid releasing agent (Polysciences, Warrington, PA). Areas selected for electron microscopic study were removed from their mounts and glued to blocks for resectioning on an ultramicrotome. For HVEM study, thick sections (2–5 μm) were cut using a dry glass knife, collected on uncoated sandwich grids, and examined at 1000 kV using the high-voltage electron microscope at the University of Colorado (Boulder, CO). Methods for HVEM preparation have been described in detail elsewhere (Wilson, 1994). Ultrathin sections for conventional electron microscopy were cut with a diamond knife and examined at 80 kV on a JEOL 200EX microscope. Because the calbindin antiserum did not fully penetrate the vibratome sections, the selection of tissue from patch or matrix compartments could be made in the light microscope, but thin sections were collected from regions located deeper within the section where the calbindin labeling was not present. This prevented any ambiguity between the labeling of corticostriatal axons and axons of the striatal spiny neurons positive for calbindin. In addition, all axons used for these experiments were positively identified as profiles of corticostriatal axons seen in the light microscopic examination of the same specimen. Diameters of profiles in the electron microscope were measured by digitizing the images, drawing the outlines of their profiles using NIH Image software, and measuring the short and long (perpendicular) diameters through the centroid of the profile using that software.

Connectivity calculations. Connectivity calculations were made using the binomial theorem. The approach was similar to that described by Abeles (1991). To determine the number of axons making 0,1, … k synapses on spiny neurons, the probability of making a synapse on a particular cell was taken as the reciprocal of the number of candidate cells in the volume. Thus, the probability of making k synapses with n synapses per axon was given as:

where p is 1/number of candidate cells, andn is the number of synapses per axon. The number of axons in each category was calculated by multiplying the probability obtained in this way by the number of candidate axons innervating the volume.

A similar approach was used to determine the probability of shared input to single cells and the probability of two cortical axons converging on k spiny neurons. To determine the number of cortical inputs held in common by two spiny cells, the probability of a synaptic contact by a given axon was taken as the square of the quotient of cortical synapses per cell and the number of candidate cortical axons. The likelihood of two spiny neurons receiving 0,1,2, … k axons in common was calculated as above, using the probability of a contact on both cells from a single axon asp and the number of candidate axons as n. To determine the number of spiny cells jointly innervated by any pair of cortical axons, the probability of sharing any one target neuron was calculated as the square of the probability of either axon innervating the cell (as described above). The likelihood of two axons jointly innervating 0,1,2, … k spiny neurons was calculated as above, using this probability for p and the number of candidate striatal cells in the volume as n.

RESULTS

As described previously (Wilson, 1987; Cowan and Wilson, 1994), corticostriatal axonal arborizations arose either as collaterals of descending axons in the internal capsule fascicles or as arborizations of axons that did not join the internal capsule but terminated within the neostriatum. In addition to this difference in axons of origin, the cells formed one of two different kinds of arborizations. Some corticostriatal axons formed one to four small arborizations, ∼0.5 mm in diameter, usually separated by >0.5 mm. These arborizations, which will be called focal, often arose from collaterals of descending axons. The other form of axonal arborization was a single large and sparse axonal arborization, usually ≥1 mm in diameter, which will be called the extended type (Kincaid and Wilson, 1996). In all cases, the intrastriatal axons were extremely fine but showed varicosities that were easily identified in the light microscope. These varicosities were not present along the axonal trajectory through the white matter or internal capsule fascicles. Although they were easily identified in the light microscope, they were too small to measure accurately using that instrument. This was evident because their apparent diameter was <1 μm, and the diameter of intervaricose segments appeared to be <0.5 μm. For comparison with identified synaptic regions in thin sections, it was desirable to have more accurate images of the diameters of the varicosities and intervaricose segments as seen in the light microscope (LM). For this purpose, images were taken using HVEM of thick (3–5 μm) sections stained as for light microscopy. Examples showing the appearance of axonal varicosities in the LM and the HVEM are shown in Figure 1. The varicosities varied from 0.2 to 1.0 μm in diameter when measured using HVEM, whereas the intervaricose segments were ∼0.1 μm in diameter. Varicosities were more apparent in the HVEM images than in the LM. The intervaricose segments appeared to be of larger diameter in the LM because of filtration by its point spread function. For the same reason, measurements of varicosity diameter in the LM were also inaccurate, but comparison of the LM and HVEM images of the same axons showed that the location of the varicosities could reliably be determined. In thin sections cut from the same animals, biocytin-labeled axons were photographed and measured using conventional electron microscopy. A sample of 56 axonal profiles with an evident synapse and 95 profiles with no evident synapse was measured. In addition, two axons were reconstructed in serial thin sections through at least one synaptic site, allowing repeated measurements of the same axons at synaptic and nonsynaptic regions. The results of this analysis are shown in Figure1. Together, these data confirm that the axonal varicosities seen in the LM and HVEM correspond to synaptic sites seen by electron microscopy of thin sections. Furthermore, each axonal varicosity examined formed a single synapse, indicating that bouton counts within the axonal arborization are a good estimate of the total number of synapses.

The distribution of axonal varicosities along corticostriatal axons is shown in Figure 2. Figure 2, Eand F, shows distributions generated by pooling many fragments of axonal arborizations stained by extracellular injections of BDA. Most corticostriatal projections to the patch compartment arise from axons forming focal arborizations. In general, projections to the matrix are more heterogeneous, with both focal and extended arborizations contributing significantly (Kincaid and Wilson, 1996). Because the goal was to compare focal and extended arborizations, samples of the matrix were selected from the portion of the projection containing primarily extended arborizations. Thus, the matrix measurements are an estimate of primarily extended arborizations, and the patch sample is primarily focal arborizations. Matrisomal arborizations are not represented in the BDA data but were measured for single axons. As shown in Figure 2, the distribution of axonal spacings did not differ in the two compartments. The relative contribution of axons of the extended and focal types also differed in the projections from different cortical regions, with the extended type being most pronounced for the medial agranular (premotor) field. Table1 compares the intervaricose spacing for the three different cortical fields examined and shows that there were no differences among cortical fields or between projections to the patch or matrix. In all cases, the distribution was highly asymmetrical, being skewed to the right, and the tail of the distribution was approximately exponential. The distribution was not exponential at short intervaricose distances, with distances <1–4 μm being much less common than expected for an exponential distribution. A similar distribution has been reported for the spacing of varicosities along axon collaterals of pyramidal neurons in the cortex (Hellwig et al., 1994).

To further examine the possibility of differences in synaptic spacing among axons showing different arborization types, the distributions of intervaricose distances were also measured for three arborizations of single corticostriatal axons stained by intracellular injection. All three of these neurons arose from the medial agranular cortical field. Examples of one focal and one extended type arborization are shown in Figure 2, A and B, and the distributions of intervaricose segments from these are shown in Figure 2, Cand D. Although the extended axonal arborization formed many more varicosities over a much larger volume of the neostriatum, the individual branches of the arborization were separated by relatively large distances, and the spacing of varicosities along the branches was not distinguishable from that seen in the focal arborizations. Regardless of axonal type, the number of synapses generated by corticostriatal axons within a region comparable with the volume of the dendritic tree of a spiny neuron is approximately the same. Axons forming focal arborizations had more axonal branches within the volume occupied by the dendritic tree of a spiny neuron (∼400 μm radius) but still made between 20 and 40 synapses within the volume. The individual branches of the extended arborizations were generally spaced so far apart that only one branch could cross over the dendrites of any one spiny neuron but could make up to 40 synapses within that volume. The superimposition of axons in Figure 2B is attributable to the projection into two dimensions. Most axons contributing synapses within the dendritic volume of a spiny neuron would make <40, because they would not pass through the center of the dendritic tree.

The spacing of synapses along the axons of corticostriatal axons can be combined with a number of previously published observations to set upper and lower limits on the connectivity of the pathway and sharing of common inputs by nearby striatal neurons. Most corticostriatal synapses (∼95%) are formed with the dendritic spines of the spiny projection neurons of the striatum (e.g., Kemp and Powell, 1971b;Somogyi et al., 1981; Xu et al., 1989). These spines are distributed throughout the dendritic trees of the cells, except for a region within ∼20 μm of the soma. The dendrites extend in an approximately spherical manner with a diameter of ∼400 μm (Kemp and Powell, 1971a; DiFiglia et al., 1976; Wilson et al., 1983b; Wilson, 1992). Although many dendritic trees are distorted from the spherical (Kawaguchi et al., 1990; Walker and Graybiel, 1993), this is still a best estimate of the volume they occupy. Thus, the dendritic field of each spiny neuron occupies a region of ∼33,500,000 μm³. Within that volume, in the rat there are an average of 2845 neurons (based on the shrinkage-corrected estimate of 84,900 neurons/mm³ by Oorschot, 1996), most of which (∼95%) are spiny cells. The number of corticostriatal synapses that will be found in that volume can be estimated from the published report of Ingham et al. (1996), who measured the density of asymmetric synapses in the neostriatum using unbiased sampling in ultrathin sections and estimated that there are 0.91 afferent-type (asymmetric) synapses per cubic micrometer, or ∼30,500,000 within the volume occupied by the dendritic tree of one spiny neuron. Based on their studies of spine loss after lesions, Kemp and Powell (1971c) concluded that the corticostriatal and thalamostriatal inputs to spiny neurons were approximately equal. Although not a direct measurement, this estimate is consistent with more recent qualitative studies of these two pathways (Dubé et al., 1988; Xu et al., 1991; Ragsdale and Graybiel, 1991; Berendse and Groenewegen, 1990), which together account for most of the asymmetric synapses. It is also in agreement with neurophysiological studies showing approximately equal-sized monosynaptic responses of striatal neurons to stimulation of axonal pathways from the cortex and thalamus (Wilson et al., 1983a; Wilson, 1986). Assuming the cortical input as the origin of 50% of all asymmetric synapses in the striatum, there are ∼15,250,000 corticostriatal synapses within the volume occupied by one spiny neuron dendritic field in the rat. Estimates of the number of asymmetric synapses per spiny neuron have been calculated using spine density (Wilson et al., 1983b). Integration of the spine density distribution along individual dendrites published by Wilson et al. (1983b) yields an estimate of between 250 and 500 spines per spiny dendritic branch. Each neuron has 25–30 such spiny dendrites, yielding values between ∼6250 and 15,000 spines per neuron, depending on the number of dendrites on each cell. As each dendritic spine receives one asymmetric synapse (Wilson et al., 1983b), this yields the same number of asymmetric synapses per cell. Using an independent approach, the stereological measurements of Ingham et al. (1996) and Oorschot (1996) together yield an average asymmetric synapse count of 10,719 (9.1 × 10⁸ synapses/mm per 84,900 cells/mm) per striatal neuron (all types combined). This average number, which is in good agreement with that obtained by spine counts, will be used for subsequent calculations. The axonal measurements reported here indicate that individual corticostriatal axonal arborizations of both the extended and focal types usually have only one branch passing through the volume occupied by the dendritic tree of any one striatal projection neuron, and that on average a maximum of 40 asymmetrical synapses will be formed by the axon in that volume. The exceptions to this were axons of the focal arborizations, which formed <40 synapses in a volume approximately the size of a spiny cell dendritic tree. In both cases, of the 15,250,000 corticostriatal synapses present, ≤40 (0.00027%) could be formed by a single axon. Conversely, ∼381,180 different corticostriatal axons would be required to arborize in that volume to achieve the known density of corticostriatal synapses. These calculations are independent of the degree to which cortical axons make repeated contacts on single striatal cells. They are summarized in Table 2.

It is not known whether individual corticostriatal axons make multiple synaptic contacts on single spiny neurons. Because the axons do not make boutons in clusters, and the dendritic fields of the striatal neurons radiate throughout their volume, this cannot be determined from the data at hand. But even if they do so in the most extreme form, one cortical axon can represent only a tiny fraction of the total cortical innervation of any spiny neuron. If synapses are made promiscuously within the volume of the dendritic field of one cell, then each axon may contact as many as 40 (1.4%) of the 2845 cells of all types whose somata are located in that volume. The chances of any neuron receiving more than one input from the same axon would be low, so one axon could only contribute one synaptic contact (0.009%) of the 10,719 asymmetrical synapses formed on the average per neuron. Two spiny projection cells located so close to each other that their dendritic fields totally overlapped would independently sample ∼5360 cortical inputs from the 381,180 in that volume and so would have only ∼75 of their cortical afferent axons in common. Because the axonal arborizations of corticostriatal neurons are usually larger than the dendritic fields of spiny neurons, cells located farther apart but still within the region of overlap of axonal fields would have approximately the same (actually slightly higher) chance of sharing inputs as those with overlapping dendritic fields.

In the opposite extreme case in which each cortical axon makes all of its synapses on a single postsynaptic neuron, the number of corticostriatal neurons innervating a single striatal cell would be 134 instead of 5360, so an individual corticostriatal axon would account for as much as 0.75% of the cortical input of a single striatal neuron (0.37% of total asymmetric synapses). However, in that case, nearby striatal projection neurons with overlapping dendritic trees would never share common inputs. Because individual axons of the focal type project to more than one cluster and extended axonal fields extend across the dendritic trees of many cells, striatal cells that separated from each so that their dendritic fields did not overlap would be much more likely to share a common input than would nearby cells (although still not likely in an absolute sense).

A similar calculation can be made for the sharing of target neurons in the striatum by axons arborizing in the same space. If two cortical neurons arborizing in exactly the same space make synapses with spiny neurons at random in their terminal fields, they will each contact 40 (1.4%) cells of the 2845 in the volume. The chance that both axons converge onto one spiny neuron is 2 × 10⁻⁴, and on average there will not be even one neuron within that volume that receives synapses from both cortical axons. The statistics of connectivity for both the nonselective and the totally selective cases are shown in Table 3.

A number of intermediate cases can be hypothesized in which single axons are neither completely nonselective nor do they seek out single postsynaptic targets. For example, spiny neurons may receive different cortical inputs depending on whether they participate in the direct or indirect pathway. Such a division of the spiny neurons into two populations would not make a significant difference in the results. The key feature for this kind of mechanism is the ratio of cortical axons to the number of cortical synapses per spiny neuron. With only two groups of axons, there would still be an enormous excess of cortical axons innervating the volume in comparison with the number of corticostriatal synapses on each cell. Thus, single spiny neurons would still share only a tiny proportion of their input and would receive only a single input from each of the cortical neurons innervating them. To produce a substantially higher mean connectivity, the population of axons that are candidates for innervating any particular postsynaptic cell would have to be reduced so that it is close to the number of cortical synapses on each spiny neuron. If each axon belonged to a group that had a predisposed affinity to contact only a small subset of spiny neurons, this could be achieved. To ensure that each axon made an average of one synapse on all the candidate neurons in its affinity group, the axons and striatal neurons would have to be divided into 71 such groups (381,180/5359). Sharing among affinity groups would be nearly total, and there would be no sharing at all across groups. To average four synapses per candidate striatal neuron, the striatal spiny cells and the innervating axons would have to be divided into 284 affinity groups. The results for this arrangement is shown in Table 3(affinity groups). The value of 4 used in this calculation was chosen arbitrarily to illustrate the concept. There is currently no evidence to suggest any value for the number of contacts on each striatal projection cell per cortical axon. In a second method for obtaining higher mean connectivity, cortical axons could make their initial synapses in a nonselective manner but once establishing one contact with a spiny neuron establish a strong selectivity for that cell resulting in a mean of more than one synapse per axon. This could arise from the action of a growth rule that encourages multiple synapses, such as one based on correlated firing in the presynaptic and postsynaptic cells. The results from this model are also shown in Table3 (growth rule), again arbitrarily choosing four synapses per axon per cell. Table 3 shows that these two patterns produce dramatically different results. In the growth rule case, sharing is effectively reduced, because the number of spiny neurons contacted by each axon is reduced from 40 to 10 without any change in the number of candidate neurons or axons in the volume. In the affinity group case, the axons and cells are divided into 284 different subclasses, reducing the number of axons per group to one-fourth of postsynaptic sites per neuron. Each axon innervates nearly every spiny neuron in its affinity group, so all the cells in the affinity group have identical input. The total number of unique combinations of inputs represented in the volume is reduced from 2840 to 284, and each spiny neuron has exactly the same input signal as the nine other cells in its affinity group. Because connectivity is measured across all cells in the volume, the average connectivity is approximately 1/284.

DISCUSSION