Cerebellar nuclei neurons dictate cortical growth through developmental scaling of presynaptic Purkinje cells

Efficient function of neural systems requires the production of specific cell types in the correct proportions. Here we report that reduction of the earliest born neurons of the cerebellum, excitatory cerebellar nuclei neurons (eCN), results in a subsequent reduction in growth of the cerebellar cortex due to an accompanying loss of their presynaptic target Purkinje cells. Conditional knockout of the homeobox genes En1 and En2 (En1/2) in the rhombic lip-derived eCN and granule cell precursors leads to embryonic loss of a subset of medial eCN and cell non-autonomous and location specific loss of Purkinje cells, with subsequent proportional scaling down of cortex growth. We propose that subsets of eCN dictate the survival of their specific Purkinje cell partners, and in turn sonic hedgehog secreted by Purkinje cells scales the expansion of granule cells and interneurons to produce functional local circuits and the proper folded morphology of the cerebellum.


Introduction
A key challenge for development of the brain is to produce the numerous cell types in the correct proportions from different stem cell pools at particular time points, and assembling the cells into nascent networks within brain regions that grow extensively during development. The cerebellum represents a powerful system in which to study this phenomenon since by birth the specification of neuronal lineages is complete but neurogenesis of several cell types has just begun. During the third trimester and first few months of human life the cerebellum undergoes a rapid expansion from a smooth ovoid anlage into a morphologically complex folded structure with specialized subregions. The folds (lobules) are considered the cerebellar cortex, and they overlay the cerebellar nuclei (CN), two bilaterally symmetrical groups of mediolaterally-arrayed nuclei in mice (medial, intermediate, and lateral nuclei), that house the main output neurons of the cerebellum. The layered cortex has an outer molecular layer, which contains interneurons and the axons of granule cells and dendrites of Purkinje cells (PCs), that is above a single layer of PC soma intermixed with the cell bodies of Bergmann glia. Below this layer is a dense layer of granule cells called the inner granule cell layer (IGL). PC axonal projections establish the only electrophysiological and physically direct connection between the cerebellar cortex and CN. The excitatory CN neurons (eCN) are the first to be born in the embryo, followed by the PCs and the interneurons that are their presynaptic partners. Postnatal cerebellar growth in the mouse is principally driven by the expansion of two progenitor populations that produce the presynaptic partners of PCs, granule cells and interneurons as well as astrocytes. Genes regulating differentiation of most cerebellar cell types have been identified, but the mechanisms responsible for coordinating the scaling of their cell numbers is poorly understood, despite their importance for understanding the formation of cerebellar circuit assembly.
During mouse cerebellar development, neurogenesis occurs in several germinal compartments: 1) the rhombic lip (RL) which produces the eCN between embryonic day (E) 9.5-E12.5 and then unipolar brush cells directly (Wang et al., 2005;Machold and Fishell, 2005;Sekerkova et al., 2004); 2) the ventricular zone which generates inhibitory PCs by E13.5 and early born interneurons including those that populate the CN (Sudarov et al., 2011;Leto and Rossi, 2012;Leto et al., 2016); 3) a RL-derived pool of granule cell precursors (GCPs) that migrates over the cerebellum and forms an external granule cell layer (EGL) from E15.5 to postnatal day (P) 15 that contains an outer layer of proliferating cells and inner layer of postmitotic granule cells; and 4) a ventricular zone-derived intermediate progenitor pool that expresses nestin and expands in the cerebellar cortex after birth and produces astrocytes, including specialized Bergmann glia, and late born interneurons of the molecular layer (Fleming et al., 2013;Parmigiani et al., 2015). The embryonic PCs form a multi-layer beneath the nascent EGL and project to the CN by E15.5 (Sillitoe et al., 2009). Once born, granule cells descend along Bergmann glial fibers to form the IGL, and synapse onto PC dendrites in the overlying molecular layer (Hatten and Heintz, 1994;Sillitoe and Joyner, 2007). PCs secrete sonic hedgehog (SHH) after E17.5, which drives the massive postnatal neurogenic phase by stimulating proliferation of GCPs and nestin-expressing progenitors (Corrales et al., 2004;Corrales et al., 2006;Lewis et al., 2004;Fleming et al., 2013;Parmigiani et al., 2015;De Luca et al., 2015;Wojcinski et al., 2017). PCs thus act in a dual role as a synaptic bridge between the two main RL-derived glutamatergic neuronal subtypes and as a developmental regulator of the cortex. Scaling of the proportions of postnatally born cells in the cerebellar cortex has been proposed to be regulated by the number of PCs and the amount of SHH they produce.
However, how the number of CN neurons and PCs are proportioned properly during embryogenesis has not been addressed. Furthermore, it is not known whether PCs in the cerebellar cortex are dependent on CN neurons for their development or scaling.
The engrailed genes (En1/2) encoding homeobox transcription factors provide a powerful genetic entry point for studying developmental scaling of neuron types, since En mutants have a seemingly well-preserved cytoarchitecture despite suffering cerebellar hypoplasia that preferentially affects distinct lobules in each mutant (Millen et al., 1994;Sgaier et al., 2005;Cheng et al., 2010;Orvis et al., 2012). For example, specific loss of En1/2 in the Atoh1-expressing RL-lineage (Atoh1-Cre; En1 lox/lox ; En2 lox/lox conditional knockouts, referred to as Atoh-En1/2 CKOs) results in preferential loss of cerebellum volume in the vermis (medial cerebellum), with foliation defects restricted to the anterior and central vermis ( Figure 1A ; (Orvis et al., 2012)). As a basis for studying the roles of the En1/2 genes in scaling of cerebellar neurons, we confirmed that the numbers of GCs, PCs, and molecular layer interneurons in the mutants are well scaled down relative to the decrease in cerebellar area. Despite the scaling of neurons in the cortex, we found that Atoh-En1/2 CKOs have motor behavior defects. The primary defect in Atoh-En1/2 CKOs was discovered to be loss of a subset of CN neurons after E15.5 that results in an ~50% decrease in eCN in the medial and intermediate nuclei. Our embryonic analysis showed that the early loss of eCN is accompanied by a cell nonautonomous reduction of PCs and a distruption of the eCN-to-PC ratio in Atoh-En1/2 CKOs.
Circuit mapping further revealed that the PCs in distinct lobules that are differentially depleted in the vermis of mutants project to different regions of the medial CN. We propose a model whereby the number of eCN neurons sets the growth potential of the cerebellar cortex through supporting survival of a balanced PC population that allows scaling of cortical neurons based on SHH expression.

Loss of En1/2 in the rhombic lip lineage results in preferential reduction of the anterior and central vermis but scaling of neurons in these regions is largely normal
Our previous study using 3D Magnetic Resonance Imaging showed a 25% reduction in the volume of the vermis of Atoh-En1/2 CKOs but preserved cytoarchitecture (Orvis et al., 2012). In order to determine whether the Atoh-En1/2 CKOs can serve as a useful model for studying scaling of neuron numbers during development, we first tested whether the proportions of different neurons in the areas of the vermis with reduced size were indeed normal. As a proxy for analyzing cerebellum size, we quantified the area of mid-sagittal sections of ~P30 animals, and found a 31.2 ± 2.0% reduction (n=4) in Atoh-En1/2 CKOs compared to littermate controls (En1 lox/lox ; En2 lox/lox mice) ( Figure 1A). In order to determine whether particular regions of the vermis along the anterior-posterior axis were preferentially diminished in the mutants, we divided the cerebellum into three regions ( Figure 1B) -an anterior sector (ASec), anterior to the primary fissure (lobules 1-5); a central sector (CSec), between the primary and secondary fissures (lobules 6-8); and a posterior sector (PSec), posterior of the secondary fissure (lobules 9-10) -and measured the areas of each. Interestingly, the CSec had the greatest decrease in area (55.4 ± 0.03%) with the ASec having a 37.1 ± 0.04% decrease and no significant reduction in the PSec of Atoh-En1/2 CKOs compared to littermate controls ( Figure 1C). Thus, Atoh-En1/2 mutants have a differential reduction in the sizes of the central and anterior regions of the vermis.
We next determined whether the area of the layers compared to the total area of each sector and the numbers of each cell type within each sector were scaled proportionally in Atoh-En1/2 CKOs. As predicted, the areas of the IGL and molecular layer were reduced only in the ASec and CSec and their proportions were conserved relative to the area of each sector in Furthermore, quantification of the number of PCs per midline section and PC density at ~P30 based on staining for Calbindin1, revealed that the PC numbers were reduced specifically in the ASec and Csec (31.0 ± 0.1% and 54.1 ± 0.1% reduction, respectively) but their densities were not altered in all sectors of Atoh-En1/2 CKOs compared to controls ( Figure 1F

Atoh1-En1/2 mutants have motor defecits
We next tested whether a smaller cerebellum that has a well scaled cortex can support normal motor behavior, since we had shown that irradiated mice with an ~20% reduction in the area of mid-sagittal sections but well scaled layers have no obvious motor defects (Wojcinski et al., 2017). Two motor behavior paradigms and grip strength were tested. Unlike irradiated mice, significant defects in motor behavior were observed in Atoh-En1/2 CKOs. The performance of mutants on trials of the accelerating rotarod showed a significant difference on the third day, as well as the cumulative measurement of performance in Atoh-En1/2 CKOs (160.1 ± 17.2 sec) compared to littermate controls (227.7 ± 18.4 sec) (Figure 2A). In the footprint analysis of gait, mutant mice had a significant decrease in stride length (6.3 ± 0.2 cm), a trend towards a decrease in stance length (4.1 ± 0.1 cm), and an increase in sway length (2.6 ± 0.1 cm) compared to controls (7.4 ± 0.2 cm stride; ; 4.5 ± 0.1 cm stance; 2.4 ± 0.1 cm sway)( Figure 2B-C). Curiously, Atoh-En1/2 CKOs had a significant decrease in grip stength (normalized force= 4.9 ± 0.3) compared to littermate controls (normalized force= 6.3 ± 0.3) ( Figure 2D). While the decrease in grip strength in mutants could contribute to the defects in motor behaviors, this is not likely the only factor as CNS-specific conditional mutants for Cxcr4 have a decrease in grip strength but no change in stance (Huang et al., 2014) and mutants with greatly reduced grip strength can behave normally on the rotarod and have normal gait (Heck et al., 2008). Our finding that Atoh1-En1/2 mutants have motor deficits could be because the cerebellum is even smaller than in the irradiated mice we studied, and/or that there is an additional defect outside the cerebellar cortex.

Loss of En1/2 in the RL-lineage results in a preferential loss of medial and intermediate eCN neurons in the adult
Given that EN1/2 are expressed in the RL-derived eCN neurons that express MEIS2 (Wilson et al., 2011) and Atoh-En1/2 mutants lack En1/2 function in these neurons, a good candidate for an additional defect in the mutants was the CN projection neurons. In order to determine that the two nuclei that are reduced in Atoh-En1/2 CKOs specifically receive input from cortical structures that are also reduced in the mutants (vermis/paravermis lobules 1-8), this result suggests there could be a causal relationship between the loss of eCN and their PC presynaptic targets ( Figure 1H).
As a means to assess whether scaling of PCs and eCN was preserved in adult mutants, we compared the decrease in the number of eCN in the medial nucleus of Atoh-En1/2 CKOs to the number of PCs in the ASec and CSec per midline section, since the PCs in lobules 1-8 of the medial vermis project primarily to the medial nucleus. The PCs in much of lobule 9 and all of 10 project outside the cerebellum to the vestibular nuclei (Walberg and Dietrichs, 1988;Leto et al., 2016). Unlike the scaling of granule cells and interneurons to PCs in the cerebellar cortex, the number of medial eCN in Atoh-En1/2 CKOs was reduced to 38% of that of controls, whereas the number of PCs in the midline was reduced to 55% ( Figure 3M). The changes in neuron numbers resulted in an estimated 1.4 ± 0.1 fold increase in the ratio of the number of PCs to medial eCN in the ASec and CSec of Atoh-En1/2 CKO animals compared to controls.
Our finding that in control mice there are ~20 PCs per eCN is in line with estimates that in rodents there is a functional convergenence of 20-50 PCs per eCN (Person and Raman, 2011).
Thus, it appears that the PCs did not fully scale in proportion to the loss of medial eCN.
Furthermore, the inbalance between the number of eCN and PCs might contribute to the motor defects in Atoh1-En1/2 mutants.

A cerebellum growth defect can be detected in Atoh1-En1/2 CKO embryos
Given the possibility of a causal relationship between the reduction in the number of eCN and PCs in Atoh-En1/2 adult mutants, we examined when a growth defect is first detected during cerebellum development, and whether the timing correlates with when eCN and/or PC numbers are reduced. Our previous analysis showed a clear growth and foliation defect in Atoh-En1/2 mutants at P1 (Orvis et al., 2012); therefore, we analyzed embryonic stages ( Figure 4A-C).
Quantification of the cerebellar area of mid-sagittal sections at E17.5 of mutants and controls revealed a small reduction in area at E17.5 in Atoh-En1/2 CKOs compared to littermate controls (13.3 ± 5.3 %) ( Figure 4C). In addition, there appeared to be a delay in the formation of the earliest fissures at E17.5 ( Figure 4A-B). Thus, a phenotype is first apparent in Atoh-En1/2 CKOs when the main cell types that have been generated in the cerebellum are CN neurons and PCs, and long before the major expansion of GCPs.

EN1/2 are dynamically expressed in the medial CN at E12.5-17.5
We next characterized the expression of EN1/2 proteins in the developing CN in more detail, as En1/2 are expressed in subsets of all cerebellar cell types from as early as E8.5 (Davis et al., 1991;Millen et al., 1995;Wilson et al., 2011) and we previously only reported expression of the proteins in a small percentage of the medial MEIS2+ eCN at E17.5 (Wilson et al., 2011). An antibody that detects both EN1 and EN2 (Davis et al., 1991)

ASec and CSec PCs project to the distinct regions of the medial CN
We finally asked whether the PCs of the ASec and CSec preferentially project to distinct regions of the medial CN, since PCs broadly innervate the nuclei closest to them -medial vermis PCs project to the medial nuclei, hemispheric PCs project to the lateral nuclei, with the intermediate nucleus being innervated by the paravermis and lateral vermis (Leto et al., 2016). Although a comprehensive study has not been conducted as to whether PC axons project to the CN in a topographic manner based on their anterior-posterior position in lobules, neurons of the more posterior region of the medial CN, known as the fastigial oculomotor region, receive functional inputs from PCs in lobules 6 and 7 of the vermis (Zhang et al., 2016;Herzfeld et al., 2015;Person and Raman, 2011;Noda et al., 1990). As our data indicate that the posterior region of the medial CN is particularly diminished in Atoh-En1/2 CKOs, and the size of the CSec is reduced to the greatest extent in these mutants, we asked whether axons from ASec and CSec PCs project to the anterior and posterior regions of the medial nucleus, respectively. Since most PCs of the PSec innervate the vestibular nucleus rather than the CN, we omitted the PSec from our CN-PC axon tracing analysis. We injected a Cre-inducible tracer virus (AAV5-EF1a-DIO-mCherry) into lobules 3-5, representing the ASec, or lobules 6/7 representing the CSec of ~P30 Pcp2 Cre/+ mice ( Figure 7A PCs preferentially innervate the anterior and posterior medial nucleus, respectively, parallels the regional differences in cerebellar hypoplasia seen in Atoh1-En1/2 CKOs.

Discussion
In summary, we have uncovered that the cerebellum is constructed in a sequential order whereby the earliest-born neurons, the eCN, determine the cell number of their later-born presynaptic partners, PCs, likely based on secretion of a survival factor by eCN. In turn, the PCderived mitogenic factor, SHH, then drives the production of all postnatally derived neurons and astrocytes of the cerebellar cortex (Figure 7-figure supplement 1) (Corrales et al., 2004;Corrales et al., 2006;Lewis et al., 2004;Fleming et al., 2013;Parmigiani et al., 2015;De Luca et al., 2015;Wojcinski et al., 2017). This progression of neurogenesis and maintenance of the overlying circuit constitutes a means by which developmental defects affecting the CN will lead to near scalar adaptation of cytoarchitecture in the cerebllar cortex. Nevertheless, we found that Atoh1-En1/2 CKOs have motor behavior deficits, possibly because the PCs do not fully scale down to the number of eCN, and/or the smaller size of the cerebellum can not support robust long range neural circuits. Thus, both proper scaling and size regulation are necessary to generate robust neural circuits. The basic principles of our model can likely be applied to how circuits that span across brain regions could be scaled during development.
We found that scaling between the eCN and PCs does not appear to be as precise as the scaling within the cortex of Atoh-En1/2 CKOs. One possibility for the ~1.4 fold higher ratio of PCs to eCN is that the difference reflects the mechanism by which scaling is attained. In the case of eCN:PC scaling, the process likely depends on the availability of a survival factor (such as a neurotrophin), whereas the PC:GC or PC:interneuron scaling depends on the amont of mitogen produced (SHH). An interesting additional possibility related to eCN:PC scaling is that since each PC projects to many eCN, if the survival of PCs is dependent on a factor secreted by eCN, then it might be that a greater proportion of PCs can survive than in normal homeostasis because some PCs continue to project to enough of the remaining eCN in mutants to receive sufficient survival factor. In contrast, the action of a mitogen is more likely to be concentrationdependent.
The results of our study indicate that if PCs are scaled back by birth by a specific genetic defect or by injury, then the other neurons generated postnatally in the cerebellar cortex will be scaled back in numbers to produce a normally proportioned cytoarchitecture. Considering the cerebellar cortex as a multilayer structure comprised of unitary tiles containing a single PC, which is able to support and specify postnatally-derived cells that contribute to its local circuit, the size of the PC pool can be thought of as a predictor of total postnatal cerebellum growth capacity. As the PCs redistribute into a monolayer sheet across the cerebellar cortex after birth, the smaller population of PCs in Atoh-En1/2 CKOs is not able to spread out to form the normal length of the PC layer, since they have the same density at P30 as controls. The GCP pool is consequently reduced in size in mutants. As SHH expressed by PCs is required for expansion of the two proliferating precursor populations in the postnatal cerebellum, the scaling back in Atoh-En1/2 CKOs of granule cells and interneurons, produced by GCPs and nestin-expressing progenitors, is likely due to the reduced amount of SHH present in the mutant cerebellum. In the context of the cerebellar cortex possibly being made up of repeated tiles of neurons, it is interesting to note that our results show that PCs regulate the numbers of their presynaptic neurons.
Based on our finding that PCs scale back in their numbers soon after many eCN die in late embryonic development in Atoh-En1/2 CKOs, our study has provided evidence that the survival of PCs is dependent on CN. The timing of innervation of eCN by PCs fits with this proposal as axons from PCs extend into the CN by E15.5 (Sillitoe et al., 2009). Furthermore, in vitro assays have shown that PC survival is dependent on cell-cell interactions (Baptista et al., 1994) or on neurotrophins, and mouse mutants have shown that Bdnf and p75 NTR null mutants exhibit cerebellar growth and foliation defects with some similarities to Atoh1-En1/2 mutants (Schwartz et al., 1997;Carter et al., 2002;Carter et al., 2003). Based on gene expression in the Allen Institute Database and our analysis in Atoh-TDTom mice, Bdnf is expressed specifically in the CN at E15.5 (Figure 7-figure supplement 2); thus, it is a good candidate for a CN-derived survival factor for PCs. Gdnf is also detected in the CN after birth, suggesting that it could also contribute to long-term survival of PCs in the cerebellum.
As our model asserts that eCN neurons maintain the survival of their presynaptic PC neurons (Figure 7-figure supplement 1), we predicted that neurons in the medial nucleus that appear to be lost in the greatest numbers in the Atoh-En1/2 CKOs should preferentially be innervated by PCs in the vermis lobules that also exhibit the most diminution. Stereotactic injection of AAV virus into the cerebellum to determine the projection pattern of labeled PC axons into the CN showed that PCs of the vermis central sector, where lobule growth and PC depletion are most pronounced, do indeed preferentially innervate the posterior region of the medial CN, which is preferentially reduced in cell number. In a complementary fashion, the PCs of the ASec preferentially project to the anterior medial nucleus and part of the intermediate nucleus.
Our study revealed that a primary defect in Atoh-En1/2 CKOs is death of eCN starting at ~E15.5, indicating that En1/2 are required in eCN for their survival in the embryo. En1/2 have been shown to be required for survival of other neurons in the brain (Fox and Deneris, 2012;Sonnier et al., 2007). Similar to ablation of En1/2 in eCN as they are being generated in the embryo, conditional knockout of En1/2 in embryonic postmitotic serotonergic (5-HT) neuron precursors of the dorsal Raphe nucleus (DRN) results in a normal number of 5-HT neurons being initially generated, but the cells then become disorganized through abnormal migration pathways and undergo significant cell death around birth (Fox and Deneris, 2012). Our study of the eCN in Atoh-En1/2 CKOs indicates a similar role for EN proteins in the settling of eCN into three nuclei and in their survival.
En1/2 are ablated not only in the eCN of the cerebellum of Atoh-En1/2 mutants, but also in the GCPs, which undergo their major expansion after birth. Some of the postnatal growth defects could therefore be due to a minor requirement for En1/2 after birth in the GCPs, although we found that the EGL scales back in size but preserves a normal ratio of proliferating GCPs in the EGL. We nevertheless did recently show that deletion of En1/2 in GCPs along with over-activation of SHH signaling results in a small increase in mutant cells remaining in the proliferative GCP pool, suggesting En1/2 could play a minor role in promoting differentiation of GCPs (Tan et al., 2018). In addition to the RL-lineage, Atoh1-Cre deletes En1/2 in the precerebellar nuclei, some of which express En1/2. Thus, some of the phenotype could be a secondary (cell-nonautonomous) effect of loss of En1/2 in structures outside the cerebellum. If this is the case, it will be interesting to determine whether the loss of eCN is due in part to lack of a survival factor that is normally secreted by presynatic partners.
In conclusion, En1 and En2 are required soon after the eCN are produced by the RL for

Mouse strains
All animal experiments were performed in accordance with the protocols approved and guidelines provided by the Memorial Sloan Kettering Cancer Center's Institutional Animal Care and Use Committee (IACUC). Animals were given access to food and water ad libitum and were housed on a 12-hour light/dark cycle.
All mouse lines were maintained on a Swiss-Webster background: En1 lox (Sgaier et al., 2007), En2 lox (Cheng et al., 2010) (Zhang et al., 2004). Noon of the day that a vaginal plug was discovered was designated developmental stage E0.5. Both sexes were used for all experiments and no randomization was used. Exclusion criteria for data points were sickness or death of animals during the testing period. For behavioral testing, investigators were blinded to genotype during the data collection and analyses.

Behavioral Testing
Five-week-old animals (Control: n=8 and Atoh-En1/2: n=9) were used to for all of the motor behaviour testing described below.
Rotarod: Analysis was performed 3 times a day on 3 consecutive days. Animals were put on an accelerating rotarod (47650, Ugo Basile), and were allowed to run till the spead reached 5 rpm.
Then, the rod was accelerated from 5-40 rpm over the couse of 300 seconds. Latency to fall was recorded as the time of falling for each animal. Animals rested for 10 minutes in their home cage between each trial.
Grip Strength: A force gauge with a horizontal grip bar (1027SM Grip Strength meter with single sensor, Columbus Instruments) was used to measure grip strength. Animals were allowed to hold the grip bar while being gently pulled away by the base of their tail. Five measurements with 5 minute resting intervals were performed for each animal and the data was reported as the average of all trials, normalized to the mouse's weight (Force/gram).
Footprinting Analysis: After painting the forefeet and hindfeet with red and blue nontoxic acrylic paint (Crayola), respectively, animals were allowed to walk on a strip of paper. Experiments were performed in a 50 cm long and 10 cm wide custom-made Plexiglass tunnel with a dark box at one end. Each mouse was run through the tunnel 3 times and the distance between the markings were measured and averaged.

Genotyping
The DNA primers used for genotyping each allele and transgene were as follows:

Tissue Preparation and Histology
The brains of all embryonic stages were dissected in cold PBS and immersion fixed in 4% PFA for 24 hours at 4 o C. All postnatal stages were transcardial perfused with PBS followed by 4% PFA, and brains were post-fixed in 4% PFA overnight, and washed 3 times in PBS. Specimens for paraffin embedding were put through an ethanol-xylene-paraffin series, then embedded in paraffin blocks, and sectioned to 10 µm on a microtome (Leica Instruments). Specimens for cryosectioning were placed in 30% sucrose/PBS until they sank, embedded in OCT (Tissue-Tek), frozen in dry ice cooled isopentane, and sectioned at 14 µm on a cryostat unless otherwise stated (Leica, CM3050S).

Immunohistochemistry
Sections of cryosectioned tissues were immersed in PBS for 10 min. After these initial stages of processing, specimens were blocked with blocking buffer (5% Bovine Serum Albumin (BSA, Sigma) in PBS with 0.2% Triton X-100). Primary antibodies in blocking buffer were placed on slides overnight at 4 o C, washed in PBS with 0.2% Triton X-100 (PBST) and applied with secondary antibodies (1:1000 Alexa Fluor-conjugated secondary antibodies in blocking buffer) for 1 hour at room temperature. Counterstaining was performed using Hoechst 33258 (Invitrogen). The slides were then washed in PBST, then mounted with a coverslip and Fluorogel mounting medium (Electron Microscopy Sciences).
Haematoxylene and Eosin (H&E) staining was performed for histological analysis and cerebellar area measurements, except at E17.5 where DAPI staining was used.
Nissl staining was used for sterology analysis in the eCN in adult brains.

Antibodies
The following antibodies were used at the listed concentrations: Primers were flanked in the 5' with SP6 (antisense) and T7 (sense) promoters. Specimen treatment and hybridization were performed as described previously (Blaess et al., 2011).

Image Acquisition and Analysis
All images were collected with a DM6000 Leica fluorescent microscope or a Zeiss Axiovert 200 with Apotome and processed using ImageJ (NIH) or Photoshop (Adobe). Image quantification was performed with ImageJ.
For the cerebellar, sector, IGL, and ML area, H&E stained slides were used. A region of interest was defined by outlining the perimeter of the outer edges of the region quantified. Three midline parasagittal sections/brain were analyzed and values were averaged for each brain.
Cell counts were obtained using the Cell Counter plugin for ImageJ (NIH). PC numbers were averaged from 3 midline parasagittal sections/brain. PC density was calculated by dividing the number of PCs by the length of the PCL. Granule cell density was measured by counting the NeuN+ cells in a 40x frame of the IGL from 3 midline parasagittal sections/brain and dividing the number of cells by the area counted. GC density for different sectors was obtained from lobules 3 (anterior), 6-7 (central), and 9 (posterior). GC numbers/midline parasagittal sections were calculated by multiplying the GC density by the area of the IGL. Parvalbumin+ cell counts in the ML were obtained from lobules 3 (anterior), 6-7 (central), and 9 (posterior) at the midline and the number of cells were divided by the ML area measured. Due to the high variability of the cell counts between sections, 5 midline parasagittal sections were quantified for this purpose. The number of ML Parvalbumin+ interneurons was extrapolated by multiplying the density with the ML area at the midline parasagittal sections.
Ratios of the different CB neurons with respect to each other were calculated using the numbers obtained for parasagittal midline sections as described above. The ratio of PCs to eCN was obtained by dividing the number of PCs determined above on midline sagital sections/brain from control and mutant animals at P30 by the average number of eCN at P30 from a different cohort of control and mutant mice.

Stereology
Brains were paraffin embedded, as described above, and sectioned coronally at 10 µm. The sections were Nissl stained and every other section was analyzed to prevent double counting neurons split in serial sections. For each analyzed section in sequential order from rostral to caudal, the section perimeter of the CN on one half of the cerebellum was traced and each large projection neuron was registered. Sections were then aligned into a 3D representation in NeuroLucida.

Stereotactic injection
One-month-old mice were anesthetized by isoflurane inhalation and head fixed in a stereotactic frame (David Kopf Instruments) with an isoflurane inhaler. The head of the animal was shaved, disinfected with ethanol and betadine, and a midline incision was made from between the eyes to the back of the skull. Coordinate space for the system was calibrated by recording the coordinates of Bregma and Lambda. After a small hole was drilled in the skull over the injection site, the needle was robotically injected into the cerebellum position specified by atlas coordinate (Neurostar StereoDrive). For targeting the ASec and PSec, coordinates of the injection were -6.00mm from bregma, -2.2mm deep from dura, and 8.5mm from bregma, 4.2mm deep from dura, respectively. One µL of 10 12 Tu/mL AAV5 virion in PBS was injected in 20 millisecond pulses at 10 psi with a Picospritzer. The needle was left in situ for 5 minutes, and then removed by 50 µm increments over about a minute. The scalp was then sealed by Vetbond adhesive, 0.1 µg/g of buprenorphine was administered for postoperative analgesia, and the animal was placed in a heated chamber for recovery. Brains from these animals were analyzed 1.5 weeks after surgery. Brains were processed for cryosectioning as above but were sectioned at 30 µm. To establish the accuracy of the injections to the appropriate sectors, R26 tdTom/tdTom P30 animals were injected stereotactically with either AAV5-pgk-Cre virus or trypan blue dye in the midline of either the ASec (lobules 3-5) or CSec (lobules 6-7). Whole mount imaging of TDTom signal verified that the transduced cells remained restricted to the injection area and spread minimally in the lateral axis beyond the vermis. The tracing was done by injecting AAV5-EF1a-DIO-mCherry virus into Pcp2 Cre/+ animals. The AAV-EF1a-DIO-mCherry plasmid was constructed by Karl Deisseroth and virus was packaged as serotype 5 and prepared to 10 12 Tu/mL by the UNC Chapel Hill Vector Core.

Tissue Delipidation for Tracing Analysis
After perfusion, postfix, and PBS washes as described above, brains were delipidated with a modified Adipo-Clear procedure (Chi et al., 2018)

Statistical Analysis
Prism (