Modular output circuits of the fastigial nucleus for diverse motor and nonmotor functions of the cerebellar vermis

1The cerebellum has been implicated in several cognitive functions and neuropsychiatric disorders, which are more typically associated with the cerebral cortex and basal ganglia. Although it is widely assumed that such nonmotor functions are mediated by the cerebellar hemispheres and their connections with the thalamus, increasing functional and anatomical evidence points to roles for the vermis an evolutionarily old portion of the cerebellum best known for its influence on brainstem circuits for posture and eye movements. Structural and functional abnormalities of the vermis have been associated with various psychiatric disorders and conditions, including autism, schizophrenia, mood disorders, chronic pain, and addiction. Remarkably little is known, however, about the specific cell types and circuits responsible for diverse nonmotor functions of the vermis.

2The cerebellum is thought to be organized in parallel circuit modules that comprise specific sets of inferior olive (IO) neurons, Purkinje cells (PCs), and vestibular or cerebellar nucleus neurons. The cerebellar vermis, caudal medial accessory olive, and fastigial nucleus (FN; medial cerebellar nucleus) collectively constitute the broad ‘A’ module, which is likely to include several submodules. Although the fastigial nucleus has been implicated in diverse motor and nonmotor functions in human imaging studies, its small size has precluded precise functional localization. Mono- and multi-synaptic connections with the midbrain, hippocampus, basal ganglia, and cerebral cortex are likely to mediate vermis and fastigial influences on affective and cognitive functions but the specific fastigial cell types responsible for these influences are not known.

3In this study, we hypothesized that the diverse motor and nonmotor functions of the cerebellar vermis are mediated by multiple types of fastigial output neurons with distinct circuit connections. By combining single-cell gene expression, immunohistochemical, and circuit connectivity analyses, we identified several molecularly and anatomically distinct types of excitatory projection neurons in the mouse fastigial nucleus. Anterograde, transsynaptic, and retrograde tracing analyses indicate segregated, modular circuit connectivity; each fastigial cell type is linked with a specific set of PCs and IO neurons and makes divergent projections to functionally-related downstream targets. Disynaptic connections with the basal ganglia, basal forebrain, and cerebral cortex revealed that specific fastigial cell types are linked with circuits responsible for distinct aspects of cerebellar motor and nonmotor functions.

4The fastigial nucleus (FN) is the medial cluster of cerebellar nucleus neurons, delineated in mammals by surrounding white matter. Despite its small size, the FN comprises at least three subdivisions: a rostral part, a caudal part, and a dorsolateral protuberance (DLP), which is well developed in rodents. Each of these subdivisions have been linked with distinct sets of Purkinje cells, inferior olive subnuclei, and downstream brain regions.

5To identify markers that could distinguish cell types in the FN, we searched in situ hybridization data in the Allen Brain Atlas (http://mouse.brain-map.org/) for genes expressed differentially across FN subregions. We then evaluated candidate marker genes (Figure 1—figure supplement 1) with immunostaining and confocal microscopic analyses of serial cerebellar sections. Antibodies for SPP1 (osteopontin), SNCA (alpha-synuclein), and CALB2 (calretinin) reliably labeled specific subsets of neurons that were located predominantly in distinct subregions of the FN (Figure 1; Figure 1—figure supplement 2). In caudal regions of the FN (Figure 1B), SPP1-immunopositive (SPP1+) neurons were prominent in the caudal portion of the DLP (cDLP) and were sparsely distributed ventrally. In contrast SNCA+ neurons were prominent ventrally in the caudal fastigial nucleus (cFN), but were sparse in the cDLP. In rostral regions of the FN (Figure 1C), the majority of neurons were SPP1+. Neurons strongly immunopositive for CALB2 (CALB2+) were prominent in rostrally in ventral and lateral parts of the fastigial nucleus (vlFN).

6Double-immunostaining revealed five populations of neurons that were distinguished by their marker gene expression and anatomical distribution. Neurons that exclusively expressed SPP1 were found in two distinct regions: the rostral FN (rFN) (Figure 1E) and the rostral DLP (rDLP). In contrast, neurons that coexpressed SPP1 and SNCA (Figure 1H) were found in the cDLP (Figure 1—figure supplement 2). They were also scattered through the cFN, where they intermingled with a distinct population of neurons which exclusively expressed SNCA (Figure 1F). CALB2+ neurons (Figure 1G), which were distributed in the vlFN, coexpressed SNCA but not SPP1.

7Although the majority of neurons in the cerebellar nuclei are glutamatergic, distinct populations of glycinergic and GABAergic neurons have been reported. To identify neurotransmitter associated with each cell type, we performed immunostaining for SNCA, SPP1, and CALB2 on cerebellar nucleus sections from mouse lines that express fluorescent reporters for glutamatergic neurons (VgluT2-Cre;Ai14), GABAergic neurons (Gad2-nls-mCherry) and glycinergic neurons (GlyT2-EGFP) (Figure 1—figure supplement 3). Notably, most (93%; n = 954) of the identified glutamatergic neurons, but none of the GABAergic neurons, were immunostained by either SPP1 or SNCA (Figure 1—figure supplement 3A–C,E). Glycinergic neurons in the FN comprise two distinct populations; we found that large glycinergic projection neurons, located ventrally in the rFN, were robustly immunostained by SPP1 (but not SNCA) (Figure 1—figure supplement 3D). In contrast, small glycinergic neurons were not labeled by either SPP1 or SNCA (Figure 1—figure supplement 3D). Collectively, these results indicate that the majority of glutamatergic fastigial neurons can be classified into five major types by localization and expression of SPP1, SNCA, and CALB2.

8To verify the anatomical analyses of cell types, we performed single-cell qPCR analyses on acutely isolated fastigial cells using a strategy previously developed for distinguishing cell classes among vestibular nucleus neurons (Figure 2—source data 1; ). From an initial pool of 130 randomly harvested fastigial cells, we identified 50 cells which expressed ion channel genes associated with action potentials (Scn8a and Kcna1) and lacked non-neuronal markers (Mobp and Cd68), and were thus considered as neurons. Most of these neurons (84%: 42/50) expressed Slc17a6 (vesicular glutamate transporter 2, VgluT2, Figure 2A), indicating that they were glutamatergic. The remainder expressed inhibitory neuronal markers Gad1, Gad2, and/or Slc6a5. We focused subsequent expression analyses on the glutamatergic excitatory neurons.

9Nearly all excitatory neurons (97.6%: 41/42) significantly expressed at least one of the cell-type markers (Spp1, Snca, and Calb2), as confirmed with immunostaining in VgluT2-Cre;Ai14 line (Figure 1—figure supplement 3C). Hierarchical clustering based on these markers revealed four cell types in the fastigial glutamatergic population, which we termed F1-F4 (Figure 2A). Two cell types expressed Spp1 and were distinguished by the absence (F1) or presence (F2) of Snca. The other two cell types both expressed Snca and were separated by strong Calb2 expression in F3 but not F4. The combinatorial marker expression patterns corresponded with those observed in immunostaining (Figure 1): F1 with Spp1+ neurons in the rFN (F1R) and the rDLP (F1rDLP), F2 with Spp1+/Snca+ neurons in the cDLP, F3 with Calb2+/Snca+ neurons in the vlFN, and F4 with Snca+ neurons in the cFN.

10To further assess distinctions across cell types, we examined expression levels of neurofilament genes. Nefl, Nefm, and Nefh were highest in F1, intermediate in F2, and lowest in F3 and F4 neurons (Figure 2A), suggesting that the axon diameter of these cell types are in the order of F1 >F2>F3/F4. Differences across cell types in axonal caliber were confirmed with local injections of adeno-associated virus (AAV.hSyn.TurboRFP) into the rFN (predominantly F1) and cFN (predominantly F4) (Figure 2—figure supplement 1A–C). As predicted, axons from the rFN were thicker than those from the cFN (1.9 ± 0.6 s.d. µm vs 1.0 ± 0.3 s.d. µm, n = 30 vs. 25, respectively). Neurofilament expression levels were also well correlated with cell body area assessed in immunohistochemically identified fastigial cell types (Nefl in Figure 2B; r2 = 0.996, p=0.002; Nefm and Nefh in Figure 2—figure supplement 1D–F).

11Excitatory projection neurons in the cerebellar nuclei can be distinguished from local interneurons and inhibitory nucleo-olivary neurons by their ability to fire at high rates. Each of the excitatory FN neurons expressed Scn8a (Nav1.6), Scn4b (Navb4), Kcnc1 (Kv3.1), and Syt2 (synaptotagmin 2), as predicted for fast-firing neurons. Previous studies in vestibular nucleus neurons, which share multiple properties with cerebellar nucleus neurons, including high spontaneous firing rates and direct innervation by Purkinje cells, demonstrated that variations in neuronal firing capacities can be predicted by the absolute expression levels of these and other ‘fast-spiking’ genes. Fastigial cell types F1-F4 exhibited different expression levels of action potential genes Scn8a and Kcnc1, but with an almost constant ratio (r2 = 0.98, Figure 2D). Nefl, Nefm, Nefh, Scn4b, and Syt2 followed the same trend (Figure 2—figure supplement 1G–I); absolute expression levels of these genes were consistently in the order of F1 >F2>F3/F4, suggesting that F1, F2, and F3 and F4 would have the fastest, intermediate, and the slowest firing capacities.

12Although projections from rostral vs caudal fastigial nucleus are known to differ, little is known about the downstream targets of specific fastigial cell types. We performed a series of anterograde, transsynaptic, and retrograde anatomical tracing experiments to identify global and cell-type specific connectivity patterns. Pan-fastigial injections of anterograde tracer AAV9.hSyn.TurboRFP (Figure 3A) revealed divergent fastigial projections to over 60 distinct brain regions (Figure 3 and Figure 3—figure supplement 1, Figure 3—source data 1), which were confirmed with complementary injections of anterograde transsynaptic tracer AAV1.hSyn.Cre in Ai14 reporter mice (; Figure 3A). Projection patterns identified in these pan-fastigial injections were quite consistent across individuals (n = 6 males for axonal labeling; n = 4 male and n = 3 female for transsynaptic labeling). Fastigial axonal terminals and postsynaptic neurons contralateral to injection sites were prominent in cervical spinal cord (Figure 3C), cerebellar cortex (Figure 3—figure supplement 1F), and several regions of the medulla (Figure 3D), pons (Figure 3—figure supplement 1C), midbrain (Figure 3E, Figure 3—figure supplement 1D), and diencephalon (Figure 3F,G, Figure 3—figure supplement 1E). Notably, fastigial projections to the thalamus were not limited to the 'motor thalamus' (ventrolateral (VL) and ventromedial (VM) nuclei), but also robustly to intralaminar thalamus (centrolateral (CL) and parafascicular (PF)) and the mediodorsal (MD) nucleus (Figure 3F,G and Figure 3—figure supplement 1E). These projections were considered to derive from excitatory neurons because inhibitory neurons target different brain regions; glycinergic FN neurons project ipsilaterally, to hindbrain and spinal cord, and GABAergic FN projections exclusively target the IO, as confirmed with selective anterograde tracing by injecting Cre-dependent AAV into the FN of Gad2Cre mice (Figure 3—source data 1).

13To identify linkages between specific fastigial cell types and downstream target nuclei, we performed localized anterograde tracing experiments via stereotaxic injections of AAVs (AAV9.hSyn.eGFP, AAV9.hSyn.TurboRFP, and AAV1.hSyn.Cre) into anatomically defined subregions of the FN (Figure 1; Figure 3—source data 2). Subsequent retrograde tracing combined with immunostaining for the fastigial cell-type markers was performed to confirm FN cell types of origin.

14To distinguish projections from F1R, F3, and F1rDLP, we made localized injections of AAVs into the rFN, vlFN, and rDLP, respectively, which resulted in differential terminal labeling in several regions of the hindbrain, including nucleus reticularis gigantocellularis (NRG), ventral medullary (MdV) and intermediate (IRt) portions of the reticular formation, and inferior vestibular nucleus (IVN) (Figure 4A,B, Figure 3—source data 1). Distinct projections from each cell type were confirmed with complementary retrograde tracing experiments in which FastBlue or retrobeads were injected into NRG/MdV, IVN, and IRt, which are the major projection targets of F1R, F3, and F1rDLP, respectively. Those injections resulted in labeling of SPP1+ large neurons in the rFN (Figure 4C), CALB2+ small neurons in the vlFN (Figure 4D), and SPP1+ large neurons in the rDLP (Figure 4E).

15Anterograde axonal tracing paired with transsynaptic tracing identified the projections of F1R, F3, and F1rDLP as follows. Consistent with the known functions of the rostral fastigial nucleus in posture and locomotion, F1R neurons in the rFN made extensive projections to the spinal cord, MdV, NRG, lateral paragigantocellularis (LPGi), IVN, and lateral vestibular nucleus (LVN) (Figure 4—figure supplement 1), as summarized in Figure 4J and Figure 3—source data 1. Axonal terminals of F1R neurons densely innervated the somata and proximal dendrites of huge neurons (diameter >35 µm) in the LVN and NRG (Figure 4F), providing a circuit substrate for rapid cerebellar modulation of vestibulospinal, reticulospinal, and reticuloarousal neurons. Brainstem autonomic nuclei implicated in cardiovascular and respiratory functions, including the paramedian nucleus (PMn, Figure 4F; Figure 4—figure supplement 1) and LPGi, were also targeted by F1R neurons, as expected from physiological studies in cats. A previously undescribed projection from the rFN to the subcoeruleus region of the dorsal pons (Figure 4F) was revealed by transsynaptic labeling in tyrosine hydroxylase (TH) immunopositive neurons, which are known to comprise the coeruleospinal pathway.

16In contrast with the extensive postsynaptic targets of F1R neurons, the projections of F3 neurons in the vlFN were restricted to the dorsal aspect of the medulla (Figure 4—figure supplement 1), as summarized in Figure 4K and Figure 3—source data 1. Labeled terminals were identified in the Kölliker-Fuse nucleus (KF; Figure 4G), which has been implicated in postural and locomotory modulation of respiration, and in the medial portion of the IVN (Figure 4A), which is associated with autonomic function. Of note, although both F1R and F3 neurons project to the IVN, their postsynaptic targets differ in size and location, with large lateral vs small medial IVN neurons targeted by F1R and F3 neurons, respectively (Figure 4H; somata area, 299 ± 117 s.d. µm2 vs 208 ± 121 s.d. µm2, n = 40 and 44 from two injections each; t(82) = 3.06, p=0.001, Welch’s t-test).

17F1rDLP neurons in the rDLP projected to the brainstem regions associated with orofacial motor control, including lateral medullary regions (IRt and PCRt; Figure 4B; Figure 4—figure supplement 1) and the facial motor nucleus, as summarized in Figure 4L and Figure 3—source data 1. Retrograde labeling from injections in the IRt labeled exclusively SPP1+ neurons in the rostral DLP (F1rDLP, Figure 4E). Transsynaptic labeling demonstrated that F1rDLP neurons synapse onto CHAT+ neurons in the facial nucleus (Figure 4I), congruent with a previous report demonstrating monosynaptic inputs from the FN to facial motoneurons.

18Anterograde tracing localized to caudal regions of the FN indicated projections to the brainstem, midbrain, and thalamus (Figure 5; Figure 5—figure supplement 1). To distinguish projections from caudally located fastigial cell types, we made paired AAV injections targeted to the cDLP (exclusively F2) and the cFN (predominantly F4, with scattered F2; Figure 1B). These injections revealed predominantly non-overlapping fastigial thalamic projections (Figure 5A); VM, CL, and MD nuclei were innervated by axons originating from the cFN whereas the VL nucleus was innervated by axons from the cDLP. To determine whether these segregated projections originated from distinct fastigial cell types, we made retrobead injections to the VM, CL, or VL thalamus and performed immunostaining for fastigial cell type markers. Retrogradely labeled neurons from CL and VM injections were found in the cFN and expressed SNCA (Figure 5B), confirming their identity as F4. In contrast, VL injections retrogradely labeled neurons in the cDLP that expressed SPP1 (Figure 5C), confirming their identity as F2.

19Localized tracing experiments indicated that F2 neurons in the cDLP projected to midbrain and pontine nuclei associated with orienting movements of the eyes and head, including the superior colliculus (SC), interstitial nucleus of Cajal (INC), caudal pontine reticular formation (PnC), periaqueductal gray (PAG), brainstem nucleus reticularis gigantocellularis (NRG), and cervical spinal cord (Figure 5D and Figure 3—source data 1). Retrograde labeling confirmed that projections to SC, NRG, and PAG originated from F2 neurons (SPP1+/medium sized cFN neurons). These projections were strikingly consistent with those of the fastigial oculomotor region in primates. F2 neurons were also retrogradely labeled from localized injections to the PF thalamic nucleus (Figure 5—figure supplement 2A,B), which is implicated in flexible and goal directed behavior, and the zona incerta (ZI: Figure 5—figure supplement 2A,B), which subserves sensory-motor gating. The collective targets of F2 neurons are summarized in Figure 5F.

20F4 neurons projected to several brainstem nuclei associated with arousal and neuromodulation, including the supramammillary region (SuM), substantia nigra pars compacta (SNc), laterodorsal tegmental (LDTg), peduncular tegmental (PTg) nuclei, and the nucleus incertus (NI), as shown in Figure 5E. Inputs to SuM, SNc, and LDTg were confirmed with retrograde tracing experiments to originate from F4 neurons (Figure 5—figure supplement 2C,D). Transsynaptic labeling from the caudoventral FN, combined with immunostaining for TH, indicated that F4 neurons projection to both dopaminergic (Figure 5E) and non-dopaminergic SNc neurons. TH+ neurons in the ventral tegmental area (VTA), recently shown to mediate cerebellar output for social behavior, and in the retrorubral field (RRF) were also transsynaptically labeled, although fastigial axonal terminals in the VTA were very sparse (Figure 3E and Figure 3—figure supplement 1D). CHAT immunostaining demonstrated that F4 neurons project to both cholinergic and non-cholinergic neurons in the LDTg and PTg (Figure 5E), consistent with observations in primates. The targets of F4 neurons are summarized in Figure 5G.

21Several regions were connected with multiple fastigial cell types. The brainstem reticular nuclei PnC, NRG, and MdV were targeted by F1R, F1rDLP, and F2 (Figure 4—figure supplement 1; Figure 5—figure supplement 1A,B). Localized anterograde tracing revealed that fastigial cell types projected to distinct subregions of these nuclei: F2 to dorsal and most medial regions, F1 to more ventral and lateral regions, and F1rDLP projected to dorsal and lateral regions (Figure 4—figure supplement 1; Figure 5—figure supplement 1), implying segregation of postsynaptic targets. Projections to cerebellar cortex and contralateral cerebellar nuclei by each fastigial cell may also be segregated as indicated in previous reports.

22Collectively, these results establish modular connectivity patterns between the fastigial cell types and their downstream targets. Large Spp1+ F1 neurons in the rFN and rDLP connect with premotor nuclei of the caudal brainstem and spinal cord associated with posture and locomotion, and orofacial motor control, respectively. Small Snca+/Calb2+ F3 neurons in the vlFN connect specifically with neurons involved in vestibulo-autonomic and respiratory function. Medium-large Spp1+/Snca+ F2 neurons in the cDLP connect with pontine, midbrain, and spinal neurons related to orienting movements of the eyes and head and to thalamic nuclei VL and PF. Small Snca+ F4 neurons in the cFN connect with neuromodulatory nuclei of the dorsal pons and midbrain and with 'nonspecific' nuclei of the thalamus including VM, MD, and CL.

23Nonmotor functions of the cerebellum are thought to be mediated largely by cerebellar nucleus linkages with the forebrain, but little is known about cell-type specific circuit connections. The substantial thalamic inputs from caudally located F2 and F4 fastigial neurons could potentially influence several subcortical and cortical areas. Accordingly, we performed AAV1- mediated transsynaptic tracing experiments to visualize axonal and synaptic terminals of fastigial-recipient thalamic neurons (Figure 6A, see Materials and methods).

24AAV1.hSyn.Cre injected in the cFN and cDLP (F2 and F4 regions) of the fastigial nucleus of Ai14 mice produced robust transsynaptic axonal labeling in the cerebral cortex (Figure 6B–D and Figure 6—figure supplement 1). Two distinct patterns of terminal labeling were observed: widespread, diffuse labeling of layer 1 (e.g. layer 1 of secondary motor cortex in Figure 6B, bottom) vs localized, specific labeling of layers 3–5 (e.g. layers 3–5 of motor cortices in Figure 6D). Layer one terminals were evident throughout much of the cortex, including the sensorimotor, cingulate, insular, prelimbic, frontal association, lateral and ventral orbital, parietal association, and visual cortices (Figure 6E,F and Figure 6—figure supplement 1). In contrast, layer 3–5 terminals were restricted to the sensorimotor cortices (including somatosensory S1, barrel fields, and S2 and motor regions M1 and M2), frontal association cortex, and ventral/lateral orbitofrontal cortex (Figure 6E,G and Figure 6—figure supplement 1). We did not observe significant labeling in the infralimbic, medial orbitofrontal, retrosplenial, auditory or temporal cortical areas (Figure 6—figure supplement 1).

25Disynaptic projections from the FN to subcortical forebrain regions were robust in the dorsal striatum (Figure 6C,D,H), consistent with a recent study using rabies virus, with a notably dense input to the rostrolateral striatum (Figure 6C). Axonal terminals were also prominent in the nucleus accumbens (NAcc) of the ventral striatum (Figure 6I). In addition, several nuclei of the basal forebrain received disynaptic fastigial input, including the nucleus of the diagonal band of Broca (Figure 6J) and the medial septum, which was sparsely but consistently labeled (Figure 6K). In contrast with early, widely cited reports that suggested relatively direct connections from the vermis to hippocampus and amygdala, we found no evidence for either mono- or disynaptic connections between the FN and amygdala (Figure 6—figure supplement 1I) or hippocampus. These results suggest that affective and cognitive functions of the vermis could be mediated by fastigial connections with the cerebral cortex (Figure 6L), basal ganglia (Figure 6M), and basal forebrain.

26The cerebellum is assumed to comprise modular circuits formed by interconnected groups of inferior olive (IO) neurons, Purkinje cells (PCs), and cerebellar or vestibular nucleus neurons (;;;;; Figure 7A). Molecularly distinct groups of PCs, arranged in longitudinal stripes distinguished by the expression of Aldolase C (Aldoc, aka zebrin II; Figure 7B,C;; ), are innervated by specific groups of IO neurons which, in turn, are interconnected with regions of the cerebellar nuclei innervated by of the corresponding group of PCs. To determine whether and how fastigial cell types correspond with modules comprising Purkinje cell stripes and IO neurons, we made localized injections of retrograde and anterograde tracers to FN subregions (Figure 7D–K).

27Injections of tracers restricted to the ventral FN (F3 region) retrogradely labeled PCs confined to narrow, parasagittal bands; their mediolateral location and immunopositivity for Aldoc indicates that these PCs correspond with the 1+//1+ and 2+//3+ stripe (Figure 7F and Figure 7—figure supplement 1B; see Methods for stripe nomenclature). In contrast, PCs located between these bands, in the 1-//1-/2- stripe, were retrogradely labeled from rFN (F1R region) (Figure 7G and Figure 7—figure supplement 1A). rDLP injections (F1rDLP region) retrogradely labeled PCs in the paravermal regions of the simple lobule and Crus II, which were immunonegative for Aldoc and thus identified as 2b-//4a- and c-//4b- stripes (Figure 7H). Injections into the caudalmost portion of the FN, including the cFN (F4 region) and cDLP (F2 region), retrogradely labeled PCs that were restricted to the a+//2+ stripe in vermis lobules VI-IX and to the c+//4b+ stripe in Crus I (Figure 7I). Injections of AAV1.hSyn.Cre to label PCs in the medial part of Crus I (c+//4b+ region) of Ai14 mice transsynaptically labeled F2 neurons in the cDLP (Figure 7L). In contrast, PC axonal terminals in the F4 region of the cFN were labeled by Cre-dependent AAV injections to lobule VIII in L7Cre mice (Figure 7L). These connectivity patterns are consistent with results from single axon tracing studies in rats.

28Complementary anterograde tracing experiments revealed that fastigial connections with IO subnuclei are also organized modularly. Pan-fastigial injections of AAV1.hSyn.Cre to Ai14 mice resulted in transsynaptic neuronal labeling throughout the contralateral caudal medial accessory olive (cMAO) and neighboring beta nucleus (Figure 7D). Each subdivision of the caudal IO was transsynaptically labeled from a specific subregion of the FN; injections in the vlFN, rFN and rDLP labeled neurons in the subnuclei a, b, and c of the cMAO, respectively (Figure 7F–H). Notably, climbing fibers from cMAO subnuclei a, b, and c innervate PCs associated with the vlFN (F3 region), rFN (F1R region), and rDLP (F1rDLP region), respectively. Injections in the cFN transsynaptically labeled neurons in the beta subdivision of the IO (Figure 7K), which project to PCs that innervate the cFN (F4 region). Injections that included both the cFN and cDLP additionally labeled neurons interposed between beta and subnucleus c which we have termed subnucleus 'd' (Figure 7J, Figure 7—figure supplement 2, see Methods). IO neurons in subnucleus d innervate PCs in lobules VIc/VII and Cr I (Figure 7—figure supplement 2E,F) which are linked with cDLP (F2). Collectively, these results demonstrate that the excitatory fastigial cell types identified in this study are each linked with a specific group of interconnected PCs and IO neurons (Figure 7M).

29This study demonstrated that medial cerebellar outputs are mediated by molecularly distinct fastigial cell types which are modularly connected with specific sets of Purkinje cells, inferior olive neurons, and downstream targets (Figure 8). We identified five major types of glutamatergic projection neurons, which can be divided into two classes. Large F1R and F1rDLP neurons, innervated by Aldoc-negative PCs, connect primarily with large brainstem neurons associated with online control of motor and autonomic functions. In contrast, smaller F2, F3, and F4 neurons, innervated by Aldoc-positive PCs, connect with multiple downstream circuits associated with sensory processing, motor preparation and arousal. Each excitatory fastigial cell type receives convergent inputs from widely distributed Purkinje cells associated with a specific set of IO neurons and makes divergent projections to a functionally related collection of downstream targets. These results suggest that diverse functions of the cerebellar vermis are mediated by the parallel operation of several discrete multineuronal circuit modules. Specific disynaptic linkages with prefrontal cortex, striatum, basal forebrain, and brainstem arousal circuits made by caudal fastigial neurons (F2 and F4) could underlie the cognitive and affective disturbances associated with vermal malfunction.

30Although the fastigial nucleus was known to comprise multiple cell types, it has been broadly assumed that outputs are mediated predominantly by large excitatory neurons. Our findings demonstrate multiple subtypes of glutamatergic projection neurons which vary in size, input-output connectivity, and expression levels of genes associated with fast firing and rapid signal transmission. An additional population of large glycinergic neurons in the rostral fastigial nucleus project ipsilaterally to brainstem nuclei targeted by contralateral F1 excitatory fastigial neurons. GABAergic nucleo-olivary neurons, abundant in the other cerebellar nuclei, are relatively sparsely distributed in each subregion of the fastigial nucleus. Interestingly, as with fastigial F3 and F4 neurons, small glutamatergic neurons in the dentate (lateral) cerebellar nucleus are located ventrally and are associated with nonmotor functions of the cerebellum.

31The principle that the nervous system minimizes axonal caliber and energy usage suggests that large, fast-spiking cerebellar nucleus neurons may be specialized to meet evolutionarily critical demands. Purkinje cells with the fastest firing capacity (Aldoc-negative:; ) densely innervate the largest fastigial neurons (F1R), which in turn make extensive synapses onto somata and proximal dendrites of gigantic brainstem neurons responsible for rapid posturomotor reflexes. The largest glutamatergic fastigial cell types can transform Purkinje cell synaptic inhibition into precisely timed spikes, as has been shown for their counterparts in the interpositus and dentate nuclei. On the other hand, physiological properties of the smallest glutamatergic fastigial cell types (F3 and F4) have not been explicitly reported, likely reflecting challenges in isolating and targeting them for recordings. However, their small size and lower expression of genes related to fast spiking suggest that their responses to synaptic inputs may be slower and less time-locked than those of larger cell types. We conjecture that cell size differences across fastigial projection neurons reflect their distinct temporal operating domains as discussed below: fast online control of axial and orofacial actions by the largest cells (F1R and F1rDLP), orienting responses by intermediately sized cells (F2), and tonic modulation of autonomic functions and arousal by the smallest cells (F3 and F4).

32Although it has long been appreciated that fastigial nucleus neurons target widespread subcortical regions, with rostral vs caudal fastigial neurons projecting predominantly to hindbrain vs midbrain and thalamus, the input-output linkages made by specific fastigial cell types have not been previously identified. Our results demonstrate that each major excitatory fastigial cell type is differentially linked with a specific set of inferior olive neurons, Purkinje cells, and functionally related downstream targets (Figure 8). This remarkable circuit modularity provides a heuristic framework for considering the diverse functions associated with the cerebellar vermis and fastigial nucleus, as described below.

33The F1R module includes brainstem and spinal nuclei associated with axial motor control, locomotion speed, cardiorespiratory control, and generalized arousal. Vermis PCs in the F1R module respond to proprioceptive, somatosensory, and vestibular signals related to self-motion. The corresponding IO neurons in the subnucleus b of the cMAO convey error signals from cutaneous and proprioceptive spino-olivary afferents from the trunk and hindlimb, including group III afferents, which encode muscle fatigue. Collectively, these circuit connections could enable F1R neurons, together with their ipsilaterally projecting glycinergic counterparts, to adaptively coordinate somatomotor, autonomic, and arousal functions during upright stance, changes in posture, and locomotion.

34The F1rDLP module includes medullary nuclei associated with orofacial motor control, respiratory modulation, and arousal, consistent with responses of the DLP neurons to signals related to whisking, breathing, and licking. PCs in the F1rDLP module, located in medial parts of the simple lobule and Crus II, receive orofacial tactile signals, and fire action potentials time-locked to licking and whisking, as do the associated molecular layer interneurons. Inferior olive neurons in the F1rDLP module (cMAO-c) respond to perioral stimuli driven by indirect trigeminal inputs from lateral superior colliculus and the mesodiencephalic junction. These circuit connections make the F1rDLP module well suited for contextual modulation of trigemino-motor reflexes and the adaptive coordination of multiple oromotor behaviors and breathing.

35The F3 module includes caudal vestibular nuclei (IVN and MVN), which mediate postural modulation of autonomic functions, the Kölliker Fuse nucleus, which modifies sensory responsiveness of brainstem respiratory circuits, and the parabrachial complex, thought to be critical for arousal responses to homeostatic distress. Notably, localized stimulation of the ventral fastigial nucleus evokes increases in blood pressure, and chemosensitive neurons responsive to CO2 are similarly localized ventrally, consistent with a role for F3 fastigial neurons in cardiovascular and respiratory responses to head tilt and hypercapnia. PCs in the F3 module extend over cerebellar cortical midline regions that receive vestibular and proprioceptive signals related to head and body position with respect to gravity. The F3 region of the medial accessory olive (cMAO-a) receives inputs from the lumbosacral spinal cord and from cardiorespiratory regions of the nucleus tractus solitarius. These circuit connections suggest that the F3 module contributes to adaptive adjustments of autonomic reflexes during changes in body position. The F3 module, together with nodulus/uvula connections with vestibular and parabrachial nuclei may be critical for postural regulation of blood pressure and airway patency; dysfunction of these circuits could account for the cerebellar links with orthostatic hypotension and sleep-disordered breathing.

36The F2 module encompasses several brainstem, midbrain, and thalamic nuclei that subserve distinct aspects of the orienting response to novel stimuli. Projection targets of F2 neurons are remarkably congruent with those of the primate fastigial oculomotor region and are related to eye and head movement, threat processing, sensory gating, stimulus salience, and behavioral flexibility. PCs in the F2 module, located in lobules VIc and VII (aka 'oculomotor vermis': ) and medial Crus I, are downstream of pontine mossy fibers which convey signals from superior colliculus, motor, premotor, cingulate, and prelimbic cortices, and subthalamic nucleus. IO neurons in the F2 module (cMAO-d) receive inputs from the medial superior colliculus and frontal cortical regions. Circuit connections with superior colliculus, basal ganglia, frontal cortex, and premotor brainstem could enable the F2 module to coordinate behavioral, cognitive, and arousal responses to novel or unexpected events. Accordingly, dysfunction of the F2 module could impair both motoric and nonmotoric aspects of orienting to environmental stimuli.

37The F4 module includes pontine, midbrain, and thalamic nuclei implicated in arousal and vigilance, consistent with classical reports of fastigial contributions to the ascending reticular activating system and to regulation of affect. Robust connections with cholinergic and noncholinergic neurons in the LDTg and PTg, which are associated with vigilance and arousal, have not been previously reported, possibly reflecting restricted tracer uptake or selective cytotoxicity of small F4 neurons. Connections with the nucleus incertus, supramammillary region, and VM thalamic nuclei enable F4 neurons to coordinate activity of the hippocampus, basal forebrain, and broad regions of the cerebral cortex. PCs in the F4 module are located in posterior vermal lobules associated with affective dysregulation, pain, and addiction. IO beta neurons in the F4 module receive inputs from medial frontal cortex and from vestibular neurons which encode head tilt, pitch, and translation. Consistent with a role in signaling changes in arousal level, IO beta neurons are activated by anesthesia, vestibular stimuli, vagal nerve stimulation, and drug-induced hyperactivity. Accordingly, the E4 module could provide a widely broadcasted alerting signal that coordinately engages the basal forebrain, hippocampus, and cerebral cortex under conditions that require vigilant arousal.

38The small size of the fastigial nucleus and the overlapping trajectory of axonal projections from distinct cell types made it technically challenging to identify the postsynaptic targets associated with each cell type. When used in isolation, circuit tracing techniques can each produce ambiguous results which are subject to misinterpretation. Retrograde tracers can be taken up by axons of passage, some ‘anterograde’ tracers can be transported in the wrong direction, many types of tracers suffer from cell type selective infectivity, and confining injections to small structures can be difficult. We relied on a combination of retrograde and anterograde tracing, careful assessment of a large number of cases, and strict inclusion criteria for injection sites to rigorously disambiguate circuit connections.

39The AAV1-mediated transsynaptic tracing method applied in this study resulted in robust labeling of neurons in brain regions innervated by fastigial terminals. We consider these neurons to be postsynaptic to the fastigial nucleus given that synaptic release mechanisms mediate the transsynaptic transport. A few limitations, however, should be noted. First, tropism of this AAV for certain cell-types can over- or under-estimate the synaptic connectivity. For example, transsynaptic transport of this virus to neuromodulatory neurons is ineffective, consistent with our observations of sparse postsynaptic labeling in the PAG (Figure 3E), where the majority of the fastigial projections terminate on dopaminergic cells. AAV tropism should also be considered when interpreting disynaptic fastigial input to the forebrain, as some cell groups in the thalamus might be more efficiently infected by this virus. Relatedly, rabies virus (e.g. ) also has tropism limitations; indeed, robust fastigial or vermis connection with the forebrain were not identified in previous rabies tracing studies. Second, the retrograde infectivity of the AAV should be considered when interpreting results. We took advantage of this to retrogradely identify PCs that project to specific fastigial subregions. Third, we have observed occasional labeling of the presumed third order neurons (e.g. pyramidal neurons; Figure 6—figure supplement 1F), in contrast with the original description of the method, in which the transsynaptic transport was reported to be exclusively monosynaptic. Assuming that the third order labeling is a result of our 10-fold more copies of injections than the original report, this method may require specific titers for the transsynaptic labeling to indicate monosynaptic vs disynaptic transport.

40Although cerebellar functions have typically been linked with lobules, we demonstrate that cerebellar outputs are organized in modules which extend across multiple lobules. For example, vermis lobule VIII is a composite of three cerebellar modules which are differentially linked with brainstem nuclei subserving somatomotor, autonomic, and arousal functions (F1R, F3, and F4; see Figure 8), consistent with the mixed motor and mon-motor representations of this lobule identified in human imaging studies. Similarly, each of the vermal lobules I-IX comprises multiple modules (Figure 8). Differences in the combinations and proportions of individual modules across lobules are likely to underlie different aspects of the same broad functions distributed across lobules, such as fear-learning by lobule VI/V vs freezing by lobule VIII. The parasagittal distribution of PCs in each module contrasts with the transverse organization of parallel fibers, enabling each FN cell type to integrate signals from multiple types of mossy fibers. Given that many of the FN projection targets are positioned to serve as circuit hubs which coordinate complex functions by distributing signals to a wide set of postsynaptic neurons, each fastigial cell type can be thought of as a superhub. Multiple modules are likely to operate in parallel to subserve broad organismal functions; parallel fibers within each lobule could serve to connect functionally related modules.

41In contrast to the widely accepted linkages of the cerebellar hemispheres and dentate nucleus with prefrontal cortex and cognitive functions, whether the vermis and fastigial nucleus participate in nonmotor functions has been controversial. By using a sensitive AAV-mediated anterograde transsynaptic tracing methods, we identified robust disynaptic fastigial nucleus connections with several regions of prefrontal cortex mediated predominantly by small, ventrally located F4 neurons. Consistent with long standing physiological findings that stimulation of the FN evokes prominent changes in electroencephalographic activity throughout much of the cerebral cortex, we demonstrated strikingly dense disynaptic input from the FN to widespread regions of the forebrain, including the cortex, striatum, and basal forebrain. Modular connections of fastigial neurons with brainstem arousal, autonomic, and medial thalamic nuclei provide candidate circuit substrates for the cerebellar cognitive affective syndrome and could account for the therapeutic effect of vermis intervention on neuropsychiatric disorders.

42C57BL/6J and YFP-16 transgenic line backcrossed to C57BL/6J were used in single-cell harvesting at P15-34. C57BL/6J, YFP-16, GlyT2-EGFP, Gad2-nls-mCherry (stock 023140, Jackson Laboratory, Bar Harbor, ME), L7Cre (also known as Pcp2Cre, stock 004146, JAX), Ai3 (stock 007903, Jackson Laboratory), Ai14 (stock 007908, Jackson Laboratory), Ai32 (stock 024109, Jackson Laboratory), Sun1-sfGFP (stock 021039, Jackson Laboratory), VgluT2-Cre (stock 016963, Jackson Laboratory), Gad2Cre (stock 019022, Jackson Laboratory), ChatCre (stock 018957, Jackson Laboratory), and Lhx6-EGFP (stock 000246, MMRRC) mice were used in histological experiments (at >P50). Key resources table provides detailed information for the mice used. If needed, Cre-reporter mice were crossed with Ai3, Ai14, or Sun1-sfGFP reporter mice in which Cre recombination allows CAG promoter driven expression of EYFP, tdTomato, or nuclear membrane protein SUN1 fused superfolder GFP, respectively. All the experiments were performed under the protocols approved by Salk Institute Animal Care and Use Committee (11–00024) and Johns Hopkins University Animal Care and Use Committee (M014M28 and M016M464).

43Single-cell qPCR and data analyses were performed as described previously with modifications in trehalose treatment, enzymes for tissue digestion, and calcein-AM cell staining. All chemicals were obtained from Sigma-Aldrich (St. Louis, MO) unless otherwise noted. Mouse brains were dissected out after decapitation under deep anesthesia with sodium pentobarbital (100 mg/kg). Acute cerebellar coronal slices were cut at 250 µm in ice-cold low Ca artificial cerebrospinal fluid (ACSF; 125 mM NaCl, 1.25 mM KCl, 25 mM NaHCO3, 1.25 mM NaH2PO4, 1 mM CaCl2, 3 mM MgCl2, and 25 mM dextrose) with bubbling 95% O2 and 5% CO2 using a vibratome (VT1000 S, Leica Microsystems, Buffalo Grove, IL). Acute bilateral fastigial nuclei were quickly excised with a sharp knife from 2 or three cerebellar slices and were then enzymatically digested with cysteine (2 mM)-supplemented papain (40 U/ml, Worthington, Lakewood, NJ) and chondroitinase-ABC (1 U/ml) in the 37°C incubation solution, which was low Ca HEPES-buffered ACSF (140 mM NaCl, 1.25 mM KCl, 10 mM HEPES, 1.25 mM NaH2PO4, 1 mM CaCl2, 3 mM MgCl2, and 25 mM dextrose) containing blockades (0.1 µM tetrodotoxin, 20 µM 6-cyano-7-mitroquinozaline-2,3-dione, and 50 µM D-APV) and trehalose (5%). Digestion was quenched by transferring the tissues into the ice-cold incubation solution containing bovine serum albumin (1%). The tissues were triturated by gentle pipetting and the suspension was then transferred in a dish with ice-cold incubation solution. To visualize cells from wild type mice, cells were fluorescently stained by adding calcein-AM in the digestion tube (40 µM), quencher tube (40 µM), and the first dish (8 µM). Single cells were manually picked up with pulled glass capillaries under a fluorescent stereoscope (M205 FA, Leica Microsystems) attached with a high-power light source (PhotoFluor II NIR, 89 NORTH, Williston, VT). They were immediately transferred to the second dish containing the same solution to wash any residual debris. From the second dish, single cells were transferred using pulled glass capillaries to individual tubes containing cell lysis buffer and spike-in RNAs (Lys, Trp, Phe, and Thr; 1000, 100, 20, and five copies, respectively). As negative controls, we put the following materials instead of cells; 10 pg of mouse brain total RNA as positive control, and the incubation solution from the second dish after the harvesting as negative control. The cDNAs were globally amplified by performing cell lysis, reverse transcription, exonuclease I treatment, poly(dA) addition, second-strand cDNA synthesis, and 20 cycle PCR reaction as described in;. Note that this method amplifies ~700 bp of the 3' end of the cDNAs.

44Primers/probes for qPCR were designed for 3'-end sequences avoiding polyadenylation signals as previously described and purchased from Integrated DNA Technologies, Inc (IDT, Coralville, IA). The PrimerQuest Tool available at IDT’s website was also used for designing primers. Their sequences are available in Figure 2—source data 1.

45All samples were initially screened for Gapdh, a housekeeping gene, for quality control. A 10 µL reaction scale TaqMan method qPCR for Gapdh was performed using 1 µL of 1:40 diluted 20 cycle PCR products with 7900HT Fast Real-Time PCR System (Applied Biosystems, Foster City, CA) or CFX384 Touch Real-Time PCR Detection System (Biorad, Hercules CA). When Gapdh expression was detected in the negative control, the experiment batch was regarded of as contaminated and the samples were excluded from the study (2 batches out of 16, which included 34 cells in total). Samples that showed unexpectedly high Gapdh Ct values (>mean + SD), suggesting degradation of mRNAs, were also excluded. The single cell cDNA samples that passed the quality control with Gapdh were further amplified by 11 cycle PCR, as described in, to obtain large cDNA libraries for the following gene expression profiling with qPCR. Linear amplification of spike-in genes in extra-amplified samples inferred similarly linear amplification of other genes in the cDNA libraries. The samples of glutamatergic neurons were curated by performing qPCR to examine the absence of glial genes, Mobp and Cd68, to examine the presence of neuronal genes, Scn8a and Kcna1, to examine the absence of inhibitory neuronal genes, Gad1, Gad2, and Slc6a5, and then to examine the presence of glutamatergic neuronal gene, Slc17a6. The qPCR for gene expression profiling was performed in triplicated 10 µL scale reactions. Each reaction plate had at least four wells of standard reaction which was cDNA of 1 pg Trp. The threshold to determine Ct was set so that Ct values of the standard reaction became identical across all the reaction plates. Averaged Ct values, without normalization, were used for the following analysis.

46The analysis of the expression data was performed in R (https://www.r-project.org/) and Igor (WaveMetrics, Portland OR) software. The data were subjected to the hierarchical clustering analysis without normalization. To eliminate influence of fluctuating stochastic gene expression at low levels, the Ct values greater than the average of spike-in RNA Thr (23.43; corresponding to five copies input mRNA) were regarded as not determined (ND). For clustering, euclidean distance was calculated between any pairs of samples and hierarchical clustering was performed with Ward's method using ‘ward.D2’ method in ‘hclust' function in R.

47Stereotaxic tracer injections were made into adult mice. AAV-mediated anterograde transsynaptic tracing was performed in the Ai14 mouse line. For anterograde axonal tracing, we used AAV9.hSyn.TurboRFP.WPRE.rBG (titer 6.64 × 1013 GC/ml), AAV9.hSyn.eGFP.WPRE.bGH (titer 8.88 × 1013 GC/ml), AAV1.hSyn.eGFP.WPRE.bGH (titer 2.24 × 1013 GC/ml), AAV1.hSyn.TurboRFP.WPRE.rBG (titer 2.15 × 1013 GC/ml), AAV9.CAG.Flex.eGFP.WPRE.bGH (titer 2.28 × 1013 GC/ml), AAV9.CAG.Flex.tdTomato.WPRE.bGH (titer 1.25 × 1013 GC/ml), and AAV9.CAG.hChR2(H134R)-mCherry.WPRE.SV40 (titer 1.71 × 1013 GC/ml) (all from Penn Vector Core at University of Pennsylvania). For anterograde transsynaptic tracing, we used AAV1.hSyn.Cre.WPRE.hGH (titer 4.37 × 1013 GC/ml) (from Penn Vector Core). For retrograde tracing, we used FastBlue (5% in distilled water, 17740–1, Polysciences, Inc, Warrington, PA), fluorescent latex microspheres (red retrobeads IX or green retrobeads IX, Lumafluor, Naples FL), AAV2retro.CAG.Cre (titer 5.3 × 1012 GC/ml, UNC Vector Core at University of North Carolina, Chapel Hill, NC) dextrans conjugated with Texas Red (10% in saline, D3328, Thermo Fisher Scientific) and with biotin (BDA, MW3000, 10% in saline, D7135, Thermo Fisher Scientific), and glycoprotein deleted recombinant rabies virus carrying mCherry gene (RVdG-mC) (titer 9.6 × 109 TU/ml, from GT3 core at the Salk Institute). A mouse was placed on the stereotaxic apparatus (David Kopf Instruments, Tujunga, CA) under isoflurane anesthesia (2% in 1.0 L/min oxygen). A small incision was made in the head skin overlying the skull of the mouse and a small craniotomy was drilled in the skull with a dental drill. Pulled glass pipette (tip inner diameter of 5–15 µm) filled with a tracer was stereotaxically inserted in the brain using Angle One stereotaxic instrument (myNeuroLab.com; currently Leica Instruments) and a small amount of the tracer (5–300 nL) was pressure injected using Picospritzer II (Parker Hannifin, Hollis, NH) with nitrogen (15–30 psi) at the target. For the tracer injections into the FN, local field potential was also monitored through extracellular amplifier (ER-1, Cygnus, bandpass frequency range 1–3000 Hz, Cygnus Technology, Delaware Water Gap, PA), 50/60 Hz noise eliminator (HumBug, Quest Scientific, North Vancouver, BC), and a speaker. Injections to the cerebellar cortex were made in specific lobules which were identified through a craniotomy. Ten minutes after the injection, the glass pipette was removed from the brain and the skin was sutured. The mice survival times were 3 weeks for AAV axonal tracing, 4 weeks for AAV transsynaptic somatic labeling, 5 weeks for AAV transsynaptic axonal tracing, 4–7 days for retrobead, dextran, and FastBlue, and 4–5 days for RVdG-mC.

48After appropriate survival periods, mice were deeply anesthetized with 2,2,2-tribromoethanol (also known as avertin, 0.5 mg/g) and were then transcardially perfused with PBS containing heparin (10 U/ml) followed by 4% paraformaldehyde (PFA) in PBS. Brains were dissected out from the skull, postfixed overnight in 4% PFA in PBS and cryoprotected in 30% sucrose PBS. Those brains were then embedded in gelatin in order to prevent separation of the cerebellum from the brainstem. The gelatin blocks were hardened on ice and were then trimmed and fixed overnight with 4% PFA in 30% sucrose PFA. Coronal or sagittal serial sections were cut at a thickness of 40 µm with freezing microtome. After rinsed with PBS containing 0.15% Triton-X (PBST), the sections were stored in PBS containing 0.1% sodium azide at 4°C until use.

49For immunostaining, sections were incubated overnight on a shaker at 4°C with primary antibodies and 5% normal donkey serum (NDS) in PBST. Primary antibodies used were mouse anti-alpha synuclein (1:100, 610786, BD Bioscience, San Jose, CA), goat anti-osteopontin (1:300, AF808, R and D Systems, Minneapolis, MN), rabbit anti-calretinin (1:500, AB5054, Millipore), rabbit anti-tyrosine hydroxylase (1:1000, AB152, Millipore, Burlington, MA), rabbit anti-GFP (1:1000, AB3080, Millipore), chicken anti-GFP (1:1000, GFP-1020, Aves Labs), rabbit anti-RFP (1:1000, PM005, MBL International, Woburn, MA), goat anti-Chat (1:500, AB144P, MilliporeSigma), rabbit anti-PLCb4 (1:100, sc-20760, Santa Cruz Biotechnology, Dallas TX), rabbit anti-Aldoc (1:8000 of 14.66 mg/mL stock, Dr. Izumi Sugihara), rabbit anti-orexin (1:500, T4074, Peninsula Laboratories, San Carlos, CA), mouse anti-SMI32 (NEFH, 1:1000, SMI-32R-100, Covance, Princeton, NJ). After being rinsed five times with PBST for more than an hour in total, sections were incubated overnight at 4°C with donkey secondary antibodies that had been processed for minimum cross reactivity by the manufacturer and were conjugated with AlexaFluor488, AlexaFluor594, or AlexaFluor647 fluorescent dye (Jackson Immunoresearch) and 5% NDS in PBST. BDA was visualized with streptavidin conjugated with AlexaFluor488 or AlexaFluor594 dye. Some sections were counterstained by adding fluorescent Nissl (NeuroTrace 435/455 or 640/660, Thermo Fisher Scientific, Waltham, MA) or DAPI to the incubation with secondary antibody. The stained sections were then rinsed five times with PBS for more than an hour in total, mounted on slide glass, and coverslipped with VECTASHIELD (H-1400, Vector Laboartories, Burlingame, CA) or Fluoroshield (F6937, MilliporeSigma).

50Notably, we found that the anterograde transsynaptic tracing method by, could also robustly visualize the axons of postsynaptic (second order) neurons with a long (5 weeks) post-injection survival period. Thus, we applied this modified method to map disynaptic input from the FN to the forebrain (Figure 6). Although the transneuronal viral transport is reported to be only be monosynaptic, our injections occasionally labeled presumed third order neurons (e.g. cortical pyramidal neurons). This might be because we injected 10-fold more AAV copies than in the original report. The effect was, however, estimated to be very minor (for example, only a few labeled pyramidal neurons were found across the entire cortex per case, see Figure 6—figure supplement 1) and axonal labeling from those tertiary neurons was regarded to have little or no impact on the interpretation of disynaptic projections.

51We used the Paxinos mouse brain atlas for anatomical nomenclature, supplemented by nomenclature based on the literature. Images were taken with a confocal microscope system (FV1000, Olympus, Tokyo, Japan) or a CCD camera (ORCA-100, Hamamatsu Photonics, Hamamatsu, Japan) attached to an epi-fluorescent microscope (BX61, Olympus). Contrast and brightness were adjusted in Photoshop CS6 (Adobe, San Jose, CA). In some panels, pseudo-low magnification images were made by tiling several photos taken at higher magnification.

52To analyze whether glutamatergic, glycinergic, and GABAergic fastigial neurons express SPP1, SNCA, and CALB2, we performed immunostaining for SPP1, SNCA, and CALB2 of fastigial sections of the reporter mouse lines of glutamatergic, glycinergic, and GABAergic neurons, which are VgluT2-Cre;Ai14, GlyT2-EGFP, and Gad2-nls-mCherry. Images of the fastigial subregions were taken with single confocal scans using a 40x objective lens. Cell-counting was performed only when the nucleus of the neurons was identified.

53Neuronal size measurements were analyzed from epifluorescent microphotographs of individual neurons taken with a 20x objective lens with the focus centered at the neuronal nucleus. Neuronal somata were manually outlined with the measurement tool in ImageJ (https://imagej.nih.gov/ij/), which calculates the area of each circumscribed region.

54Axon diameters were assessed with ImageJ from confocal micrographs of AAV-injected FN. Confocal z-stack images of the entire thickness of each section (40 µm) were taken with a 100x lens at the level of the superior cerebellar peduncle. To reliably image axons, which typically are >0.75 µm, we used z-stack steps of 0.36 µm. Axon diameter was calculated as the average of 3 points measured from each axon. Measurements were obtained only from smooth axons that did not exhibit degenerative morphology such as swelling.

55For each tracing experiment, injection site was carefully checked for the spread of the tracers to neighboring (sub)nuclei. Only the cases without those spread, which were listed in Figure 3—source data 2, were included in the analyses.

56Mapping of retrogradely traced fastigial neurons was performed on our standard map of the fastigial nucleus which was obtained from Nissl stained serial sections of an adult mouse. One in three 40 µm thick sections from each injection case was used for the mapping. Correspondence of rostrocaudal levels between the standard map and the sample section was confirmed by assigning relative coordinates of 0% being caudal end and 100% being rostral end of the FN. Each of the retrogradely labeled neurons was mapped. For figure panels, three representative levels were chosen from the standard map and the mapping results were combined on the drawings of corresponding levels.

57For analysis of PCs stripes in cerebellar zones, an anatomical atlas produced in previous studies was used. The scheme of Aldoc expression map on the unfolded cerebellar cortex was redrawn based on. The pattern of PC stripes is highly reproducible across individuals and across mammalian species, and each of the stripes has its established nomenclature (e.g. 1+, 2+, a+, etc.). Since individual IO neurons typically project to two distinct stripes that are separately located and termed in the anterior and posterior lobes of the cerebellum, these pairs of stripes are referred to as, for example, a+//2+, in which a+ and 2+ indicate the stripes in anterior and posterior lobes, respectively, and '//' indicates anteroposterior pairing of the stripes. Identification of the distinct Purkinje cell (PC) populations was based on the mediolateral level from the midline and the immunoreactivity for marker molecules, Aldoc or PLCb4. Subdivisions of inferior olivary subnuclei were identified by referring to;. In addition, we designated an additional subarea, which we termed subnucleus 'd' of the caudal medial accessory olive, based on input connectivity with the superior colliculus (; Figure 7—figure supplement 2) and cholinergic axons as well as output connectivity with distinct Purkinje cells that were located at lobule VIc/VII, Crus I or Crus II (;; Figure 7—figure supplement 2).

58For mapping the disynaptic input to the cortex, we used the borders of cortical functional areas in with some simplification. The density of labeled axons at layer one or at deeper layers in each functional area was manually and qualitatively assessed and then those areas were categorized in three schemes as dense, moderate, or not significant. Color-coding was performed based on these three categories.