Neurogenic timing of the inferior olive subdivisions is related to the olivocerebellar projection topography

The olivocerebellar projection is organized into an intricate topographical connection from the inferior olive (IO) subdivisions to the longitudinally-striped compartments of cerebellar Purkinje Cells (PCs), to play an essential role in cerebellar coordination and learning. However, the central mechanisms for forming topography need to be clarified. IO neurons and PCs are generated during overlapping periods of a few days in embryonic development. Therefore, we examined whether their neurogenic timing is specifically involved in the olivocerebellar topographic projection relationship. First, we mapped neurogenic timing in the entire IO by using the neurogenic-tagging system of neurog2-CreER (G2A) mice and specific labeling of IO neurons with FoxP2. IO subdivisions were classified into three groups depending on their neurogenic timing range. Then, we examined the relationships in the neurogenic-timing gradient between IO neurons and PCs by labeling topographic olivocerebellar projection patterns and PC neurogenic timing. Early, intermediate, and late groups of IO subdivisions projected to late, intermediate, and early groups of the cortical compartments, respectively, except for a few particular areas. The results indicated that the olivocerebellar topographic relationship is essentially arranged according to the reverse neurogenic-timing gradients of the origin and target.

The olivocerebellar projection is organized into an intricate topographical connection from the inferior olive (IO) subdivisions to the longitudinally-striped compartments of cerebellar Purkinje Cells (PCs), to play an essential role in cerebellar coordination and learning. However, the central mechanisms for forming topography need to be clarified. IO neurons and PCs are generated during overlapping periods of a few days in embryonic development. Therefore, we examined whether their neurogenic timing is specifically involved in the olivocerebellar topographic projection relationship. First, we mapped neurogenic timing in the entire IO by using the neurogenic-tagging system of neurog2-CreER (G2A) mice and specific labeling of IO neurons with FoxP2. IO subdivisions were classified into three groups depending on their neurogenic timing range. Then, we examined the relationships in the neurogenictiming gradient between IO neurons and PCs by labeling topographic olivocerebellar projection patterns and PC neurogenic timing. Early, intermediate, and late groups of IO subdivisions projected to late, intermediate, and early groups of the cortical compartments, respectively, except for a few particular areas. The results indicated that the olivocerebellar topographic relationship is essentially arranged according to the reverse neurogenic-timing gradients of the origin and target.
IO neurons are generated in the caudal rhombic lip in the period overlapping with that of the PC generation [18][19][20] . They then migrate tangentially to settle in the ipsilateral ventral medulla [20][21][22] . Early-generated neurons settle in the dorsolateral parts while late-generated neurons settle in the medioventral parts, producing an area-dependent difference in the neurogenic timing of IO neurons 19,23 . During their migration, their growing axon extends ahead and leads the neuronal migration path. The axon crosses the midline in the ventral medulla, enters the cerebellum through the contralateral cerebellar peduncle, and forms topographic projection to PCs in the embryonic cerebellum [23][24][25] .
It has been suggested that cell adhesion molecules including cadherin and protocadherin family 26 , and ephrin and ephrin receptors 27 are involved in the formation of the topographic olivocerebellar projection. However, whether any upstream mechanisms control the expression of cell adhesion molecules in PCs and IO neurons coherently is not known.
Neuronal generation timing is one of the candidates for such upstream factors that may control the expression of cell adhesion molecules to form topographic projection patterns 28 . Early-generated and late-generated neuronal populations project to early-generated and late-generated target populations, respectively, in the output neuronal projection from the accessory and main olfactory bulbs to the telencephalon 29 and hippocampal dentate gyrus granule cell projection to CA3 pyramidal neurons 30 . However, the relationship between neurogenic timing and the olivocerebellar projection topography still needs to be clarified.
In this study, we systematically examined the neurogenic timing of IO neurons by using the neurogenin 2-CreER neurogenic-tagging system 31 . First, IO subdivisions were identified by labeling FoxP2, a specific marker of the IO neurons 16,20 . IO neurogenic timing was then systematically compared with the PC neurogenic timing 11 of the zebrin stripes of the mouse cerebellum by tracing topographic olivocerebellar projection patterns. The results indicated an inverse relationship between the neurogenic-timing gradients of IO neurons and PCs in the olivocerebellar projection topography. It is the first time this new relationship has ever been reported.

Results
Neurogenic timing-dependent reporter labeling in the G2A::H2B mouse IO. The neurogenin 2 gene is transiently expressed in PCs 32 and many other neurons, at the transition from a neural progenitor to a differentiating neuron, or neurogenesis. The G2A (neurogenin 2-CreER) mouse line is designed to label neurons which are generated at the tamoxifen administration timing 28,33 . In the ventral surface of the medulla of the whole-mount preparation of G2A::Tau mGFP-nLacZ mice, different parts of IO appear to be labeled dependent on the timing of tamoxifen administration ( Supplementary Fig. 1), indicating they are composed of neurons of different neurogenic timing. Initially, we looked at the labeling of IO neurons in G2A::Ai9::AldocV mice at about postnatal day (P) 40 with tamoxifen injection at embryonic stages 11 . Although IO neurons appeared to be labeled in these mice, dense labeling of presumable dendritic arbors prevented reliable counting of the number of labeled IO neurons (Supplementary Fig. 2a). Therefore, we used another reporter mouse strain, R26R-H2B-mCherry (abbreviated as "H2B"), which expresses fluorescent protein mCherry fused with the nuclear localization sequence 34 . In G2A::H2B mice with tamoxifen injection, the mCherry signal that is indicative of neurogenic timing-dependent labeling (designated as "(H2B) reporter labeling" or "reporter-labeled" in this report) was localized only in the nucleus with all-or-none type high contrast (Fig. 1s, Supplementary Fig. 2b, d), which facilitated quantitative observation.
To compare the efficiency of reporter labeling between Ai9 and H2B mice, we looked at zebrin stripes lateral 3− and 4+ in the simple lobule in G2A::Ai9::AldocV and G2A::H2B::AldocV mice that were given tamoxifen at E10.5, which is the timing of PC generation in these stripes 11 . The number of labeled PCs was smaller in G2A::H2B::AldocV mice than in G2A::Ai9::AldocV mice ( Supplementary Fig. 2c, d). This indicated that the labeling efficiency of H2B reporter mice was lower than that of Ai9 mice (see "Discussion"), although they both reported consistent labeling as a Cre reporter and possessed the normal zebrin striped pattern in the cerebellum (Supplementary Fig. 2e-g).
Definition of IO subdivisions with FoxP2 immunostaining. Immunostaining of FoxP2 labels almost all neurons in the IO but scarcely labels other nearby neurons 16 . The FoxP2 immunostaining signal was located in the nucleus of neurons, facilitating clear recognition of neuronal distribution ( Supplementary Fig. 3). Consequently, we could count the number of IO neurons readily and recognize the boundaries of IO subdivisions in preparations with FoxP2 immunostaining. We adopted the standard subdivision nomenclature and boundary definition of the rat and mouse IO 4,35 . Furthermore, we redefined subdivision boundaries in several places where the boundaries have not been clearly defined.
The IO is composed of five major lamellas which are generally well separated from one another; the dorsal and ventral folds of the dorsal accessory olive (dDAO, vDAO), dorsal and ventral lamellas of the principal olive (dPO, vPO), and medial accessory olive (MAO). In some particular areas, where lamellas are merged to make their distinction difficult, we temporarily defined the boundary at the position of sparse neuronal distribution as follows. The rostrolateral edge of the IO, where the vDAO and the dPO tend to merge, was included in the vDAO (Supplementary Figs. 3i, 4j), similar to the study with glutamate decarboxylase immunostaining in the rat IO 35 . The "bend" of the principal olive (PO), where the dPO and vPO merge laterally 4 , was regarded as a part of the dPO because a gap of neurons was sometimes observed between the bend and the main part of the vPO (Supplementary Figs. 3f, g, 4f-h). The medial part of the vPO is continuous with the dorsomedial subnucleus (DM), although the DM and the vPO have different topographic projection patterns 7,9 . We defined the boundary between the DM and the vPO at the position under the bulb-shaped medial end of the vDAO since neuronal density was often low at this position (Supplementary Figs. 3g-i, 4f-i). The medial accessory olive is separated into the caudal and rostral parts (cMAO and rMAO) that have different topographic projections. The boundary between the cMAO and rMAO was defined at about the 55% level in the caudorostral range of the IO, where the density of neuronal distribution was low. In addition, the rMAO defined as above showed much higher immunoreactivity to protocadherin 10 (Pcdh10, Supplementary Fig. 3f-i) than any part of the cMAO, supporting this definition.
The cMAO is divided into the lateral, intermediate, and medioventral parts that have been named subnuclei a, b and c of the cMAO (cMAO-a, cMAO-b, and cMAO-c 36 ), respectively, which project to different zebrin stripes in the cerebellar cortex 7,9 . Although these subareas are not necessarily clearly distinguished from one another, we often saw a gap of neurons in the consistent lateral part of the cMAO (Open arrowheads in Supplementary Fig. 3a-c). We tentatively defined this gap as the boundary between the cMAO-a and cMAO-b in the present study. The cMAO-c expresses the pcdh10 gene as reported in a study with pcdh10 lacZ/+ mice 26 . Pcdh10 immunostaining in the present study showed moderate immunoreactivity in the cMAO-c (filled arrowheads in Supplementary Fig. 3a-e). We tentatively defined the gap of neurons observed in the medialal edge of the Pcdh10 immunoreactive area as the boundary between the cMAO-b and cMAO-c.
The cMAO-c, the subnucleus beta, and the dorsal cap (DC) or ventrolateral outgrowth (VLO) subnucleus form the vertically-column-shaped medial part in the caudal IO. In this column-shaped part, boundaries were generally recognized by the partial gap of neuronal distribution. Furthermore, the DC showed moderate Pcdh10 immunoreactivity whereas the beta did not. The boundary between the beta and the DM was recognized at about 55% level in which neuronal density was low at their junction.
In serial sections of the IO with FoxP2 immunostaining, the number of FoxP2-positive IO neurons was counted in each IO subdivision ( Table 1). The total number of IO neurons obtained in the present study (25,470 neurons, Table 1) was comparable to the results of the preceding study (12,610 neurons on one side of the mouse IO 37 ), supporting that FoxP2 is expressed in almost all IO neurons.
In addition to defining subdivisions of the IO above, we arbitrarily divided the four large subdivisions into several parts to count the number of labeled neurons separately. The vDAO was divided into three parts of www.nature.com/scientificreports/  Fig. 1o). Although we did not characterize these lately-generated neurons, they may belong to the population different from the climbing fiber-projecting population 38 .
To quantitatively analyze the neurogenic timing, we counted the reporter-labeled neurons in each IO subdivision on the left and right sides in serial sections (Supplementary Table 2). To classify IO subdivisions based on the timing of reporter labeling in an unbiased way, we applied the hierarchical clusterogram analysis to the matrix data of reporter labeling percentage in every major IO subdivision in all mice of tamoxifen injection at various timing (Fig. 2a). In the obtained clusterogram tree, the top three groups (orange, blue and green areas of the clusterogram) showed apparently different tamoxifen-date-dependent labeling patterns. The major IO subdivisions in the left 7 columns (rMAO, cMAO-a, -b, -c, vPO, DM, and DMCC) had high percentages at TM11.0 and TM11.5 (orange, late group). Those in the right three columns (dPO, beta, and DC/VLO) had high percentages with TM10.5, TM11.0, and TM11.5 (green, intermediate group). Those in the remaining central two columns (dDAO and vDAO) had high percentages with TM10.5 and TM11.0, and low but detectable percentages with TM10.0 (blue, early group).
To confirm the group classification, we measured the mean neurogenic timing from the labeling percentage data for all subdivisions (Fig. 2c). All subdivisions in the early (blue), intermediate (green), and late (orange) groups had the mean neurogenic timing of E10.58-E10.77, E10.78-E10.92, and E11. 0-E11. 22, respectively ( Fig. 2c), supporting the classification. The distributions of mean neurogenic timings of subdivisions were significantly different among the three groups (Fig. 2c).
The time course of tamoxifen-dependent labeling was further examined by plotting the percentage of reporterlabeled neurons, averaged from all cases of tamoxifen injections at the same timing, for mediolateral smaller subdivisions of major IO subnuclei ( Fig. 2d-f). In all subdivisions of the dDAO and vDAO, labeling started with TM10.0, occurred mostly with TM10.5 and TM11.0, and disappeared with TM11.5 (Fig. 2d). In the DC/ VLO, beta, and all subdivisions of the dPO, labeling started with TM10.0, occurred mainly with TM10.5 and TM11.5, but persisted with TM11.5 only to some extent (Fig. 2e). In all subdivisions of the cMAO, rMAO, and all subdivisions of the vPO, the labeling started with TM10.5, remained with TM11.0 and peaked with TM11.5, and nearly disappeared with TM12.0 (Fig. 2e,  Among mediolateral subdivisions of major subnuclei, the plots of percentage did not show noticeable differences ( Fig. 2d-f). However, the mean neurogenic timing was later in the lateral part than in the medial part in the cMAO, and dPO, whereas it was earlier in the lateral part than in the medial part in the vDAO (plots connected with lines in Fig. 2c). Further analysis with the percentage labeling data showed that this difference was significant only between cMAO-b and cMAO-c (P = 0.042), and between cMAO-a and cMAO-c (P = 0.015). In the dPO, which belonged to the intermediate group, we additionally defined three rostrocaudal temporary subareas and re-analyzed the number of reporter-labeled neurons. No clear difference was observed among the rostrocaudal subareas (Fig. 2h).
Relationship between the neurogenic timing and the topography of the olivocerebellar projection. To identify the topographic olivocerebellar projection pattern in various IO subdivisions, we labeled IO neurons retrogradely (Fig. 3, the most left panel) by injecting neuronal tracer AF546DA into various compartments of the cerebellar cortex in Aldoc-Venus mice (Fig. 3, the second panel from the left). Then, we looked at the data set of IO neurogenic timing in IO subdivisions (Fig. 2b) as well as the data set of Purkinje cell neurogenic timing in our previous study with the neurogenic-tagging system 11 (Fig. 3, the second panel from the right, and most right panel). The neurogenic timing range of PCs in cortical compartments was classified into "early" (high degree labeling with TM10.0-TM12.0), "intermediate" (TM10.5-TM12.5), "late" (TM12.5-TM13.0) and "latest" (TM12.5-TM13.5) in the present analysis. This analysis indicated that a part of the vDAO, in which IO neurons were generated in the early timing, projected to stripe 3-in lobule III, in which PCs were generated mainly in the late timing (Fig. 3a). Parts in the beta subnucleus, VLO and dPO, in which IO neurons were generated in the intermediate timing, projected to stripe 2+ in lobule VIII, flocculus, and stripe 6+//7+ in crus I, respectively. In these cortical areas, PCs are mainly generated at the intermediate timing (Fig. 3d) or intermediate and late timing (Fig. 3b,c). Parts in the cMAO, DMCC + DM, vPO, and rMAO, in which IO neurons were generated in the late timing, projected to stripe 1− in lobule V, stripe 4+ in lobules VIII and IX, stripe 6+ in crus II, and stripe 5+ in the paramedian lobule. In these cortical areas, Purkinje cells are generated in the late (Fig. 3e, h), early (Fig. 3f), and intermediate (Fig. 3g) timings. The results indicated that the neurogenic timing of IO neurons was not simply related to the neurogenic timing of innervated PCs. On the contrary, there was often, but not always, a reverse relationship between them, i.e. early-and late-generated IO neurons often innervated late-and early-generated PCs, respectively.
To further examine this relationship, we mapped the reported topographical relationship of the olivocerebellar projection in mice and rats 6-9,39 on the reported neurogenic timing of striped subareas of the cerebellar cortex in the mouse (Fig. 4a) 11 . The dDAO and vDAO (early IO subdivisions, blue in Fig. 4b) project to the zebrin-negative and zebrin-faintly negative stripes in the paravermis and hemisphere, which corresponds to modules B and C1/ C3 [6][7][8][9]39 . These zebrin stripes belong to late compartments (yellow in Fig. 4b) 11 . The beta subnucleus (intermediate IO subdivisions, green in Fig. 4c) projects to stripe 2 + in lobule VIII-IX, which contains intermediate (lateral stripe 2 +) and late (medial stripe 2 +) compartments (green and yellow, respectively, in Fig. 4c). The DC/VLO (intermediate IO subdivisions, green in Fig. 4d left) projects to the flocculus and nodulus (lobule X), which contains early, intermediate, late and latest compartments (various colors in Fig. 4d right). The dPO (intermediate IO subdivisions, green in Fig. 4f left) projects to the most lateral area in the hemisphere (module D2), which contains mostly intermediate compartments (cyan, Fig. 4f right). The cMAO-a, cMAO-b, and cMAO-c (late IO  Table 2). The top three groups (orange, blue and green areas of the clusterogram) showed apparently different tamoxifen-date-dependent labeling patterns. Consequently, they were defined as late (orange), intermediate (green) and early (blue) groups. Color bar in the right shows the color coding of the value, subtracted by the average and then divided by the standard deviation, of each cells in the matrix table (between 3.0 and − 1.   Fig. 4i left) project to the zebrin-positive and negative stripes in the lateral paravermis (modules C2 and CX), which contains early compartments (purple in Fig. 4i right). The topographic olivocerebellar projection pattern we demonstrated above (Fig. 3) fully agreed with the pattern reported in previous studies (Fig. 4) [6][7][8][9]39 . Based on the topographic projection pattern, the relationship between the neurogenic timing ranges of the origin (IO subdivisions) and target (cerebellar cortical compartments of PCs) was clarified for the entire olivocerebellar projection. Although the relationship was variable among subdivisions, early-, intermediate-, and late-neurogenic IO subdivisions often projected to the late-, intermediate-, and early-neurogenic PC compartments (highlighted at the bottom of Fig. 4b, f, g, i). The result indicates that the topography in the majority of the olivocerebellar projections is formed according to the reverse neurogenic-timing gradients between IO subdivisions and the cerebellar compartments.

Discussion
In the present study, we clarified the neurogenic timing of IO subdivisions and re-examined the topographic relationship between IO subdivisions and the cortical compartments in the olivocerebellar projection. Referring to the neurogenic timing of PCs in the cerebellar cortex, we have shown the general reverse relationship in the neurogenic-timing gradient in the olivocerebellar projection (Fig. 5). The developmental relevance and functional significance of the findings are discussed here.
Neurogenic timing-specific labeling of IO neurons. Neurogenic timing of IO neurons has been studied with the 3 H-thymidine 40 and 5-bromo-2′-deoxyuridine (BrdU) 19 labeling methods. The study with BrdU injection at 4-h intervals in the rat 19 has shown that IO neurons are generated between E11.7 (E11 + 16 h) and E13.3 (E13 + 8 h) 19 . This study also demonstrated that neuronal generation occurs early in the DAO, intermediately in the PO, DC/VLO, and subnucleus beta, and late and with mediolateral gradient in the MAO 19 . The neurogenic-timing difference among IO subdivisions observed in the mouse in the present study was generally similar to the result in the rat study 19 , corroborating the neurogenic timing-specific labeling of murine IO neurons in G2A mice. The neurogenic-tagging system with G2A mice 31 is a type of genetic inducible fate mapping 41 . While 3 H-thymidine and BrdU label progenitor cells in the S phase at the time of injection, Neurog2, the gene that is manipulated in G2A mice, is expressed transiently in the transition time window from a neural progenitor to a differentiating neuron in many brain areas 31,32 . The peak of Cre-dependent reporter expression occurs 6-12 h after the final DNA synthesis in G2A mice in most neurons 33 . If injected at the same timing, tamoxifen would label neurons generated 6-12 h earlier than BrdU and 3 H-thymidine.
The H2B reporter mouse used in the present study had apparently an expression efficiency lower than that of the Ai9 reporter mouse (Supplementary Fig. 2). This is presumably related to the length of the STOP cassette between the two loxP sites (about 2.7 kb in H2B 34 , and about 0.9 kb in Ai9) 42 . Nevertheless, the nucleus-localized expression of fluorescence facilitated counting labeled IO neurons in the present study.
Definition of IO subdivisions. The IO subdivisions are defined primarily by their cytoarchitecture.
However, their link to the topographic axonal projection to the cerebellar cortical compartments is also characteristic 6,7,9 . By using immunostaining of FoxP2, which marks climbing fiber-projecting neurons with specificity 16 , we have confirmingly defined most of the boundaries between IO subdivisions to make a quantita- Figure 3. Retrograde tracing of the olivocerebellar topographic projection and consequent identification of the neurogenic timing relationship between the origin (IO) and target (PCs). Distribution of retrogradelylabeled IO neurons in a particular IO subarea (most left panel) labeled by localized injection of AF546DA into a particular area in the cerebellar cortex (second panel from the left), PC labeling by the neurogenic-tagging system in the same area of the cerebellar cortex (second panel from the right) and zebrin pattern of that area (most right panel) are shown for eight different positions (a-h). Images of Purkinje cell labeling with the neurogenic-tagging system were selected from the data set produced in our previous study performed with G2A::Ai9::AldocV mice and tamoxifen injection at a particular timing of embryonic stage 11 . Images in the second panel from the right and the most right panel show the same section. Circles indicate the distribution of retrogradely labeled IO neurons (most left panel), the AF564DA injection sites (second panel from the left), and approximately the same position as the AF564DA injection sites (second panel from the right and most right panel). The green pseudo-color shows the Venus signal indicating the aldolase C expression in all panels.
The magenta pseudo-color shows AF564DA signal in the most left panel and the second panel from the left, and labeling with the neurogenic-tagging system in the second panel from the right. In the second panel from the right in (c), dense neuronal labeling are seen in the cerebral cortex and medial brain stem besides labeling in some PCs. Perentage in the most left panel indicates the relative position of the section within the caudorostral extent of the IO (0%: caudal edge, 100%, rostral edge). Scale bars in (h) apply to all panels in the most left column (200 µm), and to all panels in the three other columns (500 µm      The IO subdivision that is focused on is colored on the left side in each panel. The cortical compartments that are topographically projected by the IO subdivision are colored on the right side. The relationship of neurogenic timing between the IO and PCs is indicated at the bottom of each panel, in which dark gray shadowing indicates the major relationship. In this figure, the unfolded representation of the cerebellar cortex with the longitudinally-striped zebrin (aldolase C) expression pattern is based on previous studies [5][6][7]48 . Shadowed and non-shadowed areas represent aldolase C-positive and -negative stripes, respectively. The topographic relationship of the olivocerebellar projection pattern is based on previous reports in mice 9 and rats [6][7][8]39,47 . The neurogenic timing of cerebellar PCs in each compartment or module is based on Zhang et al. 11  www.nature.com/scientificreports/ tive analysis of reporter-labeled neurons. In some parts where we needed to newly define subdivisonal boundaries in this study, we assumed the gap or a low density in FoxP2-positive neuron distribution as a boundary between subdivisions of IO. Accordingly, we have proposed some new definitions of IO boundaries. For example, the most lateral "bend" area of the PO has been considered to belong to the dPO. Such proposals are to be validated in terms of the axonal projection pattern in the future. Pcdh10 immunostaining is useful in identifying the rMAO in the present study. Our previous study has shown expression of the pcdh10 gene in the rMAO as well as in neurons in the lateral part of the posterior interpositus nucleus and in PCs in zebrin-positive stripe 4+//5+ 26 . All these three areas are topographically connected through the olivocerebellar and PC projections 26 . Thus, the expression of homophilic cell-adhesion molecule Pcdh10 in the rMAO is rather expectable. However, the Pcdh10 immunostaining signal in the DC or cMAO-C, also expected because of the pcdh10 gene expression 26 , is less strong than in the rMAO.
Cytoarchitectonic studies recognized the lateral and medial arcuate nuclei, special small subdivisions located ventrolateral to the vPO and ventral to the lateral edge of the rMAO, respectively, in the IO of the C57BL/6 mouse strain 43,44 , to which mice of the present study belong. The lateral and medial arcuate nuclei are speculated to be a part of the vPO. Whereas we recognized the lateral arcuate nucleus and included it in the vPO (c.f. Supplementary Figs. 3h, 4j), almost all IO neurons in the rMAO, except for some scattered neurons in the ventral edge (c.f. Supplementary Fig. 3g, h) showed Pcdh10 immunoreactivity surrounding the FoxP2 immunoreactivity. Thus, we could not clearly confirm the medial arcuate nucleus which is supposed to be negative in Pcdh10 expression if it belongs to the vPO.
Possible mechanisms for the relationship between neurogenic timing and olivocerebellar topography. The IO is a well-distinguished structure composed of neurons that give rise to climbing fibers, although a small number of different types of neurons, such as GABAergic neurons, are present inside or near the IO 35,38 . The IO is formed during the period between E13 and P0 in the mouse by the arrival of migrating IO neurons from the lower rhombic lip to the final IO position 20 . Since IO neurons migrate by moving upstream inside the leading axonal path 20 , the topography of the axonal projection and the formation of IO subdivisions seem to be highly linked to each other. How the neurogenic timing of IO neurons is related to these things is the question.
One mechanism to explain the formation of the topographic projection between the origin and target is that their matched neurogenic timing allows newly growing axons to find unoccupied targets in newly growing dendritic arbors 29 . Accordingly, newly generated origin neurons tend to project to newly generated target neurons, as shown in the olfactory bulb projection 29 and the dentate gyrus granule cell projection 30   www.nature.com/scientificreports/ relationship found in the present study in the neurogenic-timing gradients between the origin and the target (Fig. 5) indicates that different mechanisms are involved in the formation of the olivocerebellar topography. In the olivocerebellar projection, axon targeting is guided by various molecules such as homeobox genes and the downstream cell adhesion molecules and attractants/repellents molecules, including Eph/Ephrin molecules and cadherin/protocadherin family molecules [25][26][27]45,46 . We speculate that the reverse neurogenic-timing gradient relationship can be created if the expression of such molecules is controlled partly independently of the neurogenic timing of IO neurons and in PCs.
The results of the present study seem to propose an additional different mechanism for the formation of the topographic connection. In the medial vermis, medial paravermal area in central lobules (simple lobule, crus I, crus II and paramedian lobule) or module A2, and nodulus (lobule X) and flocculus, multiple cortical compartments of different neurogenic timing are innervated by the single or nearby IO subdivisions that have the same neurogenic timing (vertical diversion of arrows in Fig. 5b). Focal secondary differentiation of cortical compartments in these areas may be able to explain the increase in the number of striped cortical areas that contain PCs of different neurogenic timing but are innervated by nearby IO areas. On the contrary, the reverse neurogenic-timing gradient scheme fits with the majority of the cortical compartments or modules (Fig. 5a and three transversal stem arrows in Fig. 5b).
The G2A strain has a genomic BAC transgene in which the tamoxifen-inducible CreER gene has replaced the coding sequence of the neurogenin 2 (Neurog2) gene 31 . This transgene is putatively integrated into the Y chromosome. G2A male mice were mated with C57BL/6N females to obtain the next generation. Genotype was checked in the tail sample by polymerase chain reaction with the primers for the Cre gene (Aki553, TAA AGA TAT CTC ACG TAC TGA CGG TG, and Aki554, TCT CTG ACC AGA GTC ATC CTT AGC ). Since the CreER is expressed in neuronally committed cells under the Neurog2 enhancer 31,32 , Cre recombination activity is induced only in the neurons that finish the last mitosis shortly before the tamoxifen administration. G2A males were mated with H2B homozygous females to produce G2A::H2B double-heterozygous hybrid mice, which were mainly used in the present study. We also produced G2A::AldocV(homozygous) hybrid mice. G2A::AldocV males were mated with H2B homozygous females to produce G2A::H2B::AldocV triple-heterozygous mice, which were used in a part of the present study ( Supplementary Fig. 2).
The H2B strain is a Cre reporter strain that expresses mCherry fluorescent protein fused with the nucleus translocation sequence 34 . In H2B mice, the genotype was checked in the tail sample by polymerase chain reaction with the primers (P3: TCC CTC GTG ATC TGC AAC TCC AGT C, P4: AAC CCC AGA TGA CTA CCT ATC CTC C, and P5: TGT GGA ATG TGT GCG AGG CCA GAG G). H2B mice were maintained by mating homozygotes.
The Ai9 strain is a Cre reporter strain that expresses tdTomato fluorescent protein. The AldocV strain expresses Venus fluorescent protein in place of aldolase C protein 48 . Ai9 homozygous females and Ai9::AldocV hybrid homozygous females were mated with G2A males in our previous study to label PCs in the neurogenic timing-specific way 11 . Some preparations obtained in that study were used in parts of Fig. 3 and Supplementary  Fig. 2.
Histological procedures and immunostaining. The ventral medulla was dissected from the brain and coated with gelatin solution (10% gelatin, 10% sucrose in 10 mM phosphate buffer, 32 ºC). The gelatin block was hardened by chilling and then soaked overnight in a fixative with a high sucrose content (4% paraformaldehyde, 30% sucrose in 0.05 M phosphate buffer, pH 7.4). Complete sets of serial sections were cut coronally using a freezing microtome at a thickness of 40 µm. Sections were mounted on glass slides or rendered to immunostaining as follows. After washing in PBS and PBS with 0.12% Triton X-100 (PBST), each complete set of sections was processed for immunostaining. Floating sections were incubated on a shaker with goat anti-FoxP2 (Everest Biotech EB05226, 1:5000) antibody and a choice of the following antibodies, rabbit anti-FoxP2 (Abcam, ab172320, 1:1000, three cases), and rat anti-protocadherin 10 (Millipore, MABT20, 1:1500, six cases) in PBST plus 2% normal donkey serum for 72 h at 4 °C (Supplementary Table 1). The sections were then incubated with a mixture of appropriate secondary antibodies that were conjugated with fluorescent tags (Supplementary Table 1). Finally, these sections were mounted on glass slides, dried, and coverslipped with a water-soluble mounting medium (CC mount, Sigma C9368-30ML).

Specificity of antibodies.
The goat polyclonal anti-FoxP2 antibody (EB05226, Everest Biotech, Oxfordshire, UK) that was consistently used in the present study produces bands at 22, 32, 84, and 144 kDa in the P4 mouse cerebellum, the P4 mouse whole brain, and the adult mouse cerebellum in our hands 49 . Another mouse anti-FoxP2 antibody (Ab172320, Abcam plc, Cambridge, UK), which was used to check specific labeling, labels bands at 51, 67, 75, and 77 kDa in HEK293 whole cell lysate and Hela whole cell lysate according to the Manufacturer's datasheet. Although the western blot results do not match very well, these two antibodies labeled the same population of neurons in the mouse IO (see "Results"). The rat monoclonal anti-Pcdh10 antibody (MABT20 clone 5G10, Millipore, Billerica, MA) produced a single band of 137 kDa in the P0 mouse cerebellum and P0 mouse whole brain in our western blot 49 . This band disappeared completely in samples from the Pcdh10-KO mouse cerebellum 49 .

Retrograde labeling of IO neurons. We labeled IO neurons retrogradely by localized injection of Alexa
Fluor 546-conjugated dextran amine (AF546DA; D22911, Molecular Probes, Eugene, OR, USA) as described before 26 in Aldoc-Venus mice, in which the cerebellar zebrin stripes are visualized by intrinsic fluorescent protein expression. Briefly, adult heterozygous Aldoc-Venus mice were anesthetized by intraperitoneal medetomidine hydrochloride (0.75 µg/g body weight), midazolam (4.0 µg/g) and butorphanol tartrate (5.0 µg/g). The mouse was placed on a stereotaxic apparatus with the skull fixed at various nose-down rotation angle. A hole was made in the skull. A drop of AF546DA solution (about 10 nl of 10% solution in saline) was injected in various positions in the cerebellar cortex. After a survival period of 5-7 days, mice were sacrificed to dissect the brain as above. Serial coronal sections of 80-µm thickness were cut and mounted in slides. The slides were coverslipped with PBS temporarily to observe under the microscope.
Acquisition of digital images. Multiple-channel fluorescence images were digitized into a 12-bit gray scale using a monochrome CCD camera (AxioCam ICm 1, Zeiss, Oberkochen, Germany) attached to a fluorescent microscope (AxioImager.Z2, Zeiss) with an appropriate filter set. Images of the left and right IO were digitized with a 10× objective and tiling function of the software (Zen 2.6 blue edition, Zeiss, https:// www. zeiss. co. jp/ micro scopy/ produ cts/ micro scope-softw are/ zen. html) in all serial coronal sections in G2A::H2B mouse brains with a tamoxifen injection. Images were adjusted concerning contrast and brightness, with no further digital enhancement, and assembled using software (Zen 2.6; Photoshop-7.0 and Illustrator-10.3, Adobe, San Jose, CA, U.S.A., https:// www. adobe. com/ jp/). Fluorescent signals were shown with pseudo-color in the figures.
Counting the number of IO neurons. Digital image files of serial sections were opened and placed in the working sheet of Adobe Illustrator. Boundaries of the IO subareas were drawn on the image of FoxP2 immunostaining in all individual sections in Adobe Illustrator (cf. Supplementary Fig. 4). When Pcdh10 immunostaining was performed, the labeling pattern was also referred to in identifying boundaries. The number of FoxP2-positive nuclei was counted manually in each IO subdivision in all serial sections. We did not count labeled objects that had apparently different sizes, shapes or qualities from that of the ordinary nuclei of IO neurons. There was the possibility that the IO neurons that were located at the section-cutting plane were counted in two sections. No correction for this error was made in this study. The percentage of reporter-labeled neurons in each IO subdivision was obtained by dividing the number of reporter-labeled neurons by the number of FoxP2positive neurons, which was counted in one mouse (HG03b, www.nature.com/scientificreports/ map-1.0.12 software (https:// cran.r-proje ct. org/ web/ packa ges/ pheat map/ index. html) incorporated into the RStudio-2022.12.0.-353 of R-4.2.2 (https:// posit. co/ downl oad/ rstud io-deskt op/). The total codes we wrote in RStudio were as follows.
getwd() heapmap <-read.csv("heatmap.csv", header=T, row.names = 1) heapmap1 <-as.matrix( heapmap) library(pheatmap) pheatmap(heapmap1, cluster_rows = FALSE, scale = "column") The Heatmap Illustrator function of TBtools-1.112 software 50 (https:// github. com/ CJ-Chen/ TBtoo ls) also produced the same results. For these analyses, we first prepared an Excel or csv matrix table of the percentage of reporter-labeled IO neurons located in IO subareas for all mice of various tamoxifen injection timing. In case of TBtools, by inputting the matrix table data to TBtools software and selecting the scale method "column scale", the data in each column (percentage of labeled IO neurons in each IO subarea) were linearly normalized by subtracting the average and then divided by the standard deviation. Then, the algorithm of the software gave the density map which showed the grouping results among different IO subareas.
To compare the neurogenic timing among different IO subdivisions, we introduced "mean neurogenic timing (MNT)" for each IO subdivision. MNT was obtained by: in which, P(TM9.5) and so on represent the percentage of labeled IO neurons with TM9.5 averaged from all TM9.5 cases and so on.

Data availability
All data supporting the findings of this study are provided in the main text or supplementary information. This study did not generate a novel program code. This study did not generate new unique reagents. Requests for resources, datasets, protocols, and any other additional information should be directed to and will be fulfilled by the corresponding author, Izumi Sugihara (isugihara.phy1@tmd.ac.jp).