Non cell-autonomous role of DCC in the guidance of the corticospinal tract at the midline

DCC, a NETRIN-1 receptor, is considered as a cell-autonomous regulator for midline guidance of many commissural populations in the central nervous system. The corticospinal tract (CST), the principal motor pathway for voluntary movements, crosses the anatomic midline at the pyramidal decussation. CST fails to cross the midline in Kanga mice expressing a truncated DCC protein. Humans with heterozygous DCC mutations have congenital mirror movements (CMM). As CMM has been associated, in some cases, with malformations of the pyramidal decussation, DCC might also be involved in this process in human. Here, we investigated the role of DCC in CST midline crossing both in human and mice. First, we demonstrate by multimodal approaches, that patients with CMM due to DCC mutations have an increased proportion of ipsilateral CST projections. Second, we show that in contrast to Kanga mice, the anatomy of the CST is not altered in mice with a deletion of DCC in the CST. Altogether, these results indicate that DCC controls CST midline crossing in both humans and mice, and that this process is non cell-autonomous in mice. Our data unravel a new level of complexity in the role of DCC in CST guidance at the midline.

The corticospinal tract (CST) is the principal motor pathway for voluntary movements [1][2][3] . Most CST axons cross the midline at the junction between the brainstem and spinal cord, thereby forming the pyramidal decussation. To cross the midline, central nervous system (CNS) axons are guided by molecular cues whose expression, together with that of their receptors, is tightly controlled in time and space during development 4,5 . DCC (Deleted in Colorectal Cancer) is a receptor that mediates the chemoattractive activity of NETRIN-1, thereby modulating the crossing of CNS commissural axons 6 . In Dcc −/− knockout mice, midline crossing by commissural axons is altered at the level of the corpus callosum (CC), anterior commissure, hippocampal commissure 7-9 , habenulo-interpeduncular system 10 , inferior olive 11 , and spinal cord 7,12 . DCC is considered as a cell-autonomous regulator for midline crossing, as many commissural neurons that express DCC fail to cross the midline in Dcc mutants [7][8][9]12 .
The role of DCC in the development of the CST has not been investigated in Dcc −/− knockout mice. Indeed, they die within 24 hours after birth, when the CST crosses the midline and enter the spinal cord. Dcc kanga mice carry a spontaneous and viable Dcc mutation that removes the exon encoding the P3 intracellular domain 8 . The study of Dcc kanga mice provided evidence supporting a role of DCC in the development of the mouse CST. These mice are characterized by a striking "kangaroo-like" hopping gait, and replicate most of the commissural defects observed in Dcc −/− mutants. At the level of the pyramidal decussation, the CST of Kanga mutants does not cross the midline but forms two bundles that remain in the ventral ipsilateral spinal cord 8 . However, DCC has not been detected in brainstem CST axons during normal development 8,13 , raising the possibility that DCC might influence CST midline crossing in a non cell-autonomous manner.
In human, heterozygous mutations in DCC have been identified in families with autosomal-dominant congenital mirror movements (CMM) [14][15][16] . Mirror movements (MM) are involuntary symmetrical movements of one hand that mirror voluntary movements of the other hand. CMM is associated with malformations of the pyramidal decussation, at least in some cases [17][18][19] . Two CMM patients with initially unknown genetic status were eventually found to carry a DCC mutation, years after publication of their neurophysiological data. In these two patients, unilateral transcranial magnetic stimulation (TMS) of the primary motor cortex elicited bilateral motor responses, suggesting the existence of bilateral CST projections to the spinal cord [20][21][22] . However, further neurophysiological and neuroimaging data are needed to validate these results and to clarify to what extent the pyramidal decussation is morphologically and functionally abnormal in DCC-CMM patients.
The aim of the present paper was to study the role of DCC in CST midline crossing in both human and mice: we checked whether the role of DCC in the development of the pyramidal decussation is conserved in human and whether this process is cell-autonomous in mouse. First, we used an optimized multimodal approach to characterize in details the abnormalities of the CST in a group of six DCC-CMM patients. Second, we studied the motor consequences of Dcc mutations in mice. Last, for the first time, we used conditional Dcc mouse mutants to unravel the role of DCC in axon guidance at the midline. We analyzed the anatomy of the CST in various Dcc deficient mouse mutants, including a line with a conditional deletion of DCC in the neocortex (and thus in the CST).

Abnormal ipsilateral corticospinal projections in DCC-CMM patients.
To determine whether DCC is involved in the formation of the pyramidal decussation in humans, we first studied six patients with typical congenital mirror movements due to DCC mutations 14,16 . In these patients, intentional movements of one hand are accompanied by involuntary mirror movements of the other hand (Supplementary Movie 1). The patients had no additional clinical manifestations. We used single-pulse TMS to investigate how neural signals propagate along the CST (Table 1 and Fig. 1). In the healthy controls, stimulation of the cortical representation of hand muscles at rest elicited contralateral responses only (Fig. 1A). In contrast, in the six DCC-CMM patients, unilateral stimulation of the primary motor cortex at rest elicited ipsilateral responses, which were absent in all six controls. This suggested the existence of fast-conducting corticospinal projections from the hand area of the dominant primary motor cortex to motoneurons on the ipsilateral side of the spinal cord in the patients 17,18 . Ipsilateral MEPs were observed in 100% of the pulses in five DCC-CMM patients, and in 65% of the pulses in the remaining patient ( Table 1).
The relative amplitude of the contralateral and ipsilateral MEPs was variable in the DCC-CMM patients. The amplitude of the ipsilateral MEPs was smaller than the normal contralateral MEPs in two of the six patients (Fig. 1B, Table 1) and larger in three of the six patients (Fig. 1C, Table 1), whereas only ipsilateral MEPs were observed in one patient (Fig. 1D, Table 1). This variability in the amplitude of ipsilateral and contralateral MEPs could reflect differences in the relative number of ipsilateral and contralateral CST projections to the spinal cord. In patients #1-5, who had bilateral MEPs, the difference in latency between ipsilateral and contralateral MEPs was less than 1 millisecond (Table 1), which is consistent with the presence of direct corticospinal projections from the dominant hemisphere to the ipsilateral spinal cord. We then used diffusion tensor imaging (DTI) to investigate the CST projections in two patients and two controls (Fig. 2). The results suggested that the controls had more crossed CST fibers than uncrossed CST fibers, whereas the patients had more uncrossed CST fibers than crossed CST fibers (Fig. 2B,C). Together, these findings support the involvement of DCC in the development of the pyramidal decussation in humans, as previously observed in mice. The study of Dcc kanga/− mice highlights the role of DCC in the generation of asymmetric movements. Dcc kanga is a spontaneous mutation that removes the exon encoding the P3 intracellular domain of DCC, resulting in abnormal pyramidal decussation. Dcc kanga/kanga mice present a hopping gait and some of them have ataxia 8 . The human MM and the rodent hopping gait are two conditions characterized by the inability to produce asymmetric movements, but they are not equivalent. Indeed, it was recently shown that left-right alternation during locomotion relies on spinal commissural circuits rather than on proper CST wiring 23,24 . This suggests that the hopping gait is not related to the abnormal anatomy of the CST in Dcc kanga/kanga mice. In order to further characterize the motor phenotype of Dcc kanga mice, we used a battery of motor tests, and in particular the exploratory reaching test recently used to evaluate the role of the CST in motor lateralization [23][24][25] . As we were not able to generate Dcc kanga/kanga mice, Dcc kanga/+ mice were crossed with Dcc +/− mice to obtain Dcc kanga/− mice, in which one allele bears a Kanga mutation and the other is deleted. We therefore compared the performance of Dcc kanga/− mice with control mice (wildtype or Dcc kanga/+ ) with various motor tests. Five of eleven Dcc kanga/− mice had major balance disorders: they were unable to stand on their limbs and therefore moved very little during the open-field test (ANOVA F (2,25) = 33.18, p < 0.001, followed by the Bonferroni post hoc test; Fig. 3B). Because they were unable to perform most of the motor tests, they were excluded from further analysis. Dcc kanga/− mice were lighter than their littermate controls (ANOVA F (2,20) = 6.27, p = 0.008, followed by the Bonferroni post hoc test, Fig. 3A), and therefore did not perform as well as the controls in the muscle strength test ( Fig. 3G). The motor phenotype of Dcc kanga/− mice underlines the importance of DCC in the generation of alternating movements during locomotion, and of voluntary asymmetric forelimb movements. Altogether, our results demonstrate the link between DCC deficiency and the ability to produce asymmetric voluntary movements in both human and mice.

DCC expression in CST axons is not required for midline crossing.
We then investigated whether the CST midline crossing defects of Dcc kanga mice may result from a cell autonomous effect of DCC. This point remains an open question since DCC has not been detected in brainstem CST axons during normal development 8,13 .
To address this issue, we selectively abolished Dcc expression in cortical neurons by using Dcc conditional knockout mice 26 and the Emx1::cre mouse line 27 . Before comparing the CST trajectory in the different mouse lines, we performed various control experiments. We first verified that EMX1 was expressed in corpus callosum (CC) and CST neurons before they crossed the midline (at E17 and P0, respectively) [28][29][30] . Emx1::Cre mice were first crossed with Tau-lox-Stop-lox-mGFP-IRES-nls-lacZ mice (Tau mGFP ), which express a membrane-tethered GFP in axons following Cre-mediated recombination 31 . In E17 Emx1::cre;Tau GFP mice, GFP expression was detected within corpus callosum axons at the midline ( Fig. 4B,C) and at the described location of CST axons ( Fig. 4D-F). At this stage, the CST has not yet reached the pyramidal decussation ( Fig. 4G). After P2, CST axons can be identified by protein kinase C gamma (PKCγ) immunohistochemistry 32,33 . We confirmed that CST axons were GFP-positive by dual immunostaining for GFP and PKCγ at P2 ( Altogether these data demonstrate that EMX1 is expressed in CST neurons before their axons cross the midline and that DCC is lacking in the neocortex (and thus in the CST) of Emx1::cre;Dcc lox/lox mice. We then analyzed the expression of DCC along the CST at P0 (i.e. when pioneer CST axons reach the pyramidal decussation in mice 29, 34 ) on Emx1::cre;Tau GFP mice. DCC was not detected in the CST of Emx1::cre;TauGFP either at the level of the pons (Fig. 6B), in the brainstem (Fig. 6C) or at the pyramidal decussation ( Fig. 6D), in keeping with previous observations 8,13 . Last we showed that, in both Emx1::cre;Tau GFP and Emx1::cre;DCC lox/lox ;Tau GFP mouse lines, DCC was detected in the fasciculus retroflexus (FR, Fig. 6B,C), demonstrating our ability to detect DCC and the fact that the expression of DCC is still present outside the neocortex in Emx1::cre;Dcc lox/lox mice. After validating the tools, we compared the CST anatomy of Emx1::cre;Dcc lox/lox mice with various Dcc deficient mouse lines and their respective controls. Dcc kanga/− mice were compared to Dcc kanga/+ mice. Dcc +/− mice with DCC haploinsufficiency were compared to Dcc +/+ mice. The CST organization was investigated by PKCγ immunostaining and by unilateral BDA injection into the left motor cortex (Fig. 7). In Dcc +/+ control mice (n = 4/4), BDA-labeled CST axons crossed the midline at the pyramidal decussation (Fig. 7B   . DCC is required for asymmetric movements. We used behavioral tests to investigate the motor phenotype of Dcc kanga/− mutant mice. Dcc kanga/− mice (n = 11; black and red) were compared to Dcc +/+ mice or Dcc kanga/+ mice (that behave like wildtype mice, n = 17; gray). Five of the 11 Dcc kanga/− mice displayed marked balance disorders (red): they were unable to stand on their limbs and thus moved very little in the open-field test (ANOVA F (2,25) = 33.18, p < 0.001, followed by the Bonferroni post hoc test; B). Because they were unable to perform most of the motor tests, they were excluded from further analysis. Dcc kanga/− mice were lighter than their littermate controls (ANOVA F (2,20) = 6.27, p = 0.008, followed by the Bonferroni post hoc test; A) and were accordingly weaker in the muscle strength test (Student's test, p forelimbs = 0.228; p hindlimbs = 0.042; C). Dcc kanga/− mice were indistinguishable from controls in the Rotarod test (repeated-measures ANOVA with two factors. F (1,21) = 0.71, p = 0.793, followed by the Bonferroni post hoc test; D). On the treadmill, Dcc kanga/− mice displayed a striking hopping gait, frequently moving both their forelimbs and their hindlimbs simultaneously (Mann-Whitney test, p forelimbs < 0.0001; p hindlimbs < 0.0001; E, E2). In contrast, control mice made alternating movements (E, E1) of their forelimbs and hindlimbs. In the ladder test, Dcc kanga/− mice made more forelimb errors than the controls (Freeman-Halton extension of Fisher's exact test, p = 0.038; F). When placed in a new walled environment, mice have a tendency to establish contacts on the walls with their forelimbs in an asymmetric (G1, control mice) or symmetric (G2, Dcc kanga/− mice) manner. In the reaching test, Dcc kanga/− mice made more symmetric forelimb movements than the controls (Student's test, p < 0.0001; G). Interestingly, the pathway followed by CST axons was normal in Emx1::cre;Dcc lox/lox mice (n = 3/3), in which CST axons crossed the midline at the level of pyramidal decussation and continued their trajectory through the dorsal funiculus of the contralateral spinal cord (Fig. 6J-M,J'-M'). These results demonstrate that DCC deletion in the neocortex (and thus in the CST) is not sufficient to induce abnormal pyramidal decussation. The role of DCC in CST axon guidance at the midline is therefore non cell-autonomous.

Discussion
We demonstrate that DCC deficiency is associated with abnormal CST midline crossing and a reduced ability to generate asymmetric movements in both humans and mice. In addition, we show that selective suppression of DCC expression in the mouse neocortex does not affect the pyramidal decussation, demonstrating that the role of DCC in CST axon guidance at the midline is non cell-autonomous in mice.
Using a combination of TMS and DTI tractography, we obtained evidence that DCC-CMM patients have abnormal CST midline crossing at the level of the pyramidal decussation. Our TMS findings are consistent with those of previous TMS studies of two DCC-CMM patients [20][21][22] . In all six of the DCC-CMM patients studied here, stimulation of the motor cortex hand representation elicited ipsilateral MEPs, whereas in healthy volunteers the MEPs are strictly contralateral to the stimulated hemisphere 18,[35][36][37] . MEPs elicited by stimulation of the motor cortex with TMS result from the transmission of a neuronal signal from the cortex to the peripheral muscles via fast-conducting CST fibers and spinal motoneurons [38][39][40] . Direct connections of CST axons to motoneurons (direct cortico-motoneuronal connections) make a significant contribution to MEPs in humans [41][42][43][44] . In our patients, the presence of ipsilateral MEPs with latencies similar to those of contralateral MEPs indicates direct connections of CST axons from one hemisphere to hand muscle motoneurons on both sides of the spinal cord. These results are corroborated by DTI analysis of two of the DCC-CMM patients, in whom we found more uncrossed CST fibers than crossed CST fibers, contrary to the situation observed in control subjects. Our multimodal study strongly suggests that abnormal CST midline crossing, rather than aberrant CST branching in the spinal cord, is responsible for the abnormal ipsilateral MEPs observed in DCC-CMM patients.   The phenotype severity varies among the six DCC patients, but this phenotypic variation was not linked to the genotype. For example, patients 1 and 6 belong to the same family and have different phenotypes despite carrying the same mutation (Table 1).
In five of the six DCC patients, stimulation of the dominant hemisphere evoked ipsilateral responses in 100% of the pulses. In four of these patients, the amplitude of the ipsilateral MEPs was higher than that of the contralateral MEPs. In a previous study of seven RAD51-CMM patients, we found that the frequency of ipsilateral MEPs was always below 100% and that their amplitude was always smaller than that of normal contralateral MEPs 17 . In patients with X-linked Kallmann syndrome with mirror movements, the relative amplitude of the ipsilateral and contralateral MEPs was variable across individuals 45 . The relative proportion of ipsilateral and contralateral CST projections is likely to be the main determinant of the relative amplitudes of contralateral and ipsilateral MEPs 40,44,45 . In keeping with this hypothesis, DCC-CMM patients would have a majority of ipsilateral CST projections.
We found an absence of pyramidal decussation in Dcc kanga/− mice, as previously described in Dcc kanga/kanga mice 8 . The pyramidal decussation is partial in human DCC-CMM patients, normal in Dcc +/− mice and completely absent in Dcc kanga/− mice. While 95% of CST axons cross the midline in rodents [46][47][48] , this proportion varies between 75% and 90% in humans with important inter-individual differences 1,49,50 . Despite species-related differences regarding the anatomy of the pyramidal decussation, our data suggest a role for DCC in CST guidance at the midline in both mice and humans.
Besides the description of the hopping gait and ataxia 8 , careful investigation of the motor behavior of Dcc kanga/− mice had not been performed. Here, we show that Dcc kanga/− mice exhibit very specific motor impairments, as they generate symmetric movements during stereotypic locomotion (hopping gait) or voluntary symmetric forelimb movements (exploratory reaching behaviors). In Dcc kanga/− mice, DCC deficiency not only impacts on CST and CC development but also affects other DCC-expressing cell populations, such as commissural spinal cord interneurons, that are critical for locomotion 12 . Two recent studies used conditional knockout EphA4 mice to dissect the neuronal circuits responsible for their hopping gait. In Emx1::cre;EphA4 flox/flox mice, conditional EphA4 deletion in the forebrain resulted in normal stereotypic locomotion despite bilateral CST projections to the spinal cord 23,24 . In contrast, specific EphA4 deletion in the spinal cord or in glutamatergic interneurons was sufficient to induce hopping locomotor activity 23 . Together, these results show that stereotypic left-right alternation relies on spinal commissural circuits rather than on proper CST wiring. The exploratory reaching test provides a better behavioral paradigm to properly evaluate the role of the CST in motor lateralization. Emx1::cre;EphA4 flox/flox mice, which have bilateral CST projections to the spinal cord as human CMM patients, exhibit symmetric voluntary movements during this test [23][24][25] . This abnormal symmetrical reaching behavior might thus represent a good equivalent of human MM. Dcc kanga/− mice have a similar motor phenotype despite their complete lack of pyramidal decussation. Mirror movements have not been described in patients with horizontal gaze palsy with progressive scoliosis (ROBO3 mutations), who lack the pyramidal decussation and have a completely uncrossed CST, demonstrating that mirror movements are related to bilateral spinal cord projections arising from a single primary motor cortex 18,51 . By contrast, MM have been reported in one patient with Klippel-Feil syndrome and one patient with CMM both completely lacking the pyramidal decussation, suggesting that the uncrossed CST axons might have an aberrant bilateral branching within the spinal cord 52,53 . Two hypotheses might thus be proposed to explain the discrepancy between the lack of pyramidal decussation and the abnormal symmetrical reaching behavior in Dcc kanga/− mice: (i) bilateral CST projection to the spinal cord might be sufficient but not necessary to induce symmetrical reaching behaviors, or (ii) uncrossed CST axons might branch bilaterally within the spinal cord.
In mice lacking a functional DCC, CST axons fail to cross the midline at the level of the pyramidal decussation. Selective suppression of DCC in the mouse neocortex, and thus in the CST, did not alter CST midline crossing revealing a non cell autonomous effect of DCC on CST. One potential limitation of these findings stems from unresolved issues on the exact nature of the DCC kanga allele. Indeed, the Dcc kanga/kanga seemed to be lethal in our hands whereas the Dcc kanga/− that we used in this study was viable. This might indicate that the DCC kanga allele is more severe than the null allele through a dominant negative effect. However, as described previously 8, 13 , we did not detect DCC in brainstem CST axons during normal development (whereas we detected it on fasciculus retroflexus), suggesting DCC influences CST midline crossing indirectly. Altogether, these results demonstrate that the role of DCC in CST axon guidance at the midline is non cell-autonomous. Very few axon guidance receptors have been reported to have non cell-autonomous functions. The WNT binding receptor Frizzled3 has a non cell-autonomous role in guiding medium spiny neurons in mice, possibly by positioning corridor guidepost cells 54 . In Drosophila, the DCC ortholog Frazzled1 is required for the guidance of retinal cells and longitudinal axons in a non cell-autonomous manner, possibly by controlling Netrin-1 distribution and presentation 55,56 .
Many CNS commissural neurons that express DCC fail to cross the midline in Dcc mutants 6-9, 12, 13 , suggesting a cell-autonomous role for this receptor in this setting. Our work shows for the first time that DCC controls CST midline crossing in a non cell-autonomous manner and unravels a new level of complexity in the role of DCC in axon guidance at the midline.

Material and Methods
Subjects. Six right-handed CMM patients (3 males and 3 females) with documented mutations in the DCC gene 14, 16 (see Table 1) were matched for age, gender and handedness with six healthy volunteers. The severity of mirror movements was evaluated with the Woods and Teuber rating scale 57 . All the participants gave their written informed consent and the protocol was approved by the CPP Ile-de-France 6 (2013-A00616-39). All the experiments were performed according to this protocol. Patients gave their written informed consent for videos appearing in the publication.
Scientific RepoRts | 7: 410 | DOI:10.1038/s41598-017-00514-z Electrophysiological experiments. EMG signals were recorded bilaterally from the first dorsal interosseous (FDI) muscles 17 . Motor evoked potentials (MEPs) induced by single monophasic pulses delivered with a figure-of-eight coil connected to a Magstim 200 (Magstim, Dyfed, UK) were recorded from electromyographic signals. Coil positioning for the stimulation of the FDI muscles in M1 and measurements of the resting motor threshold were previously described 17 . Between 30 and 60 MEPs evoked by calibrated stimulation (1.3x the resting motor threshold) of the dominant hemisphere were recorded bilaterally in the FDI muscles to compare the frequency, latency and amplitude of the normal contralateral MEPs with those of any mirror MEPs recorded in the hand ipsilateral to the stimulation site.
Diffusion images were preprocessed as previously described with MRtrix software 17 . Raw diffusion-weighted data were corrected for motion and geometric distortions secondary to eddy currents by using a registration technique based on the geometric model of distortions 58 . The fiber orientation distribution function (ODF) was estimated by using the constrained spherical deconvolution (CSD) method in MRtrix. The sufficient angular resolution allowed high-order fiber orientation estimation algorithms. The ODF information obtained from CSD was used, with a suitable fiber-tracking algorithm, to infer the connectivity of crossing fibers. We used a probabilistic streamlines algorithm with the entire ODF as a probability density function (ODF threshold = 0.1; step size = 0.2 mm as 1/10 of the voxel size; radius of curvature = 1 mm; up-sampling of DWI data to 1 mm). In the native individual space, we performed seed-to-target analysis in regions of interest defined along the CST 17 . These regions included the anterior bundle of the CST in the upper part of the brainstem, the lower part of the brainstem, and the lateral horn of the spinal cord (see Fig. 2A). We used a probabilistic tractography algorithm: the number of fibers connecting a seed voxel to a target voxel was calculated by sampling one million draws for each fiber connecting the seed to the target. The CST tracts (the normally crossed CST and the abnormally uncrossed CST) were reconstructed for each subject. We analyzed the proportion of crossed versus uncrossed portions of the CST by using a laterality coefficient (NF Crossed − NF Uncrossed)/(NF Crossed + NF Uncrossed), where NF is the number of fibers. Ratios closer to 1 indicate greater crossed than uncrossed CST, whereas ratios closer to −1 indicate greater uncrossed than crossed CST. Animals and genotyping. Dcc 7 , Dcc kanga8 and Dcc lox26 mice, as well as the Emx1::cre 27 and Tau GF31 lines have previously been described and genotyped by PCR. Except for the Dcc kanga line, all the mouse lines were maintained on a C57B/6 J background. Dcc kanga mice arose in a C.AKR-Tgn cog research mouse colony at The Jackson Laboratory, and the Tgn cog mutation has been segregated out of the line 8 . The day of the vaginal plug was E0, and the day of birth was P0. All animal procedures were approved by the Regional Animal Experimentation Ethics Committee C2EA-05 Charles Darwin and the French Ministère de l' éducation nationale de l' enseignement supérieur et de la recherche (project N°01558.03). We strictly performed these approved procedures.
Behavioral study of Dcc deficient mice. All the behavioral studies were performed blindly to the genotype. The tests were performed on male and female mice aged between 8 and 12 weeks. For the first three days, the mice were habituated to being handled by the experimenters in order to limit stress. Mice were then tested with a partial SHIRPA protocol (grasping, clasping and auditory tests were performed, and whisker state was evaluated) in order to rule out major neurological abnormalities.
The open field test was used to evaluate spontaneous activity and locomotion: mice were placed in the center of a 0.25-m 2 arena and allowed to explore freely for 5 minutes. During this time, they were tracked and recorded with a camera fixed above the arena, and the total walking distance was calculated with Topscan software.
The Ladder test apparatus (Locotronic) consists of a 124 cm × 8 cm corridor with a floor composed of 78 bars each 1 cm apart. The mice were made to cross the corridor, and the number of slips of the forelimbs, hindlimbs and tail was automatically detected by 158 infrared captors placed on the corridor walls (sampling frequency 1000 Hz). This test evaluates the precision and coordination of limb positioning.
Treadmill. Mice were placed on a transparent treadmill (14 cm × 6 cm) moving at 12 cm/s. After a short training session, the mice had to run for ten seconds, during which period the positioning of their paws was recorded by a camera fixed under the apparatus. The numbers of symmetric and asymmetric strides were counted after excluding frames in which the mouse was not running.
Rotarod. The accelerating Rotarod (BIOSEB) consists of a horizontal rod 3 cm in diameter, turning on its longitudinal axis. The training phase consisted of walking on the rod at a rotational speed varying from 4 to 40 rpm for one minute. The mice were then subjected to four trials in which the speed of rotation increased gradually from 4 rpm to 40 rpm over 5 min. Time spent on the rod was recorded and averaged for the 4 trials. The test was repeated three days in a row with the same procedure, except that the training session was performed only on the first day.
Grip test. Forepaw muscle strength was measured with a grip test. The mouse was held by the base of its tail and allowed to firmly grab the grid of the device with its forepaws. The mouse was then pulled gently backwards until it released its grip. The peak force (N) in each trial was considered as the grip strength. Four successive measurements were averaged. The same procedure was performed with forepaws and hindpaws at the same time.
Reaching exploratory behavior. When placed in a new environment, as a glass cylinder, mice engage in "reaching" exploratory behavior, in which they contact walls with their forepaws 24 . This contact can be made with the two paws simultaneously (symmetric movement) or independently (asymmetric). Ten reaching movements were recorded with a video camera and then examined frame-by-frame to calculate the numbers of asymmetric and symmetric movements.
Statistical analysis. Data were analyzed with SPSS statistical software version 22.0 (Chicago, Illinois, USA).
The normality of variable distributions and the homogeneity of variance across the groups were assessed with the Kolmogorov-Smirnov and Levene tests, respectively. Variables that failed any of these tests were analyzed with the nonparametric Mann-Whitney test. Variables that passed the normality test were analyzed with ANOVA followed by the Bonferroni post hoc test for multiple comparisons, or with Student's t test when comparing two groups. Paired data were analyzed by repeated-measures ANOVA with two factors, followed by the Bonferroni post hoc test for multiple comparisons. Categorical variables were compared using Pearson's χ 2 test or Fisher's exact test.
Immunohistochemistry. All the immunohistochemistry experiments were performed on at least 3 animals per age and per genotype. For light microscopy, P0-P2 mice were anesthetized on ice and adult mice were anesthetized with sodium pentobarbital (50 mg/kg i.p.). Embryos were fixed by immersion in 4% paraformaldehyde with 0.12 M phosphate buffer pH 7.4, and post-natal mice were perfused through the aorta with 0.12 M phosphate buffer, pH 7.4, containing 4% paraformaldehyde. Tissue preparation and immunostaining were carried out as described in ref. 59, using the following primary antibodies: goat anti-DCC (1/100; Santa Cruz Biotechnology, Santa Cruz, California); rabbit anti-PKCγ (1/100, Santa Cruz) to reveal the CST in mature mice after P2; chicken anti-GFP (1/500, Aveslab) to reveal the CST in both newborn and mature Emx1::cre;Tau mGFP mice ; mouse anti-MBP (1/200, Chemicon, Millipore, Molsheim, France) to reveal corpus callosum in adult mice and rat anti-L1 (1/400, Millipore) to reveal corpus callosum before myelination.
Tracing of the corticospinal tract. Surgery and sample collection. Adult male or female mice were anesthetized with a mixture of ketamine (146 mg/kg) and xylazine (7.4 mg/kg) and placed in a stereotaxic frame. At each injection point, the needle was left in place for 3 min before and after the injection to minimize leakage. After surgery, the wound was cleansed and the skin sutured. Fourteen days following BDA injections, the mice were deeply anesthetized and perfused as described for immunohistochemistry procedure.
Revelation of BDA labeling after cryostat sectioning. The brain and spinal cord were treated as described above for the immunohistochemistry procedure 59 . Coronal sections 30 μm thick through the entire brain and spinal cord were cut on a cryostat. Sections were washed for 15 min in 0.1 M PBS pH 7.3 and incubated for one hour in PBSGT (PBS containing 0.25% Triton-X, 0.2% gelatin) and lysine (0.1 M). The sections were then incubated overnight in streptavidin-complex conjugated to horseradish peroxidase solution (HRP, 1/400, Sigma) in PBSGT. The sections were washed 4 × 10 min in PBST, then incubated for 40 min in 1% DAB solution (3,3′-diaminobenzidine, Sigma-Aldrich) in 0.1 M Tris pH 7.6 containing 0.015% H 2 O 2 . The sections were washed 3 × 5 min in 0.1 M Tris in order to stop the reaction, then dehydrated before mounting in Eukitt (Sigma). Images were acquired with a DMR Leica microscope.
3DISCO clearing and light-sheet imaging. We used the 3DISCO clearing, 3D light-sheet imaging and image processing procedures as previously described 10 .