Multiple Functions of Cerebello-Thalamic Neurons in Learning and Offline Consolidation of a Motor Skill in mice
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eLife Assessment
This study provides evidence that cerebellar projections to the thalamus are required for learning and execution of motor skills in the accelerating rotarod task. This important study adds to a growing body of literature on the interactions between the cerebellum, motor cortex, and basal ganglia during motor learning. The data presentation is generally sound, especially the main observations, with some limitations in describing the statistical methods and a lack of support for two segregated cerebello-thalamic pathways, which is incomplete in supporting the overall claim.
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Abstract
Motor skill learning is a complex and gradual process that involves the cortex and basal ganglia, both crucial for the acquisition and long-term retention of skills. The cerebellum, which rapidly learns to adjust the movement, connects to the motor cortex and the striatum via the ventral and intralaminar thalamus respectively. Here, we evaluated the contribution of cerebellar neurons projecting to these thalamic nuclei in a skilled locomotion task in mice. Using a targeted chemogenetic inhibition that preserves the motor abilities, we found that cerebellar nuclei neurons projecting to the intralaminar thalamus contribute to learning and expression, while cerebellar nuclei neurons projecting to the ventral thalamus contribute to offline consolidation. Asymptotic performance, however, required each type of neurons. Thus, our results show that cerebellar neurons belonging to two parallel cerebello-thalamic pathways play distinct, but complementary, roles functioning on different timescales and both necessary for motor skill learning.
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eLife Assessment
This study provides evidence that cerebellar projections to the thalamus are required for learning and execution of motor skills in the accelerating rotarod task. This important study adds to a growing body of literature on the interactions between the cerebellum, motor cortex, and basal ganglia during motor learning. The data presentation is generally sound, especially the main observations, with some limitations in describing the statistical methods and a lack of support for two segregated cerebello-thalamic pathways, which is incomplete in supporting the overall claim.
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Reviewer #1 (Public review):
This is an interesting manuscript tackling the issue of whether subcircuits of the cerebellum are differentially involved in processes of motor performance, learning, or learning consolidation. The authors focus on cerebellar outputs to the ventrolateral thalamus (VL) and to the centrolateral thalamus (CL), since these thalamic nuclei project to the motor cortex and striatum respectively, and thus might be expected to participate in diverse components of motor control and learning. In mice challenged with an accelerating rotarod, the investigators reduce cerebellar output either broadly, or in projection-specific populations, with CNO targeting DREADD-expressing neurons. They first establish that there are not major control deficits with the treatment regime, finding no differences in basic locomotor …
Reviewer #1 (Public review):
This is an interesting manuscript tackling the issue of whether subcircuits of the cerebellum are differentially involved in processes of motor performance, learning, or learning consolidation. The authors focus on cerebellar outputs to the ventrolateral thalamus (VL) and to the centrolateral thalamus (CL), since these thalamic nuclei project to the motor cortex and striatum respectively, and thus might be expected to participate in diverse components of motor control and learning. In mice challenged with an accelerating rotarod, the investigators reduce cerebellar output either broadly, or in projection-specific populations, with CNO targeting DREADD-expressing neurons. They first establish that there are not major control deficits with the treatment regime, finding no differences in basic locomotor behavior, grid test, and fixed-speed rotarod. This is interpreted to allow them to differentiate control from learning, and their inter-relationships. These manipulations are coupled with chronic electrophysiological recordings targeted to the cerebellar nuclei (CN) to control for the efficacy of the CNO manipulation. I found the manuscript intriguing, offering much food for thought, and am confident that it will influence further work on motor learning consolidation. The issue of motor consolidation supported by the cerebellum is timely and interesting, and the claims are novel. There are some limitations to the data presentation and claims, highlighted below, which, if amended, would improve the manuscript.
(1) Statistical analyses: There is too little information provided about how the Deming regressions, mean points, slopes, and intercepts were compared across conditions. This is important since in the heart of the study when the effects of inactivating CL- vs VL- projecting neurons are being compared to control performance, these statistical methods become paramount. Details of these comparisons and their assumptions should be added to the Methods section. As it stands I barely see information about these tests, and only in the figure legends. I would also like the authors to describe whether there is a criterion for significance in a given correlation to be then compared to another. If I have a weak correlation for a regression model that is non-significant, I would not want to 'compare' that regression to another one since it is already a weak model. The authors should comment on the inclusion criteria for using statistics on regression models.
(2) The introduction makes the claim that the cerebellar feedback to the forebrain and cortex are functionally segregated. I interpreted this to mean that the cerebellar output neurons are known to project to either VL or CL exclusively (i.e. they do not collateralize). I was unaware of this knowledge and could find no support for the claim in the references provided (Proville 2014; Hintzer 2018; Bosan 2013). Either I am confused as to the authors' meaning or the claim is inaccurate. This point is broader however than some confusion about citation. The study assumes that the CN-CL population and CN-VL population are distinct cells, but to my knowledge, this has not been established. It is difficult to make sense of the data if they are entirely the same populations, unless projection topography differs, but in any event, it is critical to clarify this point: are these different cell types from the nuclei?; how has that been rigorously established?; is there overlap? No overlap? Etc. Results should be interpreted in light of the level of this knowledge of the anatomy in the mouse or rat.
(3) It is commendable that the authors perform electrophysiology to validate DREADD/CNO. So many investigators don't bother and I really appreciate these data. Would the authors please show the 'wash' in Figure 1a, so that we can see the recovery of the spiking hash after CNO is cleared from the system? This would provide confidence that the signal is not disappearing for reasons of electrode instability or tissue damage/ other.
(4) I don't think that the "Learning" and "Maintenance" terminology is very helpful and in fact may sow confusion. I would recommend that the authors use a day range " Days 1-3 vs 4-7" or similar, to refer to these epochs. The terminology chosen begs for careful validation, definitions, etc, and seems like it is unlikely uniform across all animals, thus it seems more appropriate to just report it straight, defining the epochs by day. Such original terminology could still be used in the Discussion, with appropriate caveats.
(5) Minor, but, on the top of page 14 in the Results, the text states, "Suggesting the presence of a 'critical period' in the consolidation of the task". I think this is a non-standard use of 'critical period' and should be removed. If kept, the authors must define what they mean specifically and provide sufficient additional analyses to support the idea. As it stands, the point will sow confusion.
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Reviewer #2 (Public review):
Summary:
This study examines the contribution of cerebello-thalamic pathways to motor skill learning and consolidation in an accelerating rotarod task. The authors use chemogenetic silencing to manipulate the activity of cerebellar nuclei neurons projecting to two thalamic subregions that target the motor cortex and striatum. By silencing these pathways during different phases of task acquisition (during the task vs after the task), the authors report valuable findings of the involvement of these cerebellar pathways in learning and consolidation.
Strengths:
The experiments are well-executed. The authors perform multiple controls and careful analysis to solidly rule out any gross motor deficits caused by their cerebellar nuclei manipulation. The finding that cerebellar projections to the thalamus are required …
Reviewer #2 (Public review):
Summary:
This study examines the contribution of cerebello-thalamic pathways to motor skill learning and consolidation in an accelerating rotarod task. The authors use chemogenetic silencing to manipulate the activity of cerebellar nuclei neurons projecting to two thalamic subregions that target the motor cortex and striatum. By silencing these pathways during different phases of task acquisition (during the task vs after the task), the authors report valuable findings of the involvement of these cerebellar pathways in learning and consolidation.
Strengths:
The experiments are well-executed. The authors perform multiple controls and careful analysis to solidly rule out any gross motor deficits caused by their cerebellar nuclei manipulation. The finding that cerebellar projections to the thalamus are required for learning and execution of the accelerating rotarod task adds to a growing body of literature on the interactions between the cerebellum, motor cortex, and basal ganglia during motor learning. The finding that silencing the cerebellar nuclei after a task impairs the consolidation of the learned skill is interesting.
Weaknesses:
While the controls for a lack of gross motor deficit are solid, the data seem to show some motor execution deficit when cerebellar nuclei are silenced during task performance. This deficit could potentially impact learning when cerebellar nuclei are silenced during task acquisition. Separately, I find the support for two separate cerebello-thalamic pathways incomplete. The data presented do not clearly show the two pathways are anatomically parallel. The difference in behavioral deficits caused by manipulating these pathways also appears subtle.
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Reviewer #3 (Public review):
Summary:
Varani et al present important findings regarding the role of distinct cerebellothalamic connections in motor learning and performance. Their key findings are that:
(1) cerebellothalamic connections are important for learning motor skills
(2) cerebellar efferents specifically to the central lateral (CL) thalamus are important for short-term learning
(3) cerebellar efferents specifically to the ventral anterior lateral (VAL) complex are important for offline consolidation of learned skills, and
(4) that once a skill is acquired, cerebellothalamic connections become important for online task performance.The authors went to great lengths to separate effects on motor performance from learning, for the most part successfully. While one could argue about some of the specifics, there is little doubt that …
Reviewer #3 (Public review):
Summary:
Varani et al present important findings regarding the role of distinct cerebellothalamic connections in motor learning and performance. Their key findings are that:
(1) cerebellothalamic connections are important for learning motor skills
(2) cerebellar efferents specifically to the central lateral (CL) thalamus are important for short-term learning
(3) cerebellar efferents specifically to the ventral anterior lateral (VAL) complex are important for offline consolidation of learned skills, and
(4) that once a skill is acquired, cerebellothalamic connections become important for online task performance.The authors went to great lengths to separate effects on motor performance from learning, for the most part successfully. While one could argue about some of the specifics, there is little doubt that the CN-CL and CN-VAL pathways play distinct roles in motor learning and performance. An important next step will be to dissect the downstream mechanisms by which these cerebellothalamic pathways mediate motor learning and adaptation.
Strengths:
(1) The dissociation between online learning through CN-CL and offline consolidation through CN-VAL is convincing.
(2) The ability to tease learning apart from performance using their titrated chemogenetic approach is impressive. In particular, their use of multiple motor assays to demonstrate preserved motor function and balance is an important control.
(3) The evidence supporting the main claims is convincing, with multiple replications of the findings and appropriate controls.
Weaknesses:
(1) Despite the care the authors took to demonstrate that their chemogenetic approach does not impair online performance, there is a trend towards impaired rotarod performance at higher speeds in Supplementary Figure 4f, suggesting that there could be subtle changes in motor performance below the level of detection of their assays.
(2) There is likely some overlap between CN neurons projecting to VAL and CL, somewhat limiting the specificity of their conclusions.
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Author response:
Public Reviews:
Reviewer #1 (Public review):
This is an interesting manuscript tackling the issue of whether subcircuits of the cerebellum are differentially involved in processes of motor performance, learning, or learning consolidation. The authors focus on cerebellar outputs to the ventrolateral thalamus (VL) and to the centrolateral thalamus (CL), since these thalamic nuclei project to the motor cortex and striatum respectively, and thus might be expected to participate in diverse components of motor control and learning. In mice challenged with an accelerating rotarod, the investigators reduce cerebellar output either broadly, or in projection-specific populations, with CNO targeting DREADD-expressing neurons. They first establish that there are not major control deficits with the treatment regime, finding no …
Author response:
Public Reviews:
Reviewer #1 (Public review):
This is an interesting manuscript tackling the issue of whether subcircuits of the cerebellum are differentially involved in processes of motor performance, learning, or learning consolidation. The authors focus on cerebellar outputs to the ventrolateral thalamus (VL) and to the centrolateral thalamus (CL), since these thalamic nuclei project to the motor cortex and striatum respectively, and thus might be expected to participate in diverse components of motor control and learning. In mice challenged with an accelerating rotarod, the investigators reduce cerebellar output either broadly, or in projection-specific populations, with CNO targeting DREADD-expressing neurons. They first establish that there are not major control deficits with the treatment regime, finding no differences in basic locomotor behavior, grid test, and fixed-speed rotarod. This is interpreted to allow them to differentiate control from learning, and their inter-relationships. These manipulations are coupled with chronic electrophysiological recordings targeted to the cerebellar nuclei (CN) to control for the efficacy of the CNO manipulation. I found the manuscript intriguing, offering much food for thought, and am confident that it will influence further work on motor learning consolidation. The issue of motor consolidation supported by the cerebellum is timely and interesting, and the claims are novel. There are some limitations to the data presentation and claims, highlighted below, which, if amended, would improve the manuscript.
We thank the reviewer for the positive comments and insightful critics.
(1.1) Statistical analyses: There is too little information provided about how the Deming regressions, mean points, slopes, and intercepts were compared across conditions. This is important since in the heart of the study when the effects of inactivating CL- vs VL- projecting neurons are being compared to control performance, these statistical methods become paramount. Details of these comparisons and their assumptions should be added to the Methods section. As it stands I barely see information about these tests, and only in the figure legends. I would also like the authors to describe whether there is a criterion for significance in a given correlation to be then compared to another. If I have a weak correlation for a regression model that is non-significant, I would not want to 'compare' that regression to another one since it is already a weak model. The authors should comment on the inclusion criteria for using statistics on regression models.
Currently the Methods indeed explain that groups are compared by testing differences of distributions of residuals of treatment and control groups around the Deming regression of the control groups: “To test if treatments altered the relationship between initial performance vs learning or daily vs overnight learning, we compared the distribution of signed distance to the control Deming regression line between groups.” But this shall indeed be explained in more details.
The performance on a given day depends on a cumulative process, so that the average measure of performance is not fully informative on what is learned or what is changed by a treatment (this is further explained in the text p9-10).The challenge is to deal with the multivariate relationships where initial performance, daily learning, and consolidated learning are interdependent. While in control groups these quantities show linear relationships, this is far less the case in treatment groups; this may indeed be due to the variability of the effect of the treatment (efficacy of viral injections) which adds up to the intrinsic variability in the absence of treatment.
Our choice to see if there is a shift in these relationships following treatments, is to see to which extent treatment points in bivariate comparisons (initial perf x daily learning, daily learning x consolidated learning) are evenly distributed around the control group regression line. We take the presence of a significant difference in the distribution of residuals between the control and treatment group as an indication that the process represented in group is disrupted by the treatment: e.g. if the residuals of the treatment group are lower than those of the control group in the initial performance * daily learning comparison, it indicates that learning is slower (or larger). If the residuals of the treatment group are lower than those of the control group in the daily learning * consolidated learning comparison, it indicates that consolidation is lower. This shall be clarified in a revised version.
(1.2a) The introduction makes the claim that the cerebellar feedback to the forebrain and cortex are functionally segregated. I interpreted this to mean that the cerebellar output neurons are known to project to either VL or CL exclusively (i.e. they do not collateralize). I was unaware of this knowledge and could find no support for the claim in the references provided (Proville 2014; Hintzer 2018; Bosan 2013). Either I am confused as to the authors' meaning or the claim is inaccurate. This point is broader however than some confusion about citation.
The references are not cited in the context of collaterals: “They [basal ganglia and cerebellum] send projections back to the cortex via anatomically and functionally segregated channels, which are relayed by predominantly non-overlapping thalamic regions (Bostan, Dum et al. 2013, Proville, Spolidoro et al. 2014, Hintzen, Pelzer et al. 2018). ” Indeed, the thalamic compartments targeted by the basal ganglia and cerebellum are distinct, and in the Proville 2014, we showed some functional segregation of the cerebello-cortical projections (whisker vs orofacial ascending projections). We do not claim that there is a full segregation of the two pathways, there is indeed some known degree of collateralization (see below).
(1.2b) The study assumes that the CN-CL population and CN-VL population are distinct cells, but to my knowledge, this has not been established. It is difficult to make sense of the data if they are entirely the same populations, unless projection topography differs, but in any event, it is critical to clarify this point: are these different cell types from the nuclei?; how has that been rigorously established?; is there overlap? No overlap? Etc. Results should be interpreted in light of the level of this knowledge of the anatomy in the mouse or rat.
Actually, the study does not assume that CL-projecting and VAL-projecting neurons are entirely separate populations (actually it is known that there is an overlap), but states that inhibition of neurons following retrograde infections from the CL and VAL do not produce identical results.
There is indeed a paragraph devoted to the discussion of this point (middle paragraph p20). “Interestingly, both Dentate and Interposed nuclei contain some neurons with collaterals in both VAL and CL thalamic structures (Aumann and Horne 1996, Sakayori, Kato et al. 2019), suggesting that the effect on learning could be mediated by a combined action on the learning process in the striatum (via the CL thalamus) and in the cortex (via the VAL thalamus). However, consistent with (Sakayori, Kato et al. 2019), we found that the manipulations of cerebellar neurons retrogradely targeted either from the CL or from the VAL produced different effects in the task. This indicates that either the distinct functional roles of VAL-projecting of CL-projecting neurons reported in our study is carried by a subset of pathway-specific neurons without collaterals, or that our retrograde infections in VAL and CL preferentially targeted different cerebello-thalamic populations even if these populations had axon terminals in both thalamic regions.”. In other words, we actually know from the literature that there is a degree of collateralization (CN neurons projecting to both VAL and CL, see refs cited above), but as the reviewer says, it does not seem logically possible that the exact same population would have different effects, which are very distinct during the first learning days. The only possible explanation is the CN-CL and CN-VAL retrograde infections recruit somewhat different populations of neurons. This could be due to differences in density of collaterals in CL and VAL of neurons with collaterals in both regions, or presence of CL-projecting neurons without collaterals in VAL, and VAL-projecting neurons without collaterals in CL in addition to the (established) population of neurons with collaterals in both regions. The lesional approach of CN-thalamus neurons in Sakayori et al. 2019 also observed separate effects for CL and VL injections consistent with the differential recruitment of CN populations by retrograde infections.
This should be improved in a revised version of the manuscript.
(1.3) It is commendable that the authors perform electrophysiology to validate DREADD/CNO. So many investigators don't bother and I really appreciate these data. Would the authors please show the 'wash' in Figure 1a, so that we can see the recovery of the spiking hash after CNO is cleared from the system? This would provide confidence that the signal is not disappearing for reasons of electrode instability or tissue damage/ other.
We do not have the wash data on the same day, but there is no significant change in the baseline firing rate across recording days.
(1.4) I don't think that the "Learning" and "Maintenance" terminology is very helpful and in fact may sow confusion. I would recommend that the authors use a day range " Days 1-3 vs 4-7" or similar, to refer to these epochs. The terminology chosen begs for careful validation, definitions, etc, and seems like it is unlikely uniform across all animals, thus it seems more appropriate to just report it straight, defining the epochs by day. Such original terminology could still be used in the Discussion, with appropriate caveats.
This shall be indeed corrected in a revised version.
(1.5) Minor, but, on the top of page 14 in the Results, the text states, "Suggesting the presence of a 'critical period' in the consolidation of the task". I think this is a non-standard use of 'critical period' and should be removed. If kept, the authors must define what they mean specifically and provide sufficient additional analyses to support the idea. As it stands, the point will sow confusion.
This shall be indeed corrected in a revised version
Reviewer #2 (Public review):
Summary:
This study examines the contribution of cerebello-thalamic pathways to motor skill learning and consolidation in an accelerating rotarod task. The authors use chemogenetic silencing to manipulate the activity of cerebellar nuclei neurons projecting to two thalamic subregions that target the motor cortex and striatum. By silencing these pathways during different phases of task acquisition (during the task vs after the task), the authors report valuable findings of the involvement of these cerebellar pathways in learning and consolidation.
Strengths:
The experiments are well-executed. The authors perform multiple controls and careful analysis to solidly rule out any gross motor deficits caused by their cerebellar nuclei manipulation. The finding that cerebellar projections to the thalamus are required for learning and execution of the accelerating rotarod task adds to a growing body of literature on the interactions between the cerebellum, motor cortex, and basal ganglia during motor learning. The finding that silencing the cerebellar nuclei after a task impairs the consolidation of the learned skill is interesting.
We thank the reviewer for the positive comments and insightful critics below.
Weaknesses:
(2.1) While the controls for a lack of gross motor deficit are solid, the data seem to show some motor execution deficit when cerebellar nuclei are silenced during task performance. This deficit could potentially impact learning when cerebellar nuclei are silenced during task acquisition.
One of our key controls are the tests of the treatment on fixed speed rotarod, which provides the closest conditions to the ones found in the accelerating rotarod (the main difference between the protocols being the slow steady acceleration of rod rotation [+0.12 rpm per s]- in the accelerating version).
In the CN experiments, we found clear deficits in learning and consolidation while there was no effect on the fixed speed rotarod (performance of the DREAD-CNO are even slightly better than some control groups), consistent with a separation of the effect on learning/consolidation from those on locomotion on a rotarod. However, small but measurable deficits are found at the highest speed in the fixed speed rotarod in the CN-VAL group; there was no significant effect in the CN-CL group, while the CN-CL actually shows lower performances from the second day of learning; we believe this supports our claim that the CN-CL inhibition impacted more the learning process than the motor coordination. In contrast the CN-VAL group only showed significantly lower performance on day 4 of the accelerating rotarod consistent with intact learning abilities. Of note, under CNO, CN-VAL mice could stay for more than a minute and half at 20rpm, while on average they fell from the accelerating rotarod as soon as the rotarod reached the speed of ~19rpm (130s).
The text currently states “The inhibition of CN-VAL neurons during the task also yielded lower levels of performance in the Maintenance stage,[[NB: day 5-7]] suggesting that these neurons contribute also to learning and retrieval of motor skills, although the mild defect in fixed speed rotarod could indicate the presence of a locomotor deficit, only visible at high speed.” Following the reviewers’ comment, we shall however revise the sentence above in the revised version of the MS to say that we cannot fully disambiguate the execution / learning-retrieval effect at high speed for these mice.
(2.2a) Separately, I find the support for two separate cerebello-thalamic pathways incomplete. The data presented do not clearly show the two pathways are anatomically parallel.
As explained above (point 1.2a), it is already known that these pathways overlap to some degree (discussion p 20), but yet their targeting differentially affects the behavior, consistent with separate contributions. A similar finding was observed for a lesional (irreversible) approach in Sakayori et al. 2019.
(2.2b) The difference in behavioral deficits caused by manipulating these pathways also appears subtle.
While we agree that after 3-4 days of learning the difference of performance between the groups becomes elusive, we respectfully disagree with the reviewer that in the early stages these differences are negligible and the impact of inhibition on "learning rate" (ie. amount of learning for a given daily initial performance) and consolidation (i.e. overnight retention of daily gain of performance) exhibit different profiles for the two groups (fig 3h vs 3k).
Reviewer #3 (Public review)
Summary:
Varani et al present important findings regarding the role of distinct cerebellothalamic connections in motor learning and performance. Their key findings are that:
(1) cerebellothalamic connections are important for learning motor skills
(2) cerebellar efferents specifically to the central lateral (CL) thalamus are important for short-term learning
(3) cerebellar efferents specifically to the ventral anterior lateral (VAL) complex are important for offline consolidation of learned skills, and
(4) that once a skill is acquired, cerebellothalamic connections become important for online task performance.
The authors went to great lengths to separate effects on motor performance from learning, for the most part successfully. While one could argue about some of the specifics, there is little doubt that the CN-CL and CN-VAL pathways play distinct roles in motor learning and performance. An important next step will be to dissect the downstream mechanisms by which these cerebellothalamic pathways mediate motor learning and adaptation.
Strengths:
(1) The dissociation between online learning through CN-CL and offline consolidation through CN-VAL is convincing.
(2) The ability to tease learning apart from performance using their titrated chemogenetic approach is impressive. In particular, their use of multiple motor assays to demonstrate preserved motor function and balance is an important control.
(3) The evidence supporting the main claims is convincing, with multiple replications of the findings and appropriate controls.
We thank the reviewer for the positive comments and insightful critics below.
Weaknesses:
(3.1) Despite the care the authors took to demonstrate that their chemogenetic approach does not impair online performance, there is a trend towards impaired rotarod performance at higher speeds in Supplementary Figure 4f, suggesting that there could be subtle changes in motor performance below the level of detection of their assays.
This is also discussed in point 2.1 above. In our view, the fixed speed rotarod is a control very close to the accelerating rotarod condition, with very similar requirements between the two tasks (yet unfortunately rarely tested in accelerating rotarod studies). We do not exclude the presence of motor deficits, but the main argument is that these do not suffice to explain the differences observed in the accelerating rotarod. No detectable deficit was found in the CN group while very clear deficits in learning/consolidation were observed. A mild deficit is only significant in the CN-VAL group, while the deficit is not significant in the fixed-speed rotarod for the CN-CL group which shows the strongest deficit in accelerating rotarod during the first days: e.g. on day 2, the CN-CL group is already below the control group with latencies to fall ~100s (corresponding to immediate fall at ~15rpm) while the fixed speed rotarod performances at 15s of the control and CNO-treated groups show an ability to stay more than 1 min at this speed. The text shall be improved to clarify this point.
(3.2) There is likely some overlap between CN neurons projecting to VAL and CL, somewhat limiting the specificity of their conclusions.
There is indeed published evidence for some degree of anatomical overlap, but also for some differential contribution of CN-VAL and CN-CL to the task. The answer to this point is developed in the points 1.2a 2.2a above. Although this point was exposed in the discussion (p20), the text shall be improved in a revised version of the MS to clarify our statement.
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