Reviewer #3 (Public Review):
The work provides direct evidence for the coherent activity of head-direction (HD) cells in the anterior thalamus and retrosplenial cortex (RSC). RSC is one of two major direct cortical recipients of the subcortical HD signal, the other being the postsubiculum (POS). While it is established that POS inherits its HD tuning from ADN (Peyrache et al, 2015), it is not known whether HD cells in RSC show similar coordination with ADN. The manuscript employs technically challenging dual electrophysiological recordings from ADN and RSC to establish that the local internal representations of HD encoded in ADN and RSC are coherent during free exploration but also show coordinated realignment after cue rotation as well as coordinated drift in darkness. The work thus provides evidence that HD and RSC assemblies represent the same internal heading direction, at least in the behavioural paradigms tested and at the investigated temporal resolution. The manuscript also makes a claim that the RSC is unlikely to mediate the realignment of the HD signal following cue rotation because the HD signal realigns itself synchronously across the two brain regions. This claim is additionally supported by the sparse anatomical projection and the paucity of putative direct synaptic connections from RSC to ADN.
The manuscript convincingly demonstrates overall ADN-RSC coordination in two different paradigms. While such coordination is expected in instances when HD representations in both areas are precisely aligned with the current HD, it may not be the case in instances of sensory conflict or limited sensory information. The fact that internal HD in both ADN and RSC drifts coherently in darkness provides strong evidence of the tight functional coupling between the two areas. Additionally, while the cue rotation paradigm used in the study often failed to elicit the full realignment of the HD signal, this variability was certainly utilized to the manuscript's advantage as it makes the coupling evident even when the HD signal realigns only partially. The overall conclusions of the manuscript are largely supported by the presented data but the strength of the argument, especially with regard to the zero-lag coupling between ADN and RSC, is somewhat affected by the technical limitations.
1) The manuscript relies heavily on supervised decoding of the internal HD from population activity in RSC and ADN and in turn suffers from relatively low numbers of simultaneously recorded neurons, which is especially evident in the representative images in Figure 2C. The reported average decoding errors are much higher than those reported elsewhere (Peyrache et al, 2015; Viejo et al, 2018; Xu et al, 2019), which may occlude the effects of RSC activity on ADN that are more subtle and/or occur at shorter timescales than the bin size used in the decoding algorithm. The manuscript includes no discussion of how much these factors could contribute to the observed variability in the data.
2) RSC-HD cells recorded in the study are relatively poorly tuned to HD, which is contrary to the reports of HD cells recorded in RSC (Lozano et al, 2017; Javob et al, 2017; Keshavarzi et al, 2021). In fact, the median directional information score for RSC-HD cells is the same as that for non-HD cells in ADN (Supplementary Figure 2B). In fact, due to their relatively low HD modulation, it may be more appropriate to refer to them as 'HD-modulated' cells. While the electrode positions indicate that RSC was sampled across layers and sub-regions so missing the HD cell 'hot spots' like granular RSCb is unlikely, the apparent poor directional tuning of RSC cells could possibly be due to the nature of the recording environment (e.g. low light condition with the LED landmark being the only light source). Importantly, the manuscript lacks a control 'baseline' condition in which HD cells are recorded in a standard, well-lit open field, as well as a discussion of the discrepancy between the observed HD tuning and that reported in the literature.
3) Analysis of decoding error, which features prominently in the manuscript, is critically dependent on the quality of behavioural tracking - errors in tracking could lead to the accumulation of decoding errors and this could dominate decoding error analyses. Indeed, Figure 2A shows many gaps in the tracked HD of the mouse, which may point to the sub-optimal quality of the behavioural tracking. This is especially important for analyses like the one in Figure 2D which shows that internal HD representations in ADN and RSC are coordinated at zero lag (+/- 20ms). The observed zero-lag peak could be instead explained by errors in behavioural tracking dominating the analysis, which would affect both representations simultaneously and show spurious zero-lag positive correlations. As such, the analysis that is missing is the difference between internal HD decoded from ADN and RSC at different time lags, without reference to the HD tracked behaviourally.
4) The work often uses a number of trials as their 'n' sample size for statistical analyses and the methods state that tetrodes were regularly advanced, but there is no indication of whether multiple trials at the same tetrode position were included in the same statistical comparison (except for recordings '4 days apart' for the HD tuning and synaptic connectivity analyses). Multiple trials with a high likelihood of recording the same cell population should not be counted as separate samples when calculating statistical significance.

Screen capture from the movie