# The postsubiculum as a head-direction cortex

Adrian J Duszkiewicz, Desdemona Fricker, Andrea Burgalossi, Adrien Peyrache

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Adrian J Duszkiewicz, Desdemona Fricker, Andrea Burgalossi, Adrien Peyrache. The postsubiculum as a head-direction cortex. Trends in Neurosciences, 2025, 48 (11), pp.829-840. 10.1016/j.tins.2025.09.004. hal-05377294

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1 The postsubiculum as a head-direction cortex

2
3 Adrian J. Duszkiewicz¹, ‡, Desdemona Fricker², Andrea Burgalossi³,⁴, Adrien Peyrache⁵

5
6
7 ²CNRS UMR 8003, Saints-Pères Paris Institute for the Neurosciences, Université Paris
8 Cité, Paris, France

9
³Institute of Neurobiology, University of Tübingen, Tübingen, Germany

10 ⁴Werner-Reichardt Centre for Integrative Neuroscience, Tübingen, Germany

11 ⁵Montreal Neurological Institute and Hospital, McGill University, Montreal, Quebec,
12 Canada

13 ‡Present address: Division of Neuroscience, School of Biological Sciences, University of
14 Manchester, Manchester, UK

15
16 Correspondence: adrien.peyrache@mcgill.ca (Adrien Peyrache), ajd11@stir.ac.uk
17 (Adrian J. Duszkiewicz)

18
19 Abstract

20 The organization of thalamocortical modules follows a conserved structure. Traditionally,
21 these are divided into primary sensory systems that receive subcortical sensory signals,
22 and higher-order systems, driven predominantly by cortical activity. The rodent head-
23 direction system - the neural 'compass' and a key input to the hippocampal formation -
24 encodes orientation in the horizontal plane through a thalamocortical loop linking the
25 anterodorsal thalamic nucleus and the postsubiculum. Here, we argue that this circuit
26 shares several hallmark features with canonical primary sensory systems, including a
27 driver thalamic input, specific laminar targeting, and receptive field transformations.
28 Drawing on recent anatomical and physiological studies in rodents, we propose that the
29 postsubiculum functions as a primary cortex for the head-direction signal.
30 **Keywords**

31 Thalamocortical networks; spatial navigation; presubiculum; learning and memory; brain
32 states; sensory systems

33

34

35 **A sensory perspective on the head-direction system**

36 The idea of five canonical senses - sight, smell, taste, hearing, and touch - is deeply
37 embedded in both popular and scientific thought. The neuronal pathways underlying
38 these senses in mammals, from peripheral receptors to thalamocortical networks, are
39 relatively well described and, despite processing distinct types of input, share common
40 organizational features [1]. Whether such features are exclusive to the classical sensory
41 systems or also extend to pathways outside of traditional sensory modalities remains an
42 open question.

43 In this Opinion article, we focus on the rodent head-direction system, a circuit that
44 encodes the **head-direction signal** (see Glossary). This neural ‘compass’ is often
45 conceptualized as an internal representation of the horizontal orientation of an animal’s
46 head [2] in the **allocentric reference frame**, although three-dimensional representations
47 have been examined as well (see [3]). It emerges from the combined activity of
48 directionally tuned neurons, termed ‘head-direction cells’ [4]. The thalamocortical loop
49 between the anterodorsal thalamic nucleus and the postsubiculum (dorsal presubiculum)
50 forms a backbone of the head-direction system and exhibits key structural and functional
51 similarities with canonical primary sensory pathways: stereotyped connectivity between
52 the first-order thalamic nucleus and the cortical recipient area [5,6], widespread tuning to
53 a single sensory-derived variable [7–9] and a progressive transformation of the signal
54 along the pathway [10]. We thus argue that, despite its anatomical location among the
55 parahippocampal regions, the postsubiculum is best conceptualized as a primary cortex
56 for the head-direction signal. Finally, we discuss evidence that, beyond encoding of
57 current orientation, this thalamocortical system may also support memory-related
58 processing across wakefulness and sleep.
59 Sensory origin of the head-direction signal

60 Anatomical location of the postsubiculum implies a close relationship with the spatial
61 navigation systems: it is wedged between the subiculum, the main output of the
62 hippocampus proper, and the retrosplenial cortex, a midline associative cortex strongly
63 coupled with the hippocampal formation [11]. However, while the main behavioural
64 correlate of cell activity in the postsubiculum, the direction currently faced by the animal,
65 relates to allocentric space, it is largely of sensory origin. The signal is generated by the
66 circuitry spanning the dorsal tegmental nucleus in the brainstem and the lateral
67 mammillary nucleus, where the angular velocity of head turns is integrated in time to give
68 rise to directional receptive fields [12,13]. These vestibular signals are relayed to the
69 brainstem from the inner ear and are the critical sensory input driving head-direction
70 tuning [14].

71 Still, relying on vestibular inputs alone can lead to accumulation of drift with respect to the
72 allocentric reference frame. Thus, other sensory modalities, primarily vision [15] as well
73 as stereo-olfaction [16,17] and perhaps also somatosensation [18] serve to anchor the
74 head-direction signal to the external world. These modalities likely influence the head-
75 direction signal in a top-down manner via cortical inputs to the postsubiculum [19,20].

76 Two types of visual cues play a role in the stabilization of the head-direction signal: visual
77 flow, which provides continuous information about self-motion relative to the environment
78 [21], and visual landmarks, which provide reference points that anchor the head-direction
79 signal to the external world [22]. This anchoring of head-direction cell receptive fields to
80 the allocentric reference frame via external landmarks is exceptionally stable and may
81 remain unchanged in a given environment for as long as several months [23]. Conflicts
82 between individual landmarks do not appear to be resolved in a winner-take-all fashion,
83 but through weighted integration of cues according to their reliability [24,22]. Still, since
84 visual landmarks are usually not infinitely distant, they cannot serve as a perfect
85 anchoring point for the allocentric reference frame due to parallax. However, a recent
86 preprint study in mice shows that the head-direction system can partially attenuate such
87 errors through vestibular integration and by averaging across multiple visual landmarks
88 [25].
While activity in canonical sensory systems generally follows stimulus onset, head-direction cells show a progressive shift from **anticipatory firing** upstream of the postsubiculum to coding for the present head-direction in the postsubiculum itself [26]. Still, anticipatory firing in thalamic head-direction cells persists even during passive rotation [27] indicating that this phenomenon may be caused by cell-autonomous processes like spike frequency adaptation [28] rather than constitute genuine predictive coding.

96

## Thalamocortical organization of the head-direction system

The input-output structure of the thalamocortical head-direction circuit resembles that of the neocortical sensory systems (Figure 1A). The anatomical borders of the postsubiculum are outlined by dense innervation from the anterodorsal thalamic nucleus [6,29]. Although the anterodorsal nucleus, situated far from the canonical sensory thalamus, has traditionally been grouped with the anterior thalamic **higher-order nuclei**, recent mouse studies indicate that it is transcriptionally quite distinct from them [30,31]. While its transcriptional profile is also unlike that of the canonical sensory nuclei [31], the physiological characteristics of its afferent connections are similar to those of a **first-order nucleus** [1], with a strong subcortical driver input from the lateral mammillary nucleus and a weak cortical modulatory input [5]. Lesioning the upstream lateral mammillary nucleus in rats not only abolishes head-direction tuning in the anterodorsal nucleus but also strongly decreases firing rates of its cells [13], confirming the driver nature of this subcortical input.

Postsubiculum itself is a transitional cortical region with six layers, although the border between deep layers is not well-defined. As in other cortices, laminar localization of neurons in the postsubiculum corresponds to projection-specific subpopulations, reflecting distinct input/output channels [32]. While in canonical sensory systems inputs from first-order thalamic nuclei target layer 4 [33], in the postsubiculum thalamocortical axons from the anterodorsal nucleus target mainly layer 3 [34]. This thalamorecipient layer, like all superficial layers of the postsubiculum, shows unusually sparse excitatory connectivity [29,35]. Layer 3 is also postsubiculum's main cortico-cortical output: its small
pyramidal neurons project to the higher-order association cortices involved in spatial navigation, notably the medial entorhinal cortex [36]. Axons from the anterodorsal nucleus also send a projection to layer 1 (see Box 1) but avoid other layers [29,34,36–38]. At the border between superficial and deep layers, a thin sheet of large pyramidal neurons forms layer 4, providing feedback to the lateral mammillary nucleus [32,39]. This projection has been hypothesized to convey the visual landmark-related anchoring signal back to the subcortical regions that generate the head-direction signal [40], but to the best of our knowledge, this role has not yet been experimentally confirmed. Such subcortical feedback is absent in the primary visual cortex (V1) and primary somatosensory cortex (S1), but prominent in the primary auditory cortex (A1) [41]. The thalamocortical loop of the head-direction circuit is closed via the corticothalamic inputs from neurons in layers 5/6 of the postsubiculum back to the anterodorsal thalamic nucleus, chiefly via the inhibitory thalamic reticular nucleus [32,39,42]. Overall, the pattern of connectivity between the anterodorsal thalamic nucleus and the postsubiculum shares notable similarities with the connectivity in canonical sensory circuits [43,44].
<figure><img src="image_2.png" /><figcaption>Figure 1. Comparison of connectivity and neuronal tuning transformations in the head-direction circuit and canonical thalamocortical sensory systems. (A) Primary sensory thalamocortical systems are composed of a first-order thalamic nucleus (red) and a higher-order relay thalamic nucleus (blue), which project to specific layers in the corresponding primary cortical regions [45]. In primary sensory cortices, driver input from</figcaption></figure>

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139
140 the first order thalamic nucleus arrives mainly in layer 4. Deep layer (layer 5/6) cortical
141 neurons send a modulatory (weak and slow) feedback to the first order thalamic nucleus
142 and a driving (strong and fast) input to the higher-order thalamic nucleus [45].
143 Thalamocortical and corticothalamic axons make collaterals in the thalamic reticular
144 nucleus, which is also reciprocally connected with the thalamus. Thalamocortical head-
145 direction circuit shows a similar connectivity pattern [7,21,34,37], with layer 3 receiving
146 the main driver input from the anterodorsal thalamic nucleus.

147 (B) In the sensory systems, neuronal tuning undergoes various transformations from the
148 thalamus to the cortex. Cortical excitatory neurons (grey) tend to have different tuning
149 properties than neurons in the upstream first-order thalamic nucleus (red) [46,47].
150 Parvalbumin-expressing (PV+) fast-spiking inhibitory neurons, the most common type of
151 cortical interneurons (purple), are typically broadly tuned [46,48]. Similar tuning
152 differences across cell classes are apparent in the thalamocortical head-direction circuit
153 [10]. Abbreviations: TRN, thalamic reticular nucleus; V1, primary visual cortex; dLGN,
154 dorsal lateral genicular nucleus; LP, lateral posterior nucleus; S1, primary somatosensory
155 cortex; VB, ventrobasal complex; POm, posteromedial complex; A1, primary auditory
156 cortex; vMGB, ventral medial geniculate body; dMGB, dorsal medial geniculate body;
157 PoSub, postsubiculum; AD, anterodorsal nucleus; LD, laterodorsal nucleus; cpd, cycles
158 per degree. Panel A is adapted, in part, from [45].

159
160 Head-direction is the primary behavioural correlate in the postsubiculum

161 In both mice and rats allocentric direction of the head is the dominant behavioural
162 correlate within the thalamocortical head-direction circuit [9,10,49,50]. This is in contrast
163 to other cortical areas which contain head-direction cells, like the retrosplenial [51] and
164 medial entorhinal cortex [52]. Even though these cortical regions do receive sparse direct
165 inputs from the anterodorsal thalamic nucleus [53,54], canonical head-direction cells
166 recorded there are intermingled with other functional cell types.

167 Neurons in all first-order thalamic nuclei show widespread tuning to the same sensory
168 modality as their cortical targets and the anterodorsal nucleus is no exception [9,10,55].
169 Still, head-direction tuning curves in the postsubiculum tend to be narrower than those in
170 the anterodorsal thalamus [10]. While such transformations of thalamic driver inputs are
171 a shared feature of canonical primary sensory cortices [44], each cortical network
172 processes the incoming sensory signals in an idiosyncratic manner (Figure 1B). For
173 instance, excitatory neurons in rat S1 barrel cortex show more selectivity for individual
174 whiskers than their thalamocortical input neurons but have less selectivity for individual
175 directions of whisker deflection [46], indicating both refinement and convergence of
176 thalamic signals. Other examples include refinement of orientation selectivity in mouse
177 V1 [47] and population-level refinement of tuning to sound frequency in mouse A1 [56].
178 Narrowing of head-direction receptive fields in the postsubiculum matches this overall
179 pattern and suggests a degree of local processing within this circuit.

180 In contrast to principal cells, tuning of inhibitory interneurons is highly heterogenous in all
181 primary cortices [48,57-59]. This includes the postsubiculum, where head-direction
182 tuning curves of interneurons are often multipolar [10,60]. These inhibitory head-direction-
183 tuned cells share properties with canonical excitatory head-direction cells: their tuning is
184 stable and is anchored to the external world via visual inputs. While computational models
185 based on anatomical features suggest that inhibitory head-direction tuning could originate
186 from patterned thalamic inputs [61], analytical decomposition of inhibitory tuning curves
187 indicates that this tuning may be inherited from narrowly tuned excitatory cells in the
188 postsubiculum rather than from considerably broader-tuned anterodorsal thalamic
189 neurons [10].

190 While principal cells in the thalamocortical head-direction circuit primarily encode head-
191 direction, studies in rodents uncovered other, less prevalent correlates of neural activity
192 within the postsubiculum. Some postsubicular cells are conjunctively tuned to angular
193 head velocity [62] which may arise from local circuit computation [6,34] or, as in case of
194 the retrosplenial cortex [51], may be vestibular in origin. In addition, a subset of
195 postsubicular head-direction cells in mice conjunctively code for egocentric direction [49],
196 which may be inherited from the retrosplenial cortex [63]. It has also been argued that a
197 subset of cells in postsubiculum show spatial modulation [64]. Interestingly, tuning to
198 spatial variables is also present in canonical sensory cortices [65-68]. Finally, and
perhaps most intriguingly, head-direction cells in the mouse postsubiculum increase their firing rates when the animal is facing a visual landmark [69]. This visual modulation may be a hallmark of the mechanism that anchors the head-direction signal to the external world.

## Specialised functions of canonical microcircuits

Despite being an evolutionarily ancient cortical structure, microcircuit organization of the postsubiculum is not unlike that of neocortical areas, including those processing subcortical sensory information. Connectivity within the postsubiculum appears tailored to its role in anchoring of the subcortically-generated head-direction signal to the external world using top-down visual information (Figure 2A) [40]. In mice, thalamic driver inputs carrying the head-direction signal from the anterodorsal nucleus and top-down inputs from the retrosplenial cortex converge on the same layer 3 pyramidal cells (Figure 2B) [38]. These two input streams may target the same neuronal domains or branches, or compartmentalize, such that retrosplenial axons contact the apical dendrites, while thalamic axon terminals synapse onto the basal dendrites. As in S1 layer 5 neurons, the subcellular spatial arrangement of synapses allows for a range of dendritic integration mechanisms [70,71], including supralinear summation of inputs. Concurrent arrival of these two input streams onto individual layer 3 cells may match the head-direction signal from the anterior thalamus with visual landmark information from the retrosplenial cortex [38,72], and thus prevent the head-direction signal from accumulating drift with respect to the allocentric reference frame. It is unclear yet whether such coincident excitation triggers associative plasticity mechanisms in layer 3 neurons. In contrast, layer 4 neurons projecting upstream to the lateral mammillary nucleus receive little thalamic excitation directly, but they become recruited following the activation of layer 3 neurons [38], possibly to ensure that the head-direction signal is stabilized even at the subcortical stage [40].

While most excitatory neurons in rodent postsubiculum are well-tuned to the animal's head-direction [10], calbindin-positive (Calb+) neurons residing in layer 2 (see Box 1) are a notable exception [36,37]. Based on their connectivity with the laterodorsal nucleus,
229 Calb⁺ neurons might be involved in the processing of incoming visual flow information
230 used to stabilize the head-direction signal [21]. Calb⁺ cells do not seem to be
231 monosynaptically connected to head-direction neurons but in mice their activation
232 induces polysynaptic feedback inhibition in head-direction cells (Figure 2B) [37].
233 Interestingly, in mice periods of reorientation are associated with a drop in the overall gain
234 in the head-direction network [9], which raises a possibility that Calb⁺ cells take part in the
235 reorientation process by lowering the activity across the head-direction cell population in
236 response to particular visual inputs.

237 Across sensory cortices, inhibitory interneurons play diverse roles related to the gating
238 and processing of sensory signals [73,74]. For instance, cortical parvalbumin-expressing
239 (PV⁺) fast-spiking interneurons respond directly and precisely to thalamic driver inputs.
240 They help define the dynamic range of sensory responses [75,76], increase the precision
241 of cortical operations [77], and sharpen feature selectivity [78]. A study in mice has shown
242 that in the postsubiculum, analogously, PV⁺ interneurons are recruited by the thalamic
243 driver input directly and efficiently, at the onset of a spike train (Figure 2B) [34]. They
244 provide rapid feedforward inhibition to local excitatory cells and may sharpen their tuning
245 via a subtractive ‘iceberg’ effect observed in canonical sensory circuits [79,80].
246 Postsubicular PV⁺ interneurons also receive local excitatory inputs [10,35] and due to the
247 paucity of direct connections between local excitatory cells, as shown in rats [35], it is
248 conceivable that, like in the medial entorhinal cortex [81,82], PV⁺ interneurons mediate
249 the bulk of local communication. In rats, multiple postsubicular excitatory cells are often
250 reciprocally connected with individual PV⁺ fast-spiking interneurons, but not vice versa
251 (Figure 2B) [61]. Such super-reciprocal motifs are dictated by the anatomical polarization
252 of individual PV⁺ interneuron axons and may further contribute to the refinement of head-
253 direction cell tuning [61].

254 In contrast, Martinotti-type, somatostatin-expressing (SST⁺) interneurons, receive little
255 direct thalamic input. In the neocortex, they are mostly recruited by local excitatory cells,
256 with facilitating dynamics, i.e. in an activity-dependent manner [76,83]. In the
257 postsubiculum, they are also only indirectly recruited by thalamic inputs [34] and their
258 activity-dependent inhibitory feedback onto layer 3 excitatory neurons [29] could support
259 sustained firing of head-direction cells during immobility [84].

260 Interneurons expressing vasoactive intestinal peptide (VIP⁺) form the third main group of
261 cortical inhibitory neurons and in the postsubiculum they are also recruited with facilitating
262 dynamics, but directly by anterior thalamic inputs [85]. They may inhibit other interneurons
263 [86] and mediate gain control [87,88] to create a window for updating the head-direction
264 signal during reorientation [9].

<figure><img src="image_3.png" /><figcaption>Figure 2. Anatomy, connectivity and circuit motifs in the rodent postsubiculum. (A)</figcaption></figure>

267 Like the neocortex, the postsubiculum has six layers. Anterodorsal thalamic axons
268 carrying the subcortical head-direction signal and laterodorsal thalamic axons possibly
269 conveying visual flow information impinge upon superficial neurons in layers 3 and 1
270 [21,34,37]. In layer 1, axons from the anterodorsal and laterodorsal nuclei are
271
anatomically separated, matching the patch-matrix organization of layer 2 cells [37]. (B) Left, Calb⁺ and Calb⁻ modular compartments in the superficial postsubicular layers. Calb⁻ patches are targeted by anterodorsal terminals, while laterodorsal axons arborize in the surrounding Calb⁺ matrix [37]. Middle, postsubicular inhibitory circuits have similar connectivity motifs to canonical primary sensory cortices, whereby first-order thalamic inputs from the anterodorsal nucleus contact both PV⁺ and VIP⁺ inhibitory neurons [34,85]. PV⁺ inhibitory neurons exert a strong perisomatic inhibition onto pyramidal cells [34,35] while VIP⁺ neurons tend to inhibit other inhibitory neurons [85]. SST⁺ inhibitory neurons, which are not contacted directly by anterior thalamic axons, preferentially innervate apical dendrites of pyramidal cells [29]. Right, the connectivity between PV⁺ inhibitory neurons and pyramidal neurons is non-random [61], with high incidence of super-reciprocal motifs composed of two pyramidal cells mutually connected with one PV⁺ inhibitory cell. Abbreviations: AD, anterodorsal nucleus; LD, laterodorsal nucleus, TRN, thalamic reticular nucleus; LMN, lateral mammillary nucleus; RSC, retrosplenial cortex; MEC, medial entorhinal cortex. Brain diagram adapted from [89].

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## Dynamics of the head-direction signal and links to memory

Head-direction cells maintain their directional tuning even during immobility [84], when no vestibular or other inputs update the internal state of the neuronal population. This is a hallmark of a continuous attractor network [90], a network that spontaneously converges to a stable state even in absence of a structured input. Indeed, studies in mice have shown that during sleep, when sensory inputs are minimized, pairwise coupling between cells both within and across the anterodorsal thalamic nucleus and the postsubiculum is maintained across brain states [8,10] (Figure 3), consistent with the idea of an attractor network. Head-direction cell population activity is constantly low-dimensional and resides on a **manifold** characterized by a ring topology [91,92], as expected for an attractor network encoding a circular latent variable [93]. This internal head-direction can be decoded with high precision from the activity of just a handful of head-direction neurons as the ‘activity packet’ moving around the ring [91,94].

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Neuronal activity in canonical primary thalamocortical systems, while inherently high-dimensional, shows high coordination during "offline" periods, often resembling sensory-evoked patterns [95,96]. Yet, the dynamics of spontaneously occurring patterns and their exact relationships to wake activity are challenging to track. Recent studies of the rodent head-direction system have revealed some key aspects of brain activity during sleep. While disengaged from sensory experience, the internal states of the head-direction system are constantly evolving, as if the animal was turning its head in real life (Figure 3). However, the dynamics of the head-direction signal differ substantially between sleep stages. During Rapid Eye Movement (REM) sleep, when electrical activity of the cortex is strikingly similar to wakefulness [97], population activity drifts around the ring at an approximately real-time speed, reflecting the "paradoxical" nature of the REM sleep stage. Some differences exist though. Natural behaviour during wakefulness is characterized by alternation between periods of movement towards a goal, during which the head maintains a relatively stable direction, and periods of relative immobility during which animals scan the scene with rapid head turns. By contrast, the activity packet seems to move randomly around the ring during REM sleep [91], suggesting that it is not a simple reenactment of wake trajectories. This spontaneous activity likely arises from subcortical structures, including orientating circuits of the superior colliculus [98] and may influence downstream areas of the navigation system, where spatially modulated cells remain similarly organized during REM sleep [99-102]. Furthermore, in mice these fluctuations in the internal head-direction during sleep are associated with eye movements in the corresponding direction, suggesting that the circuits supporting the optokinetic reflex are coupled, directly or indirectly, with the head-direction system [103].

In contrast, during non-REM (NREM) sleep, the activity packet exhibits highly erratic dynamics, sweeping across different directions at speeds up to ten times faster than during wakefulness [8,50]. As suggested by a recent preprint study in mice, this internally-generated activity could be driven by thalamocortical rather than subcortical circuits, in contrast to REM sleep and wakefulness [104]. During NREM sleep, at times of hippocampal sharp wave-ripple (SWR) events, spatial trajectories experienced during previous wake episodes are recapitulated in the hippocampus in a temporally compressed manner [105] - a phenomenon believed to be critical for memory formation
[106]. While it is tempting to speculate that NREM time-compression in the head-direction system and in the hippocampus is mediated by common neuronal and circuit properties, periods of fast sweeps in both systems are anti-correlated: the activity of head-direction cells in mice stabilizes immediately before SWRs observed in the hippocampus [107], as if the head-direction system was providing the initial direction of recapitulated hippocampal trajectories. This suggests a key role of the head-direction system in orchestrating activity in the hippocampus during NREM, as further supported by recent computational work [108].

Thalamocortical activity during NREM sleep is characterized by slow and aperiodic alternation between UP states, when activity levels are similar to wakefulness, and DOWN states, when activity is almost absent [109]. Like other thalamocortical systems, the head-direction network shows similar fluctuation of states [50], and is believed to be a key hub that orchestrates this slow oscillation across parahippocampal areas [110]. Indeed, recent work in mice has shown that in the mouse anterior thalamus, activity of head-direction neurons (but not that of non-head-direction cells) is modulated by behaviourally-relevant stimuli, and is tightly correlated with spontaneous brain state fluctuations [111]. Together, these observations indicate that the internal compass is not a static signal but rather a dynamic one [9,107], and is likely a key node for brain state-mediated modulation of memory formation and cognitive processing [53]. Thus, the thalamocortical head-direction system may serve a dual role as both a sensory compass and a cognitive compass.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Dynamics of the head-direction signal across brain states. The manifold that constrains the ensemble activity of head-direction cells has a ring topology – it is intrinsically one-dimensional and circular [91]. During wakefulness (left column), the animal's head-direction maps onto this functional ring, and only a subset of neurons coding for similar directions (the “activity packet”) is active at any given time [8,91,112]. This ensures reliable decoding by downstream readers. During REM sleep (middle column), although the animal is immobile, the activity packet moves randomly along the ring at an average speed similar to that observed during wakefulness [8,91]. During</figcaption></figure>
NREM sleep (right column), the population activity is further modulated by the thalamocortical slow oscillation, causing fluctuations in ensemble activity between hyperpolarized DOWN states and activated UP states [50,107]. Population activity during UP states remains confined on a ring, but the activity packet drifts erratically at speeds up to 10 times greater than those observed during wakefulness [8,50]. Just before hippocampal SWRs, the activity packet stabilizes, providing the hippocampal formation with a stable internal direction [107]. Abbreviations: LFP - local field potential.

## Concluding remarks and future directions

Though traditionally regarded as part of the extended hippocampal circuit, the thalamocortical head-direction system shares several core features with canonical primary sensory pathways. These include widespread mapping of a sensory-derived variable, transformation of input from a first-order thalamic nucleus to the cortical recipient area and laminar specialization. Based on these properties, we propose that the postsubiculum can be conceptualized as a primary cortex for the head-direction signal.

Nonetheless, the head-direction system also differs from classical primary sensory systems in several important ways. The exact laminar organization of thalamic inputs, and the patterns of cortical and subcortical outputs, are specific to the postsubiculum. Neuromodulatory projections to the postsubiculum are also unlike those to primary sensory areas. For instance, its cholinergic inputs arise from the medial septum rather than the basal nucleus of Meynert. Furthermore, the anterodorsal thalamic nucleus, apart from its dense projections to postsubiculum also sends sparser but nonetheless direct projections to cortical association areas like the retrosplenial cortex [53,54]. Whether these anatomical differences reflect a fundamentally distinct architecture remains unclear, as the diversity and organization of neuronal cell types in the postsubiculum and the anterodorsal nucleus are still not fully characterized (see Outstanding questions). A key question for future research is whether these differences place the head-direction system outside the bounds of what qualifies as a primary thalamocortical circuit, or
390 whether they fall within the range of variability observed across primary sensory areas
391 more broadly.

392 Despite recent advances in the characterization of the postsubiculum, many important
393 questions about the organization and function of the thalamocortical head-direction
394 system remain open (see Outstanding questions). A critical future direction will be to
395 determine whether the micro-organization of head-direction tuning within the
396 postsubiculum follows a topographic layout, as often observed in canonical primary
397 cortices. Another key challenge is to understand the functional significance of the patch-
398 matrix modularity observed in the postsubiculum's superficial layers, and how different
399 classes of interneurons contribute to head-direction signal processing. Clarifying the
400 circuitry that anchors the head-direction signal to the external world, and how this
401 anchoring is integrated with subcortical structures, will be essential. Finally, the
402 persistence and modulation of the head-direction signal during sleep open the possibility
403 that the activity in this system contributes to memory consolidation in ways analogous to,
404 but distinct from, hippocampal replay. Addressing these issues will help define the
405 organizing principles of specialised thalamocortical circuits, clarify the broader role of the
406 head-direction system in spatial cognition and memory, and further establish it as a viable
407 model for studying neuronal function and dysfunction.

408

409 **Glossary**

410 **Allocentric reference frame:** a world-centred spatial reference frame anchored to the
411 external cues and independent of the animal's own position or orientation.

412 **Anticipatory firing:** in the context of the head-direction system, anticipatory firing refers
413 to the tendency of head-direction cells upstream of the cortex to encode the animal's
414 future head-direction tens of milliseconds in advance.

415 **First-order nucleus:** a thalamic nucleus that receives strong driver input from peripheral
416 or brainstem sources and relays these subcortical inputs to the cortex.
417 **Head-direction signal:** a neural representation of the animal's current heading direction
418 in the horizontal plane, encoded in the population activity of head-direction cells.

419 **Higher-order nucleus:** a thalamic nucleus mediating cortico-cortical communication,
420 driven mainly by cortical inputs.

421 **Manifold:** in relation to neural dynamics, a manifold is a low-dimensional geometric
422 structure that captures the dominant patterns of variation in neural population activity

423
424 **Box 1: Patch-matrix modularity in the postsubiculum**

425 Modularity is a fundamental characteristic of neocortical organization [113]. Although
426 such cortical patterning is more prominent in primates than in rodents, in which the
427 functional organization is often referred to as ‘salt-and-pepper’ [114], modular
428 organization has been observed in some rodent sensory areas [115]. Examples include
429 ocular dominance columns in V1 [116] and whisker barrels in S1 [117] where cortical
430 modularity is shaped by patterned thalamic inputs and neuronal functional properties are
431 aligned to the modules. While so far there is no evidence, to our knowledge, of
432 topographic distribution of head-direction tuning across the postsubiculum [50], recent
433 anatomical investigations in mice have uncovered a functional modularity with respect to
434 thalamic inputs [37].

435 In the postsubiculum, anterodorsal thalamic inputs to layer 3 are distributed evenly across
436 the lamina. In contrast, inputs to layer 1 are not uniformly distributed and instead create
437 zones of very dense axonal ramification, similar in this aspect to barrels in S1 [29,38]. In-
438 between those thalamorecipient zones, layer 2 Calb+ neurons form a ‘matrix’, surrounded
439 by calbindin-negative (Calb-) ‘patches’ [37,118] (Figure 2A). This patch-matrix modular
440 organization is preserved across species from mice to humans [37] and precisely
441 matches the pattern of thalamic projections, with axon bundles from the anterodorsal
442 thalamus nesting above and below the patches of Calb- neurons.

443 Besides the anterodorsal nucleus, postsubiculum receives inputs from the laterodorsal
444 thalamic nucleus, a higher-order nucleus [119] that might supply the visual flow inputs
needed to stabilize the head-direction signal [19,21]. Axons from the laterodorsal nucleus
target areas in layer 1 corresponding to the Calb⁺ matrix [37]. In mice, identified head-
direction cells align with these cortical modules, such that their layer 1 apical dendrites
are largely restricted within the Calb⁺ matrix, where they may preferentially sample
laterodorsal inputs.

450 Acknowledgements

451 AJD and AP are supported by the Simons Foundation Autism Research Initiative. AB is
452 supported by Eberhard Karls University of Tübingen and the German Research
453 Foundation (BU 3126/3-1). DF acknowledges support from France-Canada Research
454 Fund and the Centre National de la Recherche Scientifique and the Université Paris Cité,
455 and funding from the Agence Nationale de la Recherche from the ERA-NET NEURON
456 Program (ANR-20-NEUR-0005), the FLAG-ERA HBP Program (ANR-21-HBPR-0002)
457 and ANR-23-CE37-0002. We thank Anna Råstedt for examples of CA1 local field
458 potential and Noah Moore for comments on the manuscript.

459

460 Declaration of Interests

461 Authors declare no competing interests in relation to this work.

462

463 References

464 1. Halassa, M.M. and Sherman, S.M. (2019) Thalamocortical Circuit Motifs: A General
465 Framework. *Neuron* 103, 762–770

466 2. Raudies, F. et al. (2015) Head direction is coded more strongly than movement  
467 direction in a population of entorhinal neurons. *Brain Res*. 1621, 355–367

468 3. Angelaki, D.E. et al. (2020) A gravity-based three-dimensional compass in the  
469 mouse brain. *Nat. Commun.* 11, 1855

470 4. Taube, J.S. (2025) The Discovery of Head Direction Cells: A Personal Account.
471 *Hippocampus* 35, e23670
472 5. Petrof, I. and Sherman, S.M. (2009) Synaptic Properties of the Mammillary and Cortical Afferents to the Anterodorsal Thalamic Nucleus in the Mouse. *J. Neurosci.* 29, 7815-7819
473
474
475 6. Simonnet, J. and Fricker, D. (2018) Cellular components and circuitry of the presubiculum and its functional role in the head direction system. *Cell Tissue Res.* 373, 541-556
476
477
478 7. Taube, J.S. (2007) The Head Direction Signal: Origins and Sensory-Motor Integration. *Annu. Rev. Neurosci.* 30, 181-207
479
480 8. Peyrache, A. et al. (2015) Internally organized mechanisms of the head direction sense. *Nat. Neurosci.* 18, 569-575
481
482 9. Ajabi, Z. et al. (2023) Population dynamics of head-direction neurons during drift and reorientation. *Nature* 615, 892-899
483
484 10. Duszkiewicz, A.J. et al. (2024) Local origin of excitatory-inhibitory tuning equivalence in a cortical network. *Nat. Neurosci.* 27, 782-792
485
486 11. Nitzan, N. et al. (2020) Propagation of hippocampal ripples to the neocortex by way of a subiculum-retrosplenial pathway. *Nat. Commun.* 11, 1947
487
488 12. Stackman, R.W. and Taube, J.S. (1998) Firing properties of rat lateral mammillary single units: head direction, head pitch, and angular head velocity. *J. Neurosci.*
489
490
491 13. Blair, H.T. et al. (1998) Role of the lateral mammillary nucleus in the rat head direction circuit: a combined single unit recording and lesion study. *Neuron* 21,
492
493
494 14. Cullen, K.E. and Taube, J.S. (2017) Our sense of direction: progress, controversies and challenges. *Nat. Neurosci.* 20, 1465-1473
495
496 15. Taube, J.S. et al. (1990) Head-direction cells recorded from the postsubiculum in freely moving rats. II. Effects of environmental manipulations. *J. Neurosci.* 10,
497
498
499 16. Asumbisa, K. et al. (2022) Flexible cue anchoring strategies enable stable head direction coding in both sighted and blind animals. *Nat. Commun.* 13, 5483
500
501 17. Asumbisa, K. et al. (2025) Stereo olfaction underlies stable coding of head direction in blind mice. *Nat. Commun.* 16, 3545
502
503 18. Bassett, J.P. et al. (2018) Self-Organized Attractor Dynamics in the Developing Head Direction Circuit. *Curr. Biol.* 28, 609-615.e3
504
505 19. Yoder, R.M. et al. (2011) Origins of Landmark Encoding in the Brain. *Trends Neurosci.* 34, 561-571
506
507 20. Street, J.S. and Jeffery, K.J. (2024) The dorsal thalamic lateral geniculate nucleus is required for visual control of head direction cell firing direction in rats. *J. Physiol.* 602, 5247-5267
508
509
510 21. Li, Z. et al. (2025) Direction-selective laterodorsal thalamic nucleus encodes optic flow and turning in spatial navigation. *Neuron* DOI: 10.1016/j.neuron.2025.07.014
511
512 22. Jeffery, K.J. et al. (2016) Optimal cue combination and landmark-stability learning in the head direction system. *J. Physiol.* 594, 6527-6534
513
514 23. Carrasco, S.S. et al. (2024) Months-long stability of the head-direction system. *bioRxiv*, 2024.06.13.598909
515
516 24. Knight, R. et al. (2014) Weighted cue integration in the rodent head direction system. *Philos. Trans. R. Soc. B Biol. Sci.* 369, 20120512
517
518 25. Krausse, S. et al. (2025) Head-Direction Cells in Postsubiculum Show Systematic Parallax Errors During Visual Anchoring. *bioRxiv*, 2025.04.25.650191
519
520 26. Clark, B.J. et al. (2024) Comparison of head direction cell firing characteristics across thalamo-parahippocampal circuitry. *Hippocampus* 34, 168-196
521
522 27. Bassett, J.P. et al. (2005) Passive Movements of the Head Do Not Abolish Anticipatory Firing Properties of Head Direction Cells. *J. Neurophysiol.* 93, 1304-1316
523
524
525 28. Mi, Y. et al. (2014) Spike frequency adaptation implements anticipative tracking in continuous attractor neural networks. in *Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 1*, Cambridge, MA, USA, 1, pp. 505-513
526
527
528
529 29. Simonnet, J. et al. (2017) Activity dependent feedback inhibition may maintain head direction signals in mouse presubiculum. *Nat. Commun.* 8, 16032
530
531 30. Kapustina, M. et al. (2024) The cell-type-specific spatial organization of the anterior thalamic nuclei of the mouse brain. *Cell Rep.* 43
532
533 31. Phillips, J.W. et al. (2019) A repeated molecular architecture across thalamic pathways. *Nat. Neurosci.* 22, 1925-1935
534
535 32. Huang, L.-W. et al. (2017) Laminar Localization and Projection-Specific Properties of Presubicular Neurons Targeting the Lateral Mammillary Nucleus, Thalamus, or Medial Entorhinal Cortex. *eNeuro* 4
536
537
538 33. Herkenham, M. (1980) Laminar Organization of Thalamic Projections to the Rat Neocortex. *Science* 207, 532–535
539
540 34. Nassar, M. et al. (2018) Anterior Thalamic Excitation and Feedforward Inhibition of Presubicular Neurons Projecting to Medial Entorhinal Cortex. *J. Neurosci.* 38, 6411–6425
541
542
543 35. Peng, Y. et al. (2017) Layer-Specific Organization of Local Excitatory and Inhibitory Synaptic Connectivity in the Rat Presubiculum. *Cereb. Cortex* 27, 2435–2452
544
545 36. Preston-Ferrer, P. et al. (2016) Anatomical organization of presubicular head-direction circuits. *eLife* 5, e14592
546
547 37. Balsamo, G. et al. (2022) Modular microcircuit organization of the presubicular head-direction map. *Cell Rep.* 39, 110684
548
549 38. Richevaux, L. et al. (2023) Projection-specific integration of convergent thalamic and retrosplenial signals in the presubicular head direction cortex. *bioRxiv*, 2023.03.16.533014
550
551
552 39. Yoder, R.M. and Taube, J.S. (2011) Projections to the anterodorsal thalamus and lateral mammillary nuclei arise from different cell populations within the postsubiculum: Implications for the control of head direction cells. *Hippocampus* 21, 1062–1073
553
554
555
556 40. Yoder, R.M. et al. (2015) Visual Landmark Information Gains Control of the Head Direction Signal at the Lateral Mammillary Nuclei. *J. Neurosci.* 35, 1354–1367
557
558 41. Winer, J.A. (2005) Decoding the auditory corticofugal systems. *Hear. Res.* 207, 1–9
559 42. Vantomme, G. et al. (2020) A Thalamic Reticular Circuit for Head Direction Cell Tuning and Spatial Navigation. *Cell Rep.* 31, 107747
560
561 43. Sherman, S.M. and Guillery, R.W. (2002) The role of the thalamus in the flow of information to the cortex. *Philos. Trans. R. Soc. B Biol. Sci.* 357, 1695–1708
562
563 44. Harris, K.D. and Shepherd, G.M.G. (2015) The neocortical circuit: themes and variations. *Nat. Neurosci.* 18, 170–181
564
565 45. Alitto, H.J. and Usrey, W.M. (2003) Corticothalamic feedback and sensory processing. *Curr. Opin. Neurobiol.* 13, 440–445
566
567 46. Simons, D.J. and Carvell, G.E. (1989) Thalamocortical response transformation in the rat vibrissa/barrel system. *J. Neurophysiol.* 61, 311–330
568
569 47. Kerschensteiner, D. and Guido, W. (2017) Organization of the dorsal lateral geniculate nucleus in the mouse. *Vis. Neurosci.* 34, E008
570
571 48. Kerlin, A.M. et al. (2010) Broadly Tuned Response Properties of Diverse Inhibitory
572 Neuron Subtypes in Mouse Visual Cortex. *Neuron* 67, 858–871

573 49. Peyrache, A. et al. (2017) Transformation of the head-direction signal into a spatial
574 code. *Nat. Commun.* 8, 1752

575 50. Mehrotra, D. et al. (2024) Hyperpolarization-activated currents drive neuronal
576 activation sequences in sleep. *Curr. Biol.* 34, 3043-3054.e8

577 51. Keshavarzi, S. et al. (2022) Multisensory coding of angular head velocity in the
578 retrosplenial cortex. *Neuron* 110, 532-543.e9

579 52. Hardcastle, K. et al. (2017) A Multiplexed, Heterogeneous, and Adaptive Code for
580 Navigation in Medial Entorhinal Cortex. *Neuron* 94, 375-387.e7

581 53. Roy, D.S. et al. (2021) Anterior thalamic dysfunction underlies cognitive deficits in a
582 subset of neuropsychiatric disease models. *Neuron* 109, 2590-2603.e13

583 54. van der Goes, M.-S.H. et al. (2024) Coordinated head direction representations in
584 mouse anterodorsal thalamic nucleus and retrosplenial cortex. *eLife* 13, e82952

585 55. Taube, J.S. (1995) Head direction cells recorded in the anterior thalamic nuclei of
586 freely moving rats. *J. Neurosci.* 15, 70–86

587 56. Bagur, S. et al. (2025) A spatial code for temporal information is necessary for
588 efficient sensory learning. *Sci. Adv.* 11, eadr6214

589 57. Swadlow, H.A. (1989) Efferent neurons and suspected interneurons in S-1 vibrissa
590 cortex of the awake rabbit: receptive fields and axonal properties. *J.
591 Neurophysiol.* 62, 288–308

592 58. Li, L. et al. (2015) Differential Receptive Field Properties of Parvalbumin and
593 Somatostatin Inhibitory Neurons in Mouse Auditory Cortex. *Cereb. Cortex* 25,
594 1782–1791

595 59. Guy, J. et al. (2023) Direction selectivity of inhibitory interneurons in mouse barrel
596 cortex differs between interneuron subtypes. *Cell Rep.* 42

597 60. Tukker, J.J. et al. (2015) Head-Directional Tuning and Theta Modulation of
598 Anatomically Identified Neurons in the Presubiculum. *J. Neurosci.* 35, 15391–
599 15395

600 61. Peng, Y. et al. (2021) Spatially structured inhibition defined by polarized
601 parvalbumin interneuron axons promotes head direction tuning. *Sci. Adv.* 7,
602 eabg4693

603 62. Spalla, D. et al. (2022) Angular and linear speed cells in the parahippocampal
604 circuits. *Nat. Commun.* 13, 1907
605 606 63. Alexander, A.S. et al. (2023) Rethinking retrosplenial cortex: Perspectives and predictions. *Neuron* 111, 150-175

607 608 64. Cacucci, F. et al. (2004) Theta-Modulated Place-by-Direction Cells in the Hippocampal Formation in the Rat. *J. Neurosci.* 24, 8265-8277

609 610 65. Saleem, A.B. et al. (2018) Coherent encoding of subjective spatial position in visual cortex and hippocampus. *Nature* 562, 124-127

611 612 66. Flossmann, T. and Rochefort, N.L. (2021) Spatial navigation signals in rodent visual cortex. *Curr. Opin. Neurobiol.* 67, 163-173

613 614 67. Long, X. and Zhang, S.-J. (2021) A novel somatosensory spatial navigation system outside the hippocampal formation. *Cell Res.* 31, 649-663

615 616 68. Mertens, P.E.C. et al. (2023) Coherent mapping of position and head direction across auditory and visual cortex. *Cereb. Cortex* 33, 7369-7385

617 618 69. Siegenthaler, D. et al. (2025) Visual objects refine head direction coding. *Science* 389, eadu9828

619 620 70. Larkum, M. (2013) A cellular mechanism for cortical associations: an organizing principle for the cerebral cortex. *Trends Neurosci.* 36, 141-151

621 622 71. Larkum, M.E. et al. (2009) Synaptic Integration in Tuft Dendrites of Layer 5 Pyramidal Neurons: A New Unifying Principle. *Science* 325, 756-760

623 624 72. Sit, K.K. and Goard, M.J. (2023) Coregistration of heading to visual cues in retrosplenial cortex. *Nat. Commun.* 14, 1992

625 626 73. Wood, K.C. et al. (2017) Cortical inhibitory interneurons control sensory processing. *Curr. Opin. Neurobiol.* 46, 200-207

627 628 74. Isaacson, J.S. and Scanziani, M. (2011) How Inhibition Shapes Cortical Activity. *Neuron* 72, 231-243

629 630 75. Wilson, N.R. et al. (2012) Division and subtraction by distinct cortical inhibitory networks *in vivo*. *Nature* 488, 343-348

631 632 76. Yu, J. et al. (2019) Recruitment of GABAergic Interneurons in the Barrel Cortex during Active Tactile Behavior. *Neuron* 104, 412-427.e4

633 634 77. Del Rosario, J. et al. (2025) Lateral inhibition in V1 controls neural and perceptual contrast sensitivity. *Nat. Neurosci.* 28, 836-847

635 636 78. Lee, S.-H. et al. (2012) Activation of specific interneurons improves V1 feature selectivity and visual perception. *Nature* 488, 379-383
637 79. Atallah, B.V. et al. (2012) Parvalbumin-Expressing Interneurons Linearly Transform
638 Cortical Responses to Visual Stimuli. *Neuron* 73, 159–170

639 80. Shapiro, J.T. et al. (2022) Activating parvalbumin-expressing interneurons
640 produces iceberg effects in mouse primary visual cortex neurons. *Neurosci. Lett.*
641 786, 136804

642 81. Couey, J.J. et al. (2013) Recurrent inhibitory circuitry as a mechanism for grid
643 formation. *Nat. Neurosci.* 16, 318–324

644 82. Grosser, S. et al. (2021) Parvalbumin Interneurons Are Differentially Connected to
645 Principal Cells in Inhibitory Feedback Microcircuits along the Dorsoventral Axis of
646 the Medial Entorhinal Cortex. *eNeuro* 8

647 83. Beierlein, M. et al. (2003) Two Dynamically Distinct Inhibitory Networks in Layer 4
648 of the Neocortex. *J. Neurophysiol.* 90, 2987–3000

649 84. Taube, J.S. and Bassett, J.P. (2003) Persistent Neural Activity in Head Direction
650 Cells. *Cereb. Cortex* 13, 1162–1172

651 85. Nassar, M. et al. (2025) Presubicular VIP expressing interneurons receive
652 facilitating excitation from anterior thalamus. *Neuroscience* 578, 91–104

653 86. Kepecs, A. and Fishell, G. (2014) Interneuron cell types are fit to function. *Nature*
654 505, 318–326

655 87. Fu, Y. et al. (2014) A Cortical Circuit for Gain Control by Behavioral State. *Cell* 156,
656 1139–1152

657 88. Pi, H.-J. et al. (2013) Cortical interneurons that specialize in disinhibitory control.
658 *Nature* 503, 521–524

659 89. Franklin, K. and Paxinos, G. (2007) *The Mouse Brain in Stereotaxic Coordinates*,
660 Elsevier Science

661 90. Knierim, J.J. and Zhang, K. (2012) Attractor Dynamics of Spatially Correlated
662 Neural Activity in the Limbic System. *Annu. Rev. Neurosci.* 35, 267–285

663 91. Chaudhuri, R. et al. (2019) The intrinsic attractor manifold and population dynamics
664 of a canonical cognitive circuit across waking and sleep. *Nat. Neurosci.* 22,
665 1512–1520

666 92. Hermansen, E. et al. (2024) Uncovering 2-D toroidal representations in grid cell
667 ensemble activity during 1-D behavior. *Nat. Commun.* 15, 5429

668 93. Perich, M.G. et al. (2025) A neural manifold view of the brain. *Nat. Neurosci.* 28,
669 1582–1597
670 94. Rybakken, E. et al. (2019) Decoding of Neural Data Using Cohomological Feature Extraction. *Neural Comput.* 31, 68–93

672 95. Kenet, T. et al. (2003) Spontaneously emerging cortical representations of visual attributes. *Nature* 425, 954–956

674 96. Luczak, A. et al. (2009) Spontaneous events outline the realm of possible sensory responses in neocortical populations. *Neuron* 62, 413–425

676 97. Adamantidis, A.R. et al. (2019) Oscillating circuitries in the sleeping brain. *Nat. Rev. Neurosci.* 20, 746–762

678 98. Senzai, Y. and Scanziani, M. (2024) The brain simulates actions and their consequences during REM sleep. *bioRxiv*, 2024.08.13.607810

680 99. Louie, K. and Wilson, M.A. (2001) Temporally structured replay of awake hippocampal ensemble activity during rapid eye movement sleep. *Neuron* 29, 145–156

683 100. Gardner, R.J. et al. (2019) Correlation structure of grid cells is preserved during sleep. *Nat. Neurosci.* 22, 598

685 101. Trettel, S.G. et al. (2019) Grid cell co-activity patterns during sleep reflect spatial overlap of grid fields during active behaviors. *Nat. Neurosci.* 22, 609

687 102. Gardner, R.J. et al. (2022) Toroidal topology of population activity in grid cells. *Nature* 602, 123–128

689 103. Senzai, Y. and Scanziani, M. (2022) A cognitive process occurring during sleep revealed by rapid eye movements. *Science* 377, 999–1004

691 104. Viejo, G. et al. (2025) Coherent dynamics of thalamic head-direction neurons irrespective of input. *bioRxiv*, 2025.09.10.675474

693 105. Lee, A.K. and Wilson, M.A. (2002) Memory of sequential experience in the hippocampus during slow wave sleep. *Neuron* 36, 1183–1194

695 106. Girardeau, G. et al. (2009) Selective suppression of hippocampal ripples impairs spatial memory. *Nat. Neurosci.* 12, 1222–1223

697 107. Viejo, G. and Peyrache, A. (2020) Precise coupling of the thalamic head-direction system to hippocampal ripples. *Nat. Commun.* 11, 2524

699 108. Levenstein, D. et al. (2024) Sequential predictive learning is a unifying theory for hippocampal representation and replay. *bioRxiv*, 2024.04.28.591528

701 109. Sanchez-Vives, M.V. (2020) Origin and dynamics of cortical slow oscillations. *Curr. Opin. Physiol.* 15, 217–223
703 110. Gent, T.C. et al. (2018) Thalamic dual control of sleep and wakefulness. *Nat. Neurosci.* 21, 974–984

705 111. Blanco-Hernández, E. et al. (2024) Sensory and behavioral modulation of thalamic head-direction cells. *Nat. Neurosci.* 27, 28–33

707 112. Taube, J.S. et al. (1990) Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. *J. Neurosci.* 10, 420–435

710 113. Bednar, J.A. and Wilson, S.P. (2016) Cortical Maps. *The Neuroscientist* 22, 604–617

712 114. Kaschube, M. (2014) Neural maps versus salt-and-pepper organization in visual cortex. *Curr. Opin. Neurobiol.* 24, 95–102

714 115. Powell, N.J. et al. (2024) Common modular architecture across diverse cortical areas in early development. *Proc. Natl. Acad. Sci.* 121, e2313743121

716 116. Takahata, T. (2024) Development of ocular dominance columns across rodents and other species: revisiting the concept of critical period plasticity. *Front. Neural Circuits* 18

719 117. Staiger, J.F. and Petersen, C.C.H. (2021) Neuronal Circuits in Barrel Cortex for Whisker Sensory Perception. *Physiol. Rev.* 101, 353–415

721 118. Ray, S. et al. (2014) Grid-Layout and Theta-Modulation of Layer 2 Pyramidal Neurons in Medial Entorhinal Cortex. *Science* 343, 891–896

723 119. Perry, B.A.L. and Mitchell, A.S. (2019) Considering the Evidence for Anterior and Laterodorsal Thalamic Nuclei as Higher Order Relays to Cortex. *Front. Mol. Neurosci.* 12