Thalamus and claustrum control parallel layer 1 circuits in retrosplenial cortex
Activity in the granular retrosplenial cortex ( RSG ) is correlated with a wide variety of behaviors , including spatial navigation , learning , memory , fear conditioning , imagination , and planning for the future ( Alexander et al . , 2020; Alexander and Nitz , 2017; Chang et al . , 2020; Chrastil , 2018; Hinman et al . , 2018; Mao et al . , 2018; Miller et al . , 2021; Miller et al . , 2019 ) . The RSG is also among the most densely connected regions of the brain , integrating inputs from a bevy of cortical and subcortical sources and serving as part of the default mode network ( Greicius et al . , 2009; Kaboodvand et al . , 2018; Liu et al . , 2019; Whitesell et al . , 2021 ) . While these anatomical connections are well-documented ( Van Groen and Wyss , 2003; van Groen and Wyss , 1990; Whitesell et al . , 2021; Wyss and Van Groen , 1992 ) , few studies have examined their functional nature ( Nitzan et al . , 2020; Yamawaki et al . , 2019b; Yamawaki et al . , 2019a; Yamawaki et al . , 2016a ) , and cell-type specificity has yet to be sufficiently explored . Such knowledge is critical to develop a mechanistic understanding of how the RSG integrates information from multiple sources to carry out its spatial and non-spatial functions . Cortical regions , including the RSG , receive inputs from one or more thalamic nuclei ( Herkenham , 1986; Herkenham , 1980; Jones , 2001; Jones , 1998; Peters , 1979; Van Groen and Wyss , 1995 ) . Thalamic relay cells ( Clascá et al . , 2012 ) are grouped into three distinct classes: core , intralaminar , and paralaminar/ventral midline ( matrix ) nuclei ( Hanbery and Jasper , 1953; Herkenham , 1986; Jones , 2001; Jones , 1998; Morison and Dempsey , 1941; Rubio-Garrido et al . , 2009 ) . Thalamic matrix nuclei project predominantly to layer 1 of many cortical regions ( Herkenham , 1986; Herkenham , 1980 ) , resulting in subtype-specific activation of cortical inhibitory ( Anastasiades et al . , 2021; Cruikshank et al . , 2012; Delevich et al . , 2015 ) and excitatory neurons ( Collins et al . , 2018; Cruikshank et al . , 2012; Guo et al . , 2018; Rodriguez-Moreno et al . , 2020; Rubio-Garrido et al . , 2009; Van der Werf et al . , 2002; Yamawaki et al . , 2019b ) . Matrix thalamocortical ( TC ) inputs from the anterior thalamus , which contains the highest proportion of head direction cells in the brain ( Taube and Bassett , 2003 ) , influence layer 5 pyramidal cells in RSG ( Yamawaki et al . , 2019b ) . However , potential subtype-specific responses and their functional impact on the encoding of directional information in RSG have yet to be examined . The cortex , including the RSG , also receives widespread inputs from the densely connected claustrum ( Brown et al . , 2017; Crick and Koch , 2005; Goll et al . , 2015; Jackson et al . , 2018; Kim et al . , 2016; Narikiyo et al . , 2020; Wang et al . , 2017; White and Mathur , 2018 ) . As with TC signaling , the claustrum innervates both excitatory ( da Costa et al . , 2010; Narikiyo et al . , 2020 ) and inhibitory ( Jackson et al . , 2018; Narikiyo et al . , 2020; Salerno et al . , 1984 ) neurons via precise laminar targeting ( Wang et al . , 2017 ) and projects to many of the same cortical regions as the thalamus ( Burman et al . , 2011 ) . Claustrocortical ( ClaC ) projections are thought to regulate complex functions ( Crick and Koch , 2005; Goll et al . , 2015; Jackson et al . , 2018; Kitanishi and Matsuo , 2017; Narikiyo et al . , 2020; Renouard et al . , 2015; Smith et al . , 2012; White and Mathur , 2018 ) , including the coordination and amplification of correlated signals across cortical regions ( Kim et al . , 2016; Smith et al . , 2012; Smythies et al . , 2012 ) . Surprisingly , the RSG is one of few regions that does not return reciprocal connections to the claustrum ( Zingg et al . , 2018 ) . Despite the unique unidirectional nature of this connection , no studies have investigated the functional nature or subtype-specificity of ClaC inputs to RSG neurons . Each cortical region also receives inputs from select other cortical areas . The RSG receives direct innervation from the secondary motor cortex ( Yamawaki et al . , 2016a ) , contralateral RSG ( Sempere-Ferràndez et al . , 2018; Wyss et al . , 1990 ) , and anterior cingulate cortex ( ACC; Van Groen and Wyss , 2003; van Groen and Wyss , 1990 ) , among others . The RSG and ACC , in particular , have been implicated in several shared limbic and cognitive functions , including fear conditioning ( Frankland et al . , 2004; Han et al . , 2003; Yamawaki et al . , 2019a; Yamawaki et al . , 2019b ) , but the cellular targets of ACC inputs to RSG have not been identified . Thalamic , claustral , and cortical inputs all converge in the RSG , but whether they do so via parallel or integrative control of target excitatory neurons remains unknown . Within the RSG , the superficial layers contain two subtypes of principal excitatory pyramidal neurons that have strikingly distinct physiology , morphology , and computational capabilities: the low-rheobase ( LR ) neuron and the regular-spiking ( RS ) neuron ( Brennan et al . , 2020; Kurotani et al . , 2013; Yousuf et al . , 2020 ) . Here , we use channelrhodopsin ( ChR2 ) -assisted circuit mapping ( CRACM ) to study the subtype-specific circuits formed by anterior thalamic , claustral , anterior cingulate , and dorsal subicular inputs to the RSG . Our results reveal a double dissociation in the precise organization of afferent axons and principal cell dendrites that can support parallel processing in superficial RSG . Specifically , we find that anterior thalamus and dorsal subiculum preferentially control LR neurons , whereas claustrum and anterior cingulate control RS cells . We show that the synaptic dynamics of thalamic inputs allow for the robust encoding of angular speed by LR cell models , even though these inputs only explicitly contain information about head direction , not speed . Together , our results suggest that LR neurons are ideally positioned to contribute to the initial spatial orientation computations performed in superficial RSG .
Layer 3 of the granular retrosplenial cortex ( RSG ) contains two types of principal pyramidal neurons: the low-rheobase ( LR ) neuron and the regular-spiking ( RS ) neuron ( Brennan et al . , 2020; Kurotani et al . , 2013; Yousuf et al . , 2020 ) . Using whole-cell patch clamp recordings , we again distinguished LR from RS neurons by their unique intrinsic properties , predominantly the low rheobase , high input resistance , lack of adaptation , and narrow spike width ( Figure 1A–C , Figure 1—figure supplement 1 , Supplementary file 1 - Table 1 , and Supplementary file 1 - Table 2; Brennan et al . , 2020 ) . We used channelrhodopsin-assisted circuit mapping ( CRACM ) to interrogate inputs to these two cell types . Consistent with previous studies ( Odagiri et al . , 2011; Van Groen and Wyss , 2003; van Groen and Wyss , 1990; Yamawaki et al . , 2019b ) , virus injections into the anterodorsal and anteroventral thalamic nuclei ( ADAV ) resulted in ChR2-eYFP expression in thalamocortical ( TC ) axons and terminals predominantly in layer 1a ( L1a; the most superficial part of layer 1 ) and in layer 3 ( L3 ) of superficial RSG ( Figure 1D ) . To test whether these thalamocortical inputs target the LR and RS neurons in layer 3 , we stimulated the thalamic axons and terminals with 1 ms LED pulses at a 10 Hz frequency for 1 s at high LED power over the cell body of the patched neurons ( Figure 1E; see Materials and methods ) . From resting membrane potentials of approximately −65 mV , LR neurons were strongly driven past spike threshold by these thalamic inputs while RS neurons exhibited far smaller EPSPs ( Figure 1F ) . To quantify the impact of TC inputs on LR and RS spike rates , we next depolarized the cells until they were spiking at 10–25 Hz and delivered a single LED pulse ( see Materials and methods ) . To rule out effects of feed-forward inhibition in these experiments , the GABAA antagonist , picrotoxin ( 50 µM ) , was added to the bath . Compared to their baseline activity , this stimulation evoked a significant increase in spiking in LR neurons ( p=0 . 002 , Wilcoxon rank sum test ) but not RS neurons ( p=0 . 19 , Wilcoxon rank sum test; Figure 1G ) . The LR neurons thus had a significantly larger increase in spike rate evoked by the optical pulse than RS neurons ( p=0 . 0012 , Wilcoxon rank sum test; Figure 1H ) . This suggests that LR neurons receive stronger activation from TC inputs than their neighboring L3 RS neurons . LR neurons are morphologically distinct from their neighboring RS neurons ( Brennan et al . , 2020; Kurotani et al . , 2013; Yousuf et al . , 2020 ) . Given the precise laminar pattern of anterior thalamic inputs to RSG ( Figure 1D and Figure 2B ) , we next investigated the overlap between anterior thalamic afferents and the dendritic morphologies of reconstructed LR ( n = 10 ) and RS ( n = 5 ) cells ( see Materials and methods ) . Apical dendrites of LR neurons were most densely localized to L1a , with basal dendrites remaining confined to L3 ( Figure 2C ) . In contrast , RS apical dendrites rarely entered L1a , instead existing in the deeper subdivisions of layer 1 ( L1b/c ) , with basal dendrites primarily in upper layer 5 ( L5; Figure 2D ) . Projection density analysis showed localization of ADAV axons and terminal arbors in L1a and weakly in L3 ( Figure 2C&D ) . Thus , dendrites of LR , but not RS , cells selectively co-localize within layers 1a and 3 with ADAV TC afferents ( Figure 2C&D ) . This anatomical colocalization of LR , but not RS , dendrites with TC axons coupled with the increase in LR , but not RS , spiking in response to TC optical stimulation indicates that the anterior thalamic-retrosplenial circuit at least partially obeys Peters’ rule , which states that neuronal populations with anatomically overlapping axonal and dendritic arbors are more likely to show functional connectivity Peters , 1979; Peters and Feldman , 1976 . To further verify this , we examined the responses of L3 LR and RS neurons to ADAV input at L1a , where the highest projection density of ADAV inputs exist ( see Methods ) . When delivering 1 ms high LED power light pulses , we indeed found that LR neurons had a significantly larger excitatory postsynaptic potential ( EPSP ) amplitude in response to the L1a LED stimulation compared to RS cell responses ( p=0 . 0185 , Wilcoxon rank sum test; Figure 2E ) . Notably , in response to layer one stimulation , LR cells also showed significantly larger EPSP amplitudes compared to L5 RS neurons ( Figure 2—figure supplement 1 ) , which have been previously shown to respond to TC input ( Yamawaki et al . , 2019b ) . This suggests that LR neurons , rather than layer 3 or 5 RS neurons , are the predominant RSG cell type receiving and processing head direction inputs from the anterior thalamus . To further examine the effects of lamination of anterior thalamic inputs to LR and RS neurons on their resulting responses , we conducted a high-resolution protocol that used minimum thresholded LED power to optically stimulate every 20–30 µm along the neuron’s longitudinal axis ( Figure 2F; see Materials and methods ) . We found that LR neurons have the largest EPSP amplitude when the LED pulse is targeting layer 1a , corresponding with the peak projection density of ADAV axons and terminal arbors at this lamina . LR response amplitude then decreases as the LED moves away from the pia before reaching no response at the layer 1/2 border . As LED stimulation entered layer 3 , the LR EPSP amplitude increased , consistent with the increase in projection density of the ADAV axons and terminal arbors , before again decreasing until their response amplitude reached 0 mV in layer 5 ( Figure 2F ) . In contrast , the RS neuron showed much smaller EPSP amplitude with no significant variation in response across the layers ( Figure 2F&G ) . To verify this functional sublaminar correlation between thalamocortical axons and pyramidal cell dendrites , we ran a population analysis comparing the EPSP amplitudes within LR and RS cell groups from all layers relative to L1/2 , which represents our minimum projection density of ADAV inputs in the superficial layers . We found that within the LR cell population , LR cells have significantly larger responses at L1a ( p=0 . 00001 ) and cell body ( p=0 . 0006 ) compared to L1/2 ( paired t-test; Figure 2G ) . This lamination of functional responses in the LR population precisely aligns with the lamination of ADAV axons and terminal arbors within these superficial layers . When stimulating in layer 5 , there was no significant difference between EPSP amplitude at L1/2 and L5sup ( p=0 . 420 ) , while L5dp responses were significantly smaller than those at L1/2 ( p=0 . 0462; Figure 2G ) , as would be expected given the complete lack of LR dendrites in L5 . In contrast , RS EPSP amplitudes at layers 1a , cell body , L5sup , and L5dp did not differ from responses at L1/2 ( p>0 . 05 for all; paired t-test ) , indicating that there is no significant lamination of functional responses to thalamic inputs in the RS population , likely due to their relative lack of response to these inputs in general ( Figure 2G ) . These relationships persisted when inhibition blocker picrotoxin ( 50 µM ) or sodium channel blocker TTX ( 1 µM ) +4 AP ( 100 µM ) were added to the bath ( data not shown; see Materials and methods ) . Thus , the connectivity between anterior thalamic TC arbors and L3 principal neurons in RSG highlights a circuit that depends on the precise sublaminar colocalization of both local principal cells’ dendrites and incoming thalamocortical axons . This demonstrates that LR neurons are uniquely anatomically adapted to respond to incoming inputs from the anterior thalamus , where ~ 60% of neurons are head direction cells ( Taube , 1995; Taube and Bassett , 2003 ) , due to a precise overlap of their apical dendrites with the dense thalamic axons and terminals in the uppermost sublamina of L1 ( L1a ) . Two other main sources of input to RSG are the claustrum ( CLA; Van Groen and Wyss , 2003; van Groen and Wyss , 1990 ) and anterior cingulate cortex ( ACC; Shibata and Naito , 2008; Van Groen and Wyss , 2003; van Groen and Wyss , 1990 ) . Both claustrocortical ( ClaC ) and ACC corticocortical ( CC ) projections have been anatomically shown to exhibit distinct laminar organization within its target cortical layers ( Van Groen and Wyss , 2003; Vogt and Miller , 1983; Wang et al . , 2017 ) , but the precise functional targets of claustral and cingulate inputs to superficial RSG have , to our knowledge , never been examined . To address this , we next used CRACM , this time to examine CLA inputs to RSG LR and RS neurons and then compared these projections to RSG thalamic inputs . ChR2 injections into CLA ( Figure 3A ) resulted in expression of CLA axons and terminals in layers 1 c , 2 , and 5 ( Figure 3B ) . This expression pattern is distinct from the thalamic expression localized to layers 1a and 3 ( Figure 2B–D ) . Dendritic lamination plots of LR and RS dendrites and projection density plots of CLA axons and terminal arbors show that RS , but not LR , apical dendrites anatomically overlap with CLA arbors in superficial layers 1 c and two and upper layer 5 ( Figure 3D ) . Using the same targeted optogenetic stimulation approach as previously described ( see Materials and methods ) , we found that RS neurons have significantly larger responses to CLA input compared to LR neurons when stimulated at layer 1/2 ( p=0 . 0000035 , Wilcoxon rank sum test; Figure 3E ) , the area of the strongest superficial projection density of CLA arbors . Similarly , layer 5 RS neurons exhibited significantly larger EPSP amplitudes in response to CLA inputs compared to LR cells ( Figure 2—figure supplement 1 ) . This again indicates that while LR neurons may be optimally positioned to receive thalamic input , RS neurons in both RSG L3 and L5 are instead the primary recipients of CLA inputs . To further examine the lamination of ClaC inputs to LR and RS neurons and their resulting responses , we again conducted the high-resolution CRACM protocol using minimum LED power ( Figure 3F; see Materials and methods ) . We found that RS neurons have the largest EPSP amplitude when the LED pulse is stimulating both layer 1c and 5sup and weakest EPSP amplitude at layer 1a , corresponding with , respectively , the strongest and the weakest projection density of CLA afferents at these laminar locations . In contrast , the complementary LR cell had no response to LED stimulation at any of the laminar locations ( Figure 3F ) . Population analysis showed that within the RS cell population , RS cells have significantly larger responses at L1/2 ( p=0 . 00725 ) and L5sup ( p=0 . 0301 ) compared to those at L1a ( paired t-test; Figure 3G ) . This lamination of functional responses in the RS cell precisely aligns with the lamination of ClaC axons and terminal arbors within these layers . In contrast , LR EPSP amplitudes across all layers were much lower in magnitude and did not differ from responses at L1a ( p>0 . 05 for all; paired t-test; Figure 3G ) , indicating no significant lamination of functional responses to ClaC inputs in the LR population . These relationships persisted when inhibition blocker picrotoxin ( 50 µM ) or sodium channel blocker TTX ( 1 µM ) +4 AP ( 100 µM ) were added to the bath ( data not shown; see Materials and methods ) . Using the same CRACM approach to examine ACC inputs to RSG ( Figure 4A ) , we found that corticocortical inputs from the anterior cingulate target L1b/c and , to a lesser extent , L5 ( Figure 4B ) , partially resembling the laminar pattern seen with CLA arbors ( Figure 3B ) and overlapping precisely with RS , but not LR , dendrites ( Figure 3C&D ) . Indeed , when stimulating ACC arbors at L1/2 , RS cells had significantly larger EPSP amplitudes compared to LR cells ( p=0 . 0019 ) . When examining the lamination of these inputs with higher spatial resolution , we found that RS cells have the largest EPSP response to ACC inputs at L1/2 , while the same minimum LED stimulation power elicits no response in layer 1a ( Figure 4F ) . Population analysis of RS cells revealed significantly larger responses to optogenetic stimulation of ACC inputs at the L1/2 ( p=0 . 000037 ) and cell body ( p=0 . 000525 ) compared to L1a stimulation ( Figure 4G ) , reflecting the precise overlap of ACC arbors and RS dendrites . In contrast , the much smaller LR EPSP amplitudes across all layers did not differ from responses at L1a ( p>0 . 05 for all; paired t-test; Figure 4G ) . Again , the same results were seen when inhibition blocker picrotoxin ( 50 µM ) or sodium channel blocker TTX ( 1 µM ) +4 AP ( 100 µM ) were added to the bath ( data not shown; see Materials and methods ) . Thus , both claustrocortical and corticocortical inputs to RSG target RS apical dendrites at the lower divisions of L1 ( L1c and L1b/c , respectively ) , whereas thalamocortical inputs preferentially target the apical dendrites of LR cells in upper L1 ( L1a ) . This again indicates that parallel circuits in RSG process TC versus ClaC and CC information , and this parallel processing is enabled by precise sublaminar organization of afferent axons and layer three principal cell apical dendrites . Previous work has shown that dorsal subiculum ( DS ) , which serves to transmit allocentric spatial information such as axis cell and boundary vector signals ( Lever et al . , 2009; Derdikman , 2009; Olson et al . , 2017; Simonnet and Brecht , 2019; Bicanski and Burgess , 2020 ) , also precisely targets layer 2/3 principal neurons in RSG ( Nitzan et al . , 2020; Yamawaki et al . , 2019a ) . These inputs overlap with LR cell bodies and basal dendrites and have been shown to evoke larger excitatory postsynaptic currents in superficial compared to layer 5 pyramidal neurons ( Nitzan et al . , 2020; Yamawaki et al . , 2019a ) . These results suggest that DS projections to RSC may be targeting LR cells , potentially resulting in converging spatial information from both ADAV and DS onto LR cells . However , it remains unknown whether LR or layer 3 RS cells are the predominant target of these DS projections . To investigate this , we repeated our CRACM protocols and examined the functional responses of LR and layer 3 RS cells to DS inputs ( Figure 5A&B ) . We found that DS afferents to layer 3 of RSG precisely overlap with LR basal and , to a lesser degree , proximal apical dendrites ( Figure 5C ) but not RS basal dendrites ( Figure 5D ) . Correspondingly , LR neurons responded with significantly larger EPSPs compared to RS neurons when DS inputs were stimulated at the cell body in layer 3 ( p=0 . 004; Figure 5E ) . Our high-resolution protocol and population analysis also confirmed that LR cells had significantly larger responses at layers 1/2 and 3 compared to L1a ( L1/2 p=0 . 0132 , L3 p=0 . 0135; Figure 5F&G ) , suggesting the possibility of integration of synchronous anterior thalamic and dorsal subicular inputs by LR neurons . In contrast , RS cells showed no significant laminal differences in response to DS input ( p>0 . 05 for all; Figure 5G ) . Thus , inputs from both the dorsal subiculum and anterior thalamus target LR cells , reflecting their precise overlap with LR dendrites , while the claustrum and anterior cingulate cortex instead target RS cells . We next extended our physiological examination of superficial RSG circuits to include correlational analyses and dual injection experiments ( Figure 6A ) . We found that LR dendrites are strongly and significantly positively correlated with both ADAV ( r = 0 . 88 , p<0 . 001 ) and DS ( r = 0 . 69 , p=1 . 41e-254 ) axons . In contrast , RS dendrites are strongly correlated with CLA ( r = 0 . 29 , p=4 . 82e-36 ) and ACC ( r = 0 . 43 , p=5 . 73e-82 ) axons . Notably , LR dendrites are significantly negatively correlated with both CLA ( r = −0 . 49 , p=1 . 16e-110 ) and ACC ( r = −0 . 15 , p=1 . 00e-10 ) axons , and RS dendrites are negatively correlated with ADAV ( r = −0 . 55 , p=2 . 47e-145 ) and DS ( r = −0 . 44 , p=7 . 74e-85 ) axons ( Figure 6B&C ) . These anatomical results mirror our functional findings that LR neurons are preferentially driven by both ADAV and DS inputs , while RS neurons are targeted by CLA and ACC inputs . We also compared laminar expression of afferents from the four input regions and found that ADAV and DS inputs to RSG , which both at least in part target layer 3 , were significantly positively correlated with one another ( r = 0 . 55 , p=2 . 93e-143 ) . Similarly , CLA and ACC inputs , which both target the lower divisions of L1 as well as L5 , were also significantly positively correlated ( r = 0 . 23 , p=2 . 3e-23 ) . However , ADAV and DS inputs were significantly negatively correlated with both CLA and ACC inputs , confirming that these two streams target separate sublayers within RSG ( Figure 6B , C ) . Dendrite-dendrite correlations of LR and RS cell populations were also strongly anti-correlated ( r = −0 . 65 , p=3 . 00e-215; Figure 6C ) , highlighting the distinct anatomical organization of these two neighboring principal cell types . Taken together , these axon-axon , dendrite-dendrite , and axon-dendrite correlations indicate that precise , fine-grained laminar organization of LR and RS dendrites and afferent axons creates a parallel circuit in which LR neurons are selectively optimized to integrate incoming spatial information ( Figure 6D ) . Supplemental examination of contralateral RSG ( cRSG ) inputs to RSG showed lamination and resulting cell-type-specific targeting resembling that of projections from CLA and ACC ( Figure 6—figure supplement 1 ) . Specifically , cRSG inputs targeted L1c , L2 , and L5 , resulting in strong activation of RS cells , with almost no responses in LR cells ( Figure 6—figure supplement 1 ) . This again suggests that inputs from CLA , ACC and cRSG follow a structured pattern by which these inputs preferentially control RS cells , while ADAV and DS projections target LR cells . Importantly , laminar dichotomies similar to those seen here in RSG also exist between TC and ClaC/corticocortical projections to other cortical regions such as the medial prefrontal cortex ( Cruikshank et al . , 2012 ) , as also revealed by our examination of anatomical datasets from the Allen Brain Institute ( Figure 6—figure supplement 2 ) . Thus , our findings may also highlight a more universal framework by which other cortical regions integrate and process thalamic versus claustral and cortical inputs . To investigate the functional implications of these parallel circuits , we next examined the short-term dynamics of each input onto the RSG principal cells . LR short-term dynamics were examined in response to ADAV and DS inputs , while RS short-term dynamics were examined in response to CLA and ACC inputs ( see Materials and methods ) . In contrast to previously documented thalamocortical matrix inputs to both superficial pyramidal cells and interneurons ( Anastasiades et al . , 2021; Cruikshank et al . , 2012 ) , 10 Hz anterior thalamic inputs from ADAV to RSG LR neurons were uniquely and significantly depressing ( p=1 . 02e-5 , Wilcoxon rank sum test; Figure 7A&B ) . In contrast , 10 Hz DS inputs to LR neurons were not depressing and exhibited weak facilitation ( Figure 7A&B ) . Both CLA and ACC inputs to RS cells were also weakly facilitating ( Figure 7C&D ) . Thus , the synaptic depression of anterior thalamic inputs to LR neurons is unique among the inputs examined here and also distinct from anterior thalamic inputs to superficial principal neurons in PFC and ACC ( Cruikshank et al . , 2012 ) . As expected , we found that ADAV inputs to LR cells do not show synaptic depression at the much slower stimulation frequency of 0 . 1 Hz ( Figure 7—figure supplement 1 panel C ) , but 40 Hz inputs resulted in stronger depression than 10 Hz ( p=0 . 0022 , Wilcoxon rank sum test; Figure 7—figure supplement 1 panel B ) . We next used computational modeling to elucidate the functional role of synaptic depression in this circuit , especially with respect to the processing of head direction input ( Taube , 1995; Taube and Bassett , 2003 ) . Up to 60% of cells in the anterior thalamus are classical head direction ( HD ) cells ( Taube and Bassett , 2003 ) . Each HD cell has a unique preferred direction at which its firing rate is highest when the head is facing that direction . The preferred directions of all cells in the HD ensemble span the full range of compass directions ( Taube , 1998 ) . Our modeling setup consisted of a postsynaptic RSG LR cell receiving input from an ensemble of 7500 presynaptic HD cells via depressing synapses ( for full details , see Materials and methods ) . In the initial simulations shown in Figure 8 , the morphologically realistic model LR cell ( Brennan et al . , 2020 ) received uniform inputs ( all HDs being equally likely ) via depressing synapses with Tsodyks-Markram short-term dynamics ( Tsodyks et al . , 1998 ) . The synaptic parameters were fit to match the experimentally observed response of LR cells to optogenetic stimulation of thalamic afferents reported above ( Figure 7 ) . We found that the firing rate of the postsynaptic LR cell receiving HD input via depressing synapses was strongly correlated with angular head speed , giving rise to symmetrical angular head velocity tuning ( Figure 8B&C ) . Identical HD inputs transmitted via non-depressing synapses resulted in LR firing rates that were uncorrelated with angular head speed ( Figure 8B , E–F ) . It is important to note that in our model , firing rates of input HD cells were not explicitly modulated by angular head velocity; therefore , the observed speed tuning resulted strictly from the depressing synaptic dynamics . For the parameter set whose results are depicted , LR cell firing rate was optimally correlated with head speed 24 ms in the past , confirmed by both cross-correlation and mutual information analyses ( Figure 8E&F ) . We obtained the same results when modeling an ensemble of only 2500 presynaptic HD cells , indicating that our results are robust to the size of the presynaptic population ( Figure 8—figure supplement 1 ) . Taken together , these results suggest that synaptic depression of HD ensemble inputs introduces an angular head speed signal into the LR population , producing neurons that are more responsive during faster head turns , and potentially supporting the spatial orientation encoding functions attributed to the RSG ( Epstein , 2008; Ino et al . , 2007; Milczarek et al . , 2018; Miller et al . , 2019 ) . Anterior thalamic HD cells display anticipatory firing ( Blair et al . , 1997 ) , a phenomenon where an HD cell becomes most active at a fixed time interval before the animal is facing that cell’s preferred direction ( Figure 9A ) . This temporal offset associated with each cell is called its anticipatory time interval ( ATI ) . In anterior thalamus , the mean ATI has been reported as 25–50 ms ( Taube , 2010 ) . In our initial simulations , shown in Figure 8 , we drew the ATI of each HD cell randomly from distributions matching these known in vivo ranges . To more systematically understand if and how the ATI of HD cells influences angular head speed coding by LR neurons , we next performed a series of simulations using various fixed ATI values for the entire HD population ( Figure 9A ) and analyzed the resulting postsynaptic LR response . Increasing ATI from 0 ms ( no anticipation by the HD cell ) to higher values ( HD cell firing prior to facing the preferred HD ) improved the lag between LR firing rate and angular head speed , with larger ATIs resulting in shorter latency between the head movement and LR coding of that angular head speed ( Figure 9C ) . Remarkably , larger ATIs also improved the angular head speed tuning of LR neurons independent of lag , as quantified by the maximum value ( over the full range of lags ) of cross-correlation or cross-mutual information ( Figure 9B ) . Thus , anticipatory firing of HD cells may constitute a powerful coding principle in the thalamo-retrosplenial circuit , helping LR cells to not only encode the current head speed with minimal lag , but also better encode the head speed independent of the lag . In order to better understand this surprising effect , as well as how speed tuning generally arises , we analytically studied a simplified mean-field model of this thalamo-retrosplenial circuit ( Figure 9—figure supplement 1 ) . Our analysis allowed us to mathematically derive that LR activity should encode head speed with depressing synapses from simplified HD cells ( see Appendix ) . Moreover , the analysis showed that anticipatory firing compensates for the lag introduced by integration time , leading to a theoretical parameter regime for which postsynaptic speed coding can be essentially perfect ( where LR firing rate reflects head speed exactly with minimal latency ) . The observed improvement in quality of speed coding with increases in ATI corresponds to moving closer to this regime . Finally , our analysis showed that postsynaptic activity , at least at lower rotational speeds , is proportional to the square of head speed , thereby explaining the concave-up , parabolic shape of the speed-firing rate curve ( Figure 8C and Figure 8—figure supplement 2 ) . Thus , both the simulations and the analytical theory show that synaptic depression of HD cell input onto LR cells should result in angular speed coding in the LR cell firing rate , and that anticipatory firing improves both the precision and quality of this coding . In the simulations above , we utilized a uniform distribution of HD inputs to each LR cell , such that each preferred direction was equally represented . However , in practice , it is likely that there will be heterogeneity in the preferred HDs of the cells providing inputs to any given retrosplenial LR cell . To study the extent to which speed coding persists under these conditions , we simulated a population of 200 LR cells , each of which received inputs from a randomly selected distribution of preferred directions for the presynaptic HD cells ( Figure 10Ai , , Bi , Ci ) . We then analyzed the information content of each LR cell’s firing rate , assessing the correlation and mutual information with both head direction and speed . We found that single cell activity in the LR population could encode both head direction and head speed ( Figure 10Aii , Bii , Cii ) , but there was a clear tradeoff between the two types of information . This tradeoff between directional versus speed encoding was explained by the level of heterogeneity in the presynaptic preferred direction distribution ( Figure 10D–F ) , making intuitive sense . If an LR cell receives inputs that represent each HD equally , then it is not biased towards any one HD and encodes direction poorly . However , it encodes head speed very strongly in this case because it is able to sample the speed across all directions—there are no directional blind spots where the LR cell cannot detect the speed of head rotation from its presynaptic inputs . On the other hand , consider an LR cell that , by chance , gets inputs from a higher proportion of HD cells encoding a direction around 180 degrees . Now , the output of this LR cell is better correlated with direction , acting as a broadly tuned HD cell itself and preferring 180 degrees , but also firing at most other directions . However , this LR cell’s encoding of head speed gets worse because it under-samples many of the head directions faced by an animal . Thus , non-uniform HD inputs via depressing thalamocortical synapses represent a simple mechanism by which LR cells can conjunctively encode both head direction and head speed . Overall , our results predict in vivo LR neuronal spike trains that are likely to correlate with both the head direction and rotational speed of an animal , with a tradeoff between direction versus speed coding seen across individual LR cells ( Figure 10E ) .
The small , excitable LR cells are unique among pyramidal cells in RSG , and there is no evidence , to our knowledge , for such cells in any other cortical regions ( Brennan et al . , 2020; Holmgren et al . , 2003; Jiang et al . , 2015; Kurotani et al . , 2013; Wyss et al . , 1990 ) . Indeed , the ‘granular’ in granular retrosplenial cortex refers to the appearance of these dense small cell bodies in superficial RSG ( Sripanidkulchai and Wyss , 1987; Vogt and Peters , 1981 ) . Thus , LR cells are the defining morphological feature of RSG . The distinct electrophysiological properties of LR neurons , specifically , play an integral role in the RSG’s unique capacity to process anterior thalamic head direction inputs . We have previously reported that the low rheobase and lack of spike frequency adaptation of these neurons are their defining computational features ( Brennan et al . , 2020 ) . For this reason , we refer to them as low-rheobase ( LR ) neurons . They have also been called late-spiking ( LS ) neurons ( Kurotani et al . , 2013; Yousuf et al . , 2020 ) , but we argue this name is not optimal for several reasons . First , many other neurons in superficial RSG are also late spiking ( Brennan et al . , 2020 ) , with L2/3 fast-spiking ( FS ) interneurons and also some RS neurons exhibiting a substantial delay to first spike , likely due to increased Kv1 . 1 or 1 . 2 channel expression in this region compared to other cortical areas ( Kurotani et al . , 2013 ) . Thus , late-spiking is neither a distinctive feature of LR neurons nor excitatory neurons in this region . Second , the name ‘late-spiking ( LS ) neuron’ is already the accepted and widely used nomenclature referring to a distinct inhibitory neuronal subtype , the neurogliaform cells that are located throughout the cortical layers in many regions of the brain , including within layer 1 of RSG ( Cruikshank et al . , 2012; Hestrin and Armstrong , 1996; Kawaguchi and Kubota , 1997; Overstreet-Wadiche and McBain , 2015 ) . Instead , the defining computational feature of the small pyramidal cells in L2/3 of the RSG is their low rheobase , and this nomenclature serves to provide an unambiguous name for these hyperexcitable cells ( Brennan et al . , 2020 ) . Previous work has reported TC-evoked responses in layer 5 RS neurons at their apical dendrites ( Yamawaki et al . , 2019b ) , with some variation in the magnitude of responses across cells . Our results reproduce these observations ( Figure 2—figure supplement 1 ) . Layer 5 is not a homogenous layer , often divided into sublayers 5A and 5B ( Sempere-Ferràndez et al . , 2019; Sempere-Ferràndez et al . , 2018; Sigwald et al . , 2020; Sripanidkulchai and Wyss , 1987; Yamawaki et al . , 2016a ) and contains a variety of pyramidal cells , including the thin-tufted and thick-tufted neurons who have been shown to exhibit different responses to external inputs ( Sempere-Ferràndez et al . , 2018; Wyss et al . , 1990 ) . Further work is needed to determine whether any particular subtype of layer five pyramidal neurons may exhibit substantial TC-evoked responses , but our results , reporting significantly larger responses to TC input by LR neurons , suggest LR cells are the predominant spatial information-encoding subtype within RSG . The dorsal subiculum , which serves to transmit allocentric spatial information such as axis and boundary vector signals ( Lever et al . , 2009; Derdikman , 2009; Olson et al . , 2017; Simonnet and Brecht , 2019; Bicanski and Burgess , 2020 ) , also precisely targets LR neurons via projections predominantly to layer 3 of RSG ( Figure 5; Nitzan et al . , 2020; Yamawaki et al . , 2019a ) . These inputs overlap with LR cell bodies , basal dendrites , and apical dendrites in L1b/c and evoke larger excitatory postsynaptic currents in superficial cells compared to layer 5 pyramidal neurons ( Figure 5; Nitzan et al . , 2020; Yamawaki et al . , 2019a ) . Thus , the distinct morphology and intrinsic properties of LR neurons make them ideally suited to integrate head direction input from the thalamus and spatial inputs from the hippocampal formation via the dorsal subiculum . Indeed , this integration of various types of directional and distance information is often stated as the key computational function of the retrosplenial cortex as a whole ( van Wijngaarden et al . , 2020; Burgess et al . , 2001; Byrne et al . , 2007; Epstein , 2008; Ichinohe et al . , 2003; Maguire , 2001 ) , further highlighting the defining role that LR cells are likely to serve in the RSG . We have shown that thalamocortical synapses onto LR cells are depressing ( Figure 7 ) . Our modeling results demonstrate that such depressing synapses allow LR neurons to compute angular head speed from head direction input , leading to robust encoding of angular speed in the postsynaptic LR firing rate ( Figure 8 ) . This result is in line with previous studies ( Abbott et al . , 1997; de la Rocha and Parga , 2008; Puccini et al . , 2007 ) that use synaptic depression to implement neural circuits that perform rate of change computations . We also find that LR encoding of angular head speed is improved by the fact that input HD cells display anticipatory firing ( Figure 9; Blair et al . , 1997 ) . This improvement not only allows LR cells to encode current head speed with a shorter time lag ( Figure 9C ) , but also strengthens the correlation with head speed regardless of lag ( Figure 9B ) . This proposed mechanism by which depressing synapses compute head speed is fully generalizable , and thus may also be of relevance to other brain circuits employing HD-like population codes ( Maunsell and Van Essen , 1983 ) . Furthermore , we have shown that this thalamocortical synapse can support conjunctive encoding of both head direction and angular head speed by individual LR cells ( Figure 10 ) . Our results make specific predictions about the coding properties of LR cells that can be tested with in vivo recordings . First , based on their intrinsic properties ( Figure 1—figure supplement 1; Brennan et al . , 2020 ) , LR cells in superficial RSG are likely to show high firing rates and spike widths intermediate to the standard ‘broad/narrow’ criteria currently used to distinguish putative RS and FS cells in most cortical recordings . Thus , future recordings will need a large sampling of cells in L2/3 of RSG to provide enough data to identify the predicted three distinct clusters of spike shapes ( RS/LR/FS ) . Second , we expect LR cell activity to be correlated with angular head speed with a relatively small lag ( Figures 8 and 9 ) . Third , we predict that the experimentally observed head velocity tuning curves will be concave up and exhibit approximately quadratic scaling at low rotational speeds , as our analytical work suggests ( Figure 8; Appendix ) . Fourth , we anticipate a significant proportion of LR cells will show conjunctive encoding , where both angular head speed and direction are encoded . A key aspect of this conjunctive encoding , as predicted by our simulations ( Figure 10 ) , is that individual cells will show a tradeoff between directional and speed encoding . As a population , this is likely to allow LR cells to comprehensively encode conjunctive speed and directional information and provide this information to downstream targets , helping with spatial orientation computations within RSG . This predicted conjunctive encoding will also necessitate that the test of predictions 2 and 3 be carried out in a head-direction delimited manner . Our modeling work so far has focused on understanding the computational implications of thalamic inputs to LR cells . Future work , beyond the scope of the present study , will be needed to understand how these thalamic inputs interact precisely with dorsal subiculum inputs . Given the diversity of spatial and directional encoding seen in the dorsal subiculum ( Lever et al . , 2009; Derdikman , 2009; Olson et al . , 2017; Simonnet and Brecht , 2019; Bicanski and Burgess , 2020 ) , computational models will allow for the rigorous undertanding of how each possible type of subicular input ( e . g . axis versus boundary vector cells ) to LR cells interacts with thalamic head direction inputs . Very recent work on understanding the tuning properties of subicular cells in a projection-specific manner will help to narrow the functional range of possible dorsal subicular inputs to LR cells ( Kitanishi et al . , 2021 ) . We anticipate that one key impact of dorsal subicular inputs to LR cells will be to impose a spatial filter on the angular speed and directional predictions stated above . In particular , the precise organization of layer 1 dendrites and axons may make LR cells most responsive to the near-synchronous arrival of inputs from both thalamic head direction cells ( at distal apical dendrites in L1a ) and dorsal subicular boundary vector or axis cells ( at more proximal apical dendrite locations in lower L1 ) . Similar cooperative dendritic activation patterns are also a hallmark of integration of entorhinal and CA3 inputs by CA1 pyramidal cells , where they help to overcome the effects of strong dendritic inhibition and shape the firing of place cells ( Ahmed and Mehta , 2009; Golding and Spruston , 1998; Kamondi et al . , 1998; Takahashi et al . , 2012 ) . LR neurons do not synapse onto neighboring excitatory neurons within layers 2/3 ( Brennan et al . , 2020 ) , and no ( 0/9 ) pairs tested in this study between LR and layer 5 RS cells exhibited connectivity ( data not shown ) . Thus , LR cells likely do not provide any substantial input to other LR cells or any RS cells located in layers 2–5 of ipsilateral RSG . Instead , LR neurons send their axons into the corpus callosum and may likely target homotopic regions of contralateral RSG ( Brennan et al . , 2020; Kurotani et al . , 2013 ) . Indeed , retrograde injections into one RSG hemisphere have been shown to predominantly label small contralateral L2/3 cells ( Sripanidkulchai and Wyss , 1987; Van Groen and Wyss , 2003 ) , most likely corresponding to the LR cells that constitute the majority of cells in L2/3 ( Brennan et al . , 2020 ) . Our supplementary results ( Figure 6—figure supplement 1 ) show that inputs from contralateral RSG preferentially and strongly target RS neurons , with almost no recruitment of LR neurons . This is consistent with the observed distribution of afferent axons from contralateral RSG: these axons and terminals avoid L1a and L3 where all LR dendrites are located ( Figure 6—figure supplement 1 ) . Thus , we propose the following hypotheses for LR downstream targets and possible function: LR neurons in one hemisphere receive unilateral inputs from directional cells in the anterior thalamus ( Figures 1 , 2 and 6 ) . These inputs are utilized to encode information about both the speed and direction of head rotations and are subsequently transmitted to RS cells in contralateral , but not ipsilateral , RSG ( Figure 6—figure supplement 1 ) . Thus , LR cells may serve to perform a hemispheric switch of rotational speed and direction information . Given the known bidirectional connectivity between secondary motor cortex and RSG ( Yamawaki et al . , 2016a ) , RS cells may be able to utilize inputs from contralateral LR cells to perform comparisons of the actual head speed and direction signal with motor efference signals , helping to sharpen the code for spatial orientation in the RSG . However , extensive future investigations of this contralateral circuit are needed to explore these hypotheses . In contrast to thalamic and DS inputs to RSG , projections from both the claustrum and anterior cingulate cortex avoid laminar overlap with LR apical dendrites , instead projecting to the lower divisions of L1/2 and L5 to target RS apical and basal dendrites ( Figures 3 and 4 , and 6 ) . Both the CLA and ACC are heavily implicated in a range of non-spatial behaviors often described as being ‘cognitive’ or ‘mnemonic’ in function ( Botvinick , 2007; Brown and Braver , 2005; Carter et al . , 1998; Devinsky et al . , 1995; Kim et al . , 2016; Mohanty et al . , 2007; Smith et al . , 2012; Smythies et al . , 2012; Stevens et al . , 2011 ) , but there is also evidence that these regions exhibit some degree of spatial information processing ( Guterstam et al . , 2015; Jankowski and O'Mara , 2015; Sutherland et al . , 1988; Whishaw et al . , 2001 ) . Indeed , 7–15% of cells in the claustrum were found to encode place or boundary-related information ( Jankowski and O'Mara , 2015 ) , though this percentage is relatively low compared to the 60% of anterior thalamic ( Taube , 1998 ) and 61% of dorsal subicular ( Kitanishi et al . , 2021 ) neurons that are known to clearly encode elemental direction , place , and other spatial features . Regardless , retrosplenial RS neurons may be receiving direct spatial inputs from the CLA and ACC in addition to the cognitive and mnemonic information relayed by these two regions . We also speculate that retrosplenial RS neurons may receive directional and spatial information that has already been heavily integrated by LR neurons in the contralateral hemisphere ( Figure 6—figure supplement 1 ) , as discussed above . This convergence of disparate signals onto RS cells could then serve to support functions that require both spatial and non-spatial integration , such as contextual fear conditioning , a key function attributed to the RSC ( de Sousa et al . , 2019; Keene and Bucci , 2008a; Keene and Bucci , 2008b; Kwapis et al . , 2015; Yamawaki et al . , 2019a ) . Indeed , a recent study reported that selective ablation of putative retrosplenial RS cells located near the boundary and within upper layer 5 resulted in contextual fear amnesia ( Sigwald et al . , 2020 ) , indicating that these cells are involved in the fear-related functions of the retrosplenial cortex ( Lukoyanov and Lukoyanova , 2006; Yamawaki et al . , 2019a; Yamawaki et al . , 2019b ) . The laminar location of these cells corresponds well to the position of the RS cells recorded in our study that we show to preferentially receive CLA and ACC inputs . Both the CLA ( Cho et al . , 2017; Ipser et al . , 2013; Vakolyuk et al . , 1980; Vetere et al . , 2017; Zingg et al . , 2018 ) and ACC Frankland et al . , 2004; Han et al . , 2003; Steenland et al . , 2012 have been heavily implicated in fear-associated behaviors , suggesting again that CLA and ACC inputs to L3 RS cells help to support the role of these neurons in contextual fear conditioning . Future work that selectively inactivates CLA versus ACC axon terminals in RSC will be necessary to causally confirm the role of each of these synapses in fear conditioning . Another important consideration within the circuits examined here is the role of feedforward inhibition . Matrix TC inputs evoke feedforward inhibition to regulate cortical signaling through both disinhibition ( Anastasiades et al . , 2021; Delevich et al . , 2015 ) and the disynaptic inhibition of pyramidal neurons ( Cruikshank et al . , 2012; Yamawaki et al . , 2019a; Yamawaki et al . , 2019b ) . Similarly , ClaC inputs invoke feedforward inhibition in several cortical regions , particularly through recruitment of neuropeptide Y ( NPY ) and , to a lesser degree , FS cells ( Jackson et al . , 2018 ) . Long-range inhibitory signals from CA1 of the hippocampus also target apical dendrites in retrosplenial layer 1a , converging with excitatory anterior thalamic inputs , to precisely regulate these TC inputs and establish a hippocampo-thalamo-retrosplenial network ( Yamawaki et al . , 2019b ) . This fine-grained laminar overlap strongly suggests that these inhibitory signals may regulate responses to matrix TC input more strongly for LR than layer 5 RS cells and should be investigated further , particularly in the context of integration of spatial information processing . Future work will examine the effect of feedforward inhibition on the subpopulations of retrosplenial principal neurons in response to these converging inputs in order to establish a thorough understanding of the circuitry facilitating retrosplenial information processing , particularly with regard to head direction signals . In summary , our results highlight a superficial retrosplenial circuit enabled by the precise sublaminar organization of distinct principal neuronal subtypes and axonal afferents . LR neurons receive directional and spatial inputs from the anterior thalamus and dorsal subiculum . The synaptic dynamics of thalamic inputs to LR cells can give rise to rate coding of angular head speed in LR cells . In contrast , neighboring RS neurons in RSG respond very weakly to these directional inputs , as their apical and basal dendrites distinctly avoid laminar overlap with anterior thalamic and subicular afferents . Instead , RS neurons respond to claustrocortical and anterior cingulate inputs . Determining how these two parallel streams of information are integrated in downstream neurons within both the ipsilateral and contralateral granular and dysgranular retrosplenial cortices is the next critical step toward a mechanistic understanding of retrosplenial computations .
All procedures and use of animals were approved by the University of Michigan Institutional Animal Care and Use Committee . The following mouse lines were used for the CRACM experiments: Ai14 ( Jackson Laboratories , 007914 ) , Ai32 ( Jackson Laboratories , 024109 ) , C57BL6 wildtypes ( Charles River , stock #027 ) , Camk2αCre ( Jackson Laboratories , 005359 ) , Grp-KH288Cre ( RRID:MMRRC 037585-UCD ) , PvalbCre ( PV-IRES-Cre; Jackson Laboratories , 008069 ) , and PvalbCre x Ai14 ( crossed in house ) . A combined total of 70 mice of both sexes between the ages of P41–P184 were used in this study . Our model circuit consists of an RSG LR cell receiving input from an ensemble of N thalamic HD cells , via synapses exhibiting short-term depression . Thalamic HD cells exhibit an anticipatory time interval , or ATI: for each cell , there exists some constant duration Ams such that the cell tends to spike Ams prior to when the animal’s heading equals the preferred direction of the cell . We define this notion more precisely following a previous study ( Blair et al . , 1997 ) . Restrict attention to a specific HD cell , with ATI Ams , and let θ denote its PA when the angular head velocity is zero . The ATI is defined via the property that when angular head velocity equals ω , the PA of this cell shifts from θ to θ-ωA . Equivalently , we can think of HD cell PAs as static and instead say anticipatory firing effectively transforms the heading trajectory itself: if θTt describes the true angular trajectory , the effective trajectory experienced by our chosen HD cell is:θA ( t ) =θT ( t ) +A⋅θT˙ ( t ) To simulate the angular trajectory θTt , we employ in vivo mouse head tracking recordings from the data set CRCNS-th1 ( Peyrache et al . , 2015 ) . These in vivo heading recordings were originally sampled at a relatively low rate of approximately 40 Hz; in order to facilitate use of this data at the finer time scale of HD cell spiking , we linearly interpolated the raw data . Angular head velocity was computed using the standard centered approximation to the derivative:θ˙T ( ti ) ≈θT ( ti+1 ) −θT ( ti−1 ) ti+1−ti−1 In the Tsodyks-Markram ( TM ) model ( Tsodyks et al . , 1998 ) of short-term synaptic plasticity , each synapse has a finite pool from which it releases vesicles into the cleft upon arrival of a presynaptic spike . The state of the synapse at any moment in time is characterized by the triple x , u , g , specified as: Here , t is measured in milliseconds , g in umho , and the variables x and u are dimensionless . Depression results from depletion of x due to a spike train , followed by slow recovery of the vesicle pool; facilitation results from increase in u due to a spike train , followed by slow decay of this release probability . Formally , these dynamical variables satisfy the system:dxdt=1-xτd-u+x-δt-tspdudt=-uτf+U1-u-δt-tspdgdt=-gτg+Au+x-δt-tsp Here , tsp denotes an arbitrary presynaptic spike time , and the δ term specifies a discontinuous modification to the variable upon arrival of a presynaptic spike . We use the notation f±t=limh→0±ft+h , and thus u+ and u- satisfy the relation u+=u-+U1-u- . The parameters τd , τf , and τg set the timescale of depression recovery , facilitation decay , and synaptic conductance decay , respectively . Note that u+≥U always , so U represents the minimum fraction of x contributing to the conductance on each presynaptic spike arrival . Finally , the parameter A is just a tunable synaptic weight ( with units of umho ) . In the regime of τd≫τf , depression dominates the synaptic dynamics; conversely , in the regime of τf≫τd , facilitation dominates . Accordingly , the limits τf→0 and τd→0 describe depression-only and facilitation-only dynamics , respectively . On the other hand , when τf and τd are on the same order of magnitude , the synapse may exhibit combined depressing-facilitating dynamics . We utilized an implementation of the Tsodyks-Markram model as a NEURON mechanism , freely available for download from Model DB ( https://senselab . med . yale . edu/ModelDB/showmodel . cshtml ? model=3815 ) . For all simulations , we use the parameters:τd=270 ms , τf=40 ms , U=0 . 28in the TM model . We obtained this parameter set by fitting the TM model response to recorded EPSP amplitudes evoked via thalamocortical stimulation of RSG LR cells with a 10 Hz pulse train ( Figures 2 and 7 ) . This was accomplished by searching parameter space exhaustively for the parameter set minimizing a least-squares loss function . The resultant TM dynamics were moderately depressing , in accordance with the experimental results . Non-depressing synapses were modeled as standard exponential synapses with instantaneous rise time . We model the postsynaptic LR cell using the morphologically detailed model originally presented in Brennan et al . , 2020 . This model , implemented in NEURON ( Carnevale and Hines , 2006 ) , consists of Hodgkin-Huxley conductances representing a fast sodium current , a delayed rectifier potassium current , and a Kv1 . 1-mediated slow potassium current . We place each HD input → LR synapse at a random location on a distal apical dendrite of the LR cell; varying this synaptic placement does not qualitatively change results ( data not shown ) . Each postsynaptic cell receives input from N presynaptic HD cells , each of which has a unique PA . When studying postsynaptic speed coding , we initially drew the PA of each HD cell uniformly at random from 0 , 2π . Later on , we examined the effect of introducing nonuniform PA distributions . In this case , we assumed that the PA distribution of each LR cell was continuous as a function of angle , and thus modeled the PA distribution probability densities randomly as resulting from Brownian bridge processes ( to ensure 2π periodicity of the density ) . We then used inverse transform sampling to draw from the generated distributions . To quantify the extent to which postsynaptic activity reflects head turning speed , we utilized two similarity measures M: Pearson correlation and mutual information . In fact , we used the time-lagged counterparts of these measures: for a pair of time series xt , yt , their l-lagged similarity measure is Mxt , yt-l . Varying l , we obtain the cross-correlation and cross-mutual information between the two variables . Throughout the paper , when referring to an instance of measure M between time series xt , yt , we either report the function l↦Mxt , yt-l or just the maximum value of the function:maxlMxt , yt-l In order to compute mutual information , we discretized the time series for head turning speed and postsynaptic firing rate into 40 bins each and calculated the mutual information between these discrete proxies .
The granular retrosplenial cortex ( RSG ) is critical for both spatial and non-spatial behaviors , but the underlying neural codes remain poorly understood . Here , we use optogenetic circuit mapping in mice to reveal a double dissociation that allows parallel circuits in superficial RSG to process disparate inputs . The anterior thalamus and dorsal subiculum , sources of spatial information , strongly and selectively recruit small low-rheobase ( LR ) pyramidal cells in RSG . In contrast , neighboring regular-spiking ( RS ) cells are preferentially controlled by claustral and anterior cingulate inputs , sources of mostly non-spatial information . Precise sublaminar axonal and dendritic arborization within RSG layer 1 , in particular , permits this parallel processing . Observed thalamocortical synaptic dynamics enable computational models of LR neurons to compute the speed of head rotation , despite receiving head direction inputs that do not explicitly encode speed . Thus , parallel input streams identify a distinct principal neuronal subtype ideally positioned to support spatial orientation computations in the RSG .
Sitting in your car , about to drive home after a long day at work , you realize you have no idea which way to go: you recognize where you are right now , and you remember the name of the street your house is on , but you cannot figure out how to get there . This spatial disorientation happens to people with damage to a brain region called the retrosplenial cortex , whose role and inner workings remain poorly understood . Recent evidence has shown that this area contains ‘low-rheobase’ neurons which are not seen anywhere else in the brain , but what do these neurons do ? Brennan , Jedrasiak-Cape , Kailasa et al . decided to explore the role of these neurons , focusing on the brain regions they are connected to . Experiments were conducted in mice using optogenetics , a technique that activates neurons using pulses of light . This revealed that brain areas involved in processing information about direction and position preferentially communicate with low-rheobase neurons rather than with nearby , more standard neurons in the retrosplenial cortex . The way these spatial signals are sent to the low-rheobase neurons allows these cells to ‘calculate’ how fast a mouse is turning its head using only information about which direction the mouse is facing . Essentially , this neuron can turn directional compass-like signals into a gyroscope signal that can track both direction and speed of head movement . These unique neurons may therefore be ideally suited to combine information about direction and space , suggesting that they may have evolved specifically to support spatial navigation . Individuals with Alzheimer’s disease show exactly the same type of spatial disorientation as individuals with direct damage to the retrosplenial cortex . This region is also one of the first to show altered activity in Alzheimer’s disease . Exploring whether these unique retrosplenial neurons and their communication patterns are altered in Alzheimer’s disease models could help to understand and potentially treat this debilitating condition .