Our data shows specific and robust modulation of units in the parietal cortex by both respiration and θ. However, the rhythmic entrainment of units by either of the two slow oscillations depends strongly on (i) vigilance state and (ii) mean firing rate (FR). In order to gain a systematic overview, we compared all major sleep and waking states. In two of these states, active waking (AW) and REM sleep, both oscillations are simultaneously present. At the field potential level θ oscillations are dominant in both states. At the cellular (unit) level, however, entrainment by respiration is prevailing during AW while θ is more efficient during REM sleep. This observation emphasizes potential discrepancies between the observed power of network-level oscillations and behavior of individual neurons which should be kept in mind when interpreting collective neuronal signals (field potentials, EEG, MEG). A second finding of the present study is that in several states coupling of units to θ or Resp, respectively, was dependent on discharge frequency. Whether this activity-dependence of entrainment reflects differences in network integration of different cell types or of differentially active neurons of the same type is presently unclear. In any case, the correlation between neuronal activity and coupling to slow network oscillations may be important for understanding ensemble activity in oscillating networks. A further new observation is that units couple to different phases of respiration depending on the behavioral state. This finding may be explained by state-dependent differences in respiration-related synaptic input to the parietal network, by recruitment of different types of interneurons within the parietal cortex, or by other, more complex state-dependent interactions between different networks. In any case, all findings underline the strong state-dependence of unit entrainment by both, respiration and θ oscillations.
Some of the present findings from freely moving mice confirm our earlier results from head-fixed  and urethane-anaesthetized animals . In these preparations, we had already reported respiration-driven modulation of hippocampal [57, 63] and posterior parietal and prelimbic neurons [32, 65]. While our previous observations were mainly done in REM sleep or wake immobility, we here provide a systematic comparison of modulation by θ and respiration during all major states of vigilance/behavior: REM sleep, NREM sleep, waking immobility and active waking. The latter is of particular interest since it contains θ oscillations and, at the same time, strong respiration-coupled inputs from sniffing behavior. In this state, entrainment of neurons by respiration was dominant, with particularly strong effects on neurons with high discharge frequency. It is well feasible that this reflects the integration of sensory signals from nasal respiration or sniffing in the multimodal association network of the parietal cortex.
Earlier reports have shown that neurons in several neocortical regions including the parietal cortex of rats and mice are modulated by theta oscillations during locomotion and REM sleep . Here, we confirm this finding for REM sleep while foraging behavior could not be tested within the limited space inside the plethysmograph. During active waking, neurons were entrained by both θ and respiration (sniffing), with dominant modulation by respiration. A similar concomitant modulation of neurons by θ and respiration has been described by Biskamp and colleagues for medial prefrontal cortex neurons in mice . It may well be that theta becomes more efficient for unit entrainment in states of locomotion, but it may also be worth-while testing the strength of respiration-driven entrainment in this situation. In fact, theta and respiration can easily be confounded in mice due to their strongly overlapping frequency ranges .
It is unclear how respiration-entrained signals are transmitted to distant cortical brain areas. Clearly, feedback from the nasal airstream plays a role, since RR diminishes after tracheotomy , bulbectomy [4, 5], chemogenetic inhibition of the OB , depletion of the olfactory epithelium [33, 39] or nasal occlusion . It may well be that mechanic stimulation of olfactory epithelial cells by the airflow  are critical for RR generation . However, Karalis and Sirota  recently demonstrated that lesioning the olfactory epithelium abolishes RR at the field potential level but does not eliminate neuronal entrainment by respiration. This finding argues for additional non-nasal sources of respiration-related activity modulation, possibly by collateral discharges from the rhythm-generating respiratory networks in the brainstem. An additional possibility are direct mechanical effects on neuronal activity. Cortical neurons do react to weak mechanical stimulation , and mechanosensitive Piezo2 ion channels have recently been shown to be present in cortical pyramidal cells, opening the possibility that minor pressure fluctuations in the brain parenchyma may translate into rhythmic entrainment of activity [3, 14]. Mechanical transduction processes could likewise mediate the heartbeat-dependent modulation of activity [13, 25, 60] for which there is no central rhythm generator. Our present results on modulation of neuronal activity by respiration do not allow to distinguish between the different possible mechanisms which are, notably, not mutually exclusive. In any case, we confirm that the power of the local field potential is not consistently correlated with the strength of unit entrainment , suggesting that lamina-specific synaptic input is not the only mechanism of respiration-entrained neuronal discharges. Which of the two other mechanisms (corollary discharges from brainstem rhythm generators or mechanical stimulation of pyramidal cells) is responsible for the observed modulation of neuronal activity remains presently unclear.
Respiration-related network activity is a brain-wide phenomenon , and respiratory modulation of unit activity was demonstrated in a large number of brain regions [4, 5, 12, 32, 33, 35, 63]. This poses the question of its putative role for brain function. It has been suggested that the brain-wide coordination of activity by slow network oscillations contributes to signal integration between different neuronal networks [15, 28, 31, 51]. Respiration-related network oscillations (RR) may provide such a synchronizing signal, independent from their immediate relation to respiration or olfaction. The parietal cortex was found to play a critical role in decision-making processes [2, 22, 36, 40, 43] that strongly rely on the brain-wide integration of sensory information, behavioral and internal state and intended actions. It seems possible that RR provides a temporal scaffold for the underlying computations in the parietal cortex. Moreover, the parietal cortex serves important roles in spatial navigation [22, 36, 61]. Whether spatial cognition is specifically modulated by respiration is currently unknown, but would be well compatible with our present findings, especially the state-dependent expression of RR and its coordination with θ oscillations. A closely related cognitive process is spatial or declarative memory formation . Of note, respiratory signals modulate hippocampal sharp-wave ripples [33, 38] – a biomarker of memory consolidation  – implicating a role of respiration in the underlying processes [16, 23]. Importantly, the presence of localized, concurrent ripple oscillations in the parietal cortex was recently observed in rats  possibly aiding information transfer from hippocampal to neocortical networks during memory consolidation. Interestingly, a recent study by Tingley and colleagues  found that hippocampal sharp wave-ripples additionally influence metabolic processes, highlighting the embeddedness of brain function within the whole body [50, 58] in which respiratory signals potentially serve a critical role .
Taken together, accumulating evidence shows the impact of bodily signals such as respiration on brain dynamics, opening possibilities to formulate and test novel hypotheses on the interaction between neuronal activity, behavior and cognition. In addition, our present findings underline the state-dependence of entrainment of neocortical neurons, which can be driven by θ, respiration or both oscillations depending on firing rate and behavioral state.