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Neuron populations use variable combinations of short-term feedback mechanisms to stabilize firing rate [1]

['Sarah Pellizzari', 'University Of North Carolina At Greensboro', 'Greensboro', 'North Carolina', 'United States Of America', 'Min Hu', 'Lara Amaral-Silva', 'University Of Missouri', 'Columbia', 'Missouri']

Date: 2023-01 

Neurons tightly regulate firing rate and a failure to do so leads to multiple neurological disorders. Therefore, a fundamental question in neuroscience is how neurons produce reliable activity patterns for decades to generate behavior. Neurons have built-in feedback mechanisms that allow them to monitor their output and rapidly stabilize firing rate. Most work emphasizes the role of a dominant feedback system within a neuronal population for the control of moment-to-moment firing. In contrast, we find that respiratory motoneurons use 2 activity-dependent controllers in unique combinations across cells, dynamic activation of an Na + pump subtype, and rapid potentiation of Kv7 channels. Both systems constrain firing rate by reducing excitability for up to a minute after a burst of action potentials but are recruited by different cellular signals associated with activity, increased intracellular Na + (the Na + pump), and membrane depolarization (Kv7 channels). Individual neurons do not simply contain equal amounts of each system. Rather, neurons under strong control of the Na + pump are weakly regulated by Kv7 enhancement and vice versa along a continuum. Thus, each motoneuron maintains its characteristic firing rate through a unique combination of the Na + pump and Kv7 channels, which are dynamically regulated by distinct feedback signals. These results reveal a new organizing strategy for stable circuit output involving multiple fast activity sensors scaled inversely across a neuronal population.

We have been investigating mechanisms that underly reliable output of the respiratory network in amphibians [ 22 – 24 ]. Given the role of the dynamic Na + pump in locomotion [ 3 , 20 ], we investigated its role in respiratory motoneurons. In beginning this work, we identified activity-dependent feedback characteristic of the dynamic Na + pump, with intense stimulation leading to membrane hyperpolarization over the following minute. Because the dynamic Na + pump generates outward current without opening an ion channel, this “ultraslow afterhyperpolarization” (usAHP) does not usually occur with changes in membrane input resistance (R in ) [ 3 , 21 ]. Thus, we were struck as this usAHP was accompanied by a range of decreases in R in from cell to cell, spanning from small to large. This result led us to hypothesize that variable combinations of activity-dependent mechanisms involving the dynamic Na + pump and fast enhancement of a K + channel, which would decrease R in , stabilize activity across this population of motoneurons. Below, we detail how 2 feedback controllers, the dynamic Na + pump (a Na + sensor) and Kv7 channels (through voltage-sensitive potentiation), scale reciprocally across neurons for the fast control of firing rate. These results indicate that stable circuit output can arise through unique sets of rapid activity sensors spread throughout a neuronal population.

The Na + /K + ATPase is best known for its housekeeping role in ion regulation; however, it is expressed selectively in some neurons to control excitability through activity-dependent feedback [ 17 ]. After a burst of action potentials, the loading of intracellular Na + recruits a subtype of the Na + /K + ATPase with a low affinity for Na + (referred to here as the “dynamic” Na + pump). When this pump kicks on, it hyperpolarizes the membrane for tens of seconds to reduce the probability of future firing [ 18 ]. Feedback control by the dynamic Na + pump plays an important role in animal behavior, as it shapes locomotor performance in insects [ 19 ], amphibians [ 3 , 20 ], and rodents [ 21 ]. Therefore, the dynamic form of the Na + pump represents a conserved sensor of Na + dynamics, which controls neuronal output in response to recent firing.

Neural circuits must produce stable output in an ever-changing environment or else a suite of neurological disorders follow [ 1 , 2 ]. To accomplish this goal, many neurons can track their firing rate in real time and make rapid physiological adjustments to stabilize activity. One important strategy involves cellular systems that transduce firing rate through the dynamics of Ca 2+ , Na + , or voltage, which then alter excitability over the next several seconds to keep activity from drifting into an unhealthy range [ 3 – 9 ]. These mechanisms rely on fast negative feedback and have a potent stabilizing effect on neuronal output. However, they differ from what is often termed “homeostatic plasticity,” as intrinsic biochemical and physical dynamics maintain firing rate within a tight range rather than bringing activity back into line following a large perturbation [ 10 – 12 ]. Although many signals feed back onto neurons, a design feature of negative feedback systems across biology involves a dominant sensory signal for a given regulated variable, e.g., changes in pressure for yeast osmoregulation [ 13 ] and pH for blood gas regulation [ 14 ]. This organization may prevent the unstable output that occurs when multiple signals with different set points try to maintain homeostasis of a single process [ 15 , 16 ]. Thus, most studies on the moment-to-moment regulation of neuronal output address how a key feedback signal controls firing rate within a given cell type [ 3 – 9 ].

To determine the role of each feedback mechanism for the control of firing rate, we stimulated neurons in brain slices with current input that mimicked physiological synaptic drive ( Fig 4B ). This allowed us to simulate respiratory-related synaptic input in isolated motoneurons and avoid confounds associated with drug application in the entire network. Upon the sequential block of the dynamic Na + pump with 2 μM ouabain and then Kv7 with 10 μM XE-991, we observed a continuum of changes in firing rate during fictive synaptic input associated with breathing. Inhibition of the dynamic Na + pump led to progressive hyperexcitability in some neurons, and these neurons were less sensitive to the block of Kv7 channels ( Fig 4C and 4D , top). In neurons that were less sensitive to the block of the dynamic Na + pump, hyperexcitability occurred in response to inhibition of Kv7 channels along a continuum ( Fig 4C and 4D , bottom). These results indicate that reciprocally expressed sets of the dynamic Na + pump and Kv7 channels regulate firing rate during physiological bursting. To confirm the role of activity-dependent feedback, we applied each drug to silent neurons. Both blockers had little-to-no effect on the resting membrane potential ( Fig 4E and 4F ). Application of ouabain at 20 μM to inhibit the constitutively active Na + pump [ 20 ] led to depolarization and loss of the membrane potential, supporting 2 μM ouabain’s actions on the “dynamic” form of the pump ( Fig 4E and 4F ). Little-to-no influence of these currents on the resting membrane potential supports the idea that dynamic chemical and physical signals during ongoing activity engage the Na + pump and Kv7. Thus, neurons within the same motor pool regulate their firing rates during bursting through unique combinations of activity-dependent feedback that track different cellular readouts of neuronal activity.

(A) Identified vagal motoneurons receiving input from the respiratory rhythm generator exhibit slow afterhyperpolarization following rhythmic burst firing, demonstrating that physiological bursting is followed by prolonged membrane hyperpolarization, consistent with recruitment of the dynamic Na + pump and Kv7 channels. (B) Current clamp recordings of firing in response to stimulation of current input that mimics synaptic drive in slices. (C) Each neuron showed differential changes in firing rate in response to 2 μM ouabain and 10 μM XE-991 along a spectrum (n = 14 from N = 8 animals). (D) Top example shows a neuron with a large contribution of the Na + pump for the control of firing rate, with little input from Kv7 channels. Bottom example shows a neuron with little contribution from the pump but a large role for Kv7 in controlling firing rate. (E) Example recordings of resting membrane potential in silent neurons during application of 2 μM ouabain (n = 8 neurons from N = 4 animals), 10 μM XE-991 (n = 8 neurons from N = 4 animals), and 20 μM ouabain to block the “housekeeper” form of the Na + pump (n = 5 neurons from N = 3 animals). (F) Mean data for effects of each drug on resting membrane potential. The data underlying this figure can be found in S1 Data .

We last sought to determine if respiratory motoneurons experience slow activity-dependent hyperpolarization in the intact network, and then, if reciprocal co-expression of the dynamic Na + pump and Kv7 channels plays a role in regulating firing rate during realistic activity. Fig 4A shows whole-cell current clamp recordings of identified vagal motoneurons from 3 different “semi-intact preparations” receiving physiological synaptic inputs from the respiratory rhythm generator, as described in reference [ 45 ]. After rhythmic bursts associated with lung ventilation, each neuron exhibited an afterhyperpolarization that lasted for several seconds before the next burst. Therefore, slow activity-dependent hyperpolarization occurs within the native network, suggesting a role for the dynamic Na + pump and Kv7 in regulating excitability to control respiratory motor behavior.

What proxy of activity does each feedback mechanism track? Loading of intracellular Na + during spiking activates the dynamic Na + pump, hyperpolarizing the membrane over tens of seconds as it exchanges 3 Na + for 2 K + ions [ 3 ]. This is consistent with our results showing that spiking causes the usAHP in cells with small R in changes and high sensitivity to 2 μM ouabain (Figs 1E 1 and 2D ). For Kv7 channels, depolarization over several seconds can potentiate currents without spiking or Ca 2+ influx over the same time course [ 4 ]. Therefore, we tested if depolarization enhances the Kv7 component of the outward current ( S4 Fig ). For this, we measured the degree of K + current potentiation in the 25-second period following a 10-second step to −22 mV in voltage clamp, and then correlated it with the drop in R in during the usAHP measured in current clamp within the same neuron ( S4A–S4C Fig ). Neurons that reduced R in during the usAHP also had potentiated outward currents induced by depolarization, suggesting a relationship between these 2 processes ( S4A Fig ). XE-991 reduced potentiation of the outward current, indicating that Kv7 channels play a role in this response ( S4D Fig ). These results show that depolarization without spiking enhances Kv7 currents over a similar time course as spike-dependent feedback from the dynamic Na + pump.

The co-expression of ionic currents is often associated with correlated messenger RNA (mRNA) transcripts [ 11 , 25 ]. To understand the transcriptional basis of the relationship between the dynamic Na + pump and Kv7 channels, we assessed single-cell mRNA co-expression of genes that encode brain Kv7 channels (KCNQ2, KCNQ3, and KCNQ5) and the α3 subunit thought to give rise to dynamic activation of the Na + pump (ATP1A3) [ 21 , 26 ]. In contrast to the relationship at the functional level, mRNA copy numbers of KCNQ2 and KCNQ3 showed positive co-expression with ATP1A3 across neurons ( Fig 3C ). We did not observe the same correlation for KCNQ5 and ATP1A3 ( S3 Fig ). In addition, 2 glutamate receptors did not correlate with ATP1A3 ( S3 Fig ), supporting specificity of the mRNA correlation between KCNQ2-KCNQ3 and the α3 subunit of the Na + pump. Thus, mRNA transcripts that encode Kv7 and the dynamic Na + pump are positively correlated across neurons. As the functions of these 2 proteins are inversely related, cellular processes that lie between mRNA and functional protein likely flip the relationship between these 2 mechanisms.

(A) Inverse relationship between Kv7 current density and the dynamic Na + pump across neurons (n = 14 neurons from N = 10 animals); (B 1 ) shows a neuron with a relatively large Kv7 current density (XE-991 difference current recorded at −10 mV) and low function of the dynamic Na + pump (nearly no ouabain sensitivity of the remaining usAHP); (B 2 ) shows the opposite example, a neuron with relatively small Kv7 current density but a larger contribution of the dynamic Na + pump to the usAHP. (C) KCNQ2 and KCNQ3 (Kv7 subunits) mRNA expression from single neurons correlate with ATP1A3, the gene that codes for the Na + affinity α subunit of the Na + pump. Each point represents the mRNA for each gene from a single neuron (n = 19 neurons from N = 8 animals). Arrow points to values identified as outliers in the Grubbs’ test. The dotted lines indicate the regression lines for each correlation run without the outlier point, with Pearson r, p value, and slope of the relationship shown in the key. The data underlying this figure can be found in S1 Data .

We next tested directly for reciprocal function of the dynamic Na + pump and Kv7 channels across neurons. For this, we measured the Kv7 component of the total outward current in voltage clamp and then estimated pump function through the sensitivity of the remaining usAHP to ouabain. Indeed, individual neurons with large Kv7 currents had a smaller block of the usAHP by 2 μM ouabain ( Fig 3A and 3B 1 ). In contrast, neurons with relatively small Kv7 currents had greater apparent dynamic Na + pump function ( Fig 3A-B 2 ). The relationship appeared to be hyperbolic, with a steeper slope through most of the distribution and a shallow slope at the top. Some cells exhibited a residual usAHP after the application of both ouabain and XE-991, suggesting that additional feedback processes exist in some neurons. Nevertheless, these results demonstrate an inverse relationship between the dynamic Na + pump and Kv7 current density, where graded combinations of these 2 feedback mechanisms integrate recent activity history of the neuron and then alter membrane excitability over the next minute.

(A) Example recordings showing the effect of 2 μM ouabain (dynamic Na + pump, n = 12 cells from N = 8 animals), 10 μM XE-991 (Kv7, n = 17 cells from N = 5 animals), and 30 μM Cd 2+ (Ca 2+ channels, n = 14 neurons from N = 4 animals) on the usAHP. (B) 2 μM ouabain and 10 μM XE-991 reduced the usAHP in most neurons, while 30 μM Cd 2+ did not. The frequency of positive effects differed across drugs (Chi-square test; p = 0.012). (C) Mean changes in the usAHP by each drug (one-way ANOVA followed by Holm–Sidak Multiple Comparison test). (D) Correlation between sensitivity of the usAHP to ouabain and the drop in the first R in measurement following stimulation. Traces illustrate R in responses for each example neuron at different ends of the correlation. (E) Same as (D) but for XE-991. (F) Correlation between sensitivity of the usAHP and the drop in R in after block of Kv7 by XE-991. The x-axis shows the ratio of the change in R in during the usAHP after and before XE-991. Thus, greater values reflect a greater block of the R in drop following XE-991. Inset for (E) shows the ability for XE-911 to counter the drop in R in in neurons where XE-991 also reduced the usAHP. The data underlying this figure can be found in S1 Data .

A spike-sensitive usAHP with stable R in is consistent with feedback from the dynamic Na + pump [ 3 ]. However, reduced R in during the usAHP pointed to the activation of a K + conductance. At least 2 K + channels have been shown to be enhanced by short depolarization without spiking over the time course we observe here (roughly 1 minute): Ca 2+ -activation of K + leak channels [ 9 ] and depolarization-induced potentiation of Kv7 channels [ 4 ]. Therefore, we tested whether inhibitors of the dynamic form of the Na + pump (2 μM ouabain), Ca 2+ channels (30 μM Cd 2+ ), and Kv7 channels (10 μM XE-991) reduced the amplitude of the usAHP ( Fig 2A ). Ouabain and XE-991 reduced the usAHP by ≥10% in most neurons, while Cd 2+ had little-to-no effect ( Fig 2B and 2C ). These results suggest the dynamic Na + pump and Kv7 channels generate the usAHP, with no clear role for the activation of K + channels by Ca 2+ influx. Strikingly, variation in the sensitivity of the usAHP to ouabain and XE-991 was correlated with the activity-dependent drop in R in . usAHPs with a large contribution from the dynamic Na + pump, which manifested as a greater sensitivity to ouabain, had the smallest reductions in R in . Those with a lower pump contribution had larger changes in R in ( Fig 2D ). We observed the opposite trend for the Kv7 channel blocker, XE-991. Neurons with usAHPs containing a greater role of Kv7 channels had larger decreases in R in ( Fig 2E ). Moreover, the greater the block of the usAHP by XE-991, the more XE-991 opposed the decrease in R in ( Fig 2F ). Thus, Kv7 channels contribute to both the usAHP as well as the accompanying change in R in . This relationship did not exist for the block of Ca 2+ channels ( S2 Fig ). These results show that each feedback controller is scaled across neurons and suggest that cells with a greater role of the Na + pump have a smaller contribution from Kv7 channels and vice versa.

(A) Identified vagal motoneurons that innervate the glottal dilator exhibit short-term regulation of excitability following intense firing, termed the usAHP. (B) The usAHP is associated with variable R in changes across neurons, with 1 example showing largely stable R in (black/gray) and another with a decrease (blue). (C) R in during the usAHP reported as a relative change from baseline in n = 43 neurons following stimulation, color coded by no (black), modest (green), and large (blue) R in changes. (D) The usAHP does not correlate with size of the R in drop (n = 43 neurons from N = 15 animals). (E) Different activity signals drive the usAHP in association with the change in R in . Neurons with stable R in have an usAHP driven by spiking, and those with the largest R in decreases persist without spiking. (F) Mean data showing the influence of spiking on the usAHP (paired t test). Stable R in (n = 9 neurons from N = 2 animals) and R in decreases (n = 6 neurons from N = 6 animals). The data underlying this figure can be found in S1 Data .

We began this study to assess the role of feedback from the dynamic Na + pump in motoneurons that gate lung airflow in American bullfrogs (vagal motoneurons; Fig 1A ). In locomotor neurons, Na + loading during burst firing activates the pump and triggers an usAHP that lasts for approximately 30 to 60 seconds to homeostatically reduce membrane excitability [ 3 , 18 , 20 ]. Respiratory motoneurons exhibited a similar usAHP ( Fig 1A ). However, we found that hyperpolarization corresponded with decreases in R in that recovered with the membrane potential following stimulation. R in changes were variable from cell to cell, spanning from roughly no change to a 40% drop ( Fig 1B and 1C , and S1 Fig ). The slope of the usAHP did not correlate with the reduction in R in ( Fig 1D ), suggesting that multiple mechanisms combine to generate a phenotypically similar usAHP across cells. Indeed, neurons with stable R in following stimulation had an usAHP triggered by spiking, as the block of action potentials during stimulation reduced the usAHP ( Fig 1E and 1F ). In contrast, neurons with relatively large decreases in R in retained the usAHP during stimulation without spiking ( Fig 1E and 1F ). Therefore, combinations of 2 feedback mechanisms, with spike-dependent and independent components, regulate membrane excitability over the same timescale of about 1 minute.

Discussion

Neurons are thought to track the dynamics of a master command signal that follows firing rate to control their output. Many studies adhere to this interpretation for both short- and long-term regulation, stating it explicitly or implying the existence of a dominant signal that controls neuronal output over seconds to days [3,4,8,15,27–29]. Instead, we provide evidence that stable firing rates arise as neurons rapidly transduce distinct activity signals in varying combinations from cell to cell. These data reveal that consistent output from a population of neurons—ostensibly generating the same behavior—may emerge through multiple feedback systems with different relative weights across cells.

The major finding from this study is that individual neurons within the same population use unique combinations of molecular feedback controllers to maintain burst firing rates, with each process graded across the population. We attribute regulation to fast activity-dependent feedback because both the dynamic form of the Na+ pump and Kv7 respond to neuronal activity and reduce excitability following strong bursting (Fig 2A and 2B) but have little contribution to the resting membrane potential (Fig 4F). Dynamic feedback from the Na+ pump is thought to arise from the incorporation of an α3 subunit with a low affinity for intracellular Na+, which serves to hyperpolarize the neuron as it extrudes Na+ after firing [17]. Therefore, this form of the pump acts as both a spike sensor and effector for fast feedback regulation [3,17]. For Kv7 channels, membrane depolarization during activity—independent from spiking (Fig 1) and Ca2+ influx (Fig 2)—rapidly potentiates currents to constrain neuronal output (S4 Fig). Membrane depolarization per se activates PI4 kinase to induce the production of PIP2 [30], which sensitizes Kv7 currents over a similar time course as we show here [4]. Thus, Kv7 channels seem to act as effectors that respond to fast voltage-sensitive signaling during bursting, potentially linked through the production of PIP2 or some other intermediate. These forms of feedback differ from classic examples of “homeostatic plasticity.” That is, they use real-time dynamics of Na+ and voltage to stabilize neuronal output, rather than engaging compensatory cell signaling that recovers activity following a strong perturbation. Nevertheless, different forms of homeostatic plasticity may also use multiple activity sensors and integration pathways within the same cell type [11,31,32]. Thus, we suggest that reciprocal scaling of multiple control mechanisms may be a feature for both rapid and long-term regulation of neuronal output.

How do neurons “know” to express each feedback system in their own unique way? Single-cell mRNA expression provides insight into transcriptional control that may give rise to this organization. Stable neuronal output can arise through variable expression of ionic conductances [33], but channels with similar properties tend to be inversely co-expressed across neurons [34]. This aligns with our results showing a reciprocal relationship between 2 feedback systems that act in the same direction, magnitude, and timescale. In contrast, mRNA transcripts coding for Kv7 protein subunits (KCNQ2 and KCNQ3) and the dynamic Na+ pump (ATP1A3) are positively correlated across neurons. Given a reciprocal relationship at the functional level, positive mRNA correlations may seem contradictory. However, opposite relationships for mRNA abundance (positive) and corresponding channel currents (negative) have been demonstrated previously [11], and negative co-expression of channel transcripts has never been reported, even when the functional channel currents are inversely correlated [35]. Others have suggested the maintenance of channel mRNAs at roughly fixed ratios, which manifest as positive correlations across neurons, may reflect critical gene modules needed to generate certain neuronal properties regardless of the final relationship of the functional currents [35]. Why neuronal populations appear to maintain mRNAs only at linear positive relationships, and what mechanisms flip the direction of these relationships along the path from mRNA to protein function such as we present, is not known. Nevertheless, positive correlations of channel mRNAs are thought to be actively maintained largely through slow feedback from voltage-dependent signaling in rhythmic motoneurons [36]. Thus, we speculate that activity-dependent transcription constrains relevant mRNA relationships, and then through undefined cellular mechanisms, guides the proper combination of these rapid feedback systems in each cell.

Each neuron in the vagal motor pool appears to continuously sense different aspects of its activity to constrain population motor output for breathing. What is the advantage of multiple rapid feedback systems reciprocally balanced across neurons? Many behaviors require stable neuronal output. A failure to maintain stability can lead to network dysfunction if left unchecked, and fast feedback as we describe here may allow neurons to correct course nearly in real time to avoid disease states [9,37]. We suggest that scattering 2 molecular controllers across neurons may prevent the complete loss of stability at the population level during transient disturbances to 1 feedback system. For example, activity of the Na+ pump is tied to local ATP concentrations [38], and the high consumption of ATP used to fuel other costly neuronal processes may limit the ability of the pump to stabilize firing rate. Therefore, behaviors that involve energetically expensive synapses [39] or activity during severe metabolic stress [40] may spiral out of control if feedback in every neuron relied solely on the dynamic Na+ pump. Indeed, mutations in the dynamic form of the Na+ pump and Kv7 channels are implicated in epilepsy [41,42], where states of hyperexcitability are commonly associated with mitochondrial dysfunction [43]. Thus, although we uncovered this feedback organization in the amphibian brainstem, we suggest that it may extend to other species, whereby changes in the balance of these 2 feedback systems could lead to disordered circuit function.

A grand challenge for modern neuroscience is to understand how neurons maintain stable function for many days, weeks, and years [35]. As neurological disease occurs when firing rate strays from a healthy range, regulatory principles have broad implications for the treatment of vast brain disorders. Our results highlight that animals may scale different combinations of regulatory mechanisms throughout a population of neurons, which presents a challenge for defining uniform principles and applying them to disease. Neuronal stability likely involves a suite of interwoven mechanisms acting over long and short timescales through activity-dependent and neuromodulatory feedback, as well as genetic control [36,44]. Data presented here emphasize that overarching frameworks for the control of neuronal output may need to account for assortments of feedback processes spread variably across neurons of the same population that ultimately give rise to stable behaviors.

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