A computational analysis of signal fidelity in the rostral nucleus of the solitary tract

Abstract

Neurons in the rostral nucleus of the solitary tract (rNST) convey taste information to both local circuits and pathways destined for forebrain structures. This nucleus is more than a simple relay, however, because rNST neurons differ in response rates and tuning curves relative to primary afferent fibers. To systematically study the impact of convergence and inhibition on firing frequency and breadth of tuning (BOT) in rNST, we constructed a mathematical model of its two major cell types: projection neurons and inhibitory neurons. First, we fit a conductance-based neuronal model to data derived from whole cell patch-clamp recordings of inhibitory and noninhibitory neurons in a mouse expressing Venus under the control of the VGAT promoter. We then used in vivo chorda tympani (CT) taste responses as afferent input to modeled neurons and assessed how the degree and type of convergence influenced model cell output frequency and BOT for comparison with in vivo gustatory responses from the rNST. Finally, we assessed how presynaptic and postsynaptic inhibition impacted model cell output. The results of our simulations demonstrated 1) increasing numbers of convergent afferents (2–10) result in a proportional increase in best-stimulus firing frequency but only a modest increase in BOT, 2) convergence of afferent input selected from the same best-stimulus class of CT afferents produced a better fit to real data from the rNST compared with convergence of randomly selected afferent input, and 3) inhibition narrowed the BOT to more realistically model the in vivo rNST data.

NEW & NOTEWORTHY Using a combination of in vivo and in vitro neurophysiology together with conductance-based modeling, we show how patterns of convergence and inhibition interact in the rostral (gustatory) solitary nucleus to maintain signal fidelity. Although increasing convergence led to a systematic increase in firing frequency, tuning specificity was maintained with a pattern of afferent inputs sharing the best-stimulus compared with random inputs. Tonic inhibition further enhanced response fidelity.

INTRODUCTION

The rostral nucleus of the solitary tract (rNST) serves as an obligate synapse for peripheral taste signals relayed to either ascending or local reflex pathways. Although many of the elements of the rNST circuit have been characterized, including the source and distribution of the inputs and the destination of the outputs, as well as the synaptic properties and membrane characteristics of second-order neurons (reviewed in Bradley 2007b; Lundy and Norgren 2015; Spector and Travers 2005; Travers and Travers 2010), it is not well understood how these factors interact to transform taste information passing through the nucleus.

Two forms of sensory transformation are apparent. First, second-order neurons fire faster than their peripheral counterparts, and second, they are more broadly tuned to gustatory stimuli. Estimates of increases in firing rate range from a 1.3-fold increase in hamster (Travers and Smith 1979) to a threefold increase in sheep (Vogt and Mistretta 1990) and a fourfold increase in rat (Doetsch and Erickson 1970). Increases in the breadth of tuning (BOT) to gustatory stimuli in rNST compared with peripheral afferents also have been consistently reported across a variety of species (reviewed in Spector and Travers 2005; Travers et al. 1987). These increases in response frequency and BOT have generally been attributed to the convergence of excitatory afferent fibers. Indeed, there is compelling evidence for convergence from physiological studies mapping peripheral receptive fields (Grabauskas and Bradley 1996; Sweazey and Smith 1987; Travers et al. 1986; Vogt and Mistretta 1990).

Afferent convergence, however, is just one factor that can alter central firing rates and BOT. For example, gustatory afferents display a significant frequency-dependent short-term synaptic depression (STSD) that has been observed both in vivo (Hallock and Di Lorenzo 2006; Lemon and Di Lorenzo 2002; Rosen and Di Lorenzo 2009) and in vitro (Wang and Bradley 2010b). STSD could act as a gain-setting mechanism to scale output neuron responses to afferent input within their dynamic range (Abbott et al. 1997). This could provide a mechanism for maintaining specificity of BOT in the gustatory system in the presence of convergent inputs which might otherwise saturate the firing rates of rNST neurons.

Central circuitry and the intrinsic excitability of rNST neurons are additional factors that can shape the relationship between peripheral input and rNST output. Projection neurons are under the influence of local GABAergic interneurons, and there is evidence for both pre- and postsynaptic inhibition (Boxwell et al. 2013; Chen et al. 2016; Grabauskas 2005; Grabauskas and Bradley 1996; Liu et al. 1993; Sharp and Finger 2002; Wang and Bradley 1993, 1995; Whitehead 1988; Zhu et al. 2009). In addition, there is extensive literature characterizing the intrinsic properties and excitability of rNST neurons (e.g., Bradley and Sweazey 1992; Du and Bradley 1996; Grabauskas and Bradley 1996, 2003; Suwabe and Bradley 2009; Suwabe et al. 2011; Tell and Bradley 1994; Wang and Bradley 1995, 2010b), although to date, fewer studies have differentiated between the response properties of inhibitory and noninhibitory (projection) neurons (e.g., Boxwell et al. 2013; Chen et al. 2016; Corson and Bradley 2013; Suwabe and Bradley 2009; Wang and Bradley 2010a).

The goal of the current study was to generate a mathematical model of the rNST to determine whether the known properties of the system are sufficient to reproduce the increase in firing frequency and BOT observed in the rNST compared with the chorda tympani (CT). Archival data from two studies (CT: Frank 1973; rNST: Travers and Smith 1979) provided comparable data sets to model the transfer of the gustatory signal across the first synapse in the same species taken from single-unit responses to gustatory stimuli applied (exclusively) to the anterior tongue at the same concentration under similar anesthetic conditions.

To model the transfer of gustatory signals using these two data sets, we began by first characterizing the synaptic properties and intrinsic excitability of two major subtypes of rNST neurons: GABAergic (likely interneurons) and non-GABAergic (likely glutamatergic projection) neurons (Davis 1993; Lasiter and Kachele 1988). We first determined the relationship between applied current and firing frequency of identified neurons, a protocol that captures many critical aspects of neuronal excitability in a simple function and has been used as a measure of excitability in other systems (Caillard 2011; Prinz et al. 2003). We then developed conductance-based Hodgkin-Huxley-type models of the two rNST neuron types, each consisting of voltage-gated sodium and potassium currents, a leak current, and a slow voltage-gated potassium current (I_Ks), which was necessary to appropriately space the action potentials. Parameters corresponding to the maximal conductances were then chosen to replicate the empirical measurements of intrinsic excitability measured in vitro. Both modeled neuron types included an excitatory afferent input with STSD and postsynaptic current magnitudes also fit to in vitro data. This simple network configuration does not preclude the possibility of more complex central architecture (Rosen et al. 2010) but represents a minimal starting point that accounts for much of what is currently known about the system.

To model the effects of different degrees and patterns of convergence, afferent responses to gustatory stimuli from in vivo CT recordings (Frank 1973) were then used as an input to excitatory (E) and inhibitory (I) model rNST neurons, and the output responses from these neurons were compared with the best-stimulus firing frequencies and BOT of rNST neurons recorded in vivo (Travers and Smith 1979). We modeled synaptic input as 1–10 independent convergent afferents, each utilizing a three-compartment model of short-term synaptic plasticity of transmitter release. Both E and I neurons appear to receive monosynaptic input from the solitary tract (Boxwell et al. 2013; Corson and Bradley 2013; Suwabe and Bradley 2009), and preliminary observations from our laboratory suggest that some I cells are taste responsive (unpublished observations), similarly to rNST projection neurons (presumably E neurons) identified by antidromic stimulation (Cho et al. 2002; Geran and Travers 2006; Monroe and Di Lorenzo 1995; Ogawa and Kaisaku 1982). However, the pattern of afferent convergence onto identified E and I neurons is presently lacking. Thus we tested similar patterns and the degree of convergence for both E and I cells. Because GABAergic neurons and terminals are well represented in the rNST, and multiple forms of inhibition are supported experimentally, the model further assessed how presynaptic and postsynaptic inhibition modulated the excitatory effects of convergence. We modeled postsynaptic inhibition as a small tonic chloride conductance and presynaptic inhibition as release probability.

METHODS

In Vitro Mouse Slice Preparation

We used 6- to 12-wk-old mice expressing Venus under the control of the vesicular GABA transporter (VGAT) promoter to record from identified inhibitory (GABAergic and glycinergic) and noninhibitory (putative excitatory projection) neurons (Wang et al. 2009). Venus-positive neurons are abbreviated as I (inhibitory) and Venus-negative neurons as E (excitatory). The Venus fluorescent protein was developed by Dr. Atsushi Miyawaki at the RIKEN Brain Science Institute (Wako, Japan); the VGAT-Venus transgenic mouse developed by Y. Yanagawa was made available to us by Dr. Hisashi Umemori (University of Michigan Medical School, Ann Arbor, MI). This mouse has an expression pattern similar to that of the GAD67-EGFP mouse, which we used previously (Boxwell et al. 2013), and includes expression in the rostral central subdivision. Although this transgenic mouse strain identifies both GABAergic and glycinergic neurons, available evidence suggests there are relatively few glycinergic synapses in the rNST (Grabauskas 2005; Sweazey 1996). All experimental protocols were approved by the Ohio State University Institutional Animal Care and Use Committee in accordance with guidelines from the National Institutes of Health.

Acute slices were prepared for electrophysiological recording following anesthetization with isoflurane, decapitation, and rapid removal and cooling of the brain (Boxwell et al. 2013). The blocked brain stem was glued to a ceramic block using cyanoacrylate glue, and 250-µm-thick coronal brain stem slices were cut with a sapphire blade on a vibratome (model 1000; Vibratome, St. Louis, MO) in an ice-cold carboxygenated cutting solution containing (in mM) 110 choline, 25 NaHCO₃, 3 KCl, 7 MgSO₄, 1.5 NaH₂PO₄, 10 d-glucose, and 0.5 CaCl₂. Slices containing the NST rostral to where it moves laterally away from the fourth ventricle were identified and incubated in a carboxgyenated artificial cerebrospinal fluid (ACSF) containing (in mM) 124 NaCl, 25 NaHCO₃, 3 KCl, 1 MgSO₄, 1.5 NaH₂PO₄, 10 d-glucose, and 1.5 CaCl₂ at 32°C for 1 h before recording.

Slices were transferred to a recording chamber and perfused with 36°C ACSF containing 5 µM gabazine and strychnine (Sigma Aldrich, St. Louis, MO) at a rate of 1–2 ml/min. The NST and solitary tract (ST) were visualized with a Nikon E600FN microscope, and a bipolar stimulating electrode made of twisted insulated wire (67 µm, NiCr) was placed on the ST under visual control. After placement of the stimulating electrode, cells in the rNST were visualized using infrared differential interference contrast optics and epifluorescent illumination to identify cells that were either Venus-VGAT positive or negative (Fig. 1). Approximately equal numbers of Venus-positive and Venus-negative neurons were targeted throughout the course of the study. Once a neuron was identified, a whole cell patch-clamp recording was made using a 4- to 6-MΩ pulled glass pipette filled with an intracellular solution containing (in mM) 130 K-gluconate, 10 EGTA, 10 HEPES, 1 CaCl₂, 1 MgCl₂, and 2 ATP at pH 7.2–7.3 and osmolality 285–290 mosM. An initial seal of >1 GΩ and a membrane resistance of >100 mΩ were inclusion criteria for seal and cell viability. Recordings were made with an A-M Systems amplifier (model 2400) and recorded using pClamp software (Molecular Devices, Sunnyvale, CA).

Fig. 1.

Neuron expressing Venus in a VGAT-positive neuron in the rostral nucleus of the solitary tract (left; double arrowhead) is patched (black arrow) under differential interference optics (right). An unlabeled neuron is marked with a single arrowhead.

Recording protocols.

ST-evoked currents from identified rNST neurons were elicited by tract stimulation at frequencies between 1 and 60 Hz (0.15-ms pulse duration) over a 500-ms stimulus period at a rate of 0.1 Hz. Each frequency was presented between 6 and 9 times in a varied order, and responses were recorded in voltage clamp at a holding potential of −70 mV. Threshold was defined as the current intensity that evoked a response 50% of the time, and the experimental stimulus intensity was set at 10 µA above threshold to ensure a reliable response. In some cases, the presence of an additional, higher threshold-evoked response precluded the use of current values 10µA above threshold, and in these cases the highest current that did not activate the additional input was used. In a second protocol, the response of rNST neurons to small hyperpolarizing and depolarizing pulses of current injection (450 ms) were recorded in current clamp (−0.1 to 0.2 nA in 0.01-nA steps).

Data analysis.

ST-evoked currents were quantified as the total area under the curve of the current waveform relative to baseline, as calculated using Clampfit software. Stimulus artifacts were not excluded from the waveform, but since these artifacts were typically very narrow, their contribution to this metric was minimal. To characterize the magnitude of the response to ST stimulation, functions between input frequency and response magnitude were fit to a Hill-type function

$$R=\frac{R_{max}}{1+F_{50}/F}$$ (1)

where R is response magnitude and F is input frequency. The magnitude of the parameters R_max and F₅₀ were compared using a two-sample t-test.

Voltages in the current-clamp data were measured over a 50-ms portion of the current step, after the voltage had come to steady state. Action potentials were automatically detected as 0-mV crossings and counted. In a few cases, the steady-state current exceeded 0 mV after the cell had gone into depolarization block. In these cases, the threshold for action potential detection was raised above the steady state and the results were checked by hand to ensure that no action potentials in previous sweeps were missed. A “break point” was defined as the applied current at which the firing frequency peaked before going into a depolarization block that produced action potentials that failed to reach an amplitude meeting the criterion (0-mV crossing). In the cases where firing frequency plateaued over consecutive increases in applied current, break point was defined as the largest applied current eliciting peak firing frequency. Comparisons between excitatory and inhibitory neuron populations were made using a two-sample t-test.

Modeling rNST Neuronal Excitability

We were able to construct a Hodgkin-Huxley-type conductance-based neuron model that captured key features of the in vitro data. The cell’s voltage, V, satisfies the equation

$$C_m{\mathit{V\prime }}^{}=-I_{Na}-I_K-I_{Ks}-I_{leak}-I_{Cl}-I_{syn}+I_{app}$$

where C_m is the membrane capacitance, and the voltage-gated sodium (I_Na), voltage-gated potassium (I_K), slow voltage-gated potassium (I_Ks), leak (I_leak), and chloride (I_Cl) currents are of the form

$$I_{Na}=G_{Na}{m}^{3}h\left(V-E_{Na}\right),{\hspace{0.17em}I}_K=G_K{n}^4\left(V-E_K\right),\hspace{0.17em}{I}_{Ks}=G_{Ks}{n}_s^4\left(V-E_{Ks}\right)$$

$$I_{leak}=G_{leak}\left(V-E_{leak}\right),\hspace{0.17em}{I}_{Cl}=G_{Cl}\left(V-E_{Cl}\right)$$

where G and E represent the maximal conductance and reversal potential, respectively. The gating variables m, h, n, and n_s satisfy equations of the form

$${\mathit{X\prime }}^{}=\frac{\left[X_{\infty }(V)-X\right]}{{\tau }_X\left(V\right)}$$

where X = m, h, n, and n_s and

$$X_{\infty }\left(V\right)=\frac{1}{1+e^{-\left(V-{\theta }_X\right)/{\sigma }_X}},{\tau }_X\left(V\right)=a_m+\frac{b_m}{\left(1+e^{-\left(V-{\theta }_{Xa}\right)/{\sigma }_{Xa}}\right)\left(1+e^{-\left(V-{\theta }_{Xb}\right)/{\sigma }_{Xb}}\right)}$$

See Table 1 for parameter values used to create model E and I neurons fit from the in vitro data.

Table 1.

Model parameter values

ST Synapse Model Parameters
Excitatory model		Inhibitory model
D	8	D	8
R	500	R	500
PR	0.118	PR	0.118
Gsyn	0.1658 μS	Gsyn	0.00829 μS
Esyn	0 mV	Esyn	0 mV

rNST Neuron Model Parameters
Excitatory model		Inhibitory model
Cm	0.0187	Cm	0.0165
GNa	0.24 μS	GNa	0.88·0.24 μS
GK	0.011 μS	GK	0.88·0.011 μS
GKs	0.003 μS	GKs	0.0015 μS
Gleak	0.0018 μS	Gleak	0.88·0.0018 μS
GCl (when present)	0.001 μS	GCl (when present)	0.88·0.001 μS
ENa	50 mV	ENa	50 mV
EK	−90 mV	EK	−90 mV
Eleak	−59.5 mV	Eleak	−54 mV
ECl	−70 mV	ECl	−70 mV

Gating Parameters with the Same Values in Both Models
θm	−38	am	0.05
σm	5	bm	0.5
θh	−50	ah	1
σh	−3	bh	8
θn	−40	an	1.2
σn	5	bn	8
θns	−40	ans	1.2
σns	5	bns	200
θma	−20	σna	−10
σma	−10	θnb	−70
θmb	−60	σnb	−10
σmb	3	θnsa	−50
θha	−45	σnsa	−10
σha	−3	θnsb	−70
θna	−50	σnsb	−10

See text for parameter definitions.

Modeling transmitter release.

The transmitter release was modeled as a three-compartment model (Ermentrout and Terman 2010) by a system of equations with the form

$${\mathit{Y\prime }}^{}=-\frac{Y}{D}+XS;\hspace{0.17em}{\mathit{X\prime }}^{}=\frac{Z}{R}-XS;\hspace{0.17em}{\mathit{Z\prime }}^{}=\frac{Y}{D}-\frac{Z}{R}\mathrm{.}$$

where X, Y, and Z are the fractions of neurotransmitter in a readily releasable state, in the synaptic cleft, and unavailable for release, respectively. The value of Y was scaled by a postsynaptic conductance and multiplied by driving force to produce a postsynaptic current waveform,

$$I_{syn}=G_{syn}Y\left(V-E_{syn}\right)\mathrm{.}$$

The constants D and R govern the rate of removal of transmitter from the synaptic cleft and resetting of available transmitter, respectively. The variable S represents the release probability; this variable is assumed to increase by a fixed amount, P_R, whenever there is incoming stimulus and to decrease at an exponential rate between stimuli. That is, S(t_k⁺) = S(t_k⁻) + P_R if there is an incoming signal at time t = t_k, and S′ = −kS otherwise. The input times were computed from Poisson-distributed interstimulus intervals (ISIs) generated from a fixed input rate variable. For the purposes of fitting the in vitro data, this portion of the synapse model was replaced by a function that generated constant ISIs with 500-ms durations (Table 1).

Generating input-output frequency curves.

We provided input rates to each modeled afferent individually and the synaptic release models for each afferent operated independently (Fig. 2). The input rates were transformed into Poisson-distributed ISIs for 5-s baseline and stimulus periods, and the onset of the stimulus input was jittered by a random value taken from 1 to 500 ms to minimize the effect of synchronous onset of inputs. Action potentials were detected as 0-mV crossings. We ran the complete mathematical model assuming 2–10 convergent afferent inputs, each receiving an input frequency of 1–70 Hz. The average response rate over a 5-s stimulus period was plotted against the input rate to generate the input-output curve.

Fig. 2.

A: rostral nucleus of the solitary tract (rNST) neurons were modeled with Hodgkin-Huxley-type leak (I_leak), sodium (I_Na), and slow (I_Ks) and fast (I_K) potassium conductances. Response rates taken from in vivo chorda tympani recordings were passed as input rates to the modeled rNST neurons using custom software interfacing with the ODE simulator XPPAUT. Output rates were collected for a 5-s stimulus period, paralleling the duration used for the in vivo recordings. B: transmitter release from solitary tract afferents (ST) was modeled as a simple 3-compartment system: readily releasable transmitter (X), released transmitter (Y), and unavailable transmitter (Z). In the model, input rate is transformed into a gating variable (S), which fluctuates from 0 to 1, inducing the release of modeled transmitter into the synapse. The fraction of transmitter in the synapse (Y) is scaled to produce a postsynaptic conductance, which is then transformed into a synaptic current (I_syn) with a reversal potential of 0 mV, corresponding to a glutamatergic synapse. The constants D and R govern the rate of removal of transmitter from the synaptic cleft and resetting of available transmitter, respectively. Presynaptic inhibition changed the probability of release at the presynaptic terminal over a range of values; postsynaptic inhibition was modeled as a change in chloride conductance (I_Cl), similar to a GABA_A receptor.

To model the effects of inhibition on input-output functions, we systematically changed a chloride conductance to model a change in (GABA_A mediated) postsynaptic inhibition and changed the probability of neurotransmitter release to model presynaptic inhibition. Each parameter change was modeled at each level of convergence independently for E and I neurons.

Threshold linear plots.

Input-output functions were converted to threshold linear plots in which responses generated from different combinations of convergence and inhibition were normalized to the largest response and the resulting points fit to a linear equation (Atallah et al. 2012; Wilson et al. 2012). Slopes and intercepts from such linear fits have been used extensively to analyze the effects of inhibition on input-output relationships. The slope captures the proportional (divisive) effect of inhibition, and the intercept provides a measure of the subtractive effect. No effect of inhibition produces a line with a slope of 1 and an intercept equal to 0. A purely divisive effect of inhibition changes only the slope, whereas a purely subtractive effect produces a line with a slope of 1 but a change in the Y-offset (intercept).

ANOVA (Systat v.13) was used to make comparisons of the slopes and Y-intercepts derived from the threshold linear functions to analyze changes in output frequency and BOT as a function of type of input (random vs. best stimulus), type of cell (E vs. I), and inhibition [control (no inhibition), presynaptic, postsynaptic]. Adjusted post hoc tests compared the different types of inhibition vs. control. An α level of P < 0.05 was used a cutoff for significance.

Modeling Chemosensitive Response Profiles Using In Vivo Afferent Inputs

Taste responses to different qualities from (archived) in vivo CT data from a previous publication (Frank 1973) were used as afferent inputs to assess how different patterns of input, convergence, and inhibition impacted model rNST E and I neuron responses. These were compared with in vivo rNST responses from an (archived) previous publication (Travers and Smith 1979). Using a custom-built Python script interfacing with the simulator XPPAUT (Ermentrout 2002), a number of afferents ranging from 2 to 10 were randomly selected from the pool of best-stimulus classified afferents (best-stimulus condition). A second “random” condition consisted of selecting afferents without regard to their best-stimulus classification.

We ran the mathematical model using an afferent baseline rate as the input for 5 s and then applied the stimulus-evoked rate for 5 s to generate baseline and stimulus-evoked firing rates. The baseline and responses to each of three stimuli, sucrose, salt (NaCl), and acid (HCl), were used to generate net modeled output rates. A quinine-best pattern of convergence was not tested because only one quinine-best afferent was recorded in the CT data set. This process was repeated with a new, randomly chosen group of afferents to generate 25 cells for each level of convergence (2, 4, 6, 8, and 10), for each best-stimulus category (random, sucrose-best, salt-best, and acid-best), for both cell types (E and I). A convergence of 1 was also used for stimulus-best conditions.

The response rate to the most effective stimulus was determined for each input condition (best-stimulus vs. random) and level of convergence for each cell type. In addition, two measures of BOT across the four stimuli were calculated: “H,” a measure of breadth incorporating responses to all four stimuli (Travers and Smith 1979), and “R,” a measure of noise to signal, i.e., the ratio of the 2nd best response rate divided by the most effective rate (Spector and Travers 2005). The use of two measures of breadth was intended to exploit their complementary strengths and overcome some of the limitations associated with each measure, discussed in Spector and Travers (2005). ANOVA was used in factorial designs to discern differences as a function of cell type, input condition, and inhibition.

RESULTS

In Vitro Characterization of Inhibitory and Noninhibitory Neurons

We recorded postsynaptic ST-evoked currents from 21 Venus-positive (inhibitory, I) and 21 Venus-negative (excitatory, E) rNST neurons over a 500-ms stimulus duration at frequencies ranging from 1 to 60 Hz. These responses were characterized by short latencies (2.2 ms in I neurons and 1.5 ms in E neurons, P < 0.03) and low jitter values (0.19 ms in I neurons and 0.14 ms in E neurons, P < 0.004) and are therefore likely monosynaptic responses (Boxwell et al. 2013; Doyle and Andresen 2001; Wang and Bradley 2010b). In all neurons, these responses were characterized by pronounced STSD at all frequencies (Fig. 3A). The relationship between stimulation frequency and total synaptic input (measured as area under the recorded trace) was an increasing, saturating function for both E and I neurons (Fig. 3B). On average, total synaptic input to E neurons was twice as large compared with that to I neurons at all frequencies. When the Hill-type function noted as Eq. 1 above was fit to the relationship between stimulus frequency and response magnitude, the average value of R_max was about twice as large in E compared with I neurons (18.9 ± 14.2 vs. 9.5 ± 6.8, P < 0.01). In contrast, the average value of F₅₀ was equal for both cell types (32.9 ± 17.8 vs. 30.7 ± 20.1, P < 0.72).

Fig. 3.

A: example traces of solitary tract-evoked-currents in both Venus-negative (excitatory, E) and Venus-positive (inhibitory, I) neurons in the rNST display frequency-dependent short-term synaptic depression. B: the mean response magnitude for the population of E (n = 21) and I (n = 21) responses is an increasing, saturating function. Response magnitude is measured (in units of nA/ms) and corresponds to the area under the curve during the 500-ms stimulus period. Blue and green symbols indicate population averages, and red and pink symbols indicate the performance of the excitatory and inhibitory rNST neuron models, respectively, when subjected to an identical protocol. Error bars are SE.

To further characterize the intrinsic properties of E and I cells, we recorded the voltage and firing frequency of 28 I and 30 E rNST neurons in response to finely graded steps of injected current between −0.1 and +0.2 nA. The average threshold to elicit an action potential was 0.0026 nA in I neurons and 0.013 nA in E neurons. Above threshold, firing rates tended to increase linearly with additional applied current. Although it appears that I cells have nominally higher mean response rates following applied current (Fig. 4B), there was no statistical difference in the maximal frequency achieved by I neurons (59.9 Hz) and E neurons (57 Hz) before it decreased sharply at a break point (0.083 nA in I neurons, 0.13 nA in E neurons), above which the neuron’s firing rate in response to applied current decreased until it was only capable of firing a few action potentials before going into depolarization block (Fig. 4A). I neurons had nominally lower thresholds (Δ = 0.01 nA, P < 0.06) and significantly lower break points (Δ = 0.047 nA, P < 0.003) (see inset in Fig. 4B).

Fig. 4.

A: example traces show the responses of Venus-negative and Venus-positive rNST neurons to a current-clamp injection protocol. Selected current values illustrate typical responses of these neuron types over a range of applied current steps. Note the depolarization block for the Venus-negative neuron at a higher applied current (0.19 nA) compared with the Venus-positive neuron (0.1 nA). B: mean values show the response of the population to all applied current steps. Error bars indicate SE. Note that the x-axis for the current-voltage (I-V) portion of the curve is applied current, whereas the x-axis for the frequency-response portion of the curve is applied current above threshold. This is necessary to minimize the distortion of averaging on the shape of the relationship between applied current and firing frequency in the two cell types. Because mean firing frequency is measured at each applied current, it obscures peak firing frequency that occurs at slightly different applied currents. As a consequence, it only appears that Venus-negative (E) cells fire faster. When maximum firing frequency is measured regardless of applied current, there were no differences between the cell types, as can be seen in the box plots (inset), although Venus-positive I cells did have nominally lower thresholds (P < 0.06) and significantly lower breakpoints (P < 0.003). The superimposed red and pink bars on the box plots show the values of the corresponding parameters in the behavior of the excitatory (E) and inhibitory (I) rNST model neurons, respectively, when put through a protocol identical to the patch-clamp protocol.

Hodgkin-Huxley-Type Conductance-Based Model of In Vitro Data

To model the in vitro characteristics of the afferent synapse onto second-order neurons, we generated a three-compartment model of transmitter release (Fig. 2B) scaled by a postsynaptic conductance and tuned this model to the relationship between input frequency and total synaptic input measured in the in vitro data (Fig. 3B). Because both E and I neurons had virtually the same F₅₀ value, we were able to use the same presynaptic mathematical model, and we altered the postsynaptic conductance parameter to fit the magnitude of response observed at 30 Hz in each neuron type. When we fit the Hill-type equation (Eq. 1) to the modeled results, the E model neuron had an R_max of 19.2 and an F₅₀ of 31.7 (compared with in vitro values of 18.9 and 32.9, respectively), and the I model neuron had an R_max of 9.7 and an F₅₀ of 31.7 (compared with in vitro values of 9.5 and 30.7, respectively).

We constructed a Hodgkin-Huxley-type conductance-based neuron model (Fig. 2A), choosing parameters to replicate the relationship between the applied current and the voltage and firing rates measured in vitro for both E and I rNST neurons. We were able to fit resting membrane potential and firing threshold by altering the leak conductance reversal potential (−54 mV in the I model neuron, −59.5 mV in the E model neuron) and generate an appropriate break point by altering the slow potassium conductance (0.0015 μS in the I model neuron, 0.003 μS in the E model neuron). The fits between the model and the in vitro data for threshold, break point, and maximum firing frequency are shown in Fig. 4 (parameters are listed in Table 2).

Table 2.

Properties of in vitro E and I cells

	I Cells	E Cells	P Values
Latency, ms	2.22 (0.28)	1.54 (0.089)	0.03
Jitter, ms	0.19 (0.01)	0.14 (0.011)	0.004
Membrane resistance, MΩ	932.10 (97.98)	715.20 (55.37)	0.06
Capacitance, pF	16.69 (0.83)	19.68 (1.33)	0.06
Threshold, nA	0.014 (0.004)	0.002 (0.004)	0.06
Breakpoint, nA	0.082 (0.01)	0.135 (0.013)	0.003
Rmax	9.5 (6.8)	18.9 (14.2)	0.01

Parameter values for I (n = 21) and E (n = 21) cells are means (SE) except for breakpoint values, which are means (SD). R_max, maximum postsynaptic response to solitary tract stimulation.

Effects of Convergence and Inhibition on Model Input-Output Frequency Relationships

Convergence.

Despite the twofold difference in total synaptic drive and differences in postsynaptic excitability between the modeled E and I rNST neurons, the input-output curves for the two cell types were markedly similar across the range of input frequencies and levels of convergence (Fig. 5, A and B). For both E and I cells, the input-output relationships were increasing, saturating functions over a range of input frequencies similar to those recorded from peripheral afferents in vivo (e.g., Frank et al. 1988; Ganchrow and Erickson 1970; Sato et al. 1994). The slopes of these relationships increased with increasing convergence. At higher levels of convergence (e.g., 10), the input-output curve changed to an inverted u-shape, with response rates declining markedly with higher frequency inputs, suggesting that other mechanisms (e.g., inhibition) would be necessary to stabilize responses at these higher frequencies. When STSD was removed from the model (by assuming near-instantaneous resetting of transmitter from the “unavailable” to “available” states), responses broke down at much lower frequencies of afferent drive (Fig. 5A).

Fig. 5.

The relationships between input (x-axis) and output (y-axis) frequencies for model excitatory E (A) and inhibitory I cells (B) with short-term synaptic depression are increasing, saturating functions. Increased levels of convergence produce a progressive increase in the slope before saturation. Also plotted in A is the input-output function for E cells with a convergence of 6 afferents with no short-term synaptic depression (STSD; solid black line).

Postsynaptic inhibition.

The effects of postsynaptic inhibition on the output of E and I cells were modeled as a change in chloride conductance. Overall, increases in postsynaptic inhibition strongly reduced the output of both classes of cells. Figure 6A shows the input-output functions for a model E cell with six convergent inputs at each of five levels of postsynaptic inhibition. These functions were transformed to threshold linear functions (Fig. 6B), and slopes and intercepts were calculated for all levels of convergence for both E (Fig. 6, C and D) and I cells (Fig. 6, E and F). Increases in inhibition produced relatively modest reductions in the Y-intercepts across the different levels of convergence (Fig. 6, C and E) but marked decreases in slope (Fig. 6, D and F). An ANOVA with cell type and degree of inhibition as factors revealed a significant effect of inhibition on the intercept (P < 0.001) but no difference for cell type (P > 0.2); the interaction between cell type and degree of inhibition was also significant (P = 0.037). For the slopes, there was a significant effect for both inhibition (P < 0.001) and cell type (P < 0.001); the interaction was not significant (P = 0.483).

Fig. 6.

A: output frequency as a function of input frequency in model E cells receiving 6 convergent inputs is reduced with increasing levels of postsynaptic inhibition (chloride conductance). B: the input-output functions were transformed to threshold linear plots to assess changes in slope and intercept. C: Y-intercepts from the threshold linear functions for each of 5 levels of convergence show a significant reduction across different degrees of postsynaptic inhibition (see Table 3 for ANOVA results). The mean intercept across all levels of convergence is shown by the black line. D: there is a sharp (significant) reduction in slopes derived from the threshold linear functions as postsynaptic inhibition increases. The mean slope across all levels of convergence is shown by the black line. The Y-intercepts (E) and slopes (F) also show a significant reduction with increasing levels of inhibition.

Presynaptic inhibition.

We also assessed the effect of presynaptic inhibition on the input-output functions of model E and I cells. Figure 7A shows the input-output functions for an I cell with six convergent inputs for five levels of inhibition. Similarly to postsynaptic inhibition, these functions were transformed to threshold linear functions (Fig. 7B), and slopes and intercepts were plotted at different levels of convergence for both I (Fig. 7, C and D) and E cells (Fig. 7, E and F)s. Note the very small deviation in intercept for I compared with E cells. This difference between cell types was confirmed with an ANOVA that showed a significant effect for both presynaptic inhibition (P < 0.001) and cell type (P < 0.001), as well as a significant interaction (P < 0.001). ANOVA for the slopes showed a significant effect of inhibition (P < 0.001) but not cell type (P = 0.822). The significance of the lack of change in Y-intercept in I cells on (in vivo) BOT is addressed under the role of inhibition in rNST in the discussion.

Fig. 7.

A: input-output plots for model I cells with increasing levels of presynaptic inhibition. B: when converted to threshold linear functions, there appears to be little change in Y-intercept with a convergence of 6. C: across multiple levels of convergence, there is no change in Y-intercept with increasing levels of presynaptic inhibition (see Table 3 for ANOVA results). D: with increasing levels of presynaptic inhibition, there is a significant decrease in slope. E: intercepts for E cells are significantly decreased with increased levels of inhibition. F: slopes for E cells are significantly decreased with increasing levels of presynaptic inhibition.

Effects of Convergence and Inhibition on Chemosensitive Response Profiles

We next assessed chemosensitive response profiles of modeled rNST cells with different levels and patterns of convergence using afferent inputs from archived CT data (Frank 1973) and considered the impact of inhibition. The first simulation examined the effects of different levels of convergence, across a range of afferents randomly chosen from the same best-stimulus class of CT fibers, i.e., sucrose (S)-best, salt (NaCl, N)-best, or acid (A)-best. Overall, the effects were similar for E and I cells. Increases in the number of CT fibers converging on modeled rNST neurons led to a linear increase in the response rate for the most effective stimulus (best-stimulus firing frequency) for each best-stimulus type. The results of the simulations on E cells are shown in Fig. 8A. The BOT using breadth measured as H reached asymptote with only two to four afferents (Fig. 8B). Breadth measured as R also increased compared with the CT, but generally declined with increased convergence, possibly due to averaging noise over several inputs with different second-best stimuli (Fig. 8C). Interestingly, both measures of breadth increased with just one input, likely reflecting the influence of short-term synaptic depression.

Fig. 8.

A: the increased convergence of afferent fibers from the chorda tympani nerve sharing the same best stimulus leads to a linear increase in the best-stimulus frequency of modeled rNST E neurons for each of 3 best-stimulus types. B: increased convergence also increased BOT measured using H, reaching asymptote with 2–4 afferents. C: increased convergence using a ratio of the second-best stimulus to the best (R) decreased BOT, possibly due to averaging noise over several inputs with different (random) types of second-best stimuli.

A second series of simulations compared the effect of convergence of CT afferents belonging to the same best-stimulus class with convergence from a random selection of CT afferents. Effects were generally similar for E and I cells. Table 3 shows that for both cell types, the pattern of input and the degree of convergence significantly impacted output frequency for each of the three stimulus qualities. Similarly, BOT differed significantly depending on the pattern of convergence for both cell types, but in contrast to output frequency, the degree of convergence had little effect. Figure 9 depicts these comparisons for E cells, along with the mean and SD of the in vivo rNST responses. The responses elicited by the best stimulus in modeled cells with afferent convergence from the same best-stimulus class produced rates that significantly exceeded those resulting from random inputs (Fig. 9, A, D, G; Table 3). Nevertheless, for either pattern of convergence, outputs generally fell within 1 SD of the mean response to the best stimulus recorded in vivo. In contrast, the degree of correspondence between BOT for modeled and in vivo rNST neurons depended on the pattern of convergence. Random convergence produced BOT values that often fell outside the range (defined by the standard deviation) of the in vivo rNST data (Fig. 9, B, E, H; Table 3). With convergence from the same best-stimulus class, BOT of the modeled neurons was closer, but still generally higher, than that observed in vivo.

Table 3.

ANOVA results for random vs. best-stimulus inputs for model E and I cells

	Sucrose-Best			NaCl-Best			Acid-Best
	Freq.	H	R	Freq.	H	R	Freq.	H	R
E cells
Input pattern	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001
Convergence	<0.001	ns	ns	<0.001	ns	ns	<0.001	ns	ns
Interaction	<0.001	ns	<0.01	<0.001	ns	<0.003	<0.001	<0.047	ns
I cells
Input pattern	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001
Convergence	<0.001	<0.025	ns	<0.001	ns	ns	<0.001	ns	ns
Interaction	<0.001	ns	<0.014	<0.001	ns	<0.003	<0.001	<0.047	<0.04

Data are P values from ANOVA of factorial design with input (random vs. best stimulus) × level of convergence (5 levels) and an interaction term. Freq., frequency; ns, not significant. See text for explanation of H and R measures.

Fig. 9.

A, D, and G: for model E rNST neurons, firing rates elicited by the best stimulus fall within 1 SD (top and bottom horizontal lines) of mean (middle horizontal line) in vivo rNST responses for each of 3 best-stimulus classes regardless of whether convergence is random or from the same best-stimulus class of afferents. Best-stimulus inputs, however, produce significantly higher firing rates compared with random inputs (see Table 4 for ANOVA results). B, E, H: convergence from the same best-stimulus class of chorda tympani inputs produces significantly lower BOT values (H) compared with random convergence. Random convergence often produced model cell responses that fell outside the mean  ± 1 SD compared with the mean BOT of in vivo rNST neurons. C, F, I: for the BOT metric R, convergence of stimulus-best types produced significantly lower BOT values compared with random input, and values are closer to the mean rNST data.

A third series of simulations evaluated the impact of pre- and postsynaptic inhibition on the response frequency and BOT of modeled rNST neurons. To simplify the analysis, we used a pattern of best-stimulus convergence and a single “mid-range” value of inhibition (pre, 50% probability; post, 0.002 chloride conductance). Figure 10 shows that for E cells, both types of inhibition had similar suppressive effects on both the magnitude of the response (Fig. 10A) and on BOT in model neurons with NaCl-best afferent inputs (Fig. 10, B and C; Table 4). These observations were supported by post hoc pairwise comparisons following an ANOVA that showed significant differences between control and either form of inhibition, but no difference between forms of inhibition (Table 4). In contrast to E cells, presynaptic inhibition was ineffective at improving (i.e., reducing) BOT in I cells (Fig. 10, E and F), and postsynaptic inhibition was more effective than presynaptic inhibition in suppressing output frequency (Fig. 10D). These differences were again substantiated in the post hoc pairwise comparisons (Table 4), where it can be seen that for I cells, 1) presynaptic inhibition did not statistically differ from controls in either measure of BOT, and 2) there was a statistical difference between pre- and postsynaptic inhibition for both frequency and measures of BOT.

Fig. 10.

A: presynaptic and postsynaptic inhibition significantly decreased the frequency response of modeled E cells compared with control (no inhibition). There was no statistical difference between pre- and postsynaptic inhibition (see Table 4 for ANOVA results). For E cells, pre- and postsynaptic inhibition significantly lowered BOT measured as H (B) or R (C). There was no statistically significant difference between pre- and postsynaptic inhibition. D: pre- and postsynaptic inhibition significantly lowered the frequency response of modeled I cells with postsynaptic inhibition significantly more effective compared with presynaptic inhibition. In I cells, postsynaptic inhibition significantly reduced BOT measured using either H (E) or R (F), but presynaptic inhibition was ineffective.

Table 4.

Effects of inhibition on E and I cells in NaCl-best neurons

	E Cells			I Cells
	Freq	H	R	Freq	H	R
Inhibition	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001
Convergence	<0.001	ns	ns	<0.001	<0.001
Condition × convergence	<0.001	ns	<0.001	<0.001	<0.001	<0.001
Pairwise comparisons
Control × postsynaptic	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001
Control × presynaptic	<0.001	<0.001	<0.001	<0.001	ns	ns
Postsynaptic × presynaptic	ns	ns	ns	<0.001	<0.001	<0.001

Data are P values from ANOVA of factorial design with type of inhibition (control, pre-, and postsynaptic) × level of convergence (5 levels) and an interaction term. Post hoc comparisons are between the types of inhibition.

DISCUSSION

The results of our simulations suggest that convergence and inhibition counterbalance one another to maintain the frequency of the gustatory signal within the dynamic range of rNST neurons while concurrently preserving signal specificity as measured by the BOT. Because the BOT of model neurons with random inputs far exceeds the BOT of rNST neurons recorded in vivo (Fig. 9), it appears likely that rNST neurons receive input from convergent afferents with similar sensitivities. Increases in convergence had a relatively minor impact on BOT, i.e., BOT increased modestly for the first two convergent afferents and then flattened out (or even decreased). However, increasing the number of convergent afferent inputs resulted in a proportional increase in model output firing frequency that eventually saturated (and then decreased) over a range of physiologically relevant frequencies. This effect was mitigated by the addition of either pre- or postsynaptic inhibition, which maintained the frequency response and the BOT of neurons receiving stimulus-best inputs to levels similar to those in the rNST (Fig. 10). Thus we propose that rNST neurons largely receive input from convergent afferents with similar sensitivities and that the maintenance of the specificity of the gustatory signal relies on both this pattern of convergence and the presence of inhibition to further sharpen the signal.

Short-Term Synaptic Depression

Solitary tract-evoked responses were characterized by STSD as has been demonstrated both in vivo and in vitro in the rNST of rat (Doetsch and Erickson 1970; Rosen and Di Lorenzo 2009; Wang and Bradley 2010b). We found that STSD produced an increasing, saturating relationship between presynaptic firing frequency and evoked postsynaptic current (Fig. 3). When we fit a model to this relationship, mapping input frequencies to output frequencies produced similar increasing, saturating functions. When STSD was removed from the modeled synapse (by assuming near-instantaneous resetting of transmitter from the “unavailable” to “available” states), the resulting input-output relationship had a much steeper slope and, in the presence of even a modest degree of convergence, rapidly exceeded the ability of the postsynaptic neuron to repolarize, resulting in a “crash” in the output firing frequency (Fig. 5A). This suggests that one function of STSD is to ensure that output responses fall within the dynamic range of rNST neurons (see also Wang and Bradley 2010b).

Afferent Convergence in the rNST

For our mathematical model, we assumed that convergence of gustatory afferents onto rNST neurons was likely to be sparse, on the order of 10 afferents per neuron rather than hundreds or thousands. Evidence comes primarily from in vivo physiological studies mapping receptive fields in second-order neurons or stepwise recruitment in solitary tract-evoked excitatory postsynaptic currents in vitro. For example, second-order NST neurons in lambs had larger receptive fields in response to stimulation of individual fungiform papillae compared with chorda tympani (CT) fibers (Vogt and Mistretta 1990); the mean number of fungiform papillae activating a CT fiber was 10 compared with ~25 in the rNST. This implies that, on average, approximately three CT fibers converge on central neurons, a number congruent with estimates derived from recruitment profiles following afferent stimulation in patch-clamp experiments (see Fig. 7 in Corson and Bradley 2013). Applying an estimation approach used in the auditory system (Cao and Oertel 2010), we multiplied the number of afferents (600) by the degree of divergence (13) and then divided by the number of central neurons (3,000) (Farbman and Hellekant 1978; Lasiter 1992; May and Hill 2006; Zaidi et al. 2008) (King and Hill 1993). This yielded an estimate of 2.6, again suggesting that our assumption of 10 or fewer convergent afferents is reasonable, or is certainly of the right order of magnitude. Although we believe there is only a modest degree of afferent convergence in the rNST, the nature of this convergence is important.

Random Convergence vs Best-Stimulus Convergence

Convergence of in vivo CT recordings selected according to best-stimulus type produced model responses remarkably similar to in vivo rNST data in terms of both their best-stimulus firing frequency and BOT (Fig. 9). This stimulus-specific convergence pattern parallels that seen in the olfactory system, in which odorant receptor cells of the same type project to specific glomeruli (Hildebrand and Shepherd 1997), and the auditory system, in which afferents with similar tuning properties converge in an orderly fashion to create a tonotopic map in the cochlear nucleus (Cao and Oertel 2010; Oline et al. 2016; Rubel and Parks 1975).

In the model, the two measures of BOT agreed in suggesting that orderly convergence was not associated with a linear increase in BOT. Both H and R exhibited an initial increase, and then BOT reached asymptote with H and ultimately declined with R. This difference is a function of the two measures, with H taking account of all the sideband sensitivities and R measuring only the noise-to-signal ratio, as reflected in the responses to the best and “second-best” stimulus. Thus, if we assume that the “signal” in the noise-to-signal ratio is maintained as best-stimulus convergence increases and that side-band sensitivities are more random, then it follows that the second-best stimulus (noise) averaged across multiple inputs will decrease. Note also that BOT increases even with just one input, i.e., a convergence of 1, likely the result of STSD (Fig. 8, B and C). By acting as a low-pass filter (filtering out high-frequency responses), a synapse with STSD would lower the (higher frequency) “signal” while allowing lower frequency “noise” through, effectively increasing BOT.

Our conclusion favoring best-stimulus over random convergence admittedly offers just a partial prediction of the pattern of convergence within the solitary nucleus. Because the in vivo studies used a tongue chamber that prevented gustatory activation of other receptive fields, our model only considered convergence within the CT. Thus the model does not consider changes in BOT resulting from inputs from multiple nerves. For example, in the rat NST, convergence between the greater superficial petrosal and CT branches of the seventh nerve has been reported to include convergence of afferents with sensitivities to different qualities (Travers et al. 1986). Other studies, both in vivo and in vitro, further suggest additional complexities between converging seventh and ninth nerve fibers in rNST, including inhibitory interactions (Grabauskas and Bradley 1996; Sweazey and Smith 1987). On the other hand, studies in the NST that have employed whole mouth stimulation do not generally report more broadly tuned neurons than those with restricted stimulation techniques (Spector and Travers 2005), suggesting that the current conclusions regarding best-stimulus convergence are realistic. A striking example is the dichotomy of Na⁺-sensitive neurons into relatively narrowly tuned amiloride-sensitive sodium-best and more broadly tuned neurons that are sensitive to both acid and sodium but that are not amiloride sensitive (Boughter and Smith 1998; Scott and Giza 1990), types similar to those observed in the periphery (Breza et al. 2010; Hettinger and Frank 1990; Ninomiya 1996; Ninomiya and Funakoshi 1988).

Although the responses of the model assuming stimulus-specific convergence were a reasonably good fit to the in vivo rNST data, the model failed to account for any rNST response greater than 40 Hz (Fig. 9). This is likely a consequence of the input-output relationship produced by fitting both the modeled synapse and the modeled rNST neurons to the average characteristics of the excitatory and inhibitory rNST neurons recorded in vitro. It is possible that a modeling approach that reflected the heterogeneity of the in vitro data would produce heterogeneous input-output relationships that would allow us to capture the behavior of these fast-firing rNST neurons.

Inhibition in the rNST

The presence of pre- and postsynaptic inhibition is well established in rNST. Empirical studies provide evidence for presynaptic inhibition mediated by GABA_B receptors (Sharp and Finger 2002) and/or μ-opioid receptors (Boxwell et al. 2013). Likewise, GABA has a pronounced postsynaptic inhibitory effect on rNST neurons (Grabauskas and Bradley 1998; Liu et al. 1993; Wang and Bradley 1993) that originates both from a large population of intrinsic rNST neurons that can be activated by incoming afferents (Grabauskas and Bradley 1996; Wang and Bradley 1995) and from extrinsic sources, including forebrain sites and the caudal NST, that act on GABA_A and, to a lesser extent, GABA_B receptors (reviewed in Bradley 2007b; Lundy and Norgren 2015; Travers and Travers 2010).

We modeled postsynaptic inhibition as a change in chloride conductance, i.e., as a GABA_A synapse and presynaptic inhibition as the probability of neurotransmitter release. Overall, both forms of inhibition improved the fit of modeled neurons to the in vivo rNST data. Although inhibition sharply reduced the firing frequency of model E and I neurons (Figs. 6 and 7), the manner in which this reduction occurred determined whether inhibition impacted BOT. When input-output functions are transformed to threshold linear functions, the effects of inhibition can alter either (or both) the slope or intercept of the resulting linear plot. For example, in the visual cortex, GABAergic inhibition induced by stimulation of one class of interneurons changed the slope of the threshold linear function and resulted in a change in the overall “gain” of the response profile but no change in BOT. In contrast, GABAergic inhibition from a different group of interneurons increased the Y-intercept of the threshold linear function and had little effect on gain but produced a “subtractive” effect, sharpening the tuning curve (Atallah et al. 2012; Wilson et al. 2012).

We observed a systematic decrease in slope over a range of postsynaptic inhibition in both E and I cells (Fig. 6, D and F), suggesting a role for postsynaptic inhibition on “gain control” for both cell types. Indeed, this was evident when we modeled the effects of postsynaptic inhibition using in vivo CT afferent input (Fig. 10, A and D). Likewise, postsynaptic inhibition produced a modest change in intercept in both cell types (Fig. 6, C and E), and this change translated into a significant reduction in BOT (Fig. 10, B, C, E, and F). Two reports of the effects of GABAergic inhibition in vivo, in fact, show modest changes in the BOT of taste responses (Smith and Li 1998; Travers et al. 2015). Likewise, an optogenetic study of the impact of GABA release on threshold linear functions of input-output responses in the rNST, recorded in vitro, showed a larger effect on the divisive (slope) component compared with the subtractive (Y-intercept) change that would be predicted to impact BOT (Chen et al. 2016).

In contrast to postsynaptic inhibition, presynaptic inhibition produced differential effects in E and I cells (Fig. 7). Although presynaptic inhibition produced similar changes in slope in E and I cells (Fig. 7, D and F) that translated into similar reductions in firing frequency with the modeled CT input (Fig. 10, A and D), presynaptic inhibition produced virtually no change in intercept in I cells (Fig. 7C). This lack of a change in intercept translated into no change in BOT with the modeled CT input (Fig. 10F). The differential effect of presynaptic inhibition on BOT in E and I cells that is predicted by the model awaits empirical validation.

In Vitro Responses and Cell Types

Our computational model is built on the synaptic and membrane characteristics of GABAergic neurons that are thought to be primarily interneurons and of non-GABAergic neurons that include but are not necessarily limited to glutamatergic projection neurons sending projections to the parabrachial nucleus, the reticular formation, or caudal solitary nucleus (Bradley 2007a; Lundy and Norgren 2015; Travers and Travers 2010). Although both the in vitro data and in vivo data used in the present study were drawn from rodents, they were not of the same species. Practical considerations directed us to transgenic mice to differentiate GABAergic from non-GABAergic neurons. However, the in vivo CT and rNST data were from hamsters, because of the availability of gustatory responses in both peripheral and second-order rNST neurons to the same battery of stimuli at the same concentrations. Nevertheless, it is likely that rNST neurons in mice and hamsters, as well as those in rat, share many of the same fundamental properties of afferent convergence and sensitivity to inhibition.

The in vitro studies revealed differences between E and I cells. Of particular significance, I cells in the present study had significantly lower breakpoints compared with E cells. This is similar to GABAergic neurons in a transgenic GAD65 mouse, which also had significantly lower breakpoints compared with non-GABAergic neurons (Chen et al. 2016) and rat parabrachial nucleus-projecting (likely non-GABAergic) neurons that tended to be “tonic” responders to depolarization (Corson and Bradley 2013). Moreover, GABA-positive neurons in the GIN mouse were rapidly adapting; i.e., they likely had lower breakpoints (Wang and Bradley 2010a). We further observed that I cells had nominally lower thresholds to afferent stimulation and significantly lower postsynaptic potential amplitudes to afferent stimulation compared with E cells.

Despite these differences between E and I neurons, model neurons fit to the average characteristics of E and I neurons exhibited remarkably similar input-output relationships across all levels of convergence (Fig. 5). The inclusion of other cell properties, however, could be expected to impact and perhaps further differentiate E and I cell model outputs.

For example, there is heterogeneity in the expression of the hyperpolarization-sensitive voltage-gated K⁺ channel I_A and the non-specific cation channel I_h in rNST neurons (Chen et al. 2016; Corson and Bradley 2013; Suwabe and Bradley 2009; Tell and Bradley 1994). In addition, the differential expression of calcium channels can further modulate neuron excitability (Tell and Bradley 1994). In fact, a recent paper showed the importance of I_A and I_h for the input-output properties of GABA-positive and GABA-negative neurons (Chen et al. 2016). In the present study, model I cells had an output of ~9 spikes/s at 20 Hz (asymptote) compared with the in vitro data, where the whole population of GABA-positive neurons had a mean response of 4 spikes/s at 20-Hz stimulation. However, the subpopulation of GABA-positive cells with I_h had an output of 8 spikes/s at 20 Hz (asymptote), similar to the model cells. Similarly, in vitro, for GABA-negative neurons without I_A, 20-Hz stimulation produced a response of 7 Hz (where the response reached asymptote) compared with the current study in which model E cells (GABA negative) reached asymptote at 10-Hz stimulation with an output of ~8 spikes/s. In so far as the current model did not include either I_A or I_h, these are remarkably similar results.

GRANTS

This work was supported by National Institutes of Health Grants R21DC013676 (to J. B. Travers) and T32DE014320 (to College of Dentistry, Ohio State University).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

A.B., D.T., Y.Y., and J.B.T. conceived and designed research; A.B. performed experiments; A.B. analyzed data; A.B., D.T., M.F., and J.B.T. interpreted results of experiments; A.B. and J.B.T. prepared figures; A.B. drafted manuscript; A.B., D.T., M.F., and J.B.T. edited and revised manuscript; A.B., D.T., Y.Y., and J.B.T. approved final version of manuscript.