Voltage- and Calcium-Gated Membrane Currents Tune the Plateau Potential Properties of Multiple Neuron Types

Abstract

Many neurons exhibit regular firing that is limited to the duration and intensity of depolarizing stimuli. However, some neurons exhibit all-or-nothing plateau potentials that, once elicited, can lead to prolonged activity that is independent of stimulus intensity or duration. To better understand this diversity of information processing, we compared the voltage-gated and Ca²⁺-gated currents of three identified neurons from hermaphroditic Aplysia californica. Two of these neurons, B51 and B64, generated plateau potentials and a third neuron, B8, exhibited regular firing and was incapable of generating a plateau potential. With the exception of the Ca²⁺-gated potassium current (I_KCa), all three neuron types expressed a similar array of outward and inward currents, but with distinct voltage-dependent properties for each neuron type. Inhibiting voltage-gated Ca²⁺ channels with Ni⁺ prolonged the plateau potential, indicating I_KCa is important for plateau potential termination. In contrast, inhibiting persistent Na⁺ (I_NaP) blocked plateau potentials, empirically and in simulations. Surprisingly, the properties and level of expression of I_NaP were similar in all three neurons, indicating that the presence of I_NaP does not distinguish between regular-firing neurons and neurons capable of generating plateau potentials. Rather, the key distinguishing factor is the relationship between I_NaP and outward currents such as the delayed outward current (I_D), and I_KCa. We then demonstrated a technique for predicting complex physiological properties such as plateau duration, plateau amplitude, and action potential duration as a function of parameter values, by fitting a curve in parameter space and projecting the curve beyond the tested values.

SIGNIFICANCE STATEMENT Plateau potentials are intrinsic properties of neurons that are important for information processing in a wide variety of nervous systems. We examined three identified neurons in Aplysia californica with different propensities to generate a plateau potential. No single conductance was found to distinguish plateau generating neurons. Instead, plateau generation depended on the ratio between persistent Na⁺ current (I_NaP), which favored plateaus, and outward currents such as I_KCa, which facilitated plateau termination. Computational models revealed a relationship between the individual currents that predicted the features of simulated plateau potentials. These results provide a more solid understanding of the conductances that mediate plateau generation.

Introduction

Plateau potentials are intrinsic properties, expressed in a wide variety of neurons that convert graded synaptic input into an all-or-nothing burst of activity. Plateau potentials are important for integrating temporal and spatially synchronized synaptic input (Plotkin et al., 2011). This nonlinearity allows input to reach spike threshold when simple summation of voltage response would be insufficient. At the network level, plateau potentials provide an “up state” that helps synchronize neuronal activity into distinct temporal phases. For example, plateau potentials are important for effective transmission at the cortico-striatal synapse (Plotkin et al., 2011), rhythmic pattern generation in mammalian pre-Bötzinger neurons (Del Negro et al., 2002) and synaptic integration of cortical pyramidal neurons (Milojkovic et al., 2004). Plateau potentials are also important for learning mechanisms, including inducing long-term potentiation to establish hippocampal place fields (Takahashi and Magee, 2009; Bittner et al., 2017). In invertebrates, plateau potentials are important for determining the phasing of motor patterns (Plummer and Kirk, 1990; Bal et al., 1994; Zhang et al., 1995; Nargeot et al., 1999a,b; Erazo-Toscano et al., 2023) and changes in plateau properties are important for reward learning in the feeding system (Nargeot et al., 1999a,b; Brembs et al., 2002; Mozzachiodi et al., 2008; Sieling et al., 2014).

Several membrane currents have been implicated in determining the characteristics of plateau potentials. For example, the persistent Na⁺ current (I_NaP) is thought to mediate plateau potentials in many neurons (Carrillo-Reid et al., 2009) and dysregulation of this current has been implicated in sustained neuronal activity such as occurs in epilepsy (Stafstrom, 2007; Wengert and Patel, 2021). In subthalamic neurons, the bursting phenotype is explained at least in part by the ratio between I_NaP and I_leak (Del Negro et al., 2002). Similarly, the L-type voltage-gated Ca²⁺ current (I_CaL) is also thought to mediate plateau potentials in some neurons (for review, see Binder et al., 2020). However, the extent to which I_NaP is necessary or sufficient, remains an open question. What prevents plateau potentials from being generated in regular firing neurons? Moreover, in what ways do the outward currents Ca²⁺-activated K⁺ (I_KCa), delayed K⁺ (I_D), or A-type K⁺ (I_A) regulate the shape and duration of plateau potentials?

To address these questions, we performed a comparative analysis of three identified neurons from the Aplysia feeding circuit, each of which has unique firing patterns. Two of these neurons, B51 and B64, generate plateau potentials in response to brief depolarizing stimuli (Hurwitz and Susswein, 1996; Plummer and Kirk, 1990). A third neuron, B8, exhibits regular firing at a rate that is a graded function of depolarizing stimuli, and is incapable of generating a plateau potential (Morton and Chiel, 1993). Here, we combined computational and experimental approaches to determine the major membrane currents that mediate the characteristic patterns of spike activity of B8, B51, and B64.

Materials and Methods

Animals

Aplysia californica (100–120 g) were obtained from the National Resource for Aplysia (University of Miami, FL). Aplysia are hermaphroditic. Animals were housed in perforated plastic cages in aerated seawater tanks at a temperature of 15°C and were fed ∼1 g of dried seaweed three times per week.

Cell culture

Culturing procedures followed those described in Brembs et al. (2002) and Lorenzetti et al. (2008). Briefly, ganglia from adult Aplysia were treated with Dispase II (9.4 units/ml; neutral protease, grade II; Roche) at 35°C for ∼3 h and was then desheathed. Fine-tipped glass microelectrodes were used to remove individual cells from the ganglia. Each cell was isolated and plated on poly-L-lysine (0.75 mg/ml)-coated Petri dishes with culture medium containing 50% hemolymph, 50% isotonic L15 (Invitrogen). L15 was made of 350 mm NaCl, 29 mm MgCl₂, 25 mm MgSO₄, 11.4 mm CaCl₂, 10 mm KCl, 2 mm HCO₃, streptomycin sulfate (0.10 mg/ml), penicillin-G (0.10 mg/ml), dextrose (6 mg/ml), and 15 mm HEPES. The pH of the culture medium was adjusted to 7.5. Cells were maintained for 5–6 d. Before recording, the culture medium was exchanged for isotonic ASW solution containing 425 mm NaCl, 12.5 mm MgSO₄, 11.2 mm CaCl₂, 42 mm MgCl₂, 10 mm KCl, and 12.5 mm HEPES (pH 7.6 titrated with NaOH). In cases where voltage or Ca²⁺-gated K⁺-currents were examined N-methyl-D-glucamine (NMDG) substituted Na⁺ (425 mm). The NMDG substituted ASW (Na⁺-free ASW) was titrated with HCl.

Intracellular recordings and pharmacology

Intracellular recordings were performed at room temperature (20–22°C) using two fine-tipped glass microelectrodes filled with 3 m potassium acetate (resistance 7–15 MΩ). One electrode was used for monitoring membrane potential and a second for injecting current. Signals were amplified using an Axoclamp-2B (Molecular Devices), and for membrane current an LPF-202A DC amplifier (Warner Instruments, Inc). Current and voltage data were acquired at 5–10 kHz with pClamp software (version 11, Molecular Devices) and filtered with a lowpass filter using MATLAB with the cutoff between 300 and 700 Hz. Whole-cell two-electrode voltage-clamp and pharmacological techniques were used to examine the properties of voltage-gated ion currents. The voltage-clamp protocol was modified to best isolate each conductance. The pharmacological agents were dissolved in 15 ml (∼5× bath volume) and perfused at a rate of 2 ml/min.

Imaging neurons

Images of cultured neurons were taken with a charged-coupled device (CCD) camera (Microcast HD, HDXS 3CCD-1080P) with a Pro-Lite 1080p 2MP frame grabber and stored on drive using the MediCap USB300. The images were captured on the inverted Axiovert S100 (Lieca) with a 20× objective, the same microscope used for electrophysiological recordings. Multiple images were taken to cover the entire neuron and were stitched together using a built-in image registering tool in Adobe Photoshop (Fig. 1D).

Figure 1.

Physiologic properties of plateau-generating and regular-spiking neurons. A, Diagram of rostral surface of right buccal ganglion. Neurons were identified by size and position. B, Neurons were isolated and recordings were made after 5–6 d in culture. C, Firing properties of B8, B51, and B64. Activity was elicited by 1-s duration intracellular current injection in B51 and B64 with increments of 0.1 nA. The first current pulse failed to elicit activity in B51, but a plateau potential and high-frequency spike activity were produced when the current was increased by 0.1 nA. The plateau potential self-terminated after about 25 s. Similar dynamics were exhibited by B64, but the plateau potential in B64 persisted until it was terminated artificially by injecting a hyperpolarizing current. B8 was activated by 5-s duration current injection at 0.5-nA increments to illustrate regular firing that increased in frequency in response to the intensity of the stimuli. D, Images of cultured B8, B51, and B64 neurons.

Pharmacological isolation of currents

I _A

The membrane potential was held at −40 mV, stepped to −110 mV for 250 ms to de-inactivate I_A, then immediately stepped to potentials ranging from −50 to 20 mV for 500 ms. The interval between each voltage-clamp stimulus (interpulse interval) was set to 4 s. This protocol was conducted in two conditions: 200 μm 4-aminopyridine (4-AP) a concentration that does not block I_A and in 10 mm 4-AP, a concentration that inhibits I_A. Both cases Na⁺-free ASW containing 10 mm Ni²⁺ and 100 μm Cd²⁺ to block voltage-gated Ca²⁺ currents and I_KCa. The current responses during the two pharmacological conditions were subtracted to isolate I_A.

I _D

The membrane potential was held at −80 mV, stepped to −40 mV for 300 ms to inactivate I_A, then immediately stepped to potentials ranging from −30 to 20 mV for 1 s. The ISI was set to 60 s. I_D was measured in Na⁺-free ASW containing 2 mm tetraethylammonium (TEA) and 10 mm Ni²⁺ and 100 μm Cd²⁺ to block I_KCa and voltage-gated Ca²⁺ currents.

I_KCa and I_KTEA

The membrane potential was held at −80 mV, stepped to −30 mV for 300 ms to inactivate I_A, then immediately stepped to potentials ranging from −30 to 20 mV for 500 ms. The ISI was set to 3 s. This protocol was conducted in Na⁺-free ASW in control saline and in saline containing 4 mm TEA (Baxter and Byrne, 1989; Walsh and Byrne, 1989). The current responses during these two pharmacological conditions were subtracted. This resulted in a current trace with a fast Ca²⁺-independent component (I_KTEA) and slow Ca²⁺-dependent component (I_KCa). To isolate the Ca²⁺-independent component, the protocol was repeated in Ni²⁺ and Cd²⁺, which blocks voltage-gated Ca²⁺ currents. A second group of neurons was needed because both I_KCa and I_KTEA are blocked by low concentrations of TEA. The current responses were averaged (B51 n = 5, B64 n = 5, B8 n = 5) and the ratio of I_KTEA to I_KCa was calculated for each neuron (e.g., B51, B64, and B8). This average response was scaled according to ratio for each recording to isolate the I_KCa component of the 4 mm TEA subtraction.

I _CaL

The membrane potential was held at −80 mV and stepped to potentials ranging from −40 to 20 mV for 250 ms. The ISI was 30 s. This protocol was repeated in control saline and saline containing the I_CaL inhibitor nifedipine (10 μm). The current responses during the two conditions were subtracted to isolate I_CaL. Both conditions were in Na⁺-free ASW containing 10 mm 4-AP and 50 mm TEA to block I_A, I_D, and I_KCa.

I _CaR

The membrane potential was held at −80 mV and stepped to potentials ranging from −40 to 20 mV for 250 ms. The ISI was set to 30 s. This protocol was repeated with a 300-ms prepulse to −10 mV to inactivate I_CaR. Both protocols were done in the presence of Na⁺-free ASW containing 10 μm nifedipine, 10 mm 4-AP and 50 mm TEA to block I_CaL, I_A, I_D, and I_KCa. The current responses elicited by the protocol without the prepulse were subtracted from the current responses with the prepulse to isolate I_CaR.

I _NaP

The membrane potential was held at −100 mV, stepped to −40 mV for 20 ms to inactivate the fast I_Na current, then immediately stepped to potentials ranging from −60 to −20 mV for 1 s. The ISI was set to 30 s. This protocol was repeated in ASW containing the voltage-gated Na⁺ inhibitor tetrodotoxin (10 μm TTX). The current responses during the two pharmacological conditions were subtracted to isolate I_NaP.

Fitting equations to current responses

The built-in MATLAB function lsqcurvefit with the default “trust-region-reflective” or the Levenberg-Marquardt least squares algorithms was used for all automated curve fitting of current responses and steady-state activation and inactivation curves (discussed in the following section). Biologically plausible limits on the fitting parameters are indicated in parentheses.

I_A current traces were fit with the following single-exponential equation:

$$\text{f}\left(\text{t}\right)=A{e}^{\frac{-t}{s}}+b,$$ (1)

where A is a positive value representing the amplitude of the current, s is the time constant of inactivation and b is a baseline offset. This curve was fitted to a 200-ms region starting 25 ms after the start of the pulse for each command potential. The curve was extrapolated backwards 25 ms to obtain the initial current at the start of the pulse.

I_D current traces were fit with a double-exponential equation to estimate the activation time constant, as follows:

$$\text{f}\left(\text{t}\right)=\text{A}\left(1-e^{\frac{-t}{0.01}}\right)\left(1-\text{B}\left(1-{\text{e}}^{\frac{-\text{t}}{\text{s}}}\right)\right),$$ (2)

where the parameter A (1 ≥ A ≥ 1.5 times peak current) is a measure of the steady-state current during maximum activation without inactivation, the first exponential is activation with a time constant of 0.01 s, and the second exponential is inactivation. To reduce the number of fitting parameters, the activation time constant was fixed at 0.01 s, a value which provided the best fit for the data. The parameter s (s ≤ 0.16 s) is the time constant of inactivation. B is the amount of inactivation and was determined by a voltage step to 30 mV following a 1-s step to various potentials (Fig. 2K; Extended Data Fig. 2-1B). The second term of Equation 2–4 is equal to B_∞ in Equation 15 when time is conducted to infinity. The current response measured at 18.7 ms after the start of the 30-mV pulse was normalized to the current measured with the prepulse that resulted in no inactivation (−30 mV). As for I_A, I_CaL, and I_CaR, the inactivation data were fit with Equation 5. The values returned from the fitted equation are inserted for B in Equation 2.

Figure 2.

The conductances of I_A and I_D were increased in the regular firing neuron B8 compared with the plateau generating neuron B51 and B64. A, Voltage-clamp protocol to measure I_A. A 250-ms duration hyperpolarizing prepulse was used to de-inactivate I_A. 4-AP was used to block I_A (Materials and Methods). Inactivation of I_A was measured by a separate voltage-clamp protocol (Extended Data Fig. 2-1). B–D, 4-AP subtracted current response indicating I_A for B51 (B), B64 (C), and B8 (D) for each command potential. A single exponential equation (Eq. 1; Materials and Methods) was fitted to a 200-ms region beginning 25 ms after start of the command pulse (black line). E, Summary data for the inactivation (dashed line, open diamonds) and activation curves (solid line, solid diamonds). The data were fit with Boltzmann equations (Eqs. 12 and 15) with minimum A and B (minimum activation and maximum inactivation) set to 0. Data are represented as mean and standard error. F–I, Summary data for the maximum conductance (Eq. 7) half-activation, activation slope parameter, half inactivation, and inactivation slope parameter of the Boltzmann equations (Eqs. 12 and 15). Data are represented by a box-plot, median is a horizontal line and the interquartile range is represented by a rectangle. J, Maximum conductance of I_A was estimated by extrapolating the fitted exponential curve to the beginning of the pulse and calculating conductance using Ohm's law. K, Voltage-clamp protocol to measure I_D. A 300-ms duration prepulse at −40 mV was given to inactivate and reduce contamination by I_A, making use of the lower threshold of inactivation of I_A. The current responses were measured in 2 mm TEA to block I_KCa. The final 100-ms pulse to 30 mV measured the amount of inactivation. L–N, Current response indicating I_D for B51 (L), B64 (M), and B8 (N) for each command potential. The product of two exponential equations (Eq. 2) was fitted to a 1-s region beginning at the start of the command pulse (black line). O, Summary data for the inactivation (dashed line, open diamonds) and activation curves (solid line, solid diamond) and fitted Boltzmann equations (Eqs. 12 and 15). Data represented as mean and standard error. P–T, Summary data for the parameters of the Boltzmann equations. U, Maximum conductance calculated using Ohm's law. Sample sizes are: B8, n = 5; B51, n = 5; B64, n = 4 for I_A; and B8, n = 5; B51, n = 4; B64, n = 5 for I_D. For all box-plots here and subsequently, statistical significance (p < 0.05) is indicated by a star and the lack of a star indicates that the comparison did not reach statistical significance. The inactivation traces for I_A and I_D are illustrated in Extended Data Figure 2-1A,B and the time constant analyses for I_A and I_D are illustrated in Extended Data Figure 2-2A,B. The parameter values of the Boltzmann equations of all currents are provided in Extended Data Table 2-1.

I_KTEA current traces were fit with the following single exponential equation:

$$\text{f}\left(\text{t}\right)=\text{A}\left(1-\text{B}\left(1-{\text{e}}^{\frac{-\text{t}}{\text{s}}}\right)\right),$$ (3)

where A (A ≥ 0) is the maximum current. B (0 ≥ B ≥ 1) is the steady-state inactivation. For Equation 3, B was not directly measured using a separate voltage-clamp protocol. The parameter s (0.05 ≥ s ≥ 2) is the inactivation time constant.

I_CaL and I_CaR current traces were fit with the following double-exponential equation:

$$\text{f}\left(\text{t}\right)=\text{A}\left(1-e^{\frac{-t}{{\text{s}}_1}}\right)\left(1-\text{B}\left(1-{\text{e}}^{\frac{-\text{t}}{{\text{s}}_2}}\right)\right),$$ (4)

where A (−100 ≥ A ≥ 0 nA) is the maximum current. s₁ (I_CaL: 0.002 ≥ s₁ ≥ 0.05, I_CaR: 0.001 ≥ s₁ ≥ 0.05) is the activation time constant, and s₂ (I_CaL: 0.02 ≥ s₁ ≥ 0.5, I_CaR: 0.025 ≥ s₁ ≥ 0.5) is the inactivation time constant. B is the amount of inactivation and was measured by a separate voltage-clamp protocol. A 1-s prepulse that ranged from −70 to −10 mV was followed by a 200-ms pulse to 0 mV to measure the amount of inactivation. To determine the time constant of inactivation (s₂), the current response to 0 mV was fit with a single exponential (Eq. 1) and extrapolated back to the start of the pulse. B was equal to 1 minus the extrapolated current divided by the current following a −30-mV prepulse.

I_NaP current traces were fit with the following double-exponential equation:

$$\text{f}\left(\text{t}\right)=\text{A}\left(1-e^{\frac{-t}{0.001}}\right)\left(1-0.4\left(1-{\text{e}}^{\frac{-\text{t}}{\text{s}}}\right)\right),$$ (5)

where A is the maximum activation and limited to between 0 and −30 nA. The value 0.001 is the activation time constant. Initial fittings indicated that the amount of inactivation was ∼0.5 for all three neurons in the range of potentials used to measure I_NaP, so we fixed the value to 0.5 for simplification and to reduce the degrees of freedom of the fitting algorithm. s (0.2 ≥ s ≥ 5) is the inactivation time constant.

Model equations

Conductance-based models for B51, B64, and B8 were generated and simulations conducted with simulator for neural networks and action potentials (SNNAP; version 8.1; Baxter and Byrne, 2007). The three neurons were modeled as isolated compartments with no synaptic (electrical or chemical) connections between them. The membrane potential was determined by the following differential equation:

$$\frac{d{\text{V}}_{\text{i}}}{\text{dt}}=\frac{{\text{I}}_{\text{Stim}}-{{\displaystyle \sum }}_{\text{j}=1}^{\text{m}}{\text{Ivd}}_{\text{ij}}}{{\text{Cm}}_{\text{i}}},$$ (6)

where Cm_i is the membrane capacitance, I_Stim is the extrinsic stimulus current, Ivd_ij denotes voltage dependent current. Each current was determined by the following equation:

$${\text{Ivd}}_{\text{ij}}=\left({\overline{\mathrm{g}}\text{vd}}_{\text{ij}}\right){\text{A}}_{\text{ij}}^{\text{p}}{\text{B}}_{\text{ij}}\left({\text{V}}_{\text{i}}-{\text{E}}_{\text{ij}}\right)f\left(BR\right),$$ (7)

where gvd_ij is the maximum conductance, A_ij represents the voltage-dependent and time-dependent activation, B_ij the voltage-dependent and time-dependent inactivation, V_i the membrane potential. E_ij is the equilibrium potential and was −63 mV for I_leak; −70 mV for I_D, I_A, I_KCa, and I_KTEA; 60 mV for I_NaP, I_CaR, and I_CaL, and −40 mV for I_HCN. The parameter p was three for I_Na and 1 for all other channels. f(BR) is included for I_KCa and denotes regulation by a Ca²⁺ ion pool. For I_leak, A_ij, B_ij and f(BR) are fixed at 1. For I_KCa, f(BR) is determined by the following equations:

$$f\left(BR\right)=BR$$ (8)

$$\frac{dBR}{dt}=\frac{\left[C{a}^{2+}\right]-BR}{\text{τ}},$$ (9)

where τ is the time constant and was 20 s for B51 and B64 and 0.7 s for B8. The concentration of Ca²⁺ is determined by the following equation. BR is the amount of regulation of the conductance.

$$\frac{\text{d}\left[{\text{Ca}}^{2+}\right]}{\text{dt}}=K_1\left(K_2\left(Iv{d}_{CaL}+Iv{d}_{CaR}\right)-\left[{\text{Ca}}^{2+}\right]\right),$$ (10)

K₁ was set to 80 for B8 and 8 for B51 and B64. K₂ was set to 1 for all three neurons.

The activation A_ij is determined by the following Boltzmann-type equations:

$$\frac{\text{dA}}{\text{dt}}=\frac{{\text{A}}_{\infty }-\text{A}}{{\text{τ}}_{\text{A}}}$$ (11)

$${\text{A}}_{\infty }=\frac{1}{1+{\text{e}}^{\frac{\left(\text{h}-\text{V}\right)}{\text{s}}}},$$ (12)

where A is the level of activation, h is the voltage of the inflection point (half-activation), V is the voltage, and s is the slope parameter. We used a MATLAB curve fitting algorithm to estimate the parameters for this equation. The maximum current (A in Eqs. 1–5) was converted to conductance using Ohm's law. To obtain the activation level, the conductance values at each potential were normalized to the maximum conductance of all membrane potentials measured for that cell. The activation data for each cell were fit with Equation 12 (Figs. 2E,O, 3G, 4E,O, 5G, solid diamonds, solid lines). For the voltage-gated Ca²⁺ currents, h was limited to between −50 and 10 mV and s was limited to between 0 and 20.

Figure 3.

I_KCa facilitates the termination of plateau potentials. A, Application of Ni²⁺ increased the duration of the plateau potential of B51. Activity elicited by 1-s duration suprathreshold stimulation. B, Summary data of effects of Ni²⁺ on the B51 plateau potential. The duration was measured as the amount of time after the stimulus above −70 mV. Data are represented as a boxplot, median is a horizontal line and the interquartile range is represented as a rectangle. Sample size, n = 8. C, Voltage-clamp protocol to measure I_KCa. D, The current responses to a voltage step to 20 mV. Responses in control were subtracted from responses in 4 mM TEA (teal). This procedure was repeated in a second set of B51 neurons in the presence of Ni²⁺ + Cd²⁺ to measure the calcium-insensitive outward component, which was averaged (see Extended Data Fig. 3-1). This average calcium-insensitive current response was normalized to the current response in the absence of Ni²⁺ + Cd²⁺ (gray). E, I_KCa for B51. The averaged calcium-insensitive outward current at each command potential was subtracted from responses without Ni²⁺ + Cd²⁺ to isolate I_KCa. F, TEA-subtracted current responses to a 20-mV step in B64 in the absence of Ni²⁺ + Cd²⁺ (teal) and the average TEA-subtracted current responses in a second set of B64 neurons. G, There was no apparent I_KCa for B64 when the averaged calcium-insensitive outward current was subtracted from responses without Ni²⁺ + Cd²⁺. H, TEA-subtracted current responses to a 20-mV step in B8 in the absence of Ni²⁺ + Cd²⁺ (teal) and the average TEA-subtracted current responses in a second set of B8 neurons. I, I_KCa for B8. The averaged calcium-insensitive outward current was subtracted from responses without Ni²⁺ + Cd²⁺ to isolate I_KCa. J, Current response of I_KCa. Mean current of last 50 ms of −10-mV voltage step. Sample sizes: B8, n = 6; B51, n = 5; B64, n = 5.

Figure 4.

The conductances of I_CaL and I_CaR were increased in B8 compared with B51. A, Voltage-clamp protocol to measure I_CaL. The current responses in control were subtracted from responses in 10 µm nifedipine to isolate I_CaL. Inactivation for I_CaL was measured by a separate voltage-clamp protocol (Extended Data Fig. 2-2). B–D, Subtracted current responses indicating I_CaL for B51 (B), B64 (C), and B8 (D) for each command potential. A double exponential equation (Eq. 4) was fitted to a 100-ms region beginning 2 ms after start of the command pulse (black line). E, Summary data for the inactivation (dashed line, open diamonds) and activation curves (solid line, solid diamonds). The data were fit with Boltzmann equations (Eqs. 12 and 15) with minimum A and B (minimum activation and maximum inactivation) set to 0. Data are represented as mean and standard error. F–I, Summary data for the parameters of the Boltzmann equations. Data are represented by a boxplot, median is a horizontal line and the interquartile range is represented by a rectangle. J, Maximum conductance of I_CaL was calculated using Ohm's law. K, Voltage-clamp protocol to measure I_CaR. A 300-ms prepulse to −10 mV was given to inactivate I_CaR. Protocols were administered in the presence of nifedipine to block I_CaL. The current responses without prepulse were subtracted from responses with the prepulse to isolate I_CaR. Inactivation for I_CaR was measured by a separate voltage-clamp protocol (Extended Data Fig. 2-2). L–N, Subtracted current response indicating I_CaR for B51 (A), B64 (B), and B8 (C) for each command potential. A double exponential equation (Eq. 4) was fitted to a 120-ms region beginning 8 ms after the start of the command pulse (black line). O, Summary data for the inactivation (dashed line, open diamonds) and activation curves (solid line, solid diamond) and fitted Boltzmann equations (lines; Eqs. 12 and 15). Data represented as mean and standard error. P–T, Summary data for the parameters of the Boltzmann equations. U, Maximum conductance calculated using Ohm's law. Sample sizes: I_CaL B8, n = 5; B51, n = 5, and B64, n = 5; for I_CaR: B8, n = 5; B51, n = 5; B64, n = 5. The inactivation traces for I_CaL and I_CaR are illustrated in Extended Data Figure 2-1C,D, and the time constant analyses for I_CaL and I_CaR are illustrated in Extended Data Figure 2-2C–F.

For the activation time constant:

$${\text{τ}}_A=\frac{{\text{τ}}_{max}-{\text{τ}}_{min}}{\left(1+e^{\frac{\left(V-h_1\right)}{s_1}}\right)\left(1+e^{\frac{\left(V-h_2\right)}{s_2}}\right)}+{\text{τ}}_{min},$$ (13)

where V is the voltage, h_1,2 determine the voltage of the inflection points, s_1,2 are slope parameters, τ_max is the maximum time constant, and τ_min is the minimum time constant. For simplification and to aid in curve fitting of the current traces, the activation time constants of I_D, I_KTEA, I_NaP were fixed to 0.01 s and I_KCa time constant was fixed to 0.009 s. For voltage-gated Ca²⁺ currents, the activation time constants depended on the voltage-clamp potential. To incorporate this voltage dependence into the model, the voltage dependencies of the activation time constants were fit by hand with Equation 13 (Extended Data Fig. 2-2). For I_A, the parameters for voltage dependence of the activation time constant were set to: B51, τ_max = 0.03 s, τ_min = 0.001 s, h₁ = −30 mV, s₁ = −5.7; B64, τ_max = 0.02 s, τ_min = 0.002 s, h₁ = −20 mV, s₁ = 5.7; B8, τ_max = 0.025 s, τ_min = 0.007 s, h₁ = −20 mV, s₁ = 6. For all three neurons, the second term in the denominator was not included. The voltage dependence of the activation time constants in the model and the corresponding empirical data are provided in Extended Data Figure 2-2.

The inactivation, B_ij (Eq. 7), was defined by the following equations:

$$\frac{\text{dB}}{\text{dt}}=\frac{{\text{B}}_{\mathrm{\infty }}-\text{B}}{{\text{τ}}_{\text{B}}}$$ (14)

$${\text{B}}_{\mathrm{\infty }}=\frac{1-B_{min}}{1+{\text{e}}^{\frac{\left(\text{h}-\text{V}\right)}{\text{s}}}}+{\text{B}}_{min}$$ (15)

$${\text{τ}}_B=\frac{{\text{τ}}_{max}-{\text{τ}}_{min}}{\left(1+e^{\frac{\left(\text{V}-h_1\right)}{s_1}}\right)\left(1+e^{\frac{\left(\text{V}-h_2\right)}{s_2}}\right)}+{\text{τ}}_{min},$$ (16)

where V is the voltage, h_1,2 determine the voltage of the inflection points, s_1,2 are slope parameters, τ_max is the maximum time constant, τ_min is the minimum time constant. The level of inactivation (Extended Data Fig. 2-1) for each measured potential was fit with Equation 15. For I_A and voltage-gated Ca²⁺ currents, B_min was fixed at 0. For voltage-gated Ca²⁺ currents, h was limited to negative voltages. The inactivation time constants were estimated as s in the exponential decay terms in Equations 1–5. There did not appear to be any voltage dependence in inactivation time constants for I_A and I_CaL so the means of the inactivation time constants for all potentials were compared among the neurons (Extended Data Fig. 2-2A,D). There did appear to be voltage-dependence in the inactivation time constants for I_D, I_CaR, I_NaP. For I_D and I_CaR, the voltage dependence of the inactivation time constant seemed to be best fit by a sigmoidal equation and so the second term in the denominator of Equation 16 was not included. The voltage dependence of inactivation time constants of I_NaP was fit using Equation 16. The voltage dependence of inactivation time constants for I_D was fit manually or by a MATLAB curve fitting algorithm. The voltage dependence of the inactivation time constants in the model and the corresponding empirical data are provided in Extended Data Figure 2-2.

This study did not characterize Na⁺-fast (I_Na), so the model for this current was guided by data of its characterization in Aplysia pedal neurons (Gilly et al., 1997) and was identical for all three neuron models. Parameter values were as follows. In Equation 7, $\overline{g}$ = 50 µS, p = 3, E = 60 mV. In Equation 12, h = −16.6 mV, s = 6.66. In Equation 13, τ_max = 0.035 s, τ_min = 0.00024 s, h₁ = −30 mV, s₁ = 5.382, h₂ = −17, s₂ = −9.9. In Equation 15, h = −24 mV, s = 3.807; and in Equation 16, τ_max = 0.042 s, τ_min = 0.001 s, h₁ = −32 mV, s₁ = 14.47. The second term in the denominator of Equation 16 was not included for I_Na.

The medians and interquartile ranges of the parameters governing steady-state voltage dependencies of all currents, estimated by the curve fitting routines, are provided in Extended Data Table 2-1 and the parameters defining the time constants are provided in the legend of Extended Data Figure 2-2. As a first step, we attempted to simulate the current responses using the median values of these parameters. The simulated current response using the median parameter values did not match the current responses of the neurons nor did the firing patterns of the model match the simulated firing pattern. This finding is unsurprising given that the measurements of parameters were performed in cells isolated from different animals. Therefore, the parameter values were adjusted by trial and error to obtain better fits of the current responses (Extended Data Fig. 6-1) and the firing patterns of the neurons (Fig. 6E) while staying as close as possible to the median parameter values. In most cases this procedure resulted in parameter values that lie within the interquartile ranges of the empirical data.

Figure 6.

Simulations indicated that outward currents I_KCa, I_A, and I_D terminated plateau potentials and could suppress the initiation of plateau potentials. A, Diagram of the conductance-based model for the three neurons. Each neuron was modeled as a single compartment containing I_D, I_A, I_KTEA, I_KCa, I_NaP, I_Na, I_CaR, I_CaL, and I_HCN for B8. I_KTEA is described in Extended Data Figure 3-1. Comparison of the current response to voltage commands between the model and empirical data is provided in Extended Data Figure 6-1. B–D, Plots showing the dominant steady-state current for each membrane potential. I_leak and I_HCN dominate near the holding potential (−80 mV), I_NaP dominates between −60 and −30 mV, I_Na dominates between −30 mV and −10 mV, I_D and I_KCa dominate above −10 mV. E, Voltage and current responses during activity triggered by a simulated 1-s, 3-nA current injection. B8 has a pronounced sag potential (Díaz-Ríos and Miller, 2006) and rebound excitation (Kabotyanski et al., 2000); thus, we confirmed the presence of I_HCN (see Extended Data Fig. 6-2) and substituted this current for I_Leak in B8. the horizontal lines on the panels for I_leak and I_HCN indicate 0 current. Passive properties could not explain the differences in firing properties (Extended Data Fig. 6-3). The parameter values of Equations 7, 12, and 15 for all currents in the model are provided in Extended Data Table 2-1.

Data and code availability

Raw data and annotated spreadsheets are deposited on Google Drive. A link will be provided on request. The code for mathematical simulation is provided on ModelDB. The analysis routines were written in MATLAB and are provided on GitHub at https://github.com/Byrne-Lab/Neveu_2023. Any additional information for reanalyzing the data are available from the Lead Contact on request.

Statistical analyses

MATLAB was used for all statistical analyses. For all comparisons p values < 0.05 were considered significant. A Lilliefors goodness-of-fit test was used to test for normality of the distribution. Nonparametric tests were used when normality could not be assumed. The Student's t test was used for comparing two groups. ANOVA or Kruskal–Wallis with the Tukey–Kramer post hoc test was used for comparing multiple groups. The confidence intervals were calculated by a built-in MATLAB function with an α value of 0.05.

Results

Neurons B51, B64, and B8 differ in their ability to generate plateau potentials

To investigate mechanisms of plateau generation, B51, B64, and B8 were isolated from Aplysia buccal ganglia (Fig. 1A) and maintained in cell culture (Fig. 1B). In culture, 36% of B51 neurons generated a plateau potential. Once elicited the plateau in B51 always self-terminated and lasted 5.89 ± 1.62 s (n = 36) after the end of the stimulus (Fig. 1C). B64 generated a plateau potential in 85% of the cases (n = 26) and the plateau did not self-terminate in the majority of the cases (91%). In one example, the B64 plateau lasted ∼80 s before being terminated by a negative current injection (Fig. 1C). B8 exhibited tonic regular spiking activity limited to the duration of the stimulus, which increased in frequency as a function of the intensity of stimulation. Importantly, B8 failed to generate a plateau potential regardless of the amount of current injected in any of the B8 neurons examined (Fig. 1C). The activity of these neurons recapitulated their activity in the intact circuit (Plummer and Kirk, 1990; Hurwitz and Susswein, 1996; Lorenzetti et al., 2008; Mozzachiodi et al., 2008) with the exception that in situ the B64 plateau potential is eventually terminated by feedback from an inhibitory neuron (Nargeot et al., 2002).

Extended Data Figure 2-1

Inactivation measurements. A, Inactivation measurements for I_A. Currents measured at −10 mV elicited by a 1-s prepulse at the indicated potentials. Current was measured by taking the mean of a 4-ms segment 45 ms after start of pulse (arrow). The inactivation at each potential is obtained by normalizing the measurements to the measured value with a −80-mV prepulse. B, Inactivation measurements for I_D. Currents measured at 30 mV elicited by a 1-s prepulse at the indicated potentials. Current was measured 18.7 ms after the start of the pulse (arrow). The inactivation at each potential is obtained by normalizing the measurements to the measured value with a −30-mV prepulse. C, Inactivation measurements for I_CaL. Currents measured at 0 mV elicited by a 1.5-s prepulse at the indicated potentials. A single exponential was fitted to a 150-ms segment of data during the decay phase (starting 35 ms after the start of the pulse). The curve was then extrapolated back to 0 ms. The inactivation at each potential is obtained by normalizing the measurements to the measured value with a −70-mV prepulse. D, Inactivation measurements for I_CaR. The same methods were used as in Panel C. For B51, a different set of cells were used than for Figure 4K–S. Download Figure 2-1, TIF file ^{(8.5MB, tif)} .

Extended Data Figure 2-2

Voltage-dependence of activation and inactivation time constants. A, The inactivation time constants for I_A were averaged across all measured voltages. Inactivation time constant was greater in B8 I_A compared to B51 and B64 (B51 = 0.054_{(0.051, 0.063)} MΩ, B64 = 0.048_{(0.040, 0.055)} MΩ_, B8 = 0.18_(0.17,0.20) MΩ; F_(2,13) = 117.4, p = 3.8 × 10⁻⁸; post hoc B51 vs B64, p = 0.61; B51 vs B8, p = 1.4 × 10⁻⁷; B64 vs B8, p = 1.19 × 10⁻⁷). Plus signs indicate the values used for the models and were 0.035 s for B51 and B64 and 0.14 s for B8. B, The inactivation time constants for I_D. Equation 16 without the second term in the denominator was used to fit these data. Solid lines indicate the time constants for the modeled current. Parameters were: B51, τ_max = 3 s, τ_min = 0.26 s, h = −14 mV, s = 7; B64, τ_max = 5.8 s, τ_min = 0.18 s, h = −60 mV, s = 15; B8, τ_max = 2 s, τ_min = 0.15 s, h = −14 mV, s = 8. C, The activation time constants for I_CaL. Equation 16 was used to fit these data. Solid lines indicate the time constants for the modeled current. Parameters were: B51, τ_max = 0.06 s, τ_min = 0.002 s, h₁ = −15 mV, s₁ = −13, h₂ = 5, s₂ = 13; B64, τ_max = 0.0088 s, τ_min = 0.002 s, h₁ = 0 mV, s₁ = −4, h₂ = 35, s₂ = 4; B8, τ_max = 0.08 s, τ_min = 0.002 s, h₁ = −20.5 mV, s₁ = −13, h₂ = 15, s₂ = 13. D, The inactivation time constants for I_CaL were averaged across all measured voltages. Inactivation time constant was greater in B51 I_CaL compared to B8 and there was a trend toward being greater than B64 (B51 = 0.22_{(0.17, 0.27)} MΩ, B64 = 0.12_{(0.11, 0.22)} MΩ_, B8 = 0.049_(0.039,0.06) MΩ; F_(2,14) = 9.75, p = 0.003; post hoc B51 vs B64, p = 0.22; B51 vs B8, p = 0.0024; B64 vs B8, p = 0.054). Plus signs indicate the values used for the models and were 0.035 for B8, 0.12 for B51, and 0.14 for B64. E, The activation time constants for I_CaR. Equation 16 was used to fit these data. Solid lines indicate the time constants for the modeled current. Parameters were: B51, τ_max = 0.03 s, τ_min = 0.001 s, h₁ = −10 mV, s₁ = −5.3, h₂ = 14, s₂ = 5.6; B64, τ_max = 0.02 s, τ_min = 0.001 s, h₁ = 13 mV, s₁ = −12.7, h₂ = 25, s₂ = 13; B8, τ_max = 0.076 s, τ_min = 0.001 s, h₁ = −1 mV, s₁ = −7.2, h₂ = 23, s₂ = 7.2. F, The inactivation time constants for I_CaR. Equation 16 without the second term in the denominator was used to fit these data. Solid lines indicate the time constants for the modeled current. Parameters were: B51, τ_max = 0.08 s, τ_min = 0.038 s, h = 0 mV, s = 5; B64, τ_max = 0.036 s, τ_min = 0.025 s, h = 0 mV, s = 0.46; B8, τ_max = 0.043 s, τ_min = 0.025 s, h = 1 mV, s = 6. G, The inactivation time constants for I_NaP. Equation 16 was used to fit these data. Solid lines indicate the time constants for the modeled current. Parameters for B51, B64, and B8 were: τ_max = 2.5 s, τ_min = 0.25 s, h₁ = −55 mV, s₁ = −1.5, h₂ = −45, s₂ = 1.5. Download Figure 2-2, TIF file ^{(8.1MB, tif)} .

Extended Data Table 2-1

Table of all of the steady state parameters of the voltage gated ion currents. The parameter name is listed in the left column ḡ (ḡvd_ij in Eq. 7), h_act (h in Eq. 12), s_act (s in Eq. 12), h_ina (h in Eq. 12), b_ina (s in Eq. 15), B_min (B_min in Eq. 15). For each neuron, the parameter value used in the model is under the column labeled Model, and the summary data of the measured value is in the column labeled Empirical. The empirical values are represented as medians with the 25th and 75th percentiles in parentheses. The statistical results and P values comparing the empirical data of the three neurons are provided in the columns labeled Statistics and P value, respectively. P values from post hoc comparisons are provided in the right three columns. The summary data are also represented in boxplots in Extended Data Figures 2-5. * The parameters for I_KCa were estimated by manually adjusting the parameters in the model and comparing the response to simulated voltage commands to responses in the empirical data set. Model parameter values that are outside the interquartile range are in bold. # The inactivation slope for I_KTEA was fixed at −5 (see Materials and Methods). ǂ The inactivation for I_NaP was fixed at these values. I_leak was set to 0.046 nS in B51 and 0.065 nS in B64 and 0 nS in B8. Download Table 2-1, DOCX file ^{(23.6KB, docx)} .

Extended Data Figure 3-1

I_KTEA is increased in B8. A, Voltage-clamp protocol to measure I_KTEA. 10 mM 4-AP was used to block I_A and 10 mM Ni²⁺ and 100 µM Cd²⁺ was used to block voltage-gated calcium channels and I_KCa. B–D, 4 mM TEA subtracted current response indicating an unidentified outward current for B51 (B), B64 (C), and B8 (D) that we label here I_KTEA. A single exponential equation (Eq. 1) was fitted to a 500-ms region beginning 25 ms after start of the command pulse. E, Summary data for the activation curves (solid line, solid diamond). These data were fit with Boltzmann equations (Eq. 12) with minimum A (minimum activation) set to 0. Data are represented as mean and standard error. F, Summary data for the inactivation curves (solid line, solid diamond). These data were fit with Boltzmann equations (Eq. 15). Data are represented as mean and standard error. G–J, Summary data for the parameters of the Boltzmann equations (Eqs. 15 and 15). Data are represented by a boxplot, median is a horizontal line and the interquartile range is represented by a rectangle. K, Maximum conductance of I_KTEA was estimated by extrapolating the fitted exponential curve to the beginning of the pulse and calculating conductance using Ohm's law. L, Mean current responses of I_KTEA for B51, B64, and B8 compared to simulation results. The time constant parameters were: B51, τ_max = 0.8 s, τ_min = 0.08 s, h₁ = 18 mV, s₁ = −2, h₂ = 20 mV, s₂ = 2; B64, τ_max = 1.1 s, τ_min = 0.2 s, h₁ = −13 mV, s₁ = −2, h₂ = −6 mV, s₂ = 2; B8, τ_max = 1.4 s, τ_min = 0.2 s, h₁ = −2 mV, s₁ = −1.5, h₂ = 3.5 mV, s₂ = 1.5. Download Figure 3-1, TIF file ^{(10.6MB, tif)} .

Using two-electrode voltage-clamp and pharmacological techniques, we characterized the ionic currents mediating the plateau potentials in B51 and B64, and investigated whether these currents are more similar in B51 and B64 compared with the regular firing neuron B8.

Outward currents of bursting and regular firing neurons

We characterized the fast activating/inactivating I_A, the relatively slower activating/inactivating I_D, and the Ca²⁺ activated I_KCa, which are known to regulate action potential repolarization in mammals as well as Aplysia (Byrne, 1980; Baxter and Byrne, 1989).

I _A

I_A was isolated using the selective antagonist 4-aminopyridine (4-AP; see Materials and Methods). The protocol, sample traces and analysis are illustrated in Figure 2A–J. The inactivation traces are illustrated in Extended Data Figure 2-1A and the time constant analyses are illustrated in Extended Data Figure 2-2A. The maximum conductance of I_A ($\overline{g}$_A) was larger in B8 compared with B51 and B64 (Fig. 2J; F_(2,13) = 23.7, p = 0.0001; post hoc, B51 vs B64, p = 0.36; B51 vs B8, p = 7.2 × 10⁻⁴; B64 vs B8, p = 1.4 × 10⁻⁴), suggesting a role of I_A in suppressing plateau potential initiation. The half-activation of I_A in B51 is shifted to more hyperpolarized potentials compared with B64 and B8 (Fig. 2F; F_(2,13) = 22.5, p = 0.0001; post hoc, B51 vs B64, p = 0.0014; B51 vs B8, p = 0.00,014; B64 vs B8, p = 0.50) and the half-inactivation of I_A was likewise leftward shifted in B51 compared with B64 and B8 (Fig. 2H; F_(2,13) = 5.94, p = 0.018; post hoc, B51 vs B64, p = 0.029; B51 vs B8, p = 0.036; B64 vs B8, p = 0.95). The inactivation slope parameter was reduced (corresponding to a steeper curve) in B51 compared with B8 (Fig. 2I; F_(2,13) = 10.4, p = 0.0029; post hoc, B51 vs B64, p = 0.082; B51 vs B8, p = 0.002; B64 vs B8, p = 0.19). The activation slope parameter in B51 appeared to be reduced compared with B64 and B8 (Eq. 12) but the trend was not significant (Fig. 2G; F_(2,13) = 3.18, p = 0.081). For B51, the leftward shift and steeper slope in the inactivation curve would reduce I_A activation and facilitate the generation of a plateau potential in B51. For B8, the greater $\overline{g}$_A in B8 could help prevent any plateau (see below).

I _D

I_D was isolated using tetraethylammonium (TEA) subtraction (see Materials and Methods). The protocol, sample traces and analyses are illustrated in Figure 2K–U. The inactivation traces are illustrated in Extended Data Figure 2-1B and the time constant analyses are illustrated in Extended Data Figure 2-2B. The maximum conductance ($\overline{\mathrm{g}}$_D) was increased in B8 compared with B51, and B64 tended to have an increased $\overline{\mathrm{g}}$_D compared with B51 (Fig. 2U; F_(2,14) = 9.19, p = 0.0038; post hoc, B51 vs B64, p = 0.033; B51 vs B8, p = 0.0034; B64 vs B8, p = 0.43). The half-activation was not different among the three neurons (Fig. 2P; F_(2,14) = 0.36, p = 0.70), nor was the activation slope parameter (Fig. 2Q; F_(2,14) = 0.10, p = 0.90). I_D did not completely inactivate for all tested command potentials. The maximum level of inactivation (i.e., minimum B) was compared among neurons and found to be significantly greater (lower levels of B in Eq. 15) for B8 compared with B51 and B64 (Fig. 2T; F_(2,14) = 5.43, p = 0.021; post hoc, B51 vs B64, p = 0.33; B51 vs B8, p = 0.21; B64 vs B8, p = 0.016). No significant difference was observed in the half-inactivation (Fig. 2R; F_(2,14) = 1.57, p = 0.25) or inactivation slope parameter (Fig. 2S; H₍₂₎ = 5.42, p = 0.067). These data indicate that I_D would be activated by the sustained depolarization of the plateau; and thus, I_D could affect plateau duration. In addition, the larger $\overline{g}$_D in B8 could prevent the initiation of plateau potentials by repolarizing the membrane potential following each action potential.

I _KCa

I_KCa was investigated by blocking voltage-gated Ca²⁺ channels and thereby preventing the activation of I_KCa (Fig. 3A,B). The voltage-gated Ca²⁺ current blocker Ni²⁺ increased the duration of the plateau potential in B51 (paired t test, t₍₇₎ = 2.80, p = 0.027), indicating that a Ca²⁺-activated K⁺ current contributed to the termination of the plateau. Plateaus lasting longer than 80 s were terminated by negative current injection. In some cases, B51 neurons, which did not express a plateau potential in control saline, exhibited a strong plateau in the presence of Ni²⁺ (Fig. 3B), which blocks I_CaR. These data suggest that I_KCa provides an inhibitory constraint on plateau potentials and that I_KCa is activated, at least in part, by the calcium influx of I_CaR. We characterized I_KCa and compared its properties among the three neurons. I_KCa was isolated using a 4 mm TEA subtraction. This protocol was repeated in a second group of cells in the presence of Ni²⁺ + Cd²⁺ to estimate the Ca²⁺-independent component (I_KTEA; Fig. 3D,F,H; Extended Data Fig. 3-1; see Materials and Methods). The protocol, sample traces and analyses are illustrated in Figure 3C–I. I_KCa was expressed in B51 and B8, but not in B64 (Fig. 3D–I). I_KCa was increased in B8 compared with B51 and was approximately zero in B64 when measured at −10 mV (B51 = 5.07 nA, B64 = −1.48 nA, B8 = 12.59 nA; ANOVA, F_(2,18) = 17.94, p = 8 × 10⁻⁵; post hoc, B51 vs B64, p = 0.033; B51 vs B8, p = 0.018; B64 vs B8, p = 5.3 × 10⁻⁵; Fig. 3J) and more positive potentials. Surprisingly, the rates of activation and deactivation were much faster in B8 compared with B51 (compare Fig. 3I and E), which could be a result of the kinetics of the Ca²⁺ pool that activates I_KCa. The lack of I_KCa in B64 could be because of the lack of expression of the channel itself or a reduced expression of voltage-gated calcium currents. Thus, we next sought to characterize the voltage-gated Ca²⁺ currents.

Voltage-gated Ca²⁺ currents

Two Ca²⁺ currents, I_CaL and I_CaR (for review, see Kits and Mansvelder, 1996), were characterized because these currents are known to be important modulators of plateau potentials (Pierson et al., 2005; Binder et al., 2020) and I_KCa (Kim and Trussell, 2007; Duncan and Shipston, 2016).

I _CaL

I_CaL was isolated using a 10 μm nifedipine subtraction (see Materials and Methods). The protocol, sample traces and analyses are illustrated in Figure 4A–J. The inactivation traces are illustrated in Extended Data Figure 2-1C and the time constant analyses are illustrated in Extended Data Figure 2-2C,D. Similar to I_A and I_D, the maximum conductance of I_CaL was greater in B8 compared with B51 and B64 (Fig. 4J; H₍₂₎ = 10.26, p = 0.0059; post hoc, B51 vs B64, p = 0.41; B51 vs B8, p = 0.14; B64 vs B8, p = 0.004). The greater conductance could lead to greater influx of Ca²⁺ and greater activation of I_KCa, which could contribute to suppressing a plateau potential in B8. The inactivation curve of B8 was shifted to the left compared with that of B51 (Fig. 4H; H₍₂₎ = 11.1, p = 0.0040; post hoc, B51 vs B64, p = 0.18; B51 vs B8, p = 0.0026; B64 vs B8, p = 0.27). The difference in inactivation curves would tend to enhance the influx of Ca²⁺ in B8. No differences were found in the half-activation (Fig. 4F; F_(2,14) = 0.96, p = 0.41), or the slope parameters of the activation curves (Fig. 4G; F_(2,14) = 1.71, p = 0.22), or inactivation curves (Fig. 4I; H₍₂₎ = 4.5, p = 0.105).

I _CaR

I_CaR was isolated by recording in the presence of 10 μm nifedipine to block I_CaL and subtracting a response that received a 300-ms duration prepulse to −10 mV (to block I_CaR) from a control current response (see Materials and Methods). The protocol, sample traces and analyses are illustrated in Figure 4K–S. The inactivation traces are illustrated in Extended Data Figure 2-1D and the time constant analyses are illustrated in Extended Data Figure 2-2E,F. Similar to I_A, I_D, and I_CaL, the maximum conductance of I_CaR was greater in B8 compared with B51 and B64 (Fig. 4T; F_(2,14) = 31.0, p = 1.12 × 10⁻⁵; post hoc, B51 vs B64, p = 0.74; B51 vs B8, p = 1.61 × 10⁻⁵; B64 vs B8, p = 7.61 × 10⁻⁵), which could contribute to suppression of the plateau in B8. There was also a rightward shift of the inactivation curve of B51 compared with B64 and B8 (Fig. 4R; H₍₂₎ = 9.38, p = 0.0092; post hoc, B51 vs B64, p = 0.024; B51 vs B8, p = 0.020; B64 vs B8, p = 0.997) and a steeper slope of the inactivation curve in B51 compared with B64 and B8 (Fig. 4S; F_(2,14) = 25.5, p = 4.77 × 10⁻⁵; post hoc, B51 vs B64, p = 8.5 × 10⁻⁵; B51 vs B8, p = 0.0002; B64 vs B8, p = 0.82). The rightward shift and steeper inactivation slope in B51 would lead to increased inactivation and could delay the Ca²⁺ influx and I_KCa activation, allowing for the plateau potential. No significant difference was observed in the half-activation (Fig. 4P; H₍₂₎ = 0.04, p = 0.98) or slope of the activation curves among the three neurons (Fig. 4Q; F_(2,15) = 1.67, p = 0.226). The similar expression of I_CaL and I_CaR suggests that the lack of I_KCa in B64 is not because of a reduced expression of voltage-gated Ca²⁺ channels.

Persistent Na⁺ current

We hypothesized that I_NaP is more pronounced in B51 and B64 compared with B8, because of the established role of I_NaP in maintaining sustained depolarizations (Carrillo-Reid et al., 2009). As a first step, we sought to identify a pharmacologic agent that could block I_NaP without blocking the faster I_Na. Dose-effect curves were constructed for TTX, an agent that has been used by others to block I_NaP (Hsu et al., 2018). For these experiments the duration of the plateau potential and the amplitude of the action potential were used as rough estimates for the magnitude of I_NaP and I_Na respectively (Fig. 5A,B). The dose–response curve indicated that 10 μm was a reasonable concentration of TTX, because this concentration reduced the plateau duration by 91.2 ± 1.3%, but only blocked 20.6 ± 0.7% of the action potential amplitude. Therefore, 10 μm TTX was selected to characterize I_NaP.

Figure 5.

I_NaP has similar properties in both the plateau-generating neurons B51 and B64 and the regular-spiking neuron B8. A, Example neuron showing the reduction in plateau duration by varying concentrations of TTX. B, Dose-effect curve of TTX. The decrease in action potential amplitude was used as an indicator block of I_Na, whereas the percent decrease in the amount of time above −70 mV after the end of the stimulus was used as an indicator of the block of I_Nap. C, Voltage-clamp protocol to measure I_NaP. A 20-ms duration step to −40 mV was used to reduce contamination by I_Na. To isolate I_NaP, the current responses in control were subtracted from responses in 10 µm TTX. D–F, TTX subtracted current response indicating I_NaP for B51 (D), B64 (E), and B8 (F) for each command potential. A double exponential equation (Eq. 5) was fitted for a 640-ms region beginning 9 ms after the start of the command pulse (black line). G, Summary data for the activation curves (solid line, solid diamonds) and fitted Boltzmann equations (lines, Eq. 12). Data represented as mean and standard error. H, I, Summary data for the parameters of the Boltzmann equations. J, Maximum conductance calculated using Ohm's law. Sample sizes: B8, n = 7; B51, n = 8; B64, n = 8. The time constant analysis for I_NaP is illustrated in Extended Data Figure 2-2G.

Extended Data Figure 6-1

Comparison of voltage-clamp simulations and empirical data. A, Mean current responses (solid line) from experiments measuring I_A (Fig. 2A–I) for B51, B64, and B8 compared to simulations (dashed lines) of the same voltage-clamp protocol in the model neurons. B, Mean current responses of I_D (Fig. 2K–T) for B51, B64, and B8 compared to simulation results. C, Mean current responses of I_CaL (Fig. 4A–J) for B51, B64, and B8 compared to simulation results. D, Mean current responses of I_CaR (Fig. 4K–S) for B51, B64, and B8 compared to simulations results. E, Mean current responses of I_KCa (Fig. 3C–J) for B51, B64, and B8 compared to simulation results. F, Mean current responses of I_NaP (Fig. 5C–J) for B51, B64, and B8 compared to simulation results. G, Mean current responses of I_HCN for B51, B64, and B8 compared to simulation results. Download Figure 6-1, TIF file ^{(15.7MB, tif)} .

Extended Data Figure 6-2

Characterization of I_HCN of B8. A, Example sag potential and rebound excitation in B8. B, Example ZD7288 block of I_HCN in B8. 10 µM ZD7288 completely blocked I_HCN (n = 6). C, Voltage-clamp protocol. Neuron was held at −40 mV and stepped to potentials ranging from −40 to −110 mV for 10 s (prepulse) to activate I_HCN then stepped to −140 mV. The amplitude of the tail current indicated the amount of I_HCN activated during the prepulse. D, Example current response. A single exponential equation (Eq. 1) was fitted to a 3-s region beginning 70 ms after start of the command pulse (black line). E, Example tail currents during the step to −140 mV. Traces are colored according to prepulse command potential. A single exponential equation (Eq. 1) was fitted to a 330-ms region beginning 70 ms after start of the −140-mV command pulse (black line). The curve was extrapolated back to the start of the pulse to estimate the amount of activation. The activation at each potential is obtained by subtracting each measurement by the measurement with a −30-mV prepulse then normalizing to the measurement with a −110-mV prepulse. F, Steady-state activation curve. The tail current was used to measure the steady-state activation. The parameters of the activation curve are provided in Extended Data Table 2-1. G, Voltage-dependence of the activation time constant determined by the time constant of the exponential equation fit to the prepulse current responses in D. Parameters were: τ_max = 14 s, τ_min = 0.9 s, h₁ = −73 mV, s₁ = −9, h₂ = −75, s₂ = 9. Download Figure 6-2, TIF file ^{(5MB, tif)} .

Extended Data Figure 6-3

Differences in R_in and capacitance cannot explain propensity to generate plateau potentials. A, Input resistance measurements of B51, B64, and B8. Input resistance and time constant were measured by injecting a −1-nA current pulse. An exponential function was fitted to the first 1 s of the voltage trace during this current injection. Neuron B51 had a greater input resistance compared to B64 and B8 (B51 = 30.2_{(20.3, 35.8)} MΩ, B64 = 11.3_{(9.2, 13.8)} MΩ_, B8 = 14.4_(12.1,16.4) MΩ; H₍₂₎ = 50.7, p = 9.8 × 10⁻¹²; post hoc B51 vs B64, p = 9.9 × 10⁻¹⁰; B51 vs B8, p = 1.4 × 10⁻⁵; B64 vs B8, p = 0.22). B, Capacitance measurements of B51, B64, and B8. Calculated by dividing the time constant by the input resistance. Neuron B8 had a greater capacitance compared to B51 and B64 (B51 = 0.0023_{(0.0021, 0.0027)} µF, B64 = 0.0022_{(0.0020, 0.0027)} µF, B8 = 0.0098_{(0.007, 0.013)} µF; H₍₂₎ = 47.9, p = 4.0 × 10⁻¹¹; post hoc B51 vs B64, p = 0.51; B51 vs B8, p = 1.3 × 10⁻⁸; B64 vs B8, p = 1.3 × 10⁻⁹). C, Time constant measurements of B51, B64, and B8. B8 had a greater membrane time constant compared to B51 and B64 (B51 = 0.073_{(0.045, 0.090)} s, B64 = 0.024_{(0.021, 0.028)} s, B8 = 0.15_{(0.098, 0.19)} s; H₍₂₎ = 62.1, p = 3.3 × 10⁻¹⁴; post hoc B51 vs B64, p = 2.0 × 10⁻⁶; B51 vs B8, p = 6.0 × 10⁻⁴; B64 vs B8, p = 9.6 × 10⁻¹⁰). D, The capacitance was varied from 2 nF (red, B51 empirical value) to 10 nF (blue, B8 empirical value). The models for B51 or B64 did not exhibit regular firing upon increasing their capacitance. The model for B8 did not exhibit a plateau upon decreasing its capacitance. Download Figure 6-3, TIF file ^{(4.2MB, tif)} .

The protocol, sample traces and analyses of the voltage-gating properties of I_NaP are illustrated in Figure 5C–I. The time constant analysis is illustrated in Extended Data Figure 2-2G. In contrast to the other currents, I_NaP was measured by voltage-clamp recordings in the axon to better clamp the action potential. Surprisingly, there was no noticeable difference of I_NaP among the three neurons. No statistical differences were found in half-activation (Fig. 5H; F_(2,24) = 2.76, p = 0.085), slope parameter of the activation curve (Fig. 5I; F_(2,24) = 0.39, p = 0.68), or $\overline{g}$_NaP (Fig. 5J; F_(2,24) = 0.87, p = 0.43). These data indicate that although the plateau can be mediated by I_NaP (Fig. 5A,B), the different propensities to generate plateau potentials among B51, B64, and B8 are not because of differences in I_NaP, but depend on either the outward currents or the voltage-gated Ca²⁺ current. One possibility is that the larger conductances of the outward currents I_A, I_D, and I_KCa in B8 suppress plateau generation. To gain further insight into these relationships, we used computational models to examine the ways in which these conductances could contribute to the plateau potential.

Computational models recapitulate dynamics of B51, B64, and B8

To investigate the ways in which these currents interact to mediate plateau potentials, a conductance-based model of each neuron was built with the simulator for neural networks and action potentials (SNNAP; Ziv et al., 1994; Baxter and Byrne, 2007). Each neuron was modeled as a single compartment (Fig. 6A). Equations describing each current were constructed in agreement with the empirically measured voltage dependence of steady-state activation and inactivation (Extended Data Table 2-1) and estimations of the voltage dependence of the time constants (Extended Data Figs. 2-2, 6-1). The I_HCN current was also characterized and included in the B8 model because of this neuron's pronounced sag potential and ability to produce rebound excitation (Extended Data Fig. 6-2; Kabotyanski et al., 2000). A leakage conductance, I_leak, was added to B51 and B64 so that input resistance of these models could be matched to empirical data (Extended Data Fig. 6-3A). The adjustment of I_leak was made after all other currents were included in the model and held constant for all simulation experiments. I_HCN served as the leakage conductance for B8. Empirically, the passive neuronal properties were examined using a hyperpolarizing current pulse. B51 had a significantly greater input resistance than B64 and B8, but B8 had a greater capacitance and membrane time constant than B51 and B64 (Extended Data Fig. 6-3A–C). These differences were not able to explain the different propensities to generate a plateau potential among the neurons (Extended Data Fig. 6-3D). To further examine whether passive properties influence the propensity to generate plateau potentials, we compared the input resistance, capacitance, and membrane time constant between B51 neurons that exhibited a plateau potential and B51 neurons that did not. No significant differences were observed between these two groups (resistance t₍₃₄₎ = 0.798, p = 0.43; capacitance t₍₃₄₎ = 1.28, p = 0.21; tau t₍₃₄₎ = 1.31, p = 0.20). Insufficient sample size prevented a statistical comparison of the individual currents between plateaugenic and nonplateaugenic B51 neurons.

Model equations are given in the Materials and Methods. Extended Data Table 2-1 gives the steady-state parameters of each current, their model values, and their measured empirical values. Values for the parameters describing the time dependence of activation and inactivation are given in Materials and Methods and Extended Data Figure 2-2. The models reproduced the salient voltage dynamics for each neuron. The B51 model expressed a plateau potential that self-terminated, the B64 model expressed a plateau potential that did not self-terminate, and the B8 model did not express a plateau potential for any of the stimuli tested (Fig. 6E).

The models were used to examine the window currents by calculating the steady-state values for each individual current over a range of membrane potentials (Eqs. 7, 12, and 15). Each window current was normalized to the sum of all of the currents to display the dominant sustained current at each membrane potential (Fig. 6B–D). I_HCN or the leakage current I_leak was dominant at potentials more negative than −75 mV for all three neurons. I_NaP was the dominant sustained current just below spike threshold (about −40 mV), suggesting that I_NaP mediates sustained depolarization during a plateau potential. However, the large number of window currents near the resting potential (between −75 and −60 mV) indicated that even a seemingly simple phenomenon such as resting potential is affected by the sustained current of many voltage-gated ion channels. Near the resting potential, I_NaP seemed to dominate in B51 and B8, whereas I_CaL dominated in B64. Outward currents I_D and I_KCa dominated the sustained current at potentials more positive than approximately −5 mV, further supporting their role in repolarizing the membrane after an action potential.

In addition, we examined the activation of each conductance following a simulated depolarizing current injection at an intensity that elicits activity in all three neurons (Fig. 6E). I_leak and I_HCN provided a strong current mainly during the action potentials and a baseline current indicating it may counteract plateau generation. I_KTEA response was greater in B8 compared with B51 and B64, suggesting it may play a role in preventing plateau potential generation. Despite the I_Na parameters being identical in the three neurons, the peak current response was greater in B8 compared with B51 and B64. The peak I_Na gradually increased near the end of the B51 plateau, likely because of greater I_KCa activation resulting in de-inactivation of I_Na. The peak I_NaP was fairly similar among the three neuron models, however the peak currents of I_A, I_D, I_KCa, I_CaL, and I_CaR were substantially greater in B8, suppressing the plateau potential either directly (i.e., I_A, I_D, I_KCa) or indirectly by I_CaL and I_CaR activation of I_KCa. I_KCa had a substantial gradual increase near the end of the plateau in B51, making it the most likely candidate to terminate the plateau potential in physiological conditions. The most pronounced outward currents for all three neurons seemed to be I_D and I_KCa.

Simulations indicated that the timing of I_D, I_KCa, and I_Na mediates maintenance and termination of plateau potentials

To better examine how the dynamics of I_D and I_KCa affect the plateau potential, we plotted the time course of the simulation in 3-D voltage plots for each neuron, and colored each plot according to the magnitude of either I_D (Fig. 7A–C), I_KCa (Fig. 7D–F), or I_Na (Fig. 7G–I). These plots revealed the intricate timing of I_D, I_KCa, and I_Na. For example, in B51, I_D was reduced from 57 nA in the beginning of the plateau to 33 nA near the end, during the downstroke of the action potential. This decrease is noticeable as a transition from a lighter blue (bottom, front of spiral) to a darker blue (top, front of spiral; Fig. 7A). An apparent gradual increase in I_KCa from 0 to 80 nA occurred during the downstroke of the action potential as the plateau progressed. This increase is noticeable as a transition from dark blue at the beginning (bottom, front of spiral) to light green at the end of the plateau (top, front of spiral; Fig. 7D) that were both confined to the downstroke of the action potential and juxtaposed to the increase of I_Na occurring during the upstroke (Fig. 7G).

Figure 7.

I_Na, I_KCa, and I_D play key roles in maintaining and terminating plateau potentials. A–C, 3-D voltage plots of I_D in B51, B64, and B8. Activity was elicited by a 1-s duration, 3-nA depolarizing current injection. The 3-D line is colored according to I_D activation. Projections of the 3-D plot onto the xz-plane and xy-plane are colored in gray. Arrows indicate the direction of time. D–F, 3-D voltage plots of I_KCa in B51, B64, and B8. G–I, 3-D voltage plots of I_Na in B51, B64, and B8. J, Voltage responses to 1-s duration, 3-nA current injection in control simulations (black), when either I_KCa (green) or I_Na (red) was absent, or when both I_KCa and I_Na were absent (purple). A voltage-clamp step to 60 mV was given to mimic the occurrence of an action potential.

In contrast, I_D was more consistently activated in B64 and B8. In the case of B8, I_D had a greater intensity that helped to repolarize the membrane potential to resting levels. I_KCa was activated more rapidly in B8 (Fig. 7F, bright yellow in downstroke), reaching its peak intensity by the end of the 1-s stimulation, thereby ensuring B8 quickly repolarizes to the resting potential following stimulation.

A series of B51 simulations were performed to examine the relationship between the action potential, I_KCa activation, and the maintenance of the plateau potential. A 1-s duration, 3-nA current injection to B51 activated a plateau potential that self-terminated (Fig. 7J). However, when I_KCa was removed by setting its maximum conductance ($\overline{g}$) to zero, this current injection elicited a plateau that did not self-terminate. Removing I_Na while keeping I_KCa at control levels blocked the occurrence of action potentials; however, the plateau did not self-terminate, which indicates that action potentials are not necessary to sustain the plateau and instead may indirectly facilitate its termination. A voltage-clamp step that mimics an action potential (6 ms, 60 mV) effectively terminated the plateau. However, the voltage-step did not terminate the plateau when both I_KCa and I_Na were removed. These results indicate that action potentials regulate the duration of plateau potentials by activating I_KCa.

Simulations suggested that interactions among I_NaP and other membrane currents determined the unique firing patterns in the three models

One of the surprising results from the study was that voltage-clamp experiments indicated all three neurons had similar I_NaP (Fig. 5), but varied greatly in their propensity to generate plateau potentials. To further examine, via modeling, the interaction of I_NaP with the other major membrane currents, we constructed heatmaps of plateau duration by varying the maximal conductance $\overline{g}$_NaP (Eq. 7; Fig. 8A–E, horizontal axes), while also varying $\overline{g}$_A, $\overline{g}$_D, $\overline{g}$_KCa, $\overline{g}$_CaL, or $\overline{g}$_CaR (Fig. 8A–E, vertical axes). Conductances that were not being manipulated were kept at their control values. The $\overline{g}$ were chosen because these parameters modify current amplitudes without affecting voltage dependencies. The propensity to generate a plateau potential was measured by the duration of the plateau potential after the end of a sufficiently strong stimulus (5-nA, 1-s simulated current injection).

Figure 8.

Effect of ion currents on plateau potential duration and prediction of biophysical properties outside the tested parameter space. A, Heat maps of the plateau duration for varying the maximum conductance ($\overline{\mathrm{g}}$) of I_D, I_A, I_KCa, I_CaL, and I_CaR versus varying the maximum conductance of I_NaP ($\overline{\mathrm{g}}$_NaP). The $\overline{g}$ of the outward currents and Ca²⁺ currents were each varied from 0 to 6 µS, whereas $\overline{g}$_NaP was varied independently from 0 to 0.5 µS. The remaining model parameters were set according to experimental data presented in Extended Data Figures 2-1, 2-2, 3-1, 6-1, 6-2, and 6-3. A guide to interpreting the maps is provided on the right. A holding current was applied to set the membrane potential to −80 mV, similar to the empirical studies. Activity was then elicited by a 1-s duration, 5-nA simulated positive current injection. The filled circles indicate the physiological values of $\overline{g}$ (red = B51, green = B64, cyan = B8). Yellow indicates neurons with nonterminating plateau potentials. The + indicates when spike activity outlasted the duration of the stimulus. Heatmaps for I_KTEA are provided in Extended Data Figure 8-2. B–E, Voltage trace of simulations (top) for the parameter values indicated (bottom). The locations in the parameter space for B–E are indicated in A. F, The $\overline{g}$_KCa versus $\overline{g}$_NaP parameter space represented as a colored surface. For F–H, red diamonds indicate $\overline{g}$_KCa and $\overline{g}$_NaP parameter combinations within the tested parameter space having a plateau duration of 6–8 s. A second-degree polynomial was fit (red curve) to the red data points to estimate the $\overline{g}$_KCa and $\overline{g}$_NaP parameter combinations for the blue data points. In the polynomial equation, the plateau duration (PD) of the line was set to the mean of the red data points (6.99 s). Blue data points are parameter combinations predicted to have a plateau duration near 6.99 s. The plateau duration is indicated below each data point. G, Action potential duration (AD; see Extended Data Fig. 8-1J) along the fitted curve in F. The red line is a linear fit of the red data points and predicts the action potential duration of the blue data points in F. The light red regions surrounding the line in G and the fitted curve in H delineate the confidence intervals of the fits, with respect to the dependent variables (AD in G, PA in H; Materials and Methods). H, Plateau potential amplitude (PA; see Extended Data Fig. 8-1A) along the fitted curve in F. The red curve is a second-degree polynomial fit of the red data points and predicts the plateau potential amplitude of the blue data points in F.

Extended Data Figure 8-1

Heat maps of the parameter space indicate that ion channels differentially affect the depolarization of the plateau and action potential duration. A, Heat maps of the effect of the ḡ parameter space for the I_D, I_A, I_KCa, I_CaL, and I_CaR on the amount of depolarization of the plateau. The ḡ of each channel was varied from 0 to 6 µS while ḡ_NaP was varied independently from 0 to 0.75 µS. The remaining model parameters were determined by experimental data presented in Extended Data Figures 2-2, 6-2, and 6-3 and Extended Data Table 2-1. The model was held to −80 mV, similar to experiments, and activity was elicited by a 1-s, 5-nA simulated current injection. The dots indicate the default values of ḡ in the model (red = B51, green = B64, cyan = B8). Examples of the voltage traces are provided in B–E and the locations are indicated on the heatmap. A guide to interpreting the maps is provided on the right. Data from the same simulations as Figure 8. Note the similarity with Figure 8. B–E, Voltage trace of simulations (top) for the parameter values indicated (bottom). The locations in the parameter space for B–E are indicated in A. F–I, Histograms of the voltages for the simulations in B–E, respectively. The amplitude of the plateau is calculated as the location of the peak of this histogram in mV subtracted by the holding potential of the model neuron (−80 mV). J, Heat maps of the effect of the ḡ parameter space for the I_D, I_A, I_KCa, I_CaL, and I_CaR on action potential duration. The dots indicate the default values of ḡ in the model (red = B51, green = B64, cyan = B8). Examples of the voltage traces are provided in B–E and the locations are indicated on the heatmap. A guide to interpreting the maps is provided on the right. Action potential duration was calculated as the average time above 0 mV for each action potential. Download Figure 8-1, TIF file ^{(22.1MB, tif)} .

Extended Data Figure 8-2

Plateau duration, amplitude, and action potential duration heat maps of the parameter space of I_KTEA. Heat maps of the effect of the ḡ parameter space for the I_KTEA on action potential duration. The ḡ of each channel was varied from 0 to 6 µS while ḡ_NaP was varied independently from 0 to 0.5 µS. The remaining model parameters were determined by experimental data presented in Extended Data Figures 2-1, 2-2, 3-1, 6-1, 6-2, and 6-3. The model was held to −80 mV, similar to experiments, and activity was elicited by a 1-s, 5-nA simulated current injection. The dots indicate the default values of ḡ in the model (red = B51, green = B64, cyan = B8). Data from the same simulations as Figure 7. Download Figure 8-2, TIF file ^{(5.6MB, tif)} .

In many cases, the same $\overline{\mathrm{g}}$ values for a given combination of currents resulted in widely different firing properties in the three models. For example, a 0.175 µS $\overline{\mathrm{g}}$_NaP and 2.842 µS $\overline{\mathrm{g}}$_D resulted in a self-terminating plateau in the model of B51, while those same values resulted in a nonterminating plateau in the model of B64, and a regular firing phenotype in the model B8 (Fig. 8B–D). Increasing the $\overline{\mathrm{g}}$_NaP to 0.375 µS in B8 converted its dynamics to a nonterminating plateau (Fig. 8A,E). Increasing the $\overline{g}$ of currents that strongly suppress plateau potentials would require a commensurate increase in $\overline{g}$_NaP to maintain the propensity to generate a plateau potential. Conversely, currents that have little effect on plateau potentials would not require additional increases in $\overline{\mathrm{g}}$_NaP. These simulations further illustrated that in the model of B51, I_D, I_KCa, and I_CaR strongly suppressed the plateau potential whereas I_A had no effect. The I_CaL effect on the plateau duration was unique in that when the $\overline{\mathrm{g}}$_CaL is above 1.3 µS, B51 and B64 became almost exclusively plateau generating except for very small values of $\overline{\mathrm{g}}$_NaP. The facilitation of plateau potentials by I_CaL is consistent with observations in spinal motor neurons where I_CaL is important for mediating the plateau potential (Binder et al., 2020). In contrast, in B64, I_D and I_A both suppressed the plateau potential. The B64 neuron did not express I_Kca. Therefore, to determine what effect this current would have on this neuron, we inserted the I_Kca parameter values used in B8 and then varied its $\overline{g}$ values as was done for the other currents. I_Kca strongly suppressed the plateau potential in the model of B64, such that it self-terminated. The ability of I_KCa to suppress plateau potentials in a neuron that does not express this current indicates that such suppression may be a common property of this current. For B64, the $\overline{g}$_KCa was set to zero when testing the effects of currents other than I_KCa. Increasing $\overline{g}$_CaR and $\overline{g}$_CaL did not suppress, but rather enhanced, the plateau potential in B64 because of the lack of I_KCa. The majority of the B8 model parameter space exhibited regular spiking and produced plateau potentials with large values of $\overline{g}$_NaP, and in all of these cases the plateau potentials were not self-terminating. The heatmap of B8 for the I_KCa, I_NaP combinations was similar when I_leak was substituted for I_HCN, indicating that the voltage-dependent properties of I_HCN did not contribute to the propensity of B8 to generate a plateau potential.

Taken together, these results indicated that I_D and I_KCa strongly suppressed plateau potentials regardless of cell type; however, I_A and I_CaR only suppressed plateau potentials in particular neurons. Interestingly, by manipulating one parameter of a single current, a model neuron could be converted from one that generates plateau potentials into a regular-spiking neuron that is incapable of generating plateau potentials. A neuron that is regular spiking can similarly be converted into a plateau-generating neuron by manipulating a single parameter.

In addition to plateau duration, we examined the amplitude of the plateau potential (measured at the troughs between action potentials) and found that plateau potential voltage heatmaps were visibly similar to plateau duration heatmaps in that increases in $\overline{g}$_NaP and/or decreases in outward currents corresponded to an increased amplitude in the plateau potential (Extended Data Fig. 8-1A–I). Interestingly, a heatmap of the action potential duration (Extended Data Fig. 8-1J) had a more complex patterning highlighting the complex relationship among the ionic currents and shape of the action potential. We did notice a general trend that decreasing $\overline{g}$_NaP and/or increasing the outward currents increased the action potential duration, because of the reduced plateau potential amplitude presumably by removing the inactivation of I_Na between action potentials. We also examined similar heatmaps for the unidentified 4 mm TEA-sensitive, Ca²⁺-insensitive potassium current denoted I_KTEA (Extended Data Fig. 8-2) mentioned in Figure 3D,F,H. These heatmaps illustrate a general trend in which increased I_KTEA reduces the plateau duration and amplitude.

Finally, we examined whether the heatmaps within the tested parameter space could be used to predict voltage dynamics for parameter values that lie outside the tested space. To test this possibility, we examined the heatmap for I_KCa. We considered the B51 I_KCa plateau-duration heatmap in Figure 8A as a 3-D surface while maintaining its coloring (Fig. 8F). The surface is relatively smooth in regions where the plateau duration is <40 s, suggesting that this surface could be used to predict the plateau duration of parameter combinations outside the range of values examined. We therefore selected points in the simulated data set with a 6- to 8-s plateau duration (Fig. 8F, red diamonds) and projected these data points onto the $\overline{g}$_NaP/$\overline{g}$_KCa axis plane. The remaining model parameters were set according to experimental data presented in Figures 1–5 and Extended Data Figures 2-1, 2-2, 3-1, 6-1, 6-2, and 6–3. When projected on the $\overline{g}$_NaP/$\overline{g}$_KCa axis plane, these data points could be fit with a second-degree polynomial. This second-degree polynomial is plotted in Figure 8F. The portion of Figure 8F with the colored surface corresponds to the tested parameter space, and the red curve corresponds to the polynomial. The plateau duration on this curve is the mean of the selected data points (6.99 s). We predicted that points along this polynomial curve when extrapolated beyond the surface would provide parameter combinations that would yield plateau durations near 6.99 s. Simulations indicated plateau durations that were close to, although not equal to, the predicted duration of 6.99 s (Fig. 8F, points marked with blue diamonds). For a $\overline{g}$_NaP value corresponding to one of the extrapolated points, we additionally examined what $\overline{g}$_KCa value would result in a plateau duration equal to 6.99 s. Simulations indicated that, for $\overline{g}$_NaP = 0.45 µS, a $\overline{g}$_KCa of 8.56 µS yielded a plateau of 6.996 s, and was within the 95% confidence interval of [8.45, 9.82] µS $\overline{g}$_KCa calculated for the extrapolated polynomial at 0.45 µS $\overline{g}$_NaP (see Materials and Methods for confidence interval calculation). Therefore, the polynomial reasonably predicted the correct $\overline{g}$_KCa.

We further examined whether this polynomial fit could also predict other complex physiological processes such as action potential duration and plateau amplitude. The data points from Figure 8F were projected onto the AP duration/$\overline{g}$_NaP axis plane. When projected onto this plane, these data points had a linear relationship (Fig. 8G). A linear equation fitted to the red data points predicted the action potential duration for parameter combinations along the extrapolated line (blue data points). The data points from Figure 8F were then projected onto the plateau amplitude/$\overline{g}$_NaP axis plane. When projected onto this plane, the red points could be fit with a second-degree polynomial (Fig. 8H). The fit predicted the plateau amplitude for parameter combinations along the extrapolated curve. Thus, the heatmaps of the parameter space provided a framework to predict complex phenotypes.

Discussion

This study examined three identified neurons that varied in their ability to produce all-or-nothing plateau potentials, a phenomenon shared by various neurons in many different species (Nargeot et al., 1999a,b; Carrillo-Reid et al., 2009; Plotkin et al., 2011; Bittner et al., 2017). These data indicated that regular-spiking neurons like B8 can be more complex than what might be expected, containing many of the same currents as plateau-generating neurons. Interestingly, I_NaP was similar in all three neurons. The main difference among these neurons was greater outward currents and voltage-gated Ca²⁺ currents in B8. The similarity in the repertoire of membrane currents suggests that additional currents are not needed to enable a plateau potential, but rather a release of inhibitory constraints mediated by currents such as I_D and I_KCa. The role of I_D, I_KCa, and I_NaP in plateau potentials was further supported by simulations with biologically realistic conductance-based models. Model neurons with similar I_NaP exhibited different propensities to generate plateau potentials. Because of the similarity of voltage-gated currents in Aplysia to those in other systems, we predict that in other systems outward K⁺ currents are major distinguishing factors between plateau generating and regular firing neurons.

The mechanism of plateau generation is still under intense investigation. In some neurons, plateau potentials result from the coactivation of multiple synaptic connections that converge on a small dendritic region, releasing the Mg²⁺ block of NMDA receptors and activating various voltage-dependent currents (Milojkovic et al., 2004; Plotkin et al., 2011). In other neurons, plateau potentials are a result of intrinsic voltage-dependent currents that can be activated even when isolated from the circuit (Lorenzetti et al., 2008; Tryba et al., 2011). For example, cortical pyramidal neurons from excised tissue of patients with intractable seizures generated rhythmic bursts even in the presence of excitatory synaptic blockers, but were blocked by rilizule, a I_NaP blocker (Tryba et al., 2011).

Voltage-gated Ca²⁺ channels are involved in sustaining the plateau potential neurons of other systems (Zhang et al., 1995; Beurrier et al., 1999; Vergara et al., 2003). However, a blocker for voltage-gated calcium channels, Ni²⁺, enhances the plateau potential in B51 (Fig. 3). Simulations indicated that lowering I_CaR increased plateau potential generation by reducing I_KCa activation (Fig. 8). Thus, I_KCa produces feedback inhibition of plateau generating mechanisms, because of its activation by Ca²⁺ influx. Lengthening of the plateau potential by zero Ca²⁺ or by TEA was also observed in B63 (Bédécarrats et al., 2023) suggesting that I_KCa could be a common mechanism of plateau termination. However, in some neurons, Ni²⁺ can block plateau potentials (Aplysia bag neurons; Tam et al., 2009) and bursting (hippocampal neurons; Metz et al., 2005). In part, the different roles of voltage-gated Ca²⁺ currents may be explained by their proximity to outward current channels (Shah et al., 2021). Our simulations also indicated that I_CaR enhances plateaus in neurons without I_KCa such as B64, and that I_CaL enhances plateau potentials in B51 and B64, supporting a direct role of voltage-gated Ca²⁺ in plateau generation. Similarly, I_CaL contributes to plateau potentials in mammalian barrelette cells (Lo and Erzurumlu, 2002).

We used TEA (a blocker for BK) to block I_KCa and characterize its properties, suggesting that BK channels in other systems may also suppress the plateau potential. The Ca²⁺-gating makes I_KCa an ideal timing mechanism for limiting the duration of plateau potentials. As the plateau potential progresses, the Ca²⁺ buildup leads to activation of I_KCa that eventually terminates the plateau. On the other hand, I_D and I_A reach their peak activation near the beginning of the plateau. Therefore, in the absence of I_KCa, if I_D or I_A are insufficient to terminate the plateau soon after initiation, then the plateau will persist indefinitely as is the case for B64.

In all three neurons, we isolated a rapidly activating and rapidly inactivating voltage-dependent outward current that persisted in 4AP, was insensitive to Cd²⁺ and Ni²⁺ and inhibited by low concentrations of TEA, therefore we designated the current as I_KTEA. This current was capable of modulating the duration of the plateau potential (Extended Data Fig. 8-2). The activation curve was shifted to the right compared with I_A and I_D indicating that this current can only be activated during an action potential where it helps mediate the after-hyperpolarization (AHP; Fig. 6). One possibility is that I_KTEA is the Ca²⁺-unbound form of I_KCa. Several lines of evidence indicate that Ca²⁺ binding shifts the activation curve to a more negative potential (Cui et al., 1997; Cox, 2014).

Inhibiting I_NaP blocked plateau potentials, empirically and in simulations. Surprisingly, the properties and level of expression of I_NaP were similar in all three neurons, indicating that the presence of I_NaP is not a distinguishing factor between regular-firing neurons and neurons capable of generating plateau potentials. Rather, it is the ratio between I_NaP and outward currents such as I_D and I_KCa. Investigations in leech found that a major counteracting current to I_NaP was current generated by the Na⁺/K⁺ pump (Erazo-Toscano et al., 2023). We predict that Na⁺/K⁺ pump could also play an important role in regulating B51 and B64 plateau potentials. What role does I_NaP have in regular-spiking neurons? One possibility is that I_NaP serves to increase the nonlinearity of the spike frequency response. I_NaP is not the only inward current that could underly the plateau potential. The Aplysia B63 neuron and in rat substantia nigra GABAergic neuron plateau potentials are mediated, at least in part, by the calcium-activated nonspecific cation channel (I_CaN) and I_NaP (Lee and Tepper, 2007; Bédécarrats et al., 2023).

The present study characterized two major voltage-gated Ca²⁺ currents, I_CaR and I_CaL, because of their importance to I_KCa regulation and plateau potentials (Pierson et al., 2005; Kim and Trussell, 2007; Duncan and Shipston, 2016; Binder et al., 2020). However, other voltage-gated Ca²⁺ currents such as I_CaT, I_P/Q, I_N could potentially play a role in regulating I_KCa and plateau potentials in B51 and B64.

In the models, regular-spiking neurons can be converted to neurons that generate plateau potentials relatively simply, by manipulating relatively few parameters (for example, compare Fig. 8B and E). Similarly, changes of a few parameters of a model of Aplysia neuron R15 could switch spiking into bursting (Canavier et al., 1991, 1993, 1994). These results indicate that plateau generating neurons and regular-spiking neurons can be highly similar in their ion channel composition, yet generate drastically different firing properties. This similarity may help explain why in some cases, neurons can be bistable and alternate between bursting and regular firing, as in subthalamic nucleus (Beurrier et al., 1999) and R15 in Aplysia (Lechner et al., 1996).

The relationship between individual parameters and complex physiological processes is often complex and nonlinear. We have demonstrated one technique for predicting complex physiological properties such as plateau duration, plateau amplitude, and action potential duration as a function of parameter values, by fitting a curve in parameter space and projecting the curve beyond the tested values (Fig. 8G,H). We predict, with sufficient sampling, a similar approach could be used to predict neuronal dynamics when three or more parameters are altered. Thus, complex physiological properties can be predicted by following and projecting a trajectory described by features of the tested parameter space.