Frequency-Dependent Action of Neuromodulation

Abstract

In oscillatory circuits, some actions of neuromodulators depend on the oscillation frequency. However, the mechanisms are poorly understood. We explored this problem by characterizing neuromodulation of the lateral pyloric (LP) neuron of the crab stomatogastric ganglion (STG). Many peptide modulators, including proctolin, activate the same ionic current (I_MI) in STG neurons. Because I_MI is fast and non-inactivating, its peak level does not depend on the temporal properties of neuronal activity. We found, however, that the amplitude and peak time of the proctolin-activated current in LP is frequency dependent. Because frequency affects the rate of voltage change, we measured these currents with voltage ramps of different slopes and found that proctolin activated two kinetically distinct ionic currents: the known I_MI, whose amplitude is independent of ramp slope or direction, and an inactivating current (I_MI-T), which was only activated by positive ramps and whose amplitude increased with increasing ramp slope. Using a conductance-based model we found that I_MI and I_MI-T make distinct contributions to the bursting activity, with I_MI increasing the excitability, and I_MI-T regulating the burst onset by modifying the postinhibitory rebound in a frequency-dependent manner. The voltage dependence and partial calcium permeability of I_MI-T is similar to other characterized neuromodulator-activated currents in this system, suggesting that these are isoforms of the same channel. Our computational model suggests that calcium permeability may allow this current to also activate the large calcium-dependent potassium current in LP, providing an additional mechanism to regulate burst termination. These results demonstrate a mechanism for frequency-dependent actions of neuromodulators.

Keywords: calcium; central pattern generator; modeling; neuromodulation; stomatogastric.

Graphical abstract

Figure 1.

Voltage-clamp paradigms. A, Extracellular lateral ventricular nerve (lvn) and intracellular LP neuron recording. The lvn carries the axons of several neurons participating in the triphasic pyloric rhythm. The largest action potentials in the lvn recording are from the LP neuron. Different units can be recognized by different amplitudes. The follower neuron LP oscillates in time with the pyloric rhythm because of strong periodic inhibitory input and fires bursts of action potentials on rebound from inhibition. B, Canonical waveform of LP. This prerecorded waveform was used to drive LP’s membrane potential in voltage clamp to mimic a realistic LP neuron activity. In the voltage-clamp experiments, the slow-wave oscillation was scaled so that it ranged from a trough potential of −60 mV to −20 mV. C, LP’s depolarization rate can be approximated with different slopes (colored lines) for different pyloric cycle periods. D, These slopes were used to construct symmetrical ramp or ramp-and-hold stimuli to sample I-V relationships for proctolin-activated currents at different polarization rates, which roughly correspond to different cycle periods (Extended Data Fig. 1-1). The same color-code for slopes is used for all figures with purple colors for positive (+) ramps and green colors for negative (–) ramps.

Figure 2.

Proctolin-activated currents depend on ramp slope and direction. Ai, Proctolin-activated currents (I_Proc) evoked by symmetrical ramp stimulations with four different slopes (color-coded for ramp steepness and ramp direction), averaged over the last three (out of five) sweeps from one experiment. Aii, Overlay of the proctolin currents shown in Ai, normalized by time. B, I-V curves for I_Proc shown in A, separated by ramp slope. Gray curves show raw recordings, colored curves show logistic fits that were used to smoothe the raw data. C, Quantitative analysis of the peak inward current I_max (Cii, left, indicated by dashed horizontal lines in Ci) and voltage at peak inward current V_Imax (Cii, right, indicated by dashed vertical lines in Ci) for different ramp slopes and ramp directions (N = 17). Dots represent data from individual experiments. I_max and V_Imax are both sensitive to ramp slope on the + ramp. On the – ramp, I_max and V_Imax are only significantly different between extreme slope differences (two-way RM ANOVA; Table 1; results in Extended Data Fig. 2-1). Asterisks indicate significant differences between slopes within the same direction, daggers indicate significant differences between directions within the same slope at α = 0.05.

Figure 3.

Proctolin-activated currents show slow inactivation. A, Proctolin-activated currents (I_Proc) in response to 30 sweeps of ramp-and-hold stimuli with different slopes (color-coded). The gray dots connected by lines depict the average I_Proc for each sweep in this experiment. We refer to I_Proc during the first sweep as initial state, and to the average of the last five sweeps as steady state (gray box). B, First (initial state) and averaged last five (steady state) sweeps from the experiment in A. C, Ratio of I_Proc between steady state and initial state. The slow inactivation of I_Proc is greater at 100 mV/s ramps compared with 200 and 400 mV/s ramps (RM ANOVA; Table 1; results in Extended Data Fig. 3-1). Each dot represents an individual experiment. D, Time constants for slow inactivation. Each dot represents an individual experiment. Time constants were not significantly different between slopes (ANOVA on ranks; Table 1; results in Extended Data Fig. 3-2). Asterisks indicate significance at α = 0.05. n.s. indicates no significant changes.

Figure 4.

Steady-state levels of the proctolin-activated currents elicited by a periodic ramp-and-hold stimulus depend on ramp slope and direction. A, Proctolin-activated currents (I_Proc) in response to the last three of 30 sweeps of ramp-and-hold stimuli with different slopes (color-coded). Data are from the same experiments as Figure 3A. B, Steady-state I-V curves for different ramp slopes (color-coded) from one experiment (same experiment as in A). Gray lines show raw current recordings, colored lines show logistic fits that were used to smoothe the raw data. C, Quantitative analysis of I_max (left) and V_Imax (right) for different ramp slopes and ramp directions (N = 10). Dots represent data from individual experiments. I_max is sensitive to ramp slope on the + ramp but not to the – ramp (two-way RM ANOVA; Table 1; results in Extended Data Fig. 4-1). Asterisks indicate significant differences between slopes within the same direction, daggers indicate significant differences between directions within the same slope at α = 0.05. n.s. indicates no significant changes.

Figure 5.

Slope-sensitivity of proctolin-activated currents is different during ongoing LP activity. Ai, The last three (of 20) sweeps of the proctolin-activated currents I_Proc in response to voltage clamping with a realistic LP waveform. Shown is one experiment at different cycle frequencies (color-coded). Aii, Overlay of the averages of the last five cycles (same experiment as Ai), normalized to time. B, I_max and phase of I_max (ϕ_Imax) are sensitive to cycle frequency (RM ANOVA; Table 1; results in Extended Data Fig. 5-1). Dots represent data from individual experiments. Asterisks indicate significant differences between frequencies at α = 0.05.

Figure 6.

A model with only I_MI and I_MI-T adequately captures the fast and slow inactivations. A, Model parameters for I_MI and I_MI-T were tuned to capture the steady-state I_Proc trajectories, i.e., a larger inward current on the positive ramps, and larger inward currents with larger slopes. Ai, Overlay of the biological (red) and model (black) I_Proc trajectories in response to steady-state ramp-and-hold stimuli. Aii, I-V curves separated by positive (purple) and negative (green) ramps similar to those shown in Ai. I-V curves for the positive ramps were obtained after holding the voltage at –80 mV to remove inactivation, and the negative ramps after holding the voltage at +20 mV to maximize inactivation of the transient current. Bi, Time constants for the activation (solid lines) and inactivation (dashed lines) gates of the model I_MI (green) and I_MI-T (pink). Bii, Model response to realistic LP waveform stimulations with different cycle frequencies (based on the biological data from the same preparation as in Ai). The gray shading around V_comm. indicates the voltage range of the ramp and ramp-and-hold stimuli used in Ai. Biii, Model response to the same waveforms as in Bii but with an upscaled amplitude that is similar to the amplitude of the ramp and ramp-and-hold stimuli. C, The slow inactivation of the proctolin-activated current can be mimicked in a computational model by modeling I_MI-T as Ca²⁺ current following the Goldman–Hodgkin–Katz formalism.

Figure 7.

Decreasing the amplitude of ramps to that of the realistic waveforms removes the slope dependence of I_MI-T. A, I_Proc measured in LP in response to downscaled ramp-and-hold stimuli with an amplitude similar to the realistic LP wave stimulus. B, Quantification of steady state I_max and V_Imax for the downscaled ramp-and-hold stimuli (N = 6). Dots represent data from individual experiments. There is no significant slope dependence (n.s.; two-way RM ANOVA; Table 1; results in Extended Data Fig. 7-1).

Figure 8.

Proctolin-activated currents are partially blocked by cadmium. Ai, Proctolin-activated currents in Cd²⁺ saline evoked by symmetrical ramp stimulations with four different slopes (color-coded), averaged over the last three of five sweeps of one experiment. Aii, Overlay of the proctolin currents shown in Ai, normalized by time. B, Example I-V curves for I_proc shown in A, 100 mV/s. Gray solid lines show original current recordings, colored solid lines show logistic fits. C, Quantitative analysis of I_max (left) and V_Imax (right) for different ramp slopes and ramp directions (N = 4). Dots represent data from individual experiments. Ramp slope and direction show statistically significant interactions for I_max (two-way RM ANOVA; Table 1; results in Extended Data Fig. 8-1). Asterisks indicate significant differences between slopes within a direction, daggers indicate significant differences between directions within a slope at α = 0.05. n.s. indicates no significant changes. D, Linear fits for I_max. Di, Example showing the fits from a linear regression model to the I_max for different ramp slopes and directions in normal saline and Cd²⁺ saline. Dii, Slopes of linear fits for I_max in normal saline (filled boxes) and Cd²⁺ saline (hatched boxes). Cd²⁺ significantly reduced the slope of I_max for the + ramps (purple), but not the – ramps (green), indicating a reduction of I_MI-T in the presence of Cd²⁺ (two-way ANOVA; Table 1; results in Extended Data Fig. 8-2). E, Example (same preparation as in A) showing the initial (black) and steady-state (gray, average of the last five sweeps) responses to ramp-and-hold stimuli in Cd²⁺ saline. In all four experiments, I_Proc was not significantly different between initial and steady state (two-way RM ANOVA; Table 1; results in Extended Data Fig. 8-3).

Figure 9.

The frequency dependence of I_MI-T shifts the burst phases in a model of the LP neuron. LP model with I_K and I_Na in the axon compartment, leak current in both axon and soma/neurite compartment, and I_A, I_h, I_Ca, I_K(Ca), I_MI, and I_MI-T in the soma/neurite compartment. Calcium permeability is indicated by the subscripted addition of (Ca) to I_MI-T. Ai, Model voltage waveforms and the corresponding instantaneous spike frequencies (f_inst) within a burst with I_MI and I_MI-T where I_MI-T is either contributing to the intracellular Ca²⁺ concentration (purple; I_MI-T(Ca)) or not (black). The model received periodic inhibition (g_syn) at 1 Hz. Aii, Levels of I_K(Ca) when I_MI-T is either contributing to the intracellular Ca²⁺ concentration (purple) or not (black). The larger I_K(Ca) contributes to the earlier burst termination. The model equations and parameters are as described in Materials and Methods. B, Contribution of the different components to the activity phases of the model neuron at different cycle frequencies. Currents were matched so that the model produced the same number of spikes per burst at 1 Hz (gray rectangles in Bi). Bi, Voltage trajectories and instantaneous frequencies within a burst at 0.5, 1, and 1.66 Hz when the model contained I_MI and I_MI-T(Ca) (purple), when the model contained only I_MI but not I_MI-T(Ca) (green), and when the model contained only I_MI-T(Ca) but not I_MI (pink). Bii, Phase plots of the activity at different cycle frequencies. I_MI-T(Ca) had a substantially greater effect on phase than I_MI (Extended Data Fig. 9-1). Gray bars indicate the duration of the inhibitory synaptic current. In this panel, the model parameters for I_MI and I_MI-T were adjusted as follows: I_MI + I_MI-T(Ca): ${\overline{g}}_{\mathrm{M}\mathrm{I}}=0.227$, ${\overline{g}}_{\mathrm{M}\mathrm{I}-\mathrm{T}}=2.27$; I_MI only: ${\overline{g}}_{\mathrm{M}\mathrm{I}}=0.995$, ${\overline{g}}_{\mathrm{M}\mathrm{I}-\mathrm{T}}=0$; I_MI-T(Ca) only: ${\overline{g}}_{\mathrm{M}\mathrm{I}}=0$, ${\overline{g}}_{\mathrm{M}\mathrm{I}-\mathrm{T}}=3.63$.