Endogenous and half-center bursting in morphologically inspired models of leech heart interneurons

Abstract

Based on a detailed morphology "Full Model" of a leech heart interneuron, we previously developed a computationally efficient, morphologically inspired "Reduced Model" to expedite tuning the model to produce endogenous bursting and alternating bursting when configured as a half-center oscillator (paired with reciprocally inhibitory synapses). To find conductance density distributions that produce endogenous bursting, we implemented a genetic algorithm automated parameter search. With multiple searches, we found eight parameter sets that produced endogenous bursting in the Reduced Model. When these parameter sets were applied to the Full Model, all produced endogenous bursting, although when the simulation time was extended from 80 to 300 s, only four parameter sets produced sustained bursting in the Reduced Models. All parameter sets produced alternating half-center bursting in the Reduced and Full Models throughout the entire 300 s. When conductance amplitudes were systematically varied for each of the four sustained burster sets, the effects on bursting activity differed, both for the same parameter set in the Reduced and Full Models and for different parameter sets with the same level of morphological detail. This implies that morphological detail can affect burst activity and that these parameter sets may represent different mechanisms for burst generation and/or regulation. We also tested the models with parameter variations that correspond to experimental manipulations. We conclude that, whereas similar output can be achieved with multiple different parameter sets, perturbations such as conductance variations can highlight differences. Additionally, this work demonstrates both the utility and limitations of using simplified models to represent more morphologically accurate models.

Fig. 1

Soma membrane potential is recorded for the Reduced Model with the parameter sets that sustained bursting in all models: (A) Reduced 2, (B) Reduced 3, (C) Reduced 4, and (D) Reduced 8 Models. For A, B, C, D: 1: Endogenous bursting in Single-cell Models, shown from 280 to 300 s from start of simulation. 2: Alternating bursting in Half-center Models, shown from 280 to 300 s from start of simulation. For 1 and 2: Period and mean spike frequency are calculated for activity from 240 to 300 s after start of simulation.

Fig. 2

Soma membrane potential is recorded for the Full Model with the parameter sets that sustained bursting in all models: (A) Full 2, (B) Full 3, (C) Full 4, and (D) Full 8 Models. For A, B, C, D: 1: Endogenous bursting in Single-cell Models, shown from 280 to 300 s from start of simulation. 2: Alternating bursting in Half-center Models, from 280 to 300 s from start of simulation. For 1 and 2: Period and mean spike frequency are calculated for activity from 240 to 300 s after start of simulation.

Fig. 3

For all parameter sets chosen by the parameter optimization routine for producing endogenous bursting in the Reduced Model, conductance densities are plotted, with black crosses, by compartment type. E_Leak and R_m, which had the same value across all compartments, are plotted under the heading ‘homogeneous’. Those parameter sets that exhibited sustained bursting in all models (Single-cell, Half-center, Reduced and Full) are shown as black crosses highlighted by colored circles; legend displays parameter set number. Gray bars indicate the boundaries used by the the parameter optimization routine (see Supplemental Table 1).

Fig. 4

Conductance density distributions of Parameter Sets 2, 3, 4 and 8 are compared. Icon represents compartment types as labeled. For each conductance, densities are normalized to the maximum density occurring in any of the eight parameter sets from the genetic algorithm (regardless of compartment type). Thus, densities are scaled with respect to only those values that are associated with endogenous bursting to enable comparison of densities within a model and across models.

Fig. 5

Changes in burst characteristics due to 20% conductance variations are measured in Single-cell Reduced Models. Each conductance density, including R_m and E_Leak, was varied by +20% (A1 and A2) and -20% (B1 and B2) in all compartments where the conductance was present, and changes in period (A1 and B1) and spike frequency (A2 and B2) were measured. Open shapes correspond to changes that were deemed non-relevant, defined as the changes being within the standard deviation of burst characteristics from the original parameter set. Where conductance variations stopped bursting, activity is indicated as “No spiking” or “Tonic spiking”.

Fig. 6

Changes in burst characteristics due to 20% conductance variations are measured in Half-center Reduced Models. Each conductance density, including R_m and E_Leak, was varied by +20% (A1 and A2) and -20% (B1 and B2) in all compartments where the conductance was present, and changes in period (A1 and B1) and spike frequency (A2 and B2) were measured. Open shapes correspond to changes that were deemed non-relevant, defined as the changes being within the standard deviation of burst characteristics from the original parameter set. Where conductance variations stopped bursting, activity is indicated as “No spiking” or “Tonic spiking”.

Fig. 7

Changes in burst characteristics due to 20% conductance variations are measured in Single-cell Full Models. Each conductance density, including R_m and E_Leak, was varied by +20% (A1 and A2) and -20% (B1 and B2) in all compartments where the conductance was present, and changes in period (A1 and B1) and spike frequency (A2 and B2) were measured. Open shapes correspond to changes that were deemed non-relevant, defined as the changes being within the standard deviation of burst characteristics from the original parameter set. Where conductance variations stopped bursting, activity is indicated as “No spiking” or “Tonic spiking”.

Fig. 8

Changes in burst characteristics due to 20% conductance variations are measured in Half-center Full Models. Each conductance density, including R_m and E_Leak, was varied by +20% (A1 and A2) and -20% (B1 and B2) in all compartments where the conductance was present, and changes in period (A1 and B1) and spike frequency (A2 and B2) were measured. Open shapes correspond to changes that were deemed non-relevant, defined as the changes being within the standard deviation of burst characteristics from the original parameter set. Where conductance variations stopped bursting, activity is indicated as “No spiking” or “Tonic spiking”.

Fig. 9

Soma voltage is recorded for the Reduced 3 Model in the (A) Single-cell and (B) Half-center configurations while mimicking a microelectrode -induced soma leak.

Fig. 10

The effects of the neuromodulator myomodulin are mimicked in the models by increasing I_h conductance by 30% and inhibiting the Na/K pump (simulated by current injection; see Results). Each effect was applied separately and combined to qualitatively assess the individual and combined effects of the biophysical changes on period and spike frequency for (A) Single-cell Reduced Models, (B) Single-cell Full Models, (C) Half-center Reduced Models, and (D) Half-center Full Models. Where the full amplitude of pump current caused tonic spiking in Single-cell Models (Reduced 8, Full 3 and Full 8), we use half the amplitude of the pump current for both the Single-cell and Half-center Models. Half amplitude pump current was used for Reduced 3 only when both I_h and pump current were combined. C: Single-cell Full 8 exhibited tonic spiking even when pump current was reduced to half amplitude. D: *Half-center Full 4 exhibited asymmetric bursting such that the spike frequency of one model neuron decreased by 27.1% while the spike frequency of the other model neuron increased by 17.4%. The periods of each model neuron decreased by 17.4% and 17.5%, respectively. Heart interneuron response to myomodulin is plotted with open triangles with standard deviation bars. The response of synaptically isolated (bicuculline) heart interneurons to myomodulin is plotted with Single-cell Models under the heading “both”. The response of synaptically intact heart interneurons to myomodulin is plotted with Half-center Models: under the heading “? I_pump” when I_h is blocked by Cs⁺, and under the heading “both” when I_h and I_pump are intact (normal saline).