A modeling comparison of projection neuron- and neuromodulator-elicited oscillations in a central pattern generating network

Abstract

Many central pattern generating networks are influenced by synaptic input from modulatory projection neurons. The network response to a projection neuron is sometimes mimicked by bath applying the neuronally-released modulator, despite the absence of network interactions with the projection neuron. One interesting example occurs in the crab stomatogastric ganglion (STG), where bath applying the neuropeptide pyrokinin (PK) elicits a gastric mill rhythm which is similar to that elicited by the projection neuron MCN1, despite the absence of PK in MCN1 and the fact that MCN1 is not active during the PK-elicited rhythm. MCN1 terminals have fast and slow synaptic actions on the gastric mill network and are presynaptically inhibited by this network in the STG. These local connections are inactive in the PK-elicited rhythm, and the mechanism underlying this rhythm is unknown. We use mathematical and biophysically-realistic modeling to propose potential mechanisms by which PK can elicit a gastric mill rhythm that is similar to the MCN1-elicited rhythm. We analyze slow-wave network oscillations using simplified mathematical models and, in parallel, develop biophysically-realistic models that account for fast, action potential-driven oscillations and some spatial structure of the network neurons. Our results illustrate how the actions of bath-applied neuromodulators can mimic those of descending projection neurons through mathematically similar but physiologically distinct mechanisms.

Convergent neuromodulation onto a network neuron can have divergent effects at the network level

“…Similar to that of previous reduced modeling of the MCN1-elicited gastric mill rhythm (Manor et al, 1999; Kintos et al, 2008), our mathematical model in this study begins with a system of 3 nonlinear ordinary differential equations given by $$C_I\frac{d{V}_I}{dt}=-\underset{I_{\mathit{\text{Leak}},I}}{\underset{true︸}{g_{\mathit{\text{Leak}},I}(V_I-E_{\mathit{\text{Leak}},I})}}-\underset{I_{L\to I}}{\underset{true︸}{{ḡ}_{L\to I}{m}_{L\to I}(V_L)(V_I-E_{L\to I})}}-\underset{I_P}{\underset{true︸}{{ḡ}_{P}P(t,V_L)(V_I-E_P)}}$$ $$C_L\frac{d{V}_L}{dt}=-\underset{I_{\mathit{\text{Leak}},L}}{\underset{true︸}{g_{\mathit{\text{Leak}},L}(V_L-E_{\mathit{\text{Leak}},L})}}-\underset{I_{I\to L}}{\underset{true︸}{{ḡ}_{I\to L}{m}_{I\to L}(V_I)(V_L-E_{I\to L})}}-\underset{I_s}{\underset{true︸}{{ḡ}_{s}s{m}_{MCN1}(V_L)(V_L-E_s)}}-\underset{}{\underset{true︸}{{ḡ}_{CCAP}{m}_{CCAP}(V_L)(V_L-E_{CCAP})}}$$…”

“…As in our previous reduced models, we have produced this asymmetry among the reciprocally inhibitory CPG neurons by assigning a high value to E Leak,I and a low value to E Leak,L (see Table 1). Thus, as in our previous reduced modeling (Manor et al, 1999; Kintos et al, 2008; Kintos and Nadim, 2014), the leak current of Int1 appears as a persistent inward current to reproduce the asymmetry in the Int1-LG neuron pair that occurs in the biological system.…”

“…We first reduced a previously published 3-dimensional model of the MCN1-elicited gastric mill rhythm (Manor et al, 1999) down to 2 dimensions by using the difference in synaptic time scales that is exhibited in the biological system (Kintos et al, 2008). This reduction allowed us to perform a phase plane analysis of the network dynamics of the MCN1-elicited gastric mill rhythm using the geometric properties of the reduced 2-dimensional model.…”

“…This model builds upon previous reduced modeling of the MCN1-elicited gastric mill rhythm (Manor et al, 1999; Ambrosio-Mouser et al, 2006; Kintos et al, 2008; Kintos and Nadim, 2014). We focus on how the activation of I MI-MCN1 and I MI-CCAP in the LG neuron can influence oscillations at the network level.…”

“…We focus on how the activation of I MI-MCN1 and I MI-CCAP in the LG neuron can influence oscillations at the network level. These two currents exhibit fast dynamics in the biological system, which allows us to use a separation of time scales to obtain a reduced 2-D model of the MCN1-elicited gastric mill rhythm – similar to (Kintos et al, 2008). This enables us to analyze the network dynamics of the MCN1-elicited gastric mill rhythm via phase plane analysis.…”