A Modeling Exploration of How Synaptic Feedback to Descending Projection Neurons Shapes the Activity of an Oscillatory Network

Abstract

Rhythmic activity which underlies motor output is often initiated and controlled by descending modulatory projection pathways onto central pattern generator (CPG) networks. In turn, these descending pathways receive synaptic feedback from their target CPG network, which can influence the CPG output. However, the mechanisms underlying such bi-directional synaptic interactions are mostly unexplored. We develop a reduced mathematical model, including both feed-forward and feedback circuitry, to examine how the synaptic interactions involving two projection neurons, MCN1 and CPN2, can produce and shape the activity of the gastric mill CPG in the crab stomatogastric nervous system. We use simplifying assumptions that are based on the behavior of the biological system to reduce this model down to 2 dimensions, which allows for phase plane analysis of the model output. The model shows a distinct activity for the gastric mill rhythm that is elicited when MCN1 and CPN2 are co-active compared to the rhythm elicited by MCN1 activity alone. Furthermore, the presence of feedback to the projection neuron CPN2 provides a distinct locus of pattern generation in the model which does not require reciprocally inhibitory interactions between the gastric mill CPG neurons, but is instead based on a half-center oscillator that occurs through a tri-synaptic pathway that includes CPN2. Our modeling results show that feedback to projection pathways may provide additional mechanisms for the generation of motor activity. These mechanisms can have distinct dependence on network parameters and may therefore provide additional flexibility for the rhythmic motor output.

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

“…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.…”

“…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. More recently, we extended this reduced model of the MCN1-elicited rhythm to analyze a distinct version of the gastric mill rhythm that is driven by co-activating MCN1 plus a second projection neuron, commissural projection neuron 2 (Kintos and Nadim, 2014). In these previous modeling studies, we focused only on how the synaptic interactions among the network neurons influenced the network dynamics for each distinct version of the gastric mill rhythm.…”

“…Thus, the voltage-gated nature of the MCN1 to LG input, due to the influence of the sigmoid in Equation (9), distinguishes our current model from our previous models of the MCN1-elicited gastric mill rhythm. In cases where we need to compare this model to our previous reduced models, we set m MCN 1 ( V L ) = 1(Kintos et al, 2008; Kintos and Nadim, 2014). …”

“…Similar to the method of model reduction in our previous work (Kintos and Nadim, 2014), we divide through Equation (1) by the leak conductance of Int1, g Leak,I , to get $${\tau }_I\frac{d{V}_I}{dt}=-false(V_I-E_{\text{italicLeak},I}false)-\frac{{ḡ}_{L\to I}}{g_{\mathit{\text{Leak}},I}}{m}_{L\to I}false(V_{L}false)false(V_I-E_{L\to I}false)-\frac{{ḡ}_P}{g_{\mathit{\text{Leak}},I}}Pfalse(t,V_{L}false)false(V_I-E_{P}false),$$ where, ${\tau }_I=\frac{C_I}{g_{\mathit{\text{leak}},I}}$ is the time constant of Int1. Note that, τ I ≪ τ LO , τ HI ; see Table 1.…”

“…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.…”