Explicit maps to predict activation order in multiphase rhythms of a coupled cell network

Dynamics and bifurcations in multistable 3-cell neural networks

We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-Huxley type [Wojcik et al., PLoS One 9, e92918 (2014)]. The computational reduction to return maps for the phase-lags between neurons reveals a rich multiplicity of rhythmic patterns in such circuits. We perform a detailed bifurcation analysis to show how such rhythms can emerge, disappear, and gain or lose stability, as the parameters of the individual cells and the synapses are varied.

Mixed-mode oscillations and population bursting in the pre-Bötzinger complex

This study focuses on computational and theoretical investigations of neuronal activity arising in the pre-Bötzinger complex (pre-BötC), a medullary region generating the inspiratory phase of breathing in mammals. A progressive increase of neuronal excitability in medullary slices containing the pre-BötC produces mixed-mode oscillations (MMOs) characterized by large amplitude population bursts alternating with a series of small amplitude bursts. Using two different computational models, we demonstrate that MMOs emerge within a heterogeneous excitatory neural network because of progressive neuronal recruitment and synchronization. The MMO pattern depends on the distributed neuronal excitability, the density and weights of network interconnections, and the cellular properties underlying endogenous bursting. Critically, the latter should provide a reduction of spiking frequency within neuronal bursts with increasing burst frequency and a dependence of the after-burst recovery period on burst amplitude. Our study highlights a novel mechanism by which heterogeneity naturally leads to complex dynamics in rhythmic neuronal populations.

DOI:http://dx.doi.org/10.7554/eLife.13403.001

Each breath we take removes carbon dioxide from the body and exchanges it for oxygen. A structure called the brainstem, which connects the brain with the spinal cord, generates the breathing rhythm and controls its rate. While this process normally occurs automatically, we can also control our breathing voluntarily, such as when singing or speaking.

Within the brainstem, a group of neurons in the area known as the pre-Bötzinger complex is responsible for ensuring that an animal breathes in at regular intervals. Recordings of the electrical activity from slices of brainstem show that pre-Bötzinger neurons display rhythmic activity with characteristic patterns called “mixed-mode oscillations”. These rhythms consist of bursts of strong activity (“large amplitude bursts”), essential for triggering regular breathing, separated by a series of bursts of weak activity (“small amplitude bursts”). However, it is not clear how mixed-mode oscillations arise.

Bacak, Kim et al. now provide insights into this process by developing two computational models of the pre-Bötzinger complex. The first model consists of a diverse population of 100 neurons joined by a relatively small number of weak connections to form a network. The second model is a simplified version of the first, consisting of just three neurons. By manipulating the properties of the simulated networks, and analysing the data mathematically, Bacak, Kim et al. identify the properties of the neurons that allow them to generate mixed-mode oscillations and thus rhythmic breathing.

The models suggest that mixed-mode oscillations result from the synchronization of many neurons with different levels of activity (excitability). Neurons with low excitability have low bursting frequencies, but generate strong activity and recruit other neurons, ultimately producing large amplitude bursts that cause breathing.

Many parts of the nervous system are also made up of networks of neurons with diverse excitability. A challenge for future studies is thus to investigate whether other networks of neurons similar to the pre-Bötzinger complex generate rhythms that control other repetitive actions, such as walking and chewing.

DOI:http://dx.doi.org/10.7554/eLife.13403.002

Key bifurcations of bursting polyrhythms in 3-cell central pattern generators

We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincaré return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control.