Travelling wave patterns in a model of the spinal pattern generator using spiking neurons

Phase description of spiking neuron networks with global electric and synaptic coupling

Phase models are among the simplest neuron models reproducing spiking behavior, excitability, and bifurcations toward periodic firing. However, coupling among neurons has been considered only using generic arguments valid close to the bifurcation point, and the differentiation between electric and synaptic coupling remains an open question. In this work we aim to address this question and derive a mathematical formulation for the various forms of coupling. We construct a mathematical model based on a planar simplification of the Morris-Lecar model. Based on geometric arguments we then derive a phase description of a network of the above oscillators with biologically realistic electric coupling and subsequently with chemical coupling under fast synapse approximation. We demonstrate analytically that electric and synaptic coupling are differently expressed on the level of the network's phase description with qualitatively different dynamics. Our mathematical analysis shows that a breaking of the translational symmetry in the phase flows is responsible for the different bifurcations paths of electric and synaptic coupling. Our numerical investigations confirm these findings and show excellent correspondence between the dynamics of the full network and the network's phase description.

Propagation of sinusoidal electrical waves along the spinal cord during a fictive motor task

We present for the first time direct electrophysiological evidence of the phenomenon of traveling electrical waves produced by populations of interneurons within the spinal cord. We show that, during a fictive rhythmic motor task, scratching, an electrical field potential of spinal interneurons takes the shape of a sinuous wave, "sweeping" the lumbosacral spinal cord rostrocaudally with a mean speed of approximately 0.3 m/s. We observed that traveling waves and scratching have the same cycle duration and that duration of the flexor phase, but not of the extensor phase, is highly correlated with the cycle duration of the traveling waves. Furthermore, we found that the interneurons from the deep dorsal horn and the intermediate nucleus can generate the spinal traveling waves, even in the absence of motoneuronal activity. These findings show that the sinusoidal field potentials generated during fictive scratching could be a powerful tool to disclose the organization of central pattern generator networks.

Insights from models of rhythmic motor systems

Computational models of rhythmic motor systems are valuable tools for the study of motor pattern generation and control. Recent modeling advances, together with experimental results, suggest that rhythmic behaviors, such as breathing or walking, are influenced by complex interactions among motor system components. Such interactions occur at all levels of organization, from the subcellular through to the cellular, synaptic, and network levels to the level of neuromuscular interactions and that of the whole organism. Simultaneously, safety mechanisms at all levels contribute to network stability and the generation of robust motor patterns.

A model for the interaction of oscillations and pattern generation with real-time computing in generic neural microcircuit models

It is shown that real-time computations on spike patterns and temporal integration of information in neural microcircuit models are compatible with potentially descruptive additional inputs such as oscillations. A minor change in the connection statistics of such circuits (making synaptic connections to more distal target neurons more likely for excitatory than for inhibitory neurons) endows such generic neural microcircuit model with the ability to generate periodic patterns autonomously. We show that such pattern generation can also be multiplexed with pattern classification and temporal integration of information in the same neural circuit. These results can be interpreted as showing that periodic activity provides a second channel for communication in neural systems which can be used to synchronize or coordinate spatially separated processes, without encumbering local real-time computations on spike trains in diverse neural circuits.