Nonlinear system analysis of local reflex control of locust hind limbs

Abstract

Nonlinear Volterra type system identification models coupled with a Gaussian White Noise (GWN) stimulation signal provide an experimentally convenient and quick way to investigate the often complex and nonlinear interactions between the mechanical and neural elements of invertebrate reflex limb control systems. Previous steady state analysis has allowed the neurons in such systems to be categorised by their sensitivity to position, velocity or acceleration (system dynamics) and has improved understanding of network function. These neurons, however, are known to adapt their output amplitude or spike firing rate during repetitive stimulation and this transient response may be more important than the steady state response for reflex limb control. Furthermore, whilst the use of GWN for system identification can be theoretically and experimentally justified, the properties of this signal are very different from those received by the sensory, inter and motor neurons in the neural networks which monitor the position of the locusts leg under natural operating conditions. The current study provides improvements to the previously used experimental methods, equipment and nonlinear system identification methods. Validation of the models using biologically more realistic stimulation signals has been carried out to determine where they perform well and to identify their limitations. The use of the parsimonious cascade model structure, applied in a quasi stationary fashion coupled with Monte Carlo (MC) simulations, has been shown to provide a useful tool for the characterisation of the dynamics and nonlinear responses of the neuromuscular elements in a locust’s reflex limb control system during both transient and steady state response sections. This method been applied to test the null hypothesis that the dynamics and nonlinear responses of the locust’s Fast Extensor Tibia (FETi) motor neuron system are the same during transient and steady state sections. It can be concluded that key FETi system dynamics remain relatively unchanged during repetitive stimulation while output amplitude adaptation is occurring. Whilst some evidence of a significant change was found in parts of the system’s nonlinear response, the effect was small and probably of little physiological relevance. Analysis using biologically more realistic stimulation reinforces this conclusion.

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ORCID for D.M. Simpson: orcid.org/0000-0001-9072-5088

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