Dynamical consequences of sensory feedback in a half-center oscillator coupled to a simple motor system

Tutorial: using NEURON for neuromechanical simulations

The dynamical properties of the brain and the dynamics of the body strongly influence one another. Their interaction generates complex adaptive behavior. While a wide variety of simulation tools exist for neural dynamics or biomechanics separately, there are few options for integrated brain-body modeling. Here, we provide a tutorial to demonstrate how the widely-used NEURON simulation platform can support integrated neuromechanical modeling. As a first step toward incorporating biomechanics into a NEURON simulation, we provide a framework for integrating inputs from a "periphery" and outputs to that periphery. In other words, "body" dynamics are driven in part by "brain" variables, such as voltages or firing rates, and "brain" dynamics are influenced by "body" variables through sensory feedback. To couple the "brain" and "body" components, we use NEURON's pointer construct to share information between "brain" and "body" modules. This approach allows separate specification of brain and body dynamics and code reuse. Though simple in concept, the use of pointers can be challenging due to a complicated syntax and several different programming options. In this paper, we present five different computational models, with increasing levels of complexity, to demonstrate the concepts of code modularity using pointers and the integration of neural and biomechanical modeling within NEURON. The models include: (1) a neuromuscular model of calcium dynamics and muscle force, (2) a neuromechanical, closed-loop model of a half-center oscillator coupled to a rudimentary motor system, (3) a closed-loop model of neural control for respiration, (4) a pedagogical model of a non-smooth "brain/body" system, and (5) a closed-loop model of feeding behavior in the sea hare Aplysia californica that incorporates biologically-motivated non-smooth dynamics. This tutorial illustrates how NEURON can be integrated with a broad range of neuromechanical models.

Code available at

https://github.com/fietkiewicz/PointerBuilder.

Sensory feedback expands dynamic complexity and aids in robustness against noise

It has been hypothesized that sensory feedback is a critical component in determining the functionality of a central pattern generator. To test this, Yu and Thomas's recent work Yu and Thomas (Biol Cybern 115(2):135-160, 2021) built a model of a half-center oscillator coupled to a simple muscular model with sensory feedback. They showed that sensory feedback increases robustness against external noise, while simultaneously expanding the potential repertoire of functions the half-center oscillator can perform. However, they show that this comes at the cost of robustness against internal noise.

A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves

Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J Math Biol 74(1-2):387-407, 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the average of a quantity taken around the limit cycle. We apply the "infinitesimal shape response curve" (iSRC) introduced by Wang et al. (SIAM J Appl Dyn Syst 82(7):1-43, 2021) to study infinitesimal homeostasis for limit-cycle systems in terms of the mean value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized shape displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.

Behavioral evidence for nested central pattern generator control of Drosophila grooming

Central pattern generators (CPGs) are neurons or neural circuits that produce periodic output without requiring patterned input. More complex behaviors can be assembled from simpler subroutines, and nested CPGs have been proposed to coordinate their repetitive elements, organizing control over different time scales. Here, we use behavioral experiments to establish that Drosophila grooming may be controlled by nested CPGs. On a short time scale (5-7 Hz, ~ 200 ms/movement), flies clean with periodic leg sweeps and rubs. More surprisingly, transitions between bouts of head sweeping and leg rubbing are also periodic on a longer time scale (0.3-0.6 Hz, ~2 s/bout). We examine grooming at a range of temperatures to show that the frequencies of both oscillations increase-a hallmark of CPG control-and also that rhythms at the two time scales increase at the same rate, indicating that the nested CPGs may be linked. This relationship holds when sensory drive is held constant using optogenetic activation, but oscillations can decouple in spontaneously grooming flies, showing that alternative control modes are possible. Loss of sensory feedback does not disrupt periodicity but slow down the longer time scale alternation. Nested CPGs simplify the generation of complex but repetitive behaviors, and identifying them in Drosophila grooming presents an opportunity to map the neural circuits that constitute them.