The significance of dynamical architecture for adaptive responses to mechanical loads during rhythmic behavior

Abstract

Many behaviors require reliably generating sequences of motor activity while adapting the activity to incoming sensory information. This process has often been conceptually explained as either fully dependent on sensory input (a chain reflex) or fully independent of sensory input (an idealized central pattern generator, or CPG), although the consensus of the field is that most neural pattern generators lie somewhere between these two extremes. Many mathematical models of neural pattern generators use limit cycles to generate the sequence of behaviors, but other models, such as a heteroclinic channel (an attracting chain of saddle points), have been suggested. To explore the range of intermediate behaviors between CPGs and chain reflexes, in this paper we describe a nominal model of swallowing in Aplysia californica. Depending upon the value of a single parameter, the model can transition from a generic limit cycle regime to a heteroclinic regime (where the trajectory slows as it passes near saddle points). We then study the behavior of the system in these two regimes and compare the behavior of the models with behavior recorded in the animal in vivo and in vitro. We show that while both pattern generators can generate similar behavior, the stable heteroclinic channel can better respond to changes in sensory input induced by load, and that the response matches the changes seen when a load is added in vivo. We then show that the underlying stable heteroclinic channel architecture exhibits dramatic slowing of activity when sensory and endogenous input is reduced, and show that similar slowing with removal of proprioception is seen in vitro. Finally, we show that the distributions of burst lengths seen in vivo are better matched by the distribution expected from a system operating in the heteroclinic regime than that expected from a generic limit cycle. These observations suggest that generic limit cycle models may fail to capture key aspects of Aplysia feeding behavior, and that alternative architectures such as heteroclinic channels may provide better descriptions.

Rapid Adaptation to Changing Mechanical Load by Ordered Recruitment of Identified Motor Neurons

“…As we have shown, animals may extend the duration of the power stroke (retraction) of swallowing when load is encountered. This is consistent with predictions made by a nominal neuromechanical model of Aplysia feeding (Shaw et al, 2015;Lyttle et al, 2017). Similarly, in vertebrate and stick insect locomotion, increased load during the stance phase causes increased excitation to the leg extensor muscles (Pearson, 1995).…”

The infinitesimal phase response curves of oscillators in piecewise smooth dynamical systems

“…Section 2.1 lays out the assumptions needed to establish our results, and Section 2.2 presents the main Theorem (2.1) giving the correction to the iPRC upon crossing a switching boundary. Section 3 provides examples of iPRCs in nonsmooth systems: a planar piecewise constant system where the nonlinearities arise strictly from the boundaries in Section 3.1, a planar PWL oscillator introduced in a motor control context [55], but generalized here to a non-symmetric geometry in Section 3.2, a PWL genetic regulatory circuit model (Glass network [19,20]) in Section 3.3, a three-dimensional motor control model [54] in Section 3.4, a four-dimensional weakly diffusively coupled version of the piecewise constant system in Section 3.4.1, and a six-dimensional threshold linear network model comprising of two weakly coupled three-dimensional oscillators [42] in Section 3.4.2. In Section 4.1, we discuss the relation between our boundary-crossing correction matrix and the classical saltation matrix, in Section 4.2, we discuss the limitations of the method, and in Section 4.3, we discuss a range of possible further applications.…”

Motor neuronal activity varies least among individuals when it matters most for behavior

“…Proprioception has been shown to play a role in altering RN activity as the animal switches from biting to swallowing (Evans and Cropper 1998). Modeling work suggests that sensory feedback may play critical roles in lengthening components of behavior (e.g., the retraction phase, mediated in part by grasper closure, i.e., RN activity) due to the dynamics of Aplysia's feeding pattern generator (Shaw et al 2014). Furthermore, sensory input may move the system into and through the correct "solution space" for swallowing behavior.…”