Feedback control of variability in the cycle period of a central pattern generator

Abstract

We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle length can affect that variability. Specifically, we examine a hybrid circuit constructed of an isolated crab anterior burster (AB)/pyloric dilator (PD) pyloric pacemaker receiving virtual feedback via dynamic clamp. This virtual feedback generates artificial synaptic input to PD with timing determined by adjustable phase response dynamics that mimic average burst intervals generated by the lateral pyloric neuron (LP) in the intact pyloric network. Using this system, we measure network period variability dependence on the feedback element's phase response dynamics and find that a constant response interval confers minimum variability. We further find that these optimal dynamics are characteristic of the biological pyloric network. Building upon our previous theoretical work mapping the firing intervals in one cycle onto the firing intervals in the next cycle, we create a theoretical map of the distribution of all firing intervals in one cycle to the distribution of firing intervals in the next cycle. We then obtain an integral equation for a stationary self-consistent distribution of the network periods of the hybrid circuit, which can be solved numerically given the uncoupled pacemaker's distribution of intrinsic periods, the nature of the network's feedback, and the phase resetting characteristics of the pacemaker. The stationary distributions obtained in this manner are strongly predictive of the experimentally observed distributions of hybrid network period. This theoretical framework can provide insight into optimal feedback schemes for minimizing variability to increase reliability or maximizing variability to increase flexibility in central pattern generators driven by pacemakers with feedback.

The complexity of small circuits: the stomatogastric nervous system

“…Dynamics arising from the interactions of synaptic inputs and postsynaptic properties have recently been studied experimentally and theoretically in the context of how inhibitory feedback from follower neurons affects the pyloric pacemaker oscillation. At its usual timing with respect to the phase of oscillation, feedback inhibition has surprisingly little effect on the mean period of the rhythm, but reduces cycle-to-cycle variability and therefore stabilizes oscillations [10–12]. Similar stabilizing influences of synaptic input on irregularly firing neurons have also been theoretically demonstrated for network-based oscillations [13].…”

Automatic adaptation of model neurons and connections to build hybrid circuits with living networks

“…For example, interactions with the living system can be used to create new elements in a circuit, to assess the functional role of existing ones, or to replace damaged elements of the living system, while characterizing or sustaining a given dynamics Chamorro et al, 2012;Sakurai and 2017). A common goal for many hybrid circuits is to reach a certain level of activity, for example a specific regular rhythmic regime (Varona et al, 2001;Hooper et al, 2015).…”

“…Pioneering works in building such interactions go back almost three decades ago (Yarom, 1991) with many successfull implementation since then, e.g. see Pinto et al, 2000;Varona et al, 2001;Le Masson et al, 2002;Nowotny et al, 2003;Olypher et al, 2006;Arsiero et al, 2007;Grashow et al, 2010;Brochini et al, 2011;Wang et al, 2012;Hooper et al, 2015;Norman et al, 2016;Broccard et al, 2017;Mishchenko et al, 2018). Hybrid circuits are typically implemented through a dynamic clamp protocol that injects current computed by a model from an instantaneous voltage recording (Robinson and Kawai, 1993;Sharp et al, 1993;Prinz et al, 2004;Destexhe and Bal, 2009;Nowotny and Varona, 2014).…”

Robust dynamical invariants in sequential neural activity

“…25 Recent work has proposed that variability in cycle period can be controlled by synaptic feedback. 42,43 External and intrinsic factors continuously effect the system inducing transients and therefore making them an important element of the system functionality, which can only be observed in recordings of irregular activity.…”