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

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.

Activation of high and low affinity dopamine receptors generates a closed loop that maintains a conductance ratio and its activity correlate.

Neuromodulators alter network output and have the potential to destabilize a circuit. The mechanisms maintaining stability in the face of neuromodulation are not well described. Using the pyloric network in the crustacean stomatogastric nervous system, we show that dopamine (DA) does not simply alter circuit output, but activates a closed loop in which DA-induced alterations in circuit output consequently drive a change in an ionic conductance to preserve a conductance ratio and its activity correlate. DA acted at low affinity type 1 receptors (D1Rs) to induce an immediate modulatory decrease in the transient potassium current (IA) of a pyloric neuron. This, in turn, advanced the activity phase of that component neuron, which disrupted its network function and thereby destabilized the circuit. DA simultaneously acted at high affinity D1Rs on the same neuron to confer activity-dependence upon the hyperpolarization activated current (Ih) such that the DA-induced changes in activity subsequently reduced Ih. This DA-enabled, activity-dependent, intrinsic plasticity exactly compensated for the modulatory decrease in IA to restore the IA:Ih ratio and neuronal activity phase, thereby closing an open loop created by the modulator. Activation of closed loops to preserve conductance ratios may represent a fundamental operating principle neuromodulatory systems use to ensure stability in their target networks.