Functional Phase Response Curves: A Method for Understanding Synchronization of Adapting Neurons

Abstract

Cui J, Canavier CC, Butera R. Functional phase response curves: a method for understanding synchronization of adapting neurons. J Neurophysiol 102: 387-398, 2009. First published May 6, 2009 doi:10.1152/jn.00037.2009. Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutually coupled neurons. Previous theoretical work on pulse-coupled oscillators used single-pulse perturbations. We propose an alternate method in which functional PRCs (fPRCs) are generated using a train of pulses applied at a fixed delay after each spike, with the PRC measured when the phasic relationship between the stimulus and the subsequent spike in the neuron has converged. The essential information is the dependence of the recovery time from pulse onset until the next spike as a function of the delay between the previous spike and the onset of the applied pulse. Experimental fPRCs in Aplysia pacemaker neurons were different from single-pulse PRCs, principally due to adaptation. In the biological neuron, convergence to the fully adapted recovery interval was slower at some phases than that at others because the change in the effective intrinsic period due to adaptation changes the effective phase resetting in a way that opposes and slows the effects of adaptation. The fPRCs for two isolated adapting model neurons were used to predict the existence and stability of 1:1 phase-locked network activity when the two neurons were coupled. A stability criterion was derived by linearizing a coupled map based on the fPRC and the existence and stability criteria were successfully tested in two-simulated-neuron networks with reciprocal inhibition or excitation. The fPRC is the first PRC-based tool that can account for adaptation in analyzing networks of neural oscillators.

Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

“…We measured third-order resetting F3 ϭ 0 in all neurons; nonetheless, it is possible that adaptation of slow variables in the biological neuron could introduce error into the predictions of phase-locked period and network phase. Our PRC measurement did not account for adaptation, but a variant of this methodology (Cui et al 2009) can account for adaptation where necessary. 4) The AB/PD complex can be treated as a single oscillator, or neuron.…”

Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period

“…The role of slow adaptation in establishing the autocorrelation structure in the experimental data shown in Fig. 4 is strongly supported by the presence of a prominent slow adaptation current in these invertebrate pacemaker neurons (Cui et al 2009). …”

Neural Synchronization in Seizures

“…Substituting equation 4.3 and 4.4 into 4.5, H(∆φ) can be analytically approximated as .6 allows for the determination of the interaction function directly from experimental measurements of the period of a oscillatory element stimulated using delayed self-feedback. A similar method was developed using a synaptic stimulation function by Cui et al [105]. This method of using one oscillator to develop a phase model has also been tested using electrochemical oscillators [115].…”

“…Phase response curves (PRCs) have been measured for many different types of neurons such as cortical [98,101], mitral cells [92], stellate cells [99] and abdominal ganglion [100,105]. PRCs can be used to model larger neural networks [97,98,102,106,107].…”

“…Recently, PRCs have been measured using a fluctuating applied current, where weighting is used to correct for a variable period [108]. Another method of measuring a PRC was suggested by Cui et al [105] where the neurons received a perturbation for every cycle until a steady state was achieved. Predictions of action potential synchronization for systems of coupled neurons have been generally related to excitatory or inhibitory activity [89,99,102,106]; however, any type of stimulation can be used to control the behavior of oscillating elements [90].…”