Biophysical basis of the phase response curve of subthalamic neurons with generalization to other cell types

Abstract

Farries MA, Wilson CJ. Biophysical basis of the phase response curve of subthalamic neurons with generalization to other cell types. J Neurophysiol 108: 1838 -1855. First published July 11, 2012 doi:10.1152/jn.00054.2012.-Experimental evidence indicates that the response of subthalamic neurons to excitatory postsynaptic potentials (EPSPs) is well described by their infinitesimal phase response curves (iPRC). However, the factors controlling the shape of that iPRC, and hence controlling the way subthalamic neurons respond to synaptic input, are unclear. We developed a biophysical model of subthalamic neurons to aid in the understanding of their iPRCs; this model exhibited an iPRC type common to many subthalamic cells. We devised a method for deriving its iPRC from its biophysical properties that clarifies how these different properties interact to shape the iPRC. This method revealed why the response of subthalamic neurons is well approximated by their iPRCs and how that approximation becomes less accurate under strong fluctuating input currents. It also connected iPRC structure to aspects of cellular physiology that could be estimated in simple current-clamp experiments. This allowed us to directly compare the iPRC predicted by our theory with the iPRC estimated from the response to EPSPs or current pulses in individual cells. We found that theoretically predicted iPRCs agreed well with estimates derived from synaptic stimuli, but not with those estimated from the response to somatic current injection. The difference between synaptic currents and those applied experimentally at the soma may arise from differences in the dynamics of charge redistribution on the dendrites and axon. Ultimately, our approach allowed us to identify novel ways in which voltage-dependent conductances interact with AHP conductances to influence synaptic integration that will apply to a wide range of cell types. phase response curve; subthalamic nucleus; basal ganglia INFINITESIMAL PHASE RESPONSE CURVES (iPRCs) offer a simple representation of an autonomously oscillating neuron's response to synaptic input (Galán 2009;Gutkin et al. 2005;Rinzel and Ermentrout 1998;Winfree 2001), giving the rate at which an input current changes the neuron's oscillation phase as a function of the phase at which the input is delivered. Despite their simplicity, iPRCs can be used to predict some aspects of the collective behavior of neuronal populations, including their propensity for generating synchronized activity (Ermentrout 1996;Hansel et al. 1995;van Vreeswijk et al. 1994). This is particularly valuable for subthalamic neurons, which are embedded in a network of oscillating neurons (Bevan et al. 2002b) in which the degree of synchronous activity correlates with Parkinsonian pathology (Rivlin-Etzion et al. 2010). iPRCs can be measured experimentally or, given a realistic biophysical model, can be derived mathematically. Experimental measurement has the advantage of not requiring detailed knowledge of the cell's biophysical mechanisms but does not provi...

Phase response curves of subthalamic neurons measured with synaptic input and current injection

“…A theoretical approach might also help us address some of the other questions raised by our results, including the nature of the difference between synaptic and current pulse iPRCs and the reasons why the iPRC description works as well as it does in the STN. We develop a theoretical approach to understanding subthalamic iPRCs in a companion paper (Farries and Wilson 2012). …”

“…Nevertheless, given the size of the stimuli we used and the shape of STN PRCs, the distortions in our estimates of z() caused by inaccuracies of this approximation were small (this point is illustrated in Fig. 6A of our companion paper, Farries and Wilson 2012). Using the approximation ⌬ Ϸ qz(), we can obtain the iPRC at by dividing the stimulusgenerated phase shift ⌬ by the stimulus charge q. Equivalently, we can divide ⌬ by the membrane potential change ⌬V caused by the stimulus, since q is equal to ⌬V multiplied by the cell capacitance.…”

Phase-resetting as a tool of information transmission

“…STN neurons are regular pacemakers in vitro , but fire irregularly in healthy intact animals. The biophysical basis of their phase resetting curve has been explained [12,64]. The deterministic interaction of the measured iPRC [29] with the known noise stimulus pattern was sufficient to predict spike times under weak coupling assumptions [24].…”

Optimal number of stimulation contacts for coordinated reset neuromodulation

“…For the acoustic CR neuromodulation, however, a precise tonotopic organization of the auditory cortex and auditory pathway has to be considered (Ehret and Romand, 1997). Furthermore, one can use models based on phase response curves (PRC) (Winfree, 1980; Ermentrout, 1996; Lücken et al, 2013) and incorporate the PRC measured either experimentally or obtained by detailed modeling of the STN, globus pallidus or cortical regions (Netoff et al, 2005; Tateno and Robinson, 2007; Tsubo et al, 2007; Stiefel et al, 2008; Schultheiss et al, 2010; Farries and Wilson, 2012a,b). Detailed neuronal models, although reflecting the richness and complexity of neuronal dynamics, are, on the other hand, so complicated and specialized that they may undermine the generality of their predictions, in particular, for other stimulation modalities and target regions.…”