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

Abstract

Farries MA, Wilson CJ. Phase response curves of subthalamic neurons measured with synaptic input and current injection. J Neurophysiol 108: 1822-1837. First published July 11, 2012 doi:10.1152/jn.00053.2012.-Infinitesimal phase response curves (iPRCs) provide a simple description of the response of repetitively firing neurons and may be used to predict responses to any pattern of synaptic input. Their simplicity makes them useful for understanding the dynamics of neurons when certain conditions are met. For example, the sizes of evoked phase shifts should scale linearly with stimulus strength, and the form of the iPRC should remain relatively constant as firing rate varies. We measured the PRCs of rat subthalamic neurons in brain slices using corticosubthalamic excitatory postsynaptic potentials (EPSPs; mediated by both AMPA-and NMDA-type receptors) and injected current pulses and used them to calculate the iPRC. These were relatively insensitive to both the size of the stimulus and the cell's firing rate, suggesting that the iPRC can predict the response of subthalamic nucleus cells to extrinsic inputs. However, the iPRC calculated using EPSPs differed from that obtained using current pulses. EPSPs (normalized for charge) were much more effective at altering the phase of subthalamic neurons than current pulses. The difference was not attributable to the extended time course of NMDA receptor-mediated currents, being unaffected by blockade of NMDA receptors. The iPRC provides a good description of subthalamic neurons' response to input, but iPRCs are best estimated using synaptic inputs rather than somatic current injection.

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

“…The equilibrium potentials for the ion species are as follows: E Na ϭ ϩ50 mV, E K ϭ Ϫ90 mV, E Ca ϭ ϩ100 mV, and E leak ϭ Ϫ60 mV. The capacitance C was 100 pF, comparable to the effective cell capacitances estimated from the membrane potential change caused in STN cells by small current pulses used in our companion article (Farries and Wilson 2012; 109 Ϯ 27 pF, range 57-191 pF, n ϭ 66 cells; see below). Both inactivating (spiking) and persistent Na ϩ conductances were modeled with instantaneous activation; that is, their activation states were direct functions of voltage equal to their steady-state activation:…”

“…The methods for slice preparation, perforated-patch recording, and data analysis are described in the companion article (Farries and Wilson 2012).…”

“…In the case of synaptic input, the stimulus current waveform must be inferred from the membrane potential trajectory. The EPSP waveform is isolated by subtracting the average spontaneous voltage trajectory from the trajectory with EPSPs, as described in our companion article (Farries and Wilson 2012). The time derivative of this isolated EPSP voltage trajectory provides an estimate of the underlying synaptic current.…”

“…Subthalamic nucleus (STN) neurons are autonomously active, and their response to excitatory synaptic input appears to be well described by experimentally measured iPRCs (in the companion paper to this article: Farries and Wilson 2012). We developed a biophysical model of STN neurons to help us understand the structure of their iPRCs and to see why iPRCs appear to work so well as a predictor of their response to synaptic input.…”

“…We devised an experimental approach that allowed us to test theoretically predicted iPRCs against iPRCs estimated from the response to excitatory postsynaptic potentials (EPSPs) or injected current. We used this approach to address a number of questions raised by our data on experimentally estimated iPRCs, including the divergence between estimates made with synaptic and current pulse stimuli and the great diversity iPRC structure we encountered (Farries and Wilson 2012). This work has applications beyond the study of autonomously oscillating neurons and their response to weak perturbations; it provides new insights into how intrinsic properties shape a neuron's response to synaptic input.…”