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

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.

[1]  Charles J. Wilson,et al.  Biophysical basis of the phase response curve of subthalamic neurons with generalization to other cell types. , 2012, Journal of neurophysiology.

[2]  G. Deuschl,et al.  Neuronal activity of the human subthalamic nucleus in the parkinsonian and nonparkinsonian state. , 2008, Journal of neurophysiology.

[3]  Dieter Jaeger,et al.  Phase Response Curve Analysis of a Full Morphological Globus Pallidus Neuron Model Reveals Distinct Perisomatic and Dendritic Modes of Synaptic Integration , 2010, The Journal of Neuroscience.

[4]  A. Reyes,et al.  Effects of transient depolarizing potentials on the firing rate of cat neocortical neurons. , 1993, Journal of neurophysiology.

[5]  A. Reyes,et al.  Two modes of interspike interval shortening by brief transient depolarizations in cat neocortical neurons. , 1993, Journal of neurophysiology.

[6]  Charles J. Wilson,et al.  Intrinsic dynamics and synaptic inputs control the activity patterns of subthalamic nucleus neurons in health and in Parkinson's disease , 2011, Neuroscience.

[7]  Bard Ermentrout,et al.  When inhibition not excitation synchronizes neural firing , 1994, Journal of Computational Neuroscience.

[8]  Nancy Kopell,et al.  Synchronization of Strongly Coupled Excitatory Neurons: Relating Network Behavior to Biophysics , 2003, Journal of Computational Neuroscience.

[9]  Bard Ermentrout,et al.  Type I Membranes, Phase Resetting Curves, and Synchrony , 1996, Neural Computation.

[10]  A. Winfree The geometry of biological time , 1991 .

[11]  T. Sejnowski,et al.  Cholinergic Neuromodulation Changes Phase Response Curve Shape and Type in Cortical Pyramidal Neurons , 2008, PloS one.

[12]  W. Rall Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. , 1967, Journal of neurophysiology.

[13]  J. Dostrovsky,et al.  High-frequency Synchronization of Neuronal Activity in the Subthalamic Nucleus of Parkinsonian Patients with Limb Tremor , 2000, The Journal of Neuroscience.

[14]  H. Robinson,et al.  Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex. , 2007, Biophysical journal.

[15]  PRC estimation with varying width intervals , 2012 .

[16]  Charles J. Wilson,et al.  Synaptic Regulation of Action Potential Timing in Neostriatal Cholinergic Interneurons , 1998, The Journal of Neuroscience.

[17]  H. Bergman,et al.  The primate subthalamic nucleus. I. Functional properties in intact animals. , 1994, Journal of neurophysiology.

[18]  Hermann Cuntz,et al.  A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators , 2010, PLoS Comput. Biol..

[19]  Astrid A Prinz,et al.  Predictions of phase-locking in excitatory hybrid networks: excitation does not promote phase-locking in pattern-generating networks as reliably as inhibition. , 2009, Journal of neurophysiology.

[20]  Germán Mato,et al.  Synchrony in Excitatory Neural Networks , 1995, Neural Computation.

[21]  H. Kita,et al.  The morphology of intracellularly labeled rat subthalamic neurons: A light microscopic analysis , 1983, The Journal of comparative neurology.

[22]  H. Kita,et al.  Electrical membrane properties of rat subthalamic neurons in an in vitro slice preparation , 1987, Brain Research.

[23]  C. Wilson,et al.  Mechanisms Underlying Spontaneous Oscillation and Rhythmic Firing in Rat Subthalamic Neurons , 1999, The Journal of Neuroscience.

[24]  H. Bergman,et al.  Subthalamic nucleus functional organization revealed by parkinsonian neuronal oscillations and synchrony. , 2008, Brain : a journal of neurology.

[25]  Charles J. Wilson Dynamic modification of dendritic cable properties and synaptic transmission by voltage-gated potassium channels , 1995, Journal of Computational Neuroscience.

[26]  Robert J Butera,et al.  Neuronal oscillators in aplysia californica that demonstrate weak coupling in vitro. , 2005, Physical review letters.

[27]  G. Ermentrout,et al.  Phase-response curves give the responses of neurons to transient inputs. , 2005, Journal of neurophysiology.

[28]  Corey D. Acker,et al.  Synchronization in hybrid neuronal networks of the hippocampal formation. , 2005, Journal of neurophysiology.

[29]  John Rinzel,et al.  Synchronization of Electrically Coupled Pairs of Inhibitory Interneurons in Neocortex , 2007, The Journal of Neuroscience.

[30]  A. Prinz,et al.  Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. , 2004, Biophysical journal.

[31]  Charles J. Wilson,et al.  Response properties and synchronization of rhythmically firing dendritic neurons. , 2007, Journal of neurophysiology.

[32]  D James Surmeier,et al.  Autonomous pacemakers in the basal ganglia: who needs excitatory synapses anyway? , 2005, Current Opinion in Neurobiology.

[33]  H. Bergman,et al.  The primate subthalamic nucleus. II. Neuronal activity in the MPTP model of parkinsonism. , 1994, Journal of neurophysiology.

[34]  Charles J. Wilson,et al.  Dynamic Spike Threshold and Zero Membrane Slope Conductance Shape the Response of Subthalamic Neurons to Cortical Input , 2010, The Journal of Neuroscience.

[35]  Shlomo Elias,et al.  Computational physiology of the basal ganglia in Parkinson's disease. , 2010, Progress in brain research.

[36]  A. Reyes,et al.  Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex , 2007, The European journal of neuroscience.

[37]  G Bard Ermentrout,et al.  Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. , 2005, Physical review letters.

[38]  John A. White,et al.  Beyond Two-Cell Networks: Experimental Measurement of Neuronal Responses to Multiple Synaptic Inputs , 2005, Journal of Computational Neuroscience.

[39]  S. Johnson,et al.  Subthalamic stimulation evokes complex EPSCs in the rat substantia nigra pars reticulata in vitro , 2006, The Journal of physiology.

[40]  Roberto F. Galán,et al.  The Phase Oscillator Approximation in Neuroscience: An Analytical Framework to Study Coherent Activity in Neural Networks , 2009 .