On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro

PLoS Computational Biology, Mar 2015

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.

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On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro

March On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro Joo Couto 0 1 Daniele Linaro 0 1 E De Schutter 0 1 Michele Giugliano 0 1 0 1 Theoretical Neurobiology and Neuroengineering Laboratory, University of Antwerp, Antwerpen, Belgium 2 NeuroElectronics Research Flanders, Leuven, Belgium, 3 Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University , Onna, Okinawa , Japan , 4 Department of Computer Science, University of Sheffield , Sheffield , United Kingdom , 5 Brain Mind Institute, EPFL , Lausanne , Switzerland 1 Editor: Boris S. Gutkin, Ecole Normale Superieure, College de France , CNRS, FRANCE Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve. - Funding: Financial support from the 7th Framework Programme of the European Commission (FP7PEOPLE-ITN C7, contract no. 238214), the Interuniversity Attraction Poles Program (IUAP) of the Belgian Science Policy Office, and the University of Antwerp is kindly acknowledged. DL is a Postdoctoral Fellow of the Flanders Research Foundation (grant no. 12C9112N, http://www.fwo.be). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. single Purkinje cells at various firing rates and use it to unveil the smooth transition between flat and phasic PRC. Furthermore, we address potential explanations for the observed transition using computational modeling. The intrinsic electrical activity of Purkinje cells (PCs) exhibits a large repertoire of dynamical behaviors, including spontaneous firing of simple action potentials (APs), bistability of the firing rate, and hysteresis [14]. In addition, the extended range of PCs firing rates during behavior suggests that the rate of APs, its sudden transitions, its coherence across PCs, and the AP timing synchronization may contribute to information representation, processing, and downstream relaying. Thus, investigating how distinct firing regimes affect spontaneous and evoked response properties is imperative for dissecting cerebellar computation. Recently, key results from the mathematical theory of coupled oscillators sparked a lot of interest: a simple inputoutput characterization of the units composing a network, known as their phase response (or phase resetting) curve (PRC), is sufficient to classify and predict individual and collective properties. In the context of tonically firing neurons, the PRC quantifies the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent APs [510]. As the cell oscillates regularly, the pulse advances or delays the time of the next AP, depending on the oscillation phase corresponding to the time of pulse delivery. The resulting change of the time of the next AP can also be quantified in terms of the cells firing period and thus expressed as a phase shift . By capturing the relationship between the evoked phase shift and the phase at which the input pulse occurred, the PRC predicts how, upon receiving weak synaptic inputs, neurons transiently delay or accelerate AP firing, contribute to network-wide AP synchrony, integrate external inputs or detect their temporal coincidences. So far, not only has the PRC been considered in theoretical and computational studies, but it has also been computed in experimental works (see [11] for a review), where different methods have been (...truncated)


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João Couto, Daniele Linaro, E De Schutter, Michele Giugliano. On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro, PLoS Computational Biology, 2015, Volume 11, Issue 3, DOI: 10.1371/journal.pcbi.1004112