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.
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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)