Phase-Resetting Curves Determine Synchronization, Phase Locking, and Clustering in Networks of Neural Oscillators

Achuthan, Srisairam; Canavier, Carmen C.

doi:10.1523/jneurosci.0426-09.2009

Cited by 147 publications

(199 citation statements)

References 48 publications

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“…This can be seen dramatically if one looks at the effects of inputs to a neuronal oscillator (28,30). It is often useful to determine the influence of an input to an oscillator by measuring its phase-response curve (PRC), which captures the response of the oscillator to perturbations at different times in the oscillator's cycle (31)(32)(33)(34). Fig.…”

Section: Synaptic Strength Does Not Always Mattermentioning

confidence: 99%

Variability, compensation, and modulation in neurons and circuits

Marder

2011

Proc. Natl. Acad. Sci. U.S.A.

346

370

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I summarize recent computational and experimental work that addresses the inherent variability in the synaptic and intrinsic conductances in normal healthy brains and shows that multiple solutions (sets of parameters) can produce similar circuit performance. I then discuss a number of issues raised by this observation, such as which parameter variations arise from compensatory mechanisms and which reflect insensitivity to those particular parameters. I ask whether networks with different sets of underlying parameters can nonetheless respond reliably to neuromodulation and other global perturbations. At the computational level, I describe a paradigm shift in which it is becoming increasingly common to develop families of models that reflect the variance in the biological data that the models are intended to illuminate rather than single, highly tuned models. On the experimental side, I discuss the inherent limitations of overreliance on mean data and suggest that it is important to look for compensations and correlations among as many system parameters as possible, and between each system parameter and circuit performance. This second paradigm shift will require moving away from measurements of each system component in isolation but should reveal important previously undescribed principles in the organization of complex systems such as brains.circuit dynamics | neuronal variability | neuronal homeostasis | dynamic clamp A ll experimental biologists face a daily conundrum: on the one hand, we know that all individual biological organisms, be they lobsters, cats, or humans, are distinct individuals. On the other hand, we must do experiments on multiple individuals to ensure the reliability of our results. As biologists wishing to understand how the function of a cell, a circuit, or a brain depends on the properties of its constituent processes, we confront two issues: (i) all our data come with associated measurement error (often difficult to assess), and (ii) there is considerable natural variability in the populations we study. Consequently, we conventionally rely on statistics calculated from populations to assure ourselves that our measurements are reliable. Most commonly, we report mean data, with the underlying assumption that these means capture something akin to a "platonic ideal" of the individual neurons or animals whose properties were measured. Although this strategy has been enormously useful over the years, it has many limitations, some of which I discuss below. Multiple Solutions and Failure of AveragingDespite the widespread use of means, computational work has shown unambiguously some of the dangers and confounds that can come from exclusive reliance on mean data (1-3). One example of this comes from a study in which several thousand model neurons were generated by randomly picking the maximal conductances of the five different ionic conductances in the model (2). Fig. 1 shows three examples of single-spike bursters chosen from a population of 164 single-spike bursters generated in this study. Alth...

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Section: Synaptic Strength Does Not Always Mattermentioning

confidence: 99%

Variability, compensation, and modulation in neurons and circuits

Marder

2011

Proc. Natl. Acad. Sci. U.S.A.

346

370

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“…To date these methods have been evaluated both in model networks (Achuthan and Canavier 2009;Canavier et al 1997Canavier et al , 1999Luo et al 2004;Maran et al 2008;Oh and Matveev 2008) and in hybrid networks coupled with inhibition (Oprisan et al 2004). Here we test the applicability of PRC-based firing time maps (Ermentrout and Chow 2002) to excitatory coupling of significant strength and duration, using a wide range of synaptic strengths (from 1 to 10,000 nS) and input durations (from 0.3 to 1.5 s).…”

Section: Introductionmentioning

confidence: 99%

Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

Sieling

Canavier²,

Prinz³

2009

Journal of Neurophysiology

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“…The fPRC method can also be extended to any 1:1 phase locking between two clusters of neurons, again by analogy with published PRC methods (Achuthan and Canavier 2009). Locking between clusters of similar or disparate populations may be widespread in the nervous system.…”

Section: Discussionmentioning

confidence: 99%

“…However, as currently formulated, the fPRC method can easily be extended to the analysis of global synchrony in an N neuron network using a method analogous to that shown for the conventional PRC (Achuthan and Canavier 2009).…”

Section: Discussionmentioning

confidence: 99%

Functional Phase Response Curves: A Method for Understanding Synchronization of Adapting Neurons

Cui¹,

Canavier²,

Butera³

2009

Journal of Neurophysiology

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Cui J, Canavier CC, Butera R. Functional phase response curves: a method for understanding synchronization of adapting neurons. J Neurophysiol 102: 387-398, 2009. First published May 6, 2009 doi:10.1152/jn.00037.2009. Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutually coupled neurons. Previous theoretical work on pulse-coupled oscillators used single-pulse perturbations. We propose an alternate method in which functional PRCs (fPRCs) are generated using a train of pulses applied at a fixed delay after each spike, with the PRC measured when the phasic relationship between the stimulus and the subsequent spike in the neuron has converged. The essential information is the dependence of the recovery time from pulse onset until the next spike as a function of the delay between the previous spike and the onset of the applied pulse. Experimental fPRCs in Aplysia pacemaker neurons were different from single-pulse PRCs, principally due to adaptation. In the biological neuron, convergence to the fully adapted recovery interval was slower at some phases than that at others because the change in the effective intrinsic period due to adaptation changes the effective phase resetting in a way that opposes and slows the effects of adaptation. The fPRCs for two isolated adapting model neurons were used to predict the existence and stability of 1:1 phase-locked network activity when the two neurons were coupled. A stability criterion was derived by linearizing a coupled map based on the fPRC and the existence and stability criteria were successfully tested in two-simulated-neuron networks with reciprocal inhibition or excitation. The fPRC is the first PRC-based tool that can account for adaptation in analyzing networks of neural oscillators.

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Phase-Resetting Curves Determine Synchronization, Phase Locking, and Clustering in Networks of Neural Oscillators

Cited by 147 publications

References 48 publications

Variability, compensation, and modulation in neurons and circuits

Variability, compensation, and modulation in neurons and circuits

Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

Functional Phase Response Curves: A Method for Understanding Synchronization of Adapting Neurons

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