Abstract
A dynamic system showing stable rhythmic activity can be represented by the dynamics of phase oscillators. This would provide a useful mathematical framework through which one can understand the system's dynamic properties. A recent study proposed a Bayesian approach capable of extracting the underlying phase dynamics directly from time-series data of a system showing rhythmic activity. Here we extended this method to spike data that otherwise provide only limited phase information. To determine how this method performs with spike data, we applied it to simulated spike data generated by a realistic neuronal network model. We then compared the estimated dynamics obtained based on the spike data with the dynamics theoretically derived from the model. The method successfully extracted the modeled phase dynamics, particularly the interaction function, when the amount of available data was sufficiently large. Furthermore, the method was able to infer synaptic connections based on the estimated interaction function. Thus, the method was found to be applicable to spike data and practical for understanding the dynamic properties of rhythmic neural systems.
Highlights
Rhythmic activities in neurons and neuronal networks are thought to contribute to information transfer and processing in the brain
As long as the detailed model possesses the nature of a nonlinear oscillator, its complicated dynamics can be reduced to those described by a single variable, the phase (Ermentrout and Kopell, 1984; Kuramoto, 1984; Hansel et al, 1995)
Constructing a detailed dynamic model based on measured data is often difficult and involves the selection of an appropriate model, adjustment for many unknown parameters, and insufficient information regarding measured data used for modeling
Summary
Rhythmic activities in neurons and neuronal networks are thought to contribute to information transfer and processing in the brain. Spike-Based Estimation of Phase Dynamics achieved with a detailed model based on biophysical mechanisms such as the kinetics of ion channels responsible for a given change in neuronal membrane potential (Hodgkin and Huxley, 1952) Such a model generally consists of a considerable number of variables and parameters. As long as the detailed model possesses the nature of a nonlinear oscillator, its complicated dynamics can be reduced to those described by a single variable, the phase (Ermentrout and Kopell, 1984; Kuramoto, 1984; Hansel et al, 1995) This reduction makes impossible a quantitative comparison of the behavior of the reduced phase dynamics with experimentally observed phenomena, it provides a mathematically tractable framework through which to understand the essential properties of the dynamic system (see Figure 1a). Most previous studies have first described the detailed dynamics of the model before reducing it to the simpler phase dynamics in order to analyze its dynamic properties as a rhythmic system
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