Logo image
Back
Mean-return-time phase of a stochastic oscillator provides an approximate renewal description for the associated point process
Journal article   Open access   Peer reviewed

Mean-return-time phase of a stochastic oscillator provides an approximate renewal description for the associated point process

Konstantin Holzhausen, Lukas Ramlow, Shusen Pu, Peter J. Thomas and Benjamin Lindner
Biological cybernetics, Vol.116(2), pp.235-251
04/01/2022
DOI: https://doi.org/10.1007/s00422-022-00920-1
PMCID: PMC9068687
PMID: 35166932
Web of Science ID: WOS:000755404700001

Metrics

60 Record Views
1 Times Cited - Web of Science

Abstract

Stochastic oscillations can be characterized by a corresponding point process; this is a common practice in computational neuroscience, where oscillations of the membrane voltage under the influence of noise are often analyzed in terms of the interspike interval statistics, specifically the distribution and correlation of intervals between subsequent threshold-crossing times. More generally, crossing times and the corresponding interval sequences can be introduced for different kinds of stochastic oscillators that have been used to model variability of rhythmic activity in biological systems. In this paper we show that if we use the so-called mean-return-time (MRT) phase isochrons (introduced by Schwabedal and Pikovsky) to count the cycles of a stochastic oscillator with Markovian dynamics, the interphase interval sequence does not show any linear correlations, i.e., the corresponding sequence of passage times forms approximately a renewal point process. We first outline the general mathematical argument for this finding and illustrate it numerically for three models of increasing complexity: (i) the isotropic Guckenheimer-Schwabedal-Pikovsky oscillator that displays positive interspike interval (ISI) correlations if rotations are counted by passing the spoke of a wheel; (ii) the adaptive leaky integrate-and-fire model with white Gaussian noise that shows negative interspike interval correlations when spikes are counted in the usual way by the passage of a voltage threshold; (iii) a Hodgkin-Huxley model with channel noise (in the diffusion approximation represented by Gaussian noise) that exhibits weak but statistically significant interspike interval correlations, again for spikes counted when passing a voltage threshold. For all these models, linear correlations between intervals vanish when we count rotations by the passage of an MRT isochron. We finally discuss that the removal of interval correlations does not change the long-term variability and its effect on information transmission, especially in the neural context.
url
Mean-return-time phase of a stochastic oscillator provides an approximate renewal description for the associated point processView
Published (Version of record)link to articleCC BY V4.0,  Open

Related links

Details

Logo image