Interactions of multiple rhythms in a biophysical network of neurons

Noninvasive inference methods for interaction and noise intensities of coupled oscillators using only spike time data

Identifying interactions is essential for understanding self-organized systems because they are a source of order, function, and complexity. However, distinguishing interaction and noise effect is generally difficult because they both critically affect the stability of an ordered state. We propose methods that enable us to simultaneously infer both interaction and noise intensities. Our methods use only the time series of periodic events such as spike time data and do not require any external stimuli. Moreover, it is not necessary to assume a function form to fit. We numerically demonstrate that our methods yield reasonable inference even for a relatively short time series. These features are particularly beneficial for application in biological and chemical complex systems.

Measurements of interaction intensity are generally achieved by observing responses to perturbations. In biological and chemical systems, external stimuli tend to deteriorate their inherent nature, and thus, it is necessary to develop noninvasive inference methods. In this paper, we propose theoretical methods to infer coupling strength and noise intensity simultaneously in two well-synchronized noisy oscillators through observations of spontaneously fluctuating events such as neural spikes. A phase oscillator model is applied to derive formulae relating each of the parameters to spike time statistics. Using these formulae, each parameter is inferred from a specific set of statistics. We verify these methods using the FitzHugh–Nagumo model as well as the phase model. Our methods do not require external perturbations and thus can be applied to various experimental systems.