Approximations of Shannon Mutual Information for Discrete Variables with Applications to Neural Population Coding

Pulse-frequency-dependent resonance in a population of pyramidal neuron models

Stochastic resonance is known as a phenomenon whereby information transmission of weak signal or subthreshold stimuli can be enhanced by additive random noise with a suitable intensity. Another phenomenon induced by applying deterministic pulsatile electric stimuli with a pulse frequency, commonly used for deep brain stimulation (DBS), was also shown to improve signal-to-noise ratio in neuron models. The objective of this study was to test the hypothesis that pulsatile high-frequency stimulation could improve the detection of both sub- and suprathreshold synaptic stimuli by tuning the frequency of the stimulation in a population of pyramidal neuron models. Computer simulations showed that mutual information estimated from a population of neural spike trains displayed a typical resonance curve with a peak value of the pulse frequency at 80-120 Hz, similar to those utilized for DBS in clinical situations. It is concluded that a "pulse-frequency-dependent resonance" (PFDR) can enhance information transmission over a broad range of synaptically connected networks. Since the resonance frequency matches that used clinically, PFDR could contribute to the mechanism of the therapeutic effect of DBS.

Multiscale part mutual information for quantifying nonlinear direct associations in networks

MOTIVATION

For network-assisted analysis, which has become a popular method of data mining, network construction is a crucial task. Network construction relies on the accurate quantification of direct associations among variables. The existence of multiscale associations among variables presents several quantification challenges, especially when quantifying nonlinear direct interactions.

RESULTS

In this study, the multiscale part mutual information (MPMI), based on part mutual information (PMI) and nonlinear partial association (NPA), was developed for effectively quantifying nonlinear direct associations among variables in networks with multiscale associations. First, we defined the MPMI in theory and derived its five important properties. Second, an experiment in a three-node network was carried out to numerically estimate its quantification ability under two cases of strong associations. Third, experiments of the MPMI and comparisons with the PMI, NPA and conditional mutual information were performed on simulated datasets and on datasets from DREAM challenge project. Finally, the MPMI was applied to real datasets of glioblastoma and lung adenocarcinoma to validate its effectiveness. Results showed that the MPMI is an effective alternative measure for quantifying nonlinear direct associations in networks, especially those with multiscale associations.

AVAILABILITY AND IMPLEMENTATION

The source code of MPMI is available online at https://github.com/CDMB-lab/MPMI.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.