Uncovering Interactions in the Frequency Domain

Shuixia Guo,Jianhua Wu,Mingzhou Ding,Jianfeng Feng,Karl J Friston

doi:10.1371/journal.pcbi.1000087

Abstract

Oscillatory activity plays a critical role in regulating biological processes at levels ranging from subcellular, cellular, and network to the whole organism, and often involves a large number of interacting elements. We shed light on this issue by introducing a novel approach called partial Granger causality to reliably reveal interaction patterns in multivariate data with exogenous inputs and latent variables in the frequency domain. The method is extensively tested with toy models, and successfully applied to experimental datasets, including (1) gene microarray data of HeLa cell cycle; (2) in vivo multi-electrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of a sheep; and (3) in vivo LFPs recorded from distributed sites in the right hemisphere of a macaque monkey.

Highlights

As reviewed in [1], many novel approaches in molecular biology have been invented to improve the bulk-scale methods that measure average values for a population of genes or proteins and mask their dynamical activities which are critical for the function of cells [2,3,4]
We focused on the Granger causality, and it has become increasingly important in recent years because of the huge body of temporal data available in, for example, molecular biology and physiology
We have presented a study on the frequency decomposition for the partial Granger causality

Summary

Introduction

As reviewed in [1], many novel approaches in molecular biology have been invented to improve the bulk-scale methods that measure average values for a population of genes or proteins and mask their dynamical activities which are critical for the function of cells [2,3,4]. There is a long history of analyzing neural dynamics by recording at the single neuron, neuronal network and brain area levels. Based upon such experimental data, how to explore the network structure of genes, proteins, neurons, etc, is one of the most important issues in Systems Biology. There exist two closely related approaches (see for example [5,6,7,8]): Bayesian modeling and Granger causality analysis. The appealing properties of the Granger causality approach are: (1) the flow of time is explicitly used to define causal relationships; (2) there is a frequency decomposition that reveals the frequency at which two units or variables interact with each other. Geweke’s decomposition of a vector autoregressive process [11] led to a set of causality measures which have a spectral representation and make the interpretation more informative and useful [12]

Methods

Results

Conclusion