Quantifying Direct Dependencies in Biological Networks by Multiscale Association Analysis

Embedding entropy: a nonlinear measure of dynamical causality

Research on concepts and computational methods of causality has a long history, and there are various concepts of causality as well as corresponding computing algorithms based on measured data. Here, by considering causes and effects from a dynamical perspective, we present a unified mathematical framework for the so-called dynamical causality (DC), which can detect causal interactions over time; notably, this framework covers Granger causality, transfer entropy, embedding causality and their conditional versions. Based on this framework, we further propose a causality criterion called embedding entropy (EE) to measure the DC between two variables. Moreover, its conditional version, conditional embedding entropy (cEE), is also derived for detecting conditional/direct causality. The significant advantages of EE and cEE are that they can be employed for solving not only nonlinear causal inference but also the non-separability problem, and they can reduce the scale bias in numerical calculation. The performance and robustness of EE and cEE were demonstrated through numerical simulations, and causal inference on various real-world datasets validated their effectiveness.

Multiscale Weighted Permutation Entropy Analysis of Schizophrenia Magnetoencephalograms

Schizophrenia is a neuropsychiatric disease that affects the nonlinear dynamics of brain activity. The primary objective of this study was to explore the complexity of magnetoencephalograms (MEG) in patients with schizophrenia. We combined a multiscale method and weighted permutation entropy to characterize MEG signals from 19 schizophrenia patients and 16 healthy controls. When the scale was larger than 42, the MEG signals of schizophrenia patients were significantly more complex than those of healthy controls (p<0.004). The difference in complexity between patients with schizophrenia and the controls was strongest in the frontal and occipital areas (p<0.001), and there was almost no difference in the central area. In addition, the results showed that the dynamic range of MEG complexity is wider in healthy individuals than in people with schizophrenia. Overall, the multiscale weighted permutation entropy method reliably quantified the complexity of MEG from schizophrenia patients, contributing to the development of potential magnetoencephalographic biomarkers for schizophrenia.

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.

Network analysis with biological data of cancer patients: A scoping review

BACKGROUND & OBJECTIVE

Network Analysis (NA) is a mathematical method that allows exploring relations between units and representing them as a graph. Although NA was initially related to social sciences, the past two decades was introduced in Bioinformatics. The recent growth of the networks' use in biological data analysis reveals the need to further investigate this area. In this work, we attempt to identify the use of NA with biological data, and specifically: (a) what types of data are used and whether they are integrated or not, (b) what is the purpose of this analysis, predictive or descriptive, and (c) the outcome of such analyses, specifically in cancer diseases.

METHODS & MATERIALS

The literature review was conducted on two databases, PubMed & IEEE, and was restricted to journal articles of the last decade (January 2010 - December 2019). At a first level, all articles were screened by title and abstract, and at a second level the screening was conducted by reading the full text article, following the predefined inclusion & exclusion criteria leading to 131 articles of interest. A table was created with the information of interest and was used for the classification of the articles. The articles were initially classified to analysis studies and studies that propose a new algorithm or methodology. Each one of these categories was further screened by the following clustering criteria: (a) data used, (b) study purpose, (c) study outcome. Specifically for the studies proposing a new algorithm, the novelty presented in each one was detected.

RESULTS

& Conclusions: In the past five years researchers are focusing on creating new algorithms and methodologies to enhance this field. The articles' classification revealed that only 25% of the analyses are integrating multi-omics data, although 50% of the new algorithms developed follow this integrative direction. Moreover, only 20% of the analyses and 10% of the newly developed methodologies have a predictive purpose. Regarding the result of the works reviewed, 75% of the studies focus on identifying, prognostic or not, gene signatures. Concluding, this review revealed the need for deploying predictive and multi-omics integrative algorithms and methodologies that can be used to enhance cancer diagnosis, prognosis and treatment.