LogicNet: probabilistic continuous logics in reconstructing gene regulatory networks

Abstract

Background: Gene Regulatory Networks (GRNs) have been previously studied by using Boolean/multi-state logics. While the gene expression values are usually scaled into the range [0, 1], these GRN inference methods apply a threshold to discretize the data, resulting in missing information. Most of studies apply fuzzy logics to infer the logical gene-gene interactions from continuous data. However, all these approaches require an a priori known network structure. Results: Here, by introducing a new probabilistic logic for continuous data, we propose a novel logic-based approach (called the LogicNet) for the simultaneous reconstruction of the GRN structure and identification of the logics among the regulatory genes, from the continuous gene expression data. In contrast to the previous approaches, the LogicNet does not require an a priori known network structure to infer the logics. The proposed probabilistic logic is superior to the existing fuzzy logics and is more relevant to the biological contexts than the fuzzy logics. The performance of the LogicNet is superior to that of several Mutual Information-based and regression-based tools for reconstructing GRNs. Conclusions: The LogicNet reconstructs GRNs and logic functions without requiring prior knowledge of the network structure. Moreover, in another application, the LogicNet can be applied for logic function detection from the known regulatory genes-target interactions. We also conclude that computational modeling of the logical interactions among the regulatory genes significantly improves the GRN reconstruction accuracy.

Correlations reveal the hierarchical organization of biological networks with latent variables

“…In molecular biology, probabilistic Boolean network models have been successfully applied to infer gene regulatory networks [32][33][34] , but these methods aim at a complete network reconstruction including all logical relationships between genes (logic gates). In contrast, the statistical test presented here does not estimate model parameters.…”

Review and assessment of Boolean approaches for inference of gene regulatory networks

“…To mitigate this problem, Boolean inference methods could in addition to binarised learning data also consider data in continuous format (e.g. [74] ). For example, to select a compact and accurate subset of potential regulators for a given target gene, an information theory-based approach could compute mutual information based on discrete and continuous data.…”

Single-cell multi-omics analysis identifies context-specific gene regulatory gates and mechanisms

“…For XOR, scGATE combines the input signals from the TFs using a logical XOR operator, such that the output is high if only one of the input signals is high. With two candidate TFs ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $k=2$\end{document} ), there are four ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $2^{k}$\end{document} ) distinct ’logic combinations’ of the two TFs that can be made using logical operators, since each TF can activate or inhibit the target gene [ 15 ]. These logic combinations that are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\{TF_{1} \wedge TF_{2}, TF_{1} \wedge \overline{TF_{2}}, \overline{TF_{1}} \wedge TF_{2}, \overline{TF_{1}} \wedge \overline{TF_{2}}\}$\end{document} are represented by distinct partitions in Venn diagram and generate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\{H(tf_{1})H(tf_{2}), H(tf_{1})[1-H(tf_{2})], [1-H(tf_{1})]H(tf_{2}), [1-H(tf_{1})][1-H(tf_{2})]\}$\end{document} outputs, respectively.…”