Windowed Granger causal inference strategy improves discovery of gene regulatory networks

Abstract

Accurate inference of regulatory networks from experimental data facilitates the rapid characterization and understanding of biological systems. High-throughput technologies can provide a wealth of time-series data to better interrogate the complex regulatory dynamics inherent to organisms, but many network inference strategies do not effectively use temporal information. We address this limitation by introducing Sliding Window Inference for Network Generation (SWING), a generalized framework that incorporates multivariate Granger causality to infer network structure from time-series data. SWING moves beyond existing Granger methods by generating windowed models that simultaneously evaluate multiple upstream regulators at several potential time delays. We demonstrate that SWING elucidates network structure with greater accuracy in both in silico and experimentally validated in vitro systems. We estimate the apparent time delays present in each system and demonstrate that SWING infers time-delayed, gene-gene interactions that are distinct from baseline methods. By providing a temporal framework to infer the underlying directed network topology, SWING generates testable hypotheses for gene-gene influences.

Keywords: Granger causality; gene regulatory networks; machine learning; network inference; time-series analysis.

Fig. 1.

Overview of the SWING framework. (A) Time-series data are divided into windows with a user-specified width, $w$. (B) For each window, inference is performed by iteratively selecting response and explanatory genes. The subset of available explanatory genes is defined by the minimum and maximum user-allowed time delays. (C) Edges from each window model are aggregated into a single network representation of the biological interactions between measured variables.

Fig. 2.

SWING improves inference of 10-node in silico networks. (A) Changes in AUPR and AUROC in GNW networks. Score changes to individual networks are shown in gray. The mean (red) and median (black) of each score distribution is shown. AUPR and AUROC increase when using SWING-RF or -PLSR compared with their respective base method. SWING-LASSO outperforms LASSO in the E. coli-derived networks. The expected score based on random for each metric is shown as a dashed line. n = 20 networks, $k_{min}=1$, $k_{max}=3$, and $w=10$ for all networks. P values were calculated by using the Wilcoxon signed-rank test, ***P < 0.001; **P < 0.01; *P < 0.05. (B) SWING and non-SWING methods are grouped according to similarity of ranked predictions for 40 10-node in silico networks via PCA. PC1 largely separates inference methods based on performance (SI Appendix, Fig. S2), while PC2 separates methods based on underlying base method. Networks inferred by various SWING parameter selections cluster together according to inference type, with SWING methods forming clusters distinct from corresponding base methods.

Fig. 3.

SWING promotes edges with apparent time delays and increases correlation between genes. The true network structure is provided in SI Appendix, Fig. S7B. (A) Edge rank comparison for E. coli SOS network when using RF and SWING-RF (blue, promoted edges; red, demoted edges; black, no change; gray, false edges; green, lexA $\to$ umuDC analyzed in B). We report the lag for edges with an apparent time delay. (B, Upper) Time series for lexA and umuDC show better alignment when umuDC is shifted by one time period, (B, Lower) which improves correlation between the genes.

Fig. 4.

Application of SWING on time-delayed GRN modules in E. coli. (A) Circular diagram depicts experimentally validated interactions and gene ontologies present in each module (RegulonDb). Blue edges depict time-delayed interactions inferred by using pairwise cross-correlation from curated microarray data. (B) SWING-Community, with $w=4$, $k_{min}=1$, $k_{max}=1$ applied to RegulonDb subnetworks that are and are not enriched with time-delayed edges (fraction of delayed edges is $>$10%, $n$ = 12 subnetworks; fraction of delayed edges is $<$10%, $n$ = 14 subnetworks). (C) SWING-Community and R/L/P ensemble method applied to tdcABC regulon, which is the module found to have the highest enrichment of time-delayed edges (44% edges with a time delay of 10 min or greater).