# tvsfglasso: Time-varying scale-free graphical lasso for network estimation from time-series data

## TL;DR

The paper introduces tvsfglasso, a new method for analyzing how gene networks change over time, which can help understand complex biological processes.

## Contribution

The novel tvsfglasso method enables the estimation of high-dimensional time-varying gene co-expression networks with scale-free structure.

## Key findings

- tvsfglasso accurately captures temporal changes in gene associations using simulated and real data.
- The method reveals bursts of new regulatory links in Drosophila melanogaster embryo development.
- tvsfglasso is scalable and efficient for high-dimensional time-series gene expression data.

## Abstract

In high-dimensional gene co-expression network analysis, capturing the temporal changes of gene associations is crucial for unveiling dynamic regulatory mechanisms inherent in biological systems. Examining how these interactions change over time offers valuable insights into the developmental and adaptive processes that drive an organism’s lifecycle. Moreover, incorporating structural prior information can substantially enhance the accuracy and interpretability of the estimated sparse dynamic gene network. Methods previously proposed in the literature cannot simultaneously model sparse time-varying co-expression network structure and have the power-law degree distribution. Additionally, there is a demand of time-efficient, memory-light software implementations and possibility to utilize repeated measures at each time-point (if available). In this paper, we introduce the time-varying scale-free graphical lasso (tvsfglasso), a novel scalable framework for estimating high-dimensional time-varying gene co-expression networks under the assumption that these networks simultaneously exhibit sparse and a scale-free structure. We utilize fast algorithms developed for the graphical lasso (glasso), which makes tvsfglasso a scalable tool for high-dimensional problems. We evaluate the performance of tvsfglasso using both simulated and real-world dynamic gene expression time series datasets, demonstrating its capability to detect temporal changes in gene associations. Our results highlight the potential of tvsfglasso to advance the understanding of dynamic gene networks, making this estimator useful for more accurate modeling of complex biological processes.

Dynamic co-expression network analysis can provide insights into processes such as development, disease progression, and treatment response. However, although power-law distributions are frequently used to model co-expression networks characterized by a few hub genes and many genes with few connections, currently there are no tools to construct this type of networks from high-dimensional time-series data. We propose the time-varying scale-free graphical lasso (tvsfglasso) to investigate gene interactions over time in complex biological systems when a scale-free network is used to model gene co-expression topology. The method utilizes fast algorithms from the literature that enable the construction of dynamic gene networks with thousands of genes and only a handful of observations. We show in simulations that tvsfglasso can capture subtle changes in dynamic gene networks in high accuracy. Applied to Drosophila melanogaster embryo time-series data, it revealed bursts of new regulatory links just before key developmental transitions. This work delivers a powerful tool for constructing networks from high-dimensional time-series gene expression data.