Approximating a gene regulatory network from non-sequential data

arXiv:2401.11858v3 Announce Type: replace
Abstract: Given non-sequential snapshots from instances of a dynamical system, we design a compressed sensing based algorithm that reconstructs the dynamical system. On the theoretical side, we show that: (1) successful reconstruction is possible under the assumption that we can construct an approximate clock from a subset of the coordinates of the underlying system, and (2) computing the minimal Lyapunov exponent of the dynamical system, where the minimum is taken over all subsets of coordinates of the dynamical system, equates to computing a min-max equilibrium. We design an efficient randomized algorithm for computing the above equilibrium.
As an application of our theoretical results, we reconstruct the underlying dynamical system from publicly available RNA-seq data to: (1) predict the underlying gene regulatory networks (as opposed to individual genes) that may help differentiate between metastatic vs non-metastatic breast cancer (and also colorectal cancer), and (2) identify candidate genes that could be used as target biomarkers for basket trials. In particular, our in silico analysis suggests that RORC agonists, which are already used in colorectal cancer therapies, may be worth investigating for breast cancers.