Tensor network-based gene regulatory network inference for single-cell transcriptomic data

Deciphering complex gene-gene interactions remains challenging in transcriptomics as traditional methods often miss higher-order and nonlinear dependencies. This study introduces a quantum-inspired framework leveraging tensor networks to optimally map expression data into a lower dimensional representation preserving biological locality. Using quantum mutual information (QMI), a nonparametric measure natural for tensor networks, we quantify gene dependencies and establish statistical significance via permutation testing. From those values, we construct optimal network where genes are positioned according to their quantum informational relationships that reflects the underlying biological circuitry. To validate the proposed method, we recover two distinct single-cell RNA sequencing datasets: first, a six-gene pathway from over 28, 000 lymphoblastoid cells; second, a 16-gene panel from 47 MCF10A breast epithelial cells. Furthermore, we unveil several triadic regulatory mechanisms. By merging quantum physics inspired techniques with computational biology, our method provides insights into gene regulation, with applications in disease mechanisms and precision medicine.