sMIE: revealing critical transitions in complex biological systems using single-sample mutual information entropy.

Many complex biological systems often experience critical transitions during their progression, leading to catastrophic consequences. For instance, in the development of complex diseases, there is a critical phase between relative health and illness, marking the final opportunity for effective treatment before the disease worsens. However, the limited number of samples available for each individual in a clinical setting often impedes the effectiveness of conventional statistical techniques in determining critical transitions. Therefore, revealing critical states for complex biological systems using high-throughput biological data from small samples continues to be a formidable subject of inquiry. In this work, we present a new model-free computational framework, the single-sample mutual information entropy (sMIE), to identify critical transitions or tipping points in biological systems. Specifically, the proposed sMIE index is developed by using local gene networks to measure the differences in molecular dynamic networks of a specific single sample against reference samples. The reliability and accuracy of our sMIE were demonstrated through its successful application to a numerical simulation dataset and seven real-world datasets, comprising five bulk tumour datasets and two single-cell datasets focused on cell differentiation. Furthermore, the functional analysis of signalling genes offers valuable insights for subsequent research. This article is part of the theme issue 'Critical transitions and intelligent control in complex systems'.