# Identifying early warning signals of cancer formation

## TL;DR

This paper introduces new methods to detect early warning signals for cancer formation using thermodynamic and gene regulatory network models.

## Contribution

The study introduces entropy product rate and mean flux as novel early warning signals for cancer tipping points.

## Key findings

- Entropy product rate and mean flux show sharp changes before cancer state transitions.
- Time-irreversible measure ΔC detects precancerous signals in gene expression data.
- These signals appear earlier than traditional indicators like critical slowdown.

## Abstract

It is increasingly clear that cancer is a complex systemic disease and one of the most fatal diseases in humans. Complex systems, including cancer, exhibit critical transitions in which the system abruptly shifts from one state to another. However, predicting these critical transitions is difficult as the system may show little change before the tipping point is reached. Models for predicting cancer are generally not accurate enough to reliably predict where these critical transitions will occur. Additionally, there is often a gap between theoretical results and clinical practice. To address these issues, we conducted a study using gastric cancer as a representative to reveal the tipping point of cancer and develop a feasible method for clinical monitoring. We used gene regulatory networks and a landscape framework to quantify the formation of gastric cancer. Since the dissipation cost of cancer cells is different from that of normal cells, we calculated the entropy product rate (EPR) and mean flux to quantify the thermodynamic cost and dynamical driving force in predicting critical transitions of cancer, which can serve as early warning signals. Both the EPR and mean flux change sharply near the point when the cancer state is about to emerge and/or the normal state is about to disappear. Moreover, the peak or sharp upward trends of the signals occur much earlier than critical slowdown and flickering frequency. These significant variations can be used as early warning signals for cancer. To further explore early warning signals in clinical and experimental trials, we calculated the difference in cross correlations (ΔC) forward and backward in time for the stochastic gene expression time series. This time‐irreversible measure gives a rise to peak before the bifurcation points, which can help detect precancerous and metastatic early warning signals in clinical practice rather than just theoretical calculation. This study is crucial for effectively identifying early warning signals for cancer in clinical and experimental settings.