上海科技大学知识管理系统

Heterogeneity plays an important role in cancer genesis and progression. In this paper, we theoretically and computationally show that the increase of heterogeneity signals predeterioration during tumor progression by unified random ordinary differential equations (RODEs). Tumor formation results from a systematic change in organisms, and its causality is complex. Heterogeneity may be one of the key factors under some conditions. Specifically, the interactions between cell populations are modeled by random community matrices in normal tissues, benign tumors, and malignant tumors, and then we prove that the RODEs system describing the cell density of normal tissues or benign tumors becomes unstable as heterogeneity of cell populations or species increases. The increase of heterogeneity is an important signal. Heterogeneity can be viewed as a feature to distinguish benign tumors from malignant tumors under certain circumstances. Furthermore, we show that with the increase of heterogeneity, the divergence speed of the RODEs system becomes faster, which implies that malignant tumors with higher heterogeneity may develop faster and have poorer prognoses. Our theoretical findings can explain some noteworthy phenomena in various datasets in tumor patients and our biological experiments in mice from a mathematical viewpoint. Particularly, clinical data and mutation information from the cancer genome atlas and our experiments in mice revealed that tumors with higher heterogeneity usually show shorter survival time, whereas tumors with lower heterogeneity tend to have better prognosis, which also indicates that heterogeneity can be used as a potential biomarker in future clinical diagnosis. Targeting the heterogeneity may be a potential strategy for the cancer treatment. Copyright © by SIAM.