Manasvita Vashisth, Sangkyun Cho, Jerome Irianto, Yuntao Xia, Mai Wang, Brandon Hayes, Daniel Wieland, Rebecca Wells, Farshid Jafarpour, Andrea Liu, Dennis E Discher

Nonlinear scaling analyses pervade polymer physics and chemistry, yielding characteristic exponents that conceivably apply to expressed genes and their assemblies. Stoichiometric scaling and fractal scaling indeed emerge as gene-gene power laws in human cancer data for key structural polymers in nuclei or extracellular matrix. Only one nuclear envelope factor, lamin-B1, scales with tumor proliferation genes, predicting poor survival for multiple cancers, including liver cancer. These genes include one transcription factor that directly regulates lamin-B1 and broadly categorizes prognosis. In contrast, collagen-1 scales with fibrosis genes, increases in tumors relative to adjacent tissue, and predicts “wound that heals”–type survival only for liver cancer—albeit intertumor comparisons show no correlation without adjacent referencing. Scaling thus identifies and characterizes fundamental gene-gene interrelationships.