Spatiotemporal relationships between genes expressed in tissues likely reflect physicochemical principles that range from stoichiometric interactions to co-organized fractals with characteristic scaling. For key structural factors within the nucleus and extracellular matrix (ECM), gene-gene power laws are found to be characteristic across several tumor types in The Cancer Genome Atlas (TCGA) and across single-cell RNA-seq data. The nuclear filament LMNB1 scales with many tumor-elevated proliferation genes that predict poor survival in liver cancer, and cell line experiments show LMNB1 regulates cancer cell cycle. Also high in the liver, lung, and breast tumors studied here are the main fibrosis-associated collagens, COL1A1 and COL1A2, that scale stoichiometrically with each other and superstoichiometrically with a pan-cancer fibrosis gene set. However, high fibrosis predicts prolonged survival of patients undergoing therapy and does not correlate with LMNB1. Single-cell RNA-seq data also reveal scaling consistent with the pan-cancer power laws obtained from bulk tissue, allowing new power law relations to be predicted. Lastly, although noisy data frustrate weak scaling, concepts such as stoichiometric scaling highlight a simple, internal consistency check to qualify expression data.
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