Scaling concepts in 'omics: nuclear lamin-B scales with tumor growth and predicts poor prognosis, whereas fibrosis can be pro-survival

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 super-stoichiometrically 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. ClassificationApplied Physical Sciences (major) and Cell Biology (minor) Significance StatementNon-linear scaling analyses pervade polymer physics and chemistry and conceivably provide new insight into polymeric assemblies of genes expressed in tissues as well as co-regulated gene sets. Fractal scaling and stoichiometric scaling are among the gene-gene power law results identified here for key structural polymers in nuclei or extracellular matrix in human cancer data. Among nuclear envelope factors that might scale with DNA mass, only one nuclear filament scales with tumor proliferation and predicts poor survival in some cancer types. Collagen-1 scales with fibrosis and also tends to increase in multiple tumor types, but patients in therapy surprisingly survive longest with the highest levels of fibrosis, consistent with a therapeutic response.