Universal principles of cell population growth follow from local contact inhibition

Cancer cell populations often exhibit remarkably similar growth laws despite their heterogeneity. Explanations of universal cell population growth remain partly unresolved to this day. Here, we present a growth-law unification by investigating the connection between the microscopic assumptions that affect the expected contact inhibition leading to five classical tumor growth laws: exponential, radial growth, fractal growth, generalized logistic, and Gompertzian growth. All five can be seen as manifestations of a single microscopic model. Agent-based simulations substantiate our theory, and we can explain differences in growth curves in experimental data from in vitro cancer cell population growth. Thus, our framework offers a possible explanation for many mean-field laws used to empirically capture seemingly unrelated cancer or microbial growth dynamics. Our results highlight that the interplay between contact inhibition and other assumptions (e.g., well-mixed) can influence our quantitative understanding of how cancer cells grow and, in turn, how they may interact.