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A scaling law relates the expected number of mutants to the total population size of cells in a spatially constrained but growing population, which could help clinicians predict when cancers or bacterial infections might develop resistance to treatment.

Given a small number of cells in a population subject to a strong fitness pressure, such as a drug intended to kill the cells, mutations are likely to arise. However, it is difficult to predict when those mutations might arise and become common in the population because simulating all of the many possible futures for mutants in a growing population is computationally expensive.

in PNAS Nexus, Dominik Wodarz and colleagues derive general laws that describe how the number of mutants in a growing system scales with the total population based on the system's dimensionality—whether it is a two-dimensional sheet of cells like a biofilm or a 3D mass like a tumor.

The laws incorporate intermediate mutants with varying fitness, such as those with gene amplifications, where genes are duplicated within the genome. The scaling law also covers mismatch repair deficiency cells, which cannot correct their own mutations because they have a mutation in their own DNA repair system.

Key variables in the scaling law include the size of the whole colony (or the time it has been growing), and a power that varies depending on factors such as the number of mutations, system's dimensionality, and whether mutations are advantageous to the cells. According to the authors, the scaling law has implications for the study of evolutionary biology as well as biomedicine.