Evidence of non-poissonian dynamics in cancer mutations

It is a common assumption in various work on modelling mutation dynamics that mutations follow a Poisson dynamics; that is, in a given portion of genome the number of mutations follow a Poisson law. Equivalently, the distance between to mutations follows an exponential distribution. This can actually be verified when Human and Chimpanzee genomes are compared. It is of interest to see if this law generalizes also to somatic mutations which cause cancer. A recent survey published a catalogue of somatic mutations in cancer genome analysing 4,938,362 mutations from 7,042 cancers of 30 different cancer types. We have analysed this data to find the interoccurence time (space) distributions for different types of cancer. It has been found that specific cancer types show a power-law in interoccurrence distances, instead of the expected exponential distribution dictated with the Poisson assumption. Cancer genomes exhibiting power-law interoccurrence distances were enriched in cancer types where the main mutational process is described to be the activity of the APOBEC protein family, which produces a particular pattern of mutations called Kataegis. Therefore, the observation of a power-law in interoccurence distances could be used to identify cancer genomes with Kataegis. It is our objective to develop parametric models to differentiate between cancer and non-cancer mutations and between different cancer types.