Critical growth of cerebral tissue in organoids: theory and experiments

We develop a Fokker-Planck theory of tissue growth with three types of cells (symmetrically

dividing, asymmetrically dividing and non-dividing) as main agents to study the growth dynamics

of human cerebral organoids. Fitting the theory to lineage tracing data obtained in next generation

sequencing experiments, we show that the growth of cerebral organoids is a critical process. We

derive analytical expressions describing the time evolution of clonal lineage sizes and show how

power-law distributions arise in the limit of long times due to the vanishing of a characteristic

growth scale.