Centrioles are barrel-shaped structures that duplicate when a mother centriole gives birth to a single daughter that grows from its side. Polo-like-kinase 4 (PLK4), the master regulator of centriole biogenesis, is initially recruited around the mother centriole but it quickly concentrates at a single focus that defines the daughter centriole assembly site. How this PLK4 asymmetry is generated is unclear. Two previous studies used different molecular and mathematical models to simulate PLK4 symmetry breaking. Here, we extract the core biological ideas from both models to formulate a new and much simpler mathematical model where phosphorylated and unphosphorylated species of PLK4 (either on their own, or in complexes with other centriole duplication proteins) form the two-components of a classic Turing reaction-diffusion system. These two components bind/unbind from the mother at different rates, and so effectively diffuse around the mother at different rates. This allows a slow-diffusing activator species to accumulate at a single site on the mother, while a fast-diffusing inhibitor species rapidly diffuses around the centriole to suppress activator accumulation. Our analysis suggests that phosphorylated and unphosphorylated species of PLK4 can form a Turing reaction-diffusion system to break symmetry and generate a single daughter centriole. ### Competing Interest Statement The authors have declared no competing interest.