How the Tulip Breaking Virus Creates Striped Tulips

The beauty of tulips has enchanted mankind for centuries. The striped variety has attracted particular attention for its intricate and unpredictable patterns. A good understanding of the mechanism that drives the striped pattern formation of the broken tulips has been missing since the 17th century. It is known since 1928 that these patterned tulips suffer from a viral infection by the tulip breaking virus. Here, we present a mathematical model to understand how a virus infection of the petals can lead to stripes, thereby solving a 350 year old mystery. The model, which describes the viral inhibition of pigment expression (anthocyanins) and their interaction with viral reproduction, incorporates a pattern formation mechanism identified as an activator-substrate mechanism, similar to the well-known Turing instability, working together with a Wolperts positional information mechanism. The model is solved on a growing tulip petal shaped domain, whereby we introduce a new method to describe the tulip petal growth explicitly. This work contributes to the theory of pattern formation of reaction-diffusion systems on growing domains applied to the fields of virology and botany.