Travelling waves in our immune system

In various biological scenarios, cells rely on the diffusion of signaling molecules to communicate, yet information needs to be communicated quickly and over large distances. How can the limitations of diffusion be surpassed? One solution Nature utilizes relies on "diffusive relays": upon sensing the signal, cells release more of it, thus creating an outgoing information wave. Mathematically, this mechanism manifests itself as an additional, non-linear, term in the diffusion equation, allowing for propagating wave solutions. The properties of these waves strongly depend on system dimensionality, and manifest intriguing phenomena, including regimes where wave velocity is independent of the diffusion constant. We proposed that such waves arise in the immune system, where upon sensing a signal, white blood cells known as neutrophils release a signaling molecule. However, in this case the waves must be self-extinguishing, since the range of cell recruitment must be limited. After introducing diffusive relays, I will discuss new mathematical models of self-extinguishing relays, and compare them to recent experiments on neutrophils.