Cells are often moving by a successions of runs and tumbles. The most common case is when a chemical signal attracts the cells (chemotaxis). Here we are interested in the direct self-attraction between cells by local sensing, according to a model proposed by Loy and Preziosi. A concentration phenomena has been observed which is related to the instability of the steady state. The concentration profile can be described using the Hopf-Cole transform and a striking new feature is a concave-convex Hamiltonian which explains sawthooth concentration porofiles.