  The large scale behaviour of a population of cells that grow and interact
through the concentration field of the chemicals they secrete is studied using
dynamical renormalization group methods. The combination of the effective
long-range chemotactic interaction and lack of number conservation leads to a
rich variety of phase behaviour in the system, which includes a sharp
transition from a phase that has moderate (or controlled) growth and regulated
chemical interactions to a phase with strong (or uncontrolled) growth and no
chemical interactions. The transition point has nontrivial critical exponents.
Our results might help shed light on the interplay between chemical signalling
and growth in tissues and colonies, and in particular on the challenging
problem of cancer metastasis.
