  Chemotaxis plays a crucial role in a variety of processes in biology and
ecology. Quite often it acts to improve efficiency of biological reactions. One
example is the immune system signalling, where infected tissues release
chemokines attracting monocytes to fight invading bacteria. Another example is
reproduction, where eggs release pheromones that attract sperm. A macro scale
example is flower scent appealing to pollinators. In this paper we consider a
system of PDE designed to model such processes. Our interest is to quantify the
effect of chemotaxis on reaction rates compared to pure reaction-diffusion. We
limit consideration to surface chemotaxis, which is well motivated from the
point of view of many applications. Our results provide the first insight into
situations where chemotaxis can be crucial for reaction success, and where its
effect is likely to be limited. The proofs are based on new analytical tools; a
significant part of the paper is dedicated to building up the linear machinery
that can be useful in more general settings. In particular we establish precise
estimates on the rates of convergence to ground state for a class of
Fokker-Planck operators with potentials that grow at a logarithmic rate at
infinity.
  These estimates are made possible by a new sharp weak weighted Poincar\'e
inequality improving in particular a result of Bobkov and Ledoux.
