Maybe it is too far fetched. But I heard of the so called Conley index theory which deals with the question of existence/non-existence of equilibria in dynamical systems. It involves homology groups of the occurring manifolds. So I think of dynamical systems which one might find in some situation in biology/pharmacology etc. and apply the Conley index theory to it. Check also http://wwwb.math.rwth-aachen.de/~barakat/MTNS2010/Conley.pdf