We make use of isospin constraints to study the parametric coupling model and the properties of asymmetric nuclear matter. Besides the usual constraints for nuclear matter---the effective nucleon mass and the incompressibility at saturation density---and the neutron star constraints---maximum mass and radius---we study the properties related to the symmetry energy. These properties constrain the parameters of the model to a small range. We apply our results to study thermodynamic instabilities in the liquid-gas phase transition as well as neutron star configurations.