Do effective interactions depend on the choice of coordinates?

A common approach to complex systems such as colloidal suspensions or polymer solutions describes the mesoscopic behavior using effective interactions. These potentials act between the macromolecular entities and can be derived by integrating out the microscopic degrees of freedom. The remaining macroparticle coordinates need to be chosen a priori. Two obvious choices are (i) the centers of mass and (ii) distinct microscopic entities, such as special "tagged" monomers. Here we compare both in the framework of the Asakura-Oosawa colloid-ideal polymer mixture. Using computer simulations, we find that although the effective pair interaction between colloid and polymer differ markedly, correlation functions are in fair agreement.