To model proton transfer in biological systems, we consider a modified H5O2+ system, in which each of the two outermost hydrogens (H*) is assigned a large mass in order to represent a backbone. For the potential energy surface of our model, we add a harmonic function, called the "backbone term", to the potential energy function of Ojamae, Shavitt, and Singer for H5O2+. This backbone term holds the H* atoms apart and, thus, provides various oxygen-oxygen distances and barriers for proton transfer. Variational transition-state theory (CVT) rate constants converge for H* masses greater than 1000 amu. These rate constants decrease exponentially as the backbone-backbone equilibrium distance increases. CVT rate constants also decrease as the backbone-term force constant increases and converge in the limit of a large backbone-term force constant. Tunneling effects are more important at low temperature and for larger values of backbone-term force constants or backbone-backbone equilibrium distances. The motion of the system along the minimum energy path from the saddle point to the product involves the motion of the proton between two relatively fixed oxygens followed by fragment motion and relaxation into the product well.