To simplify the general cell model for receptor binding and trafficking in L\&L, assume the following: a. L is present in excess and can thus be taken to be constant b. L binds surface receptors, Rs, to form surface complexes, Cs. c. Only complexes are internalized, at a rate proportional to their concentration, rate constant keCCC (Free receptors are not internalized: keReR=0 ). d. Internalized receptors, Ri, are recycled to the surface as Free receptors at a rate proportional to their concentration, rate constant ksee.. As in L\&L, we are not modeling dissociation of ligand from the internalized complex. This is equivalent to the assumption that dissociation occurs instantaneously upon internalization.) e. There is no receptor degradation (fR=0). f. There is no synthesis of new receptors (Vs=0). 1. Write the reaction scheme for this reduced model. 2. Write the kinetic balance equations for Rs and RTi 3. Assume that the surface binding reaction, Rs+LCs (forward and reverse reaction rates kd and ks, respectively) is in rapid equilibrium ( kc>>ksec). Use that approximation and receptor conservation to get dtdRTi in terms of RTi only. 4. Solve for RTi with initial condition RTi(0)=0 5. Use the equilibrium and receptor conservation expressions to find Rs and Cs