Model for cooperativity of biological membranes

We present a mathematical model for the complex cooperativity observed in biological membranes. In our model, it is assumed that the proteins bound on the membrane are noncooperative and possess a Bohr proton. It is further assumed that the net charge of the unliganded state of the protein is different from that of the liganded state owing to the structural change upon binding the ligand. With this model, we show how an all-or-none response, a graded response, and a noncooperative response arise in the binding curve of such biological membranes. In addition, we show how an effector, which can alter the pKa involved in the binding site, induces a complex cooperativity.