A THEORETICAL APPROACH TO THE BELL-SHAPED DEPENDENCY OF CELL-PROLIFERATION ON THE HORMONE CONCENTRATION

Binding of human growth hormones (hGH) to the receptors was studied wi th a theoretical, molecular-level model. An hGH has two sites bindable to different receptors with different binding energies. In the model the hGHs diffusively moved in a box (i.e. the volume of solution), and receptors on the bottom face of the box (i.e. a membrane). The system consisted of a number of hGHs and receptors, which could form hGH-[re ceptor](2) or hGH-receptor complexus. In a complex, small inter-molecu lar positional fluctuations were allowed with keeping the inter-molecu lar binding. Partition function of the system was calculated. In a low hGH-concentration range, free receptors were dominant on the membrane ; in a medium concentration range, hGH-[receptor](2) complexus, which induce cell-proliferation, were dominant; and in a high concentration range, hGH-receptor complexus, which inhibit the proliferation, were d ominant. This dependency (bell-shaped dependency) of formation of hGH- [receptor](2) complex on the hGH concentration agreed well with experi mental observation. The values of EC50 (hGH concentration at that the cell-proliferation rate rose to 50% of the maximum rate by the formati on of hGH-[receptor](2) complexus) and IC50 (hGH concentration at that the proliferation rate decreased to 50% of the maximum by the formati on of hGH-receptor complexus) from my method were 18 pM and 2.2 mu M, respectively. By calculating thermodynamic quantities (i.e. entropy an d enthalpy), factors that determine the bell-shaped dependency were ob tained. At the medium concentration, the entropy of free hGHs played a n important role in stabilizing the hGH-[receptor](2) complex. Small c hanges in binding energies or in inter-molecular positional fluctuatio ns largely changed the dependency of the complex formation on the hGH concentration. This method is useful in explaining the experimental re sults that small molecular modification largely changes the formation of the complex. (C) 1997 Academic Press Limited.