Insulin binding to an insulin receptor of a cell stimulates tyrosine kinase activity. However, uncontrollably high number of insulin-insulin receptor binding causes negative impacts on cellular viability. A researcher developed a new ligand X that can act as a scavenger of the insulin by binding to an insulin receptor. Researchers find that if given enough time, 85% of insulin receptor forms a complex with the ligand X.
Consider that the initial concentration of the ligand X is 220mM and the dissociation constant is known to be 5.37 × 10−4 s−1, estimate how long it takes for half of insulin receptors to form complexes with the ligand X. Assume there is no insulin-insulin receptor complex and there is no insulin in the solution.