Calculating the mean time to capture for tethered ligands and its effect on the chemical equilibrium of bound ligand pairs

We present here the calculation of the mean time to capture of a tethered ligand to the receptor. This calculation is then used to determine the shift in the partitioning between (1) free, (2) singly bound, and (3) doubly bound ligands in chemical equilibrium as a function of the length of the tether. These calculations are used in the research article Fibroblast Growth Factor 2 Dimer with Superagonist in vitro Activity Improves Granulation Tissue Formation During Wound Healing (Decker et al., in press [1]) to explain quantitatively how changes in polymeric linker length in the ligand dimers modifies the efficacy of these molecules relative to that of free ligands.