Fig 6. Spatial cPCH can be used to estimate the dissociation constants in a receptor-ligand system with two different binding sites on the receptor and a fluorescent ligand.

A) Spatial cPCH can accurately estimate concentrations if the concentration of the doubly-labeled receptor R₁₁ is lower than that of the singly-bound receptor R₁. The actual concentrations are indicated with crosses and the estimated concentrations are indicated by the open squares. The initial concentration of receptors is R₀ = 10 nM. We specified the (apparent) dissociation constants for the singly and doubly bound receptors as $K_1^{*}=2\text{nM}$ and $K_2^{*}=12\text{nM}$ and find the actual dissociation constants from Eq S9. These apparent dissociation constants arise because we cannot distinguish using either fluorescence or diffusion which site the ligand has bound on a receptor that has bound only one ligand (Sec. S5). The simulation employed a laser dwell time of 10 μs with images of 512 × 512 pixels and an image size of 4 μm by 4 μm, so that the pixel size is just under 12 nm. The line retracing time is 1 ms and the frame retracing time is 50 ms. We generated 2 sets of data with 25 images each for all of the concentrations used, except for the lowest initial value of ligand, which used 1 set of 70 images. B) The apparent dissociation constants ($K_1^{*}=LR/R_1=2\text{nM}$ and $K_2^{*}=LR/R_{11}=12\text{nM}$) can be estimated using the measured concentrations provided the concentration of singly labeled receptors R₁ is greater than the concentration of doubly labeled receptors R₁₁.