Fig. 6

Binding in spatially restricted domains. a The system consists of 100 boxes where binding is restricted to 8 consecutive boxes \(i_\mathrm{trap}\) such that \(\rm{N}_\mathrm{i,b}^\mathrm{max} = \rm{N}_\mathrm{b}^\mathrm{max}\) for \(i=i_\mathrm{trap}\) and \(\rm{N}_\mathrm{i,b}^\mathrm{max} =0\) elsewhere. Synthesis sites are at boxes \(i_\mathrm{syn} = 7,\,...,14\) (blue) and boxes with traps (yellow) are located in a specific distance \(k_\mathrm{dist}\) to the synthesis site as indicated. Further system parameters are binding affinity \(\kappa _\mathrm{bin}={2e-2\,.} \Delta t^{-1}\), diffusion rate \(\widetilde{D}={9.8e-3\,.} \Delta t^{-1}\), and synthesis rate \(\alpha _\mathrm{syn}={2e-4\,.} \Delta t^{-1}\). b Total number of bound proteins in the biochip at different time points and distances between synthesis sites and traps. The bold line corresponds to the time point in (c), which shows the distributions of bound proteins for different trap distances \(k_\mathrm{dist}\)