Many biological objects, such as transmembrane receptors or
gene promoters, sense concentrations of chemical entities by binding
them specifically. However, in many situations, competing ligands may
bind non-specifically to the target, potentially interfering with the
signal of the correct ligand, creating cross-talk. What is the best
accuracy of concentration sensing one can achieve in the face of this
cross-talk? I will show how to derive the best achievable performance
using the principle of maximum likelihood, and will discuss how the
mathematical solution can inspire new network designs based on the
principle of kinetic proof-reading.