  Biological systems, from cells to organisms, must respond to the ever
changing environment in order to survive and function. This is not a simple
task given the often random nature of the signals they receive, as well as the
intrinsically stochastic, many body and often self-organized nature of the
processes that control their sensing and response and limited resources.
Despite a wide range of scales and functions that can be observed in the living
world, some common principles that govern the behavior of biological systems
emerge. Here I review two examples of very different biological problems:
information transmission in gene regulatory networks and diversity of adaptive
immune receptor repertoires that protect us from pathogens. I discuss the
trade-offs that physical laws impose on these systems and show that the optimal
designs of both immune repertoires and gene regulatory networks display similar
discrete tiling structures. These solutions rely on locally non-overlapping
placements of the responding elements (genes and receptors) that, overall,
cover space nearly uniformly.
