The topography of tuning

Allosteric proteins globally adjust their conformation upon binding a ligand in order to control the activity of a distant active site. Inspired by such a system, we explore how mechanical systems achieve a specified complex function such as strain propagation in mechanical networks. We investigate computationally the maximum complexity of a tuned function that can be achieved as a function of network size. Further, we identify the structural features responsible for function in these tuned networks. We show how we can use topographical information to improve the tuning process and how the complexity of the tuned function scales with network size. Using persistent homology, we show that networks tuned to perform such functions develop characteristic features that are similar for different networks that perform the same function, regardless of differences in the local link connectivity.