From Wiring to Function and Back: A Case Study in Feed-Forward Networks

Biological and technological systems process information by means of cascades of signals. Be they interacting genes, spiking neurons, or electronic transistors, signals travel across these systems, producing, for each set of external conditions, an appropriate response. In technology, circuits that perform specific, complex tasks are designed by humans. In biology, however, design has to be ruled out, confronting us with the question of how these systems could have arisen by accumulation of small changes. The key factor is the genotype-phenotype map, which modulates the adaptation process profoundly. Although a detailed study of RNA secondary structures has helped illuminate the structure of this map for combinatorial molecules, until now it wasn't known whether this idea had a more general applicability. Here we show that some important features of the genotype-phenotype map of simple feed-forward circuits follow a similar pattern: they have a large degree of neutrality, by which a circuit can be completely rewired keeping its input-output function intact, and there is a relatively small neighborhood of a given circuit containing almost all phenotypes. However, some key differences arise, the most important being that across the connected webs of neutral neighbors, circuits have vastly different degrees of evolvability.