Resonant Learning in Large Scale-Free Networks

Abstract

Biological regulatory networks have evolved "master regulator" genes that often display oscillating expression profiles, showing periodic bursts of activation over time. While the amplitude of activation is important in controlling cellular behavior, recent work suggests that the period between bursts of activation is equally significant in determining cellular behavior. Though this phenomenon has been experimentally observed, the advantages that oscillating levels of activation can provide to network-based learning has not been studied. We take a Boolean network modeling approach to demonstrate how these oscillations can provide a network-level advantage. First, we characterize how random, dynamical Boolean networks respond when the largest hub node in the network is forced to oscillate with square wave inputs. We find that oscillating inputs can imprint robust and novel network-behaviors that vary as a function of the input period. Moreover, we observe that Boolean networks can simultaneously learn to produce specific target behaviors as a function of different input oscillation periods. We term this network-based learning strategy "resonant learning," as it depends on the propagation of an oscillating input signal from the master regulator node. We find that evolving random networks toward a target function with resonant learning leads to convergence over an order of magnitude quicker than standard evolutionary learning procedures for a similar task. Our results suggest a compelling evolutionary advantage for the naturally occurring, observed oscillations in master regulator gene activation.