Heterogeneity and its impact on Thermal Robustness and Attractor Density

There is considerable research relating the structure of Boolean networks to their state space dynamics. In this paper, we extend the standard model to include the effects of thermal noise, which has the potential to deflect the trajectory of a dynamical system within its state space, sending it from one stable attractor to another. We introduce a new “thermal robustness” measure, which quantifies a Boolean network's resilience to such deflections. In particular, we investigate the impact of structural homogeneity on two dynamical properties: thermal robustness and attractor density. Through computational experiments on cyclic Boolean networks, we ascertain that as a homogeneous Boolean network grows in size, it tends to underperform most of its heterogeneous counterparts with respect to at least one of these two dynamical properties. These results strongly suggest that during an organism's growth and morphogenesis, cellular differentiation is required if the organism seeks to exhibit both an increasing number of attractors and resilience to thermal noise.