Choices of regulatory logic class modulate the dynamical regime in random Boolean networks

Abstract

Random Boolean networks (RBNs) have been widely explored as models for understanding complex systems, in particular gene regulatory networks (GRNs). Stability (order) and instability (chaos), critical characteristics of any dynamic system, have naturally been a central focus in RBN research. Several measures have previously been introduced to assess stability, e.g., via damage spreading or via statistical properties of attractors such as their number, lengths or basin sizes. Undoubtedly, network topology plays an important role in shaping the dynamics of RBN. Another key factor influencing the dynamics is the Boolean functions (BFs) assigned to each node. In this work, we conduct a systematic investigation to examine the influence of five different classes of BFs on the dynamics of RBNs. By employing various dynamical stability measures, we show that biologically meaningful BFs consistently drive the dynamics toward the stable regime compared to random BFs. This observation holds across networks with varying size, connectivity, and degree distributions. Additionally, we show that the change in the values of our stability measures with increasing connectivity or size of RBNs is different across the BF classes. For most observables, random BFs change the values significantly, pushing the dynamics toward a more chaotic regime with increasing connectivity or network size. In contrast, biologically meaningful BFs show very minimal fluctuations for most stability measures. These findings emphasize the advantage of restricting to biologically meaningful classes in the reconstruction and modeling of biological systems within Boolean framework.