A multi-objective differential evolutionary approach toward more stable gene regulatory networks

Abstract

Models are of central importance in many scientific contexts. Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles of living systems. Biological models, such as gene regulatory models, can help us better understand interactions among genes and how cells regulate their production of proteins and enzymes. One feature shared among living systems is their ability to cope with perturbations and remain stable, a property that is the result of evolutionary fine-tuning over many generations. In this study we use random Boolean networks (RBNs) as an abstract model of gene regulatory systems. By applying Differential Evolution (DE), an evolution-based optimization technique, we produce networks with increased stability. DE requires relatively few user-specified parameters, has fast convergence and does not rely on initial conditions to find the global minima within multi-dimensional search spaces. The stability of networks is evaluated by taking parameters such as their network sensitivity, attractor cycle length and number of attractor basins into account. In this study we present an evolutionary approach to produce networks with specific properties (high stability) starting from chaotic regimes. From this chaotic regime and randomly generated classical RBNs with static input degree, our evolutionary approach is able to produce networks with homogenous Boolean functions and highly structured state spaces.