A double swarm methodology for parameter estimation in oscillating Gene Regulatory Networks

S-systems are mathematical models based on the power-law formalism, which are widely employed for the investigation of Gene Regulatory Networks (GRNs). Because of their complex dynamics — characterized by multi-modality and non-linearity — the parameterization of S-systems is far from straightforward, demanding global optimization techniques. The problem of parameter estimation of S-systems is further complicated when the desired dynamics is characterized by oscillations. In this work, we describe a novel methodology based on Particle Swarm Optimization for the automatic parameterization of oscillating S-systems. In this methodology, two swarms perform independent optimizations, and cooperate by periodically exchanging the best particles. The two swarms exploit two different fitness functions: a traditional point-to-point distance, and a spectra-based fitness function. We show that this cooperative approach allows the double swarm to outperform the common methodology, based on a single swarm exploiting a single fitness function. We demonstrate the effectiveness of our method using a GRN of five genes, performing tests of increasing complexity, up to the simultaneous inference of 17 parameters.