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 nonlinearity-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 Ssystems. 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.