Gene Regulatory Network Model Identification Using Artificial Bee Colony and Swarm Intelligence Zary Forghany * , Mohsen Davarynejad † and B.Ewa Snaar-Jagalska * * Gorlaeus Laboratory, Institute of Biology, Leiden University, The Netherlands Email: Z.Forghany@umail.leidenuniv.nl, B.E.Snaar-Jagalska@biology.leidenuniv.nl † Systems Engineering Section, Faculty of Technology, Policy and Management, Delft University of Technology, The Netherlands Email: M.Davarynejad@tudelft.nl Abstract—Gene association/interaction networks have complex structures that provide a better understanding of mechanisms at the molecular level that govern essential processes inside the cell. The interaction mechanisms are conventionally modeled by nonlinear dynamic systems of coupled differential equations (S- systems) adhering to the power-law formalism. Our implemen- tation adopts an S-system that is rich enough in structure to capture the dynamics of the gene regulatory networks (GRN) of interest. A comparison of three widely used population-based techniques, namely evolutionary algorithms (EAs), local best particle swarm optimization (PSO) with random topology, and artificial bee colony (ABC) are performed in this study to rapidly identify a solution to inverse problem of GRN reconstruction for understanding the dynamics of the underlying system. A simple yet effective modification of the ABC algorithm, shortly ABC* is proposed as well and tested on the GRN problem. Simulation results on two small-size and a medium size hypothetical gene regulatory networks confirms that the proposed ABC* is superior to all other search schemes studied here. I. I NTRODUCTION A genome-wide interaction analysis would open new hori- zons for biologists, providing a unique ubiquitous structural component of the genetic architecture of human diseases. Since many diseases are the result of polygenic and pleiotropic effects controlled by multiple genes, genome-wide interaction analysis are preferable over single locus study. The activation and inhibition of genes are governed by fac- tors within a cellular environment and outside of the cell. This level of activation and inhibition of genes are integrated by gene regulatory networks (GRNs), forming an organizational level in the cell with complex dynamics [7]. Mathematical modeling of gene is becoming popular in the post-genome era [18], [21], providing a powerful tool not only for the better understanding of such complex systems but also for developing new hypotheses on underlying mechanisms. The availability of high-throughput technologies provide time course expression data; and GRN model built by reverse engineering, may explain the data [24]. Model parameter estimation is a challenging task and is normally formulated as an optimization problem [27]. Based on gene expression data over time, these optimization techniques enable genetic network architectures to be reconstructed. In this studies, S- systems, a set of non-linear differential equations of a special form belonging to the power-law formalism are adopted as model. S-system based GRN inference was formulated by Tomi- naga et al. [28] as an optimization problem to minimize the difference between the model and the system. To optimize the network parameters and to capture the dynamics in gene expression data, they used standard evolutionary algorithms (EAs) to estimate the model parameters. Evolutionary compu- tation is becoming a popular approach for solving S-system parameter optimization [23], [3], [17], mainly due to the multimodality and strong non-linear parameter-dependencies in the problem. Extensive simulations were reported in [26] where the performance of different genetic and evolution- ary strategies are compared. [20] presents a hybrid genetic algorithm-particle swarm optimization method to infer appro- priate network parameters. The results are compared to that of standard PSO. To the best of our knowledge, this is the first attempt to evaluate the ABC algorithm for S-system parameter op- timization for GRN inference by reverse engineering of three gene networks. We have also proposed a simple modification to the ABC algorithm. Moreover, when comparing heuristic optimization methods, a PSO with random topology is adopted here. Numerical experiments show that the proposed enhance- ment on standard ABC algorithm attain higher accuracy and computational efficiency compared to that of EAs, PSO with random topology and the standard ABC. The remainder of this paper is organized as follows. A short introduction to GRNs and to S-systems is provided in Section II. The population based model for S-system parameter identification is presented in Section III with a short introduction to EA and PSO with random topology. ABC and ABC* (a simple yet effective modification on standard ABC algorithm) are presented in Section III-C and III-D respec- tively. Experimental setup adopted to check the suitability of ABC and ABC* for gene network estimation as well as a comparison with EA and PSO are presented in Section IV. The final section draws conclusions and considers implications for future research.