The identifiability of gene regulatory networks: the role of observation data.

Identifying gene regulatory networks (GRN) from observation data is significant to understand biological systems. Conventional studies focus on improving the performance of identification algorithms. However, besides algorithm performance, the GRN identification is strongly depended on the observation data. In this work, for three GRN S-system models, three observation data collection schemes are used to perform the identifiability test procedure. A modified genetic algorithm-particle swarm optimization algorithm is proposed to implement this task, including the multi-level mutation operation and velocity limitation strategy. The results show that, in scheme 1 (starting from a special initial condition), the GRN systems are of identifiability using the sufficient transient observation data. In scheme 2, the observation data are short of sufficient system dynamic. The GRN systems are not of identifiability even though the state trajectories can be reproduced. As a special case of scheme 2, i.e., the steady-state observation data, the equilibrium point analysis is given to explain why it is infeasible for GRN identification. In schemes 1 and 2, the observation data are obtained from zero-input GRN systems, which will evolve to the steady state at last. The sufficient transient observation data in scheme 1 can be obtained by changing the experimental conditions. Additionally, the valid observation data can be also obtained by means of adding impulse excitation signal into GRN systems (scheme 3). Consequently, the GRN systems are identifiable using scheme 3. Owing to its universality and simplicity, these results provide a guide for biologists to collect valid observation data for identifying GRNs and to further understand GRN dynamics.