Inferring gene regulatory networks using pre- and post-perturbation data

The inference of biological networks is essential for understanding the complex regulations among biomolecules. Jacobian matrices serve as an effective means for uncovering network topologies by providing linear approximations of nonlinear regulations. Reconstructing Jacobian matrices often requires integrating experimental data with mathematical modeling techniques. A significant challenge is determining the type of experimental data required and the adequate amount of data to accurately reconstruct the Jacobian matrices. In this paper, we employ multiple pre- and post-perturbation data to infer the Jacobian matrices with the help of Taylor expansions. Furthermore, we integrate the expansions with differential approximations of the partial derivative to offer supplementary information. These data enable accurate inference of not only the signs and directions of regulations but also the strength of self-feedback in both steady-state and oscillatory systems. Comparative analysis reveals that incorporating differential approximations can significantly improve the accuracy of inference.