Conclusions
In this paper, we developed a novel approach to restore original GRNs to be consistent with time-course mRNA expression data based on the combinatorial transcription model. Since we applied a state space representation with the nonlinear system equation in the context of data assimilation, the conditional distributions of the hidden variables can be non-Gaussian distributions. In contrast to the previous approaches using particle filter, Gaussian approximation and regression-based solutions, our proposed approach, HMEnPF, can retain the first, second, third central and fourth central moments through filtering steps to estimate near optimal parameter values by the EM-algorithm.
According to the comparison results using six synthetic data based on the real biological pathways, the proposed algorithm successfully explored better models than the previous methods, G1DBN and GeneNet, considering linear relevance. Moreover, the proposed algorithm using HMEnPF outperformed that of using UKF. This concludes that HMEnPF retaining parts of higher moment information can improve the accuracy of the estimation of the parameter values beyond unscented approximation (that cannot retain any moment through filtering steps based on Gaussian approximation). Through the experimental results, we also observed that the performance of the restoration algorithm strongly depends on the original network, which was prepared by literature information or some GRNs inference methods. Thus, one of significant points is to select methods to infer the original network. On the other hand, the proposed method has some limitations. For example, we require time-course data in which the number of time points should be more than 10 or so. Moreover, due to its heavy computational costs, the calculation for more than 20−30 genes without TF information can be infeasible.
As an application example, we prepared corticosteroid pharmacogenomic pathways in rat skeletal muscle that have been investigated and established a part of regulatory relationships and related genes. Additionally, the intracellular concentration of corticosteroid that directly/indirectly affects gene expression can be obtained by the previously developed differential equations and TF information for rat genes can also be utilized. In summary, we inferred the regulatory relationships among 40 genes and corticosteroid with fixing the established pathways and restricting that only TF candidates can regulate other genes. G1DBN was employed to construct the original model for the proposed algorithm. Consequently, several combinatorial regulations and regulations by corticosteroid were inferred by extending the original network. Since previous linear models may not be able to infer these regulations, the proposed algorithm can be valuable to restore inferred and literature-based networks to be consistent with the data.