Indeterminacy of reverse engineering of Gene Regulatory Networks: the curse of gene elasticity

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. A number of reverse engineering approaches have been developed to help uncover the regulatory networks giving rise to the observed gene expression profiles. However, this is an overspecified problem due to the fact that more than one genotype (network wiring) can give rise to the same phenotype. We refer to this phenomenon as "gene elasticity." In this work, we study the effect of this particular problem on the pure, data-driven inference of gene regulatory networks.

We simulated a four-gene network in order to produce "data" (protein levels) that we use in lieu of real experimental data. We then optimized the network connections between the four genes with a view to obtain the original network that gave rise to the data. We did this for two different cases: one in which only the network connections were optimized and the other in which both the network connections as well as the kinetic parameters (given as reaction probabilities in our case) were estimated. We observed that multiple genotypes gave rise to very similar protein levels. Statistical experimentation indicates that it is impossible to differentiate between the different networks on the basis of both equilibrium as well as dynamic data.

We show explicitly that reverse engineering of GRNs from pure expression data is an indeterminate problem. Our results suggest the unsuitability of an inferential, purely data-driven approach for the reverse engineering transcriptional networks in the case of gene regulatory networks displaying a certain level of complexity.