Network evaluation from the consistency of the graph structure with the measured data

A knowledge-based network, which is constructed by extracting as many relationships identified by experimental studies as possible and then superimposing them, is one of the promising approaches to investigate the associations between biological molecules. However, the molecular relationships change dynamically, depending on the conditions in a living cell, which suggests implicitly that all of the relationships in the knowledge-based network do not always exist. Here, we propose a novel method to estimate the consistency of a given network with the measured data: i) the network is quantified into a log-likelihood from the measured data, based on the Gaussian network, and ii) the probability of the likelihood corresponding to the measured data, named the graph consistency probability (GCP), is estimated based on the generalized extreme value distribution.

The plausibility and the performance of the present procedure are illustrated by various graphs with simulated data, and with two types of actual gene regulatory networks in Escherichia coli: the SOS DNA repair system with the corresponding data measured by fluorescence, and a set of 29 networks with data measured under anaerobic conditions by microarray. In the simulation study, the procedure for estimating GCP is illustrated by a simple network, and the robustness of the method is scrutinized in terms of various aspects: dimensions of sampling data, parameters in the simulation study, magnitudes of data noise, and variations of network structures. In the actual networks, the former example revealed that our method operates well for an actual network with a size similar to those of the simulated networks, and the latter example illustrated that our method can select the activated network candidates consistent with the actual data measured under specific conditions, among the many network candidates.

The present method shows the possibility of bridging between the static network from the literature and the corresponding measurements, and thus will shed light on the network structure variations in terms of the changes in molecular interaction mechanisms that occur in response to the environment in a living cell.