A generalized framework for network component analysis

The authors recently introduced a framework, named network component analysis (NCA), for the reconstruction of the dynamics of transcriptional regulators' activities from gene expression assays. The original formulation had certain shortcomings that limited NCA's application to a wide class of network dynamics reconstruction problems, either because of limitations in the sample size or because of the stringent requirements imposed by the set of identifiability conditions. In addition, the performance characteristics of the method for various levels of data noise or in the presence of model inaccuracies were never investigated. In this article, the following aspects of NCA have been addressed, resulting in a set of extensions to the original framework: 1) The sufficient conditions on the a priori connectivity information (required for successful reconstructions via NCA) are made less stringent, allowing easier verification of whether a network topology is identifiable, as well as extending the class of identifiable systems. Such a result is accomplished by introducing a set of identifiability requirements that can be directly tested on the regulatory architecture, rather than on specific instances of the system matrix. 2) The two-stage least square iterative procedure used in NCA is proven to identify stationary points of the likelihood function, under Gaussian noise assumption, thus reinforcing the statistical foundations of the method. 3) A framework for the simultaneous reconstruction of multiple regulatory subnetworks is introduced, thus overcoming one of the critical limitations of the original formulation of the decomposition, for example, occurring for poorly sampled data (typical of microarray experiments). A set of Monte Carlo simulations we conducted with synthetic data suggests that the approach is indeed capable of accurately reconstructing regulatory signals when these are the input of large-scale networks that satisfy the suggested identifiability criteria, even under fairly noisy conditions. The sensitivity of the reconstructed signals to inaccuracies in the hypothesized network topology is also investigated. We demonstrate the feasibility of our approach for the simultaneous reconstruction of multiple regulatory subnetworks from the same data set with a successful application of the technique to gene expression measurements of the bacterium Escherichia coli.