gNCA: A framework for determining transcription factor activity based on transcriptome: identifiability and numerical implementation

Network Component Analysis (NCA) is a network structure-driven framework for deducing regulatory signal dynamics. In contrast to classical approaches such as principal component analysis or independent component analysis, NCA makes use of the connectivity structure from transcriptional regulatory networks to restrict the decomposition to a unique solution. However, the existing version of NCA cannot incorporate information beyond the network topology such as information obtained from regulatory gene knockouts that constrain the dynamics of regulatory signals. The ability of incorporating such information enables a more accurate and self-consistent analysis over different experiments and extends NCA to systems that may not satisfy the identifiability criteria of NCA. In this paper, we derive a generalized form of NCA, gNCA, which significantly expands the capability of transcription network analysis by incorporating regulatory signal constraints arising from genetic knockouts. The theoretical bases including criteria for uniqueness of solution and distinguishability between networks are derived. In addition, numerical techniques for robust decomposition are discussed. gNCA is then demonstrated using an Escherichia coli wild-type strain and an isogenic arcA deletion mutant during a carbon source transition.