Inferring algebraic gene networks using local decoding

Modeling the coupled dynamics of gene expression patterns is an important task in systems biology. It is most accurately performed via systems of coupled differential equations, derived by analyzing involved biochemical reactions of the cell cycle (bottom-up approach). Probabilistic Boolean networks (PBN) represent stochastic extensions of Boolean models [5, 7] that allow inference by reverse engineering from a given data set (top-down approach). In a PBN, a list of Boolean functions is associated with each node in the network, and each time the state of a gene is updated, only one of these functions is randomly chosen to compute the new state of the gene [7]. Recently [1], we presented a constructive approach for reverse engineering gene expression dynamics casted within the algebraic framework developed in [6] that can be seen as a generalization of PBN. We showed that, in a probabilistic framework, reverse engineering under this model is closely related to problems arising in coding theory. In particular, we applied list-decoding of Reed-Muller codes to address randomness, measurement errors, and small sample size issues. In this contribution we show how the concept of local decoding can be used to reduce the decoding complexity and aid experimental design.