Network inference by combining biologically motivated regulatory constraints with penalized regression

Reconstructing biomolecular networks from time series mRNA or protein abundance measurements is a central challenge in computational systems biology. The regulatory processes behind cellular responses are coupled and nonlinear, leading to rich dynamical behavior. One class of reconstruction algorithms uses regression and penalized regression to impose sparseness on the solution, as requested biologically. Motivated by the five-gene challenge in the Dialogue for Reverse Engineering Assessments and Methods 2 (DREAM2) contest, we extend and test penalized regression schemes both on data from simulations and real qPCR measurements. The methods showing best performance are the Adaptive Ridge (AR) regression and a new extension thereof, in which we impose a biological constraint to the reconstructed network. Specifically, we request from the solutions that the outgoing links have the same regulatory sign, which is a reasonable approximation for most prokaryotic transcriptional networks. In other words, a given regulator must be either an activator or a repressor but not both. The constraints can be implemented with quadratic programming, and we show that this improves the reconstruction performance significantly. While linear models are not sufficiently general to encompass most complex behaviors, they offer powerful tools for network reconstruction, particularly for systems operating near a steady state. In particular, the optimization problems are well behaved and methodologies allow finding global optima efficiently. Adding constraints reflecting biological circuit designs is one of the most important aspects of network inference. We propose one such constraint, namely the consistency in the signs of outgoing links, which will facilitate the inference of transcriptional regulatory networks.