We present a weighted-LASSO method to infer the parameters of a first-order vector auto-regressive model that describes time course expression data generated by directed gene-to-gene regulation networks. These networks are assumed to own prior internal structures of connectivity which drive the inference method. This prior structure can be either derived from prior biological knowledge or inferred by the method itself. We illustrate the performance of this structure-based penalization both on synthetic data and on two canonical regulatory networks (the yeast cell cycle regulation network and the E. coli S.O.S. DNA repair network).