This paper uses a newly developed and extended formal quantum chemical method in an attempt to advance the knowledge of the relationship between the variation of several local atomic descriptors of the electronic structure of a set of pyrido[2,3-d]pyrimidine analogues and the variation of their inhibitory potencies in genotypes 1a and 1b hepatitis C virus (HCV) replicon assays and cytotoxicity in Huh-7 cells. Despite the lack of knowledge of the mechanism(s) of inhibition of the HCV replicons and of Huh-7 cell proliferation good quantitative structure-activity relationships (QSAR) were obtained for all biological activities studied. The equations relating structure and inhibitory capacity for 1a and 1b genotypes HCV replicons seem to be quite similar and involve mainly empty molecular orbitals localized on very specific atoms of the drugs. In the case of the cytotoxicity against Huh-7 cells the corresponding equation contains only contributions from occupied molecular orbitals localized on another set of specific atoms of the drugs. On the basis of our results a concrete atomic site is proposed as target to modify the biological activities.