Some membrane-active peptides undergo drastic changes of conformation and/or orientation on water-lipid interfaces. Among the most notable examples is penetratin (pAntp), a short cell-penetrating peptide. To delineate the driving forces behind pAntp-membrane interactions, we used, in this series of two papers, a combined modeling approach that includes: (1) molecular dynamics simulations of pAntp in zwitterionic and anionic lipid bilayers, (2) free energy perturbation calculations of model residue-residue contacts, and (3) detailed analysis of spatial hydrophobic/hydrophilic properties of the peptide/membrane systems. In this first article, we consider the role of conformational plasticity of the peptide in different membrane surroundings, as well as the ability of pAntp to form stable specific residue-residue interactions and make contacts with particular lipids. It was shown that pAntp displays a complicated conformational behavior. Basic and aromatic residues of the peptide form energetically favorable pairs in water and apolar environments, which facilitate membrane insertion of the peptide and stabilization of the membrane-bound state. These residues are also capable of "trapping" lipid heads, thereby affecting their dynamics and microscopic organization of the water-lipid interface. The latter effect is much more pronounced in anionic bilayers and might be related to the initial stage of peptide-induced destabilization of lipid bilayers.