The coiled-coil forming peptides 'K' enriched in lysine and 'E' enriched in glutamic acid have been used as a minimal SNARE mimetic system for membrane fusion. Here we describe atomistic molecular dynamics simulations to characterize the interactions of these peptides with lipid bilayers for two different compositions. For neutral phosphatidylcholine (PC)/phosphatidylethanolamine (PE) bilayers the peptides experience a strong repulsive barrier against adsorption, also observed in potential of mean force (PMF) profiles calculated with umbrella sampling. For peptide K, a minimum of -12 kBT in the PMF provides an upper bound for the binding free energy whereas no stable membrane bound state could be observed for peptide E. In contrast, the electrostatic interactions with negatively charged phosphatidylglycerol (PG) lipids lead to fast adsorption of both peptides at the head-water interface. Experimental data using fluorescently labeled peptides confirm the stronger binding to PG containing bilayers. Lipid anchors have little effect on the peptide-bilayer interactions or peptide structure, when the peptide also binds to the bilayer in the absence of a lipid anchor. For peptide E, which does not bind to the PC bilayer without a lipid anchor, the presence of such an anchor strengthens the electrostatic interactions between the charged side chains and the zwitterionic head-groups and leads to a stabilization of the peptide's helical fold by the membrane.