The core structure of pentaerythritol has been used as a replacement for one or both sugars in lipid A, leading to the generation of a series of lipid A analogs. These lipid A analogs may further differ from lipid A with respect to, e.g., the number, nature and location of negatively charged groups, and the number, nature and location of the lipid chains. The lipid A analogs may be lipid A agonists useful as immunostimulatory agents, or lipid A antagonists useful in the treatment of septic shock. In a like manner, a residue of pentaerythritylamine may be used as a replacement for an amino sugar residue in a carbohydrate ligand having a biological activity of interest, generating a series of ligand analogs. These are useful, e.g., as haptens, inhibitors of bacterial-host cell adhesion, etc.