Metal-organic frameworks (MOFs) provide new possibilities for their potential use in catalysis, gas storage/separation, and drug delivery. In this work, a computational study is performed on the interaction of biologically important organic molecules such as caffeine, urea, niacin, and glycine with the undercoordinated copper centers of the HKUST-1 MOF. Density functional theory calculations are used to identify the adsorption sites of the organic molecules in HKUST-1 and to calculate their interaction energies. Two types of interactions are calculated: (i) strong binding via their nitrogen or oxygen atoms with the copper atoms of the paddlewheel and (ii) hydrogen bonds with the carboxylate groups of the MOF. Certain molecules such as caffeine and niacin can interact simultaneously with more than two paddlewheels, thus making the interactions even stronger. The interaction energies vary from 75 kJ mol-1 for glycine to 200 kJ mol-1 for caffeine. The confinement of the guest molecules in the cage windows of the framework can also create strong interactions. To take into account the effect of coordination with multiple paddlewheels, a very large model of the HKUST-1 needs to be used. The numbers of (i) copper sites interacting with the guest molecule and (ii) hydrogen bonds between the carboxylate groups of the MOF and the guests have a major impact on binding strength. This is important information when applying rational design to create new MOFs that should serve as drug carriers.