There is a growing appreciation that mechanical signals can be as important as chemical and electrical signals in biology. To include such signals in a systems biology description for understanding pathobiology and developing therapies, quantitative experiments on how solution-phase and surface chemistry together produce biologically relevant mechanical signals are needed. Because of the appearance of drug-resistant hospital 'superbugs', there is currently great interest in the destruction of bacteria by bound drug-target complexes that stress bacterial cell membranes. Here, we use nanomechanical cantilevers as surface-stress sensors, together with equilibrium theory, to describe quantitatively the mechanical response of a surface receptor to different antibiotics in the presence of competing ligands in solution. The antibiotics examined are the standard, Food and Drug Administration-approved drug of last resort, vancomycin, and the yet-to-be approved oritavancin, which shows promise for controlling vancomycin-resistant infections. The work reveals variations among strong and weak competing ligands, such as proteins in human serum, that determine dosages in drug therapies. The findings further enhance our understanding of the biophysical mode of action of the antibiotics and will help develop better treatments, including choice of drugs as well as dosages, against pathogens.