A microbial infection in an eye of a subject is treated or prevented by topically administering to the eye an effective amount of a macromolecule or a pharmaceutically acceptable salt thereof that includes a dendrimer of 1 to 8 generations with one or more sulfonic acid- or sulfonate-containing moieties attached to one or more surface groups of the outermost generation of the dendrimer. Compositions containing the macromolecule or salt are useful in these methods.