Nanometer-scale hydrogels are formed from a polymer film by exposing said film to a focused electron beam of 1 to 10 nm diameter. The hydrogels may be formed in regular patterns, such as arrays, or in irregular patterns. The hydrogels have a plurality of functional groups that can form covalent bonds with proteins while preserving the natural functionality of the proteins. Such functionalized nanohydrogels may serve as a substrate for attachment of other proteins or cells, or may be used in other biological applications.