Random copolymers, crosslinked thin films of the random copolymers and cell culture substrates comprising the crosslinked thin films are provided. Also provided are methods of making and using the copolymers, thin films and substrates. The copolymers are polymerized from glycidyl methacrylate monomers and vinyl azlactone monomers. The crosslinked thin films are substrate independent, in that they need not be covalently bound to a substrate to form a stable film on the substrate surface.