The adsorption of proteins on nanoparticles results in the formation of the protein corona, the composition of which determines how nanoparticles influence their biological surroundings. We seek to better understand corona formation by developing models that describe protein adsorption on nanoparticles using computer simulation results as data. Using a coarse-grained protein model, discontinuous molecular dynamics simulations are conducted to investigate the adsorption of two small proteins (Trp-cage and WW domain) on a model nanoparticle of diameter 10.0 nm at protein concentrations ranging from 0.5 to 5 mM. The resulting adsorption isotherms are well described by the Langmuir, Freundlich, Temkin and Kiselev models, but not by the Elovich, Fowler-Guggenheim and Hill-de Boer models. We also try to develop a generalized model that can describe protein adsorption equilibrium on nanoparticles of different diameters in terms of dimensionless size parameters. The simulation results for three proteins (Trp-cage, WW domain, and GB3) on four nanoparticles (diameter = 5.0, 10.0, 15.0, and 20.0 nm) illustrate both the promise and the challenge associated with developing generalized models of protein adsorption on nanoparticles.