We use molecular dynamics (MD) simulation to study the adsorption and desorption of two widely different proteins, bovine serum albumin (BSA) and lysozyme, on a graphite surface. The adsorption is modeled using accelerated MD to allow the proteins to find optimum conformations on the surface. Our results demonstrate that the "hard protein" lysozyme retains much of its secondary structure during adsorption, whereas BSA loses it almost completely. BSA has a considerably larger adsorption energy compared to that of lysozyme, which does not scale with chain length. Desorption simulations are carried out using classical steered MD. The BSA molecule becomes fully unzipped during pull-off, whereas several helices survive this process in lysozyme. The unzipping process shows up in the force distance curve of BSA as a series of peaks, whereas only a single of few, depending on protein orientation, force peaks-occur for lysozyme. The maximum desorption force is larger for BSA than for lysozyme, but only by a factor of about 2.3.