At the moment two competing explanations exist for the experimental finding that net negatively charged proteins adsorb on or absorb in negatively charged polyelectrolyte brushes. One explanation is based on the possibility of charge regulation. The idea is that a protein can reverse its charge when it is in the presence of the high electrostatic potential of the brush and then can be inserted. The other explanation relies on the charge anisotropy of proteins, that is, that it carries positively charged and negatively charged patches. The positively charged region gains more energy from interacting with the negative brush than the negative charged patch loses, especially when the charge densities and electrostatic potentials are high, thus providing a net attraction. We present a model in which both mechanisms are combined. We confirm that both charge anisotropy and charge regulation effects on their own can be responsible for protein uptake at the "wrong" side of the isoelectric point (IEP). In addition, we find that the respective effects are additive. Indeed, taking both effects into account results in a stronger attraction between a PE brush and protein at the IEP, and the attraction is found further above the IEP than the individual effects would have made possible. Still, for patchiness to have a strong contribution, the patches need very high charge densities. Therefore, we argue that for most types of protein charge reversal will be the main driving force for adsorption on the wrong side of the IEP, while patchiness will contribute less.