Recent experiments showed significant adsorption of bovine serum albumin (BSA) in spherical polyelectrolyte brushes (SPB) consisting of polyacrylic acid, even for pH values above the isoelectric point of the protein, when both protein and polyion are negatively charged. To describe these experimental findings theoretically, we have constructed a spherical box model for an annealed brush consisting of a weak polyelectrolyte that includes the adsorption of BSA. At equilibrium the chemical potential of BSA in solution equals that at each location in the brush, while the net force on the polyions (including osmotic, stretching, and excluded volume terms) is zero at each location. Protein adsorption is predicted above the isoelectric point and -in agreement with experimental data- is a strong function of ionic strength and pH. Adsorption of protein in the brush is possible because the pH in the brush is below the isoelectric point and protein reverses its charge from negative to positive when it adsorbs.