The high concentration of macromolecules (i.e., macromolecular crowding) in cellular environments leads to large quantitative effects on the dynamic and equilibrium biological properties. These effects have been experimentally studied using inert macromolecules to mimic a realistic cellular medium. In this paper, two different experimental in vitro systems of diffusing proteins which use dextran macromolecules as obstacles are computationally analyzed. A new model for dextran macromolecules based on effective radii accounting for macromolecular compression induced by crowding is proposed. The obtained results for the diffusion coefficient and the anomalous diffusion exponent exhibit good qualitative and generally good quantitative agreement with experiments. Volume fraction and hydrodynamic interactions are found to be crucial to describe the diffusion coefficient decrease in crowded media. However, no significant influence of the hydrodynamic interactions in the anomalous diffusion exponent is found.