We explore the separation of aqueous protein - polysaccharide solutions into two liquid phases. In particular, we have studied the combinations beta-lactoglobulin/pullulan, alpha-lactalbumin/pullulan, and other examples from the literature under a variety of conditions such as varying salt content, pH (in most cases at the isoelectric point), and protein radius. We restrict ourselves to relatively small proteins (globular) and long polysaccharide chains, The mechanism behind the phase separation is explained in terms of the depiction interaction (i.e., the cross-interaction) in a suspension of small spheres (proteins) immersed in a semidilute solution of coils (polysaccharide) forming an entangled network. Weak, attractions between the spheres have been taken into account by assuming the formation of small clusters. As a general rule, we Find that the depletion free energy per protein particle governing the protein partitioning in the phase equilibrium is linear in the polysaccharide concentration over the whole range of experimentally accessible coexistence curves. Furthermore, the proportionality constant is shown to be a very useful quantity to understand the characteristics of the coexistence curves. The linearity thus found is supported by theoretical arguments developed by de Gennes and Odijk.