We present a model describing the binding of biological signaling proteins to highly charged polymer networks. The networks are formed by polyelectrolyte chains for which the distance between two charges at the chain is smaller than the Bjerrum length. Counterion condensation on such highly charged chains immobilizes a part of the counterions which do no more contribute to the osmotic pressure. The Donnan-equilibrium between the polymer network and the aqueous solution with salt concentration csb is used to calculate the salt concentration of the co- and counterions csg entering the network. Two factors lead to adsorption of proteins to charged polymer networks: i) The electrostatic interaction between the network and the protein is given by the Donnan-potential of the network and the net charge of the protein. In addition to this leading term, a second term describes the change of the Born-energy of the proteins when entering the network. ii) The interaction of the protein with the highly charged chains within the network is governed by counterion release: Patches of positive charge at the protein become multivalent counterions of the polyelectrolyte chains thus releasing a concomitant number of condensed counterions. The model is compared to experimental data obtained on a set of biohybrid polymer networks composed of crosslinked glycosaminoglycan chains that interact with a mixture of key signaling proteins. The analysis of the experimental binding constants reveals that the counterion release mechanism is decisive for protein adsorption to the network at physiological salt concentration.
