A model describing the binding of biological signaling proteins to highly charged polymer networks is presented. 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. The Donnan-equilibrium between the polymer network and the aqueous solution with salt concentration is used to calculate the salt concentration of the co- and counterions entering the network. Two factors are decisive: 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 in 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 compares favorably 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.
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