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Mesoporous polymer networks were prepared via the cross-linking radical copolymerization of non-toxic hydrophilic N-vinylpyrrolidone (VP) with triethylene glycol dimethacrylate (TEGDM) and poly(ethylene glycol) methyl ester methacrylate (PEGMMA) in bulk, using appropriate soluble and thermodynamically compatible macromolecular additives with a branched structure as porogens. The branched copolymers of various monomer compositions were obtained by radical copolymerization in toluene, controlled by 1-decanethiol, and these materials were characterized by a wide set of physical chemical methods. The specific surface areas and surface morphology of the polymer networks were determined by nitrogen low-temperature adsorption or Rose Bengal (RB) sorption, depending on the copolymer compositions and scanning electron microscopy. The electrochemical properties of RB before and after its encapsulation into a branched VP copolymer were studied on a glassy carbon electrode and the interaction between these substances was observed. Quantum chemical modeling of RB-VP or RB-copolymer complexes has been carried out and sufficiently strong hydrogen bonds were found in these systems. The experimental and modeling data demonstrate the high potency of such mesoporous polymer networks as precursors of molecularly imprinted polymers for the recognition of fluorescent dyes as nanomarkers for biomedical practice.