Polymerization of methyl methacrylate (MMA) in aqueous collagen (Col) dispersion was studied in the presence of tributylborane (TBB) andp-quinone: 2,5-di-tert-butyl-p-benzoquinone (2,5-DTBQ),p-benzoquinone (BQ), duroquinone (DQ), andp-naphthoquinone (NQ). It was found that this system leads to the formation of a grafted cross-linked copolymer. The inhibitory effect ofp-quinone determines the amount of unreacted monomer, homopolymer, and percentage of grafted poly(methyl methacrylate) (PMMA). The synthesis combines two approaches to form a grafted copolymer with a cross-linked structure—“grafting to” and “grafting from”. The resulting products exhibit biodegradation under the action of enzymes, do not have toxicity, and demonstrate a stimulating effect on cell growth. At the same time, the denaturation of collagen occurring at elevated temperatures does not impair the characteristics of copolymers. These results allow us to present the research as a scaffold chemical model. Comparison of the properties of the obtained copolymers helps to determine the optimal method for the synthesis of scaffold precursors—synthesis of a collagen and poly(methyl methacrylate) copolymer at 60 °C in a 1% acetic acid dispersion of fish collagen with a mass ratio of the components collagen:MMA:TBB:2,5-DTBQ equal to 1:1:0.015:0.25.