Non-covalent polymer–protein conjugation is emerging as a potential route to improve pharmacokinetics and pharmacodynamics of protein therapeutics. In this study, a family of structurally related block copolymers of mPEG_2k – poly(glutamic acid) with linear A-B (mPEG_2k-lin-polyGA) and miktoarm A-B₃ (mPEG_2k-mik-(polyGA)₃) structure was synthesised by N-carboxyanhydride (NCA) ring-opening polymerisation to assess the effect of macromolecular topology of the copolymers on polymer–protein complexation. The data illustrate that the synthesised copolymers are capable of complexing a model protein, lysozyme, at optimal pH conditions through non-covalent interactions, with complexation efficiencies depending on the copolymers composition and molecular architecture. In native gel electrophoresis experiments, linear mPEG_2k-lin-GA₁₀ copolymer, possessing a short polyanionic polyGA block, shows a low level of complexation, which does not change when the number of polyGA branches of the same size is increased, using a miktoarm mPEG_2k-mik-(GA₁₀)₃ copolymer. However, enhanced complexation is observed when the same number of ionisable GA units (30) are displayed on a linear macromolecular scaffold; mPEG_2k-mik-(GA₁₀)₃vs. mPEG_2k-lin-GA₃₀. Again complexation efficiency did not increase when the number of complexing polyGA branches were increased; mPEG_2k-lin-GA₃₀ vs. mPEG_2k-mik-(GA₃₀)₃. Nanoparticle tracking analysis (NTA) showed that the copolymer–protein complexes possessed hydrodynamic diameters in the 50–200 nm range, suggesting a degree of control in the assembly process. Sequestration of lysozyme within polymer complexes resulted in a decrease in its apparent enzymatic activity, which was re-established on the complexes dissociation upon a treatment with competitive complexant. Intrinsic fluorescence and circular dichroism (CD) studies suggested structural conformation of the protein was not altered following complexation with mPEG_2k-polyGA copolymers. Taken together, these results provide an initial structure–function relationship for protein-complexing mPEG_2k-polyGA copolymers with variable macromolecular topology, opening the way for their future application in biological and biomedical studies.