2025

Butovych Halyna

This thesis is devoted to the study of complex formation in polymer-enzyme mixtures and the chelate structures of heavy metal ions. The binding of enzyme molecules to polymer chain scaffolds, which plays an important role in biocatalytic processes during biofuel production, was investigated using a coarse-grained model and computer simulations based on Langevin dynamics. The formation of heavy metal chelation complexes in an aqueous environment, relevant to wastewater treatment, was studied at the atomistic level using classical molecular dynamics (MD) and by quantum-chemical modelling using the density functional theory (DFT). The thesis consists of four chapters and is organised as follows: a literature review, a study of polymer-enzyme complex formation, an investigation of mercury ion chelation by linear polyethyleneimine (PEI) in an aqueous solution, and an analysis of the chelation of heavy metal ions by ethylenediaminetetraacetic acid (EDTA). Chapter 1 reviews the literature addressing the problems that are central to this thesis, the methods used to tackle them, and the progress achieved in the respective research areas. Chapter 2 introduces a coarse-grained model and the theoretical approach to describing complexation in a polymer-enzyme system, represented as patchy chains and patchy monomers. This system is effectively described using a modified version of Wertheim’s first-order thermodynamic perturbation theory. The calculated degrees of binding between polymer and enzyme molecules as a function of the enzyme concentration at two temperatures show that the proposed theoretical mod6 ification significantly improves the predictions compared to the unmodified version. Computer simulations performed using Langevin dynamics at different parameters confirm an accuracy of the theory, while also highlighting its limitations in the case of closely functionalised chains. A particular feature of this study is the analysis of how the arrangement of functional groups, either at the intermediate or at the terminal monomers of the polymer chain, affect enzyme binding. It is shown that accounting for this factor is essential for the accurate description of complex formation within the proposed theoretical approach. Since the model is suitable for describing polymer-enzyme conjugates, it may be applied to computer simulations in the field of biofuel production, for example, to optimise industrial process parameters. Moreover, the model is adaptable to other types of macromolecular hybrids, provided the interaction parameters are appropriately chosen. The theoretical approach used in this study allows for similarly accurate yet computationally inexpensive predictions. Chapter 3 investigates the chelation of mercury ions (Hg2+) by polyethyleneimine (PEI) in an aqueous solution. For linear, electroneutral PEI chains of varying lengths (4, 5, and 10 nitrogen-containing units), the structures and stability of the formed PEI-Hg complexes were analysed. To this end, MD simulations were performed under ambient conditions, and DFT calculations were used to refine the chelate structures and validate the MD results. This approach yielded detailed atomic structures of the complexes, allowing the calculation of characteristic distances between Hg ions and nitrogen atoms in PEI, as well as between Hg ions and water molecules in the first coordination shell. Conformational features of the polymer were also evaluated based on nitrogen-nitrogen distances. The effect of the PEI chain length on mercury chelation and multi-ion binding to a single PEI chain were investigated. Complex stability was evaluated based on adsorption energy values obtained from both MD and DFT calculations. It was shown that linear PEI forms stable complexes with mercury ions, and the PEI chain with five nitrogen-containing units demonstrated the highest stability. These findings enhance our understanding of the chelating properties of PEI and