Computer simulations of polymer-enzyme complexes and chelate structures of heavy metal ions

Abstract

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 may be used in designing functional nanomaterials based on PEI for efficient mercury ion removal from aqueous environments.

Chapter 4 focuses on the mechanisms of heavy metal chelation by ethylenediaminetetraacetic acid (EDTA) in water under ambient conditions. It begins with an investigation of the structure and stability of mercury-EDTA complexes depending on the protonation state of the ligand. This is followed by a comparison of the structural features and stability of EDTA complexes with the divalent heavy metal ions Hg2+, Cd2+, and Pb2+, which are extremely toxic even in very low doses. It is shown that EDTA binds most effectively to metal ions when it is fully deprotonated, which occurs in alkaline environments. As acidity increases, protons bind to EDTA’s carboxyl groups, weakening its chelating ability. Similarly to the PEI case, the study involved MD simulations and quantum-chemical DFT calculations. MD simulations enabled the formation and analysis of chelate complexes and the estimation of their adsorption energy. The configurations of these complexes were then refined using DFT optimisations based on several approximations, enabling also the calculation of the Gibbs free energy of complexation. The results were compared with experimental data available in the literature and analysed in the context of other theoretical studies. The strong dependence of EDTA’s chelating ability on its protonation state enables the pH control of complex formations with metal ions. This approach has potential applications in various technological processes, including wastewater treatment, the chemical industry, and medicine.

To summarise, this study improves the understanding of the mechanisms underlying heavy metal ion chelation in aqueous environments and enables the prediction of binding degrees in polymer-enzyme systems. The findings provide valuable insights for both fundamental studies and practical applications, for example, in the removal of toxic elements from water and in enhancing the efficiency of biocatalysis during biofuel production from cellulosic biomass. Based on this work, two research articles, a preprint, and three conference presentations have been produced.