In this chapter, we have presented a study of the competitive ion binding on a highly charged globular polyelectrolyte with the exemplification of Mg2+ and Na+ ion-exchange on the G2-dPGS, studied using ITC. ITC measurements carried out at a range of dPGS, Na+and Mg2+ concentrations indicate a high Mg2+ sorption in a low c0++ range, while the saturation in binding occurs at a high c0++ range. The ITC binding isotherm is then compared and fitted with the theoretical binding models, viz., the PPB and the MMvH models, presented in chapter 5. There is a rapid ion-exchange during the initial stages of the titration, while the exchange slows down at the later stages when the dPGS is significantly charge renormalized. We ascertain that this ion-exchange is driven by Mg2+– dPGS electrostatic interaction, as well as the entropic gain due to the simultaneous release of previously bound Na+ cations, while the energetic effects due to solvation/desolvation are canceled out [134, 136, 142, 400, 401, 402].
However, it is clear that the biomolecular complexation/binding processes involving PE–ion, PE–PE systems are complex, and the ITC attempts to observe these processes, however, only indirectly by probing into the incremental heat exchange occurring during the binding equilibrium. In that sense, theoretical binding models such as the PPB and MMvH models take into account the microscopic interaction details, and thus are helpful
in meaningfully complimenting the ITC results. This perspective can help in the possible developments of more intricate binding models that are directly applicable to fit the ITC results.
7.1 Summary of the thesis
Dendritic PEs are known to be the emerging class of functional PEs, having attracted con-siderable interest in the scientific community in the last years, due to their versatility in bioapplications. In this thesis, we conducted a systematic characterization of the electro-static and hydration properties of the dendritic PEs in a monovalent salt, and described a competitive sorption of mono- vs. divalent counterions into highly charged globular PEs, with the exemplification of dPGS. The electrostatic properties of dPGS are quantified in terms of its effective charge and size, which are described with the help of both the simulations and well-established theoretical frameworks such as the Debye–Hückel theory and the concept of counterion condensation. Also, several theoretical models based on the standard PB, Donnan, Manning, Langmuir models are devised and discussed to describe the effective charge of dPGS during the competitive ionic sorption.
In particular, in the chapter4, owing to the charged renormalization of dPGS induced by the condensed counterions, we address the challenges of how to obtain a well-defined effective charge and surface potential of the dPGS for practical applications using the implicit- and explicit-solvent approaches applied to the explicit-water, AA MD computer simulations. Atomic specificity provides us a deeper insight into the effective pair inter-action between dPGS and counterions, and allows us to characterize dPGS by calculating the molecular distributions. Furthermore, explicit treatment of water allows us to ob-serve the equilibrium properties of the hydration structures around charged species, and rationalizing the energetics of dPGS–water interaction. To electrostatically characterize dPGS, we discuss well-known methods in the literature which are constructed for simple charged hard spheres with smooth surfaces, viz., Alexander prescription on the electro-static potential and on the counterion PMF obtained from simulation and the inflection point criterion. We find that the charge renormalization effect on dPGS strengthens with the generation, and consequently, effective charge has much weaker dependence on the dPGS generation than the bare charge. It is concluded that all approaches give consistent values for the effective charge and size but within an uncertainty window of the size of one water molecule. Furthermore, the nature of the dPGS–water interaction was studied. The PE–water interaction depends very specifically on the physicochemical properties of the interaction environment. It was found that there is a net repulsion between the dPGS and
water, which can be attributed to the hydrophobic dPGS scaffold and weakly attractive sulphate–water interaction compared to water–water interaction, due to the chaotropic nature of the monovalent sulphate groups.
Having completed the systematic depiction of the dPGS electrostatics in a monovalent salt, the growing number of its bioapplications highlight the importance to study its interactions with a mixture of mono- and divalent counterions, available in the in vivo environment, and the resultant competitive ion sorption. In the chapter4, we thus perform the explicit water, AA MD simulations of dPGS with Na+, Mg2+, and Cl - ions. Given that the conventional non-polarizable AA force-fields struggle to model multivalent ions, owing to their ability to polarize surrounding media [200,201,204,208], we evaluate the performances of several recently advanced divalent ion force-fields optimized to ensure a reasonable balance between ion–ion, ion–water and water–water interactions [201, 208, 217, 218] and their effect on the dPGS electrostatic attributes. While it is challenging to conclude the simulation results in a quantitative way due to the unavailability of the suitable benchmark properties from experiments, qualitative trends show that the effective charge and potential reach a saturation level as Mg2+ concentration increases, while the effective size remains unchanged.
In the chapter5, we tackle the same problem of the competitive ion sorption via theoret-ical modeling in a more generic fashion by representing dPGS as a part of highly charged globular PEs. We modify a few existing electrostatic binding theories such as Donnan, Langmuir, Manning and Poisson–Boltzmann approaches and present a few transferable ion binding models. We then inform these models via the coarse-grained computer simu-lation data, and use the models to predict the competitive ionic sorption for different salt concentrations and PEs of different sizes. Such knowledge can help predict the biological immune response to the PE, its metabolic fate, and the efficacy of the PE drug in different environments for biomedical and biotechnological applications. In particular, we present the novel two-state discrete binding site model for a binary heterogeneous ligand system with a reasonable accuracy and a computational advantage over the standard PB theory and simulations.
In the chapter 6, we now use the opportunity to utilize the binding models presented in the chapter 5to quantitatively rationalize the isotherms of the competitive binding of Mg2+ and Na+ cations to dPGS, obtained via ITC experiments. Here, the ITC obtained information in the form of the heat signals as a function of the Mg2+ concentration are mapped to the number of bound counterions and the effective charge of dPGS. It is found that there is a rapid ion-exchange during the initial stages of the titration. The driving
force behind this is attributed to the presence of unoccupied dPGS binding sites and the entropy gain in the release of Na+ cations. The ion-exchange slows down in the later stages of titration, when the dPGS is significantly charge renormalized.