Interaction of Lysozyme with a Dendritic Polyelectrolyte: Quantitative Analysis of the Free Energy of Binding and Comparison to Molecular Dynamics Simulations.

We present a comprehensive analysis of the energetics of the binding of lysozyme to dendritic polyglycerolsulfate (dPGS) in aqueous solution. This system is a perfect model for studying the interaction of proteins with polyelectrolytes. We discuss and model the free energy of binding ΔGb = -kBT ln Kb as the function of the two decisive variables, namely, the salt concentration cs and the temperature T. The system lysozyme/dPGS exhibits a strong enthalpy-entropy compensation throughout the entire range of temperature, similar to the one observed for the interaction of DNA with various proteins. Following a suggestion of Dragan et al. [Eur. Biophys. J. 2017, 46, 301], the free energy ΔGb can be split up into ΔGb = ΔGres + ΔGci, where ΔGci denotes the part due to counterion release, whereas ΔGres is the part obtained by extrapolation of ΔGb to 1 M salt concentration. Plots of dlog Kb/dlog cs lead to perfectly straight lines that can be extrapolated to cs = 1 M in order to obtain ΔGres. Both ΔGres and ΔGci can be independently obtained by implicit solvent molecular dynamics simulations made up to salt concentrations of 1 M. Good agreement of the experiment and simulation within prescribed limits of error is found. Moreover, ΔGres is shown to be caused by direct unscreened electrostatic contacts or salt bridges between dPGS and lysozyme. Because ΔGci = -TΔSci where ΔSci is the entropy due to counterion release, the entire binding entropy ΔSb can be split up as ΔSb = ΔSci + ΔSres. Plots of the binding enthalpy ΔHb versus ΔSres lead to a perfect master curve for the system dPGS/lysozyme. These findings suggest that the strong enthalpy-entropy cancellation found for this system is an entirely nonelectrostatic phenomenon solely due to solvation or desolvation by water. Thus, the results obtained here on the model system dPGS and lysozyme are in full agreement with the conclusion drawn by Dragan et al. for the binding of DNA to various proteins.