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

Abstract

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 ∆G_b=-k_B T ln\u2061 K_b as the function of the two decisive variables, namely the salt concentration c_s 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 ∆G_b can be split up into ∆G_b=∆G_res+ ∆G_ci where ∆G_ci denotes the part due to counterion release whereas ∆G_res is the part obtained by extrapolation of ∆G_b to 1M salt concentration. Plots of dlog KB/dlog cs lead to perfectly straight lines that can be extrapolated to c_s = 1M in order to obtain ∆G_res. Both ∆G_res and ∆G_ci can be independently obtained by implicit solvent molecular dynamics simulations done up to salt concentrations of 1M. Good agreement of experiment and simulation within prescribed limits of error is found. Moreover, ∆G_res is shown to be caused by direct unscreened electrostatic contacts or salt bridges between dPGS and lysozyme. Since ∆G_ci= -T∆S_ci where ∆S_ci is the entropy due to counterion release, the entire binding entropy ∆S_b can be split up as ∆S_b=∆S_ci+∆S_res. Plots of the binding enthalpy ∆H_b vs. ∆S_res 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 non-electrostatic phenomenon solely due to solvatation 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.