An Explicit Consideration of Desolvation is Critical to Binding Free Energy Calculations of Charged Molecules at Ionic Surfaces

Identifying factors that control the strength and specificity of interactions between peptides and nanoparticles is essential for understanding the potential beneficial and deleterious effects of nanoparticles on biological systems. Computer simulations are valuable in this context, although the reliability of such calculations depends on the force field and sampling algorithm, as well as how the binding constant and binding free energy are defined; the latter must be carefully defined with a clear connection to microscopic models based on statistical mechanics. Using the example of formate binding to the rutile titanium dioxide (TiO2) (110) surface, we demonstrate that a reliable description of the binding process requires an explicit consideration of changes in the solvation state of the binding site. Specifically, we carry out metadynamics simulations in which the solvent coordination number of the binding site, s, is introduced as a collective variable in addition to the vertical distance of the adsorbate to the surface (z). The resulting two-dimensional potential of mean force (2D-PMF) clearly shows that explicitly including the local desolvation of the binding site on the TiO2 surface strongly impacts the convergence and result of the binding free energy calculations. Projecting the 2D-PMF into a one-dimensional PMF along either z or s leads to large errors in the free energy barriers. Results from metadynamics simulations are quantitatively supported by independent alchemical free energy simulations, in which the solvation state of the binding site is also carefully considered by explicitly introducing water molecules to the binding site as the adsorbate is decoupled from the system. On the other hand, preliminary committor analysis for the approximate transition state ensemble constructed based on the 2D-PMF suggests that to properly describe the binding/unbinding kinetics, variables beyond s and z, such as those describing the hydrogen bonding pattern of the adsorbate and surface water, need to be included. We expect that the insights and computational methodologies established in this work will be generally applicable to the analysis of binding interactions between highly charged adsorbates and ionic surfaces in solution, such as those implicated in peptide/nanoparticle binding and biomineralization processes.