Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures

Abstract

Ion binding is known to affect the properties of biomolecules and is directly involved in many biochemical pathways. Because of the highly polar environments where such ions are found, a quantum-mechanical treatment is preferable for understanding the energetics of competitive ion binding. Due to computational cost, a quantum mechanical treatment may involve several approximations, however, whose validity can be difficult to determine. Using thermodynamic cycles, we show how intuitive models for complicated ion binding reactions can be built up from simplified, isolated ion-ligand binding site geometries suitable for quantum mechanical treatment. First the ion binding free energies of individual, minimum energy structures determine their intrinsic ion selectivities. Next, the relative propensity for each minimum energy structure is determined locally from the balance of ion-ligand and ligand-ligand interaction energies. Finally, the environment external to the binding site exerts its influence both through long-ranged dispersive and electrostatic interactions with the binding site as well as indirectly through shifting the binding site compositional and structural preferences. The resulting picture unifies field-strength, topological control, and phase activation viewpoints into a single theory that explicitly indicates the important role of solute coordination state on overall reaction energetics. As an example, we show that the Na+ →K+ selectivities can be recovered by correctly considering the conformational contribution to the selectivity. This can be done even when constraining configuration space to the neighborhood around a single, arbitrarily chosen, minimum energy structure. Structural regions around minima for K+- and Na+-water clusters are exhibited that display both rigid/mechanical and disordered/entropic selectivity mechanisms for both Na+ and K+. Thermodynamic consequences of the theory are discussed with an emphasis on the role of coordination structure in determining experimental properties of ions in complex biological environments.

An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics

“…This is consistent with Z [ ] of the last section as well as the free energy cost for inserting a hard core solute into solution [27] or imposing a constraint on the geometry of an ion binding site [28]. …”

Octa-Coordination and the Aqueous Ba2+ Ion

“…While any shape may be selected, 35,36 we choose a sphere of radius r = λ centered around the ion for convenience.…”

“…[32][33][34][35][36] The coupling of structure with thermodynamic predictions provides an advantage for validating the results compared to more standard studies of structure alone. Also, structural data obtained by molecular simulation contains information about the spatial distributions of each neighboring solvent molecule.…”

Ion Binding Sites and Their Representations by Reduced Models

“…Indeed, a number of studies of selectivity in ion channels were based directly on the standard form of QCT 4,5,13 or SSGCE 8 . However, there are some critical differences with ion solvation in bulk phase that must be noted.…”