Ion selectivity from local configurations of ligands in solutions and ion channels

Ion binding sites and their representations by reduced models

The binding of small metal ions to complex macromolecular structures is typically dominated by strong local interactions of the ion with its nearest ligands. Progress in understanding the molecular determinants of ion selectivity can often be achieved by considering simplified reduced models comprised of only the most important ion-coordinating ligands. Although the main ingredients underlying simplified reduced models are intuitively clear, a formal statistical mechanical treatment is nonetheless necessary in order to draw meaningful conclusions about complex macromolecular systems. By construction, reduced models only treat the ion and the nearest coordinating ligands explicitly. The influence of the missing atoms from the protein or the solvent is incorporated indirectly. Quasi-chemical theory offers one example of how to carry out such a separation in the case of ion solvation in bulk liquids, and in several ways, a statistical mechanical formulation of reduced binding site models for macromolecules is expected to follow a similar route. However, there are also important differences when the ion-coordinating moieties are not solvent molecules from a bulk phase but are molecular ligands covalently bonded to a macromolecular structure. Here, a statistical mechanical formulation of reduced binding site models is elaborated to address these issues. The formulation provides a useful framework to construct reduced binding site models, and define the average effect from the surroundings on the ion and the nearest coordinating ligands.

Mechanism of ion permeation and selectivity in a voltage gated sodium channel

The rapid and selective transport of Na(+) through sodium channels is essential for initiating action potentials within excitable cells. However, an understanding of how these channels discriminate between different ion types and how ions permeate the pore has remained elusive. Using the recently published crystal structure of a prokaryotic sodium channel from Arcobacter butzleri, we are able to determine the steps involved in ion transport and to pinpoint the location and likely mechanism used to discriminate between Na(+) and K(+). Na(+) conduction is shown to involve the loosely coupled "knock-on" movement of two solvated ions. Selectivity arises due to the inability of K(+) to fit between a plane of glutamate residues with the preferred solvation geometry that involves water molecules bridging between the ion and carboxylate groups. These mechanisms are different to those described for K(+) channels, highlighting the importance of developing a separate mechanistic understanding of Na(+) and Ca(2+) channels.

A local entropic signature of specific ion hydration

Monovalent ion hydration entropies are analyzed via energetic partitioning of the potential distribution theorem free energy. Extensive molecular dynamics simulations and free energy calculations are performed over a range of temperatures to determine the electrostatic and van der Waals components of the entropy. The far-field electrostatic contribution is negative and small in magnitude, and it does not vary significantly as a function of ion size, consistent with dielectric models. The local electrostatic contribution, however, varies widely as a function of ion size; the sign yields a direct indication of the kosmotropic (strongly hydrated) or chaotropic (weakly hydrated) nature of the ion hydration. The results provide a thermodynamic signature for specific ion effects in hydration and are consistent with experiments that suggest minimal perturbations of water structure outside the first hydration shell. The hydration entropies are also examined in relation to the corresponding entropies for the isoelectronic rare gas pairs; an inverse correlation is observed, as expected from thermodynamic hydration data.

Probing the thermodynamics of competitive ion binding using minimum energy structures

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 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.

Two mechanisms of ion selectivity in protein binding sites

A theoretical framework is presented to clarify the molecular determinants of ion selectivity in protein binding sites. The relative free energy of a bound ion is expressed in terms of the main coordinating ligands coupled to an effective potential of mean force representing the influence of the rest of the protein. The latter is separated into two main contributions. The first includes all the forces keeping the ion and the coordinating ligands confined to a microscopic subvolume but does not prevent the ligands from adapting to a smaller or larger ion. The second regroups all the remaining forces that control the precise geometry of the coordinating ligands best adapted to a given ion. The theoretical framework makes it possible to delineate two important limiting cases. In the limit where the geometric forces are dominant (rigid binding site), ion selectivity is controlled by the ion-ligand interactions within the matching cavity size according to the familiar "snug-fit" mechanism of host-guest chemistry. In the limit where the geometric forces are negligible, the ion and ligands behave as a "confined microdroplet" that is free to fluctuate and adapt to ions of different sizes. In this case, ion selectivity is set by the interplay between ion-ligand and ligand-ligand interactions and is controlled by the number and the chemical type of ion-coordinating ligands. The framework is illustrated by considering the ion-selective binding sites in the KcsA channel and the LeuT transporter.

Assessing the accuracy of approximate treatments of ion hydration based on primitive quasichemical theory

Quasichemical theory (QCT) provides a framework that can be used to partition the influence of the solvent surrounding an ion into near and distant contributions. Within QCT, the solvation properties of the ion are expressed as a sum of configurational integrals comprising only the ion and a small number of solvent molecules. QCT adopts a particularly simple form if it is assumed that the clusters undergo only small thermal fluctuations around a well-defined energy minimum and are affected exclusively in a mean-field sense by the surrounding bulk solvent. The fluctuations can then be integrated out via a simple vibrational analysis, leading to a closed-form expression for the solvation free energy of the ion. This constitutes the primitive form of quasichemical theory (pQCT), which is an approximate mathematical formulation aimed at reproducing the results from the full many-body configurational averages of statistical mechanics. While the results from pQCT from previous applications are reasonable, the accuracy of the approach has not been fully characterized and its range of validity remains unclear. Here, a direct test of pQCT for a set of ion models is carried out by comparing with the results of free energy simulations with explicit solvent. The influence of the distant surrounding bulk on the cluster comprising the ion and the nearest solvent molecule is treated both with a continuum dielectric approximation and with free energy perturbation molecular dynamics simulations with explicit solvent. The analysis shows that pQCT can provide an accurate framework in the case of a small cation such as Li(+). However, the approximation encounters increasing difficulties when applied to larger cations such as Na(+), and particularly for K(+). This suggests that results from pQCT should be interpreted with caution when comparing ions of different sizes.