Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures

Center for Biological and Materials Sciences, MS 0895, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
The Journal of Physical Chemistry B (Impact Factor: 3.3). 07/2011; 115(29):9116-29. DOI: 10.1021/jp2012864
Source: PubMed


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.

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    • "Small metal ions are a fundamental component to the structure and function of biological systems. Although detailed computation have a central role to play in trying to understand the molecular determinants of ion selectivity in these complex systems, progress may be achieved by pursuing theoretical studies based on simplified reduced models comprised of only the nearest ion-coordinating ligands [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]. By construction, such reduced binding site models only treat the ion and the nearest coordinating ligands explicitly, while the influence of the missing atoms from the surroundings (protein or solvent) is incorporated indirectly. "
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    ABSTRACT: 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.
    The Journal of Physical Chemistry B 04/2012; 116(23):6966-79. DOI:10.1021/jp3007365 · 3.30 Impact Factor
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    • "Quasi-chemical theory, which is relevant to the ion selectivities discussed here (Asthagiri et al., 2010), follows directly from inherent structure concepts (Hummer et al., 1997). If the system presents more than one binding mode, perhaps including multiion binding, these additional complications can be treated by calculating a set of structurally constrained free energies (Rogers and Rempe, 2011). Free energy differences, determined experimentally, are not as clear for binding sites as in liquids. "
    The Journal of General Physiology 06/2011; 137(6):479-88. DOI:10.1085/jgp.201010579 · 4.79 Impact Factor
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    ABSTRACT: Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complex thermodynamic models by successively adding physical information. We present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics. From this foundation we derive a theory for ion channel kinetics, identifying a nonequilibrium 'process' free energy functional in addition to the well-known integrated work functionals. The Gibbs-Maxwell relation for the free energy functional is a Green-Kubo relation, applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient thermal and mechanical driving forces. Comparing the physical significance of the Lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance. Our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally-relevant and computable models. By construction, these models may use information from more detailed atomistic simulations. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes. The information loss identifies a novel contribution from the instantaneous information entropy that ensures non-negative loss.
    Journal of Statistical Physics 10/2011; 145(2):385-409. DOI:10.1007/s10955-011-0358-9 · 1.20 Impact Factor
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