A depiction of the origin of selectivity via the RLF mechanism.

<p>Selectivity arises from the difference in the entropy change from unconstrained ligands () to constrained ligands () between K⁺ and Na⁺. The brown regions represent the volume in which two ligands can move about the ion. As the ligands' fluctuations become constrained, the ligands experience a greater decrease in available volume and thus entropy when coordinating a large ion than when coordinating a smaller ion.</p

Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth

This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh₂) and triphenyl bismuth (BiPh₃). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin–orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scalesnot in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh₂ with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin–orbit relativistic effects

Composition of the amino acid transporter model ion binding sites.

*<p>indicates that both oxygen atoms are present in the carboxylate group.</p

Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth

This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh₂) and triphenyl bismuth (BiPh₃). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin–orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scalesnot in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh₂ with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin–orbit relativistic effects

A decomposition of

<p><b>(magenta), in the absence of cavity strain, into </b><b>(black) and </b><b>(brown) components of ion selectivity between Na⁺ and Li⁺ for (A) 4 fold, (B) 5 fold, (C) 6 fold and (D) 7 fold coordination states.</b> The green region indicates a contribution toward Li⁺ selectivity, while the blue region indicates a contribution toward Na⁺ selectivity.</p

Decomposition of

<p><b>(magenta) into </b><b>(black) and </b><b>(brown) for the Na⁺</b><b>K⁺ morph for (A) Glt_Ph:Na1, (B) Glt_Ph:Na2, (C) LeuT:Na1 and (D) LeuT:Na2.</b> Negative values (blue region) indicate Na⁺ selectivity, positive values (red region) indicates K⁺. Similar plots for the Na⁺ Li⁺ situation are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002914#pcbi.1002914.s001" target="_blank">Text S1</a>.</p

The effect of reducing the size of the ligand thermal fluctuations on selectivity between Li⁺ and Na (solid magenta line) with increasing harmonic constraint constant,

<p><b>for (A) 4 fold, (B) 5 fold, (C) 6 fold and (D) 7 fold coordination states.</b> These are compared with a strained cavity model at ion-ligand distance optimised for Li⁺ (dotted green line) and Na⁺ (dotted blue line). A negative value (blue region) of indicates the model site is selective for Na⁺, a positive value (green region) indicates Li⁺ selectivity.</p

The effect of reducing the size of the ligand thermal fluctuations on selectivity between Na⁺ and K⁺ (solid magenta line), controlled by increasing harmonic constraint constant

<p><b>, for (A) 5-fold, (B) 6-fold, (C) 7-fold and (D) 8-fold coordination states.</b> These are compared with a strained cavity model at ion-ligand distance optimised for Na⁺ (dotted blue line) and K⁺ (dotted red line). A negative value (blue region) of indicates the model site is selective for Na⁺, a positive value (red region) indicates K⁺ selectivity. The non-zero value of selectivity when is due to the chemical nature and number of ligands as discussed elsewhere <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002914#pcbi.1002914-Thomas1" target="_blank">[12]</a>.</p

The effect of reducing the fluctuations of the ligands in the amino acid transporter model sites.

<p>(A) Na⁺ in the Glt_Ph model sites Na1 and Na2 being morphed to K⁺ (orange and dark red) or Li⁺ (light green and dark green). (B) Na⁺ in the LeuT model sites Na1 and Na2 being morphed to K⁺ (solid orange and dotted dark red) and Li⁺ (dotted light green and solid dark green). (C) The same free energies as (A) plotted against RMS fluctuations. The grey area corresponds to the observed RMS fluctuations in full system simulations of Glt_Ph conducted in other studies <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002914#pcbi.1002914-Thomas1" target="_blank">[12]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002914#pcbi.1002914-Celik1" target="_blank">[34]</a>. (D) The same free energies as (B) plotted against RMS fluctuations. Negative values (blue region) indicate Na⁺ selectivity, positive values (red regions) indicates K⁺ or Li⁺ selectivity.</p

A decomposition of

<p><b>(magenta), in the absence of cavity strain, into </b><b>(black) and </b><b>(brown) components of ion selectivity between Na⁺ and K⁺ for (A) 5 fold, (B) 6 fold, (C) 7 fold and (D) 8 fold coordination states.</b> The red region indicates a contribution toward K⁺ selectivity, while the blue region indicates a contribution toward Na⁺ selectivity.</p