Assigning crystallographic electron densities with free energy calculations—The case of the fluoride channel Fluc

<div><p>Approximately 90% of the structures in the Protein Data Bank (PDB) were obtained by X-ray crystallography or electron microscopy. Whereas the overall quality of structure is considered high, thanks to a wide range of tools for structure validation, uncertainties may arise from density maps of small molecules, such as organic ligands, ions or water, which are non-covalently bound to the biomolecules. Even with some experience and chemical intuition, the assignment of such disconnected electron densities is often far from obvious. In this study, we suggest the use of molecular dynamics (MD) simulations and free energy calculations, which are well-established computational methods, to aid in the assignment of ambiguous disconnected electron densities. Specifically, estimates of (i) relative binding affinities, for instance between an ion and water, (ii) absolute binding free energies, i.e., free energies for transferring a solute from bulk solvent to a binding site, and (iii) stability assessments during equilibrium simulations may reveal the most plausible assignments. We illustrate this strategy using the crystal structure of the fluoride specific channel (Fluc), which contains five disconnected electron densities previously interpreted as four fluoride and one sodium ion. The simulations support the assignment of the sodium ion. In contrast, calculations of relative and absolute binding free energies as well as stability assessments during free MD simulations suggest that four of the densities represent water molecules instead of fluoride. The assignment of water is compatible with the loss of these densities in the non-conductive F82I/F85I mutant of Fluc. We critically discuss the role of the ion force fields for the calculations presented here. Overall, these findings indicate that MD simulations and free energy calculations are helpful tools for modeling water and ions into crystallographic density maps.</p></div

Water and fluoride at F82 and F85 sites, taken from snapshots of the relative binding free energy simulations.

<p>Several representative snapshots taken from the alchemical transformation simulations are depicted. Fluoride (A,B,C,D) is shown as purple spheres and water (E,F,G,H) as red (oxygen) and white (hydrogen) spheres. Some of the amino-acid side-chains in the F82 (A,C,E,G) and F85 (B,D,F,H) sites are depicted in colored sticks. Some of the hydrogen bonds established between the protein and the water/fluoride are highlighted with black dashed triangles.</p

Relaxed potential energy scans (PESs) of fluoride and benzene.

<p>(A) Illustration of the coordinate <i>R</i> as the distance of fluoride (cyan sphere) from the center of mass of the benzene ring (green/white spheres), taken in the plane of the ring. The left cyan sphere indicates the position of the potential energy minimum. (B) Relaxed PESs using quantum-chemical calculations at different quantum levels and using different basis sets, as indicated in the legend (black, red, and green curves), revealing a potential energy minimum of ∼ −50 kJ mol⁻¹. The non-polarizable (additive) Amber99sb force field with ion parameters by Joung and Cheatham [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0196751#pone.0196751.ref043" target="_blank">43</a>] strongly underestimate fluoride-benzene interactions (blue). In contrast, the polarizable CHARMM-Drude force field [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0196751#pone.0196751.ref057" target="_blank">57</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0196751#pone.0196751.ref059" target="_blank">59</a>] provides a PES in reasonable agreement with quantum-chemical calculations.</p

Fluc channel simulation system and structure.

<p>(A) Fluc channel simulation system with blocking L2 monobodies. Fluc is depicted as orange and yellow ribbons, L2 monobodies are showed as pink thick ribbons, lipids heads are shown as purple volume and lipid tails as white sticks. Water molecules not shown for the sake of clarity. (B) Close-up of Fluc channel electron densities (cyan) at F82 (blue) and F85 (green) sites. The sodium ion at the TM3 site is also highlighted in yellow. (C) Fluc channel simulation system without blocking L2 monobodies.</p

Maximum-likelihood estimates <i>τ</i>_<i>ml</i> (nanoseconds) for the lifetime of fluoride and water molecules at Fluc F82 and F85 positions.

<p>Maximum-likelihood estimates <i>τ</i>_<i>ml</i> (nanoseconds) for the lifetime of fluoride and water molecules at Fluc F82 and F85 positions.</p

Absolute binding free energy Δ<i>G</i>_bind (kJ mol⁻¹) of water at F82, F85, F82I, and F85I sites.

<p>Absolute binding free energy Δ<i>G</i>_bind (kJ mol⁻¹) of water at F82, F85, F82I, and F85I sites.</p

G77 and T80 residue positions in MD simulations.

<p>(A) Positions of G77 and T80 residues in a 10 ns MD simulation in which a sodium ion is at the TM3 site. The positions of G77 and T80 residues are shown as thin sticks in which oxygen is colored in red, hydrogen in white, nitrogen in blue, and carbon in cyan. The positions of the G77 and T80 residues in the crystal structure are depicted in thick sticks following the same color scheme. The protein secondary structure is showed in white and gray ribbons. (B) Positions of G77 and T80 residues in a 10 ns MD simulation in which a water molecule is at the TM3 site. The G77 residue that adopts a significantly different orientation in the simulation compared with the crystal structure is highlighted in a dashed circle.</p

Potential of Mean Force Calculations of Solute Permeation Across UT‑B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM

Membrane channels facilitate the efficient and selective flux of various solutes across biological membranes. A common approach to investigate the selectivity of a channel has been the calculation of potentials of mean force (PMFs) for solute permeation across the pore. PMFs have been frequently computed from molecular dynamics (MD) simulations, yet the three-dimensional reference interaction site model (3D-RISM) has been suggested as a computationally efficient alternative to MD. Whether the two methods yield comparable PMFs for solute permeation has remained unclear. In this study, we calculated potentials of mean force for water, ammonia, urea, molecular oxygen, and methanol across the urea transporter B (UT-B) and aquaporin-1 (AQP1), using 3D-RISM, as well as using MD simulations and umbrella sampling. To allow direct comparison between the PMFs from 3D-RISM and MD, we ensure that all PMFs refer to a well-defined reference area in the bulk or, equivalently, to a well-defined density of channels in the membrane. For PMFs of water permeation, we found reasonable agreement between the two methods, with differences of ≲3 kJ mol^–1. In contrast, we found stark discrepancies for the PMFs for all other solutes. Additional calculations confirm that discrepancies between MD and 3D-RISM are not explained by the choice for the closure relation, the definition the reaction coordinate (center of mass-based versus atomic site-based), details of the molecule force field, or fluctuations of the protein. Comparison of the PMFs suggests that 3D-RISM may underestimate effects from hydrophobic solute-channel interactions, thereby, for instance, missing the urea binding sites in UT-B. Furthermore, we speculate that the orientational averages inherent to 3D-RISM might lead to discrepancies in the narrow channel lumen. These findings suggest that current 3D-RISM solvers provide reasonable estimates for the PMF for water permeation, but that they are not suitable to study the selectivity of membrane channels with respect to uncharged nonwater solutes