High-resolution neutron and X-ray diffraction room-temperature studies of an H-FABP–oleic acid complex: study of the internal water cluster and ligand binding by a transferred multipolar electron-density distribution

Neutron and high-resolution X-ray crystallography were used to determine fully the structure of the internal water cluster in H-FABP. Analysis of the orientation and electrostatic properties of the water molecules showed significant alignment of the permanent dipoles of the water molecules with the protein electrostatic field.


Supplementary material
Text S1. Estimation of uncertainties on charge density derived properties.
In order to assess the significance of our results, we computed uncertainties on the reported properties following a statistical approach. First we assumed that errors on electrostatic and on AIM topological properties originate from uncertainties affecting atomic coordinates and transferred multipole parameters values. To account for these sources of errors, a total of 30 models were generated from the original H-FABP structure, where the atomic parameters (orthogonal coordinates, valence populations and non-zero multipole parameters) were randomly perturbed using Gaussian error functions. The standard deviations (±) associated to these normal distributions were adjusted to the errors estimated on the corresponding parameters.
Here, errors on transferred (non-zero) multipole coefficients and atomic valence populations were taken as equal to the standard errors on the averaged values stored in the ELMAMII library, as distributed with the MoPro program suite. Errors on atomic coordinates were derived from Cruickshank diffraction precision index (DPI) formula (Cruickshank, 1999) using the "Online_DPI" web server (Kumar et al., 2015).
Using this method, errors on atomic coordinates are functions of isotropic B factors and of diffraction data and model quality. However, in our case, the perdeuterated H-FABP crystal structure was jointly refined against average resolution 1.9 Å neutron and 0.98 Å atomic resolution X-ray data sets. Hence, as the orientation of the water molecules and the position of hydrogen atoms (seen as deuterium) not determined by stereochemistry were provided by the neutron diffraction experiment, their coordinates errors were computed on the basis of the neutron data set (DPI = 0.29 Å), while those on all the other atoms were obtained using the high resolution X-ray data set (DPI = 0.03 Å). This choice resulted, as expected, on large uncertainties on hydroxyl group's and water molecule's hydrogen atoms, clearly reflecting uncertainties on their actual orientation ( Figure S1). In a last step, on order to avoid including in the computations stereo chemically invalid models (as atomic coordinates perturbations were applied randomly and independently on each atoms), all the resulting 30 perturbed structures were subsequently regularized using standard stereo chemical restraints.
Finally, all electrostatic and QTAIM computations were re-performed for each of the 30 perturbed models. Hence, in this study, the electric field magnitudes, angles between electric field and water molecules dipole moment vectors, as well as electron density and Laplacian values on intermolecular bond critical points are given with standard errors on the mean values of properties obtained from these 30 independent computations, using a Student t distribution with 29 degrees of freedom (t = 2.75).  Water molecules marked with asterisk are buried in the protein but are not located in the water cluster which fills the binding pocket along with the FA: W1 is the resident water conserved among nine different members of the FABP protein family (Likic et al., 2000). W28 is in contact with the FA, but located on the other side than the water cluster; W38 is visible at the entrance of the water channel linking the hydration shell and the binding cavity.

Figure S1
Superimposition of the 30 perturbed structures, represented in the region of the water cluster. The uncertainty on the water molecule's orientations is seen through the continuum of acceptable orientations, arising from the neutron data resolution and the atomic B factors. The fatty acid can be seen at the bottom of the picture.

Figure S2
Relation between electric field magnitudes at water molecules center of mass and the raw angle measured between the electric field vector and the water molecule's dipole moments. Error bars correspond to standard error on the mean associated to these values (see materials and methods).

Figure S3
Superimposition of A-FABP apo form (PDB code: 3RZY, green waters and molecule) and the present structure showing that the water cluster molecules keep their position.