Structure and diffusive dynamics of aspartate α-decarboxylase (ADC) liganded with d-serine in aqueous solution

Incoherent neutron spectroscopy, in combination with dynamic light scattering, was used to investigate the effect of ligand binding on the center-of-mass self-diffusion and internal diffusive dynamics of Escherichia coli aspartate α-decarboxylase (ADC). The X-ray crystal structure of ADC in complex with the d-serine inhibitor was also determined, and molecular dynamics simulations were used to further probe the structural rearrangements that occur as a result of ligand binding. These experiments reveal that d-serine forms hydrogen bonds with some of the active site residues, that higher order oligomers of the ADC tetramer exist on ns–ms time-scales, and also show that ligand binding both affects the ADC internal diffusive dynamics and appears to further increase the size of the higher order oligomers.


Amber99SB-ILDN force-field parameters
All parameters given below are in the Gromacs format. We followed the Gromacs manual for adding the residues: http://www.gromacs.org/Documentation/ How-tos/Adding_a_Residue_to_a_Force_ Field

Atom types, charges and bonded interactions
The lines below were added to aminoacids.rtp in the force field folder. Atom names in the pdb need to be adjusted accordingly before processing.
;     Figure S6: Energy resolution of the time-of-flight spectrometer IN5 for the employed cylindrical sample geometry with 22 mm cylinder diameter, for q = 0.6Å −1 , measured using Vanadium foil as the sample (symbols). The solid lines represent Gaussian functions and their sum fitted to the measured data. The sum of Gaussians is used to analytically describe the resolution function.

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Using DLS, a time autocorrelation function was measured over the angular range 30-150 • (figure S10). The correlation function for a monodisperse sample is given as In case of more than one populations of clusters with different diffusion coefficients, the following equation is used as the fit function: where Γ is the decay rate and t the time. The first order autocorrelation function was treated as a monoexponential decay (equation 1) in order to extract the decay rate. Γ can then be plotted versus q 2 which follows Fickian diffusion, where D t is the translational diffusion coefficient and q is the momentum transfer defined as where θ is the scattering angle, n 0 the refractive index of the sample, and λ the wavelength of the incident beam. Due to the linear relation of Γ and q 2 (equation 3) a linear fit of the q-dependence gives the long-time translational diffusion coefficient D t (figure S11).  5 Radial hydrogen density distribution calculated from the pdb files Figure S12: Radial hydrogen density distribution calculated from the respective pdb files for ADC tetramers without ligand, ADC dimers liganded with D-Serine, and ADC tetramers liganded with D-Serine, respectively, as assigned in the legend.
6 Apparent hydrodynamic radius and cluster size assuming compact spherical clusters Figure S13: Apparent hydrodynamic radius R h,app calculated using equation 9 from the main part of the manuscript. The radius calculated from the QENS results (cf. assignment in the legend) only represents an apparent radiuswhich largely underestimates the actual radius -, because the rotational and translational contributions to the diffusion coefficient have not been separated (cf. figure S14). The hydrodynamic radius calculated from the HYDROPRO (denoted 'HYD' in the legend) and DLS results is exact, because these methods directly provide the translational diffusion coefficient. The different solvent viscosities in the presence and absence of excess D-Serine have been taken into account (cf. table S1 in this Supporting Information). Since the apparent radius underestimates the actual radius, a crowding-induced enhanced cluster formation can be deduced when comparing to the dilute limit (HYDROPRO and DLS).  Figure S14: The considerations on the cluster hydrodynamic radius (figure S13) can be carried even further: Assuming compact spherical clusters and the radial hydrogen density distribution ρ H (r) = 4r 0 πr 2 Θ(R h,cluster −r) with the normalization factor r 0 and Heaviside step function Θ (which reasonably approximates a distribution as in figure S12), the theoretical translational D t and apparent D = D(D t , D r ) diffusion coefficients can be calculated as explained in the main part of the manuscript. To this effect, the cluster hydrodyamic radius R h,cluster has been assumed to follow the simple volume scaling R h,cluster = (n · R 3 h ) (1/3) , where n is the number of tetramers in the cluster and R h the tetramer hydrodynamic radius from HYDROPRO. The above figure is identical to figure 8 in the main part of the article, but contains additional dash-dotted and dotted lines representing the cluster D and D t , respectively, assuming n = 10 tetramers for the apo form of ADC and n = 58 tetramers for ADC liganded with D-Serine. With these crude assumptions, the experimental values for D measured with QENS can be described. The corresponding cluster radii in these assumptions amount to R h,cluster = 63.8Å for the apo form and 127.0Å for the liganded form.

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7 Tabled HYDROPRO input and output parameters and experimental diffusion coefficients  Table S2: Diffusion coefficients obtained from QENS, DLS and HYDROPRO at T = 295 K, and hydrodynamic radius calculated from the DLS results using the Stokes-Einstein relation. The errors denote 67% confidence bounds on the fits and do not account for systematic errors arising from the choice of the model. Note that the hydrodynamic radii R h have been calculated from D t accounting for the different viscosities in the presence and absence of excess D-Serine in the solvent (cf. table 1 above).