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Introduction

Starting from a PDB or PQR file, this website will calculate its theoretical SAXS profile and determine how well it fits to your experimental SAXS data.
Go to the Compute SAXS profile page to compute a SAXS profile from your model, as illustrated by the image below, using urate oxydase as an example.

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How do we compute SAXS profiles?

In a nutshell, when you perform a SAXS experiment you basically measure your sample's excess in electron density. This excess density is due to the presence of the solute in the solvent, as compared to the solute-free solvent.
The solute perturbs the solvent in two ways:
i) it excludes it from the volume occupied by the solute
ii) in the vicinity of the solute, water molecules depart from their bulk-organization and rearrange around the solute atoms.


SAXS profiles are computed using the following equation:

where q=(q,Ω) is the scattering vector of norm q and direction Ω and c1 and c2 determine the weights of the excluded volume and the hydration shell, respectively. The water density is taken as ρw=0.334 by default.

The scattered intensity at q is the result of the spherical averaging (with the cubature formula - see Ref. for details) of the Fourier Transform A of the excess electron density in the system, and its conjugate A*.
This quantity A, called the "excess" structure factor, is the result of 3 contributions:
- the solute's structure factor Fprotein
- the solute excluded volume's structure factor Fexcluded-volume
- the hydration shell's structure factor Fhydration-shell.
The three contributions need to be adjusted to yield a good fit to the experimental data and this is done by adjusting the relative weights c1 and c2 (see below).
While there is a general consensus on how to evaluate the first two terms, here we propose a new method to compute the last term.

How do we account for the solvent exclusion?
To account for the excess electron density in the solute, we follow, as others [1][2], the method of the effective-atomic-scattering-factor [3]. In this approximation, each solute atom contributes a form factor resulting from the difference between its form factor in vacuo and the form factor of a dummy atom of similar volume, representing the displaced solvent volume.
Note that a shortcoming of this approach arises from the fact that the excluded solvent-volume is not a well-described quantity, leading to the need of a global expansion factor G(q,c1) (see [1] for details) that is determined during the fit to the experimental data.

How do we account for the solute hydration?
As stated above, when a solute is immersed into the solution, water molecules rearrange around its atoms and create the so-called hydration shell, whose density is different from the bulk's.
We propose an original approach to account for the hydration shell's contribution, more physically based, using the Poisson-Boltzmann formalism [4][5]. In this approach, the solute's fixed charges are surrounded by free charges (the ion atmosphere) and a collection of orientable dipoles that represent the solvent. Extremizing the free energy of the system yields the optimum distribution of the solvent dipoles around the solute at equilibrium. In particular, it has been shown [4] that this distribution follows what is expected form the chemical nature of the nearby solute's exposed atoms (polar atoms attract more water than non-polar).
For comparison, we also provide an efficient way to account for solvation, as described recently [2]; it states that the contribution of the hydration shell is related to the solvent-accessible surface of the protein. Again, a scaling factor is needed to adjust the contribution of this term, when experimental data is available.
The user can either build himself/herself the solvent map (the program AquaSol is freely available [5]), or let the software do it in a default mode.
Note that one can feed AquaSAXS with solvent maps derived from any method (e.g. 3D -RISM), since there is just a format requirement for the map (CNS, and more as soon as possible).

References
[1] Svergun et al. - J. App. Cryst. 28 (1995)
[2] Schneidman-Duhovny et al. - NAR 38 (2010)
[3] Fraser et al. - J. App. Cryst. 11 (1978)
[4] Azuara et al. - NAR 34 (2006) and Biophys. J. 95 (2008)
[5] Koehl and Delarue - J. Chem. Phys. 132 (2010)




  Marc Delarue http://lorentz.dynstr.pasteur.fr
Page last modified 12:08 February 18, 2015.