small angle x - ray scattering ( saxs ) is a technique that allows the study of the structure and interactions of biological molecules in solution .
it can be used to probe proteins , nucleic acids , and their complexes under a variety of conditions , from near physiological to highly denaturing , without the need to crystallize the sample and without the molecular weight limitations inherent in other methods such as nmr spectroscopy .
the increasing availability of high - flux , third - generation synchrotron sources , improvements in detector technology and algorithmic developments for data analysis have made saxs a technique of choice for a range of biological applications ( 1 ) .
the basic principle of saxs is to scatter x - ray photons elastically off molecules in solution , and to record the scattering intensity as a function of the scattering angle .
the intensity profile of the buffer is subtracted from the profile of the macromolecule in the buffer , yielding an excess intensity profile , related to the excess electronic density of the molecule and its environment .
the saxs profile provides information about the global structure and conformation of the studied molecule(s ) .
several reviews on the physical principles and theory of saxs describe in detail how the scattering data can be analyzed and how different parameters can be fit and interpreted ( 26 ) .
existing computational approaches for modeling a macromolecular structure based on its saxs profile can be separated into two classes : profile - to - model ( ab initio methods ) and model - to - profile approaches .
the former aims at proposing coarse shapes represented by dummy beads that fit the experimental profile ( 1016 ) , while the latter aims at comparing the theoretical profile of a given atomic or coarse grained model to the experimental one ( 17,18 ) .
the model - to - profile approach consists in computing the theoretical profile of a given atomic structure and providing a measure of the goodness - of - fit to the experimental profile .
it is useful for many applications where one needs to decide whether the proposed model is in agreement with the experiment , and to make assumptions about why they differ , if they do .
several tools have been designed for that purpose , following various methods ( 1924 ) . to our knowledge ,
the most accurate method to date for computing saxs profiles of a given macromolecule has been achieved by treating the solvent ( excluded and hydrating ) explicitly ( 24 ) . through this method ,
even higher resolution profiles resulting from wide angle x - ray scattering ( waxs ) experiments were also reasonably reproduced .
all other methods rely on a continuum representation of the solvent - excluded volume , first proposed by fraser et al .
( 25 ) : the effective - atomic - scattering - form - factor method .
the programs sassim ( 22 ) and fast - saxs ( 23 ) rely on configurational averaging over molecular dynamics simulations to treat the excess in electron density of the hydration layer relative to bulk solvent .
the widely used program crysol ( 19 ) makes the assumption that the hydration shell surrounding the solute is a constant density layer of given thickness , while foxs ( 20 ) attributes an additional term to every effective - atomic - scattering - form - factor proportional to their solvent accessible area to account for the hydration layer 's contribution .
aquasaxs aims at providing a new way to treat the solvation layer accurately without the need for extensive molecular dynamics simulations . to achieve this goal
, aquasaxs takes advantage of recently developed methods that compute the solvent - distribution around a given solute on a 3d grid such as the poisson 
boltzmann  langevin ( pbl ) formalism ( 26 ) ; pbl is implemented in aquasol that is freely available online as a web server ( 27 ) or as a software available upon request from the authors ( 28 ) . here
, aquasaxs can also take advantage of other methods that compute the solvent - distribution surrounding a macromolecule .
for example , outputs from 3d - rism ( three dimensional - reference interaction site model ) calculations can readily be used by aquasaxs .
the 3d - rism theory has been implemented in the latest ambertools package ( 29 ) .
in addition , aquasaxs provides a way for the user to check and/or tune the atomic types and the corresponding parameters that are used for computing the solute and the solvent - excluded - volume contribution to the saxs profile . in the following sections , we describe the method and interface of aquasaxs .
in the infinite dilution limit , assuming that the macromolecule has one preferential conformation , the scattering intensity of a sample solution containing the macromolecule is proportional to the scattering intensity of a single macromolecule of scattering density  ( r ) , surrounded by a solvent of average electron density .
the scattering intensity   of this macromolecule at a given value of the wavevector norm q is the spherical average of the scattering intensity on the sphere of radius q in reciprocal space ( equation 1 ) . 

( 1 ) 
 where a is the excess form factor of the system and   are respectively the form factor of the solute in vacuo and of the solvent - excluded - volume .  
we perform the spherical averaging using the cubature formulae ( 30 ) . following the effective - atomic - scattering - form - factor method ( 25 ) ,
the solute and the solvent - excluded - volume 's form factors are computed as a sum over all n non - hydrogen atoms of the solute ( equations 2 and 3 ) . 

( 2 ) 
 ( 3 ) 
 where fj is the atomic form factor in vacuo ( 19 ) , computed as a sum of a constant and four gaussians whose parameters depend on the atom type ,   is the solvent volume displaced by atom j.   is an overall expansion factor , as defined in ( 19 ) , with c1 being the ratio of the adjusted and computed average atomic radii ( default value  =  1.0 ) .
programs such as aquasol ( 28 ) [ or 3d - rism / amber ( 29 ) ] compute solvent density maps around the solute , based on the physical interactions within the system .
boltzmann formalism , where the solvent is no longer described as a continuum dielectric medium but rather as an assembly of self - orienting dipoles of variable density on a grid .
it was shown that the resulting water distribution is in good agreement with experimental data and with the chemical nature of the atoms exposed to the solvent , both at the atomic and residue - level ( 26 ) .
these maps are typically cubic grids of given size and resolution ( a ) , where each grid point r is associated to a given density value .
basically , in such maps , one expects a density of 0 inside the solute , and 1 ( in units of bulk density ) in the bulk region of the solvent , i.e. far from the solute . at the boundary between the solute and bulk region ,
( 4 ) 
 the sum runs over all points with nonzero density . in practice , to reduce computation time , grid points with a density close to 1 ( i.e. typically within 1.10 ) are removed from the sum .
on urate oxidase ( example mentioned below ) , allowing a tolerance of 1.10 slowed down the computation by a factor of three and did not affect the resulting profile : the same fitting parameters were found , and the goodness - of - fit   ( cf equation 6 ) was similar ( 1.688 versus 1.691 ) . besides the solute and solvent , another possible contributor to the saxs profile is the ion atmosphere surrounding the solute .
aquasol ( 28 ) computes the density maps of free cations and anions , and , in principle , these maps could be used to compute the excess form factors of ions . however , at physiological concentrations ( 200  mm nacl ) the ratio of the fugacities of ions and water is  <  0.5% . at this stage ,
the contribution of ions was not implemented into aquasaxs , except in the form of explicitly bound and fixed ions .
nevertheless , the presence of free ions can indirectly affect the solvent density in the hydration shell ( screening effect ) , so the user is prompted for the ionic strength of the solution .
alternatively , the hydration shell 's form factor can be computed as in foxs ( 20 ) , following equation 5 . 

( 5 ) 
 where   is the fraction of solvent accessible surface of the atom j ( 31 ) and   is the water form factor .   is a scale factor used to adjust the hydration shell 's contribution ( default value  =  1.0 ) .
the computed profile   is fitted to a given experimental saxs profile   ( with experimental error ) by minimizing the goodness - of - fit function   with respect to three adjustable parameters : c1 , c2 and c ( equation 6 ) . 

( 6 ) 
 c1 and c2 values are scanned within a given range ( ,   and ) , in steps of 0.0055 , 0.014 and 0.04 , resp .
, and for each pair , a linear - least - squares minimization is performed to adjust the scaling constant c. the pair leading to the minimal  is kept to compute the returned profile .
aquasaxs was successfully tested with all pdb ( 32 ) structures that have an experimental saxs profile in the open access bioisis database ( 33 ) , and gave results similar to crysol and foxs .
the calculation scales linearly with the number of points at which the profile is sampled ( ) , as well as with the number of non - hydrogen atoms of the solute .
it scales to the cube of the number of points per grid edge , although this expensive cost is attenuated by a preliminary compressing process discarding all points with an excess density close to zero . for the solvent - map solvation option , for maps with 65 grid points per edge ( about 2   grid size )
, the calculation typically takes from less than a minute to a few minutes for systems of a few thousands atoms to dozens of thousands of atoms ( with ) , which is a few times slower than crysol and foxs . for a waxs spectrum , . for the surface - accessible solvation option
figure 1 shows the flowchart of a typical aquasaxs calculation . starting with a pdb file or a pqr file ,
the user is expected to make two decisions , namely the selection of the solvation method , and whether a comparison is made with an experimental saxs profile or not . 

a pdb or pqr file is mandatory for the calculation , and depending on the chosen method for solvation , a solvent map in cns format must be fed into the server , or the pdb file must be in pqr format .
if one wants to fit a theoretical profile to an experimental one , the latter must be provided as a formatted separate file . after the calculation
, the web browser is redirected to the result 's page , where the profiles and relative residuals are displayed , as well as a summary of the run .
a pdb or pqr file is mandatory for the calculation , and depending on the chosen method for solvation , a solvent map in cns format must be fed into the server , or the pdb file must be in pqr format .
if one wants to fit a theoretical profile to an experimental one , the latter must be provided as a formatted separate file . after the calculation
, the web browser is redirected to the result 's page , where the profiles and relative residuals are displayed , as well as a summary of the run .
there are three options for the solvation method : either a solvation map is provided as input , or a solvation map is computed using aquasol ( 28 ) , or a hydration layer is defined using the accessible surface of each atom , following the method introduced in foxs ( 20 ) .
the solvent - map solvation option will account for the hydration layer following equation 4 .
if a solvent map ( in cns format ) is provided by the user in input , it will be taken into account .
if no solvent map is provided , aquasol ( 28 ) will be run in default mode prior to aquasaxs ; in that case , the pdb input file must be in pqr format ( 34 ) ( partial charges and atomic radius must be known for all atoms ) .
the surface - accessible solvation option uses a form factor   defined as in equation 5 .
optionally , an ascii text file containing the experimental saxs profile can be given as input to aquasaxs .
lines containing data must consist of at least two columns and an optional , but recommended , third one .
the first column contains the values of the wavevector q. by default , aquasaxs defines q as   in  , where   is the scattering angle and   is the wavelength of the incident x - ray beam .
if not provided , the experimental error will be assumed to be equal to the difference between the intensity in qn , and the average intensity at qn1 and qn+1 .
if the corresponding atom is a hydrogen or belongs to a water molecule , it is discarded .
otherwise , the residue and atom 's names are parsed among the standard pdb protein , nucleic acids and ligands library ( 32 ) .
thirteen atom types are currently recognized : carbons with zero , one , two or three bound hydrogens , nitrogen with zero , one , two or three bound hydrogens , oxygen with zero or one bound hydrogen , sulfur with zero or one bound hydrogen , and phosphorus .
once the atomic type of atom j has been recognized , its position rj is stored and it is assigned the corresponding form factor fj , excluded volume   and radius . on the  flowchart web - page
, the user is given the possibility to check whether the atomic types of the residues in the provided pdb / pqr file can be recognized .
if the user wants to define other atomic types than those listed above , two optional files can be given as input to the program : one listing the atom types of a given residue , the other listing the atomic parameters of new atom types .
several other options / parameters can be set : the maximum q - value considered , the sampling resolution of the profile , the bulk average electron density ( in e. ) , the subset chains in the structure to be considered , as well as the values of c1 and c2 in the nonfitting mode .
the computation is performed in real time and the browser is redirected to the result 's page when the calculation has finished .
if an email address is provided , an email will be sent to the user .
depending on the system 's size and server 's queue load , the typical running time ranges from less than a minute to a few minutes .
the result 's page displays a plot of the computed profile ( see figure 2 ) , superimposed to the experimental profile , if provided , as well as the run logfile .
links to three output files are displayed , to retrieve the logfile , the profile file , and a pdb file listing all the atoms that have been considered in the calculation .
possibly , links toward the output files of aquasol ( 28 ) are displayed too ( computed solvent map and logfile ) . 

65 points per edge , equally spaced by 2.2   define the cubic grid ( using a higher resolution map did not significantly improve the fit ) .
the solute was immersed in an ion atmosphere of 0.1  m nacl , and the solute region was defined by its solvent - accessible surface ( with a probe radius of 1.4   ) .
one of the profile displayed here ( in blue ) was output by aquasaxs after fitting , along with the fitting parameters : c1  =  1.021 and c2  =  1.022 .
the goodness of fit is :   =  1.69 . the computation took less than 5  minutes .
the profiles fitted using foxs ( green ) and crysol ( orange ) are shown for comparison .
their respective values for the goodness - of - fit   is 2.46 and 1.53 .
foxs used c1  =  1.09 and c2  =  2.9 as fitting parameters , while crysol used  =  0.025 , ra  =  1.560   and vol  =  179  493   ( which corresponds to a volume 20% more important than the volume actually deduced from the average radius ra ) .
additional parameters for crysol were the use of up to the 30th order of spherical harmonics , and 18th order for the fibonacci grid . in every case ,
the bulk density was set at 0.334  e..the figure in inset displays the goodness - of - fit computed by aquasaxs for the range of c1 and c2 scanned by the program
. only values of   between the minimum and 6 are shown , for clarity .
65 points per edge , equally spaced by 2.2   define the cubic grid ( using a higher resolution map did not significantly improve the fit ) .
the solute was immersed in an ion atmosphere of 0.1  m nacl , and the solute region was defined by its solvent - accessible surface ( with a probe radius of 1.4   ) .
one of the profile displayed here ( in blue ) was output by aquasaxs after fitting , along with the fitting parameters : c1  =  1.021 and c2  =  1.022 .
the profiles fitted using foxs ( green ) and crysol ( orange ) are shown for comparison .
their respective values for the goodness - of - fit   is 2.46 and 1.53 .
foxs used c1  =  1.09 and c2  =  2.9 as fitting parameters , while crysol used  =  0.025 , ra  =  1.560   and vol  =  179  493   ( which corresponds to a volume 20% more important than the volume actually deduced from the average radius ra ) .
additional parameters for crysol were the use of up to the 30th order of spherical harmonics , and 18th order for the fibonacci grid . in every case ,
the bulk density was set at 0.334  e..the figure in inset displays the goodness - of - fit computed by aquasaxs for the range of c1 and c2 scanned by the program .
in addition to single conformation fitting of experimental saxs profiles , aquasaxs provides two methods to deal with multiple structure files .
the first one , called  sequential fit , provides a way to compute the saxs profile of a set of pdb / pqr files in a single run . that way ,
if an experimental profile is provided , the user can readily compare the relevance of provided models , without having to rerun the server several times .
the second method , called  ensemble fit , aims at plugging in all possible models and refining their population , and is directly inspired from ( 35 ) .
another interesting way to take profit of this approach would be the following : starting from a given pdb structure , several models are built along a given deformation parameter ( e.g. a normal mode ) ; the best value for this deformation parameter would likely be detected by the refinement process . in practice
, this method couples a mean - field optimization of the model 's populations with a simulated annealing protocol .
let us consider an ensemble of m models , each model m being associated the scattered intensity .
noting pm the associated probability ( or population ) of model m , the total scattered intensity ( in the limit of infinite dilution ) is then : 
 ( 7 ) 
 if one defines a free energy f of the form : 
 ( 8) 
 where   is defined as in equation 6 , s is the entropy , and t is the temperature , then minimizing the free energy with respect to pm gives : 
 ( 9 ) 
 where   is the inverse of ,   and   is a normalization constant given by .
the refinement starts with uniform values of the probabilities , which are updated at each cycle of the refinement until a self - consistent solution is obtained ; at each cycle the derivative are evaluated at the current solution , i.e. the current set of pm values .
the temperature governs the contrast between the different populations , the contrast being higher as the temperature is lower .
after convergence at a given temperature , the set of populations found is used as initial guess for a new mean - field refinement at lower temperature , until the final temperature is reached . results of both methods applied on synthetic data are presented in supplementary materials .
we have described a program that allows structural biologists to compare their saxs data to the theoretical one for a model given as a pdb or pqr file .
its major novelty resides in the possibility to better model the hydration layer through a physically sound representation of the solvent density map , combined with the use of the cubature method for spherical averaging .
the user - friendly interface allows to modify ( or add new entries to ) the list of scatterers and their parameters .
the possibility to fit the data with multiple models , either independently , or through population refinement has also been implemented .
future developments will allow for the possibility to refine the coordinates of the model against the experimental data .
in that case , care must be taken to use as few degrees of freedom as possible .
one possibility is to restrict the deformation of the model along a small number of 
finally , the possibility to compute the theoretical anomalous saxs profile of a solute containing atoms with anomalous contribution ( e.g. bromide or cesium ions ) will be made available soon .
 small angle x - ray scattering ( saxs ) techniques are becoming more and more useful for structural biologists and biochemists , thanks to better access to dedicated synchrotron beamlines , better detectors and the relative easiness of sample preparation . 
 the ability to compute the theoretical saxs profile of a given structural model , and to compare this profile with the measured scattering intensity , yields crucial structural informations about the macromolecule under study and/or its complexes in solution . 
 an important contribution to the profile , besides the macromolecule itself and its solvent - excluded volume , is the excess density due to the hydration layer . 
 aquasaxs takes advantage of recently developed methods , such as aquasol , that give the equilibrium solvent density map around macromolecules , to compute an accurate saxs / waxs profile of a given structure and to compare it to the experimental one . here 
 , we describe the interface architecture and capabilities of the aquasaxs web server ( http://lorentz.dynstr.pasteur.fr/aquasaxs.php ) . 
INTRODUCTION
AQUASAXS METHOD
PERFORMANCE OF AQUASAXS
AQUASAXS WEB SERVER
ADDITIONAL FEATURES
CONCLUSION
SUPPLEMENTARY DATA
FUNDING