saxs is becoming a widely used technique for low - resolution structural characterization of molecules in solution ( 16 ) . unlike em , nmr and x - ray crystallography , the key strength of saxs is that it can be performed under a wide variety of solution conditions , including near physiological conditions . the experiment is performed with 1.0 mg / ml of a macromolecular sample in a 15 l volume , and usually takes only a few minutes on a well - equipped synchrotron beam line ( 4 ) . the saxs profile of a macromolecule , i(q ) , is computed by subtracting the saxs profile of the buffer from the saxs profile of the macromolecule in the buffer . the profile can be converted into an approximate distribution of pairwise atomic distances of the macromolecule ( i.e. the pair - distribution function ) via a fourier transform . computational approaches for modeling a macromolecular structure based on its saxs profile can be classified into ab initio and rigid body modeling methods ( 3 ) . on the one hand , the ab initio methods search for coarse 3d shapes represented by dummy atoms ( beads ) that fit the experimental profile ( 79 ) . on the other hand , rigid body modeling approaches refine an atomic model of the molecule with the aim to fit the computed saxs profile to the experimental one ( 10 ) . therefore , rigid body modeling can be used only if an approximate structure of the studied molecule or its components are available . rigid body modeling approaches require the computation of the saxs profile of a given atomic structure and its comparison with the experimental profile . here foxs can be used as a tool for numerous saxs - based modeling applications , such as comparing solution and crystal structures ( 4 ) , modeling of a perturbed conformation ( e.g. modeling active conformation starting from non - active conformation ) ( 11 ) , structural characterization of flexible proteins ( 12,13 ) , assembly of multi domain proteins starting from single domain structures ( 14 ) , assembly of multi protein complexes ( 10 ) , fold recognition and comparative modeling ( 15,16 ) , modeling of missing regions in the high - resolution structure ( 17 ) , and determination of biologically relevant states from the crystal ( 18,19 ) . there are several methods and software tools for calculating a saxs profile of a given molecular structure . the methods differ in the use of the inter - atomic distances and in the treatment of the solvation layer ( 20 ) . inter - atomic distances can be computed and used explicitly ( 5,14 ) . the most popular method crysol ( 21 ) , also available as a web server , uses multipole expansion for fast calculation of the spherically averaged scattering profile . another widely used approach is monte carlo sampling of the distances in the model ( 22 ) . coarse graining that combines several atoms in a single scattering center can also be used to speed up the calculation ( 23,24 ) . the solvation layer can be treated explicitly by introducing water molecules ( 24,25 ) or implicitly by a continuous envelope surrounding the model ( 21 ) . foxs is a rapid and accurate web server for calculating a saxs profile of a given molecular structure that explicitly computes all inter - atomic distances as well as models the first solvation layer based on the atomic solvent accessible areas . the server also provides an optimization of the hydration layer density as well as the excluded volume of the protein , to maximize the fit of the computed profile to the experimental profile . additional optimization is achieved by adjusting the  background of the experimental profile for wider scattering angles ( 26 ) . the method for computing saxs profiles is based on the debye formula ( 27 ) : 
 ( 1 ) 
 where the intensity , i(q ) is a function of the momentum transfer q = ( 4 sin )/ , where 2 is the scattering angle and  is the wavelength of the incident x - ray beam ; dij is the distance between atoms i and j , and n is the number of atoms in the molecule . in our model , the form factor fi(q ) takes into account the displaced solvent as well as the hydration layer : 
 ( 2 ) 
 where fv(q ) is the atomic form factor in vacuo ( 21 ) , fs(q ) is the form factor of the dummy atom that represents the displaced solvent ( 28 ) , si is the fraction of solvent accessible surface of the atom i ( 29 ) , and fw(q ) is the water form factor . the parameter c1 is used to adjust the total excluded volume of the atoms ( default value = 1.0 ) and c2 is used to adjust the density of the water in the hydration layer ( default value = 0.0 ) . i(q ) is calculated rapidly per equation 1 as described in detail in ( 14 ) . the computed profile is fitted to a given experimental saxs profile by minimizing the  function with respect to c , c1 and c2 : 
 ( 3 ) 
 where iexp(q ) and i(q ) are the experimental and computed profiles , respectively , (q ) is the experimental error of the measured profile , m is the number of points in the profile , and c is the scale factor . the minimal value of  is found by enumerating c1 and c2 ( 0.95  c1  1.12 and 0  c2  4.0 ) , in steps of 0.005 and 0.1 respectively ) , and performing the linear least - squares minimization to find the value of c that minimizes  for each c1,c2 combination . in addition , foxs has an option to adjust the background of the experimental profile ( 26 ) . foxs was successfully tested with all pdb structures ( 30 ) that have an experimental saxs profile in the open access saxs database ( http://bioisis.net/ ) ( 4 ) as well as a number of additional cases ( in preparation ) . the web server has one mandatory input , a structure file in the pdb format ( or a zip archive with multiple pdb files ) . the server assigns form factors for the standard pdb protein and nucleic acid atoms . for other types of molecule , hydrogen atoms are considered implicitly for proteins and nucleic acids by adding their form factors to that of their bound heavy atom . if the input structure includes other groups , such as lipids or sugars , it is recommended to add all the hydrogens explicitly and turn off the the optional input includes an experimental saxs profile , which must be obtained for the exact molecule specified in the input pdb file ( including all loops , linkers and his tags ) . the profile is specified in a text file with three columns : q , i(q ) , (q ) 
 # q intensity error0.00000 3280247.73 1904.0370.00060 3280164.59 1417.0310.00120 3279915.19 1840.032 
 where q = ( 4sin)/ , 2 is the scattering angle and  is the wavelength of the incident x - ray beam . it is recommended to provide an accurate error estimate of (q ) because it is used for the profile fitting . if the third column is not given , foxs will assume the error is distributed according to the poisson distribution with  = 10 . 0.00000 3280247.73 1904.037 0.00060 3280164.59 1417.031 0.00120 3279915.19 1840.032 the server also has several optional input parameters . a user can specify an e - mail address for emailing a link to the results page . maximal q value determines the range for calculating the profile ( default qmax = 0.5  ) . a user can also control the sampling resolution of the profile by setting the number of points in the profile . the profile will be sampled at the resolution equal to the maximal q value divided by the number of profile points . for example , if the qmax value is 0.5 and a user asks for 1000 profile points , the resulting profile will be uniformly sampled at the interval of 0.0005 . in addition , a user can also decide whether or not to include the hydration layer in the profile computation ( included by default ) . it is also possible to decide whether or not to adjust the excluded volume of the protein ( c1 value  adjusted by default ) and the background of the experimental profile ( not adjusted by default ) . once the inputs are defined , foxs computes the saxs profile of the input pdb structure(s ) and fits it to the experimental profile , if provided . for fitting , the computed profile is resampled at the q values sampled by the experimental profile , with the computed intensities estimated using linear interpolation . the server does not modify the input experimental profile , unless background adjustment is requested . the computation is performed in real time and the server page is updated once the calculation has finished . the typical running time is less than a second for a system of a thousand of atoms , and can extend to a few minutes for tens of thousands of atoms . the output page displays a plot of the computed profile as well as a plot of the computed profile fitted to the experimental profile ( figure 1 ) . in addition , the values of  , c1 and c2 for the current profile fit are displayed . the profiles and their fit can be downloaded . in case of multiple pdb files in the input , the server will display computed profile plots for each pdb file , as well as plots with their fit to the experimental profile . in addition , a single plot with all the computed profiles and a plot with computed profiles fitted to the experimental profile are displayed . computed profiles of two pdb files are compared to the experimental saxs profile of malic enzyme ( data from http://bioisis.net/ , pf1026 ) . the first structure ( pdb_model ) includes a model of the unfolded his tag region ( 35 residues ) , while the second structure ( 2dvm ) does not . the server was run with the default parameters and the hydration layer modeling was disabled . plots on the left display the theoretical profiles and plots on the right display their fit to the experimental profile . the top two plots are for the structure with the modeled unfolded region ( pdb_model ) , the middle two plots are for the original pdb file ( 2dvm ) , the bottom left plot overlay the profiles for the two input structures , and the bottom right plot shows their fit to the experimental profile . the structure with the modeled unfolded region shows a better fit to the experimental profile with the value of  = 2.88 , compared to  = 6.33 for the original crystallographic structure . snapshot of a foxs output page . computed profiles of two pdb files are compared to the experimental saxs profile of malic enzyme ( data from http://bioisis.net/ , pf1026 ) . the first structure ( pdb_model ) includes a model of the unfolded his tag region ( 35 residues ) , while the second structure ( 2dvm ) does not . the server was run with the default parameters and the hydration layer modeling was disabled . plots on the left display the theoretical profiles and plots on the right display their fit to the experimental profile . the top two plots are for the structure with the modeled unfolded region ( pdb_model ) , the middle two plots are for the original pdb file ( 2dvm ) , the bottom left plot overlay the profiles for the two input structures , and the bottom right plot shows their fit to the experimental profile . the structure with the modeled unfolded region shows a better fit to the experimental profile with the value of  = 2.88 , compared to  = 6.33 for the original crystallographic structure . a saxs profile can provide significant insight into the structures of macromolecules , especially when combined with other information . saxs experiments are gaining in popularity due to the technological advances that allow rapid and accurate data collection for a relatively small amount of the sample . , we described a rapid , accurate , and user - friendly web server for calculating a saxs profile of a given atomic structure and its fitting to the experimental profile . the web server can be used in a wide range of saxs , such as comparing solution and crystal structures , modeling of a perturbed conformation ( e.g. modeling active conformation starting from non - active conformation ) , structural characterization of flexible proteins , assembly of multi domain proteins starting from single domain structures , assembly of multi protein complexes , fold recognition and comparative modeling , modeling of missing regions in the high - resolution structure , and determination of biologically relevant states from the crystal . weizmann institute advancing women in science postdoctoral fellowship to dsd ; sandler family supporting foundation , national institutes of health ( r01 gm083960 ) ; national institutes of health ( u54 rr022220 ) ; national institutes of health ( pn2 ey016525 ) ; doe program integrated diffraction analysis technologies ( idat ) , pfizer inc .
small angle x - ray scattering ( saxs ) is an increasingly common technique for low - resolution structural characterization of molecules in solution . 
 saxs experiment determines the scattering intensity of a molecule as a function of spatial frequency , termed saxs profile . 
 saxs profiles can contribute to many applications , such as comparing a conformation in solution with the corresponding x - ray structure , modeling a flexible or multi - modular protein , and assembling a macromolecular complex from its subunits . 
 these applications require rapid computation of a saxs profile from a molecular structure . 
 foxs ( fast x - ray scattering ) is a rapid method for computing a saxs profile of a given structure and for matching of the computed and experimental profiles . here 
 , we describe the interface and capabilities of the foxs web server ( http://salilab.org/foxs ) .