The Free R Factor

Blind trust in the power of least squares programs has often been betrayed, and it has been responsible for many, if not most of the errors that have crept into protein structure determination. This problem was largely remedied, however, in the early 1990s by the introduction by Brunger (1992) of the R free. The R free is basically free of the tendency of programs to over-refine structures, to produce low R factors (now commonly called the working R factor) and incorrect structures. 

The idea with the R free is to omit from the least squares calculations, from the observational equations, a subset of the observed structure amplitudes. This set usually constitutes about 10% of the total data and is chosen to be representative of all resolution and magnitude ranges of the reflections. The least squares procedure is then executed as before, but this time only the reflections in the omitted subset are used in the calculation of R free. Two things are true. If the refinement indeed led to an improved model that is closer to the truth, 

The use of the Rfree has had a near revolutionary effect on protein structure refinement. It is now de rigueur to report Rfree values for any protein structure refinement. The only point that remains in contention is what value constitutes an appropriate Rfree, given a particular resolution, data quality, molecular weight, and so on. 

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One possibility is to run simulated annealing refinement in torsion angle space as implemented in CNS (Briinger et ah, 1998). As this is one of the most powerful programs in terms of radius of convergence, it is especially useful to look for the decrease of the free-R-factor (Adams et al., 1999), but this is a rather cpu-intensive task if several possible solutions are to be tested. 

In using cross-validation it is essential to avoid, or at least minimize, bias to the free R factor itself. In the era of emerging automated procedures for modelling and refinement a frequent mistake is to set aside a fraction of reflections for minimization of the residual in reciprocal space and, at the same time, to use all data for computation of electron density and model rebuilding. Since local adjustment of the model in real space is equivalent to global phase adjustment in reciprocal space, the free reflection set becomes biased towards the current model and loses its validation credibility. 

Interpretation of the electron density map allowed the chain tracing for most parts of the polypeptide chain. Refinement has been carried out using X-PLOR and REFMAC, and manual model rebuilding resulted in an R-factor of 22.4% for all 2a data between 10.0 and 2.8 A resolution. Using a 5% reflection test set (1,380 reflections) the free R-factor [2] value is 29.0%. 

One complementary criterion of model quality during the refinement is the free-R factor, which is computed with a small set of randomly chosen intensities, the test set, which are not used in the refinement. 

The final result of structure determination is a coordinate, or protein database (pdb) file, that describes the model that was built from the scattering data/electron density map. This file contains the Cartesian coordinates for the protein, any bound ligands, numerous water molecules, as well as any other atoms/ molecules whose positions are relatively fixed in the crystal. The accuracy of this model can be assessed using a number of parameters, including (i) a comparison of the R-factor to the free R-factor, (ii) the temperature (or B) factor, and (iii) the number of Ramachandran outliers. Although these factors can be combined to form a single quality index (Brown and Ramaswamy, 2007), it is useful to discuss the individual parameters since these parameters can often be directly obtained from the downloaded coordinate file. 

The form of the free volume factor /(r) is so far generally taken to be... 

Unlike the native integration of DIVCON with the sander module in AMBER, the integration of CNS was done at the file system level. For every step of hybrid minimization, CNS, after receiving atomic coordinates from sander, calculates and outputs the forces as the gradient of Ex-ray in Eq. (13-11), which is then read by sander. Sander combines the forces from Ex-ray and Eqm/mm potential and updates the coordinates accordingly. This process proceeds until the R and free R factors converge, which usually takes a few hundreds of steps. 

Free R-factor. Since refinement programs aim at minimizing the difference between observed and calculated amplitudes, that is the f -factor, another unbiased indicator is needed to monitor the progress of refinement. Briinger proposed to exclude a subset of reflections from refinement and to use these reflections only for the calculation of free f -factors. ° If refinement is progressing correctly the free f -factor will drop, but if the model contains serious errors it will remain stalled above 35%. For correct structures, the free / -factor is generally below 30%. 

The next most important mechanism affecting the surface tension at a single component simple fluid gas-liquid interface is, we believe, associated with the nonlocality of the repulsive interactions. To account for this mechanism, observe that it enters by way of the excluded volume effect. In the coarse-grained GvdW(S) theory above, the free volume factor /(r) is given by... 

Where, /(k) is the sum over N back-scattering atoms i, where fi is the scattering amplitude term characteristic of the atom, cT is the Debye-Waller factor associated with the vibration of the atoms, r is the distance from the absorbing atom, X is the mean free path of the photoelectron, and is the phase shift of the spherical wave as it scatters from the back-scattering atoms. By talcing the Fourier transform of the amplitude of the fine structure (that is, X( )> real-space radial distribution function of the back-scattering atoms around the absorbing atom is produced. 

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