BUSTER tutorial 5

Refinement of a 40% incomplete MR search model after rigid-body refinement

This tutorial illustrates the use of BUSTER for the early stages of refinement of a model after rigid-rody refinement of a Molecular Replacement solution.

The structure of the complex between the porcine pepsin ("PP", 326 residues) and its major protein inhibitor ("PI-3", 149 residues) from the Ascaris suum worm was solved by molecular replacement by Ng et al. in 2000 at 2.4 Å using search models from the native structures of the pepsin and the PI-3 inhibitor[1]. The structure was deposited with PDB accession code 1F34.

Early efforts to solve the structure of the PP_PI-3 complex by phasing with the Molecular Replacement solution for PP alone were not successful: this incomplete model for PP represents only 42% of the complex. To give an example of the difficult early stages of refinement of a severely incomplete MR solution, we present here the BUSTER refinement of the same incomplete PP MR search model, straight after rigid-body refinement.

What does BUSTER do here

There are three separate steps in this job:

1. cycle 0: the first BUSTER run uses the starting structural model (PP + bulk solvent) to phase the structure factor amplitudes; from these phases a 2Fo-Fc electron density map is computed and a prior distribution for the location of the missing atoms is derived; the output of this scaling-phasing only job is LIST.0.html
2. cycles 1-10: the second step is the Maximum Likelihood refinement of the PP partial structure model, while the distribution for the missing atoms is kept equal to the initial one; data up to 2.4 Å are used for refinement.
3. cycles 11-13: the third step is the Maximum Entropy density modification of the density for the missing PI-3, using data up to 3.0 Å, while the model for the partial structure is kept to what is was at the end of refinement.

Input Preparation

A few parameters need some attention: see the simple quick input guide

Main items of the output

1. Observed and calculated structure factor amplitudes plots: with no model traced for PI-3 at all, a good model for the scattering from the bulk solvent is not straightforward to construct. Here we compare the plots of calculated and observed F's with bulk solvent model (from the BUSTER calculation described in this document ) and without it (a different one):

   With bulk solvent: the lowest-resolution model amplitudes are too low with respect to the observed ones: the bulk solvent mask based on PP alone is too large, and the masking effect too pronounced. Still, this is the best we can do with the BUSTER code as it is now. See on the side the effects of omitting the bulk solvent model altogether.

   No bulk solvent: the model F's(from a different BUSTER calculation ) would be too strong with respect to the observed F's at low-resolution: the masking of the partial structure F's would be effected by the flat regions of the missing atoms envelope only. Omitting the bulk solvent mask would not be a good choice. Notice also that the absence of a bulk solvent model bends the scaling, and the values of <Fobs> on absolute scale as plotted here are be quite different from the ones in the plot aside (the scale factor of this calculation comes out as 1.3 instead of 1.1)

2. R-factors and Log-likelihood gain plots: the simplest way of checking if the model parameters are indeed improving the fit to the working- and free-set.

   The R values at after the first round of scaling, at cycle 0 are around 40%. During refinement (cycles 1-10) the R factors decrease; the final working-set and free-set Rfactors do not differ by less than one percent. The Maximum Entropy completion (cycles 11-13) overfits but manages to reduce the Rfree nevertheless.

   The plot of Log-Likelihood gain vs. cycle number shows an increase of the LLG, starting from the initial value of 0; The working-set LLG is bound to increase because the refinement is driven by maximising the likelihood of the model with respect to the working set; more important is to check that the free-set LLG increases as well. Again, as observed with R factors, some overfitting is introduced but a small improvement in the free LLG is evident.

3. Correlation coefficients plots: the correlation coefficients curves are a good tool to monitor the improvement in the structural model during refinement and MaxEnt completion; they are independent of the overall scale factor but do depend on the values of the relative scale factors between the partial and missing structures.

   The (F_obs,F_frag) and (F_obs,F_calc) curves only differ at low resolution because in F_calc there are contributions from the solvent and the low-resolution envelope for the missing atoms, while in F_frag only the atoms in the PDB model for the partial structure are taken into account.

   Most importantly, the (F_calc,F_expct) curve depends on the imperfection parameters that parameterise the BUSTER internal error model. The larger the internal estimate for the error on the calculated F, the more this CC curve departs from unity. A comparison between the (F_calc,F_expct) and the (F_obs,F_calc) correlation coefficients curves can inform as to the adequacy of the BUSTER internal error model: if the latter is correct, after the first cycle the two curves should be close to one another.

   The (F_obs,F_obs+d) curve is a measure of the noise on the data vs. resolution. This correlation coefficient is lower than unity when the noise on the data becomes large (typically at high resolution, where the I/s(I) is lowest).

   • It is useful to compare the Correlation Coefficient curves between cycle 0 and cycle 10:

     Cycle 0: At the outset, you can see that the ``observed correlation'' (Fobs,Fcalc) roughly matches the ``predicted correlation'' (Fcalc,Fexpct). The initial error model is adequate.

     Cycle 10: At the end of the last cycle of refinement the high-resolution CC values are closer to unity than they were at the beginning: this is due to the improvement of the model for the partial structure. If we were to continue for longer, the CC values would only ever so slightly improve. This usually indicates that the partial structure contains errors which the refinement is unable to correct. Manual rebuilding is in order. The imperfection Bfactor for the partial structure at the end of refinement has a value around 7.9 (see curves below): the ``predicted correlation'' (Fcalc,Fexpct) is in good agreement with the ``observed'' one, (Fobs,Fcalc). Only the very low resolution has worsened, because the solvent model is still very inadequate and its associated error model has increased (see below).

   • Let's now see the Correlation Coefficient curves at the end of the Maximum Entropy calculation (cycle 13).

     Cycle 13: At the end of the Maximum Entropy calculation, the fit to the working-set low-resolution amplitudes is very good, but as seen above there is some overfitting. No improvement is brought about to the missing atoms model past the 3.0 Å limit because no Lagrange multipliers were used for those data. The (Fobs,Ffrag) CC curve remains unchanged because no changes are made to the partial structure. The imperfection parameters for the missing atoms model and the bulk solvent (see curve on the side) keep the error model so large that the ``predicted correlation'' (Fcalc,Fexpct) is lower than the observed (Fobs,Fcalc): but recalling the values of the free likelihood gain during Maximum Entropy completion, this ''pessimistic'' error model is probably correct.

     B imperfection factors refinement: the plot of the imperfection B factors can be used to confirm that the partial structure is improving during refinement and that the error model becomes smaller. As refinement progresses, the value of the imperfection B for the partial structure should decrease. In this case Bimpf frag levels off to a value around 7.9. Again, this is a sign that the refinement is unable to correct the error in the partial structure: manual rebuilding is in order. At the same time, the variance is taken up by the Bimpf solv the measure of the imperfection of the bulk solvent model.

Final Results

• The coordinate files of the refined partial structure are in the PDB file: shell.01/PP_PI-3.0.final.pdb.

  If you inspect the 2Fo-Fc and Fo-Fc maps, together with the deposited PDB model for the PP_PI-3 complex, you notice how parts of the PI-3 missing inhibitor are already visible (e.g.the B1-B13 strand; the poly-Pro helix B139-B143; parts of the long helix B97-B120). It is also apparent that PP needs rebuilding in many points (e.g. serines A49, A68, A72, A294, A207; Glu A70)

• The next step will be to start a refinement after manual rebuilding, with a model for the missing atoms computed from the map from this calculation - the latter option only being available to users of a level higher than standard.

References