The SHELX approach to the experimental phasing of macromolecules. George M. Sheldrick, Göttingen University

Transcription

1 The SHELX approach to the experimental phasing of macromolecules IUCr 2011 Madrid George M. Sheldrick, Göttingen University

2 Experimental phasing of macromolecules Except in relatively rare cases where atomic resolution data permit the phase problem to be solved by ab initio direct methods, experimental phasing usually implies the presence of heavy atoms. In order to locate the heavy atoms, we need their structure factors F A. The phases φ A calculated for the heavy atom substructure enable us to estimate starting phases φ T for the full macromolecular structure by: φ T = φ A + α After refining these phases we can use them and the native structure factors F T to calculate an electron density map of the macromolecule. As we will see, α, F A and F T can all be estimated from the experimental data.

3 Data files used for shelxc/d/e shelxc reads the experimental data and writes three files in addition to some useful statistics that are output to the console (and can be displayed graphically by Thomas Schneider s hkl2map). These files are: name.hkl reflection indices, merged native intensity for density modification with shelxe and possibly later refinement with shelxl. name_fa.ins running shelxd. instruction file for name_fa.hkl reflection indices, F A and α.

4 The analysis of MAD data Karle (1980) and Hendrickson, Smith & Sheriff (1985) showed by algebra that the measured intensities in a MAD experiment, assuming only one type of heavy atom, should be given by: F ± 2 = F T 2 + a F A 2 + b F T F A cosα ± c F T F A sinα where a = (f 2 +f 2 )/f 02, b = 2f /f 0, c = 2f /f 0 know f and f for each wavelength. and α = φ T φ A. We need to In a 2-wavelength MAD experiment, we have 4 equations for the 3 unknowns F A, F T and α, so with error-free data we should get a perfect map! For SIRAS, we have 2 equations for the derivative plus a native dataset. Given perfect isomorphism, the phase problem is solved. Unfortunately for SAD we only have 2 equations for the 3 unknowns.

5 SAD phasing For a single wavelength SAD experiment, we only have equations for F + 2 and F 2. Subtracting the second from the first, we obtain: F + 2 F 2 = 2c F A F T sinα For a small anomalous difference, we can assume: F T ~ ½ ( F + + F ) So using F + 2 F 2 = ( F + + F ) ( F + F ) we obtain: F + F = c F A sinα where c is 2f / f 0. c could be calculated but we would still require F A, not F A sinα, to find the heavy atoms. Lacking a better estimate, we have to input F + F (generated by SHELXC) into SHELXD. For MAD and SIRAS we can use F A, so there is no problem.

6 Starting atoms consistent with Patterson Dual space recycling for SHELXD substructure solution Based on the method introduced in the SnB program by Weeks, Hauptman et al. (1993) reciprocal space: refine phases SF calculation FFT Many cycles E > E min real space: select atoms First the F A values are normalized to E-values. The correlation coefficient CC between E obs and E calc is used to select the best solution. CC(weak) is also calculated for the reflections with E < E min ; these were not used for the substructure solution refine occupancies, save best solution so far

7 SAD substructure determination To find the heavy atoms using SHELXD, originally written for ab initio phasing using atomic resolution data, we would like to input F A, but we actually have to input F + F = c F A sinα. Why does this work? 1. SHELXD first normalizes F + F to get E-values. This gets rid of c and its resolution dependence! 2. Although all the reflections are used at the end for the occupancy refinement and the calculation of CC values, the direct methods location of the heavy atoms only uses the strongest reflections. These are likely to be the ones with sinα close to ±1. So to an adequate approximation, F + F is equal to F A!

8 SHELXD histograms and occupancies for Elastase 1 solution in 100 trials Diagrams from the hkl2map GUI S-SAD I-SIRAS

9 Critical parameters for SHELXD The Patterson-seeded dual-space recycling in SHELXD is effective at finding the heavy atoms, however attention needs to be paid to: 1. The resolution at which the data are truncated, e.g. where the internal CC between the signed anomalous differences of two randomly chosen reflection subsets falls below 30%. 2. The number of sites requested should be within about 20% of the true value so that the occupancy refinement works well (and reveals the true number). 3. In the case of a soak, the rejection of sites on special positions should be switched off. 4. For S-SAD, DSUL (search for disulfides in addition to atoms) can be very useful. 5. In difficult cases it may be necessary to run more trials (say 50000). The multiple-cpu version of SHELXD is recommended!

10 hits per tries CC CCweak Tendamistat CC, CCweak and hits per tries Occupancy (from SHELXD) of supersulfur peak 8 Occupancy of peak 9

11 SHELXD_MP multi-cpu heavy atom location The heavy atom search may require a large number of trials for weak SAD signals or when there are a large number of heavy atoms. It is however a good candidate for multi-tasking because only very limited communication is needed between different trials. shelxd has been parallelized using openmp. The scaling up is quite respectable (about 29 times for a computer with 32 real CPUs). In addition to reorganizing the output, an improved criterion is used for selecting the best solution: CFOM = CC + CC(weak) A beta-test is available on request.

12 The heavy atom enantiomorph problem The location of the heavy atoms from the F A -values does not define the enantiomorph of the heavy-atom substructure; there is exactly a 50% chance of getting the enantiomorph right. When the protein phases are calculated from the heavy atom reference phases, only one of the two possible maps should look like a protein, as this enables the correct heavy atom enantiomorph to be chosen. If the space group is one of an enantiomorphic pair (e.g. P and P ) the space group must be inverted as well as the atom coordinates. For three of the 65 Sohnke space groups possible for chiral molecules, the coordinates have to be inverted in a point other than the origin! These space groups and inversion operations are: I4 1 (1 x,½ y,1 z); I (1 x,½ y,¼ z); F (¼ x,¼ y,¼ z).

13 Simulations with one heavy atom in P1 MAD or SIRAS SIR SAD A perfect MAD or SIRAS experiment should give perfect phases! A centrosymmetric array of heavy atoms is fatal for SIR, but one heavy atom is enough for SAD even in space group P1, because it is easy to remove the negative image by setting negative density to zero!

14 Density modification The heavy atoms can be used to calculate reference phases; initial estimates of the protein phases can then be obtained by adding the phase shifts α to the heavy atom phases. These phases are then improved by density modification. Clearly, if we simply do an inverse Fourier transform of the unmodified density we get back the phases we put in. So we try to make a chemically sensible modification to the density before doing the inverse FFT in the hope that this will lead to improved estimates for the phases. Many such density modifications have been tried, some of them very sophisticated. Major contributions have been made by Peter Main, Kevin Cowtan and Tom Terwilliger. One of the simplest ideas, truncating negative density to zero, is actually not too bad (it is the basic idea behind the program ACORN).

15 The sphere of influence algorithm The variance V of the density on a spherical surface of radius 2.42 Å is calculated for each pixel in the map. The use of a spherical surface rather than a spherical volume was intended to save time and add a little chemical information (2.42 Å is a typical 1,3-distance in proteins and DNA). V gives an indication of the probability that a pixel corresponds to a true atomic position. Pixels with low V are flipped (ρ S = γρ where γ is usually set to 1.0). For pixels with high V, ρ is replaced by [ρ 4 /(ν 2 σ 2 (ρ)+ρ 2 )] ½ (with ν usually 0.5) if positive and by zero if negative. This has a similar effect to the procedure used in the CCP4 program ACORN. For intermediate values of V, a suitably weighted mixture of the two treatments is used. An empirical weighting scheme for phase recombination is used to combat model bias.

16 Density histograms Bernhard Rupp & Peter Zwart Although SHELXE makes no use of histogram matching, the sphere of influence algorithm is able to bring the histogram much closer to the one for the correct structure!

17 The free lunch algorithm The free lunch algorithm (FLA) is an attempt to extend the resolution of the data by including, in the density modification, reflections at higher resolution than have been measured. Although discovered independently and first published by the Bari group (Acta Cryst. D61 (2005) and ), the first successful implementation of the FLA was probably in 2001 in the program ACORN, but was not published until 2005 (Acta Cryst. D61 (2005) ). The unexpected conclusion was that if these phases are now used to recalculate the density, using very rough guesses for the (unmeasured) amplitudes, the density actually improves! The FLA is incorporated in SHELXE and tests confirm that the phases of the observed reflections improve, at least when the native data have been measured to a resolution of 2 Å or better.

18 Maps before and after a free lunch Best experimental phases after density modification (MapCC 0.57) After expansion to 1.0 Å with virtual data (MapCC 0.94) Isabel Usón et al, Acta Cryst. D63 (2007)

19 Why do we get a free lunch? It is not immediately obvious why inventing extra data improves the maps. Possible explanations are: 1. The algorithm corrects Fourier truncation errors that may have had a more serious effect on the maps than we had realised. 2. Phases are more important than amplitudes (see Kevin Cowtan s ducks and cats!), so as long as the extrapolated phases are OK any amplitudes will do. 3. Zero is a very poor estimate of the amplitude of a reflection that we did not measure.

20 The SHELXE autotracing algorithm A fast but very crude autotracing algorithm has been incorporated into the density modification in SHELXE. It is primarily designed for iterative phase improvement starting from very poor phases. The tracing proceeds as follows: 1. Find potential α-helices in the density and try to extend them at both ends. Then find other potential tripeptides and try to extend them at both ends in the same way. 2. Tidy up and splice the traces as required, applying any necessary symmetry operations. 3. Use the traced residues to estimate phases and combine these with the initial phase information using sigma-a weights, then restart density modification. The refinement of one B-value per residue provides a further opportunity to suppress wrongly traced residues.

21 Extending chains at both ends The chain extension algorithm looks two residues ahead of the residue currently being added, and employs a simplex algorithm to find a best fit to the density at the atom centers as well at holes in the chain. The quality of each completed trace is then assessed independently before accepting it. Important features of the algorithm are the generation of a no-go map that defines regions that should not be traced into, e.g. because of symmetry elements or existing atoms, and the efficient use of crystallographic symmetry. The trace is not restricted to a predefined volume, and the splicing algorithm takes symmetry equivalents into account.

22 Criteria for accepting chains The following criteria are combined into a single figure of merit for accepting traced chains: 1. The overall fit to the density should be good. 2. The chains must be long enough (in general at least 7 aminoacids); longer chains are given a higher weight. 3. There should not be too many Ramachandran outliers. 4. There should be a well defined secondary structure (φ /ϕ pairs should tend to be similar for consecutive residues). 5. On average, there should be significant positive density 2.9 Å from N in the N H direction (to a hydrogen bond acceptor): C C α N H O

23 Is the structure solved? If the CC for the structure factors calculated for the trace against the native data is better than 25%, it is extremely likely that the structure is solved. Another good indication is whether one can see side-chains.

24 Fibronectin autotracing This structure illustrates the ability of the autotracing to start from a noisy S-SAD map. Recycling the partial (but rather accurate) traces leads to better phases and an almost complete structure. N-terminus C-terminus Cycle 1: Cycle 2: Incorrectly traced C α Cycle 3: C α deviation: < 0.3Å < < 0.6Å < < 1.0Å < < 2.0Å < In the first cycle, 41% was traced with C α within 1.0Å, 33% within 0.5Å and 4% false. After 3 cycles the figures were 94%, 87% and 0%.

25 Fibronectin map quality MPE[ ] mapcc Standard S-SAD [ h s0.35]: S-SAD with FLA [ m200 h s0.5 e1]: S-SAD with autotracing [ h s0.35 a3]: S-SAD, autotracing and FLA [ h s0.35 a3 e1]: However, combining the FLA (free lunch algorithm) with autotracing did not produce much further improvement. Although the FLA had proved very useful in solving several borderline cases, with the phase improvement that arises from autotracing the FLA has almost been relegated to the role of cosmetic map improvements!

26 ACA2011 SHELXE Poly-Ala trace for 1y13-test In this case, assuming threefold NCS ( n3) found 50 residues more than without NCS. However the treatment of NCS in shelxe is quick and dirty and needs rewriting.

27 Extension of small MR fragments using SHELXE It often happens that a search model for structure solution by molecular replacement (MR) corresponds to only a small fraction of the total scattering power, and in such case expansion to the full structure can be tedious. For input to the beta-test shelxe, the PDB file of the MR solution is renamed to name.pda where the merged intensity data (e.g. from shelxc) are in the file name.hkl. Then e.g. shelxe name.pda -a30 -s0.5 -y2.0 -q -e1 can be used to run shelxe. A large number of tracing cycles may be needed (-a30)! A critical parameter is -y, the resolution at which to truncate the phases calculated from the MR solution. Experience suggests that -y2.0 is often best, with the implication that this approach works best with native data to a resolution of 2.0 Å or better.

28 Progress of fragment extension For this test, the variation of the CC value with the iteration number was unexpected. Instead of gradually improving, it meanders randomly at a about 10% and then suddenly, in the course of four or five iterations, jumps to a value well above 25%, indicating a solved structure. This strongly resembles the behavior of small-molecule direct methods, with the important differences that they involve data to about 1 Å or better, and start from random phases.

29 ARCIMBOLDO ab initio protein structure solution? Isabel Usón s arcimboldo uses a supercomputer to produce a large number of phaser MR solutions using very small but precise search fragments such as a 14-residue α-helix. Many potential solutions with (say) 1, 2 or 3 placed fragments are fed into shelxe, using the phaser TFZ as a broad-pass filter. If one or more shelxe attempts exceed the magic CC value of 25%, the structure has been solved! The only requirements are native data to about 2.1 Å or better, massive computing power and the presence of at least one α-helix (the more the better) in the structure. In principle any common fragment would do, but α-helices tend to have the most tightly conserved geometry. Since the median resolution of protein structures in the PDB is about 2.1 Å, the method should be able to solve at least 25% of the structures in the current PDB without using any experimental phase or other information! Isabel <iufcri@ibmb.csic.es> is currently setting up an arcimboldo supercomputer server.

30 ANODE The new program ANODE reads a PDB format file to calculate φ T and a file from shelxc containing F A and α. The heavy atom substructure phases are then calculated using φ A = φ T α. A Fourier map calculated with phases φ A and amplitudes F A then reveals the heavy atom substructure from a SAD, MAD or SIRAS etc. experiment. anode lyso would read the PDB format file lyso.ent and the lyso_fa.hkl file from shelxc. Lysozyme SAD-phased by four I3C 'sticky triangles' gave the following averaged anomalous densities: Averaged anomalous densities (sigma) I2_I3C I1_I3C I3_I3C SD_MET S_EPE (EPE is HEPES buffer) SG_CYS C9_EPE C4_I3C

31 ANODE (continued) This table is followed by a list of the highest unique anomalous peaks and the nearest atoms to each. In addition, a.pha file is written for displaying the anomalous density in coot. This approach always produces density with the same unit-cell origin as the original PDB file. Where alternative reflection indexing is possible it may be necessary to take it into account (with the switch -i). This figure clearly shows disulfides and other sulfurs, even though the anomalous data were too weak to find them using shelxd.

32 Acknowledgements I am particularly grateful to Isabel Usón, Thomas Schneider, Tim Gruene, Tobias Beck, Christian Grosse, Andrea Thorn and Navdeep Sidhu for discussions and testing various half-baked ideas. Andrea also prepared many of the pictures. Posters (Saturday 27th / Sunday 28th) MS58.P01/C591 Isabel Usón, Arcimboldo MS58.P05/C592 Christian Hübschle, shelxle MS58.P11/C595 Andrea Thorn, MR + shelxe MS58.P14/C596 Dayte Rodriguez Arcimboldo. References: SHELXC/D/E: Sheldrick (2010), Acta Cryst. D66, ARCIMBOLDO: Rodríguez, Grosse, Himmel, González, de Ilarduya, Becker, Sheldrick & Usón (2009), Nature Methods 6, The beta-tests of anode, shelxc, shelxd_mp and the autotracing shelxe are available on request to gsheldr@shelx.uni-ac.gwdg.de