1. EMBL-EBI MSDpisa a web service for studying Protein Interfaces, Surfaces and Assemblies Eugene Krissinel http://www.ebi.ac.uk/msd-srv/prot_int/pistart.html

2. EMBL-EBI What PISA is about Crystal = translated Unit Cell More than 80% of protein structures are solved by means of X-ray diffraction on crystals. An X-ray diffraction experiment produces atomic coordinates of the crystal’s Asymmetric Unit (ASU). In general, neither ASU nor Unit Cell has any relation to Biological Unit, or stable protein complex which acts as a unit in physiological processes. Is there a way to infer Biological Unit from the protein crystallography data? Unit Cell = all space symmetry group mates of ASU PDB file

3. EMBL-EBI ? no image or bad image In (very) simple words … 2 crystallisation 3 in crystal ?? good image but no associations in vivo 1

4. EMBL-EBI At first glance … … the solution is simple as 1-2: 1.Evaluate all protein contacts (interfaces) in crystal 2.Leave only the strongest (“biologically relevant”) ones - and what you get will have chances to be a stable protein complex. Small technical problem: How to discriminate between “real” (biologically relevant) and “superficial” (inter-assembly, or crystal packing) interfaces?

5. EMBL-EBI Real and superficial protein interfaces Most often used discrimination criteria - interface area. A cut-off at 900 Å 2 gives about 80% success rate of discrimination between monomers and dimers. Big proteins would be always sticky if this criteria is true …

6. EMBL-EBI Free energy gain of interface formation. A cut-off at -8 kcal/M gives about 82% success rate of discrimination between monomers and dimers. Can energy measure be uniform for all weights and shapes? Real and superficial protein interfaces

7. EMBL-EBI Real and superficial protein interfaces P-value of hydrophobic patches. A measure of probability for the interface to be more hydrophobic than found. A cut-off at 0.2 gives about 60% success rate of discrimination between monomers and dimers.

8. EMBL-EBI Real and superficial protein interfaces Packing edge factor. A measure showing how closely the mass packing edge matches the actual interface. A cut-off at 0.3 gives about 60% success rate of discrimination between monomers and dimers interface packing edge

9. EMBL-EBI  No ultimate discriminating parameter for the identification of biologically relevant protein interfaces may be proposed at present even for dimeric complexes Jones, S. & Thornton, J.M. (1996) Principles of protein-protein interactions, Proc. Natl. Acad. Sci. USA, 93, 13-20.  Formation of N>2 -meric complexes is most probably a corporate process involving a set of interfaces. Therefore significance of an interface should not be detached from the context of protein complex Real and superficial protein interfaces

10. EMBL-EBI Making assemblies from significant interfaces  PQS server @ MSD-EBI (Kim Henrick) Trends in Biochem. Sci. (1998) 23, 358 Method: recursive splitting of the largest complexes as allowed by crystal symmetry. Termination criteria is derived from the individual statistical scores of crystal contacts. The results are not curated.  PITA software @ Thornton group EBI (Hannes Ponstingl) J. Appl. Cryst. (2003) 36, 1116 Method: progressive build-up by addition of monomeric chains that suit the selection criteria. The results are partly curated. Despite failure to find an ultimate measure for interface biological relevance, two approaches were developed that use scoring of individual interfaces:

11. EMBL-EBI  It is not properties of individual interfaces but rather chemical stability of protein complex in general that really matters  Protein chains will most likely associate into largest complexes that are still stable  A protein complex is stable if its free energy of dissociation is positive: Chemical stability of protein complexes How to calculate  G diss ?

12. EMBL-EBI Protein affinity Solvation energy of protein complex Solvation energies of dissociated subunits Free energy of H-bond formation Number of H- bonds between dissociated subunits Free energy of salt bridge formation Number of salt bridges between dissociated subunits Dissociation into stable subunits with minimum Choice of dissociation subunits:  G int is function of protein interfaces

13. EMBL-EBI Solvation free energy Atomic solvation parameters Atom’s accessible surface area Atom’s accessible surface area in reference (unfolded) state protein solvent Eisenberg, D. & McLachlan, A.D. (1986) Nature 319, 199-203.

14. EMBL-EBI Entropy of macromolecules in solutions Translational entropyRotational entropySidechain entropy Mass Solvent-accessible surface area Tensor of inertia Murray C.W. and Verdonik M.L. (2002) J. Comput.-Aided Mol. Design 16, 741-753. Symmetry number c t, c r and F are semiempirical parameters

15. EMBL-EBI Entropy of dissociation Fitted parameter Mass of i-th subunit k-th principal moment of inertia of i-th subunit  S is function of protein complex

16. EMBL-EBI How to identify an assembly in crystal? We now know (or we think that we know) how to evaluate chemical stability of protein complexes. Given a 3D-arrangement of protein chains, we can now say whether there are chances that this arrangement is a stable assembly, or biological unit. But how to get potential assemblies in first place?

17. EMBL-EBI How to catch a Desert Lion? Method of Desert Lion Catch all lions and keep One living in Desert

18. EMBL-EBI Enumerating assemblies in crystal  crystal is represented as a periodic graph with monomeric chains as vertices and interfaces as edges  each set of assemblies is identified by engaged interface types  all assemblies may be enumerated by a backtracking scheme engaging all possible combinations of different interface types Example: crystal with 3 interface types Assembly set Engaged interface types 1000- only monomers 2001- dimer N1 3010- dimer N2 4011 Assembly set Engaged interface types 5100- dimer N3 6101 7110 8111- all crystal

19. EMBL-EBI Clever backtracking The number of different interface types may reach a hundred. The algorithm is not going to complete backtracking of 2 100 combinations unless it is clever enough to  check geometry and engage induced interfaces as soon as they emerge  check geometry and terminate backtracking if assembly contains two identical chains in parallel orientations  see the future and terminate backtracking if there are no stable assemblies down the current branch of the recursion tree Engaged interfaces Induced interface Otherwise assembly will be infinite due to translation symmetry in crystal Based on the observation that entropy of dissociation of unstable assemblies only increases down the recursion tree … only then the algorithm completes in 0.1 secs to 1.5 hours depending on the structure …

20. EMBL-EBI Detection of Biological Units in Crystals 1.Build periodic graph of the crystal 2.Enumerate all possibly stable assemblies 3.Evaluate assemblies for chemical stability 4.Leave only sets of stable assemblies in the list and range them by chances to be a biological unit : Larger assemblies take preference Single-assembly solutions take preference Otherwise, assemblies with higher  G diss take preference Method Summary

21. EMBL-EBI Are we any close? Assembly classification on the benchmark set of 218 structures published in Ponstingl, H., Kabir, T. and Thornton, J. (2003) Automatic inference of protein quaternary structures from crystals. J. Appl. Cryst. 36, 1116-1122. 198+20 198 homomers and 20 heteromers Fitted parameters: 1.Free energy of a H-bond : 2.Free energy of a salt bridge : 3.Constant entropy term : 4.Surface entropy factor : = 0.51 kcal/mol = 0.21 kcal/mol = 11.7 kcal/mol = 0.57·10 -3 kcal/(mol*Å 2 ) Classification error in  G diss : ± 5 kcal/mol

22. EMBL-EBI A better method?  PQS server :78% (not optimised on the benchmark set, but manually curated)  PITA software : 84% (optimised with 18 parameters, system overfit(?))  Present study :90% (optimised with 4 parameters, system underfit) Percent of successful classifications, as measured on the same benchmark set of 218 PDB entries:

23. EMBL-EBI What is beyond the benchmark set? Classification results obtained for 366 recent depositions into PDB in reference to manual classification in MSD-EBI : 321+45 321 homomers and 45 heteromers Classification error in  G diss : ± 5 kcal/mol

24. EMBL-EBI Is it ever going to be 100%?  theoretical models for protein affinity and entropy change upon protein complexation are primitive  coordinate (experimental) data is of a limited accuracy  there is no feasible way to take conformations in crystal into account  experimental data on multimeric states is very limited and not always reliable - calibration of parameters is difficult  protein assemblies may exist in some environments and dissociate in other - a definite answer is simply not there Nobody should be that naive, because :

25. EMBL-EBI Web-server PISA A new MSD-EBI tool for working around Protein Interfaces, Surfaces and Assemblies http://www.ebi.ac.uk/msd-srv/prot_int/pistart.html

26. EMBL-EBI

29. Conclusions  Stable protein complexes, which are likely to be biological units, may be calculated from protein crystallography data at 80-90% success rate  Biological relevance of a particular protein interface cannot be reliably inferred from the interface properties only. Instead, one should conclude about significance of an interface from the analysis of the relevant protein assemblies Acknowledgement. This work has been supported by research grant No. 721/B19544 from the Biotechnology and Biological Sciences Research Council (BBSRC) UK.