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The Greek Key Motif

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  1. The Greek Key Motif Shuo Xiang (Alex) Dr. Ming Li CS 882 Course Project Presentation Fall 2006

  2. Outline • Introduction • What is a Greek key? • Where do Greek keys occur? • History of the Greek key motif • Formal Definition • Preparatory knowledge • Formal definition of Greek key • Classification of Greek key

  3. Outline • Operational Definition and Machine recognition of Greek keys • Motivation • PDB • DSSP • PROMOTIF • Greek key hunter • Greek key hunter in action • Setup • Results

  4. Part 1Introduction

  5. What is a Greek Key • A Greek key is a series of four consecutive β strands taking on the conformations shown to the right when viewed in a topology diagram (Branden and Tooze, 1999)

  6. What is a Greek key • Note, however, that topology diagrams are a simplified way of representing proteins, in real life, Greek keys look more like the object shown to the right. The picture is generated by PyMOL on PDB file 4GCR for γ crystallin with residues 34-62 displayed and everything else masked.

  7. What is a Greek Key • The Greek keys were so named because of their visual affinity to decorational patterns used in ancient Greek vases shown below (Li, 2006)

  8. Where do Greek keys occur? • Being a β-motif, Greek keys obviously occur only in proteins having β-strands. • This means that α-only proteins such as myoglobin and hemoglobin will not have Greek keys • From Dr. Li’s lectures, we also know that γ-crystallins are a very important class of proteins whose Greek key motifs have evolutionary significance

  9. Where do Greek keys occur? • According to Dr. Hutchinson and Dr. Thornton, (Hutchinson and Thornton, 1993), Greek key motifs could also be found in the following proteins: • Trypsin • Haemmagglutinin • Tumour necrosis factor (TNF) • Immunoglobulins • Azurin

  10. Where do Greek keys occur? • Prealbumin • PapD (which is a chaperon) • Nitrite reductase • Insecticidal δ-endotoxin • Bacterial cellulase • Sperical virus capsid proteins

  11. History of Greek key • The Greek key motif was first studied and formally characterized by Dr Jane S. Richardson in her paper “β-Sheet topology and the relatedness of proteins” (Richardson, 1977) • In (Richardson, 1977) Dr. Richardson has compared Greek key motifs to the Greek keys found on a black Greek vase

  12. History of Greek key

  13. History of Greek key • The earliest Greek key containing protein whose structure has entered the PDB is Immunoglobulin FAB (7FAB) • Its structure is determined by Dr. F.A. Saul and Dr. R.J. Poljak using x-ray diffraction in August 27, 1976 (Saul and Poljak, 1992)

  14. Part 2Formal Definition

  15. Preparatory Knowledge • Three dimensional protein representations are often too complex for any useful patterns to be extracted. • Therefore, a simpler, two dimensional abstraction of proteins, known as a “topology diagram” is used. • In a topology diagram, α-helices and β-strands are laid out across a role, with their spatial orientations and connections (coils) preserved. β-sheets are also preserved to a certain extent.

  16. Preparatory Knowledge • It is when one lays out the topology diagram for proteins that structural motifs such as the Greek key becomes apparent. • Dr. Jane Richardson was the earliest researcher to study topologies of β-structures. • During her study, she has created a nomenclature for β-strand topologies (Richardson, 1981)

  17. Preparatory Knowledge

  18. Preparatory Knowledge • Therefore, Dr. Richardson’s nomenclature of β-strand topologies may be summarized as: • “+y” : coil goes yβ-strands to the right, starting β-strand and destination β-strand are anti-parallel to each other • “-y” : coil goes yβ-strands to the left, starting β-strand and destination β-strand are anti-parallel to each other • “+yX” : coil goes yβ-strands to the right, starting β-strand and destination β-strand are parallel to each other • “-yX” : coil goes yβ-strands to the left, starting β-strand and destination β-strand are parallel to each other

  19. Formal Definition of Greek key • With Dr. Richardson’s nomenclature, Greek keys could now be formally defined as any set of 4 consecutive β-strands having the topology of “-3, +1, +1” or “-1, -1, +3” (Hutchinson and Thornton, 1993)

  20. Classification of Greek key • However, not all four β-strands of the Greek key falls within the same β-sheet. • Hence there arises a need to classify Greek key structures according to their distribution of β-strands amongst β-sheet(s). • Dr. Hutchinson and Dr. Thornton has given such a classification in (Hutchinson and Thornton, 1993)

  21. Classification of Greek key • If all four β-strands of the Greek key lie in the same β-sheet, then it is called a (4,0) Greek key, meaning that there are four strands in one β-sheet and zero strands in the other β-sheet. • Note that β-strands of a Greek key can go into at most two β-sheets. More than two β-sheets would make it very hard to decide whether a Greek key exists instead of some other random β-structure.

  22. Classification of Greek key • Furthermore, (4,0) Greek keys come in two flavours — an “N” version where the N-end of the Greek key is on the outside, and a “C” version where the C-end of the Greek key is on the outside. This is shown in the diagram below.

  23. Classification of Greek key • Similarly, (Hutchinson and Thornton, 1993) classified the following as (3,1)N and (3,1)C Greek keys. Note that the green arrow represents β-strands from a different β-sheet.

  24. Classification of Greek key • (Hutchinson and Thornton, 1993) also classified the (2,2) structures as having an “N” version and a “C” version • However, from an examination of the PROMOTIF outputs (to be covered later) and the fact that the “N” version could be rotated to produce the “C” version, and so the two versions are topologically equivalent to each other, I conclude that there is only one flavour of (2,2) structure.

  25. Classification of Greek key • For this project the classification of (Hutchinson and Thornton, 1993) is extended to include the following additional combinations of four β-strands from two different β-sheets

  26. Part 3Operational definition and machine recognition of Greek keys

  27. Motivation • In the previous part, we have developed a “formal” definition of what Greek keys are in terms of topological diagrams • But we need an “operational” definition of what Greek keys are so that computers will be able to identify them from PDB files • The “formal” definition, while fine for humans, remains too sketchy and ambiguous for computers to work with

  28. Motivation • In this part the various software whose output the “Greek key hunter” depends on will be examined • I will then show the working principles of “Greek key hunter” • With the “Greek key hunter” it will be possible for computers to automatically identify both the Hutchinson and Thornton classification and the extended classification of Greek keys for this project.

  29. PDB • The Protein Data Bank (PDB) is a repository of protein structures that have been obtained through X-Ray crystallography or Nuclear Magnetic Resonance (NMR). • Almost every structural bioinformatics project makes use of the PDB in some way. • For this project, PDB data acts as input for the DSSP algorithm. • Thanks go out to Gao, Xin and Sun, Yang for giving me the PDB data so that I do not have to download it myself.

  30. DSSP • DSSP is the standard algorithm used in structural bioinformatics to characterize secondary structures of a protein molecule. • It is written by Wolfgang Kabsch and Chris Sander (Kabsch and Sander, 1983) • In this project DSSP processes PDB data to produce output that will be worked on by the PROMOTIF software.

  31. PROMOTIF • PROMOTIF is one of the key software for this project. • It takes the DSSP output and further refines them to produce data that are more relevant to motif-analyses. • For this project, PROMOTIF produces the Richardson topology information that will be vital to the recognition of Greek keys. • PROMOTIF is written by Dr. Hutchinson and Dr. Thornton using the programming language FORTRAN. Fortunately it could be compiled on Linux using the f77 compiler.

  32. Greek key hunter • The PROMOTIF suite of software was easy to use and its β-structure analyzer worked efficiently with the PDB files to fully characterize all the β-strands in the protein of a given PDB file • Unfortunately there is a very important component that is absent from the PROMOTIF framework — (gasp) a Greek key analyzer

  33. Greek key hunter • This lack of a Greek key analyzer provides me with an opportunity to write such a analyzer that not only identifies the Greek key structures classified by Drs. Hutchinson and Janet, but also the extended classification I have developed for this project. • The objective is then to write a program that could identify Greek keys from the β-structural output of the PROMOTIF software and other relevant data. In other words, a “Greek key hunter”.

  34. Greek key hunter • There is a first principle of Greek keys that vastly simplifies their search in the pdb#.str file — Greek keys always contain “four sequentialβ-strands” (Hutchinson and Thornton, 1993) • This means that only consecutive quartets of lines needs to be grouped and searched for Greek keys in the pdb#.str file.

  35. Greek key hunter • This is the PROMOTIF β-strand analyzer output for 1FNB — Ferredoxin reductase • The first principle dictates that line n and the next three lines comprise Greek key candidate n

  36. Greek key hunter • Once we have four lines representing a potential Greek key candidate, how do we develop the rules that would allow the computer to judge these four lines as representing either a valid or an invalid instance of Greek key? • I have found that the best way to deriving these rules is through the pragmatic approach of “learning by examples”.

  37. Greek key hunter • In their paper, Drs. Hutchinson and Thornton has listed Greek-key containing proteins for each Greek key class defined in part 2. • By looking at the pdb#.str output file and the PDB files (in PyMOL) of the representative proteins of each Greek key class, I would be able derive the rules that would characterize different classes of Greek keys and differentiate Greek keys from non-Greek keys. • These rules would then be coded into the Greek key hunter

  38. Greek key hunter • I have decided to start with the easiest class of Greek keys to characterize — the (4,0) class of Greek keys • The first entry for the (4,0) Greek keys in Table II of (Hutchinson and Thornton, 1993) is “Ferredoxin reductase” (1FNB). • Before I looked into 1FNB.str, I expected the “topology” column of that file to read either “-3, +1, +1” or “+3, -1, -1”.

  39. Greek key hunter • …But the actual topology read-out was wildly different and came as a shock!

  40. Greek key hunter • The residue columns indicated that these 4 sequential β-strands extended from residues 57 to 116, (Hutchinson and Thornton, 2006) says the Greek key extends from residue 56 to 117. So I know I am looking at the right quartet. • But the topology column reads “+3, +1, -5” !!!

  41. Greek key hunter • Upon examining the PDB file for ferredoxin reductase in PyMOL, it became all clear why the assigned topology of “+3, +1, -5” was appropriate.

  42. Greek key hunter • In fact, the topology diagram for the Greek key in residues 56-117 of ferredoxin reductase looks like this →(the coils associated with the middle two strands are omitted for clarity)

  43. Greek key hunter • Therefore, to enable an operational definition of the (4,0)C Greek key, we must relax the original formal definition somewhat • Operational definition of (4,0)C Greek key: let the Richardson topology of four sequential β-strands be (+x, +y, -z) or (-x, -y, +z), where x, y and z are positive integers, if (x + y) < z, then the β-strands form a (4,0)C Greek key.

  44. Greek key hunter Assume that we are currently processing line i to line i+3 of pdb#.str. If not(sheet # of line i == sheet # of line i+1 == sheet # of line i+2 == sheet # of line i+3) then print(“Not a (4,0)[C] Greek key!”) return false; end if x = Richardson topology number of line i y = Richardson topology number of line i+1 z = Richardson topology number of line i+2 if any of x, y or z contain the suffix ‘X’ then print(“Not a (4,0)[C] Greek key!”) return false; end if

  45. Greek key hunter if not(x > 0 and y > 0 and z < 0) and not(x < 0 and y < 0 and z > 0) then print(“Not a (4,0)[C] Greek key!”) return false end if x = absolute_value(x) y = absolute_value(y) z = absolute_value(z) if x + y < z then print(“(4,0)[C] Greek key found!”) return true else print(“Not a (4,0)[C] Greek key!”) return false end if

  46. Greek key hunter • Likewise, the operational definition of (4,0)N Greek keys could be easily derived by comparing it to the (4,0)N Greek keys.

  47. Greek key hunter • Operational definition of (4,0)N Greek key: let the Richardson topology of four sequential β-strands be (+x, -y, -z) or (-x, +y, +z), where x, y and z are positive integers, if (y + z) < x, then the β-strands form a (4,0)N Greek key. • And here is the pseudo-code for machine recognition of a (4,0)N Greek key.

  48. Greek key hunter Assume that we are currently processing line i to line i+3 of pdb#.str. If not(sheet # of line i == sheet # of line i+1 == sheet # of line i+2 == sheet # of line i+3) then print(“Not a (4,0)[N] Greek key!”) return false end if x = Richardson topology number of line i y = Richardson topology number of line i+1 z = Richardson topology number of line i+2 if any of x, y or z contain the suffix ‘X’ then print(“Not a (4,0)[N] Greek key!”) return false end if

  49. Greek key hunter if not(x > 0 and y < 0 and z < 0) and not(x < 0 and y > 0 and z > 0) then print(“Not a (4,0)[N] Greek key!”) return false end if x = absolute_value(x) y = absolute_value(y) z = absolute_value(z) if y + z < x then print(“(4,0)[N] Greek key found!”) return true else print(“Not a (4,0)[N] Greek key!”) return false end if

  50. Greek key hunter • Now we are ready to tackle the operational definition of Greek keys that spreads across two β-sheets • Continuing our “learning by examples”, let us study the (3,1)C Greek key of γ crystallin, whose evolutionary significance has been discussed in Dr. Li’s notes and lecture