1. Recursive domains in proteins
Teresa Przytycka
NCBI, NIH
Joint work with G.Rose & Raj Srinivasan; JHU

2. Domain: “Polypeptide chain (or a part of it) that can independently fold into stable tertiary structure” (Baranden & Tooze; Introduction to Protein Structure)
Two-domain protein.

3. The 3D structure of a protein domain can be described as a compact arrangement of secondary structures
Alpha helix
Beta strand

4. These arrangements are far from random:

5. There are not so many of them :
PDB contains about structures and less than 1000 different folds.
Proportion of "new folds" (light blue) and "old folds" (orange) for a given year (fold = fold domain)

6. Possible sources of restricted number of folds:
Evolutionary history.
Given enough time would domains look “more random”?
Existence of general restrictions/rules which render some (compact) arrangements of secondary structures non-feasible.
Can real protein domains be seen as sentences in a language, which can be generated by an underlying grammar?

7. Can protein domains be described using a set of folding rules?
We restrict our attention to all beta domains:
they admit variety of topologies
they are difficult to predict from sequence

8. Understanding b-folds
Patterns in b-sheets
Richardson 1977
folding rules for b-sheets
Zhang and Kim 2000
Hydrogen bonding pattern
Polypeptide chain seems to avoid “complications”
Properties of b-sandwiches
Woolfson D. N., Evans P. A., Hutchinson E. G., and Thornton J. M. 1993
Parallel anti-parallel mixed
“forbidden” crossed conformation

9. Expectations for good folding rules
We need to look at fold properties that occur in non-homologous proteins.
Preferably: The provide a model for the folding process.

10. Super-secondary structures as precursors of folding rules
Super-secondary structure – frequently occurring arrangements of a small number of secondary structures
The occurrences of super-secondary structures in unrelated families supports possibility of their independent formation.

11. Example 1: Hairpin

12. b-b-b-unit

13. Example 2: Greek key and suggested folding pathway for it
for Greek key
proposed by Ptitsyn.
Pattern from a Greek vase

14. Two level of folding rules:
Primitive folding rules – based on super secondary structures
Closure operation – allows for hierarchical application of the primitive rules

15. supersecondary structures -primitive folding rules
hairpin
Hairpin rule
Bridge
Greek key

16. Direct wind
Indirect wind

17. Closure-composite rules
Super-secondary structures are composed of secondary structures that are neighboring in the chain sequence
However from the presence of a super-secondary structure, like a hairpin, in a protein structure follows that residues that are non consecutive become neighboring in space.
Closure - “short cut” in the sequence due to a folding rule

18. Example 1 applying folding rules to jelly roll

19. Recursive domains
Recursive domain is a part of a protein fold that can be generated using folding rules supported with the closure operation.
A protein that can be fully generated using folding rules has one recursive domain.

20. Examples
Example 1
Example 2
Example 3
Example 4

21. Recursive domains
Recursive domain is a part of a protein fold that can be generated using folding rules supported with the closure operation.
A protein that can be fully generated using folding rules has one recursive domain.

22. Graph theoretical tools and recursive domains
Fold graph: Vertices – strands Edges – two types:
Neighbor edges: directed edges between strands that are neighbors in chain or vie the closure operation.
Domain edge: edges between stands used in the same folding rule
Recursive domains = connected component of the fold graph without neighbor edges.

23. Can the rules generate all known folds?
Comparison with the partition for computer generated set of all possible 8-strand sandwiches
Partition into recursive components for small (<=10 strands) proteins
Control
Protein data
One recursive fold

24. Offenders
Hedhehog intein domain

25. Given a fold, is there a unique sequence of folding steps leading to it?
Usually no.
Usually there alternative sequences of folding steps leading to a construction of the same domain.
Do such alternative folding sequences correspond to alternative folding pathways?

26. Are the rules complete? Probably not.
e.g.: For propeller, each blade is in one recursive domain but we do not have a rule that will put the blades together.

27. It is so nice outside. It would be nice to take the dog for a walk!
Conclusions: We are getting some idea how things work...
It is so nice outside. It would be nice to take the dog for a walk!
Nice… dog… walk

28. Conclusions Protein folds can be described by simple folding rules.
The folding rules capture at least some aspects of fold simplicity and regularity.
The sequence of folding steps leading to a given fold is usually not unique.
The folding rules generate protein-like structures.

29. Future directions Can folding rules guide fold prediction?
Would hierarchical description of a fold provided by folding rules be useful for fold classification / comparison ?
Adding statistical evaluation of a recursive domain.

30. Acknowledgments George Rose Raj Srinivasen Rohit Pappu Venk Murthy
NIH, K01 grant