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

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.

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

These arrangements are far from random:

There are not so many of them : PDB contains about 17000 structures and less than 1000 different folds. Proportion of "new folds" (light blue) and "old folds" (orange) for a given year. (fold = fold domain)

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?

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

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

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.

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.

Example 1: Hairpin

b-b-b-unit

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

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

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

Direct wind Indirect wind

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

Example 1 applying folding rules to jelly roll

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.

Examples Example 1 Example 2 Example 3 Example 4

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.

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.

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

Offenders Hedhehog intein domain

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?

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.

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

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.

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.

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