Recursive domains in proteins

Teresa PrzytyckaNCBI, 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.

Alpha helix

Beta strand

The 3D structure of a protein domain can be described as a compact arrangement of

secondary structures

These arrangements are far from random:

There are not so many of them :

Proportion of "new folds" (light blue) and "old folds" (orange) for a given year. (fold = fold domain)

PDB contains about 17000 structures and less than 1000 different folds.

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 -folds• Patterns in -sheets

– Richardson 1977 • folding rules for -sheets

– Zhang and Kim 2000• Hydrogen bonding pattern• Polypeptide chain seems to avoid

“complications”

• Properties of -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

-unit

Example 2: Greek key and suggested folding pathway for it

Folding pathway 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 rule

Bridge

hairpin

Greek key

Indirect wind

Direct 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 1applying

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.

Partition into recursive components

for small (<=10 strands) proteins

Comparison with the partition for computer generated set of all possible 8-strand sandwiches

recursive domains for proteins with at most 10 strands

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Distribution of recursive domains in all sandwich like '"folds"

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Can the rules generate all known folds?

Protein data Control

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.

Nice… dog… walk

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...

• 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.

Conclusions

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