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”
Parallel
anti-parallel mixed
• Properties of b-sandwiches
– Woolfson D. N., Evans P. A.,
Hutchinson E. G., and
Thornton J. M. 1993
“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
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
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
Distribution of recursive domains in all sandwich like '"folds"
recursive domains for proteins with at most 10 strands
3000
45
40
2500
number of folds
30
25
recursive domains
20
15
number of generated "folds"
35
2000
1500
Series1
1000
10
500
5
0
1
2
3
4
5
6
7
8
number of recursive domains
0
1
One recursive fold
2
3
4
5
number of recursive domains
6
7
8
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.
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