A computational study of protein folding pathways

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A computational study of protein folding pathways

• Reducing the computational complexity of the
  folding process using the building block folding
  model.
• Nurit Haspel, Chung-Jung Tsai, Haim Wolfson and
  Ruth Nussinov

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The building blocks model(Chung Jung Tsai)

• Protein folding is a hierarchical process.
• A protein is constructed from HFUs.
• HFU - the result of a combinatorial assembly of
  building blocks.
• Building block - a contiguous, highly populated
  fragment.
• The building block model allows illustrating the
  protein folding pathway.

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An outline of the building blocks algorithm

• Scoring function - measures the relative
  stability of a candidate building block
• Three ingredients
• Compactness
• Degree of isolation
• hydrophobicity
• The result - an anatomy tree that illustrates
  the most probable folding route.

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The Scoring Function
Z - Compactness H - hydrophobicity I - Isolation
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Compactness, Hydrophobicity and Isolation
definitions

• Compactness -
• Hydrophobicity -
• Isolation -

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The Cutting Procedure

• Locating a basket of candidate building blocks
  (relatively stable contiguous fragments)
• Assign a stability score to all the candidate
  fragments
• Collect the local minima in the fragment map
  (best score in a given radius).
• Recursively splitting the protein top-down
• Search the basket for a set of fragments that
  constitute the whole fragment, allowing a short
  overlap (7 residues) and a gap of up to 15
  residues.
• Minimum building block size - 15.
• No node can have only one child (except for the
  root)
• Stop when the node can not be split any further
• In this work, building blocks up to level 6.

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Example - Annexin III
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Example (cont.)
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Example (cont.)
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Usefulness of the anatomy tree

• It is possible to see whether a protein folds
  through single or multiple route(s).
• These routes can be observed by inspecting the
  fragment map (there can be more than one way to
  construct a tree).
• Sequential versus non-sequential folding.
• Sequential contact made only between
  consecutive building blocks.
• Binary anatomy tree sequential folder.
• Fast versus slow folding
• Sequential folding proteins usually fold faster.
• Climbing up the tree allows us to illustrate the
  folding process.

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Critical building blocks (Sandeep Kumar)

• Some building blocks may be considered critical
  for correct folding.
• A critical building block is in contact with
  other building blocks in the protein.
• It likely to be inserted between sequentially
  connected building blocks.
• Without it, the other building blocks are likely
  to mis-associate.
• The structure and sequence of a critical BB is
  more likely to be conserved.

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Critical building block algorithm

• For each building block
• Compute its diff. contacting surface area .
• Compute its Critical building block index
• Compute its Z-score

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Critical building blocks (cont.)
A building block is critical if

• It is found at most levels below the hydrophobic
  folding unit level
• It has a consistently high CIndex at different
  levels
• Its CIndex is significant by at least 2 standard
  deviations in at least one level of protein
  anatomy

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The goals of my research

• Clustering the building blocks according to their
  3-D structures, using a rigid matching algorithm.
• Analyzing the building blocks Sequence,
  stability distribution, size.
• Analyzing the clusters Size, stability score
  distribution, sequence conservation, criticalness
  conservation.

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The goals of my research (cont.)

• Analyzing the critical building blocks position
  within the protein, relative stability, sequence
  and structure conservation.
• Developing an algorithm that assigns a set of
  building blocks to a protein sequence, using
  sequence similarity, relative stability and more
  information.

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Clustering the building blocks

• Each cluster has representative members (one or
  more)
• For each building block structure
• Go over the clusters.
• Match with cluster representative(s).
• If matches (1.5A rmsd, 70 size) - join the
  building block to the cluster.
• If no match found - open a new cluster with this
  building block as a representative.

Problem -O(n²) comparisons n - number of clusters
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Clustering of the building blocks
Cluster 1
Cluster 2
Cluster n

?
?
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Making clustering more efficient

• Dividing the building blocks into SCOP families
  (proteins from the same family usually produce
  the same building blocks).
• Clustering each family and then merge all the
  clusters - reduces the number of clusters at each
  instance.

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Building block and cluster data
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Distribution of number of clusters
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An example of a cluster
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Sequence analysis of the clusters

• Sequence clustering of each structural cluster
  (using BLAST).
• Creating a non-redundant sequence dataset.
• Goal - finding a connection between (short)
  sequences and structures.

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Statistical analysis of the clusters and of the
critical building blocks

• Stability score distribution among cluster
  members.
• Criticalness score distribution among cluster
  members.
• Position distribution of the critical building
  blocks.
• Stability score as a function of criticalness
  score.

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An example of stability distribution
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Criticalness score distribution within a cluster
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An N-terminus critical building block example
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A C-terminus critical building block example
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A mid-sequence critical building block example
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Distribution of the position inside the protein -
all-alpha, level 3
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Stability vs. Criticalness score example
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Stability score of critical and non-critical
building blocks (histogram)
Non-critical
Critical
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Final goal

• Given a sequence and using the information
  accumulated so far - is there a way of matching a
  set of building blocks to it?

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The building block assignment algorithm

• Perform sequence alignment of the protein
  sequence against the building block sequence
  database.
• Construct a directed, acyclic graph.
• Each matching building block is a graph vertex
  and is assigned a score depending on the sequence
  alignment score, building block stability and
  other parameters.
• Directed edges connecting the fragments that
  match to consecutive areas in the protein
  sequence, allowing short overlaps and small gaps.
  
• Edge score average score of connected vertices.

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The building block assignment algorithm (cont.)

• Add fictitious start and target vertices.
• Connect start to all starting vertices
• Connect all ending vertices to target.
• Find shortest path from start to target using the
  Single source shortest path algorithm.
• The path is an optimal building block
  assignment covering the protein sequence.

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Illustration of the algorithm
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Example ROP protein from E. coli (1rpo)
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Example Myoglobin from sea hare (1mba)
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Suggestions for future work

• Improving the algorithm and adding new parameters
  to it (secondary structure alignment, trying
  other building blocks from the same cluster as
  the matching building blocks etc.).
• Combinatorial assembly Yuvals work.
• Further cluster analysis inquiring into
  sequence conservation
• Conformation stability measurements (molecular
  dynamics)

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Conclusions

• Using the hierarchical folding model, It may be
  possible to reduce the folding complexity,
  assigning local substructures and then assembling
  them.