Proteins are long chains of Amino Acid AA

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Introduction

• Proteins are long chains of Amino Acid (AA)
• There are 20 different AAs

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StructureFunction
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Experimental methods

• Crystallography- Performed by X-ray diffraction
  and neutron-diffraction.
• Nuclear Magnetic Resonance (NMR)
• Very expensive and time consuming

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Methods for Protein folding

• Homology modeling
• When one can find a known structure protein
  with good sequence similarity (over 30) to the
  protein we wish to fold.
• Protein threading
• Less conclusive similarity
• Ab-initio
• No homology is available

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Protein threading

• Form a database of known folds
• Given a sequence, find most likely structure from
  database
• Thread sequence through structure

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If we have an efficient threading algorithm

• Form a database of known folds
• Given a sequence, thread this new sequence
  through all the models in the library
• See which one does best

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Protein threading

• Profile method
• Core threading method
• -branch and bound
• Dynamic Programming
• -divide and conquer

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Core threading
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• Protein threading problem definition
•          Input   Given protein sequence A
              Core structural model M
              Score functions g1, g2.            
  Output  A threading T.             In short 
  Align A to model T.
•         Given             A Protein sequence
  of length n a1, a2, a3, , an             M
  m core segments C1, C2, C3, , Cm            
  c1, c2, c3, , cm length of core segments
              l1, l2, l3, , lm-1 loop regions
  connecting core segments             l1max,
  l2max, l3max, ,  lm-1max maximum lengths of
  loop regions             l1min, l2min, l3min,
  ,  lm-1min minimum lengths of loop regions
              Properties of each amino acid
              F, g1, g2 score functions to
  evaluate threading
•     

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Score function
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Output  T  t1, t2, t3, , tm  start locations
for core segments
where, g1 and g2  are based on the given model
M.  g1 shows how each segment corresponds to core
segment i in the model, and g2 deals with the
interactions between segments.  So to solve the
threading problem, we have to decide on  t1, t2,
t3, , tm, so that the overall score is maximum. 
Thus the threading problem, or alignment problem,
is converted to an optimization problem.  
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Threading constraints
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Branch and Bound

• Set of all possible threadings defined by initial
  position bounds
• Divide possible threadings into smaller sets, and
  compute new position bounds for each set
• Compute a quick score lower bound for each set of
  threadings
• Keep re-dividing the set with smallest lower
  bound, until set size if 1.

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Branch and Bound
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Branch and Bound

• Given a set of threadings defined by position
  bounds, one possible score lower bound is

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Branch and Bound-Issues

• Constructing score function
• Calculating lower bound
• Choosing split segment
• Choosing split point

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Dynamic Programming
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Dynamic Programming

• Detect local region of high similarity among the
  target and the template sequence.
• Local alignment
• Exploit sequence as well as structural signals

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Dynamic Programming

• Any pair of locally aligned segments divides the
  unmatched region of both protein into two parts.
• They can be processed independently with the same
  approach. Divide-and-conquer.
• After dividing, the changed structural features
  of the template are recorded

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Dynamic Programming

• The algorithm proceeds recursively, until in the
  local alignment step no more significant similar
  segment pairs are found. E.g. only ONE core
  structure.

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Dynamic Programming
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Dynamic Programming

• We can give more than one candidate while doing
  local alignment.
• This produces a tree.
• At the end, we assemble the respective threading
  alignments and compute their scores

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PROSPECT

• Use Divide and Conquer
• References
• Xu, Y.D., D. Xu, and E.C. Uberbacher, "An
  Efficient Computational Method for Globally
  Optimal Threading", Journal of Computational
  Biology, 5 (3), 597-614, 1998.
• Xu, Ying and D. Xu, "Protein Threading using
  PROSPECT design and evaluation", Protein
  Structure, Function, Genetics, Vol 40, pp 343 -
  354, 2000.

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PROSPECT

• Energy function
• In the early edition, all ?s are set to be 1

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