Protein

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Protein Protein Interactions

• Lisa Chargualaf
• Simon Kanaan
• Keefe Roedersheimer
• Others Dr. Izaguirre, Dr. Chen, Dr. Wuchty,
  ChengBang Huang

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What are proteins?

• Basis of most living functions
• Building blocks of life
• Substrates
• Products
• Enzymes
• One cell contains thousands of different
  proteins the human body contains 50 to 100
  thousand proteins!

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Proteins

• Composed of sequences of amino acids
• Variations of 20 primary/basic amino acids
• Rules governing structure
• AAs close in the folded structure may/may not be
  close in primary structure
• Hydrophobic residues generally buried in core
  hydrophilic are usually exposed
• Protein strings cannot form knots
• Related proteins generally have similar
  structures
• Similar structures can exist without having
  similar sequences

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What is a proteinprotein, P-P, interaction and
why is it important?

• Derived from the nuclear material within a cell,
  proteins fold and interact in intricate
  arrangements that provide functionality to the
  components of a cell, which in turn work
  cooperatively to form whole body systems.
• Protein-protein interactions serve as the
  chemical basis of all living organisms.
• Understanding protein interactions helps us
  understand the protein network.

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What causes P-P interactions?

• Many speculations arise when it comes to the
  driving force behind proteins interacting with
  each other
• Primary sequence dictating interaction between
  attached functional groups
• Protein domains drive proteins to fold and
  interact as they do.

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What are protein domains?

• significant portions of proteins
• composed of distinct peptides
• the key to intricate arrangements

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Domains and Proteins

• A single protein molecule can possess multiple
  domains, causing difficulty in discovering a
  simple formula that dictates the manner by which
  protein-protein interactions occur.
• Yet, certain affinities exist between certain
  protein domains and are frequently seen in living
  organisms.
• This drives our research that seeks to
  extrapolate the mechanism of protein-protein
  interactions to focus on domain-domain
  interactions as a factor.
• The model system used for these proceedings is
  the yeast cell, with several of its proteins
  serving as the test cases. This is done using a
  protein family data bank available online.

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Our Formula dictating which P-P interactions
occur

• A data bank gives a list of protein interactions.
• A protein interaction, (P1, P2), is explained by
  a domain pair, (D1, D2), if P1 includes one
  domain and P2 includes the other.
• Find the minimum number of domain pairs that
  explains the databank. Equivalent to Minimum Set
  Cover problem.

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Minimum Set Cover Problem

• The problem of finding the minimum size set of
  sets whose union is equal to the union of all the
  sets.
• NP complete problem.

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Why the Minimum Set of Domains?

• Lets look at the following case
• P1 contains domains D2
• P2 contains domains D2 and D3
• P3 contains domains D2 and D4
• P4 contains domains D2 and D5
• And lets assume the protein interactions are
• P1 - P1
• P1 - P2
• P1 - P3
• P1 - P4

• P-P interactions explained by
• (D2 - D2)
• (D2 - D3)
• (D2 - D4)
• (D1 - D5)
• Or by
• (D2 - D2)

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Mapping to MSC

• Let
• P1 - P1 0
• P1 - P2 1
• P1 - P3 2
• P1 - P4 3
• Each pairs interactions
• D2-D20,1,2,3
• D2-D31
• D2-D42
• D1-D53

• This maps to the integer MSC problem with a
  global set of 0,1,2,3 and subsets of
  0,1,2,3,1,2,3
• Solution is D2-D2, more difficult for larger
  problems.

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Implementation/Algorithm

• This base algorithm consists of functions that
  can record the protein structure and interaction
  information and store them into different data
  structures.
• It also builds a domain-domain matrix.
• This matrix holds information about interacting
  domains. Each entry in the matrix represents the
  number of times domains Di and Dj were observed
  as the possible cause in different
  protein-protein interactions.
• Example
• P1D1, D2, D3 and P2 D1, D5 interact.
• (D1, D1), (D1, D5), (D2, D1), (D2, D5), (D3, D1)
  and (D3, D5).

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Exact Problems

• In the worst case, ( of domains)2 number of
  domain interactions, corresponding to subsets.
• Large number of proteins corresponding to a
  global set.

• MSC is an NP complete problem, the exact solution
  requires considering all combinations of subsets.
  
• Computationally expensive, impractical for more
  than 10 domains. There are thousands in a real
  problem.

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Implementation/Algorithm

• Algorithm approximates the minimum set of domains
  pairs.
• Algorithm needs to be able to choose d-d pairs in
  an educated, not a randomized fashion.
• This educated way can be done using weight
  functions. Where each domain pair is given a
  weight, and the largest of the weights is chosen.

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Different Functions

• Different weight functions were considered.
• Decided on looking at two for now
• MSC
• MSC by probability
• Also looked at running MSC twice with the
  addition of adding pairs with a high probability
  of interacting.

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MSC

• Assumption
• most common observed interacting domain pair
  among the protein interactions is probably the
  cause of the protein interactions.
• While there are P-P interactions to be explained
• Chooses the most common observed interacting
  domain Di-Dj.
• Removes Di-Dj
• Removes all P-P interactions from the data being
  observed
• Undoes P-P interactions effect on matrix

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MSC by Probability

• Assumption
• Incorporate the absence of p-p interactions.
• Initialize matrix just like MSC.
• go through every element in the matrix and divide
  that entry by the total number of proteins that
  contain the first domain times the number of
  proteins which contain the second domain.
• Now each element now represents the probability
  that domains i and j interact.
• Then the weight function goes about choosing the
  highest probability in the matrix, seeing which
  proteins this domain pair explains, remove these
  proteins influence from the data and then
  performing the same tasks again.

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Prediction

• Input set of proteins with known structure.
• Set of domains pairs obtained from algorithm
  being observed.
• Go through each interacting domain pair (Di, Dj)
• Every protein contained domain Di is considered
  interacting with a protein containing Dj.

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Testing

• Running MSC approximation VS. MSC exact on very
  small sets to see how good the approximation
  really is to exact solution.

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Testing

• Building different size training data using swiss
  pfam A database among others.
• Running The aproximation algorithms on these
  sets.
• Running AM on the same sets.
• Attempting to use similar size sets to MLE for
  comparisons sake.

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Testing

• Compares calculated P-P interactions with
  observed interactions. (number of matches, false
  positive, and false negative p-p interactions)
• Calculate fold, specificity, and sensitivity in
  order to compare to previous research.

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Results
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Results
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Results
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Future Work

• Finish Testing and comparing different Weight
  Functions.
• Getting some stats by running different
  algorithms multiple times on different size data
  sets.
• Testing MSC exact vs. different weight functions