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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 “ protein – protein ”, 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 pair’s interactions D2-D2={0,1,2,3} D2-D3={1} D2-D4={2} D1-D5={3} 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: – P1:{D1, 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

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Approximation Algorithms Department of Mathematics and Computer Science Drexel University.

Approximation Algorithms Department of Mathematics and Computer Science Drexel University.

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