A demonstration of clustering in protein contact maps for α-helix pairs Robert Fraser, University of Waterloo Janice Glasgow, Queen’s University

2 Hypothesis Properties of the three-dimensional configuration of a pair of α-helices may be predicted from the contact map corresponding to the pair.

3 What to expect The α-helix Protein structure prediction Packing of helices Prediction of packing Future work

4 Where do proteins come from? What we’re interested in Image from

5 Amino acid residues Two representations of the same α-helix Left helix shows residues only Right helix shows all backbone atoms

6 Why α-helices? Protein Structure Prediction –The 3D structure of a protein is primarily determined by groups of secondary structures –The α-helix is the most common secondary structure

7 Protein Structure Prediction is hard. There are many different approaches Crystallization techniques are time-consuming Tryptych –Case based-reasoning approach to prediction –Uses different experts as advisors –Works from a contact map

8 The Goal 2D representation  3D Toy example: A C B C450 B305 A034 ABC

9 The Goal If we apply a threshold of 4.5 units, can we still determine the shape? C450 B305 A034 ABC AC B CTFT BTTF ATTT ABC ?

10 Protein Structure Prediction Build (or predict) contact map Predict the three-dimensional structure from the contact map N×N matrix, N= # of amino acids in the protein C(i,j) = true if the distance from amino acid i to j is less than a threshold (ie. 7Å) ?

11 Refining a contact map Contact map for entire protein Contact map for pair of α-helices Interface region of contact map

12 Hypothesis (again) Properties of the three-dimensional configuration of a pair of α-helices may be predicted from the contact map corresponding to the pair.

13 Packing of helices A nice simple boolean property Found by rotating both helices to be axis- aligned, then comparing coordinates packingnon-packing 90° not 90°

14 Prediction of packing Need a map comparison method

15 Comparing maps Comparing two maps is not straightforward Reflections are insignificant

16 Comparing maps Translations are (generally) insignificant

17 Prediction of packing Classify the maps based on contact locations central corner edge

18 Packing classes

19 Packing data by class No clustering to be done on the central and edge classes Reflections of each corner map were used to build the data set

20 Clustering Corner Maps Each corner map is transformed to a 15×15 map A map corresponds to a 225 character binary string Distance can measure using cosine

21 Clustering Results

22 Nearest Neighbour Closest neighbour by cosine distance Of the 862 contact maps in the data set, only 9 had a packing value different from the nearest neighbour Almost 99% accuracy!

23 Contributions Prediction of helix pair properties –1 st to establish that contact maps cluster –Developed a novel contact map classification scheme for helix pairs –1 st to demonstrate that helix pair properties may be predicted from contact maps

24 Future Work Implement the packing advisor (done) Explore other properties of α-helices that could be predicted from contact maps –Interhelical angle –Interhelical distance

25 Thanks Questions? Supported by NSERC, PRECARN IRIS, Queen’s

26 Clustering Results Non-packingMixed Packing

27 Levels of Structure Primary Secondary

28 α-helix properties

29 Tryptych

30 Chothia packing model