Accelerating the Prediction of Protein Interactions

Transcription

1 Accelerating the Prediction of Protein Interactions Alex Rodionov, Jonathan Rose, Elisabeth R.M. Tillier, Alexandr Bezginov October 21 21

2 Motivation The human genome is sequenced, but we don't know what all the genes do Genes code for proteins Genome function = protein interaction We can learn about proteins and the genome by studying protein-protein interactions

3 Motivation Best known way of studying interactions is in the lab ( high-throughput experiments ) Lots of proteins, O(N2) possible pairs We would like to be able to predict which protein pairs interact before undertaking tedious and expensive lab experiments

4 Coevolution One way to predict protein-protein interactions is by using coevolution: two proteins that interact tend to evolve over time at similar rates.

5 Coevolution: Background Protein = string of amino acids protein amino acids Amino acids = coded by DNA {A,G,T,C} ^3 = 64 possible amino acids (2 occur in nature)

6 Coevolution: Background Proteins interact physically at amino acid sites Protein A Protein B

7 Coevolution: Background Mutations can cause amino acid substitutions Protein A! Protein B' Breaks interactions organism more likely to die

8 Coevolution: Background Pressure for BOTH proteins to evolve together Protein A' Protein B' Interaction is maintained

9 Coevolution: Summary Shared evolutionary history Coevolution Interaction

10 MatrixMatchMaker A method of protein coevolution detection Developed by Elisabeth Tillier & Robert Charlebois (Department of Molecular Biophysics) Has been shown to work better than other methods, at the expense of compute time

11 MMM: Big Picture Looks at the evolutionary histories of two proteins Measures the similarity of the histories by looking for common sections of those histories Generates a numerical score indicating the strength of evidence for coevolution

12 MMM: Homologous Proteins There can exist many versions of one protein, with slight variations, found in different species These homologous protein variations form a family. amino acids Human Mouse Chicken Rabbit Frog G T S Q R V Q N S L R G A S N Y L P N S K P S T V N W V R F E L Q S A N E W L E F E V T V A E S L P I Y V T T

13 MMM: Homologous Proteins The differences amongst the homologous proteins provide an evolutionary context/history of the family How to quantify these differences and history?

14 MMM: Distance Matrices Protein = sequence of amino acids = string Can take two such strings and calculate a number representing how different they are (=distance) MADSTHRNMILEVNDEFHT MLEIMTHRNMILEVNRRFYY MAD-STHRNMILEVNDEFHT MLEIMTHRNMILEVNRRFYY.4

15 MMM: Distance Matrices Multiple Sequence Alignment takes all the members of a protein family and generates all possible pairwise distances These distances form a distance matrix p1 p1 p2 p3 p4 MAD-STHRNMILEVNDEFHT MVDASTHRNMILEVNDEFTI MID-MTHRNMILEVNDEFHT MLEIMTHRNMILEVNRRFYY p1 p2 p3 p p p p

16 MMM: Evolutionary History Distance matrix implies evolutionary history of protein Submatrices represent histories of subsets of the homologous variations p1 p1 p2 p3 p p p p p1 p2 p3 p4

17 MMM: Big Picture Revisited MMM looks at two distance matrices A and B, which represent the evolutionary histories of two proteins (two families of homologous proteins) Measures the similarity of the histories by looking for similar sub-matrices The size of the largest similar sub-matrices is output as a score, indicating the strength for the evidence of co-evolution

18 MMM: Sub-matrix Similarity Distance within a matrix is relative to the family, not absolute submatrix equality isn't enough for similarity Use instead equality up to a scale factor (with some tolerance) similar

19 MMM: Sub-matrix Similarity a2 Sub-matrices need to be at least size 3 (for concept of similarity to make sense) x x always similar y y Two similar sub-matrices of size K*K create K pairings of homologous proteins a2 a8 a9 b3 b5 b7 a a b b5 b7 Pairs: a2 b3 a8 b5 a9 b7

20 MMM: Sub-matrix Similarity Additional constraint: both proteins in a pairing must belong to the same species Size of largest similar submatrices = amount of coevolution Homologous proteins paired up by submatrices are useful for other purposes (downstream analysis tools)

21 MMM: Problem Definition Inputs: distance matrices A and B, tolerance α A a1 a2 a3 B a4 a1 a2... an b1 b1 A2,4 b2... B1,2 b2 a3... a4 bm... an [,1] bm

22 MMM: Problem Definition A' a'1 a'2 a'1 a'k A'1,2... A'1,k a'2 A'2,1... b'1... b'k B'1,2... B'1,k b'2 B'2, B'2,k A'2,k b'1 b'2... a'k A'k,1 A'k,2... b'k B'k,1 B'k, B' Submatrices A' of A and B' of B form a match M={(a'1,b'1), (a'2,b'2),, (a'k,b'k)} iff: ' ' ' A A A 1 u, v 1 u, v i, j 1: ' ' ' i j, u v 1 Bu, v 1 B u, v Bi, j 2: A'i, j, B'i, j i j 3: species a 'i =species b 'i i

23 MMM: Problem Definition α : more strict matching α 1 : more lenient matching Goal: Find the set of matches of largest size Outputs: Largest match size, protein pairs for each match

24 Initial Algorithm Tillier et al. already had a first try at an algorithm It took 6 days to process ~6 million matrix pairs

25 Initial Algorithm For all protein triplets (a,b,c) from A For all protein triplets (w,x,y) from B If {(a,w), (b,x), (c,y)} is a match then * For remaining proteins d from A! For remaining proteins z from B If current match plus (d,z) is also a match, add (d,z), goto * Else record current match Remove latest pair from match, goto! to resume loop Keep largest matches, clear list when larger example found, report match list at the end Slow, exhaustive, no pruning of recursion tree

26 New Algorithm Our (ECE) work begins here Make a faster algorithm, maintain correctness Big picture: recast MMM problem as a graph problem, use well-known and efficient algorithms to solve sub-problems

27 New Algorithm: Representation Vertices = allowable protein pairs Edges = ratio of distance matrix entries a1 a2 a3 a4 a3b1 b1 a4b2 b bm... an B 1,2 A3,4

28 New Algorithm: Representation a1 a2 b1 b2 a3 a4... an R 1 and R 2 are compatible within tolerance [,1] iff : 1 R1 R 2 R1 R1... R2 with 1 = 1 bm compatible range for R2 decreasing ratio 1 R1 R1 increasing ratio R1 Compatible edges = similar ratios

29 New Algorithm: Representation Match = clique with mutually compatible edges a1 b1 b2 b3 b4 a2 a3 a4 a5 a6 Match: a1 a3 a5 a6 b4 b1 b3 b2

30 New Algorithm: Method Every match has edge of minimum ratio Edges in match are mutually compatible iff they are forward-compatible with the edge of minimum ratio R=R 3 min R2 R1 R4 R5 R6 forward-compatible range for Rmin decreasing ratio 1 Rmin Rmin R2 R5 R1 R6 R4 R min increasing ratio

31 New Algorithm: Method Go through every edge e in the graph Assume e is the edge of minimum ratio of some match(es) Work backwards to find the largest of those matches After picking e, this just means finding the maximum cliques on a subgraph H: V(H) = vertices adjacent to e E(H) = edges forward-compatible with e Repeat for all e Find all largest matches

32 New Algorithm: Method Step 1: Pick a vertex vx, sort its neighbours by increasing ratio foreach vertex vx sorted ascending by ratio

33 New Algorithm: Method Step 2: Pick a neighbour vy, set minratio to that of the edge between vx and vy vx minratio vy foreach neighbour vy with y > x

34 New Algorithm: Method Step 3: Find vertices whose edges to both vx and vy are forward-compatible vx can ignore due to sorting vy minratio * delta

35 New Algorithm: Method Step 4: Run maximum clique algorithm on the subgraph induced by candidates to find matches. All matches also include vx and vy. find all maximum cliques ignore non-forward-compatible edges between vertices vx vy + largest matches

36 New Algorithm: Method Repeat Every choice of vx and vy creates a max clique problem Keep list of largest matches, and the largest match size

37 Max Clique Algorithm Using Ostergard (22) algorithm Recursive, branch and bound algorithm: clique:,5 (less than max, no report) clique:,3,5 (new max) clique:,6 (less than max, no report) back out: can't match or beat max of 3 etc

38 Max Clique Algorithm Outer loop: MSPV[ ] perform B&B algorithm on last vertex to the end record max clique size in MSPV work backwards new bound condition: if current size + MSPV[v] < max size then leave early

39 Max Clique Algorithm Ordering of vertices important for performance Recommended ordering (Ostergard): Perform greedy vertex coloring Sort vertices by decreasing color class Sort by decreasing degree within color class

40 New Algorithm: Results Data set: ~35 matrices, ~6 million matrix pairs Matrices represent proteins with at least 1 human variant Tolerance (alpha) set to.1 Compared total and per-problem runtime of new vs. old algorithms

41 New Algorithm: Results Only 88 pairs had nonzero 'new' runtimes Geometric mean speedup: 97x Total speedup: 377x (6 days 21 minutes)

42 Hardware Acceleration FPGA-related part of this talk Max clique is NP-complete Setup portion of algorithm is O(n^4) Max clique time 1% for larger problems Setup tasks include things like sorting best leave this on the CPU Max clique algorithm is mostly serial, but there are LOTS of max clique problems to solve!

43 Max Clique: FPGA vs GPU Recursive, depth-first Not data parallel at all Input data = adjacency matrix = can be represented as array of bits

44 Hardware Platform Terasic DE3 Stratix III L34 USB 2. 1GB DDR2 memory Hopefully porting to DE4 PCI Express!

45 HW SW Interface 'Ports' package over USB 2. Looks like open/read/write C calls to SW Data sent via TCP/IP to computer hosting the DE3 Auto-generated hardware block feeding desired signals + handshaking to design Work in progress itself

46 Hardware: System Block Diagram matrices MMM executable MMM ports Algorithm lib USB daemon cliques Host PC DE3 USB PHY Stratix III FPGA (Max Clique Solver) DDR2 Memory

47 Hardware: FPGA block diagram to DDR2 matrices 266MHz cliques DDR2 IP Core control signals FIFO to USB p o r t m u x m a I n fillmem sched c t l FIFO DDR2 Interface WU WU WU Clique Buffer 15MHz 3MHz WU...

48 Hardware: Work Unit to clique buffer max clique size to Main Control to DDR2 interface update clique unit vertices stack ptrs main SM first vertex MSPV Array isect SM Intersection Pipeline Cache (32kb) vstack pointers Pointer Stack Vertex Stack

49 Hardware: Progress and Future Work No speed results yet Version 1: One WU, no DDR2, no MMM support Used to verify WU operation Version 2: One WU, DDR2 Hardware ready, software support coming Version 3: Multiple WU, DDR2 Problem: USB 2. bandwidth need PCIe

50 Conclusion Interesting biological problem Interesting mathematical problem Great algorithmic/software speedup achieved Hardware work in progress

51 Done Questions?