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High-Performance Computing for Reconstructing Phylogenies from Gene-Order Data

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### High-Performance Computing forReconstructing Phylogenies fromGene-Order Data

David A. Bader

Electrical & Computer Engineering

University of New Mexico

http://hpc.eece.unm.edu/

Acknowledgment of Support

- National Science Foundation
- CAREER: High-Performance Algorithms for Scientific Applications (00-93039)
- ITR: Algorithms for Irregular Discrete Computations on SMPs (00-81404)
- DEB: Ecosystem Studies: Self-Organization of Semi-Arid Landscapes: Test of Optimality Principles (99-10123)
- ITR/AP: Reconstructing Complex Evolutionary Histories (01-21377)
- DEB Comparative Chloroplast Genomics: Integrating Computational Methods, Molecular Evolution, and Phylogeny (01-20709)
- ITR/AP(DEB): Computing Optimal Phylogenetic Trees under Genome Rearrangement Metrics (01-13095)
- PACI: NCSA/Alliance, NPACI/SDSC, PSC
- Sun Microsystems

High-Performance for Phylogeny Reconstruction, David A. Bader

Algorithms that Scale from the Blade to the Fire

High-Performance for Phylogeny Reconstruction, David A. Bader

Commercial Aspects of Phylogeny Reconstruction

- Identification of microorganisms
- public health entomology
- sequence motifs for groups are patented
- example: differentiating tuberculosis strains
- Dynamics of microbial communities
- pesticide exposure: identify and quantify microbes in soil
- Vaccine development
- variants of a cell wall or protein coat component
- porcine reproductive and respiratory syndrome virus isolates from US and Europe were separate populations
- HIV studied through DNA markers
- Biochemical pathways
- antibacterials and herbicides

Glyphosate (Roundup, Rodeo , and Pondmaster ): first herbicide targeted at a pathway not present in mammals

- phylogenetic distribution of a pathway is studied by the pharmaceutical industry before a drug is developed
- Pharmaceutical industry
- predicting the natural ligands for cell surface receptors which are potential drug targets
- a single family, G protein coupled receptors (GPCRs), contains 40% of the targets of most pharm. companies

High-Performance for Phylogeny Reconstruction, David A. Bader

GRAPPA: Genome Rearrangements Analysis

- Genome Rearrangements Analysis under Parsimony and other Phylogenetic Algorithms
- http://www.cs.unm.edu/~moret/GRAPPA/
- Open-source
- already used by other computational phylogeny groups, Caprara, Pevzner, LANL, FBI, PharmCos.
- Gene-order Phylogeny Reconstruction
- Breakpoint Median
- Inversion Median
- over one-million fold speedup from previous codes
- Parallelism
- Scales linearly with the number of processors
- Developed using Sun Forte C

High-Performance for Phylogeny Reconstruction, David A. Bader

Molecular Data for Phylogeny

- simple DNA sequence: nucleotides
- low-level functionality: amino acids, etc.
- genomic level: genes
- (next is functional level: proteomics, etc.)

Biologists now have full gene sequences for many single-chromosome organisms and organelles (e.g., mitochondria, chloroplasts) and for more and more larger organisms

High-Performance for Phylogeny Reconstruction, David A. Bader

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Gene Order Phylogeny- Many organelles appear to evolve mostly through processes that simply rearrange gene ordering (inversion, transposition) and perhaps alter gene content (duplication, loss).
- Chloroplast have a single, typically circular, chromosome and appear to evolve mostly through inversion:

The sequence of genes i, i+1, …, j is inverted and

every gene is flipped.

High-Performance for Phylogeny Reconstruction, David A. Bader

Gene Order Phylogeny (cont’d)

- The real problem
- Reconstruct the “true” tree, identify the “true” ancestral genomes, and recover on each edge the “true” sequence of evolutionary changes
- The optimization problem (parsimony)
- Reconstruct a tree and ancestral genomes so as to minimize the sum, over all tree edges, of the inferred evolutionary distance along each edge
- The surrogate problem
- Do the optimization problem with a measure of inferred evolutionary distance that lends itself to analysis

High-Performance for Phylogeny Reconstruction, David A. Bader

Breakpoint Analysis:A Surrogate for Gene Order

- Breakpoint:
- an adjacent pair of genes present in one genome, but absent in the other
- Breakpoint distance:
- the total number of breakpoints between two genomes (a true metric, similar to Hamming distance)
- Breakpoint phylogeny:
- the tree and ancestral genomes that minimize the sum, over all edges of the tree, of the breakpoint distances

Naturally, it is an NP-hard problem, even with just 3 leaves.

High-Performance for Phylogeny Reconstruction, David A. Bader

Breakpoint Analysis(Sankoff & Blanchette 1998)

- For each tree topology do
- somehow assign initial genomes to the internal nodes
- repeat
- for each internal node do
- compute a new genome that minimizes the distances to its three neighbors
- replace old genome by new if distance is reduced
- until no change

Sankoff & Blanchette implemented this in a C++ package

(2n-5)!! = (2n-5) (2n-7) … 5 3 trees

unknown iterative heuristic

NP-hard

High-Performance for Phylogeny Reconstruction, David A. Bader

Algorithm Engineering Works!

- We reimplemented everything –
- the original code is too slow and not as flexible as we wanted.
- Our main dataset is a collection of chloroplast data from the flowering plant family Campanulaceae (bluebells):
- 13 genomes of 105 gene segments each
- On our old workstation:
- BPAnalysis processes 10-12 trees/minute
- Our implementation processes over 50,000 trees/minute
- Speedup ratio is over 5,000!!
- On synthetic datasets, we see speedups from 300 to over 50,000…

High-Performance for Phylogeny Reconstruction, David A. Bader

So… What did we do?!

*

(~ 10x)*

- Absolutely no high-level algorithmic changes
- Three low-level algorithmic changes:
- better bounding
- strong upper bound initialization
- “condensing”
- Completely different data representation
- Two low-level algorithmic changes
- all memory is pre-allocated
- some loops are hand-unrolled
- Written in C instead of C++

~10x

~10x

~ 6x

?

(convenience)

* Well, so I lied just a little bit…

High-Performance for Phylogeny Reconstruction, David A. Bader

One high-level algorithmic change

- (Ok, so I lied a little…)
- Avoid labeling the tree if possible
- Use current best score as an upper bound.
- Compute lower bound & prune tree away if lower bound > upper bound
- Lower bound:
- Get circular ordering of leaves, x1 x2 … xn
- Compute D = d(x1,x2) + d(x2,x3) + … + d(xn,x1)
- Then ½ D is a lower bound because
- d(.) obeys the triangle inequality
- every tree edge is used twice in a tree-based version of D

High-Performance for Phylogeny Reconstruction, David A. Bader

Algorithmic Changes (~ 10x)

- Better bounding: skip edges that would cause degree 3 or premature cycle
- “Condensing”: whenever the same
- gene subsequence appears in all genomes, it can be condensed into a single “superfragment”
- done as static processing and on the fly before each TSP
- Initializing the new median with the best of the old one and its three neighbors.
- Condensing is very effective on real data within families, but easily defeated by large evolutionary distances.
- (1) and (3) cause over half of the TSP instances (for finding computing “median-of-three” updated internal nodes) to be pruned away instantly.

High-Performance for Phylogeny Reconstruction, David A. Bader

Data Representation (~ 10x)

- No distance matrix for reduction of “median-of-three” to Traveling Salesperson Problem (TSP): at most 4n edges can be of interest – the others are treated as an undifferentiated pool. The adjacency lists have length 4.
- thus, linear time at each step and reduced storage.
- Backtracking search has a small list of edges and only searches among edges of cost 1 and 2 (– and 0 are always included) – still NP-hard, but often easy
- When search runs out of edges, tour is completed in linear time from the pool of edges of cost 3
- Many auxiliary arrays (á la Fortran!) to carry information on flags, degrees, other end of chains, …

High-Performance for Phylogeny Reconstruction, David A. Bader

Low-Level Coding Changes (~ 6x)

- All storage allocated at start, with large #s of pointers passed to subroutines (no globals, to allow parallel execution).
- Avoids malloc/free overhead; Improves cache locality
- Avoid recomputations.
- Use local variables for intermediate pointers
- Hand unroll loops on adjacencies to preserve locality (and to avoid “mod” operations with circular genomes)
- Speeds up addressing – never deference! & Improves cache locality

BPAnalysis uses 65MB and has a real memory footprint of ~ 12MB on our real data

Our reimplementation uses 1.6MB with a footprint of 0.6MB

High-Performance for Phylogeny Reconstruction, David A. Bader

And… How did we do it?

- 3 strategies: Profile, Profile, Profile

(and use your engineering sense/nose/… )

Sun Forte 6 Analyzer

- We began with 4 main culprits:
- preparing adjacency lists for the TSP
- computing breakpoint distances
- computing lower bounds in TSP
- backtracking in TSP
- Over 10 – 12 major iterations, each of which yielded a 1.5 – 2 fold speed-up, these four switched places over and over.

High-Performance for Phylogeny Reconstruction, David A. Bader

Profiling

- And our final tally (still on the Campanulaceae dataset) is:

30% backtracking (excl. LB)

20% preparing adjacency lists

20% condensing & expanding

15% computing LB

8% computing distances

7% miscellaneous overhead

- (no obvious culprits left)

High-Performance for Phylogeny Reconstruction, David A. Bader

High-Performance Computing Techniques

- Availability of hundreds of powerful processors
- Standard parallel programming interfaces (Sun HPC)
- Message passing interface (MPI)
- OpenMP or POSIX threads
- Algorithmic libraries for SMP clusters
- SIMPLE
- Goal: make efficient use of parallelism for
- exploring candidate tree topologies
- sharing of improved bounds

High-Performance for Phylogeny Reconstruction, David A. Bader

Parallelization of the Phylogeny Algorithm

- Enumerating tree topologies is pleasantly parallel and allows multiple processors to independently search the tree space with little or no overhead
- Improved bounds can be broadcast to other processors without interrupting work
- Load is evenly balanced when trees are cyclically assigned (e.g. in a round-robin fashion) to the processors
- Linear speedup

High-Performance for Phylogeny Reconstruction, David A. Bader

Final Remarks

- Our reimplementation led to numerous extensions as well as to new theoretical results
- GRAPPA has been extended to inversion phylogeny, with linear-time algorithms for inversion distance and a new approach to exact inversion median-of-three.
- Better bounding in the next version of GRAPPA yields two more orders of magnitude speedup.
- These insights and improvements are made possible by mature development tools (Forte)
- Algorithmic engineering techniques are widely applicable
- We may not always get 6 orders of magnitude, but 3 – 4 orders should be nearly routine with most codes. (We are starting work on TBR and exact parsimony solvers.)

High-Performance for Phylogeny Reconstruction, David A. Bader

Final Remarks (cont’d)

- High-performance implementations enable:
- better approximations for difficult problems (MP, ML)
- true optimization for larger instances
- realistic data exploration (e.g., testing evolutionary scenarios, assessing answers obtained through other means, etc.)
- Our analysis of the Campanulaceae dataset confirmed the conjecture of Robert Jansen et al. – that inversion is the principal process of genome evolution in cpDNA for this group.

High-Performance for Phylogeny Reconstruction, David A. Bader

Work-In-Progress and Future Work

- Tree enumeration using circular ordering
- Handle unequal gene content and duplicate genes using exemplars
- Parallel branch and bound techniques (optimized for Sun HPC Servers) for searching tree space
- Improved SPR and TBR techniques (local searches around good trees)
- Exact Algorithm for Maximum Parsimony

High-Performance for Phylogeny Reconstruction, David A. Bader

Recent publications (2001)

- A New Implementation and Detailed Study of Breakpoint Analysis, B.M.E. Moret, S. Wyman, D.A. Bader, T. Warnow, M. Yan, Sixth Pacific Symposium on Biocomputing 2001, pp. 583-594, Hawaii, January 2001.
- High-Performance Algorithm Engineering for Gene-Order Phylogenies, D.A. Bader, B. M.E. Moret, T. Warnow, S.K. Wyman, and M. Yan, DIMACS Workshop on Whole Genome Comparison, DIMACS Center, Rutgers University, Piscataway, NJ, March 2001.
- Variation in vegetation growth rates: Implications for the evolution of semi-arid landscapes, C. Restrepo, B.T. Milne, D. Bader, W. Pockman, and A. Kerkhoff, 16th Annual Symposium of the US-International Association of Landscape Ecology, Arizona State University, Tempe, April 2001.
- High-Performance Algorithm Engineering for Computational Phylogeny, B. M.E. Moret, D.A. Bader, and T. Warnow, 2001 International Conference on Computational Science, San Francisco, CA, May 2001.
- Cluster Computing: Applications, David A. Bader and Robert Pennington, The International Journal of High Performance Computing, 15(2):181-185, May 2001.
- New approaches for using gene order data in phylogeny reconstruction, R.K. Jansen, D.A. Bader, B. M. E. Moret, L.A. Raubeson, L.-S. Wang, T. Warnow, and S. Wyman. Botany 2001, Albuquerque, NM, August 2001.
- GRAPPA: a high-performance computational tool for phylogeny reconstruction from gene-order data, B. M.E. Moret, D.A. Bader, T. Warnow, S.K. Wyman, and M. Yan. Botany 2001, Albuquerque, NM, August 2001.
- Inferring phylogenies of photosynthetic organisms from chloroplast gene orders, L.A. Raubeson, D.A. Bader, B. M.E. Moret, L.-S. Wang, T. Warnow, and S.K. Wyman. Botany 2001, Albuquerque, NM, August 2001.
- Industrial Applications of High-Performance Computing for Phylogeny Reconstruction, D.A. Bader, B. M.E. Moret, and L. Vawter, SPIE ITCom: Commercial Applications for High-Performance Computing, Denver, CO, SPIE Vol. 4528, pp. 159-168, August 2001.
- Using PRAM Algorithms on a Uniform-Memory-Access Shared-Memory Architecture, D.A. Bader, A. Illendula, B. M.E. Moret, and N.R. Weisse-Bernstein, Fifth Workshop on Algorithm Engineering, Springer-Verlag LNCS 2141, 129-144, Aarhus, Denmark, August 2001.
- A Linear-Time Algorithm for Computing Inversion Distance Between Two Signed Permutations with an Experimental Study, D.A. Bader, B. M.E. Moret, and M. Yan, Journal of Computational Biology, 8(5):483-491, October 2001.

High-Performance for Phylogeny Reconstruction, David A. Bader

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