Frank Dehne Parallel Computational Biochemistry

Frank Dehne www.dehne.net

Parallel Computational Biochemistry


Proteins, DNA, etc.

DNA encodes the information necessary to produce proteins

Proteins are the main molecular building blocks of life (for example, structural proteins, enzymes)


• Proteins are formed from a chain of molecules called amino acids

Proteins, DNA, etc.


• The DNA sequence encodes the amino acid sequence that constitutes the protein

Proteins, DNA, etc.


• There are twenty amino acids found in proteins, denoted by A, C, D, E, F, G, H, I, ...

Proteins, DNA, etc.


Multiple Sequence Alignment


Databases of Biological Sequences

>BGAL_SULSO BETA-GALACTOSIDASE Sulfolobus solfataricus.MYSFPNSFRFGWSQAGFQSEMGTPGSEDPNTDWYKWVHDPENMAAGLVSGDLPENGPGYWGNYKTFHDNAQKMGLKIARLNVEWSRIFPNPLPRPQNFDESKQDVTEVEINENELKRLDEYANKDALNHYREIFKDLKSRGLYFILNMYHWPLPLWLHDPIRVRRGDFTGPSGWLSTRTVYEFARFSAYIAWKFDDLVDEYSTMNEPNVVGGLGYVGVKSGFPPGYLSFELSRRHMYNIIQAHARAYDGIKSVSKKPVGIIYANSSFQPLTDKDMEAVEMAENDNRWWFFDAIIRGEITRGNEKIVRDDLKGRLDWIGVNYYTRTVVKRTEKGYVSLGGYGHGCERNSVSLAGLPTSDFGWEFFPEGLYDVLTKYWNRYHLYMYVTENGIADDADYQRPYYLVSHVYQVHRAINSGADVRGYLHWSLADNYEWASGFSMRFGLLKVDYNTKRLYWRPSALVYREIATNGAITDEIEHLNSVPPVKPLRH

NCBI: 14,976,310 sequences

15,849,921,438 nucleotides

Swiss-Prot: 104,559 sequences

38,460,707 residues

PDB: 17,175 structures


Sequence comparison

• Compare one sequence (target) to many sequences (database search)

• Compare more than two sequences simultaneously


Applications

• Phylogenetic analysis

• Identification of conserved motifs and domains

• Structure prediction



Phylogenetic Analysis


Structure Prediction

Genomic sequences

> RICIN GLYCOSIDASEMYSFPNSFRFGWSQAGFQSEMGTPGSEDPNTDWYKWVHDPENMAAGLVSGDLPENGPGYWGNYKTFHDNAQKMGLKIARLNVEWSRIFPNPLPRPQNFDESKQDVTEVEINENELKRLDEYANKDALNHYREIFKDLKSRGLYFILNMYHWPLPLWLHDPIRVRRGDFTGPSGWLSTRTVYEFARFSAYIAWKFDDLVDEYSTMNEPNVVGGLGYVGVKSGFPPGYLSFELSRRHMYNIIQAHARAYDGIKSVSKKPVGIIYANSSFQPLTDKDMEAVEMAENDNRWWFFDAIIRGEITRGNEKIVRDDLKGRLDWIGVNYYTRTVVKRTEKGYVSLGGYGHGCERNSVSLAGLPTSDFGWEFFPEGLYDVLTKYWNRYHLYMYVTENGIADDADYQRPYYLVSHVYQVHRAINSGADVRGYLHWSLADNYEWASGFSMRFGLLKVDYNTKRLYWRPSALVYREIATNGAITDEIEHLNSVPPVKPLRH

Protein sequences

Protein structures


Our Contributions

• Parallel min vertex cover for improved sequence alignments (to appear in Journal of Computer and System Sciences)

• Parallel Clustal W (ICCSA 2003)

• In progress: “Clustal XP” portal at http://cgm.dehne.net


Clustal W


Progressive Alignment

Scerevisiae [1]Celegans [2] 0.640Drosophia [3] 0.634 0.327Human [4] 0.630 0.408 0.420Mouse [5] 0.619 0.405 0.469 0.289

S.cerevisiaeC.elegans

DrosophilaMouse

Human

1. Do pairwise alignment of all sequences and calculate distance matrix

2. Create a guide tree based on this pairwise distance matrix

3. Align progressively following guide tree. • start by aligning most closely related pairs of sequences• at each step align two sequences or one to an existing subalignment


Parallel Clustal

• Parallel pairwise (PW) alignment matrix

• Parallel guide tree calculation

• Parallel progressive alignment

Scerevisiae [1]Celegans [2] 0.640Drosophia [3] 0.634 0.327Human [4] 0.630 0.408 0.420Mouse [5] 0.619 0.405 0.469 0.289

S.cerevisiaeC.elegans

DrosophilaMouse

Human


Relative Speedup


Clustal XP vs. SGI

SGI data taken from Performance Optimization of Clustal W: Parallel Clustal W, HT Clustal, and MULTICLUSTAL

By: Dmitri Mikhailov, Haruna Cofer, and Roberto Gomperts


Parallel Clustal - Improvements

• Optimization of input parameters– scoring matrices, gap penalties - requires many

repetitive Clustal W calculations with various input parameters.

• Minimum Vertex Cover– use minimum vertex cover to remove erroneous

sequences, and identify clusters of highly similar sequences.


Minimum Vertex Cover

Conflict Graph– vertex: sequence

– edge: conflict (e.g. alignment with very poor score)

TASK: remove smallest number of gene sequences that eliminates all conflicts

NP-complete


FPT Algorithms

• Phase 1: Kernelization

Reduce problem to size f(k)

• Phase 2: Bounded Tree Search

Exhausive tree search; exponential in f(k)


Kernelization

Buss's Algorithm for k-vertex cover

• Let G=(V,E) and let S be the subset of vertices with degree k or more.

• Remove S and all incident edges

G->G’ k -> k'=k-|S|.

• IF G' has more than k x k' edges THEN no k-vertex cover exists

ELSE start bounded tree search on G'


Bounded Tree Search

VC={}

VC+=... VC+=... VC+=...

VC+=... VC+=... VC+=...

VC+=... VC+=... VC+=...


Case 1: simple path of length 3

VC+={v,v2}

VC={...}

VC+={v1,v2} VC+={v1,v3}

search tree

v

v1

v2

v3

in graph G'

remove selected vertices from G'k' - = 2


Case 2: 3-cycle

v

v1

v2

in graph G'

VC+={v,v1}

VC={...}

VC+={v1,v2} VC+={v,v2}

search tree

remove selected vertices from G'k' - = 2



v

v1

v2

in graph G'

VC={...}

VC+={v1}

search tree

remove v1, v2 from G'k' - = 1



v

v1

in graph G'

VC={...}

VC+={v}

search tree

remove v, v1 from G'k' - = 1


Sequential Tree Search

Depth first search– backtrack when k'=0 and

G'<>0 ("dead end" ))

– stop when solution found (G'={}, k'>=0 )


Parallel Tree SearchBasic Idea:

– Build top log p levels of the search tree (T ')

– every proc. starts depth-first search at one leaf of T '

– randomize depth-first search by selecting random child

T 'log p


Analysis: Balls-in-bins

sequential depth-first search path total length:L, #solutions: m

expected sequential time (rand. distr.): L/(m+1)

parallel search path

expected parallel time (rand. distr.): p + L/(p(m+1))expected speedup: p / (1 + (m+1)/L)if m << L then expected speedup = p


Simulation Experiment

number of processors

0 50

50

pre

dict

ed s

pee

dup

L = 1,000,000

m = 10m = 100m = 1,000m = 10,000m = 100,000

100

150

200

100 150 200

L = 1,000,000


Implementation

• test platform:– 32 node HPCVL Beowulf cluster– each node: dual 1.4 GHz Intel Xeon, 512 MB

RAM, 60 GB disk– gcc and LAM/MPI on LINUX Redhat 7.2

• code-s: Sequential k-vertex cover

• code-p: Parallel k-vertex cover


Test Data

• Protein sequences

• Same protein from several hundred species

• Each protein sequence a few hundred amino acid residues in length

• Obtained from the National Center for Biotechnology Information (http://www.ncbi.nlm.nih.gov/)


Test Data

• Somatostatin

– neuropeptide involved in the regulation of many functions in different organ systems

– Clustal Threshold = 10, |V| = 559, |E| = 33652, k = 273, k' = 255


Test Data

• WW

– small protein domain that binds proline rich sequences in other proteins and is involved in cellular signaling



Test Data

• Kinase

– large family of enzymes involved in cellular regulation



Test Data

• SH2 (src-homology domain 2)

– involved in targeting proteins to specific sites in cells by binding to phosphor-tyrosine



Test Data

• Thrombin

– protease involved in the blood coagulation cascade and promotes blood clotting by converting fibrinogen to fibrin



Test Data

• PHD (pleckstrin homology domain)

– involved in cellular signaling



Test Data

• Random Graph

|V| = 220, |E| = 2155, k = 122, k' = 122

• Grid Graph

|V| = 289, |E| = 544, k = 145, k' = 145


Test Data

|VC| ~ |V| / 2 k' = k


Sequential Times

Kinase, SH2, Thombin: n/a


Code-p on Virtual Proc.


Parallel Times


Speedup: Somatostatin


Speedup: WW


Speedup: Rand. Graph


Speedup: Grid Graph


Clustal W

+Parallel Clustal

…

Parallel FPT MVC

Clustal XP

Web Portal

Clustal XPin progress X : Extended

P : Parallel


http

://cg

m.d

ehne

.net

Clustal XP


Documents

Frank Dehne Parallel Computational Biochemistry