ApplicabilityofLoop ApplicabilityofLoop - - PowerPoint PPT Presentation

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ApplicabilityofLoop ApplicabilityofLoop - - PowerPoint PPT Presentation

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ApplicabilityofLoop ApplicabilityofLoop RecombinationinCiliatesusing RecombinationinCiliatesusing theBreakpointGraph theBreakpointGraph RobertBrijder,Hendrik Hendrik Jan

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SLIDE 1

Sept.27-29,2006

CompLife'06

ApplicabilityofLoop ApplicabilityofLoop RecombinationinCiliatesusing RecombinationinCiliatesusing theBreakpointGraph theBreakpointGraph

LeidenInstituteofAdvanced LeidenInstituteofAdvanced ComputerScience, ComputerScience, LeidenUniversity LeidenUniversity

RobertBrijder, RobertBrijder,Hendrik Hendrik Jan JanHoogeboom Hoogeboom, , andMichael andMichaelMuskulus Muskulus

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SLIDE 2

Sept.27-29,2006 CompLife'06

Overview Overview

  • Briefoverviewofgeneassemblyinciliates.

Briefoverviewofgeneassemblyinciliates.

  • Briefoverviewofaformalmodel.

Briefoverviewofaformalmodel.

  • Recallreductiongraph.

Recallreductiongraph.

  • Introducegraph`ontopof

Introducegraph`ontopof’ ’ reduction reduction graph,andshowitsuses. graph,andshowitsuses.

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SLIDE 3

Sept.27-29,2006 CompLife'06

GeneAssemblyinCiliates GeneAssemblyinCiliates

  • Ageneofthe

AgeneoftheSterkiella Sterkiella nova nova

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SLIDE 4

Sept.27-29,2006 CompLife'06

GeneAssembly GeneAssembly

  • Thegeneassemblyprocessisdoneusing

Thegeneassemblyprocessisdoneusing molecularoperations. molecularoperations.

  • Withtheaidof

Withtheaidofpointers pointers theseoperations theseoperations `know `know’ ’ howthesepartsneedtobeglued howthesepartsneedtobeglued together. together.

3

Actually 2 b 2 3 4 3 e 4

1 2 4

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SLIDE 5

Sept.27-29,2006 CompLife'06

GeneAssembly GeneAssembly

Thegeneassemblyprocessisaccomplished Thegeneassemblyprocessisaccomplished usingthreemolecularoperations: usingthreemolecularoperations:

  • Looprecombination

Looprecombination

  • Hairpinrecombination

Hairpinrecombination

  • Double

Double-

  • looprecombination

looprecombination

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SLIDE 6

Sept.27-29,2006 CompLife'06

GeneAssembly GeneAssembly

  • Looprecombination

Looprecombination

  • Hairpinrecombination

Hairpinrecombination

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SLIDE 7

Sept.27-29,2006 CompLife'06

GeneAssembly GeneAssembly

  • Double

Double-

  • looprecombination

looprecombination

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SLIDE 8

Sept.27-29,2006 CompLife'06

GeneAssembly GeneAssembly

Theprocessisirreversible: Theprocessisirreversible: whenamolecularoperationisappliedona whenamolecularoperationisappliedona pointer,thenthispointercannotbeused pointer,thenthispointercannotbeused again. again.

slide-9
SLIDE 9

Sept.27-29,2006 CompLife'06

Overview Overview

  • Briefoverviewofgeneassemblyinciliates.

Briefoverviewofgeneassemblyinciliates.

  • Briefoverviewofaformalmodel.

Briefoverviewofaformalmodel.

  • Recallreductiongraph.

Recallreductiongraph.

  • Introducegraph`ontopof

Introducegraph`ontopof’ ’ reduction reduction graph,andshowitsuses. graph,andshowitsuses.

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SLIDE 10

Sept.27-29,2006 CompLife'06

ModelingGeneAssembly ModelingGeneAssembly

4 2 3 342

legalstring

2 b 2 3 4 3 e 4

SPRS

  • ,...}.

3 , 3 , 2 , 2 { = Π

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SLIDE 11

Sept.27-29,2006 CompLife'06

ModelingGeneAssembly ModelingGeneAssembly

xz xppz snrp = ) (

Looprecombination Looprecombination-

  • Stringnegativerule

Stringnegativerule

: ,

  • and
  • For

*

Π ∈ Π ∈ z x p

. ) (

  • e.g.,

4545 45 3 3 45

3

= snr

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SLIDE 12

Sept.27-29,2006 CompLife'06

ModelingGeneAssembly ModelingGeneAssembly

Hairpinrecombination Hairpinrecombination-

  • Stringpositiverule

Stringpositiverule

1 1 2 1

x x x u x x x u p p

n n n

  • −

=

  • =

=

where

z y x z p xpy sprp = ) (

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SLIDE 13

Sept.27-29,2006 CompLife'06

ModelingGeneAssembly ModelingGeneAssembly

Double Double-

  • looprecombination

looprecombination-

  • Stringdoublerule

Stringdoublerule

xuzyw xpyqzpuqw sdr

q p

= ) (

,

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SLIDE 14

Sept.27-29,2006 CompLife'06

ModelingGeneAssembly ModelingGeneAssembly

4 2 3 342

λ

  • correspondstoasuccessfulassembledgene.
  • Non-deterministicprocess.
  • Nodeadlocks.
  • Finiteprocess.Pointersareremovedineverystep.

b e

2

spr

4 3,

sdr λ 3434

2

spr

4

spr

3

spr

2 2 4 2 4 2

  • Successfulreductions:
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SLIDE 15

Sept.27-29,2006 CompLife'06

Overview Overview

  • Briefoverviewofgeneassemblyinciliates.

Briefoverviewofgeneassemblyinciliates.

  • Briefoverviewofaformalmodel.

Briefoverviewofaformalmodel.

  • Recallreductiongraph.

Recallreductiongraph.

  • Introducegraph`ontopof

Introducegraph`ontopof’ ’ reduction reduction graph,andshowitsuses. graph,andshowitsuses.

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SLIDE 16

Sept.27-29,2006 CompLife'06

ReductionGraph ReductionGraph

Conceptofbreakpointgraph: reality-and-desire

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SLIDE 17

Sept.27-29,2006 CompLife'06

ReductionGraphExample ReductionGraphExample

  • Doubleedgesaretherealityedges,singleedgesthe

desireedges

  • Thereisacycliccomponent.
  • Thisisthelessgeneralversionofreductiongraph.
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SLIDE 18

Sept.27-29,2006 CompLife'06

Aknownresult Aknownresult

rules.

  • negative
  • string
  • exactly
  • has
  • f
  • reduction
  • successful

every

  • Then
  • .
  • in
  • components

cyclic

  • f
  • number
  • the
  • be
  • let
  • and
  • string,
  • legal
  • a
  • be
  • Let

N u R(u) N u

Complexity:

|) (| u O

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SLIDE 19

Sept.27-29,2006 CompLife'06

Example Example

. , , , : reductions

  • Successful

rule.

  • negative
  • string
  • ne

exactly

  • has
  • f
  • reduction
  • successful

every

  • Thus,
  • component.

cyclic

  • ne
  • has
  • Then
  • string.
  • legal
  • a
  • be
  • Let

2 3 4 2 4 3 4 2 3 4 3 2

34 4 2 23 spr spr snr spr spr snr spr spr snr spr spr snr u R(u) u =

slide-20
SLIDE 20

Sept.27-29,2006 CompLife'06

Overview Overview

  • Briefoverviewofgeneassemblyinciliates.

Briefoverviewofgeneassemblyinciliates.

  • Briefoverviewofaformalmodel.

Briefoverviewofaformalmodel.

  • Recallreductiongraph.

Recallreductiongraph.

  • Introducegraph`ontopof

Introducegraph`ontopof’ ’ reduction reduction graph,andshowitsuses. graph,andshowitsuses.

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SLIDE 21

Sept.27-29,2006 CompLife'06

Motivation Motivation

  • Nowweknow

Nowweknowhowmany howmany Snr Snr rulesare rulesare needed,canwealsodetermine needed,canwealsodetermineonwhich

  • nwhich

pointers pointersthese theseSnr Snr rulesareappliedin rulesareappliedin successfulreductions? successfulreductions?

  • Previousexample:

Previousexample:Snr Snr domainsare{2}, domainsare{2}, {3},{4}. {3},{4}.

  • Ifso,isthis`information

Ifso,isthis`information’ ’ retainedinthe retainedinthe reductiongraph? reductiongraph?

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SLIDE 22

Sept.27-29,2006 CompLife'06

MorecomplicatedExample MorecomplicatedExample

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SLIDE 23

Sept.27-29,2006 CompLife'06

MorecomplicatedExample MorecomplicatedExample

Whichis:

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SLIDE 24

Sept.27-29,2006 CompLife'06

PointerComponentGraph PointerComponentGraph

5 6 4 3 2 7

  • Amultigraph.Noticethatloopsandparallel

edgesareallowed.

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SLIDE 25

Sept.27-29,2006 CompLife'06

PointerComponentGraph PointerComponentGraph

Whichis: R isthelinearconnectedcomponent,andthe

  • thersarecycliccomponents.
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SLIDE 26

Sept.27-29,2006 CompLife'06

Result Result

set.

  • a
  • such
  • in
  • ccur
  • never
  • will

7

  • Also,
  • {2,3}.
  • r
  • {2,5,6}

not

  • but
  • {2,4,6},
  • {2,3,5},

e.g.

  • :

example

  • the
  • In

.

  • f
  • graph
  • PC
  • the
  • in
  • tree
  • spanning
  • a
  • induces
  • iff
  • pointers
  • f
  • set
  • the
  • n
  • snr
  • applies
  • which
  • f
  • reduction
  • successful
  • a
  • is
  • there

,

  • string
  • legal
  • each
  • For

u D D u u

slide-27
SLIDE 27

Sept.27-29,2006 CompLife'06

Example Example

. applicable

  • is
  • rule
  • snr
  • no
  • and
  • pointer
  • n

applied

  • be
  • can
  • peration
  • No
  • .
  • E.g.,

stuck.

  • get
  • always
  • we

then

  • ,
  • take
  • we

if

  • However,

.

  • f
  • reduction
  • successful
  • a
  • is
  • e.g.,
  • then,
  • ,

.

  • f
  • reduction
  • successful
  • a
  • is
  • e.g,
  • then,
  • ,

, ,

6 346 2 4 3 62 4 3 2 6 4 2 5 3 2

7 5 3 5 4 7 2 6 6 4 7 3 2 5

  • )(u)

spr (spr } , , { D u sdr snr spr snr snr } , , { D u sdr spr snr snr snr } , , { D = = = = = = ϕ ϕ

. 346 7 54372562

  • u =
slide-28
SLIDE 28

Sept.27-29,2006 CompLife'06

Nextquestion Nextquestion

Weknow: Weknow:

  • Howmany

Howmany Snr Snr rulesareneededin rulesareneededin successfulreductions. successfulreductions.

  • Onwhichpointers

OnwhichpointersSnr Snr rulesareappliedin rulesareappliedin successfulreductions. successfulreductions. Next: Next:

  • Whatis

Whatistheorder theorder ofthe

  • ftheSnr

Snr rulesin rulesin successfulreductions? successfulreductions?

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SLIDE 29

Sept.27-29,2006 CompLife'06

Extendedresult Extendedresult

: example

  • in
  • tree
  • Spanning

. component)

  • linear
  • (the
  • root
  • with

by

  • determined
  • is
  • applied
  • are
  • rules
  • snr
  • which

in

  • rder
  • the
  • then
  • graph,
  • PC
  • the
  • in
  • tree
  • spanning
  • a
  • induces
  • If

R T T D

Linearorderings

3 5 4 7 2 6 7 5 3 2 4 6

6 2 4 6 4 2

,

  • e.g.

) , , (

  • e.g.

) , , ( sdr snr spr snr snr spr spr spr snr snr snr = → = → ϕ ϕ Reveals(in)dependence ofstringnegativerules

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SLIDE 30

Sept.27-29,2006 CompLife'06

Conclusion Conclusion

Conceptofpointer-componentgraphprovesuseful withinthetheoryofgeneassembly. Inbiologicalterms:itallowsforacharacterizationof applicabilityoflooprecombinationoperationsfor agivenmicronuclear gene. Thesecharacterizationscorrespondtoefficient algorithms(makingthegraphandfinding spanningtreesinagraphareboth computationallyeasy).

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SLIDE 31

Sept.27-29,2006 CompLife'06

TheEnd TheEnd

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SLIDE 32

Sept.27-29,2006 CompLife'06

Definitions Definitions

.

  • to
  • applicable
  • is
  • if
  • ,
  • a
  • called
  • is
  • rules
  • reduction
  • f
  • n

compositio A u

  • fu

reduction ϕ ϕ

. 4 2 3 342

  • f
  • reduction
  • successful
  • a
  • is
  • )

(

  • :

Example

3 4 2

= = u spr spr spr ϕ

. 2 2 ) (

  • since

, 4 2 3 342

  • f
  • reduction
  • a
  • is
  • )

(

  • :

Example

3 4

= = = u u spr spr ϕ ϕ

.

  • if
  • ,
  • called
  • is
  • u
  • f
  • reduction

A (u) successful = ϕ ϕ

  • }.

, , { ) (

  • :

Domain 4 3 2 2 3 34 = dom