DNA Implementation of a Royal Road DNA Implementation of a Royal Road Fitness Evaluation Fitness Evaluation

Ji Yoon ParkJi Yoon Park

Dept. of BiochemDept. of Biochem

Hanyang UniversityHanyang University

Elizabeth Goode, David Harlan Wood, and Junghuei ChenElizabeth Goode, David Harlan Wood, and Junghuei Chen

AbstractAbstract

1. A model for 1. A model for DNA implementation DNA implementation of Royal Road evoluof Royal Road evolutionary computationtionary computation

- for - for separation by fitnessseparation by fitness : : 2-d DGGE, PAGE2-d DGGE, PAGE

2. Suggestion for possible use of the MutS and MutY2. Suggestion for possible use of the MutS and MutY - mismatch-binding proteins in combination with gel- mismatch-binding proteins in combination with gel

shift assays for separation by fitnessshift assays for separation by fitness

The Royal RoadThe Royal Road

* * A class of A class of evolutionary computationsevolutionary computations

- - van Nimwegen van Nimwegen et alet al

▪ ▪ The population dynamics of various Royal Road fitness functionsThe population dynamics of various Royal Road fitness functions

▪ ▪ Only a relatively few generation Only a relatively few generation ▪ ▪ Don’t support theoretical results on the stasis Don’t support theoretical results on the stasis ▪ ▪ Limitation of genetic variation Limitation of genetic variation - By implementing Royal Road problems - By implementing Royal Road problems using DNAusing DNA, ,

◊ ◊ Use populations many others of magnitude larger than the populations Use populations many others of magnitude larger than the populations

available using conventional computers available using conventional computers

◊ ◊ Huge DNA storage capacityHuge DNA storage capacity permits exploring populations with permits exploring populations with

much much greater genetic diversitygreater genetic diversity ◊ ◊ Test precisely theoretical predictionsTest precisely theoretical predictions van Nimwegen van Nimwegen

Focus on…Focus on…

☞ ☞ Fitness-based separationFitness-based separation of individuals of individuals for a Royal for a Royal

Road problem Road problem

* DNA model for simulating Royal Road computation* DNA model for simulating Royal Road computation

- Potential of computing with - Potential of computing with very large population !very large population !

- Separation : 2-d DGGE, PAGE - Separation : 2-d DGGE, PAGE

Evolutionary AlgorithmsEvolutionary Algorithms

- Population(possibly random) - Population(possibly random)

- Selection - Selection → → fitness functionfitness function - Reproduction- Reproduction → → reproduce the next generation of individualsreproduce the next generation of individuals according to some according to some reproduction strategy which may include reproduction strategy which may include mutation and crossovermutation and crossover exex)) MaxOnes MaxOnes -- Begins with a random set of individual bitstringsBegins with a random set of individual bitstrings of 0 and 1, each of length of 0 and 1, each of length nn.. -- For a given initial population size, the goal is to generation For a given initial population size, the goal is to generation such perfect individualssuch perfect individuals

Royal Road Fitness FunctionRoyal Road Fitness Function

* * Generation of the MaxOnes fitness functionGeneration of the MaxOnes fitness function

- The population - The population

: : Strings which contain discreteStrings which contain discrete blocksblocks which are subsequences of bitswhich are subsequences of bits

- - Each blockEach block is evaluated is evaluated for fitnessfor fitness

▶▶ Each block in a given individual bitstring which satisfies its predefinedEach block in a given individual bitstring which satisfies its predefined

block fitness criterion contributes to the block fitness criterion contributes to the fitness rating of that fitness rating of that

individual individual

▶ ▶ Any deviations from the required specification fails to contributes the Any deviations from the required specification fails to contributes the

total fitness for the bitstringtotal fitness for the bitstring

▶ ▶ The sum of the block contributionsThe sum of the block contributions constitutes constitutes the total fitness for the the total fitness for the

bitstring bitstring

▶▶ Blocks are assigned Blocks are assigned fitness 1 if they are perfectfitness 1 if they are perfect, and , and fitness 0 otherwisefitness 0 otherwise..

1. 1. Examine the population dynamicsExamine the population dynamics in instances of the Royal Road in instances of the Royal Road problem problem ▶▶The potential of generating previously unobtained information(10The potential of generating previously unobtained information(1012 12 >)>)

2. 2. Feasibility of the necessary laboratory stepsFeasibility of the necessary laboratory steps for DNA implementationfor DNA implementation

* * The enormous storage capacityThe enormous storage capacity of DNAof DNA ▶▶The potential gain in computing evolutionary algorithmsThe potential gain in computing evolutionary algorithms using DNA using DNA rather than silicon is unprecedentedrather than silicon is unprecedented

The preliminary Example for Royal The preliminary Example for Royal Road Fitness-Proportional SelectionRoad Fitness-Proportional Selection

* Let * Let A={A={C, T, GC, T, G}} be be working set of symbolsworking set of symbols* * The block is B={The block is B={C, TC, T}} ▶▶ The population of interestThe population of interest is a set of bitstrings of is a set of bitstrings of length 88length 88 written written over A, each containing over A, each containing 2 blocks2 blocks written over B of written over B of length 6length 6 in bit in bit positions 25-30 and 57-62 positions 25-30 and 57-62 ▶▶ The population contains The population contains at most at most 2212 12 individualsindividuals ▶▶ The individuals, once encoded in DNA, must be physically separaThe individuals, once encoded in DNA, must be physically separa

ble by fitnessble by fitness ▶▶ Fitness 1Fitness 1 for each perfect block containing for each perfect block containing all all TTss ▶▶ A perfect individual contains onlyA perfect individual contains only T T in each of its blocks: in each of its blocks: fitness 2fitness 2 ▶▶ Doing Doing selectionselection over the entire population of one generation in over the entire population of one generation in one one

dayday (possible to treat populations of size (possible to treat populations of size 10101616) )

PrinciplePrinciple

◈ ◈ Fisher and LermanFisher and Lerman (1983);(1983); Myers et al (1987); Sheffield et al (1989) Myers et al (1987); Sheffield et al (1989)

▶▶When When ds DNA migratesds DNA migrates through through increasing concentrations of urea increasing concentrations of urea and formamide and formamide, the , the complementary strands will dissociatecomplementary strands will dissociate in a do in a domain-dependent fashion.main-dependent fashion.

▶▶The dissociation causes an abruptThe dissociation causes an abrupt decrease decrease in the in the mobility mobility of the frof the fragment in polyacrylamide gels.agment in polyacrylamide gels.

▶▶The The presence of a mutationpresence of a mutation may may change the stability of its local dochange the stability of its local domainmain and hence and hence alter its pattern of migrationalter its pattern of migration. .

ExperimentalExperimental

◈◈ When preparing DNA for analysis by DGGE, When preparing DNA for analysis by DGGE,

▶▶ PCRPCR is used to attach an is used to attach an ~~40 bp G-C clamp to one end of the fragment. 40 bp G-C clamp to one end of the fragment.

** ClampClamp: : highly stablehighly stable, , denaturation-resistant domain denaturation-resistant domain

▶▶ Allow Allow mutations mutations in lower melting domains to be in lower melting domains to be acertainedacertained

▶▶ Heteroduplexes Heteroduplexes between a wild-type strand and a potential mutant strand wibetween a wild-type strand and a potential mutant strand will be ll be destabilized by the single base-pair mismatchdestabilized by the single base-pair mismatch and will and will migrate more slomigrate more slowlywly than either homoduplex than either homoduplex

▶ ▶Heteroduplexes generated during PCR amplification of heterozygous genomiHeteroduplexes generated during PCR amplification of heterozygous genomic DNA can greatly assist c DNA can greatly assist in the detection of mutationsin the detection of mutations

Strengths/LimitationsStrengths/Limitations

◈◈Advantage: Advantage:

▶▶ Used to Used to analyzeanalyze PCR-amplified, PCR-amplified, G-C clamped segments of DNA < 500 bp G-C clamped segments of DNA < 500 bp in length. in length. ▶▶ Best suited to Best suited to scanning multiple samples for mutationsscanning multiple samples for mutations in the same DNA in the same DNA fragment fragment ▶▶ A change from A change from A/TA/T toto G/CG/C usually usually increase the stabilityincrease the stability of the local domain of the local domain ▶▶ A change from A change from G/CG/C to A/T to A/T usually has a usually has a destabilizing destabilizing effect effect

◈◈ Disadvantage:Disadvantage: ▶▶ The The exact position and nature of the mutationexact position and nature of the mutation must be must be confirmed by confirmed by DNADNA sequencing sequencing ▶▶ Requires Requires specialized equipmentspecialized equipment and a distinctly user-unfriendly and a distinctly user-unfriendly computer computer programprogram, which is needed to select sequences for oligonucleotide primers , which is needed to select sequences for oligonucleotide primers

Perpendicular 2-d DGGEPerpendicular 2-d DGGE

* Separation by fitness * Separation by fitness

▶▶ Denaturing gradient gel electrophoresis(DGGE)Denaturing gradient gel electrophoresis(DGGE)

- - ds DNA is moved through the gradient gel environmentds DNA is moved through the gradient gel environment by by

electrophoresiselectrophoresis

- - Partial dehybridization of ds DNAPartial dehybridization of ds DNA in a denaturing environment in a denaturing environment

reduces the mobility of DNA reduces the mobility of DNA

- The different m.p of different seqs- The different m.p of different seqs

▶▶differences between the movement of those seqs, even if those differences between the movement of those seqs, even if those

seqs are the same lengthseqs are the same length

- - To determine an optimal denaturing gradientTo determine an optimal denaturing gradient between candidates between candidates

of different fitnessof different fitness

- - Separation is verified with PAGESeparation is verified with PAGE

The Candidate IndividualsThe Candidate Individuals

* Candidate* Candidate

▶▶ ss DNAss DNA consisting of consisting of 8888 bases bases each each

▶▶ Each individual strand consists of 5 concatenated seqs of Each individual strand consists of 5 concatenated seqs of C, G and TC, G and T

▶▶ All concatenates of the following five seqsAll concatenates of the following five seqs

: : Clamp1 Clamp1 - - Block1 Block1 - - Clamp2 Clamp2 - - Block2 Block2 - - Clamp3Clamp3

▶▶ Clamps Clamps are distinct, but constant for all candidates, and haveare distinct, but constant for all candidates, and have lengths lengths

24, 26 and 2624, 26 and 26 and and G-C rich regionsG-C rich regions

▶▶ BlocksBlocks have have length 6,length 6, and contain a and contain a mixture of C and Tmixture of C and T, varying among , varying among

different candidates. different candidates.

▶▶ The The ‘perfect candidate’‘perfect candidate’ has has only T in Block1 and Block2only T in Block1 and Block2

The candidate strands can be dividedThe candidate strands can be divided

- - Physically Physically divide candidate strands into equivalence classesdivide candidate strands into equivalence classes

* * To separationTo separation ▶▶ Anneal the various ‘imperfect’ candidatesAnneal the various ‘imperfect’ candidates to targetto target

◊◊ fitness = 0: fitness = 0: at least one C in each of B1 and B2at least one C in each of B1 and B2 ◊ ◊ fitness = 1: one perfect block containing fitness = 1: one perfect block containing only Tonly T, and, and one imperfect block containing one imperfect block containing at least one C at least one C ◊ ◊ fitness = 2(perfect candidate): fitness = 2(perfect candidate): only T in both B1 and B2only T in both B1 and B2

* Clamp: constant for all individuals* Clamp: constant for all individuals ▶▶ only one seq associated with a perfect individual only one seq associated with a perfect individual

Candidate perfect:Candidate perfect: 5’ - - 5’ - - GGGCGGCCTCGCCTCCCCTGCTGGGGGCGGCCTCGCCTCCCCTGCTGG TTTTTTTTTTTT

CCTTCTCCCTCTGTCGGGCTCGCGTTCCTTCTCCCTCTGTCGGGCTCGCGTT TTTTTTTTTTTT TTGTTGCTTCGTTTGTCCTTCCGTCCTTGTTGCTTCGTTTGTCCTTCCGTCC - - 3’ - - 3’

Candidate 2.1:Candidate 2.1: 5’ - - 5’ - - GGGCGGCCTCGCCTCCCCTGCTGGGGGCGGCCTCGCCTCCCCTGCTGG TTTTTT TTTTTT

CCTTCTCCCTCTGTCGGGCTCGCGTTCCTTCTCCCTCTGTCGGGCTCGCGTT CCTTTTTTTTTT TTGTTGCTTCGTTTGTCCTTCCGTCCTTGTTGCTTCGTTTGTCCTTCCGTCC - - 3’ - - 3’

Candidate 2.6:Candidate 2.6: 5’ - - 5’ - - GGGCGGCCTCGCCTCCCCTGCTGG GGGCGGCCTCGCCTCCCCTGCTGG TTTTTT TTTTTT

CCTTCTCCCTCTGTCGGGCTCGCGTT CCTTCTCCCTCTGTCGGGCTCGCGTT CCCCCCCCCCCC TTGTTGCTTCGTTTGTCCTCCTCCTTGTTGCTTCGTTTGTCCTCCTCC - - 3’ - - 3’

Candidate 1.6-2.6:Candidate 1.6-2.6: 5’ - - 5’ - - GGGCGGCCTCGCCTCCCCTGCTGGGGGCGGCCTCGCCTCCCCTGCTGG CCCCCCCCCCCC

CCTTCTCCCTCTGTCGGGCTCGCGTT CCTTCTCCCTCTGTCGGGCTCGCGTT CCCCCCCCCCCC TTGTTGCTTCGTTTGTCCTTCCGTCCTTGTTGCTTCGTTTGTCCTTCCGTCC - - 3’ - - 3’

Target strand:Target strand: exact complement of Candidate Perfectexact complement of Candidate Perfect 5’ - - CGACGGAAGGACAAACGAAGCAACAA AAAAAA 5’ - - CGACGGAAGGACAAACGAAGCAACAA AAAAAA

AACGCGAGCCCGACAGAGGGAGAAGG AAAAAA AACGCGAGCCCGACAGAGGGAGAAGG AAAAAA CCAGCAGGGGAGGCGAGGCCGCCC - - 3’ CCAGCAGGGGAGGCGAGGCCGCCC - - 3’

= 1+ 1= 1+ 1

= = 22

= 1 + 0 = 1 + 0

= = 11

= 1 + 0 = 1 + 0

= = 11

= 0 + 0= 0 + 0

= = 00

FitnessFitness

Separation by FitnessSeparation by Fitness

¶ ¶ 2-d DGGE in combination with PAGE2-d DGGE in combination with PAGE

◊ ◊ SeparationSeparation of a subset of candidate strands of a subset of candidate strands by fitness classby fitness class

◊◊ Different candidate strands annealed to the Target strand Different candidate strands annealed to the Target strand

should should run run differently differently according according to their fitnessto their fitness

◊◊ CandidatesCandidates having blocks which having blocks which perfectly anneal to Targetperfectly anneal to Target

strand are predicted to strand are predicted to run more quicklyrun more quickly through a gel than through a gel than

candidate strands candidate strands

2-d DGGE2-d DGGE

PAGEPAGE

Lane 1: Lane 1: 25bp ladder25bp ladder

Lane 2: Lane 2: Candidate PerfectCandidate Perfect/Target/Target

Lane 3: Lane 3: Candidate2.1Candidate2.1/Target/Target

Lane 4: Lane 4: Candidate 2.6Candidate 2.6/Target/Target

PAGEPAGE

Mobility Shift AssayMobility Shift Assay

ConclusionConclusion

“ “ Can Can 2-d DGGE and PAGE2-d DGGE and PAGE be used for be used for separating candidatesseparating candidates according according to fitness in a Royal Road evolutionary computationto fitness in a Royal Road evolutionary computation?”?”

▶▶ Fitness-based separationFitness-based separation

- - Clamp-block style encoding of individualsClamp-block style encoding of individuals is useful is useful for DNAfor DNA

implementationimplementation of a Royal Road problem of a Royal Road problem

- - Verify a complete separation abilityVerify a complete separation ability for the Royal Road fitness for the Royal Road fitness

function function

- - 2-d DGGE and PAGE separation2-d DGGE and PAGE separation

: useful for : useful for implementing fitness separationimplementing fitness separation for the Royal Road for the Royal Road

problem and for problem and for other evolutionary algorithmother evolutionary algorithm