Homochirality:Homochirality:models and resultsmodels and results

Axel Brandenburg, Anja Andersen, Axel Brandenburg, Anja Andersen, Susanne HSusanne Höfneröfner, Martin Nilsson, Martin Nilsson

To appear in Orig. Life Evol. Biosph., q-bio.BM/0401036To appear in Orig. Life Evol. Biosph., q-bio.BM/0401036

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PhotosynthesisPhotosynthesisRequires chlorophyllRequires chlorophyll

as catalystas catalystWhat about chiralitry?What about chiralitry?

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Aminoacids in protein: left-handedAminoacids in protein: left-handedSugars in DNA and RNA: right-handedSugars in DNA and RNA: right-handed

Louis PasteurLouis Pasteur(1822-1895)(1822-1895)

animoanimogroupgroup

carboxylcarboxylgroupgroup

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Racemic mixtureRacemic mixture(from lecture of(from lecture ofAntoine Weiss)Antoine Weiss)

RacemizationRacemizationdating methoddating method

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Miller/Urey experimentMiller/Urey experiment

15 organic compounds15 organic compounds2% amino acids (11 different ones)2% amino acids (11 different ones)

racemic mixtureracemic mixture

Wait 1 weekWait 1 week

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Chirality and origin of lifeChirality and origin of life

• Dead stuff not chiral, so is chirality– with racemic mixture: structure fragile

• Importance:– Prerequisite of life (provides curvature and twist)– Consequence of life (enzymatic reactions)

• Miller-Urey amino acids: both chiralities– in Murchison meteorite: mostly left-handed!– but contamination is debated…

• Reasons discussed: circularly polarized light, beta-decay (weak force), homochiral template

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Relevant experiments: nucleotidesRelevant experiments: nucleotides

template-directed oligomerizationtemplate-directed oligomerizationpoly (Cpoly (CDD) ) oligo (G oligo (GDD))

Mononucleotides with wrongMononucleotides with wrongChirality terminate chain growthChirality terminate chain growth

cytosinecytosine guanineguanine

okok

poisonedpoisoned

Joyce, et al. (incl. Orgel) (1984)Joyce, et al. (incl. Orgel) (1984)

(using HPLC)(using HPLC)

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Contergan: was sold as racemic mixtureContergan: was sold as racemic mixture

causes misformationscauses misformations Cures morning sicknessCures morning sicknessduring pregnancyduring pregnancy

(abundaned in December 1961)(abundaned in December 1961)

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Relevant experiments: crystalsRelevant experiments: crystals

Crystal growth with stirring:Crystal growth with stirring:primary nucleation suppressedprimary nucleation suppressed

Crystal growth, many differentCrystal growth, many differentnucleation sites: racemic mixturenucleation sites: racemic mixture

Autocatalytic self-amplification?Autocatalytic self-amplification?Frank (1953), Goldanskii & Kuzmin (1989), …Frank (1953), Goldanskii & Kuzmin (1989), …

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Auto-catalytic effect in dead matterAuto-catalytic effect in dead matter

Alkanol with 2% e.e.Alkanol with 2% e.e.Treated withTreated with

carboxylaldehydecarboxylaldehyde

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Model by Saito & Hyuga (Jan 2004) Model by Saito & Hyuga (Jan 2004)

Bimodal behaviorBimodal behavior

ssrksdt

ds

rsrkrdt

dr

)1(

)1(

2

2

)1(

)1(

srkdt

ds

srkdt

dr

s

r

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Model by Sandars (Dec 2003, OLEB) Model by Sandars (Dec 2003, OLEB)

]][[2][ 11

211

LLkLdt

d

LLL

nSn

nk

nS

]][[2][

]][[2][

111

111

LLkLdt

d

LLkLdt

d

nS

nSn

Reaction for left-handed monomersReaction for left-handed monomers

Loss term for each constituentLoss term for each constituent

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Combined equationsCombined equations

N

nnS

nnSn

LLkLdt

d

LLLkLdt

d

111

11

][][2][

][][][2][

Loss term for each constituentLoss term for each constituent

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Including enantiomeric cross-inhibitionIncluding enantiomeric cross-inhibition

N

nnS

nnIn

RLRkRdt

d

RLRLRkRLdt

d

1111

11111

][][2][

][][][2...][

Loss term for each constituentLoss term for each constituent

]][[2][ 11

12

1

RLkRLdt

d

RLRL

nIn

nk

nI

Racemic solution ~2Racemic solution ~21-n1-n

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Coupling to substrate Coupling to substrate SS

QQL L comes from substratecomes from substrate

acts as a sink of acts as a sink of SSSS sustained by source sustained by source QQ

)(][ RL QQQSdt

d

Catalytic properties of substrateCatalytic properties of substrate(depending on how much (depending on how much LL and and RR one has) one has)

QQLL = = QQRR((LLnn,R,Rnn) )

N

nnSL LLkQL

dt

d

111 ][][2][

Source of LSource of L11 monomers monomers QQLL

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Self-catalytic effectSelf-catalytic effect

Form of Form of QQLL = = QQRR((LLnn,R,Rnn) )

LRCR

RLCL

CfCfSkQ

CfCfSkQ

11][

11][

21

21

21

21

(our work)][

2004)Coveney & (Wattis][

y)possibilit(another ][

2003) (Sandars][

n

n

M

N

L

Ln

L

L

L

C

Possible proposals for Possible proposals for CCLL (similarly for (similarly for CCRR))

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Birfurcation properties Birfurcation properties

Mononucleotides with wrongMononucleotides with wrongChirality terminate chain growthChirality terminate chain growth

1/ SI kk

1.0/ SI kk

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StabilityStability

Relative perturbation ofRelative perturbation ofracemic solution, 10racemic solution, 10-4-4

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Conservation Conservation lawlaw

N

nnL LnE

1

][

][][1 11

1 RRLnEN

nnLR

termssurf. QEEdt

dLRLR

Dependence on fidelityDependence on fidelity

wherewhere

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Differences to SandarsDifferences to Sandars

• Coupling to substrate: here proportional to EL

– in Sandars: [LN]

• Outer boundary condition: here open– in Sandars: prescribed damping term

• Future extensions:– Chain braking– add spatial 3D dynamics

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Reduced equationsReduced equations

Quantitatively close to full modelQuantitatively close to full model

ryryy

rxrxx

22

22

~/

~/

yxr

yxr

~ 222

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Initial biasInitial bias

Effect in reality very weakEffect in reality very weak

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Spatially extended modelSpatially extended model

Propagating front solutionsPropagating front solutions

Reaction-diffusion equationReaction-diffusion equation

YrYrYY

XrXrXX222

222

~/

~/

Proto type: Fisher’s equationProto type: Fisher’s equation

'')1( XXXX

)( ctxfX 2cwave speedwave speed

wwith Tuomas Multamith Tuomas Multamääkiki

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1D model (reaction-diffusion equation)1D model (reaction-diffusion equation)

Propagation into racemic environmentPropagation into racemic environment

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2D model (reaction-diffusion equation)2D model (reaction-diffusion equation)

Short runShort run

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2D model (reaction-diffusion equation)2D model (reaction-diffusion equation)

Time scale longer than for simple frontsTime scale longer than for simple fronts

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P polymerization olymerization in 1DP polymerization olymerization in 1D

chain growth, Rn and Ln in different placeschain growth, Rn and Ln in different places

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The RNA worldThe RNA world

• Central dogma of chemistry of life– DNA RNA protein

enzyme

• all enzymes are themselves proteins?

Walter GilbertWalter Gilbert(1986)(1986)

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RNA itself as enzymeRNA itself as enzyme

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pre-RNA worldspre-RNA worldsMany problems: stability of sugarsMany problems: stability of sugars

2-amino ethyl glycin2-amino ethyl glycin(AEG)(AEG)

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pre-RNA worldspre-RNA worlds

PE Nielsen (1993)PE Nielsen (1993)

better alternative: Nelson, Levi, Miller (2000)better alternative: Nelson, Levi, Miller (2000)