Homochirality through Homochirality through enantiomeric cross-inhibitionenantiomeric cross-inhibition

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

2

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

3

PNA world prior to RNA worldPNA world prior to RNA world

PE Nielsen (1993)PE Nielsen (1993)

Nielsen (1993)Nielsen (1993)Nelson, Levi, Miller (2000)Nelson, Levi, Miller (2000)

CHCH22

NHNH22

C00HC00H

CHCH22C0C0 BaseBase

CHCH22

NHNH

CHCH22

NN

C0C0

CHCH22

NHNH22

C0C0

CHCH22

NHNH

C00HC00H

glycineglycinedipeptidedipeptide

CHCH22

CHCH22

NHNH22

C00HC00Hcarboxylcarboxyl

groupgroup

aminoaminogroupgroup

CHCH

NHNH22

C00HC00H

CHCH33PeptidePeptidenucleotidenucleotide

alaninealanineachiralachiral chiralchiral

4

Chirality and origin of lifeChirality and origin of life

• Life: plausible with left/right handed nucleotides• Origin of life: possibly achiral (e.g. PNA world)

– chiral nucleotides preferred: structurally more stable

• Source of chirality:– Polarized light, electroweak interaction

– auto-catalytic (enzymatic) reactions during polymerization

chirality as a consequence of life

5

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

(using HPLC)(using HPLC)

enantiomeric cross-inhibitionenantiomeric cross-inhibition

6

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 autocatalytic self-amplificationself-amplification

Frank (1953), Frank (1953), Goldanskii & Kuzmin Goldanskii & Kuzmin

(1989), …(1989), …

competition important competition important

Alkanol with 2% e.e.Alkanol with 2% e.e.treated withtreated with

carboxylaldehydecarboxylaldehyde

Kondepudi et al. (1990)Kondepudi et al. (1990)

Soai et al. (1995)Soai et al. (1995)

7

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

Can the right model be found by trial/error?Can the right model be found by trial/error?

)1(

)1(

LRkLdt

dL

LRkRdt

dR

)1(

)1(

LRkdt

dL

LRkdt

dR

LLRkLdt

dL

RLRkRdt

dR

)1(

)1(

2

2

)1(

)1(

2

2

LRkLdt

dL

LRkRdt

dR

non-autocatalyticnon-autocatalytic linearly autocatalyticlinearly autocatalytic

nonlinearlynonlinearlyautocatalyticautocatalytic nonlin+autocat.nonlin+autocat.

with backreactionwith backreaction

)1(

)1(

RkLdt

dL

LkRdt

dR

Frank (1953)Frank (1953)

8

Polymerization model of SandarsPolymerization model of Sandars

]][[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

Orig. Life Evol. Biosph. (Dec 2003)Orig. Life Evol. Biosph. (Dec 2003)

9

Combined equations: traveling waveCombined equations: traveling wave

N

nnSL

nnSn

LLkQLdt

d

LLLkLdt

d

111

11

][][2][

][][][2][

Loss term for each constituentLoss term for each constituent

const][1

N

nnLn

(if Q(if QLL=0)=0)

10

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

StabilityStability

11

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

12

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))

fidelityfidelity

13

Birfurcation properties Birfurcation properties

exponential growthexponential growth growth rate growth rate

Degree ofDegree ofhomochiralityhomochirality LR

LR

EE

EE

te

Red line: source Q from fragmented polymers (“waste”)Red line: source Q from fragmented polymers (“waste”)

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Reduced equationsReduced equations

Quantitatively close to full modelQuantitatively close to full model

ryrydt

dy

rxrxdt

dx

22

22

~/

~/

yxr

yxr

~ 222

Initial bias Initial bias

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ConclusionsConclusions

• Polymerization model:– Based on measurable processes– Predicts wavelike chromatograms (HPLC)

• Reduction to accurate simplified model– Homochirality in space (earth, interstellar, etc)