Homochirality through enantiomeric cross-inhibition Axel Brandenburg, Anja Andersen, Susanne...
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Transcript of Homochirality through enantiomeric cross-inhibition Axel Brandenburg, Anja Andersen, Susanne...
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”)
14
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
15
ConclusionsConclusions
• Polymerization model:– Based on measurable processes– Predicts wavelike chromatograms (HPLC)
• Reduction to accurate simplified model– Homochirality in space (earth, interstellar, etc)