Homochirality: models and results

1
Homochiralitymodels and results

• Axel Brandenburg, Anja Andersen, Susanne Höfner,
  Martin Nilsson

To appear in Orig. Life Evol. Biosph.,
q-bio.BM/0401036
2
Photosynthesis
Requires chlorophyll as catalyst What about
chiralitry?
3
Aminoacids in protein left-handedSugars in DNA
and RNA right-handed
carboxyl group
animo group
Louis Pasteur (1822-1895)
4
Racemic mixture
(from lecture of Antoine Weiss)
Racemization ?dating method
5
Miller/Urey experiment
Wait 1 week
15 organic compounds 2 amino acids (11 different
ones) racemic mixture
6
Chirality 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

7
Relevant experiments nucleotides
? Mononucleotides with wrong Chirality terminate
chain growth
ok
poisoned
template-directed oligomerization poly (CD) ?
oligo (GD)
(using HPLC)
guanine
cytosine
Joyce, et al. (incl. Orgel) (1984)
8
Contergan was sold as racemic mixture
Cures morning sickness during pregnancy
causes misformations
(abundaned in December 1961)
9
Relevant experiments crystals
Crystal growth, many different nucleation sites
racemic mixture
Crystal growth with stirring primary nucleation
suppressed
Autocatalytic self-amplification? Frank (1953),
Goldanskii Kuzmin (1989),
10
Auto-catalytic effect in dead matter
Alkanol with 2 e.e. Treated with carboxylaldehyde
11
Model by Saito Hyuga (Jan 2004)
Bimodal behavior
12
Model by Sandars (Dec 2003, OLEB)
Reaction for left-handed monomers
Loss term for each constituent
13
Combined equations
Loss term for each constituent
14
Including enantiomeric cross-inhibition
Loss term for each constituent
Racemic solution 21-n
15
Coupling to substrate S
Source of L1 monomers QL
QL comes from substrate acts as a sink of S S
sustained by source Q
Catalytic properties of substrate (depending on
how much L and R one has) ? QL QR(Ln,Rn)
16
Self-catalytic effect
Form of QL QR(Ln,Rn)
Possible proposals for CL (similarly for CR)
17
Birfurcation properties
? Mononucleotides with wrong Chirality terminate
chain growth
18
Stability
Relative perturbation of racemic solution, 10-4
19
Conservation law
Dependence on fidelity
where
20
Differences 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

21
Reduced equations
Quantitatively close to full model
22
Initial bias
Effect in reality very weak
23
Spatially extended model
with Tuomas Multamäki
Reaction-diffusion equation
Proto type Fishers equation
Propagating front solutions
wave speed
24
1D model (reaction-diffusion equation)
Propagation into racemic environment
25
2D model (reaction-diffusion equation)
Short run
26
2D model (reaction-diffusion equation)
Time scale longer than for simple fronts
27
P polymerization olymerization in 1D
chain growth, Rn and Ln in different places
28
The RNA world
Walter Gilbert (1986)

• Central dogma of chemistry of life
• DNA ? RNA ? protein
• enzyme
• all enzymes are themselves proteins?

29
RNA itself as enzyme
30
pre-RNA worlds
Many problems stability of sugars
2-amino ethyl glycin (AEG)
31
pre-RNA worlds
better alternative Nelson, Levi, Miller (2000)
PE Nielsen (1993)