Homochirality in spatially extended systems

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Homochirality in spatially extended systems
Domain walls Front propagation Time scales Large
scale motions
Int. J. Astrobio. 3, 209 (2004), 4, 75
(2005), Orig. Life Evol. Biosph. 35, 225 (2005),
35, 507 (2005) Astrobiology 7, 725 (2007)
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Spatial extended systems
Concentrations vary spatially
Define e.e. as spatial average
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Shibata et al.
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Hochberg Zorzano
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Racemization by noise
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Front propagation
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(i) Polymerization model of Sandars
Orig. Life Evol. Biosph. 33, 575-587 (2003)
Reaction for left-handed monomers
Loss term for each constituent
Number of left-handed Building blocks const
(if QL0)
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Chain growth in the Sandars model
Orig. Life Evol. Biosph. 33, 575-587 (2003)
Reaction for left-handed monomers
Combined equations
Loss term for each constituent
Number of left-handed Building blocks const
(if QL0)
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Including enantiomeric cross-inhibition
Loss term for each constituent
Racemic solution 21-n
Stability
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Polymerization polymerization in 1D
chain growth, Rn and Ln in different places
Int. J. Astrobio. 3, 209 (2004)
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(iii) Spatially extended model
with Tuomas Multamäki, Int. J. Astrobio. 3, 209
(2004)
Reaction-diffusion equation
1350
1349
Proto type Fishers equation
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Propagating front solutions
1347
wave speed
Spread of the black death
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1D reduced model (reaction-diffusion equation)
Propagation into racemic environment
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2D model (reaction-diffusion equation)
Short run
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2D model (reaction-diffusion equation)
Time scale longer than for simple fronts
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Piecewise linear increase
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Piecewise linear increase
Reduced equations
add/subtract
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(ii) RNA versus peptide worlds
peptide world
RNA world

• Activation D ? D, L ? L
• Polymerization DD? DD, LL ? LL
• Epimerization DL ? LL, LD ? DD
• Depolymerization DD ? DD, LL ? LL

• Template-directed (PCR-like)
• Enantiomeric cross-inhibition
• Autocatalytic production of new mono-nucleotides
  (? but uncertain)
• RNA stability

APED model (Plasson et al.)
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APED model (Plasson et al. 2004)
a activation p polymer. a inhibition h
depolym.
e epimerization on N-terminal DL?LL not DL? DD
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Net reactions
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APED model equations
Consider limit of large h and e
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APED model equations
limit of large h and e
corresponding reaction
? D catalyzes conversion of both D and L into D
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Reduced APED model
a one way round-about
For nearly racemic state
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Exponential evolution
106 molecules
1012 molecules
For nearly racemic state
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Initial e.e. not related to final e.e.
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Where could this work?
a) hydrothermal vents
Braun Libchaber (2003)
b) Deep biosphere
ideas about first Protocells
Michael J. Russell (2006, Am. Sci. 94, 32-39)
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Effects of turbulence
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Pencil Code

• Started in Sept. 2001 with Wolfgang Dobler
• High order (6th order in space, 3rd order in
  time)
• Cache memory efficient
• MPI, can run PacxMPI (across countries!)
• Maintained/developed by 20 people (CVS!)
• Automatic validation (over night or any time)
• Max resolution so far 10243 , 256 procs

• Isotropic turbulence
• MHD, passive scl, CR
• Stratified layers
• Convection, radiation
• Shearing box
• MRI, dust, interstellar
• Sphere embedded in box
• Fully convective stars
• geodynamo
• Other applications
• Homochirality
• Spherical coordinates

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Conclusions

• Domain walls
• ee (final) different
• To be checked in experiments
• With flows shorter mixing times