How long can left and right handed life forms coexist?

1. How long can left and right handed life forms coexist? Axel Brandenburg, Anja Andersen, Susanne Höfner, Martin Nilsson, Tuomas Multamäki (Nordita) Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036 Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008

2. Aminoacids in proteins: left-handedSugars in DNA and RNA: right-handed Is chirality: (i) prerequisite (ii) consequence of life? carboxyl group Louis Pasteur (1822-1895) animo group chlorophyll

3. Contergan: was sold as racemic mixture Cures morning sickness during pregnancy causes misformations (abandoned in December 1961)

4. Homochirality and origin of life • If prerequisite for life: • Due to polarized light, electroweak force, magnetic fields, … • If consequence of life: • Must have emerged during polymerization of first replicating molecules • Difference at different places on Earth?? • Reaction-diffusion-advection equation

5. Time line First life planetesimals Sun ignites All gas gone Remaining dust settles 104 yr 106 yr 108 yr 109 yr

6. Chirality selection during polymerizationof the first replicating molecule? lipid world PNA world dual world RNA world achiral DNA RNA proteins RNA chiral Rasmussen et al (2003) Isotactic polymer (same chirality) R Polymerization “waste” (enantiomeric cross-inhibition) L

7. PNA world prior to RNA world PE Nielsen (1993) NH NH2 NH2 CH2 CH2 CH2 CH2 carboxyl group C00H C0 Base N C0 CH2 NH2 NH NH2 amino group CH2 CH3 CH CH2 CH2 Peptide nucleotide C0 C00H C00H alanine C00H achiral chiral glycine dipeptide

8. Relevant experiments: nucleotides  Mononucleotides with wrong chirality terminate chain growth ok poisoned template-directed oligomerization poly (CD)  oligo (GD) (using HPLC)  enantiomeric cross-inhibition guanine cytosine Joyce et al. (1984)

9. Relevant experiments: crystals Crystal growth, many different nucleation sites: racemic mixture Crystal growth with stirring: primary nucleation suppressed Kondepudi et al. (1990)  competition important Alkanol with 2% e.e. treated with carboxylaldehyde  autocatalytic self-amplification Frank (1953), Goldanskii & Kuzmin (1989), … Soai et al. (1995) now also: proline-catalyzed reaction (Blackmond 2004)

10. Simplistic models: trial and error? Frank (1953) unspecific quenching Specific antagonism catalyst anti-catalyst chemically unrealistic (Blackmond 2002) our model (BAHN 2005) Saito & Hyuga (2004)

11. Polymerization model of Sandars Orig. Life Evol. Biosph. (Dec 2003) Reaction for left-handed monomers Combined equations Loss term for each constituent Number of left-handed Building blocks const (if QL=0)

12. Coupling to substrate S Source of L1 monomers QL Refinements finite fidelity f QL acts as a sink of substrate S Possible proposals for CL(or CR) Auto-catalytic properties of polymers

13. Including enantiomeric cross-inhibition Loss term for each constituent Racemic solution ~21-n Stability

14. Reduced equations 2-mode reduction Adiabatic elimination of rapidly adjusting variables Quantitatively close to full model BAHN (Orig. Life Evol. Biosph. 2005) Initial bias 

15. Spatially extended model with Tuomas Multamäki, Int. J. Astrobio. 3, 209 (2004) Reaction-diffusion equation Proto type: Fisher’s equation Propagating front solutions wave speed Spread of the black death

16. 1D model (reaction-diffusion equation) Propagation into racemic environment

17. Polymerization polymerization in 1D chain growth, Rn and Ln in different places

18. 2D model (reaction-diffusion equation) R L short run

19. 2D model (reaction-diffusion equation) Time scale longer than for simple fronts

20. Piecewise linear increase Reduced equations add/subtract:

21. Effects of turbulence

22. The Pencil Code • History: as many versions as there are people?? • CVS maintained, 20+ people actively contributing • High order (6th order in space, 3rd order in time) • Cache & memory efficient • MPI, can also run PacxMPI (across countries!) • Online data processing/visualization • Ideal for linux clusters • Pencil formulation (advantages, avoiding headaches) • Automatic validation (over night or any time) • Max resolution so far 10243 , 256 procs

23. Range of applications • Isotropic turbulence • MHD (Haugen), passive scalar (Käpylä), cosmic rays (Snod, Mee) • Stratified layers • Convection, radiative transport (T. Heinemann) • Shearing box • MRI (Haugen), planetesimals, dust (A. Johansen), interstellar (A. Mee) • Sphere embedded in box • Fully convective stars (W. Dobler), geodynamo (D. McMillan) • Other applications and future plans • Homochirality (models of origins of life, with T. Multamäki) • Spherical coordinates

24. Pencil formulation • In CRAY days: worked with full chunks f(nx,ny,nz,nvar) • Now, on SGI, nearly 100% cache misses • Instead work with f(nx,nvar), i.e. one nx-pencil • No cache misses, negligible work space, just 2N • Can keep all components of derivative tensors • Communication before sub-timestep • Then evaluate all derivatives, e.g. call curl(f,iA,B) • Vector potential A=f(:,:,:,iAx:iAz), B=B(nx,3)

25. A few headaches • All operations must be combined • Curl(curl), max5(smooth(divu)) must be in one go • out-of-pencil exceptions possible • rms and max values for monitoring • call max_name(b2,i_bmax,lsqrt=.true.) • call sum_name(b2,i_brms,lsqrt=.true.) • Similar routines for toroidal average, etc • Online analysis (spectra, slices, vectors)

26. CVS maintained • pserver (password protected, port 2301) • non-public (ci/co, 21 people) • public (check-out only, 127 registered users) • Set of 15 test problems in the auto-test • Nightly auto-test (different machines, web) • Before check-in: run auto-test yourself • Mpi and nompi dummy module for single processor machine (or use lammpi on laptops)

27. Switch modules • magnetic or nomagnetic (e.g. just hydro) • hydro or nohydro (e.g. kinematic dynamo) • density or nodensity (burgulence) • entropy or noentropy (e.g. isothermal) • radiation or noradiation (solar convection, discs) • dustvelocity or nodustvelocity (planetesimals) • Coagulation, reaction equations • Homochirality (reaction-diffusion-advection equations)

28. Pencil Code check-ins

29. (i) Higher order – less viscosity

30. (ii) High-order temporal schemes Main advantage: low amplitude errors 2N-RK3 scheme (Williamson 1980) 2nd order 3rd order 1st order

31. Bottleneck effect: 1D vs 3D spectra Compensated spectra (1D vs 3D)

32. Relation to ‘laboratory’ 1D spectra

33. Hyperviscous, Smagorinsky, normal height of bottleneck increased Haugen & Brandenburg (PRE, astro-ph/0402301) onset of bottleneck at same position Inertial range unaffected by artificial diffusion

34. 256 processor run at 10243

35. Structure function exponents agrees with She-Leveque third moment

36. Wallclock time versus processor # nearly linear Scaling 100 Mb/s shows limitations 1 - 10 Gb/s no limitation

37. Sensitivity to layout onLinux clusters yprox x zproc 4 x 32  1 (speed) 8 x 16  3 times slower 16 x 8  17 times slower Gigabit uplink 100 Mbit link only 24 procs per hub

38. Why this sensitivity to layout? All processors need to communicate with processors outside to group of 24

39. Use exactly 4 columns Only 2 x 4 = 8 processors need to communicate outside the group of 24  optimal use of speed ratio between 100 Mb ethernet switch and 1 Gb uplink

40. Pre-processed data for animations

41. Ma=3 supersonic turbulence

42. Animation of B vectors

43. Animation of energy spectra Very long run at 5123 resolution

44. MRI turbulenceMRI = magnetorotational instability 2563 w/o hypervisc. t = 600 = 20 orbits 5123 w/o hypervisc. Dt = 60 = 2 orbits

45. Spherical/cylindrical geometries

46. Conclusions • Polymerization model: • Based on measurable processes • Predicts wavelike chromatograms (HPLC) • Reduction to accurate simplified model • Homochirality in space (earth, interstellar, etc) • Timescales 500 Myr; fossil evidence of spatially fragmented homochirality? • Pencil Code: just google for it • Detailed manual, …