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/ Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/

2 Aminoacids in proteins: left-handed Sugars in DNA and RNA: right-handed Louis Pasteur ( ) animogroup carboxylgroup chlorophyll Is chirality: (i) prerequisite (ii) consequence of life?

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

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 Homochirality and origin of life

5 Time line 10 4 yr 10 6 yr 10 8 yr 10 9 yr planetesimals Sun ignites All gas gone Remaining dust settles First life

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

7 PNA world prior to RNA world PE Nielsen (1993) CH 2 NH 2 C00H CH 2 C0 Base NH N C0 NH 2 C0 CH 2 NH C00H glycinedipeptide NH 2 C00H carboxylgroup aminogroup CH C00H CH 3 Peptidenucleotide alanine achiral chiral

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

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

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

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

12 Coupling to substrate S Q L acts as a sink of substrate S Auto-catalytic properties of polymers Source of L 1 monomers Q L Possible proposals for C L (or C R ) finite fidelity f Refinements

13 Including enantiomeric cross-inhibition Loss term for each constituent Racemic solution ~2 1-n Stability

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

Spatially extended model Propagating front solutions Reaction-diffusion equation Proto type: Fisher’s equation wave speed with Tuomas Multamäki, Int. J. Astrobio. 3, 209 (2004) 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) short run RL

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

20 Piecewise linear increase add/subtract: Reduced equations

21 Effects of turbulence

22 The Pencil Code History: as many versions as there are people?? –CVS maintained, 20+ people actively contributing High order (6 th order in space, 3 rd 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 , 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 3 rd order 2 nd order 1 st order 2N-RK3 scheme (Williamson 1980)

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

32 Relation to ‘laboratory’ 1D spectra

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

processor run at

35 Structure function exponents agrees with She-Leveque third moment

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

37 Sensitivity to layout on Linux 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 resolution

44 MRI turbulence MRI = magnetorotational instability w/o hypervisc. t = 600 = 20 orbits w/o hypervisc.  t = 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, …