how long can left and right handed life forms coexist?

How long can left and right How long can left and right handed life forms coexist?handed life forms coexist?

Axel Brandenburg, Anja Andersen, Axel Brandenburg, Anja Andersen, Susanne HSusanne Höfneröfner, Martin Nilsson,, Martin Nilsson,

Tuomas MultamTuomas Multamäkiäki

((NorditaNordita))

Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008

2

Aminoacids in proteins: left-handedAminoacids in proteins: left-handedSugars in DNA and RNA: right-handedSugars in DNA and RNA: right-handed

Louis PasteurLouis Pasteur(1822-1895)(1822-1895)

animoanimogroupgroup

carboxylcarboxylgroupgroup

chlorophyllchlorophyll

Is chirality:Is chirality:(i) prerequisite(i) prerequisite

(ii) consequence(ii) consequenceof life?of life?

3

Contergan: was sold as racemic mixtureContergan: was sold as racemic mixture

causes misformationscauses misformations Cures morning sicknessCures morning sicknessduring pregnancyduring pregnancy

(abandoned in December 1961)(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 lifeHomochirality and origin of life

5

Time lineTime line104 yr 106 yr 108 yr 109 yr

planetesimalsplanetesimals

Sun ignitesSun ignitesAll gas goneAll gas gone

Remaining dust Remaining dust settlessettles

First lifeFirst life

6

Chirality selection during polymerizationChirality selection during polymerizationof the first replicating molecule?of the first replicating molecule?

RR

LL

Isotactic polymer (same chirality)

“waste” (enantiomericcross-inhibition)

dual worlddual worldRNA worldRNA worldPNA worldPNA worldlipid worldlipid world

RNARNADNADNARNARNA

proteinsproteins

Rasmussen et al (2003)Rasmussen et al (2003)

achiralachiral

chiralchiral

PolymerizationPolymerization

7

PNA world prior to RNA worldPNA world prior to RNA worldPE Nielsen (1993)PE Nielsen (1993)

CHCH22

NHNH22

C00HC00H

CHCH22C0C0 BaseBase

CHCH22

NHNH

CHCH22

NN

C0C0CHCH22

NHNH22

C0C0

CHCH22

NHNH

C00HC00H

glycineglycine dipeptidedipeptide

CHCH22

CHCH22

NHNH22

C00HC00Hcarboxylcarboxyl

groupgroup

aminoaminogroupgroup

CHCH

NHNH22

C00HC00H

CHCH33PeptidePeptidenucleotidenucleotide

alaninealanineachiralachiral chiralchiral

8

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

9

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)

now also: proline-catalyzed reaction (Blackmond 2004)now also: proline-catalyzed reaction (Blackmond 2004)

Simplistic models: trial and error?Simplistic models: trial and error?

)1(

)1(

LRkLdt

dL

LRkRdt

dR

)1(

)1(

RkLdt

dL

LkRdt

dR

LLRkLdt

dL

RLRkRdt

dR

)1(

)1(

2

2

Frank (1953)Frank (1953) unspecific quenchingunspecific quenching

Saito & Hyuga (2004)Saito & Hyuga (2004)

RLLRkLdt

dL

RLLRkRdt

dR

)1(

)1(

Specific antagonismSpecific antagonism

chemically unrealistic (Blackmond 2002)chemically unrealistic (Blackmond 2002)

catalystcatalyst anti-catalystanti-catalyst

LRLLR

L

dt

dL

RRLLR

R

dt

dR

)(

)(

22

2

22

2

our model (BAHN 2005)our model (BAHN 2005)

11

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)

N

nnSL

nnSn

LLkQLdt

d

LLLkLdt

d

111

11

][][2][

][][][2][

Combined equationsCombined equations

const][1

N

nnLn

(if Q(if QLL=0)=0)

Number of left-handedNumber of left-handedBuilding blocks constBuilding blocks const

12

Coupling to substrate Coupling to substrate SS

QQL L acts as a sink of substrate acts as a sink of substrate SS

)(][ RL QQQSdt

d

Auto-catalytic properties of polymersAuto-catalytic properties of polymers

N

nnSL LLkQL

dt

d

111 ][][2][

Source of LSource of L11 monomers monomers QQLL

]][[

]][[

NCR

NCL

RSkQ

LSkQ

(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 (or (or CCRR))

LRCR

RLCL

CfCfSkQ

CfCfSkQ

11][

11][

21

21

21

21

finite fidelity finite fidelity ff

RefinementsRefinements

13

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

14

Reduced equationsReduced equations

Quantitatively close to full modelQuantitatively close to full model

Initial bias Initial bias

BAHN (Orig. Life Evol. Biosph. 2005)BAHN (Orig. Life Evol. Biosph. 2005)

LRLLR

L

dt

dL

RRLLR

R

dt

dR

)(

)(

22

2

22

2

][][][2][ 1212 LLLkLdt

dS

][][][20 121 LLLkS Adiabatic eliminationAdiabatic eliminationof rapidly adjusting variablesof rapidly adjusting variables

2-mode reduction2-mode reduction

Spatially extended modelSpatially extended model

Propagating front solutionsPropagating front solutions

Reaction-diffusion equationReaction-diffusion equation

Proto type: Fisher’s equationProto type: Fisher’s equation

'')1( XXXX

)( ctxfX 2c

wave speedwave speed

wwith Tuomas Multamith Tuomas Multamääki, Int. J. Astrobio. 3, 209 (2004)ki, Int. J. Astrobio. 3, 209 (2004)

Spread of the black Spread of the black deathdeath

LLRLLR

L

dt

dL

RRRLLR

R

dt

dR

222

2

222

2

)(

)(

16

1D model (reaction-diffusion equation)1D model (reaction-diffusion equation)

Propagation into racemic environmentPropagation into racemic environment

17

Polymerization polymerization in 1DPolymerization polymerization in 1D

chain growth, Rn and Ln in different placeschain growth, Rn and Ln in different places

18


short runshort runRR LL

19


Time scale longer than for simple frontsTime scale longer than for simple fronts

SAA

A

t

Ad

1

1

d

d

2

2

20

Piecewise linear increasePiecewise linear increase

SAA

A

t

Ad

1

1

d

d

2

2

SSS 221

ASAAS

ASA 2

22

222

add/subtract:add/subtract:

LRLLR

L

dt

dL

RRLLR

R

dt

dR

)(

)(

22

2

22

2

Reduced equationsReduced equations

21

Effects of turbulenceEffects of turbulence

22

The Pencil CodeThe 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 applicationsRange 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 formulationPencil 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 headachesA 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 maintainedCVS 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 modulesSwitch 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-insPencil Code check-ins

29

(i) Higher order – less viscosity(i) Higher order – less viscosity

30

(ii) High-order temporal schemes(ii) High-order temporal schemes

),( 111 iiiii utFtww

Main advantage: low amplitude errors

iiii wuu 1

3)1()(

0 , uuuu nn

2/1 ,1 ,3/1

1 ,3/2 ,0

321

321

1 ,2/1

2/1 ,0

21

21

1

0

1

1

3rd order

2nd order

1st order

2N-RK3 scheme (Williamson 1980)

31

Bottleneck effect: Bottleneck effect: 1D vs 1D vs 3D3D spectra spectra

Compensated spectra

(1D vs 3D)

32

Relation to ‘laboratory’ 1D spectraRelation to ‘laboratory’ 1D spectra2222

3 )(4)( kuku kdkE kD yxkyxkE zzD d d ),,(2)(

2

1 u

kkkkkkkzk

z d )(4d ),(42

0

2

uu

kk

E

zk

D d 3

0zk

222zkkk

33

Hyperviscous, Smagorinsky, normalHyperviscous, Smagorinsky, normal

Inertial range unaffected by artificial diffusionHau

gen

& B

rand

enbu

rg (

PR

E, a

stro

-ph/

0402

301)

height of bottleneck increased

onset of bottleneck at same position

34

256 processor run at 1024256 processor run at 102433

35

Structure function exponentsStructure function exponents

agrees with She-Leveque third moment

36

Wallclock time versus processor #

nearly linearScaling

100 Mb/s showslimitations

1 - 10 Gb/sno limitation

37

Sensitivity to layout onSensitivity to layout onLinux clustersLinux clusters

yprox x zproc

4 x 32 1 (speed)

8 x 16 3 times slower

16 x 8 17 times slower

Gigabituplink 100 Mbit

link only

24 procsper hub

38

Why this sensitivity to layout?

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5

6 7 8 9 0 1 2 3 4

All processors need to communicatewith processors outside to group of 24

39

Use exactly 4 columns

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

16 17 18 19

20 21 22 23

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

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 animationsPre-processed data for animations

41

Ma=3 supersonic turbulenceMa=3 supersonic turbulence

42

Animation of B vectorsAnimation of B vectors

43

Animation of energy spectraAnimation of energy spectra

Very long run at 5123 resolution

44

MRI turbulenceMRI turbulenceMRI = magnetorotational instabilityMRI = magnetorotational instability

2563

w/o hypervisc.t = 600 = 20 orbits

5123

w/o hypervisc.t = 60 = 2 orbits

45

Spherical/cylindrical geometriesSpherical/cylindrical geometries

46

ConclusionsConclusions• 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, …

how long can left and right handed life forms coexist?

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