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How long can left and right handed life forms coexist?. Axel Brandenburg, Anja Andersen, Susanne H öfner , Martin Nilsson, Tuomas Multam äki ( Nordita ). Orig. Life Evol. Biosph. (in press), q-bio.BM/0401036 Int. J. Astrobio. 3, 209 (2004), also q-bio.BM/0407008. - PowerPoint PPT Presentation
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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
2D model (reaction-diffusion equation)2D model (reaction-diffusion equation)
short runshort runRR LL
19
2D model (reaction-diffusion equation)2D model (reaction-diffusion equation)
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, …