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Munich, 19.11.18 Replication in a thermal trap Jongseo Kim, Simon Langnickel

Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

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Page 1: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

Munich, 19.11.18

Replication in a thermal trapJongseo Kim, Simon Langnickel

Page 2: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�2Jongseo Kim, Simon Langnickel

Introduction

• Primordial soup hypothesis• Panspermia – microscopic life came to earth by asteroids• RNA world• Clay hypothesis

There are still a lot of hypothesis!

image: https://www.youtube.com/watch?v=PjnWOBext-E image: archaeologynewsnetwork.blogspot.com/2013/04/power-behind-primordial-soup-discovered.html#v0IZILgYd7KYhDv0.97

Page 3: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�3Jongseo Kim, Simon Langnickel

Introduction

Deep sea vent hypothesis:

Did we come from porous rock of hydrothermal vents?

image: www.marum.de/en/Discover/Hydrothermal-Vents.html

Page 4: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�4Jongseo Kim, Simon Langnickel

Content

Thermal trap modelling: 1. Convection driven PCR2. Convection in a closed pore3. Convection in an open pore

Page 5: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�5Jongseo Kim, Simon Langnickel

Convection driven PCR

Convection driven PCR

Page 6: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�6Jongseo Kim, Simon Langnickel

Convection driven PCR

Polymerase chain reaction (PCR):

image: www.abmgood.com/marketing/knowledge_base/polymerase_chain_reaction_introduction.php

c(t) = c0 · 2t/⌧<latexit sha1_base64="MiuLx3gCxI31ig7MnwG+uOV0cJI=">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</latexit><latexit sha1_base64="MiuLx3gCxI31ig7MnwG+uOV0cJI=">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</latexit><latexit sha1_base64="MiuLx3gCxI31ig7MnwG+uOV0cJI=">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</latexit><latexit sha1_base64="MiuLx3gCxI31ig7MnwG+uOV0cJI=">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</latexit>

Page 7: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�7Jongseo Kim, Simon Langnickel

Convection driven PCR

Convection driven PCR

• We do not have to heat up and cool down the whole sample

➡ 4 times faster than a standard PCR thermocycler• Exponentially increase the amount of DNA

Similar reactions could occur in natural environment!

cPCR

standard PCR

Page 8: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�8Jongseo Kim, Simon Langnickel

Convection in a closed pore

gravity

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

Convection in a closed pore

Page 9: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�9Jongseo Kim, Simon Langnickel

Convection in an open pore

selection pressure for longer strands

BIOCHEMISTRY: MILLS ET AL.

0o II 10 so0 9~ V

1~~~~~~~~~~~~~I10X 1° 0CL[

on10.~~~ ~ ~ ~ ~ ~ ~ ~~RATO

I*10Ed

I 6~~~~,10 20

FRACTION

(Above) FIG. 2.-Sedimentation analysis of 0.15th TRANfER P0PRUCT1st transfer reaction. As described in Methods, 20 B I6S / 200.02 ml of the 0 reaction was used to initiate a 23s I I s4reaction for a 1st transfer reaction product. ;After completion, this reaction was adjusted 0 I t Ito 0.2% SDS, an aliquot was withdrawn, o l odiluted to 0.2 ml in TE buffer (0.01 M Tris K l lpH 7.4, 0.003 M EDTA), and then layered E l l |onto a 5-ml linear sucrose (2-20% in 0.1 M 10 I I3 l0ETris, pH 7.4, and 0.003 M EDTA) and run as , Iidescribed in Methods (section b). H3-labeled 0 . Clbulk RNA of E. coli was included as internal - \bsize markers. I

(Right) FIG. 3.-Sedimentation analysis of9th transfer (A) and 15th transfer (B) reac- 10 20tion products. Details are as in Fig. 2. FRACTION

shows (Fig. 2) the 28S peak characteristic of Qf3-RNA as well as the peaks cor-responding to the usual complexes observed during the in vitro synthesis.12 Com-parison with subsequent transfers reveals, however, dramatic changes in the natureof the replicating entity. Thus, by the ninth transfer (Fig. 3A) there is no materialsynthesized corresponding to the original 28S viral RNA. In its place we see amajor component at about 20S and a minor one at about 15S. This pattern is es-sentially maintained through the 15th transfer (Fig. 3B).By the 30th transfer (Fig. 4A) the major component has decreased to 15S and

the minor one to about 14S. The product of the 38th transfer shows variant RNAwhich no longer splits into two peaks, a feature retained through subsequent trans-fers. It will be noted (Fig. 5A and B), however, that the single peak moves moreslowly so that by the 74th transfer it is at about 12S.

(b) Gel electrophoresis of variant RNA: At this point it was decided to ex-amine the nature of the variant in greater detail. Transfer 75 was expanded withreplicase to a total of 120 ,ug of RNA and subjected to analysis by polyacrylamidegel electrophoresis (Fig. 6). Clearly, the apparently homogeneous peak of Figure5B is composed of at least two distinct RNA species. As may be seen from Figure6, the major component is sensitive to ribonuclease whereas the minor one is resis-tant. It would appear that the faster component is the single-stranded variantand that the slower minor peak contains a mixture of the Hofschneider'3 and Frank-

220 PROC. N. A. S.

BIOCHEMISTRY: MILLS ET AL.

20 30th TRANSFER 10 54 th TRANSFER

A P32FPRODUCT 20AI30

201 20

2330 ?6S 4s P32 PRODUCT30

o'\i~~~~~~~ ~~ _0 I~~~~~~ ~~~~Yl~4s

E 0 i\E 100

n~~~~~~§ Il K al IW

FIG. 4. i a s o

0 20

relative~ ~ ~ ~~~~lIlcrpoeimoilt (RM Cslnaleae nesl otem leu

10 20~~~~~~~~~02FRACTION~ ~ ~ ~ ~ ~ FRCTO

303wthTRANSFERP32nPRODUCT 20 3075Cth TRANSFER 40

Be23v B23isPa PRODUCTindcaehatearanRAasa olcuarwegh oaou 16s 41 s

I; ~ ~ 10 / *1* go~~ ~ ~ ~ ~~~~, Ito II0~~~~~~o

trphreis In thi recin l orrbncetietihsh swr aeewihpa h -psto Mtos seto I. Th RN prdc of tis reatio

10

was~~puife tiebge lcrpoeihdlyd,an anlzd0sdscie

15- -10O 0 tO 1 20 C

FRACTION FRACTION

FIG. 4.-Sedimentation analysis of the 30th FIG. 5.-Sedimentation analysis of the 54thtransfer (A) and the 38th transfer (B) reaction transfer (A) and the 75th transfer (B) reactionproducts. Details are as in Fig. 2. products. Details are as in Fig. 2.

linU structures observed first in vivo and seen in in vitro synthesis ofQav-RNA withpurified replicase.n2, 15

(c) Molecular weight of variant JRNA: We have previously shown10 that therelative electrophoretic mobility (REM) is linearly related inversely to the molecu-lar weight of single-stranded RNA. Consequently, to determine the molecularweight, the single-stranded variant RNA was subjected to gel electrophoresis withseven internal marker RNA's of known size. The results are shown in Figure 7 andindicate that the variant RNA has a molecular weight of about 1.7 X 1O5 daltons.

(d) Base composition of variant RNA: To determine its base composition,a standard reaction mixture was initiated with the variant isolated by gel elec-trophoresis. In this reaction, all four ribonucleotide triphosphates were labeledwith P32 at the a-position (Methods, section f). The RNA product of this reactionwas purified twice by gel electrophoresis, hydrolyzed, and analyzed as describedin Methods (section f). Comparison with the base composition of the originalQ13-RNA (Table 1) indicates that there has been a considerable (5 mole %) increasein the G content in the variant RNA. On the other hand, A and C have decreasedby 2.4 mole per cent, the uridine content remaining constant.

VOL. 58, 1967 221

Spiegelmann, 1967

Page 10: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�10Jongseo Kim, Simon Langnickel

Convection in an open pore

Closed Pore Open Pore

gravity

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

Page 11: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�11Jongseo Kim, Simon Langnickel

Convection in an open pore

Differential survival of replicating strands. Combining all of theabove, we show how the joint thermally induced trapping andreplication enables this arrangement to overcome Spiegelman’sevolutionary dilemma of the degeneration of strand length andtherefore loss of genomic information11. We followed thecomposition of a heterogeneous DNA population that replicatescontinuously inside the open pore. A 2.5 mm short capillary wasseeded with a population of unlabelled template DNA strandswith identical primer binding sites and a binary lengthdistribution of 36 bp and 75 bp at a concentration of 1 nM each.

A temperature gradient from 61 °C to 94 °C was applied to a con-tinuous upwards flux of template-free PCR buffer that containednucleotides, polymerase and 7 nM fluorescently labelled primersand was run through the system at a speed of 6 µm s−1. Over thecourse of the experiment (seven hours), the trapping volume wasexchanged approximately 150 times with the template-free feeding

buffer. Aliquots that contained the product of the continuouslyrunning reaction were taken from the outflow and analysed usinggel electrophoresis. As the primers carried the labels, only replicatedDNA strands were detected (Fig. 4c).

We observed that only the long strands were able to replicate suf-ficiently to withstand the diluting flow through the pore. This deter-mined the increase of the relative concentration of the long, viablestrands with respect to the total amount of DNA (Fig. 4d, yellow).The twofold shorter strands became diluted and then extinct.

This competitive replication and selection of two genetic poly-mers in favour of larger molecular lengths can be understoodeasily with a simple model. The determinants of the growth kineticsdci /dt = (repi − dili)ci for either the short or the long speciesi = {S, L} are given by the replication rates repi and the dilutionrates dili. Expressing the relative concentration of the longstrands yields cL /(cS + cL) = (1 + Ae−Δkt)−1. A = c0S /c

0L is the initial

d

DNA strand length (bp)

Trap

ped

DN

A fr

actio

n

0.0

0.2

0.4

0.6

0.8

1.0

100 120 14040 60 80

98.587654.53.5

vs (μm s–1)

vs (μm s–1)3.5 4.5 5 6 7 7 8 8.5 9

In Outflowc

60

40

20

100

200

b

Out

Trapped

Concentrationprofile

+Inflow

+convection

Flow profile

Transport(flow × concentration)

pp

Gra

vity

Outflow

Inflow

60

40

20

100

200

vs = 6 µm s–1

a

Trapped

Col

d

Col

d

War

m

War

m

Figure 3 | Heat-driven filter selecting for strand length. a, A steady upwards feeding flow is triggered by opening the asymmetrically heated pore. A ladderof dsDNA (20–200 bp, 20 bp steps) was injected into the trap. Subsequent flushing of the capillary with pure buffer at a single velocity (vs = 6 µm s–1)revealed the filter’s thresholding characteristics—lengths ≤80 bp flow through the pore whereas longer strands are trapped. b, An asymmetric flow pattern isgenerated by the superposition of the upwards flow and the convection. Thermophoresis pushes the long strands into the downwards flow and traps them.Short strands are subjected to the overall upwards flow and leave the pore. The trapping is a function of the feeding flow speed. c, The velocity of theexternal flow vs tunes the fractionation of nucleic acids. As in the experiment before, a DNA ladder was initially introduced at a low flow velocity, which wasthen sequentially increased. The released DNA was measured using gel electrophoresis. d, The fraction of trapped DNA obtained from the electrophoresisgel constitutes a selection landscape of this thermal habitat in favour of long oligonucleotides. The velocity-dependent trapped fraction is described by a fluiddynamics model (see Methods). Error bars reflect the signal-to-noise ratio of the gel images (see Supplementary Fig. 11 for details).

NATURE CHEMISTRY DOI: 10.1038/NCHEM.2155 ARTICLES

NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry 3

Differential survival of replicating strands. Combining all of theabove, we show how the joint thermally induced trapping andreplication enables this arrangement to overcome Spiegelman’sevolutionary dilemma of the degeneration of strand length andtherefore loss of genomic information11. We followed thecomposition of a heterogeneous DNA population that replicatescontinuously inside the open pore. A 2.5 mm short capillary wasseeded with a population of unlabelled template DNA strandswith identical primer binding sites and a binary lengthdistribution of 36 bp and 75 bp at a concentration of 1 nM each.

A temperature gradient from 61 °C to 94 °C was applied to a con-tinuous upwards flux of template-free PCR buffer that containednucleotides, polymerase and 7 nM fluorescently labelled primersand was run through the system at a speed of 6 µm s−1. Over thecourse of the experiment (seven hours), the trapping volume wasexchanged approximately 150 times with the template-free feeding

buffer. Aliquots that contained the product of the continuouslyrunning reaction were taken from the outflow and analysed usinggel electrophoresis. As the primers carried the labels, only replicatedDNA strands were detected (Fig. 4c).

We observed that only the long strands were able to replicate suf-ficiently to withstand the diluting flow through the pore. This deter-mined the increase of the relative concentration of the long, viablestrands with respect to the total amount of DNA (Fig. 4d, yellow).The twofold shorter strands became diluted and then extinct.

This competitive replication and selection of two genetic poly-mers in favour of larger molecular lengths can be understoodeasily with a simple model. The determinants of the growth kineticsdci /dt = (repi − dili)ci for either the short or the long speciesi = {S, L} are given by the replication rates repi and the dilutionrates dili. Expressing the relative concentration of the longstrands yields cL /(cS + cL) = (1 + Ae−Δkt)−1. A = c0S /c

0L is the initial

d

DNA strand length (bp)

Trap

ped

DN

A fr

actio

n

0.0

0.2

0.4

0.6

0.8

1.0

100 120 14040 60 80

98.587654.53.5

vs (μm s–1)

vs (μm s–1)3.5 4.5 5 6 7 7 8 8.5 9

In Outflowc

60

40

20

100

200

b

Out

Trapped

Concentrationprofile

+Inflow

+convection

Flow profile

Transport(flow × concentration)

pp

Gra

vity

Outflow

Inflow

60

40

20

100

200

vs = 6 µm s–1

a

Trapped

Col

d

Col

d

War

m

War

m

Figure 3 | Heat-driven filter selecting for strand length. a, A steady upwards feeding flow is triggered by opening the asymmetrically heated pore. A ladderof dsDNA (20–200 bp, 20 bp steps) was injected into the trap. Subsequent flushing of the capillary with pure buffer at a single velocity (vs = 6 µm s–1)revealed the filter’s thresholding characteristics—lengths ≤80 bp flow through the pore whereas longer strands are trapped. b, An asymmetric flow pattern isgenerated by the superposition of the upwards flow and the convection. Thermophoresis pushes the long strands into the downwards flow and traps them.Short strands are subjected to the overall upwards flow and leave the pore. The trapping is a function of the feeding flow speed. c, The velocity of theexternal flow vs tunes the fractionation of nucleic acids. As in the experiment before, a DNA ladder was initially introduced at a low flow velocity, which wasthen sequentially increased. The released DNA was measured using gel electrophoresis. d, The fraction of trapped DNA obtained from the electrophoresisgel constitutes a selection landscape of this thermal habitat in favour of long oligonucleotides. The velocity-dependent trapped fraction is described by a fluiddynamics model (see Methods). Error bars reflect the signal-to-noise ratio of the gel images (see Supplementary Fig. 11 for details).

NATURE CHEMISTRY DOI: 10.1038/NCHEM.2155 ARTICLES

NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry 3

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

Differential survival of replicating strands. Combining all of theabove, we show how the joint thermally induced trapping andreplication enables this arrangement to overcome Spiegelman’sevolutionary dilemma of the degeneration of strand length andtherefore loss of genomic information11. We followed thecomposition of a heterogeneous DNA population that replicatescontinuously inside the open pore. A 2.5 mm short capillary wasseeded with a population of unlabelled template DNA strandswith identical primer binding sites and a binary lengthdistribution of 36 bp and 75 bp at a concentration of 1 nM each.

A temperature gradient from 61 °C to 94 °C was applied to a con-tinuous upwards flux of template-free PCR buffer that containednucleotides, polymerase and 7 nM fluorescently labelled primersand was run through the system at a speed of 6 µm s−1. Over thecourse of the experiment (seven hours), the trapping volume wasexchanged approximately 150 times with the template-free feeding

buffer. Aliquots that contained the product of the continuouslyrunning reaction were taken from the outflow and analysed usinggel electrophoresis. As the primers carried the labels, only replicatedDNA strands were detected (Fig. 4c).

We observed that only the long strands were able to replicate suf-ficiently to withstand the diluting flow through the pore. This deter-mined the increase of the relative concentration of the long, viablestrands with respect to the total amount of DNA (Fig. 4d, yellow).The twofold shorter strands became diluted and then extinct.

This competitive replication and selection of two genetic poly-mers in favour of larger molecular lengths can be understoodeasily with a simple model. The determinants of the growth kineticsdci /dt = (repi − dili)ci for either the short or the long speciesi = {S, L} are given by the replication rates repi and the dilutionrates dili. Expressing the relative concentration of the longstrands yields cL /(cS + cL) = (1 + Ae−Δkt)−1. A = c0S /c

0L is the initial

d

DNA strand length (bp)

Trap

ped

DN

A fr

actio

n

0.0

0.2

0.4

0.6

0.8

1.0

100 120 14040 60 80

98.587654.53.5

vs (μm s–1)

vs (μm s–1)3.5 4.5 5 6 7 7 8 8.5 9

In Outflowc

60

40

20

100

200

b

Out

Trapped

Concentrationprofile

+Inflow

+convection

Flow profile

Transport(flow × concentration)

pp

Gra

vity

Outflow

Inflow

60

40

20

100

200

vs = 6 µm s–1

a

Trapped

Col

d

Col

d

War

m

War

m

Figure 3 | Heat-driven filter selecting for strand length. a, A steady upwards feeding flow is triggered by opening the asymmetrically heated pore. A ladderof dsDNA (20–200 bp, 20 bp steps) was injected into the trap. Subsequent flushing of the capillary with pure buffer at a single velocity (vs = 6 µm s–1)revealed the filter’s thresholding characteristics—lengths ≤80 bp flow through the pore whereas longer strands are trapped. b, An asymmetric flow pattern isgenerated by the superposition of the upwards flow and the convection. Thermophoresis pushes the long strands into the downwards flow and traps them.Short strands are subjected to the overall upwards flow and leave the pore. The trapping is a function of the feeding flow speed. c, The velocity of theexternal flow vs tunes the fractionation of nucleic acids. As in the experiment before, a DNA ladder was initially introduced at a low flow velocity, which wasthen sequentially increased. The released DNA was measured using gel electrophoresis. d, The fraction of trapped DNA obtained from the electrophoresisgel constitutes a selection landscape of this thermal habitat in favour of long oligonucleotides. The velocity-dependent trapped fraction is described by a fluiddynamics model (see Methods). Error bars reflect the signal-to-noise ratio of the gel images (see Supplementary Fig. 11 for details).

NATURE CHEMISTRY DOI: 10.1038/NCHEM.2155 ARTICLES

NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry 3

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�12Jongseo Kim, Simon Langnickel

Convection in an open pore

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

vs (μm s–1)3.5 4.5 5 6 7 7 8 8.5 9

In Outflowc

60

40

20

100

200

Selection for long strands:

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�13Jongseo Kim, Simon Langnickel

Convection in an open pore

Differential survival of replicating strands. Combining all of theabove, we show how the joint thermally induced trapping andreplication enables this arrangement to overcome Spiegelman’sevolutionary dilemma of the degeneration of strand length andtherefore loss of genomic information11. We followed thecomposition of a heterogeneous DNA population that replicatescontinuously inside the open pore. A 2.5 mm short capillary wasseeded with a population of unlabelled template DNA strandswith identical primer binding sites and a binary lengthdistribution of 36 bp and 75 bp at a concentration of 1 nM each.

A temperature gradient from 61 °C to 94 °C was applied to a con-tinuous upwards flux of template-free PCR buffer that containednucleotides, polymerase and 7 nM fluorescently labelled primersand was run through the system at a speed of 6 µm s−1. Over thecourse of the experiment (seven hours), the trapping volume wasexchanged approximately 150 times with the template-free feeding

buffer. Aliquots that contained the product of the continuouslyrunning reaction were taken from the outflow and analysed usinggel electrophoresis. As the primers carried the labels, only replicatedDNA strands were detected (Fig. 4c).

We observed that only the long strands were able to replicate suf-ficiently to withstand the diluting flow through the pore. This deter-mined the increase of the relative concentration of the long, viablestrands with respect to the total amount of DNA (Fig. 4d, yellow).The twofold shorter strands became diluted and then extinct.

This competitive replication and selection of two genetic poly-mers in favour of larger molecular lengths can be understoodeasily with a simple model. The determinants of the growth kineticsdci /dt = (repi − dili)ci for either the short or the long speciesi = {S, L} are given by the replication rates repi and the dilutionrates dili. Expressing the relative concentration of the longstrands yields cL /(cS + cL) = (1 + Ae−Δkt)−1. A = c0S /c

0L is the initial

d

DNA strand length (bp)

Trap

ped

DN

A fr

actio

n

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100 120 14040 60 80

98.587654.53.5

vs (μm s–1)

vs (μm s–1)3.5 4.5 5 6 7 7 8 8.5 9

In Outflowc

60

40

20

100

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b

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Concentrationprofile

+Inflow

+convection

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pp

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vity

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Inflow

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vs = 6 µm s–1

a

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m

Figure 3 | Heat-driven filter selecting for strand length. a, A steady upwards feeding flow is triggered by opening the asymmetrically heated pore. A ladderof dsDNA (20–200 bp, 20 bp steps) was injected into the trap. Subsequent flushing of the capillary with pure buffer at a single velocity (vs = 6 µm s–1)revealed the filter’s thresholding characteristics—lengths ≤80 bp flow through the pore whereas longer strands are trapped. b, An asymmetric flow pattern isgenerated by the superposition of the upwards flow and the convection. Thermophoresis pushes the long strands into the downwards flow and traps them.Short strands are subjected to the overall upwards flow and leave the pore. The trapping is a function of the feeding flow speed. c, The velocity of theexternal flow vs tunes the fractionation of nucleic acids. As in the experiment before, a DNA ladder was initially introduced at a low flow velocity, which wasthen sequentially increased. The released DNA was measured using gel electrophoresis. d, The fraction of trapped DNA obtained from the electrophoresisgel constitutes a selection landscape of this thermal habitat in favour of long oligonucleotides. The velocity-dependent trapped fraction is described by a fluiddynamics model (see Methods). Error bars reflect the signal-to-noise ratio of the gel images (see Supplementary Fig. 11 for details).

NATURE CHEMISTRY DOI: 10.1038/NCHEM.2155 ARTICLES

NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry 3

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

Selection for long strands:

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�14Jongseo Kim, Simon Langnickel

Convection in an open pore

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

Competitive Replication and Selection

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Differential growth rate

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dili<latexit sha1_base64="4qqyYbXhE1VB1V4sC7kekpFAfvU=">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</latexit><latexit sha1_base64="4qqyYbXhE1VB1V4sC7kekpFAfvU=">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</latexit><latexit sha1_base64="4qqyYbXhE1VB1V4sC7kekpFAfvU=">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</latexit><latexit sha1_base64="4qqyYbXhE1VB1V4sC7kekpFAfvU=">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</latexit>

dilution rate

replication rate

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�15Jongseo Kim, Simon Langnickel

Convection in an open pore

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

BIOCHEMISTRY: MILLS ET AL.

0o II 10 so0 9~ V

1~~~~~~~~~~~~~I10X 1° 0CL[

on10.~~~ ~ ~ ~ ~ ~ ~ ~~RATO

I*10Ed

I 6~~~~,10 20

FRACTION

(Above) FIG. 2.-Sedimentation analysis of 0.15th TRANfER P0PRUCT1st transfer reaction. As described in Methods, 20 B I6S / 200.02 ml of the 0 reaction was used to initiate a 23s I I s4reaction for a 1st transfer reaction product. ;After completion, this reaction was adjusted 0 I t Ito 0.2% SDS, an aliquot was withdrawn, o l odiluted to 0.2 ml in TE buffer (0.01 M Tris K l lpH 7.4, 0.003 M EDTA), and then layered E l l |onto a 5-ml linear sucrose (2-20% in 0.1 M 10 I I3 l0ETris, pH 7.4, and 0.003 M EDTA) and run as , Iidescribed in Methods (section b). H3-labeled 0 . Clbulk RNA of E. coli was included as internal - \bsize markers. I

(Right) FIG. 3.-Sedimentation analysis of9th transfer (A) and 15th transfer (B) reac- 10 20tion products. Details are as in Fig. 2. FRACTION

shows (Fig. 2) the 28S peak characteristic of Qf3-RNA as well as the peaks cor-responding to the usual complexes observed during the in vitro synthesis.12 Com-parison with subsequent transfers reveals, however, dramatic changes in the natureof the replicating entity. Thus, by the ninth transfer (Fig. 3A) there is no materialsynthesized corresponding to the original 28S viral RNA. In its place we see amajor component at about 20S and a minor one at about 15S. This pattern is es-sentially maintained through the 15th transfer (Fig. 3B).By the 30th transfer (Fig. 4A) the major component has decreased to 15S and

the minor one to about 14S. The product of the 38th transfer shows variant RNAwhich no longer splits into two peaks, a feature retained through subsequent trans-fers. It will be noted (Fig. 5A and B), however, that the single peak moves moreslowly so that by the 74th transfer it is at about 12S.

(b) Gel electrophoresis of variant RNA: At this point it was decided to ex-amine the nature of the variant in greater detail. Transfer 75 was expanded withreplicase to a total of 120 ,ug of RNA and subjected to analysis by polyacrylamidegel electrophoresis (Fig. 6). Clearly, the apparently homogeneous peak of Figure5B is composed of at least two distinct RNA species. As may be seen from Figure6, the major component is sensitive to ribonuclease whereas the minor one is resis-tant. It would appear that the faster component is the single-stranded variantand that the slower minor peak contains a mixture of the Hofschneider'3 and Frank-

220 PROC. N. A. S.

BIOCHEMISTRY: MILLS ET AL.

20 30th TRANSFER 10 54 th TRANSFER

A P32FPRODUCT 20AI30

201 20

2330 ?6S 4s P32 PRODUCT30

o'\i~~~~~~~ ~~ _0 I~~~~~~ ~~~~Yl~4s

E 0 i\E 100

n~~~~~~§ Il K al IW

FIG. 4. i a s o

0 20

relative~ ~ ~ ~~~~lIlcrpoeimoilt (RM Cslnaleae nesl otem leu

10 20~~~~~~~~~02FRACTION~ ~ ~ ~ ~ ~ FRCTO

303wthTRANSFERP32nPRODUCT 20 3075Cth TRANSFER 40

Be23v B23isPa PRODUCTindcaehatearanRAasa olcuarwegh oaou 16s 41 s

I; ~ ~ 10 / *1* go~~ ~ ~ ~ ~~~~, Ito II0~~~~~~o

trphreis In thi recin l orrbncetietihsh swr aeewihpa h -psto Mtos seto I. Th RN prdc of tis reatio

10

was~~puife tiebge lcrpoeihdlyd,an anlzd0sdscie

15- -10O 0 tO 1 20 C

FRACTION FRACTION

FIG. 4.-Sedimentation analysis of the 30th FIG. 5.-Sedimentation analysis of the 54thtransfer (A) and the 38th transfer (B) reaction transfer (A) and the 75th transfer (B) reactionproducts. Details are as in Fig. 2. products. Details are as in Fig. 2.

linU structures observed first in vivo and seen in in vitro synthesis ofQav-RNA withpurified replicase.n2, 15

(c) Molecular weight of variant JRNA: We have previously shown10 that therelative electrophoretic mobility (REM) is linearly related inversely to the molecu-lar weight of single-stranded RNA. Consequently, to determine the molecularweight, the single-stranded variant RNA was subjected to gel electrophoresis withseven internal marker RNA's of known size. The results are shown in Figure 7 andindicate that the variant RNA has a molecular weight of about 1.7 X 1O5 daltons.

(d) Base composition of variant RNA: To determine its base composition,a standard reaction mixture was initiated with the variant isolated by gel elec-trophoresis. In this reaction, all four ribonucleotide triphosphates were labeledwith P32 at the a-position (Methods, section f). The RNA product of this reactionwas purified twice by gel electrophoresis, hydrolyzed, and analyzed as describedin Methods (section f). Comparison with the base composition of the originalQ13-RNA (Table 1) indicates that there has been a considerable (5 mole %) increasein the G content in the variant RNA. On the other hand, A and C have decreasedby 2.4 mole per cent, the uridine content remaining constant.

VOL. 58, 1967 221

Survival of long strands!

Competitive Replication and Selection

Spiegelmann, 1967

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�16Jongseo Kim, Simon Langnickel

Conclusion

gravity gravity

• cPCR • cPCR• Accumulation

• cPCR• Accumulation• length selection

Page 17: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�17Jongseo Kim, Simon Langnickel

Conclusion

images: de.wikipedia.org/wiki/Raucher_(Hydrothermie)

Thank you for your attention!

Page 18: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�18Jongseo Kim, Simon Langnickel

Sources

Sources:

1. Braun D, Goddard NL, Libchaber A. "Exponential DNA replication by laminar convection." Physical Review Letters. 2003 Oct 10;91(15):158103. Epub 2003 Oct 9.

2. Mast CB, Braun D. "Thermal trap for DNA replication.“Physical Review Letters. 2010 May 7;104(18):188102. Epub 2010 May 7.

3. Kreysing M, Keil L, Lanzmich S, Braun D. "Heatflux across an open pore enables the continuous replication replication and selection of oligonucleotides towards increasing length.“ Nature Chemistry. 2015 volume 7, pages 203-208

4. Mills DR, Peterson RL, and Sol Spiegelman. "An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule." Proceedings of the National Academy of Sciences 58.1 (1967): 217-224.

Page 19: Replication in a thermal trap - uni-muenchen.de · relativeIlcrpoei~ ~ ~ ~~~~lmoilt (RM Cslnaleae nesl otem leu 1020~~~~~02 FRACTION~ ~ FRCTO 303wthTRANSFERP32nPRODUCT 20 75Cth30

�19Jongseo Kim, Simon Langnickel

Convection in an open pore

Kreysing, Keil, Lanzmich & Braun, Nature Chemistry 2015

Dynamics:dcidt

= (repi � dili) · ci<latexit sha1_base64="IGmWF8REaLTODf4fJhG8cfVMDEE=">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</latexit><latexit sha1_base64="IGmWF8REaLTODf4fJhG8cfVMDEE=">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</latexit><latexit sha1_base64="IGmWF8REaLTODf4fJhG8cfVMDEE=">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</latexit><latexit sha1_base64="IGmWF8REaLTODf4fJhG8cfVMDEE=">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</latexit>

i = {S,L}<latexit sha1_base64="nx0Q4dK2ezEstfnw5RcnHfXIFao=">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</latexit><latexit sha1_base64="nx0Q4dK2ezEstfnw5RcnHfXIFao=">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</latexit><latexit sha1_base64="nx0Q4dK2ezEstfnw5RcnHfXIFao=">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</latexit><latexit sha1_base64="nx0Q4dK2ezEstfnw5RcnHfXIFao=">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</latexit>

ci = c0i e(repi�dili)·t

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�k = (repL � repS)� (dilL � dilS)<latexit sha1_base64="sNL8yvgL1ONdhrqdRxCRyRnipGc=">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</latexit><latexit sha1_base64="sNL8yvgL1ONdhrqdRxCRyRnipGc=">AAAC9XichVFNTxRBEH0MypeCCx69dNyYLCRsZowJXkwIoPGgCQYWSIBsemabtbO9M5OeXggQ/oN/wJvxyo2r/g39LR583QwmSgw96XnVr6peV3WlpdGVi+MfY9H4vfsTk1PTMw8ezs49aswv7FTFyGaqkxWmsHuprJTRueo47YzaK62Sw9So3XSw7v27x8pWusi33WmpDoeyn+sjnUlHqttYOthQxkkxEK9Ey6qy+04sC49bi8utnjbh7HFrsdtoxu04LHHbSGqjiXptFo2fOEAPBTKMMIRCDkfbQKLit48EMUpyhzgnZ2np4Fe4wAxzR4xSjJBkB/z3edqv2Zxnr1mF7Iy3GG7LTIFn3G+CYspof6uiXRF/cZ8Frv/fG86Dsq/wlJhScToovifv8JERd2UO68ibWu7O9F05HOFl6EazvjIwvs/sj84GPZbcIHgEXofIPjXScD7mC+TEDivwr3yjIELHPaIMqIJKXitK6lmif33WwzEn/w71trHzvJ3E7eTDi+bqWj3wKTzBU7Q41RWs4i02WUeGT7jCN3yPTqLP0Zfo63VoNFbnPMZfK7r8DREinQ0=</latexit><latexit sha1_base64="sNL8yvgL1ONdhrqdRxCRyRnipGc=">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</latexit><latexit sha1_base64="sNL8yvgL1ONdhrqdRxCRyRnipGc=">AAAC9XichVFNTxRBEH0MypeCCx69dNyYLCRsZowJXkwIoPGgCQYWSIBsemabtbO9M5OeXggQ/oN/wJvxyo2r/g39LR583QwmSgw96XnVr6peV3WlpdGVi+MfY9H4vfsTk1PTMw8ezs49aswv7FTFyGaqkxWmsHuprJTRueo47YzaK62Sw9So3XSw7v27x8pWusi33WmpDoeyn+sjnUlHqttYOthQxkkxEK9Ey6qy+04sC49bi8utnjbh7HFrsdtoxu04LHHbSGqjiXptFo2fOEAPBTKMMIRCDkfbQKLit48EMUpyhzgnZ2np4Fe4wAxzR4xSjJBkB/z3edqv2Zxnr1mF7Iy3GG7LTIFn3G+CYspof6uiXRF/cZ8Frv/fG86Dsq/wlJhScToovifv8JERd2UO68ibWu7O9F05HOFl6EazvjIwvs/sj84GPZbcIHgEXofIPjXScD7mC+TEDivwr3yjIELHPaIMqIJKXitK6lmif33WwzEn/w71trHzvJ3E7eTDi+bqWj3wKTzBU7Q41RWs4i02WUeGT7jCN3yPTqLP0Zfo63VoNFbnPMZfK7r8DREinQ0=</latexit>

fL =cL

cL � cS= (1 +Ae��kt)�1

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A = c0S/c0L

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Ansatz: