www.sciencemag.org/cgi/content/full/339/6125/1316/DC1

Supplementary Materials for

Circadian Control of Chloroplast Transcription by a Nuclear-Encoded Timing Signal

Zeenat B. Noordally, Kenyu Ishii, Kelly A. Atkins, Sarah J. Wetherill, Jelena Kusakina,

Eleanor J. Walton, Maiko Kato, Miyuki Azuma, Kan Tanaka, Mitsumasa Hanaoka, Antony N. Dodd*

*To whom correspondence should be addressed. E-mail: antony.dodd@bristol.ac.uk

Published 15 March 2013, Science 339, 1316 (2013)

DOI: 10.1126/science.1230397

This PDF file includes

Materials and Methods Figs. S1 to S9 Tables S1 to S5 Full References

Other Supplementary Material for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/339/6125/1316/DC1)

Spreadsheet S1 as an Excel file

1

Supplementary Materials for

Circadian Control of Chloroplast Transcription by a Nuclear-Encoded Timing Signal

Zeenat B. Noordally, Kenyu Ishii, Kelly A. Atkins, Sarah J. Wetherill, Jelena Kusakina, Eleanor J.

Walton, Maiko Kato, Miyuki Azuma, Kan Tanaka, Mitsumasa Hanaoka, Antony N. Dodd.

Correspondence to: antony.dodd@bristol.ac.uk

This PDF file includes:

Materials and Methods

Figs. S1 to S9

Tables S1 to S5

Other Supplementary Materials for this manuscript includes the following:

Spreadsheet S1

2

Materials and Methods

Arabidopsis cultivation and germplasm

Arabidopsis thaliana was cultivated under sterile conditions using Sanyo MLR-352 growth

chambers as described previously (22). Seedlings were entrained to cycles of 12 h white light/12 h

darkness at 19 °C before transfer to continuous white light after 11 days for bioluminescence

imaging, 12 days for RNA timecourses and 16 days for delayed fluorescence (DF) imaging.

Custom-built LED panels supplied red (660 nm) or blue (440 nm) light for experiments involving

colored light treatments. sig5-2 is a homozygous T-DNA insertion (SAIL Garlic 1232 H11)

characterized elsewhere (4). sig5-3 is a homozygous T-DNA insertion line (SALK 141383C,

obtained from NASC) and is a new allele that we genotyped (Fig. S9). Genomic DNA PCR

confirmed the presence and location of the T-DNA insert and homozygous nature of the line using

the primers 5’-TCTCATACCCGCTTGACAAAG-3’ (LP), 5’-GTTCAGCTGCAAGATCTCCAC-

3’ (RP) and ATTTTGCCGATTTCGGAAC (SALK LBb1.3). We also confirmed that full-length

SIG5 transcripts and psbD BLRP transcripts were absent in sig5-3.

Real-time PCR and Northern analysis

For real-time PCR and Northern analysis, aerial tissue was harvested using 10 seedlings per

timepoint that comprised 5 seedlings from each of two Petri dishes. Two independent biological

repeats were performed for every experiment. Total RNA for real-time PCR was extracted from

frozen tissue using Macherey-Nagel Nucleospin RNAII kits. cDNA was synthesized as previously

(22). 1/200 cDNA dilutions were analyzed using an ABI Prism 7300, ABI SybrGreen Power Mix

and primers in Table S4, with default reaction conditions for all transcripts except psbD BLRP,

which used conditions described previously (27). Data were processed using ABI SDS v1.2.

Rhythmic data were analyzed using the cosine wave fitting package COSOPT (14). Northern

analysis was performed as described previously (4).

3

Bioluminescence imaging of promoter-luciferase reporters and delayed fluorescence

Homogyzous sig5-3 mutants expressing CCA1::LUCIFERASE, TOC1::LUCIFERASE and

CCR2::LUCIFERASE were generated by crossing and backcrossing luciferase reporter lines into

homozygous sig5-3. Bioluminescent F2 seedlings were PCR screened using primers flanking the T-

DNA insert within the SIG5 coding sequence to identify seedlings homozygous for the T-DNA

insertion. F3 seed collected from homozygous sig5-3 seedlings was used for imaging. The

promoter-luciferase background used for crossing was the imaging control. Bioluminescence

imaging was performed as described previously (22), using a Photek HRPCS intensified CCD

photon counting camera (Photek Ltd., UK). Data were analyzed using Image32 (Photek) and

BRASS (www.amillar.org). For DF experiments, images were captured hourly using 60 s

integrations with the camera driven in binary slice mode. DF data were analyzed as elsewhere (12).

Generation of TOC1::SIG5 and SIG5::LUCIFERASE transgenic plants

To create the TOC1::SIG5 construct, the TOC1 -1000 upstream sequence was ligated between

HindIII and PstI sites in the binary vector pGREENII0229 (www.pgreen.ac.uk). The SIG5 coding

sequence was positioned downstream of the TOC1 promoter and upstream of a CaMV 35S

terminator using flanking BamHI sites. To create SIG5::LUCIFERASE, the SIG5 -2460 bp

upstream sequence was ligated between the PstI and BamHI restriction sites in pGREENII0229, and

the luciferase+ coding sequence was ligated between the BamHI and SacI sites in this vector, before

of a NOS terminator. The T-DNA was transformed into sig5-3 (TOC1::SIG5) and Col-0 wild type

(SIG5::LUCIFERASE) Arabidopsis using Agrobacterium-mediated transformation. Transformants

were identified by BASTA resistance screening and validated with genomic DNA PCR and RT-

PCR. Homozygous T3 lines were used for experimentation. Two independent transgenic lines

expressing TOC1::SIG5 were investigated.

Chloroplast ChIP-qPCR

4

Chloroplast chromatin immunoprecipitation followed by qPCR analysis (Chloroplast ChIP-qPCR)

was performed as elsewhere (29), using the primer sets in Table S5 to detect potential SIG5 binding

to chloroplast gene promoters.

Meta-analysis of circadian regulation of chloroplast genome

Chloroplast-encoded genes with circadian oscillations in transcript abundance were identified using

the HAYSTACK pattern-matching algorithm and DIURNAL interface (diurnal.mocklerlab.org).

We analysed transcriptome studies using HAYSTACK rather than with cosinor analysis because we

wished to identify the maximum number of chloroplast transcripts with the potential for circadian

regulation. HAYSTACK compares transcript profiles against a variety of waveforms and has been

demonstrated to identify the widest range of oscillating transcripts (2). We found that the default

DIURNAL correlation threshold of 0.8 suggested for nuclear-encoded genes excluded chloroplast

transcripts demonstrated previously to be rhythmic (e.g. psbDC), so titrated the threshold to 0.65 in

order to capture these transcripts within the analysis (Spreadsheet S1).

5

Fig. S1. Circadian rhythms of delayed fluorescence in wild type and sig5 mutant seedlings. Data are

means from five clusters of between 10 and 15 16-day old seedlings ± S.E.M., from (A)

experimental repeat 1 and (B) experimental repeat 3 in Fig. 1B. Vertical gray lines indicate the

timing of each delayed fluorescence peak in the wild type, to allow direct comparison with the

timing of each peak in sig5-2 and sig5-3 mutants. Hatched bars on x axes indicate subjective dark

period.

Time in constant light (h)

24 36 48 60 72 84 96

-2000

-1500

-1000

-500

0

500

1000

1500

Mea

n n

orm

aliz

ed d

ela

yed f

luore

scen

ce

inte

nsity

-1500

-1000

-500

0

500

1000

-1500

-1000

-500

0

500

1000

1500

2000

-3000

-2000

-1000

0

1000

2000

3000

Mea

n n

orm

aliz

ed d

ela

yed f

luore

scen

ce

inte

nsity

-3000

-2000

-1000

0

1000

2000

Time in constant light (h)

24 36 48 60 72 84 96 108 120

-3000

-1000

1000

3000

Col-0 wild type

sig5-2

sig5-3

sig5-2

sig5-3

Col-0 wild typeA B

6

Fig. S2. SIG5 is required for circadian oscillations in abundance of psbD BLRP mRNA and does

not modulate overall chloroplast transcription. Col-0 wild type blots are from Fig. 1A and

reproduced alongside sig5-2 blots to allow direct comparison. Northern blot analysis shows

abundance of mRNAs for both nuclear (SIG1, SIG5, CAB3) and plastid (psbA, psbD BLRP, rbcL)

encoded transcripts in (A) Col-0 wild type and (B) sig5-2 mutant. Seedlings were grown and

harvested as for qRT-PCR experiments. The positions of RNA markers are indicated as nucleotides

(nt) on the right.

7

Fig. S3. (A) Circadian oscillations of SIG5 promoter activity in Col-0 wild type seedlings measured

using a SIG5::LUCIFERASE transcriptional fusion reporter. Seedlings were entrained previously to

light/dark cycles and luciferase bioluminescence was integrated for 900 s at 2 h intervals under

constant light. (B) Three types of known circadian-regulated cis element occur within the region

upstream of the SIG5 gene coding region. Gene promoters containing the CACGTG (ABA response

element /ABRE) motif are frequently phased to the subjective day, those containing the GATAA

motif are frequently phased to late subjective day, and those with the CCACA (‘morning element’)

are frequently phased to early subjective day (35). In (B), the SIG5 upstream and coding regions are

indicated in green and orange respectively, the precise location of cis elements indicated by black

vertical lines, and the identity of cis elements by black symbols.

ABRE (CACGTG)-like

GATAA late day motif-like

‘Morning element’ CCACA

SIG5 upstream region SIG5 coding sequence

ATG-2000

A

B

Time in constant light (h)

24 36 48 60 72 84 96 108120132144

Mea

n S

IG5::LU

CIF

ER

AS

Eb

iolu

min

escence

(cou

nts

in 9

00 s

)5000

10000

15000

20000

25000

30000

35000

8

Fig. S4. (A, B) psbD BLRP transcripts were arrhythmic in TOC1::SIG5 line 2 that had low

amplitude oscillations of SIG5 transcripts; (C) Circadian oscillations of LHY transcripts are

unaltered in two independent transgenic lines expressing TOC1::SIG5 in the sig5-3 mutant.

Relative abundance of SIG5 and psbD BLRP transcripts quantified as ACT2-normalized mean RQ ±

S.E.M.

Time in constant light (h)

24 36 48 60 72 84 96

Re

lative

tra

nscri

pt

ab

und

ance

0.0

0.2

0.4

0.6

0.8

1.0

1.2SIG5 psbD BLRP

A

LHY

Time in constant light (h)

24 36 48 60 72 84 96

Re

lative

tra

nscri

pt

abun

dan

ce

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Col-0 wild type

sig5-3 TOC1::SIG5 Line 1

sig5-3 TOC1::SIG5 Line 2

C

sig

5-3

TO

C1::S

IG5 re

lativ

etra

nscrip

t abu

nda

nce0.1

0.2

0.3

0.4

0.5

Time in constant light (h)

24 36 48 60 72 84 96

Co

l-0 r

ela

tive tra

nscrip

tab

und

ance

0.0

0.5

1.0

1.5

2.0

2.5 B

9

Fig. S5. The period of the circadian oscillator controls the period of SIG5 and psbD BLRP

transcripts. (A) For wild type, toc1-1 and ztl-1, comparison for LHY of estimated circadian period

and pMMC-β from COSOPT cosinor analysis. (B) Relative abundance of LHY transcripts in C24

wild type, toc1-1 and ztl-1. (C, D) Circadian oscillations of SIG5 and psbD BLRP transcripts in

C24, toc1-1 and ztl1. Relative transcript abundance is ACT2-normalized mean RQ ± S.E.M.

Time in constant light (h)48 60 72 84 96

02468

101214

Rela

tive tra

nscri

pt a

bund

ance

0

4

8

12toc1-1

ztl-1

0

5

10

15

20

25

30C24 wild type

Period estimate (h)

21 22 23 24 25 26 27 28 29

pM

MC

- β

0.0

0.1

0.2

0.3

0.4

0.5

B

A

toc1-1 C24 ztl-1

48 60 72 84 96

0

1

2

3

4

5

0123456

01234567

48 60 72 84 96

0.5

1.0

1.5

1.0

1.5

2.0

2.5

0.4

0.8

1.2

1.6

2.0C24 wild type

toc1-1

ztl-1

Time in constant light (h) Time in constant light (h)

Rela

tive tra

nscript abu

ndan

ce

Rela

tive

tra

nscri

pt abund

ance

C DC24 wild type

toc1-1

ztl-1

LHY SIG5 psbD BLRP

LHY

10

Fig. S6. Blue light regulation of SIG5 and psbD BLRP transcripts. (A) SIG5 transcripts are induced

rapidly by BL but not RL. (B) psbD BLRP are induced by BL but not RL, and this is SIG5-

dependent. (C) Blue light-induced SIG5 transcripts degrade rapidly in darkness. In all experiments,

seedlings were placed in constant darkness and temperature for 24 h prior to induction with 1 h of

10 µmol m-2

s-1

RL or BL. Relative abundance of SIG5 and psbD BLRP transcripts quantified as

ACT2-normalized mean RQ ± S.E.M.

Time after 1 h light pulse (minutes)

0 20 40 60 80

Rela

tive

tra

nscri

pt ab

und

ance

0

20

40

60

80

100

Blue light

Red light

Time after 1 h light pulse (h)

0 1 2 3 4 5 6 7

Re

lative

tra

nscript a

bun

dan

ce

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Blue light, Col-0 wild type

Red light, Col-0 wild type

Blue light, sig5-2 mutant

Time after transfer to darknessfollowing 1 h light pulse (h)

0 1 2 3 4 5 6 7

Rela

tive

tra

nscri

pt ab

und

ance

0

40

80

120

160

Blue light

Red light

SIG5

psbD BLRP

SIG5

A

B

C

11

Figure S7. A screen for additional targets of SIG5. ChIP-qPCR (29) was performed to detect

potential SIG5 binding with DNA. The quantity of immunoprecipitated DNA of promoter regions

listed was calculated, and shown as percent recovery against total input DNA. Genes with

significantly increased DNA recovery, identified by one-way ANOVA and post-hoc Tukey

analysis, were selected for further study. rps15 was excluded because its promoter is NEP-

dependent (36, 37). p-values indicated when DNA recovery was significantly different, other

promoters not significant (p > 0.025). Data are means from two experiments ± standard deviation.

Broken horizontal line indicates mean DNA recovery across promoters.

psb

A

psb

KI

atp

FA

rpo

BC

trn

EY

D

psb

DC

psa

AB

nd

hC

atp

B

rbcL

accD

psb

EF

LJ

pe

tLG

clp

P

psb

BT

psb

N

trn

I-rp

l23

ycf2

rps1

2-7

trn

V

ycf1

rps1

5

rpl3

2

DN

A r

eco

very

(%

)

0.00

0.02

0.04

0.06

0.08p

< 0

.00

1

p =

0.0

08

p <

0.0

01

p <

0.0

01

p =

0.0

06

Chloroplast promoter

12

Fig. S8. SIG5 modulates the amplitude of circadian oscillations of several chloroplast genes

identified by ChIP-PCR. (A) The abundance of psaAB and psbA transcripts is increased

significantly by SIG5 during the subjective light period, and psbBT may be increased slightly. (B)

rbcL and psbDC formed negative and positive controls respectively; psbDC is SIG5-regulated (Fig.

1A, C), whereas rbcL was not identified during a ChIP screen for potential SIG5-binding

promoters. rbcL transcript abundance was unaltered in sig5-2 and psbDC transcripts abundance was

reduced at many timepoints. Relative transcript abundance quantified as ACT2-normalized mean

RQ ± S.E.M. Statistically-significant differences between wild type and sig5-2 mutant are indicated

by asterisks (* p < 5%, ** p < 1%, *** p < 0.1% from two-sample t-tests; unmarked data points not

significantly different between sig5-2 and wild type).

rbcL

Time in constant light (h)

24 36 48 60

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Col-0

sig5-2

psbBT

Time in constant light (h)

24 36 48 60

0.4

0.8

1.2

1.6

2.0

2.4

psbA

Rela

tive

tra

nscrip

t ab

und

an

ce

0.5

1.0

1.5

2.0

2.5

psbDC

Re

lative tra

nscript a

bu

nd

ance

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

psaAB

0.4

0.8

1.2

1.6

2.0

***

*

**

*

****

*

**

*

*

*** ***

*

****

**

A

B

13

Fig. S9. The sig5-3 mutant is a homozygous T-DNA insertion mutant. (A) Genomic DNA PCR to

verify location of T-DNA insert within genome. Individual seedlings are homozygous and contain

an inverted repeat of T-DNAs. LP and RP are primers that anneal with genomic DNA flanking the

T-DNA, and LB is a primer that anneals within the T-DNA insert. (B) Real-time PCR

demonstrating that SIG5 and psbD BLRP transcript abundance is reduced by comparable magnitude

in sig5-2 and sig5-3.

14

Col-0 sig5-2 sig5-3

Experiment 1 24.6 ± 0.6 h 24.5 ± 0.9 h 25.4 ± 0.3 h

Experiment 2 24.2 ± 0.6 h 24.6 ± 0.3 h 24.9 ± 0.2 h

Experiment 3 24.0 ± 0.8 h 25.2 ± 0.4 h 24.7 ± 0.6 h

Table S1. Period estimates of circadian oscillations of delayed chlorophyll fluorescence in Col-0

wild type, and sig5-2 and sig5-3 mutants for three independent experiments, ± S.E.M. Of three

experiments, Experiment 3 was experimenter-blind throughout experimentation and analysis.

15

COSOPT period estimate

(h) ± s.e.m.

COSOPT relative phase

(h) ± s.e.m.

Transcript Col-0 sig5-2 Col-0 sig5-2

CCA1 23.8 ± 0 23.6 ± 0.2 -5.3 ± 0.2 -4.8 ± 0.4

CHE 23.4 ± 0.6 24.0 ± 0.1 -10.6 ± 0.3 -10.1 ± 0.2

GI 23.5 ± 0.2 23.8 ± 0.4 10.6 ± 0.3 11.6 ± 0.3

PRR7 23.2 ± 0.2 22.9 ± 0 -11.5 ± 0.1 -11.4 ± 0.1

TOC1 23.7 ± 0.2 23.5 ± 0.2 7.7 ± 0.2 7.8 ± 0.3

LHY 25.6 ± 0.1 25.6 ± .01 -2.7 ± 0.4 -2.2 ± 0.1

COSOPT mean expression

level ± s.e.m.

Transcript Col-0 sig5-2

CCA1 0.3 ± 0.1 0.3 ± 0.0

CHE 1.3 ± 0.1 1.2 ± 0.1

GI 6.0 ± 0.1 4.8 ± 0.4

PRR7 4.9 ± 0.1 4.6 ± 0.4

TOC1 3.1 ± 0.1 2.8 ± 0.1

LHY 0.4 ± 0.1 0.5 ± 0.0

Table S2. The period, phase and mean expression level of transcripts encoding circadian oscillator

components was unaltered in sig5-2 relative to wild type. Period, phase and mean expression levels

16

of CCA1, CHE, GI, PRR7, TOC1 and LHY was calculated from real time PCR data (Fig. 3A) using

COSOPT cosinor analysis.

Reporter Period (h ± s.e.m.) Phase (h ± s.e.m.) Amplitude (counts ±

s.e.m.)

Genotype Col-0 sig5-3 Col-0 sig5-3 Col-0 sig5-3

CCA1::LUC 24.9 ± 0.1 25.2 ± 0.1 3.8 ± 0.4 3.8 ± 0.4 3.7 ± 0.3 3.4 ± 0.2

TOC1::LUC 25.6 ± 0.1 25.4 ± 0.1 16.8 ± 0.4 17.3 ± 0.4 9.1 ± 0.7 8.5 ± 0.4

CCR2::LUC 23.8 ± 0.2 24.3 ± 0.2 6.4 ± 0.4 7.8 ± 0.7 5.4 ± 1.0 4.1 ± 1.1

Table S3. Period, phase and amplitude of circadian oscillations of CCA1::LUCIFERASE,

TOC1::LUCIFERASE and CCR2::LUCIFERASE bioluminescence in Col-0 and sig5-3. Parameters

were calculated using BRASS. CCA1::LUC amplitude is expressed as x104 bioluminescence

counts, TOC1::LUC as x103 counts, and CCR2::LUC as x10

2 counts.

17

Primer Sequence (5’ to 3’)

ACT2 Forward TGAGAGATTCAGATGCCCAGAA

ACT2 Reverse TGGATTCCAGCAGCTTCCAT

psbD BLRP Forward GGAAATCCGTCGATATCTCT

psbD BLRP Reverse CTCTCTTTCTCTAGGCAGGAAC

CCA1 Forward GCACTTTCCGCGAGTTCTTG

CCA1 Reverse TGACTCCTTTCTTACCCTGTTATTCTG

CHE Forward TCCACCGGAAATGGTTTTTG

CHE Reverse GGCGGAAGCTTGCTGTTG

GI Forward ATGGTGTAGTGGTGTAATGGGTAAATAT

GI Reverse CAGATCCTCGAGAAGCAATGG

LHY Forward ACGAAACAGGTAAGTGGCGACA

LHY Reverse TGGGAACATCTTGAACCGCGTT

PRR7 Forward CCACGAGCGGTATCTCTATGG

PRR7 Reverse ACTGATTACTTGGAAACTCAGGGTTAG

psbD Forward AGATGGTGATGGTGCAAATACATT

psbD Reverse AGCGGTGACCATTGAATAAGTTTC

18

psaAB Forward TGCTCGTAGCTCGCGTTTAA

psaAB Reverse CATCACAAGGGAAACGAAAACC

psbA Forward GGGTCGTGAGTGGGAACTTAGT

psbA Reverse GCTGAATATGCAACAGCAATCC

psbB Forward TGGGTATCCGACCCTTATGG

psbB Reverse CCCCACGCCGGGTTTA

rbcL Forward GATGGGCTTACCAGCCTTGA

rbcL Reverse CTGGAACGGGCTCGATGT

SIG5 Forward GTGTTGGAGCTAATAACAGCAGACA

SIG5 Reverse TGTCGAATAACCAGACTCTCTTTCG

TOC1 Forward TCTTCGCAGAATCCCTGTGAT

TOC1 Reverse GCTGCACCTAGCTTCAAGCA

Table S4. Primer sets used for real time PCR experiments. psbD BLRP primers above are as

described elsewhere (27).

19

Promoter Forward (5' to 3') Reverse (5' to 3')

psbKI TTGATCATTACATAGAAT AACAAAAATTGGTGTTCT

psbDC AATAAAATCAAAAATTTTG AGCGATCCTCCTATTCA

rbcL ATGAAAGAATATACAATAA AAGTCCCTCCCTACAAG

accD ATCCTTCTTTTCATTTAG AGAGCTTCTGGCCTCTA

petLG TGAATTGAGTTCTTTTTA GAAGGGACTCAATAAAA

psbBT TTGGTACTTATCGGATAT GGAAATACCCCTTTATCA

ycf2 GCCAATTCCAATAGACTT TGATTCCTCCTAAATTGC

trnV ATGGCTCGAATCCGTAGT TCCCCCATCAAGAAATAG

rpl32 ATTATTTAAATGAGTACT TCAAAAATGAAAAAAAAT

ycf1 TTTAATAGGGAACCTCAA AAACCTCCCTTTTTTCTT

rps15 GATACCAATTATAGCGGA AAAAAGAAATCCTTCCCC

rps12-7 GTATGGATATGTAAAATACA TTGTAGGGTGGATCTCG

trnI-rpl23 ATCCCACTGAATTGAATTG TTAGTGGGGATCCTCGT

psbN TTTACCATATTCGGAATT TATTATAGAATTGAAAGA

clpP TAGTTTTATTCATTCTCT GAAATGAAAAAAAAAGAG

psbEFLJ ATTATGTAACACCCCATT ACTGAACTCCAGATATTC

atpB AGGTTTCAGTTAGTTGA AATAAAAAAAATATGTTAAA

ndhC CTATTAAGTAATAAGTGTA AGACGAACTCCTATGAA

psaAB CATAATAGATCCGAACACT TGAGTCCTCCTCTTTCC

trnEYD AATATAAAAAGAAAGTATAT ATACTTGCTCAACCGC

rpoBC TTCCAATTGAATATAGTC CTTTTTTGAATTTCCCAT

20

atpFA ATAAGTCTCATTATTATTA ATAATCTCCTCTTCTAG

psbA GTGGATTCGCTTCTAATT GGTAAAATCCTTGGTTTA

Table S5. Primer sets used for ChIP-qPCR analysis, as described previously (29).

21

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