Biological clocks in theory and experiments www.amillar.org

Current:

Megan Southern

Laszlo Kozma-Bognar

Kieron Edwards

Vacancy !

Paul Brown

James Locke

Domingo Salazar

Ozgur Akman

Vacancy !

Past:Simon ThainKamal SwarupRuth BastowHarriet McWattersShigeru HananoSeth DavisMandy Dowson-DayGiovanni MurtasNeeraj SalathiaMaria ErikssonAnthony HallAlex MortonBoris ShulginNickiesha BromleyVictoria Hibberd

CollaboratorsIPCR - Matthew Turner (Physics) David Rand (Maths) Bärbel Finkenstädt (Statistics) Mark Muldoon and David

Broomhead (Manchester) Lorenz Wernisch (Birkbeck)

Antony Dodd, Alex Webb, Julian Hibberd (Cambridge)

Ferenc Nagy (Szeged)Eberhard Schäfer, Stefan

Kircher (Freiburg)Mark Doyle, Scott Michaels,

Rick Amasino (Madison)Graham King (HRI), Mike

Kearsey (Birmingham)

Funding: BBSRC, Gatsby, EPSRC, DTI

Genome-wide circadian rhythms

~ 12% RNA transcripts rhythmic in white light

~ 3,000 genes of 22,000 on array

• Functional clustering• 68% of rhythmic transcripts

also stress-regulated, (Kreps et al. 2002)

Edwards et al. unpublished

Time in LL (h) 26 30 34 38 42 46 50 54 58 62 66 70 74 0h

Mutant plants identify genes in the clockwork

?

• Negative regulation during the day - CCA1/LHY• Positive regulation at night• Mathematical model to test potential for regulation

Alabadi et al., 2001

Luciferase (LUC) reporter

• Luminescence reflects transcription rate of promoter• Unstable activity reports dynamic regulation• Spatial resolution, high throughput

+camera

CAB/ LHCB LUC protein code

LUC: identifies mutants in clock genes

Hicks et al, Science, 1996McWatters et al., Nature, 2000

Reed et al., Plant Phys. 2000

0

200

400

600

800

1000

0 24 48 72 96 120

Time (hours)

Photons/ seedling/ 25mins

elf3-1WTelf3-7

CAB:LUC rhythm

EARLY-FLOWERING 3 (elf3): arhythmic in light

CCA1:LUCrhythm

0

10000

20000

30000

0 12 24 36 48 60

Time (hours)

Counts/sdlg/

second

EARLY-FLOWERING 4 (elf4): arhythmic in all conditions,Fails to express CCA1Doyle et al., Nature, 2000

WT

elf4

The circadian clock in Arabidopsis

CAB

morphology

+ 3600 genes

OvertRhythms

Oscillator

Input Modelling Design principles Extension of network

ELF3 zeitnehmer(PHY/CRY rhythms)

phyA, B, D

cry1, 2

Acute light response

LHYCCA1

TOC1

Projects in circadian rhythms - Current

Central loop:ODE, SDE, Simplified, etc.

Reporter genesRNA (PCR, arrays)Mutant plants

Data Models

Model analysis

Clock mechanism.Functions of interlocking loops,multiple light inputs

Understanding

Data preparationRhythm detectionParameter estimation(MCMC, cost functions)

Data analysis

Predictions

IRCs,Flexibility

Software

dLHYm = vT TOCn4 - vLCLHYm - kd1 LHYm

dt kT + TOCn4 k1 + LHYm

dLHYc = kLLHYm – kLCLHYc + kLPLHYn - vDCLHYc

dt kLC + LHYc

dLHYn = kLCLHYc – kLPLHYn + vDNLHYn

dt kLN + LHYn

dTOCm = vTOC - vDTTOCm - kd TOCm

dt kLHY + (LHYn)4 kT + TOCm

dTOCc = kTOCTOCm – kTCTOCc + kTPTOCn - vDTTOCc

dt kTC + TOCc

dTOCn = kTCTOCc – kTPTOCn + vDTPTOCn

dt kTP + TOCn

Single-loop network model

Locke, Millar and Turner, J Theor Biol, 2005. Global parameter search.

Random Sobol

Interlocking loop model for Arabidopsis clock

• Model- J. Locke

• Hypothetical components X, Y

• Cost function fit to WT and mutant behaviour

• Predicts X and Y expression

TOC1TOC1

LHY

Y

X

X

Y

LHY LHY

mR

NA

LHY

mR

NA

TO

C1

mR

NA

TO

C1

mR

NA

Time (h)

WT

cca1;lhy

Experiments to identify Y turn up a good candidate

• Prediction = dashed line

• M. Southern tested candidate genes by qRT-PCR. Data = crosses

• Unexpected light response of GIGANTEA RNA matches prediction

• GI also matches other predictions for Y from literature

WT

cca1;lhy

Projects in circadian rhythms - Current

Central loop:ODE, SDE, Simplified, etc.

Data Models

Model analysisUnderstanding

Data preparationRhythm detectionParameter estimation(MCMC, cost functions)

Data analysis

Data analysis: CAB:LUC in 16h L:8h D

raw

prepared

synthesis rate

Morton, Finkenstadt

Parameter estimation: simple model for synthesis rate

dY

dt(t) Y (t)Model: sde version of

%(t) a

0 a

kcoskt b

ksinkt

k1

p

(t) %(T ) cIT e

where T t d mod L

IT e

Comparison of WT and elf3 mutant waveforms

clock effect

WT

elf3 mutant

• Quantify distinct features within the timeseries

• Now apply to parameters of simple clock models

Projects in circadian rhythms - Current

Central loop:ODE, SDE, Simplified, etc.

Reporter genesRNA (PCR, arrays)Mutant plants

Data Models

Model analysis

Clock mechanism.Functions of interlocking loops,multiple light inputs

Understanding

Data preparationRhythm detectionParameter estimation(MCMC, cost functions)

Data analysis

Predictions

IRCs,Flexibility

Software

Projects in circadian rhythms – Future collaboration

Photoreceptors,secondary loops

Reduced/synthetic systemsProtein data(2-D gels)Biochemistry(parameters)

Data Models

Model analysis

Stochastic processesNoise (internal and external)

Understanding

Fitting directlyto multiple data typesNetwork inference(dynamic Bayes nets)

Data analysis

Adding to modelInverse problem

DatabaseDatabase

Software