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Modeling Rhythms on Differents Levels: Cells, Tissues, and Organisms
Hanspeter HerzelInstitute for Theoretical Biology (ITB)
Charité and Humboldt University Berlin
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3rd ventricle
optic chiasm
Synchronization
clock-genes(e.g. Period2)
positiveelements
activation
nucleus
SCN-neuron
negativeelements
inhibition
Oscillation
Molecular Chronobiology
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Clock genes and feedback loops
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The core clock in Drosophila – negative and positive feedback
loops
D. Bell-Pedersen et al. 2005
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The core clock in mammals
D. Bell-Pedersen et al. 2005
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Limits of quantitative models
single cellsadvanced models of feedback loops incl.PER/CRY loops and RORE-loops
• noisy reporter signals of at most 44 days
• few PRCs (mostly phase resetting)
• kinetic parameters mostly unknown
models data
Relogio et al. PLoS Comp. Biol. 2011 Abraham, Schlichting et al., in revision
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Limits of quantitative models
neuronal networksnetwork models with heterogeneity ,different coupling schemes etc.
• movies with waves and tides
• multiple coupling mechanisms debated
• some PRCs (VIP, AVP, optogenetics…)
• splitting rare
models data
Bernard et al. PLoS Comp. Biol. 2007 Yamaguchi et al., Science 2003
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Limits of quantitative models
on organismic level• long actograms• many PRCs incl. dead zones• entrainment/jetlag protocols• saisonal variations
models data
Aschoff and Pohl, 1978
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Challengegenetic feedback + coupling network modelsmodels
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Challengegenetic feedback + coupling network modelsmodels Example of complexity:single cell oscillator: amplitude, phase, +-4h PRC
resonant coupling
strong, rigid network oscillator with +-1h PRC regarding cells versus ensembles see also:Rougemont & Naef 2007; vanderLeest…Meijer 2009; Bordyugov et al. 2011; John,Taylor et al. 2014; Pia Rose 2015
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Complex network dynamicsin insects as well
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From cells to networks to organisms
1. Single cell rhythms: many detailed models but limited single cell data
2. Synchronization: sloppy oscillators useful, coupling phase matters
3. Coupling makes oscillators “strong” (small PRCs, narrow entrainment range)
4. Strong oscillators have flexible entrainment phases
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Some open questions
o How is fine-tuning of periods possible despite molecular noise (e.g. transcriptional bursts)?
o How long delays (6-12 hours needed) are realized?
o What are the most essential switches?
o How do transcriptional feedback loops interact with other oscillators (cell cycle, metabolism, peroxiredoxins)?
o Where are the feedbacks in the cyanobacterial clock?
o How to get robust synchronization and entrainment instead of splitting and chaos?
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E-boxes, ROR-elements and D-boxes drive clock genes
H Ukai, HR Ueda: Annu Rev Physiol 72: 579-603 (2010)
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Science 19, 349-354, 2012
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D. Bell-Pedersen et al. 2005
Negative feedbacks as a common design principle
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Delayed nuclear import in DrosophilaP. Meyer, L. Saez, M. W. Young, Science 2006
J.C. Dunlap 2006
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FASPS: Per phosphorylation controls delay
Vanselow et al., Genes & Dev, 2006
mass spec.
Entrainment6 days 35/39° C
Constant37° C
0 1 2 3
Rel
. lum
ines
cenc
e PER2 wtFASPS
Time (days)
live cellimaging
+CHX
PER2 wt
β-Actin
FASPS
β-Actin
0 0.5 1 2 3 4 6 8 h
bio-chemistry
Measurements
cellbiology
wild-typeq1 = 0q12 = 0.75
Time (days)0 1 2 3 4 N
orm
aliz
ed c
once
ntra
tion
Model prediction Test of predictionMathematical Model
Time (days)1 2 3 4 5 6
Rel
. lum
ines
cenc
e
solventCKI-7 (50 µM)CKI-7 (200 µM)
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Jin Young Kim et al. 2014
Huge protein complexes regulate transcription
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B. Ananthasubramaniam et al. 2014
Synergy of negative (orange) and positive (blue) regulations
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Take home messages
➢ Delayed negative feedback are necessary but not sufficient for self-sustained oscillation
➢Delays are tuned by transcription, translation, complex formation, phosphorylation, nuclear translocation, stability, epigenetics, …
➢Nonlinearities (switches) can result from cooperativity, positive feedbacks and sequestration
➢Understanding synchronization and entrainment requires oscillator theory (PRCs, limit cycles, Arnold tongues….)
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Negative PER/CRY Loop in Early Models
Forger, Peskin PNAS 2003
Leloup, Goldbeter PNAS 2003
Becker-Weimann Biophys. J. 2004
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Both loops can generate rhythms
Relogio et al. PLoS Comp. Biol. 2011
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by courtesy of Marc Lefranc
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Construction of a core clock model using • representative genes: activators (Bmal1, Dbp)+ early inhibitors (Per2, Rev-Erb)+late inhibitor (Cry1)• experimentally verified binding sites
• known degradation rates
• reasonable delays
• fitted transcriptional parameters
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Regulatory elements in clock gene promoters
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A. Korencic et al., Scientific Reports 4:5782 (2014)
Expression profiles in liver & adrenal gland
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Anja Korencic et al., Scientific Reports 2014
Core-clock model from expression profiles and promoters
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Quantitative agreement of experimental data and simulations with DDEs
Expression profiles were fitted by sinusoidal functions with harmonics
Simulations
etc.
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Multiple loops can generate sustained rhythms
Patrick Pett
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What are the most essential regulations?
• we test ON/OFF configurations of 17 regulations
• OFF: regulatory term is clamped to its mean
• out of 131072 configurations 14125 are rhythmic
• percentage of ON relates to relevance of regulation
• e.g. cyclic activation of Per2 is ON for only 2.99% but Rev-Erb inhibits Cry1 in 94.26%
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Frequencies of Cyclic Regulatory Interactions
Patrick Pett et al. 2015
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„Repressilator genes“ are essential for clock
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Serial repression via Cry1, Rev-Erba, and Per2 confirmed
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Lessons from Modeling
How to design a minimal core clock model?
- Five genes represent most regulations
- DDEs require few parameters
- Transcriptional regulations remain heuristic
- Per/Cry loop, Rev-Erba loop and repressilator possible
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Synchronization of sloppy oscillators
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Sloppy oscillators synchronize wellindependent of specific coupling scheme
S. Bernard, D. Gonze, B. Cajavec, H. Herzel, and A. Kramer: Synchronization-Induced Rhythmicity of Circadian Oscillators in the Suprachiasmatic Nucleus, PLoS Comp. Biol. (2007) 3:e68.
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Damped oscillators synchronize wellindependent of specific coupling scheme
S. Bernard, D. Gonze, B. Cajavec, H. Herzel, and A. Kramer: Synchronization-Induced Rhythmicity of Circadian Oscillators in the Suprachiasmatic Nucleus, PLoS Comp. Biol. (2007) 3:e68.
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B. Ananthasubramaniam, E. D. Herzog, H. Herzel. PLoS Comp. Biol. 2014
Coupling phase controls synchronization
Implications for dual role of GABA (J. Evans, Neuron 2013) and synchrony of neonatal versus adult SCN slices (Honma, Nature Communications 2013)
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Coupling can even synchronize Cry-DKO neonatal SCN
D. Ono, S. Honma, K. HonmaNature Communications 2013
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I.T.Tokuda et al. Biophys J. 2015
Synchronization of noisy oscillators (WT and DKO)
CV about 1
CV above 1
Better sync for WT
Coupling strengthenhances sync
Coupling phasematters strongly
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The environmental external oscillator entrains our internal oscillator
(the circadian clock)
Zeitgeber
LightTemperatur
eFood
…
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The organization of the circadian system
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Light synchronizesthe clock
Regulation ofphysiology and behavior
Clock genes(e.g. Period2)
Positiveelements
activation
nucleus
SCN-neuron
Negativeelements
inhibition
Synchronization ofperipheral clocks
The system
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The circadian oscillator
Circadian rhythm
Oster et al., 2002
Feedback loopsOscillations
Reppert and Weaver, 2001