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Systembiologie 9 – Signal Transduction Edda Klipp Sommersemester 2010
Humboldt-Universität zu Berlin Institut für Biologie Theoretische Biophysik
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Modeling of Signal Transduction
Before: Metabolismus Mass transfer Now: Signal transduction - Information transfer Typical Signals: Hormones, pheromones Heat, cold, osmotic pressure concentration of certain substances (K, Ca, cAMP,..) nutrient availability Interactive Animation of MAP Kinase Signal Transduction
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Typical Mechanism “Signal” Activation of receptor at membran
Internalization of signals G-Protein, Phosphorelay Signal transmission Activation of transcription factors mRNA Protein Transcription, Translation, Protein function biochemical response Gen Downregulation of signal
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Yeast Signaling Pathways
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Signaling Pathway Components
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Rezeptors . Simple H + R HR concept: H R KD = HR transmembrane
Ligand Extrazellular space Receptor, Binding site Membrane Rezeptor, zytosolische Domaine Intrazellular space inactive active transmembrane receive signal and transmit it conformation change active or inactive form H - Hormone R - Receptor HR - Hormone-receptor-complex Typical values : KD = M ….10-6 M Simple concept: H + R HR . H R HR KD =
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Receptor, Extended Model
vpi vps vis vsa Ri Rs Ra vsi vas vai vdi vds vda Differential equations Rate expressions ?? Mass action Hill kinetics
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Receptor, Model of Yi et al.
vpi vps Ra vis vsa Ri Rs Ra Number of Molecules vsi vas vdi vds vai vda Rs Time
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G-Proteine: „small G-proteins“
z.B. Ras-Protein GDP GTP GEF GTP GDP v1 + GDP + GTP GDPRas GTPRas v2 GEF – Guanine nucleotide exchange factor GAP – GTPase-activating protein Pi GAP Differential equations Conservation relations
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G-Proteine: „small G-proteins“
GEF or GAP =1 (const.), other varying from 0 to 10 Mass action e.g. Ras-Protein GEF GEF GTPRas GTP GDP GAP v1 GDPRas GTPRas v2 Enzyme concentration Pi GAP Michaelis Menten Differential equations GEF GTPRas GAP Enzyme concentration
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G-Proteins: „small G-proteins“
e.g. Ras-Protein GEF GTPRas GEF GTP GDP GAP v1 GDPRas GTPRas Enzyme concentration v2 Pi GAP „sigmoidal dependence“ „Ultrasensitivity“ „Switch-like regulation“ Differential equations GTPRas Enzyme: GEF
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G-Proteins: „small G-proteins“
e.g. Ras-Protein GTPRas GEF GTP GDP v1 GDPRas GTPRas Enzym: GEF v2 Pi GEF: 0 x GAP x=2.5 x=2.0 x=1.5 GTPRas x=1.0 x=0.5 Zeit
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G-Protein + + b a b a g g b a g Differential equations
GDP b a GTP b a + g g vga active receptor GTPGa GDP b GDP RGS a + g GTP vh0 vh1 GDPGabg Gbg signal slow fast Pi Pi GDPGa Gabg vsr Number of Molecules Gbg GTPGa GDPGa Differential equations Conservation relations Time
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Phosphorelay-System - Transmits individual phosphate groups
high osmolarity ? 1 Pi Pi His i 2 ATP Sln1 Asp Asp ADP Pi 3 His Ypd1 Ypd1-P 4 Ssk1-P Ssk1 Asp 5 Pi Example: Sln1 pathway, Phosphorelay system
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Phosphorelay-System A-P A B B-P C-P C Dependence of
ADP ATP 1 Three component system Dependence of steady state values Of stress strength 0.8 k1 Two components A-P 0.6 A A, B, C One component k2 0.4 B B-P 0.2 k3 1 2 3 4 5 C-P C k1 k4 P Temporal behavior, Stress – no Stress A, B, C Time
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Phosphorelay-System Dynamics Steady State v1 A-P A v2 B B-P v3 C-P C
Concentration, a.u. C B B-P v3 C-P C v4 Time a.u. Steady State 0.001 0.01 0.1 k1=1 Concentration C k1=10 Rate constant k4
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MAP Kinase Cascade = Mitogen activated protein kinase cascade MAPKKKK
inactive MAPKKK active MAPKK inactive MAPKK active MAPK inactive MAPK active Signal
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MAP Kinase Cascade - Equations
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MAP Kinase Cascade - Equations
k – Kinase, p - Phosphatase Steady state Sigmoidale dependence of concentration of activated MAP kinase on concentration of input signal.
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MAPK Cascade: Impact of Kinases and Phosphatase
1.1 0.9 MAPK-PP, a.u. MAPK-PP, a.u. 1.2 0.8 1.3 0.7 1.4 0.6 Time, a.u. Time, a.u. B D p=1 p=0.1 k=5 k=4 p=0.2 k=3 p=0.3 MAPK-PP, a.u. MAPK-PP, a.u. p=0.4 k=2 p=0.5 k=1 Time, a.u. Time, a.u. k – Kinase, p - Phosphatase
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MAP Kinase Cascade – Parameter Dependence
Sigmoide input/output dependence Signal amplification .... k – Kinase, p - Phosphatase Time courses Steady states 0.08 k = 1 0.25 k = 0.64 MAPKKKK=0.1 0.2 0.06 k = 0.36 MAPKP2 MAPKP2(t) k = 0.16 0.15 0.04 0.1 MAPKKKK=0.01 k = 0.04 0.02 0.05 2 4 6 8 10 20 40 60 80 100 Time k/p
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MAPK Cascade: Control Rates P0 1 P1,0 P1 2 3 P2,0 P2 4 5 positive P3,0
6 4 5 positive P3,0 P3 none 6 negative Rates
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MAPK Cascade: Control with complex formation Rates positive none
P0 P1,0 P1 P1X P2,0 P1 P2,0 P2 P2X P3,0 P2 P3,0 P3 P3X positive none with complex formation negative P0 P0P1,0 1 2 P1,0 P1 1 2 3 4 5 6 7 8 9 10 11 12 3 4 P1X P1P2,0 5 6 P2,0 P2 7 8 P2X P2P3,0 9 10 P3,0 P3 12 11 X – phosphatase P3X Rates
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MAPK-Cascade with Feedback and Michaelis-Menten Kinetics: Oscillations
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MAP Kinase Cascade – Scaffolding
Ste11 Ste5 Ste7 Fus3 MAPKKK Scaffold MAPKK MAPK
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MAP Kinase Cascade – Scaffolding
Double Phosphorylation of each protein Ste11 Ste5 Ste7 000 001 002 Fus3 010 011 012 020 021 022 100 101 102 110 111 112 120 121 122 200 201 202 210 211 212 220 221 222
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Quantitative Measures for Signaling
P0 (a) (b) t1 max P1 max v1f P1,0 P1 v1r t1 A1 P1 Concentration, a.u. v2f P2,0 P2 1 v2r v3f P3,0 P3 Time, a.u. v3r Transition time Signal duration Amplitude Heinrich et al., T.A. Mol.Cell, 2002
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Crosstalk & Signal Integration
X – function of amplitude, timing or integral of response Measures of crosstalk Se > Se < 1 Si > 1 Si < 1 Mutual signal inhibition amplification Dominance of extrinsic signal intrinsic signal Signal a Signal b Receptor A Receptor B Target A Target B Pheromone Pathway Filamentous Growth Pathway Crossactivation Mutual signal amplification Crossinhibition Dominance of intrinsic signal Schaber, Kofahl, Kowald & Klipp, 2006, FEBS J.
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Crosstalk (a) a a b b a,b a,b P1A P2A a = P0A b = P0B
Concentration a.u. P3A v1Af v1Bf P1A,0 P1A P1B,0 P1B v1Ar v1Br v2Af v2Bf b P1B b P2A,0 P2A P2B,0 P2B v2Ar v2Br P2B Concentration a.u. P3A P1A P2A P3B v3Af v3Bf P3A,0 P3A P3B,0 P3B v3Ar v3Br P1A a,b P1B a,b ki = 1 ki = 10 P2A P2B Concentration a.u. P3B P3A Time a.u Time a.u
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Crosstalk a b a,b Integrated Response Mutual amplification
P1A a P2A I = Pmax = tmax = Integrated Response a = P0A b = P0B Si(I) = 0.91 Concentration a.u. Se(I) = 0.097 P3A v1Af v1Bf P1A,0 P1A P1B,0 P1B Mutual amplification v1Ar v1Br v2Af v2Bf b I = Pmax = tmax = Maximal Response P2A,0 P2A P2B,0 P2B v2Ar v2Br Concentration a.u. Si(Pmax) = 0.97 P3A P1A P2A Se(Pmax) = 0.34 v3Af v3Bf Mutual amplification P3A,0 P3A P3B,0 P3B v3Ar v3Br Timing of Response P1A a,b ki = 1 ki = 10 P2A I = Pmax = tmax = Si(tmax) = 1.04 Concentration a.u. Se(tmax) = 0.197 P3A Dominance of intrinsic signal Time a.u
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Integration of Signaling Pathways
b Response coefficients of PREs FREs 20 9 5 17 19 10 11 4 21 6 22 2 10 11 4 5 4 -Fus3 phosphorylation in MAPKcascade 6 -repeated Fus3 phosphorylation 10-Kss1 phosphorylation in MAPKcascade 21-Kss1 release from Ste12Tec1 complex 21 18 9 7 12 6 Time/min Time/min
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Putting all together : the Pheromone pathway
MATa-cells MATa-cells
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Putting all together: the Pheromone pathway
MATa-cells
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Pheromone pathway Extracellular space a a Ste2 Plasma membrane Ste2 Gg
Ga Gg Ste20 Gb Ste20 Gb GDP Gb Ste50 Ste11 Cdc24 Cdc24 Cdc42 Ga Ste7 Cdc42 Ste5 Far1 Bem1 Bem1 GTP Fus3 Actin Ga Sst2 Fus3 P GDP Fus3 P Bar1 active Ste12 Dig1 Cdc24 Cdc24 Far1 Far1 P Dig2 Ste12 Kss1 P Dig1 Cdc28 Dig2 Ste12 Kss1 Cln Cytoplasm Nucleus
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Pheromone pathway Extracellular space a a Ste2 Plasma membrane Ste2 Gg
Ga Gg Ste20 Gb Ste20 GDP Gb Ste50 Gb Ste11 Cdc24 Ste7 Cdc42 Ga Ste5 Cdc24 Cdc42 Far1 Bem1 GTP Fus3 Bem1 Ga Sst2 Actin Fus3 P GDP Fus3 P Bar1 active Ste12 Cdc24 Cdc24 Dig1 Far1 Far1 P Dig2 Ste12 Kss1 P Dig1 Cdc28 Dig2 Ste12 Kss1 Cln Cytoplasm Nucleus
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Pheromone pathway Extracellular space a a Ste2 Plasma membrane Ste2 Gg
Far1 Actin Gg Ste20 Cdc42 Gb Cdc24 Bem1 Ga Gg Ste20 Gb GDP Gb Ste50 Ste11 Cdc24 Ste7 Cdc42 Ga Ste5 Bem1 GTP Fus3 Ga Sst2 Fus3 P GDP Fus3 P Bar1 active Ste12 Cdc24 Dig1 Cdc24 Far1 Far1 P Dig2 Ste12 Kss1 P Dig1 Cdc28 Dig2 Ste12 Kss1 Cln Cytoplasm Nucleus
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Pheromone pathway Extracellular space a a Ste2 Plasma membrane Ste2 Gg
Far1 Actin Gg Ste20 Cdc42 Gb Cdc24 Bem1 Ga Gg Ste20 Gb GDP Gb Ste50 Ste11 Cdc24 Cdc42 Ga Ste7 Ste5 Bem1 GTP Fus3 Ga Sst2 GDP Fus3 P Fus3 P Bar1 active Ste12 Cdc24 Dig1 Cdc24 Far1 Far1 P Dig2 Ste12 Kss1 P Dig1 Cdc28 Dig2 Ste12 Kss1 Cln Cytoplasm Nucleus
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Pheromone pathway: structural parts
Ste2 Plasma membrane Receptor activation G protein cycle Gbg MAPK scaffold Signaling cascade Fus3 Sst2 Bar1 Ste12 Far1Cdc28 Gene expression Complex formation
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Pheromone pathway: structural parts
Ste2 Plasma membrane Receptor activation G protein cycle Gbg MAPK scaffold Signaling cascade Fus3 Sst2 Bar1 Ste12 Far1Cdc28 Gene expression Complex formation Yu et al., Nature, 2008
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Pheromone pathway: time courses
In comprehensive model: regulatory feedback loops are considered mutant phenotypes can be investigated Graded response depending on concentration of a-factor 1 Cell Cycle arrest 0.8 Far1-Cdc28 0.6 Fus3PP Relative Concentration 0.4 Ste12active 0.2 Polarized growth Gbg-Far1 10-3 10-2 10-1 100 101 102 103 104 a-factor / nM Kofahl & Klipp, Yeast, 2004
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Pheromone pathway: time courses
Gbg Fus3-PP Overexpression Ga sst2D Gb defect in binding Ga Sst2 mutant Overexpression Gbg Sst2 gain of function
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Yu & Brent et al.: Experimental Data
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Yu & Brent et al.: Experimental Data
DoRA – Dose Response Alignment
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Yeast Cell as an Osmometer
Yeast cells shrink upon osmoshock Stress adaptation requires glycerol accumulation. MAPK Hog1 is considered a key player. Serge Pelet, ETH, Zürich Eriksson, Lab on Chip, 2006
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Osmotic Stress Response
Construct network from literature data and experts‘ knowledge High osmolarity Study properties of small modules, e.g. MAPK cascade, G protein cycles, … Systems equations (Set of ODEs) r – number of reactions Si – metabolite concentrations vj – reaction rates nij – stoichiometric coefficients Network properties Individual reaction properties MAPK cascade Phosphorelay Gene regulation Metabolism Sln1 Turgor Fps1 MKKK-P MKK-PP MKK MK-PP MK k p MKKKK MKKK k/p=1 k/p=2 k/p=3 k/p=4 k/p=5 0.9 0.8 0.7 0.6 Time, a.u. MAPK-PP, a.u. Parameter change Amplitude Duration Collect experimental data (time series!!!) Estimate model parameters Ypd1 Ssk1 Ssk2 Glycerol Simulate: Agreement of model/experiment? Pbs2 Protein Hog1 mRNA Sensitivity analysis Prediction of hitherto untested scenarios Deletion mutants Compound overexpression New experimental scenarios Transcriptome data – mRNA levels Proteome data – phosphorylation, concentration changes Metabolome data – concentration changes
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Osmostress Response – Full Model
Klipp, Nordlander, Krüger, Gennemark & Hohmann, Nature Biotechn, 2005
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Two Pathways for Stress Osmotic Response
Osmotic stress High osmolarity A Sln1 Turgor Fps1 Gpd1 WT Ypd1 Concentration, relative mRNA Hog1P2 Ssk1 Ssk2 Glycerol Ssk1 Pbs2 Protein Time / min Hog1 mRNA Hog1P2 Time / min wild type Fps1 open Ptp2 over Fps open+Ptp2 over mRNA Glycin Concentration, relative Protein A Gpd1D Fps1 mutant Klipp et al.,Nature Biotechn, 2005
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Osmotic stress model: Test cases
Repeated osmostress High osmolarity Single 15 min 30 min 60 min Sln1 Turgor Fps1 mRNA, relative Ypd1 Ssk1 Time/min Ssk2 Glycerol Pbs2 Protein Single 15 min 1.5 30 min x Hog1 mRNA x 60 min 1. ó ÷ Ÿ Ÿ mRNA, relative Ÿ x Ÿ x 0.5 Ÿ Ÿ Ÿ Ÿ Ÿ ÷ Ÿ Ÿ Ÿ Ÿ Time/min 30 60 90 120 Cells are competent to respond to a second shock. Klipp et al.,Nature Biotechn, 2005
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Osmotic stress response: What is the impact of specific components over time ?
High osmolarity Time-dependent Response Coefficients Related to Glycerol Concentration Sln1 Turgor Fps1 mRNA and protein production Ypd1 Closure of Fps1 Ssk1 Glycerol influx Ssk2 Glycerol Strength of osmoshock Hog1 nuclear import Inhibition of Sln1 Hog1 phosphorylation Pbs2 Protein Ssk1 dephosphorylation Hog1 mRNA Time / min Time / min Response coefficients Sln1 phosphorylation Glycerol concentration Hog1 nuclear export Hog1 dephosphorylation Glycerol export mRNA degradation Ingalls & Sauro, JTB, 2003 Time / min Time / min
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Signaling Pathways in Yeast
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Model Selection: Sho branch I
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Model Selection: Sho branch II
Different architectures – which one explains data best?
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Model Selection: Sho branch III
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Model Size – Skeleton Model
High osmolarity MAPK cascade Phosphorelay Gene regulation Metabolism Sln1 Turgor Fps1 Osmolarityex Turgor Glycerol Ypd1 Ssk1 Fps1 Ssk2 Glycerol Pbs2 Protein Hog1P2 mRNA Hog1 mRNA
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Oscillatory Input – Oscillatory Output
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Oscillatory Input – oscillatory output
x – intracellular osmotic pressure y – nuclear Hog1
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Oscillatory Input – oscillatory output
x – intracellular osmotic pressure y – nuclear Hog1
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Simplified, yet Comprehensive Model of Osmotic Stress Response
Zi et al., PLoS ONE, 2010 Data from Mettetal et al., Science, 2008
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Signal Response Gain
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Glycerol Accumulation Depends on Stress and Nutritional Conditions
Glucose Glycerol Glycerol Time Time More stress, stronger response More glucose, stronger response Glucose stress More stress, slower response More glucose, faster response
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Flows Influencing Glycerol
Total Production Net Production Transcriptionally regulated Glycerolflux Volume-regulated Export Time
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Systembiologie Systemische Betrachtung von biologischen Sachverhalten und Prozessen Zusammenspiel von Experiment und Theorie – „iterative cycle“ Häufig: Erzeugung, Analyse und Interpretation großer Datenmengen Immer öfter: gezielte Erhebung von Daten zur Modellierung Modellierung: - verschiedene Modellierungsansätze haben ihre Stärken und Schwächen - ein Sachverhalt kann mit unterschiedlichen Modellen beschrieben werden - kein sinnvolles Modell ohne sinnvolle Fragestellung
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Signal-Motive S – Signal, R – Response Kinetik Steady State Response S
linear linear R Michaelis-Menten hyperbolic sigmoid Response R (arbitrary units) hyperbolic linear Signal S (arbitrary units) Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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S – Signal, R – Response Kinetik Steady State Response Signal-Motive
One loop S linear hyperbolic R0 R Michaelis-Menten sigmoid sigmoid Response R (arbitrary units) hyperbolic linear Signal S (arbitrary units) Goldbeter-Koshland-Funktion Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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S – Signal, R – Response Kinetik Steady State Response Signal-Motive
Two loops linear S sigmoid R0 R1 R sigmoid Response R (arbitrary units) hyperbolic linear Signal S (arbitrary units) Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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S – Signal, R – Response Perfect adaptation Signal-Motive
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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S – Signal, R – Response Mutual activation Signal-Motive
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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S – Signal, R – Response Mutual inhibition Signal-Motive
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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Negative feedback: homeostasis
Signal-Motive S – Signal, R – Response Negative feedback: homeostasis Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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Negative feedback: oscillations
Signal-Motive S – Signal, R – Response Negative feedback: oscillations Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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S – Signal, R – Response Activator – Inhibitor Signal-Motive
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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Substrate-depletion oscillator
Signal-Motive S – Signal, R – Response Substrate-depletion oscillator Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
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