nutrients growth & division repellants movement

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1 Network Dynamics and Cell Physiology John J. Tyson Department of Biological Sciences & Virginia Bioinformatics Institute

2 Outline 1. Cell Signaling: Physiology 2. Cell Signaling: Molecular Biology 3. Chemical Kinetics 4. Sniffers, Buzzers & Toggles 5. Bistability & Oscillations in Frog Eggs 6. Dynamical Perspective 7. Example: Fission Yeast Cell Cycle

3 nutrients growth & division repellants movement hormones damage heat shock gene expression death

4 Bacteria Glucose 1 Lactose lactose metabolizing enzymes 0 0

5 Fission Yeast 7 m 14 m Wild type Mutant (wee1 )

6 Fibroblast Growth Factor Cell-Cell Contact PROLIFERATION Extracellular Matrix

7 Programmed Cell Death Fibroblast

8

9 Suprachiasmatic Nucleus 12hL:12hD Activity Body temp

10 Outline 1. Cell Signaling: Physiology 2. Cell Signaling: Molecular Biology 3. Chemical Kinetics 4. Sniffers, Buzzers & Toggles 5. Bistability & Oscillations in Frog Eggs 6. Dynamical Perspective 7. Example: Fission Yeast Cell Cycle

11 Signal Transduction Network Hanahan & Weinberg (2000)

12 Cyclin Cdk Cdk Cyclin Cdk P Cdk Cyclin C K I Cdk Cyclin C K I Each icon represents a chemical species. Each arrow represents a chemical reaction that occurs at a certain rate. MPF = Cyclin M-phase Promoting Factor

13 1. Synthesis X(t) = [cyclin] dx = k, X(0) = X dt Xt () = X + kt Estimate k 1 from the red data: 40 Cyclin (nm) Interphase arrested Felix et al. (1990) Nature 346:379, Fig Metaphase released Tang et al. (1993) EMBO J 12:3427, Fig Time (min)

14 dx dt 2. Degradation = k X, X (0) = X 2 0 X ( t) = X e 0 k t e k 21/2 t X ( t ) = X = X e = X k21/2 t 1/ ln2 0.7 = t1/2 = k k k 21/2 t 2 e, or 2 2 Estimate k 2 from the blue and green data above. How can it be that cyclin has different half-lives in different phases of the cell cycle?

15 3. Dimerization X(t) = [cyclin], C(t) = [Cdc2], M(t) = [dimer], dm = kc 3 () t X () t = k 3( C 0 M )( X 0 M ), M (0) = 0 dt C X (1 e ) M t k C X α t 0 0 () =, where α = 3( 0 0) α t C0 X 0e Estimate k 3 from the data below, given that C 0 = 100 nm. 40 Dimers (nm) Kumagai & Dunphy (1995) Mol Biol Cell 6:199, Fig. 3B Time (min)

16 4. Synthesis and Degradation dx dt = k k X, X (0) = 0, 1 2 k k k2 t ( ) 1 X ( t) = 1 e 2 1 Note: as t, X () t (stable steady state) k k 2 From your previous estimates of k 1 and k 2, estimate the steady state concentrations of cyclin in interphase and late anaphase (end of mitosis). Phase k 1 k 2 X ss Interphase Anaphase

17 This case is unusual in that one can write down an exact solution of the differential equation in terms of elementary functions. When an exact solution is not available, one can always take other approaches Numerical X ( t + t) X ( t) k1 k 2 X ( t) t X ( t + t) X ( t) + ( k k X ( t)) t 1 2 This always works, but doesn t provide much insight. Graphical dx/dt k 1 + k 1 / k 2 X dx/dt = 0 at X = k 1 /k 2, called a steady state solution X(t) approaches k 1 /k 2 for t large ( stable steady state)

18 Outline 1. Cell Signaling: Physiology 2. Cell Signaling: Molecular Biology 3. Chemical Kinetics 4. Sniffers, Buzzers & Toggles 5. Bistability & Oscillations in Frog Eggs 6. Dynamical Perspective 7. Example: Fission Yeast Cell Cycle

19 Gene Expression S R rate (dr/dt) 5 rate of degradation S=3 S=2 S=1 response (R) 0.5 linear dr ks kr, d rate of synthesis R = 1 2 t = 1 ss k2 R ks signal (S) Signal-Response Curve

20 Protein Phosphorylation R ATP P i Kinase ADP RP H 2 O Phosphatase 0 rate (drp/dt) response (RP) RP Signal (Kinase) 1 R 0

21 Protein Synthesis: Positive Feedback S R rate (dr/dt) S=16 S=8 S=0 response (R) 0.5 EP E R signal (S)

22 Example: Fuse response (R) 0.5 dying 0 living 0 10 signal (S) Apoptosis (Programmed Cell Death)

23 Outline 1. Cell Signaling: Physiology 2. Cell Signaling: Molecular Biology 3. Chemical Kinetics 4. Sniffers, Buzzers & Toggles 5. Bistability & Oscillations in Frog Eggs 6. Dynamical Perspective 7. Example: Fission Yeast Cell Cycle

24 S = Total Cyclin MPF Wee1 MPF-P (inactive) Cdc25-P Cdc25 Cdc25-P MPF 1 1 Cdc25-P 0.5 response (MPF) MPF signal (cyclin)

25 Solomon s protocol for cyclin-induced activation of MPF Cyclin Cell 63:1013 (1990) centrifuge Ca 2+ M cytoplasmic extract Cycloheximide Cdk1 Cyclin pellet

26 Threshold 120 CDK activity Solomon et al. (1990) Cell 63:1013. Novak & Tyson (1993) J. Cell Sci. 106: Cyclin (nm) Sha et al., PNAS 100: (2003) Pomerening et al., Nature Cell Biology 5: (2003)

27 Testing Thresholds in Cycling Extracts Testing activation threshold for Mitosis I Mitosis I MPF activity D90Cyclin B1 and 100 µg/ml CHX Interphase time Testing inactivation threshold for Mitosis I 100 µg/ml CHX Mitosis I D90Cyclin B1 Interphase Interphase

28 The activation threshold for Mitosis I is between 32 and 40 nm. D90 cyclin B (nm) : min 90 min M The inactivation threshold for Mitosis I is between 16 and 24 nm. D90 cyclin B (nm) : min 140 min M M M

29 cyclin synthesis APC cyclin degradation Cdc25 MPF Cdc25-P MPF-P (inactive) 1 MPF cyclin

30 If knock-out positive feedback loop, then oscillations become faster and smaller amplitude With + feedback Without + feedback Figure 4. Pomerening, Kim and Ferrell

31 References Tyson, Chen & Novak, Network dynamics and cell physiology, Nature Rev. Molec. Cell Biol. 2:908 (2001). Tyson, Csikasz-Nagy & Novak, The dynamics of cell cycle regulation, BioEssays 24:1095 (2002). Tyson, Chen & Novak, Sniffers, buzzers, toggles and blinkers, Curr. Opin. Cell Biol. 15:221 (2003). Csikasz-Nagy et al., Analysis of a generic model of eukaryotic cell-cycle regulation, Biophys. J. 90:4361 (2006).

32 Outline 1. Cell Signaling: Physiology 2. Cell Signaling: Molecular Biology 3. Chemical Kinetics 4. Sniffers, Buzzers & Toggles 5. Bistability & Oscillations in Frog Eggs 6. Dynamical Perspective 7. Example: Fission Yeast Cell Cycle

33 Cyclin Cdk Cdk Cdk P Cdk Cyclin Wee1 Cdc25 Cyclin C K I Cdk Cyclin C K I d MPF dt d cyclin dt = k 1 - (k wee + k 2 ) * MPF + k 25 (cyclin - MPF) = k 1 - k 2 * cyclin

34 Phase Plane dx/dt=f(x,y) dy/dt=g(x,y) MPF (x o,y o ) y=g(x o,y o ) t x=f(x o,y o ) t Cyclin

35 One-parameter bifurcation diagram variable (response) y p x x ON t Signal t Response OFF saddle-node saddle-node parameter (signal) stable steady state unstable steady state

36 One-parameter bifurcation diagram variable (response) saddle-node saddle-node Hopf stable steady state unstable steady state parameter (signal)

37 Phase Plane dx/dt=f(x,y) dy/dt=g(x,y) MPF Cyclin

38 Phase Plane dx/dt=f(x,y) dy/dt=g(x,y) MPF Cyclin

39 Phase Plane dx/dt=f(x,y) dy/dt=g(x,y) MPF Cyclin

40 Hopf Bifurcation stable limit cycle slc max x 2 sss uss min p 1

41 Hopf Bifurcation slc x 2 sss uss p 1

42 Second Parameter Second Parameter variable (response) CF Hopf subcritical parameter (signal)

43 Second Parameter variable (response) SL SNIC parameter (signal)

44 SNIC Bifurcation Invariant Circle Saddle-Node on an Invariant Circle saddle SNIC max Limit Cycle x 2 node min p 1

45 Signal-Response Curve = One-parameter Bifurcation Diagram Saddle-Node Supercritical Hopf Subcritical Hopf Cyclic Fold Saddle-Node Invariant Circle

46 Outline 1. Cell Signaling: Physiology 2. Cell Signaling: Molecular Biology 3. Chemical Kinetics 4. Sniffers, Buzzers & Toggles 5. Bistability & Oscillations in Frog Eggs 6. Dynamical Perspective 7. Example: Fission Yeast Cell Cycle

47 G1 cell division 1) Alternation of S phase and M phase. 2) Balanced growth and division. S DNA replication 3) Checkpoints M mitosis G2

48 P Wee1 Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc14 Cdc25 Cdc25 P CycB CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B CycE TFE A CycA CycD CycB CycA TFE I

49 5 S G2 MG1 S G2 MG1 S 4 mass/nucleus 3 2 P Cdk1 CycB 1 Cdk1 CycB CKI 0 Cdh1 Cdc20 Wee1 Cdc Time (min)

50 Mutants in Fission Yeast Gene Viable? Trait cdc2 - No block in G2 cdc13 - No block in G2 rum1 - Yes sterile ste9 - Yes sterile slp1 - Yes wee1 - Yes small cdc25 - No block in G2 cdc2 OP Yes wt cdc13 OP Yes wt rum1 OP No endoreplic. ste9 OP Yes wt wee1 OP Yes large cdc25 OP Yes small wee1 - rum1d No extremely small wee1 - cdc25d Yes quantized cycles wee1 - cdc25 OP No cut wee1 OP cdc25 - No block in G2

51 P Wee1 mass/nucleus 1 Cdc20 Cdc2/Cdc P CycB Wee1 S/G2 Cdc14 Cdc25 Cdc14 M P CycB TFB A Cdc2/Cdc13 TFB I 0.1 M APC APC-P Cdc mass/dna Cdc25 mass/dna CKI 10 0 CycB 10-1 M CycD CycE TFI I CycA CycD CKI Cdc2/Cdc Cdh1 TFI A CKI CycE 10-4 CKI CycA G1 Cyc E,A,B CycE TFE A mass/dna CycA CycD CycB CycA TFE I

52 3.0 M 0.8 Cdk1:CycB G1 SN 3 SN 2 Hopf SN 1 S/G2 SNIC mass/nucleus

53 P Wee1 mass/nucleus Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc14 Cdc25 Cdc25 P CycB CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B CycE TFE A CycA CycD CycB CycA TFE I

54 1.2 wee1d M Cdk1:CycB S/G2 0 G mass/nucleus

55 P Wee1 mass/nucleus Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc14 Cdc25 Cdc25 P CycB CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B CycE TFE A CycA CycD CycB CycA TFE I

56 The Start module is not required during mitotic cycles 3.0 ckid M 0.8 Cdk1:CycB G1 S/G mass/nucleus

57 P Wee1 Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc14 Cdc25 Cdc25 P CycB CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B CycE TFE A CycA CycD CycB CycA TFE I

58 2.0 ckid wee1 ts Unbalanced Growth and Division is Lethal! Cdk1:CycB M 0 G1 S/G mass/nucleus