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

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

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

Bacteria Glucose Lactose lactose metabolizing enzymes 1 0 0

Fission Yeast 14 mm 7 mm Wild type Mutant (wee1D)

Fibroblast Growth Factor PROLIFERATION Extracellular Matrix Cell-Cell Contact

Fibroblast Programmed Cell Death

Suprachiasmatic Nucleus 12hL:12hD Activity Body temp

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

Hanahan & Weinberg (2000) Signal Transduction Network

Each icon represents a chemical species. Each arrow represents a chemical reaction that occurs at a certain rate. Cyclin MPF = M-phase Promoting Factor

X(t) = [cyclin] 1. Synthesis Estimate k 1 from the “red” data:

2. Degradation 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?

3. Dimerization X(t) = [cyclin], C(t) = [Cdc2], M(t) = [dimer], Estimate k 3 from the data below, given that C 0 = 100 nM.

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). 4. Synthesis and Degradation Phasek1k1 k2k2 X ss Interphase Anaphase

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 This always works, but doesn’t provide much insight. Graphical 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)

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

R S response (R) signal (S) linear S=1 R rate (dR/dt) rate of degradation rate of synthesis S=2 S=3 Gene Expression Signal-Response Curve

R Kinase RP ATP ADP H2OH2O PiPi Protein Phosphorylation RP rate (dRP/dt) Phosphatase response (RP) Signal (Kinase) 1 R 0

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

Example: Fuse response (R) signal (S) dying Apoptosis (Programmed Cell Death) living

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

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

centrifuge Solomon’s protocol for cyclin-induced activation of MPF cytoplasmic extract pellet Ca 2+ M Cyclin Cyclo- heximide Cdk1 Wee1 Cdc25 Cyclin Cdk1 Cell 63:1013 (1990)

Threshold Cyclin (nM) CDK activity Solomon et al. (1990) Cell 63:1013. Novak & Tyson (1993) J. Cell Sci. 106:1153 Pomerening et al., Nature Cell Biology 5: (2003) Sha et al., PNAS 100: (2003)

Testing activation threshold for Mitosis I Interphase Mitosis I  90Cyclin B1 and 100 µg/ml CHX Testing Thresholds in Cycling Extracts Testing inactivation threshold for Mitosis I Interphase Mitosis I  90Cyclin B1 100 µg/ml CHX MPF activity time

 90 cyclin B (nM) : 90 min 0 min 60 min 140 min 0  90 cyclin B (nM) : M MMM The activation threshold for Mitosis I is between 32 and 40 nM. The inactivation threshold for Mitosis I is between 16 and 24 nM.

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

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

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). References

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

Wee1 Cdc25 = k 1 - (k wee + k 2 ) * MPF + k 25 (cyclin - MPF) = k 1 - k 2 * cyclin d MPF dt d cyclin dt

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

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

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

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

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

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

Hopf Bifurcation x2x2 p1p1 stable limit cycle sss uss slc max min

Hopf Bifurcation x2x2 p1p1 sss uss slc

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

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

SNIC Bifurcation Invariant Circle Limit Cycle x2x2 p1p1 node saddle Saddle-Node on an Invariant Circle max min max SNIC

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

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

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

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

mass/nucleus P Cdk1 CycB Cdk1 CycB CKI Cdh1 Cdc20 Wee1 Cdc25 Time (min) SG2MG1S G2MG1S

Mutants in Fission Yeast

P Cdc25 Wee1 P Cdc25 CycB P Cdc20 Cdh1 CKI CycB CKI CycA APC-P APC TFB I TFB A CycE CycD TFE A TFE I Cyc E,A,B CycE TFI A TFI I Cdc20 CKI CycE Cdc14 CycA CycB CycD Cdh1 CycD G1 M S/G2 M mass/nucleus M

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

wee1  mass/nucleus Cdk1:CycB G1 S/G2 M

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

Cdk1:CycB G1 S/G2 M cki  The Start module is not required during mitotic cycles

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

G1 S/G2 M cki  wee1 ts mass/nucleus Cdk1:CycB Unbalanced Growth and Division … is Lethal !