Network Dynamics and Cell Physiology

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

Outline • Cell Signaling: Physiology • Cell Signaling: Molecular Biology • Chemical Kinetics • Sniffers, Buzzers & Toggles • Bistability & Oscillations in Frog Eggs • Dynamical Perspective • Example: Fission Yeast Cell Cycle

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

Glucose Lactose Bacteria 1 lactose metabolizing enzymes 0 0

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

PROLIFERATION Fibroblast Growth Factor Cell-Cell Contact Extracellular Matrix

Fibroblast Programmed Cell Death

http://www.youtube.com/watch?v=I_xh-bkiv_c&NR=1

Suprachiasmatic Nucleus 12hL:12hD Activity Body temp

Signal Transduction Network Hanahan & Weinberg (2000)

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

1. Synthesis X(t) = [cyclin] Estimate k1 from the “red” data:

2. Degradation Estimate k2 from the “blue” and “green” data above. How can it be that cyclin has different half-lives in different phases of the cellcycle?

3. Dimerization X(t) = [cyclin], C(t) = [Cdc2], M(t) = [dimer], Estimate k3 from the data below, given that C0 = 100 nM.

4. Synthesis and Degradation From your previous estimates of k1 and k2, estimate the steady stateconcentrations of cyclin in interphase and late anaphase (end of mitosis).

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 = k1/k2, called a “steady state” solution X(t) approaches k1/k2 for t large (“stable” steady state)

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

2 1.5 response (RP) 1 rate (dRP/dt) 0.5 0.25 RP Signal (Kinase) 1 R 0 Protein Phosphorylation Kinase ADP ATP R RP H2O Pi Phosphatase

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

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

Cdc25-P MPF Wee1 S = Total Cyclin MPF MPF-P (inactive) Cdc25-P Cdc25 1 Cdc25-P response (MPF) 0.5 0 0 0.5 1 1.5 signal (cyclin) MPF

Cyclin Cdk1 Cyclin M Solomon’s protocol for cyclin-induced activation of MPF Cell 63:1013 (1990) Ca2+ centrifuge Wee1 Cyclo- heximide Cdk1 Cdc25 cytoplasmic extract pellet

Threshold Solomon et al. (1990) Cell 63:1013. CDK activity Novak & Tyson (1993) J. Cell Sci.106:1153 Cyclin (nM) Sha et al., PNAS 100:975-980 (2003) Pomerening et al., Nature Cell Biology 5:346-351 (2003)

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

The activation threshold for Mitosis I is between 32 and 40 nM. D90 cyclin B (nM) : 0 16 24 32 40 0 min 90 min M The inactivation threshold for Mitosis I is between 16 and 24 nM. D90 cyclin B (nM) : 0 16 24 32 40 60 min 140 min M M M

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

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

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,” BioEssays24:1095 (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).

Wee1 Cdc25 d MPF dt = k1 - (kwee + k2) * MPF + k25 (cyclin - MPF) = k1 - k2 * cyclin d cyclin dt

Dy=g(xo,yo) Dt Dx=f(xo,yo) Dt dx/dt=f(x,y) Phase Plane dy/dt=g(x,y) (xo,yo) MPF Cyclin

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

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

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

x2 max slc uss sss min p1 Hopf Bifurcation stable limit cycle

x2 Hopf Bifurcation slc uss sss p1

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

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

Saddle-Node on an Invariant Circle x2 SNIC max max saddle min node p1 SNIC Bifurcation Invariant Circle Limit Cycle

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

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

Wee1 P Cdc20 Cdc14 TFBA Wee1 TFBI CycB P APC-P APC Cdc14 Cdc25 P Cdc20 CycB Cdc14 Cdh1 Cdc25 CycD CKI CycB CycE TFII Cdh1 CycD CycA TFIA CKI CKI CKI CycA CycE Cyc E,A,B Cdc20 CycA CycE TFEA CycB CycD CycA TFEI

P Cdk1 CycB Cdk1 CycB 0 50 100 150 200 250 300 S G2 M G1 S G2 M G1 S 5 mass/nucleus 4 3 2 1 0 CKI Cdh1 Cdc20 Wee1 Cdc25 Time (min)

Mutants in Fission Yeast

Network Dynamics and Cell Physiology