Network Dynamics and Cell Physiology John J. Tyson Department of Biological Sciences & Virginia Bioinformatics Institute
Signal Transduction Network Hanahan & Weinberg (2000)
Gene Expression Signal-Response Curve 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 0 0 0.5 1 R 1 2 t = 1 ss k2 R ks 0 0 1 2 3 signal (S) = Lever
Protein Phosphorylation R ATP P i Kinase ADP RP H 2 O Phosphatase 0 rate (drp/dt) 2 1 1.5 1 0.5 0.25 2 response (RP) 1 0.5 0 0 0.5 1 RP 1 R 0 Goldbeter & Koshland (1981) 0 1 2 3 Signal (Kinase) Buzzer
Protein Synthesis: Positive Feedback S R rate (dr/dt) 0.6 0.5 0.4 0.3 0.2 S=16 S=8 S=0 response (R) 0.5 Open EP E 0.1 Closed 0 0 0.5 R 0 0 10 signal (S) Griffith (1968) Bistability Fuse
S = Total Cyclin MPF Wee1 MPF-P (inactive) Cdc25-P 1 0.5 Cdc25 Cdc25-P 0 0 1 2 3 MPF Cdc25-P 1 0.5 response (MPF) 1 0.5 metaphase 0 0 0.5 1 1.5 MPF 0 interphase 0 1 2 signal (cyclin)
Solomon s protocol for cyclin-induced activation of MPF Cyclin Solomon et al. (1990) Cell 63:1013. centrifuge Ca 2+ M Cycloheximide Cdk1 Wee1 Cdc25 Cdk1 Cyclin cytoplasmic extract pellet no synthesis of cyclin no degradation of cyclin
Threshold 120 CDK activity 100 80 60 40 Solomon et al. (1990) Cell 63:1013. Novak & Tyson (1993) J. Cell Sci. 106:1153 20 0 0 10 20 30 Cyclin (nm) Sha et al., PNAS 100:975-980 (2003) Pomerening et al., Nature Cell Biology 5:346-351 (2003)
The activation threshold for Mitosis I is between 32 and 40 nm. Δ90 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. Δ90 cyclin B (nm) : 0 16 24 32 40 60 min 140 min M M M
cyclin synthesis APC cyclin degradation Cdc25 MPF Cdc25-P MPF-P (inactive) negative feedback loop 1 MPF 0.5 0 0 1 2 cyclin
Pomerening, Kim & Ferrell Cell (2005)
Dynamical Perspective on Molecular Cell Biology MPF Cyclin Vector Field, Steady State, Bifurcation
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
Phase Plane dx/dt=f(x,y) dy/dt=g(x,y) MPF (x o,y o ) Δy=g(x o,y o ) Δt Δx=f(x o,y o ) Δt Cyclin k 1 / k 2 d cyclin dt = k 1 -k 2 * cyclin
One-parameter bifurcation diagram p x t t Signal Response variable (response) ON OFF saddle-node saddle-node Hopf stable steady state unstable steady state parameter (signal)
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) MPF Cyclin
Hopf Bifurcation
Second Parameter variable (response) saddle-node saddle-node Hopf supercritical parameter (signal)
variable (response) CF Hopf subcritical parameter (signal)
variable (response) SL SNIC parameter (signal)
SNIC Bifurcation Invariant Circle Saddle-Node on an Invariant Circle Limit Cycle
Signal-Response Curve = One-parameter Bifurcation Diagram
Review Molec Genetics Biochemistry Cell Biology Molecular Mechanism Kinetic Equations State Space, Vector Field Attractors, Transients, Repellors Bifurcation Diagrams
The Cell Cycle of Fission Yeast
G1 cell division The cell cycle is the sequence of events whereby a growing cell replicates all its components and divides them more-or-less evenly between two daughter cells... S DNA replication M mitosis G2
P Wee1 mass/nucleus Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc25 Cdc14 Cdc25 P CycB Cdc20 Cdh1 CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B CycE Fission TFE Yeast A CycA Cdc20 CycD CycB CycA TFE I
The mathematical model d[cycb] d t ' " ( ) = k [mass] k + k [Cdh1]+ k [Cdc20] [CycB] k [CKI][CycB] 3 4 4 4 5 synthesis degradation binding ' ' ( k6 + k6 )( T ) ( k7 + k7 ) d[cdh1] [Cdc14] [Cdh1] [Cdh1] [CycB] [Cdh1] = d t J + [Cdh1] [Cdh1] J + [Cdh1] 6 T 7 activation inactivation d[cdc20] d t k [CycB] = k + ' n 1 1 k n n 2 J1 + [CycB] [Cdc20] synthesis degradation
5 S G2 MG1 S G2 MG1 S 4 mass/nucleus 3 2 P Cdk1 CycB 1 Cdk1 CycB CKI 0 Cdh1 Cdc20 Wee1 Cdc25 0 50 100 150 200 250 300 Time (min)
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 rum1δ No extremely small wee1 cdc25δ Yes quantized cycles wee1 cdc25 OP No cut wee1 OP cdc25 No block in G2
P Wee1 mass/nucleus Cdc20 Cdc14 TFB A neg fdbk osc P CycB Wee1 TFB I APC APC-P Cdc14 Cdc25 Cdc14 Cdc25 P CycB Cdc20 Cdh1 bistable switch CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA bistable switch Cyc E,A,B Cdc20 CycE CycD TFE A Fission Yeast CycB CycA CycA TFE I
3.0 M 0.8 Cdk1:CycB 0.4 0 G1 SN 3 SN 2 Hopf SN 1 S/G2 SNIC 0 1 2 3 4 5 mass/nucleus
3.0 Wild type M Cdk1:CycB 0.8 0.4 Balanced Growth and Division 0 G1 S/G2 0 1 2 3 4 5 mass/nucleus
3.0 Wild type M Cdk1:CycB 0.8 0.4 Alternation of S phase and M phase 0 G1 S/G2 0 1 2 3 4 5 mass/nucleus
Nature, Vol, 256, No. 5518, pp. 547-551, August 14, 1975 Genetic control of cell size at cell division in yeast Paul Nurse Department of Zoology, West Mains Road, Edinburgh EH9 3JT, UK wild-type wee1δ
P Wee1 mass/nucleus Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc25 Cdc14 Cdc25 P CycB Cdc20 Cdh1 CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B Cdc20 CycE TFE A CycA CycD CycB CycA TFE I
1.2 wee1δ M Cdk1:CycB 0.8 0.4 0 S/G2 G1 0 1 2 3 4 5 mass/nucleus
P Wee1 mass/nucleus Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc25 Cdc14 Cdc25 P CycB Cdc20 Cdh1 CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B Cdc20 CycE TFE A CycA CycD CycB CycA TFE I
3.0 ckiδ M 0.8 Cdk1:CycB 0.4 0 G1 S/G2 0 1 2 3 4 5 mass/nucleus
P Wee1 Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc25 Cdc14 Cdc25 P CycB Cdc20 Cdh1 CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA Cyc E,A,B Cdc20 CycE TFE A CycA CycD CycB CycA TFE I
2.0 ckiδ wee1 ts Cdk1:CycB 0.8 0.4 M 0 G1 S/G2 0 1 2 3 4 5 mass/nucleus
The Cell Cycle of Budding Yeast
P Wee1 Cdc20 Cdc14 TFB A P CycB Wee1 TFB I APC APC-P Cdc14 Cdc25 Cdc14 Cdc25 P CycB Cdc20 Cdh1 CKI CycB CycD CycE TFI I CycA CycD CKI Cdh1 TFI A CKI CycE CKI CycA mass/nucleus Cyc E,A,B CycE TFE A CycA Cdc20 Growth CycD CycB CycA TFE I
Wild type cells CycB-dependent kinase activity 1e+0 1e-1 1e-2 1e-3 1e-4 G1 S/G2 M MDT= 90 min 120 min 150 min 1e-5 0 1 2 3 4 SNIPER mass
10 1 10 0 10-1 time (min) CycB 10-2 10-3 10-4 10-5 180 150 120 G1 Period 90 60 0 1 2 3 4 cell mass (au.)
cdh1δ ckiδ 1 0.1 0.01 0.001 cdc20δ 1e+2 1e+1 1e+0 1e-1 1e-2 1e-3 1e-4 1e-5 0 1 2 3 4 mass No CycB destruction 0 1 2 3 4 mass CycB-dependent kinase activity lack of one of the G1 enemies: viable CycB-dependent kinase activity 1 0.1 0.01 0.001 cdc14δ 1e+0 1e-1 1e-2 1e-3 1e-4 1e-5 0 1 2 3 4 mass Incomplete CycB destruction mass 0 1 2 3 4
Defects in Exit from Mitosis CycB-dependent kinase activity 10 1 A 10 0 wild-type 10-1 10-2 10-3 10-4 10-5 0 1 2 3 4 cdc20 ts pds1δ 10 1 E 10 0 10-1 10-2 10-3 MDT = 300 min 200 min 150 min 120 min 90 min APC-A cdh1δ 10 1 D 10 0 10-1 10-2 10-3 10-4 D 10-5 10 1 10 0 10-1 10-2 0 1 2 3 4 F CLB2Δdb 10-4 10-3 10-5 10-4 0 1 2 3 4 0 1 2 3 4 5 6 cell mass (au.)
Two-parameter bifurcation diagram Second parameter SNIPER SN SL CF Hopf (sub) BISTABILITY SN Hopf (super) First parameter
cell mass (au.) PHYSIOLOGY WT ckiδ GENETICS Cki synthesis
cell mass (au.) Cdc20 synthesis Cdh1 activation Cdc14 activation Sic1 synthesis cell mass (au.) cell mass (au.) cell mass (au.)
The Dynamical Perspective Molec Genetics Biochemistry Cell Biology Molecular Mechanism Kinetic Equations State Space, Vector Field Attractors, Transients, Repellors Bifurcation Diagrams Signal-Response Curves