Network Dynamics and Cell hysiology John J. Tyson Dept. Biological Sciences Virginia Tech
Collaborators Budapest Univ. Techn.. & Econ. Bela Novak Attila Csikasz-Nagy Andrea Ciliberto Virginia Tech Kathy Chen Jill Sible
A little history 1970 s Belousov-Zhabotinsky BrO 3- +CH 2 (COOH) 2 Br - +CO 2 + Fe 2+ Fe 3+ BrCH(COOH)2 ½ C 6 H 12 O 6 Yeast Glycolysis NAD NADH C 3 H 4 O 3 C 3 H 6 O 3 Higgins, rigogine general principles of kinetics & thermo. Hess, Noyes specific mechanisms of oscillations
In this manner, the class of chemical switching networks will be promising candidates for a possible new technology of chemical reaction systems.
The Cell s Computer Hanahan & Weinberg (2000)
Wee1 TFB A Wee1 TFB I AC AC- Cdc25 Cdc25 Cdh1 TFI I Cdh1 TFI A Cyc E,A,B TFE A TFE I
Machine-readable form d[c ycb ] d t ' ( ) = k + k [T F B ] k + k [C d h 1] [C ycb ] k [C K I][C ycb ] ' 1 1 2 2 3 synthesis degradation binding k [W ee1 ][C ycb ] + k [C dc25][c ycb ~ ] 4 5 phosphorylation dephosphorylation ' ( 6 + 6 )( T ) d[c dc2 5] k k [C ycb ] [C dc25] [C dc25] k 7 [ ase][c dc2 5] = d t J + [C dc25] [C dc25] J + [C d c25] 6 T 7 activation inactivation
M-phase G1 G2 S-phase
Wee1 TFB A Wee1 TFB I AC AC- Cdc25 Cdc25 Network Motifs! Cdh1 TFI I Cdh1 TFI A Cyc E,A,B TFE A TFE I
Gene Expression S R rate (dr/dt) 5 rate of degradation S=3 S=2 S=1 response (R) 0.5 linear dr k S k R, d rate of synthesis 0 0 0.5 1 R = 1 2 t = 1 ss k2 R k S 0 0 1 2 3 signal (S) Signal-Response Curve
rotein hosphorylation R AT i Kinase AD R H 2 O hosphatase 0 rate (dr/dt) 2 1 1.5 1 0.5 0.25 2 response (R) 1 0.5 0 0 0.5 1 R 1 R 0 0 1 2 3 Signal (Kinase) Buzzer Goldbeter & Koshland, 1981
rotein Synthesis: ositive 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 E E 0.1 Closed 0 0 0.5 R 0 0 10 signal (S) Bistability Fuse Griffith, 1968
Coupled Buzzers S = R total R R E 1 0.5 S=0.5 S=1 S=1.5 response (R) 1 0.5 SN SN E E 0 0 0.5 1 1.5 R 0 0 1 2 signal (S) Bistability Toggle
response (MF) 1 0.5 metaphase Frog egg 0 interphase 0 1 2 signal (cyclin) S = Total Cyclin Wee1 MF = MF MF- (inactive) Cdc25 Cdc25-
MF activity depends on total cyclin concentration and on the history of the extract Cyclin concentration increasing MF activity 14 12 10 8 6 4 2 0 0 6 12 18 24 30 60 nm cyclin B I M Cyclin concentration decreasing inactivation threshold at 90 min MF activity 14 12 10 8 6 4 2 0 Wei Sha & Jill Sible (2003) 0 6 12 18 24 30 60 nm cyclin B bistability
1 Oscillations MF 0.5 response (MF) 1 Hopf Hopf sss uss sss 0 0.0 0.5 signal (rate of cyclin synthesis) cyclin synthesis Cdc25 0 0 1 2 AC MF Cdc25- cyclin cyclin degradation MF- (inactive)
If knock-out positive feedback loop, then oscillations become faster and smaller amplitude With + feedback Without + feedback Figure 4. omerening, Kim and Ferrell
Wee1 TFB A oscillator Wee1 TFB I AC AC- bistable switch Cdc25 Cdc25 Cdh1 bistable switch TFI I Cdh1 TFI A Cyc E,A,B bistable switch TFE A oscillator TFE I
Wee1 Wee1 Cdc25 Cdc25 TFB A TFB I AC AC- Cdh1 TFI I Cyc E,A,B TFE A Fission Yeast Cdh1 TFI A TFE I
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Nature, Vol, 256, No. 5518, pp. 547-551, August 14, 1975 Genetic control of cell size at cell division in yeast aul Nurse Department of Zoology, West Mains Road, Edinburgh EH9 3JT, UK wild-type wee1
Wee1 TFB A Wee1 TFB I AC AC- Cdc25 Cdc25 Cdh1 TFI I Cdh1 TFI A Cyc E,A,B TFE A TFE I
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d T dt = k 1. M - (k 2 ' + k 2 ". Ste9 +k2'". Slp1 A ). T dste9 = k dt 3 '. 1 - Ste9 J 3 + 1 - Ste9 - (k 4'. SK + k. 4 ). Ste9 J 4 + Ste9 d Rum1 T dt = k 11 - (k 12 + k 12 '. SK + k 12 ". ). RUM1 T dslp1 A dt = k. 7 IE. Slp1 T - Slp1 A - k J 7 + Slp1 T - Slp1. Slp1 A 8 - k A J 8 + Slp1. 6 Slp1 A A? dm dt = µ. M?
Thanks to James S. McDonnell Found. DARA
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).
"!! DNA mrna rotein TACCCGATGGCGAAATGC... AUGGGCUACCGCUUUACG... Met -Gly -Tyr -Arg -he -Thr... Enzyme AT - AD Reaction Network Cell hysiology E 1 E X Y 3 E 4 Z E 2.!!"
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)&/ "!- &!1*! 2! d T dt = k 1. M - (k 2 ' + k 2 ". Ste9 +k2'". Slp1 A ). T dste9 = k dt 3 '. 1 - Ste9 J 3 + 1 - Ste9 - (k 4'. SK + k. 4 ). Ste9 J 4 + Ste9 d Rum1 T = k dt 11 - (k 12 + k 12 '. SK + k 12 ". ). RUM1 T dslp1 A = k dt. 7 IE. Slp1 T - Slp1 A - k J 7 + Slp1 T - Slp1. Slp1 A 8 - k A J 8 + Slp1. 6 Slp1 A A dm dt = µ. M!$ 3!!! & "!
Machine-readable form d[c yca ] d t = k + k [E 2F] k [C yca ] k [C K I][C yca ] ' 1 1 2 5 synthesis degradation binding d[c ycb ] d t ' ( ) = k + k [T F B ] k + k [C d h 1] [C ycb ] k [C K I][C ycb ] ' 3 3 4 4 5 synthesis degradation binding ' ' ( k 6 + k 6 )( T ) ( k 7 + k 7 ) d[c dh1] [C dc20] [C dh1] [C dh1] [C lb5] [C dh1] = d t J + [C dh1] [C d h1] J + [C dh1] 6 T 7 activation inactivation
Change parameters S R rate (dr/dt) 0.6 0.5 0.4 0.3 0.2 S=16 S=8 S=0 response (R) 1 0.5 SN SN E E 0.1 0 0 0.5 R 0 0 1 2 signal (S) Toggle Griffith, 1968