How cells make decisions?

The cell is a (bio)chemical computer Information Processing System Hanahan & Weinberg (2000) External signals outputs

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Signal transduction networks Hanahan & Weinberg (2000) p21 Smad MAPK MKK MAPK-P PP

‘Birth control’ for proteins d [protein] dt = synthesis - degradation DNA RNA protein transcription factor transciption translation

Gene expression R S k1k1 k2k2 S = mRNA R = protein response (R) signal (S) linear synthesisdegradation S=1 3 2 R rate (dR/dt) degradation synthesis Signal-response curve

Protein phosphorylation-dephosphorylation

Michaelis-Menten enzyme kinetics since [E o ] = [E] + [ES]

Protein phosphorylation R S RP ATP ADP H2OH2O PiPi k1k1 k2k2 response (RP) signal (S) sigmoidal phosphorylation dephosphorylation R 0 1 rate (dRP/dt) RP dephospho- rylation phospho- rylation ‘Buzzer’ zero order ultrasensitivity Goldbeter & Koshland, 1981 Signal-response curve graded and reversible

Multiple phosphorylation RRP RP 2 RP n …… kpkp kpkp for n=2 where K=k/p

n=2 R RP 2 K=k/p n=3 R RP 3 K=k/p n=4 R RP 4 K=k/p Hill equation: Multiple phosphorylation

Coupling of modules

Perfect adaptation S X R time adapted R S X k1k1 k2k2 k3k3 k4k4 Two linear modules R rate (dR/dt) synthesis degradation Response is independent of Signal

Feed-forward loop S R X S R X R increases for S increase R decreases for S decrease R decreases for S increase R increases for S decrease

Feed-forward loop with two buzzers X XAXA RARA R + + S RARA S XAXA Cock and fire

R’R S k1k1 k2k2 k3k3 k0k0 Another way to get perfect adaptation

R’R S k1k1 k2k2 k3k3 k0k0 The same principle, different deployment swimming (counter-clockwise) tumbling (clockwise) Bacterial chemotaxis

Feedback controls

response (R) signal (S) mutual activation R S EP E k1k1 k0k0 k2k2 k3k3 k4k4 R rate (dR/dt) synthesis degradation Linear module & buzzer Protein synthesis: positive feedback ‘Fuse’ response (R) signal (S) S crit2 S crit1 ‘Toggle’ switch bistability closed open

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

The lac operon (‘toggle’ switch) S (extracellular lactose) R S EP E k1k1 k0k0 k2k2 k3k3 k4k4 R (intracellular lactose) EP

Nature 427, (19 February 2004) Multistability in the lactose utilization network of Escherichia coli ERTUGRUL M. OZBUDAK 1,*, MUKUND THATTAI 1,*, HAN N. LIM 1, BORIS I. SHRAIMAN 2 & ALEXANDER VAN OUDENAARDEN 1 Initially uninduced cells grown for 20 hrs in 18  M TMG Initially uninduced cells (lower panel) and induced cells (upper panel) grown in media containing different concentration of TMG TMG = thio-methylgalactoside

‘Death control’ for proteins d [protein] dt = synthesis - degradation  proteasome degraded protein ubiquitilation system

response (R) signal (S) mutual inhibition Linear module & buzzer R S EP E k1k1 k0k0 k2k2 k3k3 k4k4 k2'k2' Protein degradation: mutual inhibition R rate (dR/dt) synthesis degradation

Oscillators: three modules

X R PhasePlane response (R) signal (S) S crit1 S crit2 Positive and negative feedback oscillations (activator-inhibitor) R S EP E X k0k0 k1k1 k2k2 k2'k2' k3k3 k4k4 k5k5 k6k6

p53 Mdm2 p53-CFP and Mdm2-YFP levels in the nucleus after  -irradiation Period of oscillation: 440  100 min

X R response (R) signal (S) S crit1 S crit2 R S EP E X k1k1 k2k2 k3k3 k4k4 k0'k0' k0k0 Positive and negative feedback oscillations (substrate depletion)

Negative feedback and oscillation S X Y YP R RP (1) k0k0 k1k1 k2k2 (2) k2'k2' k3k3 k4k4 k5k5 k6k6 time X YP RP response (RP) signal (S) S crit2 S crit1

R S E EP Negative feedback and homeostasis k0k0 k3k3 k4k4 k2k2 signal (S) homeostatic response (R) rate (dR/dt) R production removal

Typical biosynthetic pathway protein demand aminoacid