Modeling Yeast Cell Cycle Regulation Chao Tang California Institute for Quantitative Biomedical Research Department of Biopharmaceutical Sciences Department of Biochemistry and Biophysics University of California, San Francisco San Francisco, CA Center for Theoretical Biology Peking University Beijing, China

Collaborators Qi OUYANG Fangting LI Tao LONG (Princeton) Ying LU (Rockefeller) Mingyuan ZHONG (U of Washington) Mingyang HU Xiaojing YANG Center for Theoretical Biology and Department of Physics Peking University, Beijing, China

Components, Interactions and Systems “Elementary particles” of life DNA RNA Proteins Ligands Subcellular functions Cells Organisms Ecosystems Many body systems

Protein-DNA Interaction --transcriptional control mRNA activator repressor Gene A DNA

Protein-Protein Interaction -- kinase and phosphatase On-off switch Multiple sites Location control (nuclear entry) Tags for degradation Signal transduction P kinase phosphatase A A A P Michaelis-Menten Equation

Protein-Protein Interaction --protein-protein binding On-off switching upon binding Partner-specific Cln Clb Sic1 Cdc28 Cdc28

Regulatory Network

Design Principle of Biological Networks --A Computer Chip or a “Brownian Machine”? Specifically and reliably wired interactions in a clean and stable environment; No unwanted cross talks Weak interactions (~kT) in a noisy and fluctuating environment

Molecular Homeostasis How do cells achieve stability to internal and external fluctuations? How does a biopathway take a cell from one state to another reliably? How do some perturbations (genetic or otherwise) give rise to abnormal behavior (disease)

The Cell Cycle A vital process that is highly conserved in eukaryotes Error ~ Cancer

Regulators of the Yeast Cell Cycle Cln3 Cln1,2 Sic1 Cdh1 Clb5,6 Cdc20 Clb1,2 Simon, et al. 2001

The START of the Cycle Cell size Size Genotype Cln3 SBF MBF Cln2 Sic1 Wild type CLN3-1D 4CLN3 Dcln3 Cln3 SBF MBF Cln2 Sic1 Clb5 Bud formation DNA replication

Mitosis Clb2 Cdc20/APC Cdc14 Cdh1/APC,Sic1 Spindle checkpoint Movie

A Simplified Network of Regulators Positive regulation: Transcriptional activation Activation by phosphorylation/ dephosphorylation Negative regulation: Inhibition by binding Deactivation by phosphorylation Mark for degradation Checkpoints

A Simple Dynamic Model Protein state: Si={ 0, inactive 1, active 1 1 1 1 1 Protein state: Si={ 0, inactive 1, active 211=2048 “cell states” 1 Cln2 Clb5 Cdh1 aij (green) = 1, aij (red) = -1 1 Clb2 td = 1 Cdc14

Cell Stationary State is a Fixed Point Basin size Cln3 MBF SBF Cln2 Cdh1 Swi5 Cdc20 Clb5 Sic1 Clb2 Mcm1 1764 1 151 109 9 7 The big fixed point (1764/2048=86%) = G1 stationary state

Biopathway is a Trajectory of Dynamics START Step Cln3 MBF SBF Cln2 Cdh1 Swi5 Cdc20 Cdc14 Clb5 Sic1 Clb2 Mcm1/SFF Phase 1 START 2 G1 3 4 5 S 6 G2 7 M 8 9 10 11 12 13 Stationary G1  

Global Flow Diagram of Trajectories Biopathway G1

Overlap of Trajectories 2 2 1.5 1 3 1 1 2 1 1 1 2 1 3

Flow Diagram of a Random Network Random networks Bionetwork Convergence of trajectories

Perturbation --Stability of the fixed point

Perturbation --Stability of the biopathway Deletion, addition, color-switching -- 41.2%, 57.4%, 64.7%

A Checkpoint = A Big Fixed Point Cell size checkpoint 90.8%; W=6757 Inter-S checkpoint 99.4%; W=4257 Spindle checkpoint 89.8%; W=3821 DNA Damage checkpoint 99.8%; W=4925

Differential Equations ??Parameters??

G1 Attractor and Biopathway Parameters = Best guess  Arbitrary START G1=the global attractor Sampling the phase space

A Global Attractor and a Globally Convergent Trajectory

Parameter Sensitivity Analysis Single-parameter bifurcation analysis (Lan Ma and Pablo Iglesias (2002)) Bifurcation => qualitative change of the systems property If no bifurcation for DOR=0.9  10 fold change in parameters DOR=0.99  100 fold change in parameters

Stability of the G1 Fixed Point DOR>0.99 for 78/83 parameters Parameter DOR Range New attractor type Note 0.981 [*,54] 53_Limit cycle II T of Cln2 by SBF 0.967 [1/30,*] 1/30_ Limit cycle II D of Cln2 0.986 [*,69] 69_ M arrest Basic synthesis of Clb5 0.963 [*,27] 27_Limit cycle II Activation of SBF 0.966 [*,29] 29_Limit cycle II Positive feedback from Cln2 to SBF

Stability of Biopathway G1

Stability of Biopathway DOR>0.9 for 70/84 parameters No Name Decrease Increase New state Note 2 k2sn2 7 Limit cycle I T of Cln2 by SBF 3 kdn2 1/3 D of Cln2 5 k2sb2 1/5 S arrest T of Clb2 by Mcm1 6 kdb2 D of Clb2 19 k2s20 1/7 M arrest T of Cdc20 by Mcm1 22 kd20 D of Cdc20 51 kamcm 1/6 Mcm1 52 kimcm 54 Jimcm 65 kasbf SBF 71 epsbfn2 Positive feed back of Cln2 to SBF 74 k1sc1 4 Late G1 arrest Basil T of Sic1 79 kd2c1 D of Sic1 by cyclins Sensitive parameters are checkpoint related

S/G2 M G1 Late G1

From Network to Modules Limit cycle I Cell size checkpoint Cln2,SBF S DNA checkpoint M Mitotic arrest Clb2 Spindle checkpoint Cdc20/Cdh1 G1 Parameters  strengths of arrows

Summary Cell stationary states (checkpoints) = big attractors Biological pathways = attracting dynamical trajectories The network is pretty stable both dynamically and structurally: less demanding on parameters Boolean network Sensitive parameters lead to checkpoint arrest/bypass Effects of multiple mutations Suggests experiments