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Computational Modeling of the Cell Cycle Eric Sobie Pharmacology and Systems Therapeutics Mount Sinai School of Medicine 1

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Outline Lecture Workshop Implementation of the Tyson cell cycle model Simulations of disruptions to normal cell division Adding complexity to the model Biological background Regulation of mitosis-promoting factor (MPF) Steps that occur during rapid, post-fertilization cell cycles The Tyson (1991) cell cycle model Biology captured by the model Important model results Simplifications of the Tyson model Comparison with biology taught by Dr. Hirsch Improvements made over the years 2

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Basics of the cell cycle G 2 M transition driven by increase in MPF Cyc = cyclin Cdk = cyclin-dependent kinase Active MPF pre-MPF Two obvious ways to regulate Cdk/MPF activity: 1)synthesis/degradation of cyclin 2)Phosphorylation/dephosphorylation of Cdk MPF = Mitosis-Promoting Factor 3

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Basics of the cell cycle cyclin is alternately synthesized and degraded We will only consider M-type cyclins (aka cyclinB), not others 4

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Basics of the cell cycle Positive feedback in activation of MPF Greater MPF activity Greater cdc25 activity Greater cdc25 activity Greater MPF activity Positive feedback also referred to as: autocatalysis 5

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The Tyson (1991) cell cycle model Active MPF This minimal, and old, cell cycle model contains several simplifications compared with what we now know. cdc2 = name of yeast gene cdk1 = name of protein k for kinase 6

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The Tyson (1991) cell cycle model Active MPF Pre-MPF Plus 3 additional ODEs Each ODE reflects: rate of appearance – rate of disappearance 7

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Simplifications of the Tyson model Model 1) Autocatalytic activation of MPF Active MPF Inactive MPF Current knowledge Alberts et al., Molecular Biology of the Cell 8

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Simplifications of the Tyson model 2) What triggers degradation of cyclin? Current knowledge Active MPF Tyson considers two possibilities: 1) degradation occurs at a constant rate (k 6 = constant) 2) degradation is time-dependent, presumably reflecting changes in cell size. Model 9 Alberts et al., Molecular Biology of the Cell

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Simplifications of the Tyson model 3) Does not include wee1 Therefore MPF regulates both: 1)activation of MPF (de-phosphorylation of CDK) 2)inactivation of MPF (phosphorylation of CDK) Boutros et al. (2007) Nature Reviews Cancer 7: wee1 opposes MPF activation MPF opposes wee1 activation 10

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What did the Tyson model show? 1) The model can oscillate spontaneously Whether this oscillation occurs depends on k 4 and k 6 This result confirms the experimental observations that (1) de-phosphorylation of cdc-2 (k 4 ) and (2) degradation of cyclin (k 6 ), are the two key steps 11

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What did the Tyson model show? 2) Nonoscillating regimes show two types of behavior In region (A), [MPF] is high, as in metaphase arrest of mature oocytes. In region (C), [MPF] is low, as in nondividing somatic cells. 12

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What did the Tyson model show? 3) The model can show "excitability" This was considered analogous to growth control of cell division. In this regime, oscillations do not occur at fixed k 6, but periodic changes in k 6 can cause periodic changes in [MPF] 13

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Good models typically evolve Compare 1991 model with 1993 model Between 1991 and 1993, new processes were added to the model Tyson (1991) PNAS 88:100: Novak & Tyson (1993) J. Cell Science 106: diagram from Sible & Tyson (2007) 14

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1991 model versus 1993 model Tyson (1991) Autocatalytic activation of MPF Active MPF Inactive MPF Direct effect of [MPF] Occurs through cdc25 Active MPF Inactive MPF Novak & Tyson (1993) 15

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1991 model versus 1993 model Degradation of cyclin Active MPF Degradation occurs at a constant rate (k 6 = constant) [MPF] indirectly activates APC Active MPF Tyson (1991)Novak & Tyson (1993) 16

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Good models typically evolve Since 1993, more components have been included Generic model of cell cycle regulation Csikász-Nagy et al. (2006) Biophysical Journal 90:4361 –

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Good models typically evolve Since 1993, more components have been included A model specific to budding yeast Chen et al. (2004) Mol. Biol. Cell 15:

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Implementing the Tyson model Variable definitions Y YP C2 CP M pM cyclin cyclin-P cdc2 cdc2-P MPF = cyclin-P/cdc2 preMPF = cyclin-P/cdc2-P Matlab variable nameBiochemical name 19

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Implementing the Tyson model Complete Equations 20 Tyson (1991) PNAS 88:100:

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Implementing the Tyson model Notation 1) The equations are given in Table 1 on the paper. 2) Some rate constants are defined as k x [~P], where [~P] is the constant phosphate concentration. Thus, k 5 and k 8 in the model represent k 5 [~P] and k 8 [~P], respectively. 3) Similarly, Tyson defines the rate of cyclin synthesis as k 1 [aa], where [aa] stands for amino acids. We will just refer to this as k 1. 4) The differential equations for [M] and [pM] contain an additional function, F([M]), that is listed in the Table 1 legend. This equation, which is also provided in the notes, is critical for the proper functioning of the model. Assignments 1) Get the model to run 2) Plot all variables separately 3) Plot more informative ratios of variables 4) Explore changes in rate of cyclin degradation 5) Homework assignment: incorporate effects of wee1. 21

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Slides from a lecture in the course Systems Biology—Biomedical Modeling Citation: E. A. Sobie, Computational modeling of the cell cycle. Sci. Signal. 4, tr11 (2011).

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