Project 2: The entry into the cell cycle /G1-S transition

In 1999, a mathematical model was presented to analyse the kinetics of the restriction point (R-point) (Aguda & Tang, 1999). The restriction point is a "break" that separates the G1 phase into two phases, one phase that depends on mitogens (for example, growth factors) and another phase that does not depend on mitogens anymore for cell progression.

Pardee (1989) first introduced the idea that cells commit themselves to cell cycle events at a certain point in the G1 phase by treating the cells with cycloheximide (drug that stops synthesis of proteins). He observed that depending on the time at which the cells are treated, they respond differently. When cells are treated approximately 3 hours after division, even if protein synthesis is blocked, the cells complete the cell cycle. This turning point is called the restriction point. Supporting Pardee's idea, Zetterberg (1995) proposes the possibility of a G1 phase divided into two subphases: the G1-pm (post mitotic) and the G1-ps (pre S phase) by studying pulse treatments.

The interest of this project is not the study of the restriction point but the decision to enter the G1-S transition.

The "break" is monitored by the protein Rb. Rb (from retinoblastoma) is a tumor suppressor gene, if it is deleted, E2F is constantly active and the cell is always allowed to enter the cell cycle.

Early in the cell cycle, Rb is present and keeps E2F, a transcription factor of cyclins (here CycE and CycD), inactive by forming an inactive complex E2F-Rb. When mitogens are introduced (through MAPK here), CycD/cdk4 starts to be synthesized. The main role of the cyclin/cdk complexes is to phosphorylate proteins. When CycD/cdk4 is activated, it phosphorylates Rb in the complex E2F-Rb. Rb in its phosphorylated form, Rb~{p1}, cannot keep E2F in complex and E2F is freed. That way, more CycD/cdk4 can be made and CycE/cdk2 starts to be synthesized as well. CycE/cdk2 phosphorylates Rb even more.

Here, the cyclin/cdk complexes are regulated by synthesis and degradation of the cyclins, but also by inhibition: p21, p16 and p27 are stoichiometric cyclin dependent kinase inhibitors. They keep the complexes inactive by forming a trimer.

 


Adapted from Aguda & Tang (1999) The kinetic origins of the restriction
point in the mammalian cell cycle. Cell Prolif, 32, 321, 335 [Abstract] [PDF]

Note : On this diagram, plain arrows are considered to be biochemical reactions, whereas dashed arrows are influences of proteins on a reaction. Arrows represent positive effects whereas ----| represent inhibitory effects.

Rb has an inhibitory effect on the synthesis of p16. The synthesis rate of p16 is inversely proportional to the amount of Rb. This event will be modeled as follows.

* ks16+ks16p/(1+ks16pp*[Rb]) for _=>p16.

** Similarly, p16 has an inhibitory effect on Rb synthesis (not shown on the graph). Express Rb synthesis inhibited by p16 using a similar function (use the parameter names: ksrb, krbp, ksrbpp)

For this model, consider Myc and K~{p1,p2} to be variables (and not parameters) that do not vary much in this module and remain equal to 1. Myc is a transcription factors involved in other modules too. And K~{p1,p2} is the response of a signal (coming from mitogens) that informs the cell if it must go through a cell cycle or remain in a quiescent state. p53 is also considered as a variable but absent.

present(Myc).
present(K~{p1,p2}).
absent(p53).

Also, at the beginning of the cycle, are present p16 (initial value = 0.3), and p27(initial value = 1).

Use the following parameter values:

Myc-mediated synthesis of CycE kse=0.01 Myc-mediated synthesis of CycD ksd=0.01
E2F-mediated synthesis ksep=0.5 K~{p1,p2}-mediated synthesis of CycD ksdp=0.5
Background degradation of CycE kde=0.2 E2F-mediated synthesis of CycD ksdpp=0.05
CycE-mediated degradation of CycE kdep=0.6 Degradation of CycD kdd=0.5
Synthesis of E2F ksef=0.05 Synthesis of p27 ks27=0.1
Degradation of E2F kdef=0.05 CycE-mediated degradation of p27 kd27=1
E2F-mediated synthesis of E2F ksefp=0.01 Background degradation of p27 kd27p=0.1
Association of E2F and Rb kaefr=100 Synthesis of p21 kp21=1
Phosphorylation of Rb by CycD kdirb=0.8 Degradation of p21 kdp21=0.7
Phosphorylation of Rb by CycDp27 kdirbp=0.001 Association of CycE and p21 kae21=50
Phosphorylation of Rb by CycE kdirbpp=0.5 Dissociation of CycE and p21 kdie21=0.01
Background synthesis of p16 ks16=0.2 Association of CycE and p27 kae27=20
Rb inhibitory effect on p16 synthesis (1)* ks16p=0.1 Dissociation of CycE and p27 kdie27=0.035
Rb inhibitory effect on p16 synthesis (2)* ks16pp=0.02 Association of CycD and p21 kad21=1
Background synthesis of Rb ksrb=0.05 Dissociation of CycD and p21 kdd21=0.1
Dephosphorylation of RbP into Rb kdrbP=0.05 Association of CycD and p27 kad27=10
Degradation of p16 kd16=2 Dissociation of CycD and p27 kdd27=0.035
p16 inhibitory effect on Rb synthesis (1)** ksrbp=0.1    
p16 inhibitory effect on Rb synthesis (2)** ksrbpp=0.1    
Degradation of Rb kdrb=0.1

Once the program is written in Biocham, save it and run it for 50 min (write: "numerical_simulation(50)." in the prompt screen).

1. Show the simulation.

2. Show the diagram using Graphviz (see the Biocham documentation for help).

3. You can now test the model and compare graphs (note : there is a command "keep_plot." that allows you to keep several graphs). You can show or hide molecules using "show_molecules(Protein)." or "hide_molecules(Protein).".