yao1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000318) Biomodels notes: Bifurcation diagram as in fig. 1B of the original publication. The diagram was computed using SBW and its Auto2000 frontend (http://sys-bio.org/fbergman/files/latest/SetupAutoWrapper.exe) and gnuplot. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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A bistable Rb-E2F switch underlies the restriction point.

  • Guang Yao
  • Tae Jun Lee
  • Seiichi Mori
  • Joseph R Nevins
  • Lingchong You
Nat. Cell Biol. 2008; 10 (4): 476-482
Abstract
The restriction point (R-point) marks the critical event when a mammalian cell commits to proliferation and becomes independent of growth stimulation. It is fundamental for normal differentiation and tissue homeostasis, and seems to be dysregulated in virtually all cancers. Although the R-point has been linked to various activities involved in the regulation of G1-S transition of the mammalian cell cycle, the underlying mechanism remains unclear. Using single-cell measurements, we show here that the Rb-E2F pathway functions as a bistable switch to convert graded serum inputs into all-or-none E2F responses. Once turned ON by sufficient serum stimulation, E2F can memorize and maintain this ON state independently of continuous serum stimulation. We further show that, at critical concentrations and duration of serum stimulation, bistable E2F activation correlates directly with the ability of a cell to traverse the R-point.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1e-06 mole
3600.0 second
2.7777777777777777e-10 mole litre^(-1.0) second^(-1.0)
1e-06 mole litre^(-1.0)
0.0002777777777777778 second^(-1.0)
277.77777777777777 mole^(-1.0) litre second^(-1.0)
1.0 dimensionless
Id Name Spatial dimensions Size
cell cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
CD CycD 0.0 cell (cell)
CE CycE 0.0 cell (cell)
EF E2F 0.0 cell (cell)
MC Myc 0.0 cell (cell)
RB Rb 0.0 cell (cell)
RE Rb-E2F complex 0.55 cell (cell)
RP phosphorylated Rb 0.0 cell (cell)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
r1 ∅ > MC

cell * (kM * S / (KS + S))
r10 RP > RB

cell * (kkRBUP * RP / (Kp + RP))
r11 MC > ∅

cell * dMC * MC
r12 EF > ∅

cell * dEF * EF
r13 CE > ∅

cell * dCE * CE
r14 CD > ∅

cell * dCD * CD
r15 RB > ∅

cell * dRB * RB
r16 RP > ∅

cell * dRP * RP
r17 RE > ∅

cell * dRE * RE
r2 ∅ > CD

cell * (kkCDS * S / (KS + S))
r3 ∅ > EF

cell * (kkEF * MC * EF / ((KMC + MC) * (KEF + EF)) + kkb * MC / (KMC + MC))
r4 ∅ > CE

cell * (kkCE * EF / (KEF + EF))
r5 ∅ > CD

cell * (kkCD * MC / (KMC + MC))
r6 ∅ > RB

cell * kkRB
r7 RE > EF + RP

cell * (kkRBPP * CD * RE / (KD + RE) + kkRBPP * CE * RE / (KE + RE))
r8 EF + RB > RE

cell * kkRE * RB * EF
r9 RB > RP

cell * (kkRBP * CD * RB / (KD + RB) + kkRBP2 * CE * RB / (KE + RB))

Global parameters

Id Value
S 1.0 dimensionless

Local parameters

Id Value Reaction
KS 0.5 dimensionless r1
kM 1.0 uM per hr r1
KS 0.5 dimensionless r2
kkCDS 0.45 uM per hr r2
KEF 0.15 uM r3
KMC 0.15 uM r3
kkEF 0.4 uM per hr r3
kkb 0.003 uM per hr r3
KEF 0.15 uM r4
kkCE 0.35 uM per hr r4
KMC 0.15 uM r5
kkCD 0.03 uM per hr r5
kkRB 0.18 uM per hr r6
KD 0.92 uM r7
KE 0.92 uM r7
kkRBPP 18.0 per hr r7
kkRE 180.0 per_uM per hr r8
KD 0.92 uM r9
KE 0.92 uM r9
kkRBP 18.0 per hr r9
kkRBP2 18.0 per hr r9
Kp 0.01 uM r10
kkRBUP 3.6 uM per hr r10
dMC 0.7 per hr r11
dEF 0.25 per hr r12
dCE 1.5 per hr r13
dCD 1.5 per hr r14
dRB 0.06 per hr r15
dRP 0.06 per hr r16
dRE 0.03 per hr r17

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments
gt(time, 0) S = 20
gt(time, 5) S = 1