JWS Online

Model

Name

bai1

Notes

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000242) Biomodels notes: The model reproduces figure 2 of the reference publication. The model was integrated and simulated using Copasi v4.5 (Build 30). JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

Substance units

None

Time units

None

Volume units

None

Area units

None

Length units

None

Reaction extent units

None

Manuscript information

Theoretical and experimental evidence for hysteresis in cell proliferation.

Shaochun Bai
David Goodrich
C Dennis Thron
Edwin Tecarro
Mandri Obeyesekere

Cell Cycle 2003; 2 (1): 46-1728

PubMed: 12695688
PubMed Central: PMC1764593
DOI: 10.4161/cc.2.1.186
ISSN: 1538-4101
URL: https://ncbi.nlm.nih.gov/pubmed/12695688

Abstract

We propose a mathematical model for the regulation of the G1-phase of the mammalian cell cycle taking into account interactions of cyclin D/cdk4, cyclin E/cdk2, Rb and E2F. Mathematical analysis of this model predicts that a change in the proliferative status in response to a change in concentrations of serum growth factors will exhibit the property of hysteresis: the concentration of growth factors required to induce proliferation is higher than the concentration required to maintain proliferation. We experimentally confirmed this prediction in mouse embryonic fibroblasts in vitro. In agreement with the mathematical model, this indicates that changes in proliferative mode caused by small changes in concentrations of growth factors are not easily reversible. Based on this study, we discuss the importance of proliferation hysteresis for cell cycle regulation.

Simulations using this model 1

Simulation
bai2003_Fig2	SED-ML COMBINE Archive

Unit definitions 0

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

Compartments 1

Id	Name	Spatial dimensions	Size
cell	cell	3.0	1.0

Species 6

Id	Name	Compartment	Fixed
D_1	D	cell (cell)	✘
E_1	E	cell (cell)	✘
RS_1	RS	cell (cell)	✘
R_1	R	cell (cell)	✘
X_1	X	cell (cell)	✘
theta_1	theta	cell (cell)	✘

Initial assignments 0

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

Reactions 12

Id	Name	Reaction Equation and Kinetic Law
E2Fdegradationviacellcycleprogression_1	E2F degradation via cell cycle progression	theta_1 > ∅ cell * dtheta_1 * (X_1 / (qtheta_1 + X_1)) * theta_1
_1	cyclinD synthesis	∅ > D_1 cell * aD_1 * (GF_1 / (pow(k1_1, -1) + GF_1))
_2	pRB/E2F complex dissociation via cyclin D	RS_1 > theta_1 cell * (pD_1 * RS_1 * D_1 / (qD_1 + RS_1 + D_1))
cellcycleprogression_1	cell cycle progression go	∅ > X_1 cell * (aX_1 * E_1 + f_1 * theta_1 + g_1 * pow(X_1, 2) * E_1)
cellcycleprogressionslow_1	cell cycle progression slow	X_1 > ∅ cell * dX_1 * X_1
cyclinD_1	cyclinD degradation	D_1 > ∅ cell * dD_1 * E_1 * D_1
cyclinEdegradation_1	cyclinE degradation	E_1 > ∅ cell * dE_1 * X_1 * E_1
cyclinEsynthesis_1	cyclinE synthesis	∅ > E_1 cell * aE_1 * (GF_1 / (pow(k2_1, -1) + GF_1) + aF_1 * theta_1)
null2_1	pRB/E2F complex dissociation via cyclin E	RS_1 > theta_1 cell * (pE_1 * RS_1 * E_1 / (qE_1 + RS_1 + E_1))
null3_1	E2F synthesis	∅ > theta_1 cell * atheta_1 * (GF_1 / (pow(k3_1, -1) + GF_1) + fC_1_1 * theta_1)
pRBdeplation_1	pRB/E2F complex association	R_1 + theta_1 > RS_1 cell * Mass_Action_2_1(pS_1, R_1, theta_1)
pRBsynthesis_1	pRB synthesis	∅ > R_1 cell * (pX_1 * (RT_1 - RS_1 - R_1) * X_1 / (qX_1 + RT_1 - RS_1 - R_1 + X_1))

Parameters 0 26

Global parameters

Id	Value
GF_1	6.3
RT_1	2.5
Rb_phos	0.0
aD_1	0.4
aE_1	0.16
aF_1	0.9
aX_1	0.08
atheta_1	0.05
dD_1	0.4
dE_1	0.2
dX_1	1.04
dtheta_1	0.12
fC_1_1	0.003
f_1	0.35
g_1	0.528
k1_1	0.05
k2_1	1000.0
k3_1	1.5
pD_1	0.48
pE_1	0.096
pS_1	0.6
pX_1	0.48
qD_1	0.6
qE_1	0.6
qX_1	0.8
qtheta_1	0.3

Local parameters

Id	Value	Reaction

Rules 0 0 1

Assignment rules

Definition
Rb_phos = RT_1 - RS_1 - R_1

Rate rules

Definition

Algebraic rules

Definition

Function definitions 1

Definition
Mass_Action_2_1(k1, S1, S2) = k1 * S1 * S2

Events 0

Trigger	Assignments