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Analysis of a generic model of eukaryotic cell-cycle regulation.

  • Attila Csikász-Nagy
  • Dorjsuren Battogtokh
  • Katherine C Chen
  • Bela Novák
  • John J Tyson
Biophys. J. 2006; 90 (12): 4361-4379
Abstract
We propose a protein interaction network for the regulation of DNA synthesis and mitosis that emphasizes the universality of the regulatory system among eukaryotic cells. The idiosyncrasies of cell cycle regulation in particular organisms can be attributed, we claim, to specific settings of rate constants in the dynamic network of chemical reactions. The values of these rate constants are determined ultimately by the genetic makeup of an organism. To support these claims, we convert the reaction mechanism into a set of governing kinetic equations and provide parameter values (specific to budding yeast, fission yeast, frog eggs, and mammalian cells) that account for many curious features of cell cycle regulation in these organisms. Using one-parameter bifurcation diagrams, we show how overall cell growth drives progression through the cell cycle, how cell-size homeostasis can be achieved by two different strategies, and how mutations remodel bifurcation diagrams and create unusual cell-division phenotypes. The relation between gene dosage and phenotype can be summarized compactly in two-parameter bifurcation diagrams. Our approach provides a theoretical framework in which to understand both the universality and particularity of cell cycle regulation, and to construct, in modular fashion, increasingly complex models of the networks controlling cell growth and division.

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
Id Name Spatial dimensions Size
default_compartment 3.0 1.0
Id Name Initial quantity Compartment Fixed
APCP 0.0759140253067017 default_compartment
BCKI 0.679449200630188 default_compartment
CKI 0.02882070094347 default_compartment
Cdc20A 0.357272386550903 default_compartment
Cdc20in 0.770238757133484 default_compartment
Cdh1 0.718939363956451 default_compartment
CycA 0.0945030823349953 default_compartment
CycB 0.190358594059944 default_compartment
CycE 0.209202438592911 default_compartment
Mass 1.33826780319214 default_compartment
TriA 0.349222421646118 default_compartment
TriE 0.0 default_compartment
pB 0.0123442625626922 default_compartment
pBCKI 0.0479593835771084 default_compartment
sink 1.0 default_compartment
source 1.0 default_compartment

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
v_1 source = Mass

mu*Mass*(1 - Mass/MaxMass)
v_10 pBCKI = pB + CKI

kdissb*pBCKI
v_11 pBCKI = BCKI

V25*pBCKI
v_12 BCKI = pBCKI

Vwee*BCKI
v_13 BCKI = CKI

Vdb*BCKI
v_14 BCKI = CycB

Vdi*BCKI
v_15 pBCKI = CKI

Vdb*pBCKI
v_16 pBCKI = pB

Vdi*pBCKI
v_17 source = CKI

Vsi
v_18 CKI = sink

Vdi*CKI
v_19 CKI + CycA = TriA

kassa*CKI*CycA
v_2 source = CycB

Vsb
v_20 TriA = CKI + CycA

kdissa*TriA
v_21 TriA = CycA

Vdi*TriA
v_22 TriA = CKI

Vda*TriA
v_23 CKI + CycE = TriE

kasse*CKI*CycE
v_24 TriE = CKI + CycE

kdisse*TriE
v_25 TriE = CycE

Vdi*TriE
v_26 TriE = CKI

Vde*TriE
v_27 source = CycA

Vsa
v_28 CycA = sink

Vda*CycA
v_29 source = CycE

Vse
v_3 CycB = sink

Vdb*CycB
v_30 CycE = sink

Vde*CycE
v_31 source = APCP

Michaelis(CycB, Jaie, kaie, (1-APCP))
v_32 APCP = sink

Michaelis(1.0, Jiie, kiie, APCP)
v_33 source = Cdc20in

ks20p + ks20pp*CycB^n20/(J20^n20 + CycB^n20)
v_34 Cdc20in = sink

kd20*Cdc20in
v_35 Cdc20in = Cdc20A

Michaelis(APCP, Ja20, ka20, Cdc20in)
v_36 Cdc20A = Cdc20in

Michaelis(1.0, Ji20, ki20, Cdc20A)
v_37 Cdc20A = sink

kd20*Cdc20A
v_38 source = Cdh1

Michaelis(Vah1, Jah1, 1.0, (1-Cdh1))
v_39 Cdh1 = sink

Michaelis(Vih1, Jih1, 1.0, Cdh1)
v_4 pB = CycB

V25*pB
v_5 CycB = pB

Vwee*CycB
v_6 CycB + CKI = BCKI

kassb*CycB*CKI
v_7 BCKI = CycB + CKI

kdissb*BCKI
v_8 pB = sink

Vdb*pB
v_9 pB + CKI = pBCKI

kassb*pB*CKI

Global parameters

Id Value
Cdc14 0.0
Cdc25 0.0
CycD 0.0
CycD0 0.108
J20 10.0
Ja20 1.0
Ja25 0.1
Jafb 0.1
Jafi 1.0
Jah1 0.03
Jaie 0.1
Jatf 0.01
Jawee 0.05
Ji20 1.0
Ji25 0.1
Jifb 0.1
Jifi 2.0
Jih1 0.03
Jiie 0.1
Jitf 0.01
Jiwee 0.05
KEZ 0.2
MaxMass 10000.0
TFB 0.0
TFE 0.0
TFI 0.0
V25 0.0
Vah1 0.0
Vatf 0.0
Vda 0.0
Vdb 0.0
Vde 0.0
Vdi 0.0
Vih1 0.0
Vitf 0.0
Vsa 0.0
Vsb 0.0
Vse 0.0
Vsi 0.0
Vwee 0.0
Wee1 0.0
k14di 12.0
k25p 0.01
k25pp 5.0
ka20 1.0
ka25p 0.0
ka25pp 1.0
kafb 1.0
kafi 6.0
kah1p 0.02
kah1pp 0.8
kaie 0.1
kassa 50.0
kassb 60.0
kasse 0.0
katfapp 1.5
katfdpp 3.0
katfepp 0.38
katfp 0.0
kaweep 0.3
kaweepp 0.0
kd20 0.05
kdap 0.01
kdapp 0.16
kdappp 0.0
kdbcpp 0.15
kdbhpp 0.4
kdbp 0.003
kdeapp 0.0
kdebpp 0.0
kdeepp 0.0
kdep 0.12
kdiapp 0.1
kdibpp 0.8
kdidpp 0.1
kdiepp 0.12
kdip 0.002
kdissa 0.06
kdissb 0.05
kdisse 0.0
ki20 0.16
ki25p 0.3
ki25pp 0.0
kifb 0.15
kifibpp 0.05
kifip 0.008
kih1app 0.35
kih1bpp 0.1
kih1dpp 0.005
kih1epp 0.06
kih1p 0.001
kiie 0.15
kitfapp 0.0
kitfbpp 8.0
kitfp 0.75
kiweep 0.0
kiweepp 1.0
ks20p 0.001
ks20pp 1.0
ksap 0.0015
ksapp 0.01
ksbp 0.004
ksbpp 0.04
ksep 0.0
ksepp 0.15
ksip 0.018
ksipp 0.18
kweep 0.02
kweepp 0.2
mu 0.005776
n20 1.0

Local parameters

Id Value Reaction

Assignment rules

Definition
Cdc25 = GK(ka25p + ka25pp*CycB, ki25p + ki25pp*Cdc14, Ja25, Ji25)
Vatf = katfp + katfapp*CycA + katfepp*CycE + katfdpp*CycD
Vah1 = kah1p + kah1pp*Cdc14
Vsi = ksip + ksipp*TFI
Cdc14 = Cdc20A
CycD = CycD0*Mass
TFI = GK(kafi*Cdc14, kifip + kifibpp*CycB, Jafi, Jifi)
Vdi = (kdip + kdiapp*CycA + kdibpp*CycB + kdiepp*CycE + kdidpp*CycD)/(1.0 + k14di*Cdc14)
Vwee = kweep + kweepp*Wee1
Vse = (ksep + ksepp*TFE)*Mass
Vda = kdap + (kdapp + kdappp)*Cdc20A + kdappp*Cdc20in
V25 = k25p + k25pp*Cdc25
Vsa = (ksap + ksapp*TFE)*Mass
TFE = GK(Vatf, Vitf, Jatf, Jitf)
TFB = GK(kafb*CycB, kifb, Jafb, Jifb)
Vsb = (ksbp + ksbpp*TFB)*Mass
Vih1 = kih1p + kih1app*CycA + kih1bpp*CycB + kih1epp*CycE + kih1dpp*CycD
Vitf = kitfp + kitfapp*CycA + kitfbpp*CycB
Vdb = kdbp + kdbhpp*Cdh1 + kdbcpp*Cdc20A
Vde = kdep + kdeepp*CycE + kdeapp*CycA + kdebpp*CycB
Wee1 = GK(kaweep + kaweepp*Cdc14, kiweep + kiweepp*CycB, Jawee, Jiwee)

Rate rules

Definition

Algebraic rules

Definition
Definition
Michaelis(M1, J1, k1, S1) = k1*S1*M1/(J1 + S1)
GK(a, b, c, d) = (2*a*d)/(b - a + b*c + a*d + Sqrt((b - a + b*c + a*d)^2 - 4*a*d*(b - a)))
Trigger Assignments