********** MODEL NAME
Barr 2017 - Dynamics of p21 in hTert-RPE1 cells

********** MODEL NOTES
This model is described in the article:
DNA damage during S-phase mediates the proliferation-quiescence decision in the subsequent G1 via p21 expression
Alexis R. Barr, Samuel Cooper, Frank S. Heldt, Francesca Butera, Henriette Stoy, Jrg Mansfeld, Bela Novak, Chris Bakal

Abstract:
Following DNA damage caused by exogenous sources, the tumour suppressor p53 mediates cell cycle arrest via expression of the CDK inhibitor, p21. However, the role of p21 in maintaining genomic stability in the absence of DNA damaging agents is less clear. Using live single cell measurements of endogenous p21 protein in asynchronous cultures, we show that DNA damage incurred over S-phase causes p53-dependent accumulation of p21 across mother G2- and daughter G1-phases. High p21 levels then mediate G1 arrest via CDK inhibition, yet lower levels have no impact on G1 progression, and the ubiquitin ligases CRL4^Cdt2 and SCF^Skp2 couple to degrade p21 prior to the G1/S transition. Through mathematical modelling, we reveal that a bistable switch, created by CRL4^Cdt2, promotes irreversible S-phase entry by keeping p21 levels low, preventing premature S-phase exit upon DNA damage. Thus, we characterise how p21 levels regulate the proliferation-quiescence decision to maintain genomic stability.

********** MODEL STATES
d/dt(MrnaP21) = kSyMrna + kSyMrnaP53*P53 - kDeMrna*MrnaP21
d/dt(MrnaCy)  = kSyMrna                  - kDeMrna*MrnaCy
d/dt(MrnaP53) = kSyMrna                  - kDeMrna*MrnaP53

d/dt(tP21) = kSyP21*MrnaP21 - rDeP21*tP21
d/dt(tCy)  = kSyCy *MrnaCy  - rDeCy *tCy

d/dt(CyP21) = kAsCyP21*P21*Cy - (kDsCyP21+rDeP21+rDeCy)*CyP21

d/dt(aPcna) = kImPc - kAsPcP21*P21*aPcna + (kDsPcP21+rDeP21)*iPcna - (kExPc+kAsRcPc*pRc)*aPcna + (kDsRcPc + rDsRc)*aRc
d/dt(iPcna) =       + kAsPcP21*P21*aPcna - (kDsPcP21+rDeP21)*iPcna - (kExPc+kAsRcPc*pRc)*iPcna + (kDsRcPc + rDsRc)*iRc

d/dt(Rc)  = - rPhRc*Rc + kDpRc*pRc                                                                     - rDsRc*Rc
d/dt(pRc) =   rPhRc*Rc - kDpRc*pRc                     - kAsRcPc*(aPcna+iPcna)*pRc + kDsRcPc*(aRc+iRc) - rDsRc*pRc
d/dt(aRc) = - kAsPcP21*P21*aRc + (kDsPcP21+rDeP21)*iRc + kAsRcPc* aPcna       *pRc - kDsRcPc*aRc       - rDsRc*aRc
d/dt(iRc) =   kAsPcP21*P21*aRc - (kDsPcP21+rDeP21)*iRc + kAsRcPc*       iPcna *pRc - kDsRcPc*iRc       - rDsRc*iRc

d/dt(Dna) = kSyDna*aRc

d/dt(P53) = kSyP53*MrnaP53 - rDeP53*P53
d/dt(Dam) = kGeDam + kGeDamArc*aRc - rReDam*Dam

tP21(0)  = 0.72
aPcna(0) = 0.5
Rc(0)    = 1

MrnaP21(0) = 1
MrnaCy(0)  = 1
MrnaP53(0) = 1

********** MODEL PARAMETERS
Skp2       = 1          %AU  relative Skp2 level
Cdt2       = 1          %AU  relative Cdt2 level

kSyMrna    = 0.02       %AU/min  constitutive mRNA synthesis
kSyMrnaP53 = 0.08       %1/min  p53-dependent synthesis of p21 mRNAs
kDeMrna    = 0.02       %1/min  mRNA degradation

kSyP21    = 0.0018      %1/min  constitutive p21 synthesis
kDeP21    = 0.0025      %1/min  constitutive p21 degradation
kDeP21Cy  = 0.007       %1/(AU*min)  Cyclin:CDK2-mediated p21 degradation (Skp2-dependent)
kDeP21aRc = 1           %1/(AU*min)  aRC-mediated p21 degradation (Cdt2-dependent)

kSyCy     = 0.005       %1/min  cyclin synthesis
kAsCyP21  = 1           %1/(AU*min)  association of Cyclin:CDK2 and p21
kDsCyP21  = 0.05        %1/min  dissociation of Cyclin:CDK2:p21 complexes
kDeCy     = 0.002       %1/min  constitutive cyclin degradation
kDeCyCy   = 0.0002      %1/(AU*min)  Cyclin:CDK2-mediated cyclin degradation (Skp2-dependent)

kImPc     = 0.003       %AU/min  PCNA import into the nucleus
kExPc     = 0.006       %1/min   PCNA export from the nucleus

kPhRc     = 0.1         %1/min  Cyclin:CDK2-mediated phosphorylation/priming of RCs
kDpRc     = 0.01        %1/min  dephosphorylation of pRCs
jCy       = 1.8         %AU  CDK2 threshold for the phosphorylation/priming of RCs
n         = 6           %-  hill coefficient for the phosphorylation/priming of RCs
kAsRcPc   = 0.01        %1/(AU*min)  association of phosphorylated/primed RCs and PCNA
kDsRcPc   = 0.001       %1/min  dissociation of pRC:PCNA complexes
kAsPcP21  = 100         %1/(AU*min)  association of PCNA and p21
kDsPcP21  = 0.01        %1/min  dissociation of PCNA:p21 complexes
kSyDna    = 0.007       %1/min  DNA synthesis by aRCs

kSyP53    = 0.05        %1/min  constitutive p53 synthesis
kDeP53    = 0.05        %AU/min  DNA damage-dependent degradation of p53
jP53      = 0.01        %AU  inhibition constant of p53 degradation by DNA damage

kGeDam    = 0.001       %AU/min  random DNA damage
kGeDamArc = 0.005       %1/min  DNA damage due to DNA replication
kReDam    = 0.001       %1/min  p53-independent DNA damage repair
kReDamP53 = 0.005       %1/min  p53-dependent DNA damage repair
jDam      = 0.5         %AU  DNA damage threshold for repair

rDsRc     = 0           %1/min  disassembly of replication complexes at the end of S-phase

********** MODEL VARIABLES
Cy    = tCy   - CyP21                   %AU  free, active CDK2:Cyclin
P21   = tP21  - CyP21 - iPcna - iRc     %AU  free p21
tPcna = aPcna + iPcna + aRc   + iRc     %AU  total PCNA

********** MODEL REACTIONS
rPhRc  = kPhRc*Cy^n / (jCy^n + Cy^n)                    % phosphorylation/priming of replication complexes
rDeCy  = kDeCy  + kDeCyCy *Skp2*Cy                      % Cyclin degradation 
rDeP21 = kDeP21 + kDeP21Cy*Skp2*Cy + kDeP21aRc*Cdt2*aRc	% p21 degradation
rDeP53 = kDeP53 / (jP53 + Dam)                          % p53 degradation
rReDam = kReDam + kReDamP53*P53 / (jDam + Dam)          % DNA damage repair

********** MODEL FUNCTIONS


********** MODEL EVENTS
SphaseExit = ge(Dna, 1), rDsRc, 1

********** MODEL MATLAB FUNCTIONS

