# Please rename the file cccMaltab.ode # Model of the cell cycle (Burns & Tannock, Smith & Martin, Mackey) # The cell cycle is divided into 4 phases # G0/G1: rest/growth phase - duration has exponential distribution beta(t) # - loss rate delta(t) # - total cell number: N(t) # S: synthesis phase - fixed duration tS # - loss rate gS(t) # - total cell number S(t) # G2: gap 2 phase - time-dependent fixed duration tP(t) # - loss rate gP # - total cell number P(t) # M: mitosis - fixed duration tM # - loss rate gM # - total cell number M(t) # # # The default parameters are for human tumor cells. # # This file is intended to be run with Matlab, but can be run as a stand-alone # If you use the XPP-Matlab interface, setting parameters using the command ChangeXPPodeFile # will modify default parameter values in this file. # # contact: S Bernard, samubernard@gmail.com # =======================================TREATMENT=========================================== # ------------------------------INPUT FROM THE TREATMENT------------------------------------- par ton=24, tdur=4, duration=5, dstart=3,killing=8, period=24 # Square wave treatment of duration tdur (h) # tr_wave(t)=heav(t)-heav(t-tdur) # Smooth wave treatment gaussian within a window of length tdur tr_wave(t)=(heav(t+tdur/2)-heav(t-tdur/2))*gauss(t,0,tdur/4) # Wave type sin(2t) 12 h # tr_wave(t)=(heav(t)-heav(t-12))*(1-cos(4*pi/Tclock*(t)))/12 treat(t)=sum(0,duration-1)of(tr_wave(t-ton-period*i'-24*dstart)) # Flat treatment equivalent to smooth wave treatment ## treat(t)=(heav(t-24*dstart)-heav(t-24*(duration+dstart)))*1.7642/24 # Flat treatment equivalent to sin2t wave treatment # streat(t)=(heav(t-24*dstart)-heav(t-24*(duration+dstart)))/24 # ------------------------------------------------------------------------------------------- # ======================================CELL CYCLE=========================================== # -----------------------LOSS RATE FUNCTIONS: TREATMENT DEPENDENT---------------------------- par gS0=0.01, gP0=0.01, gM0=0.01, delta0=0.004 # S PHASE DRUG gS(t)=gS0+killing*treat(t) gP(t)=gP0 gM(t)=gM0 delta(t)=delta0 # G0 PHASE DRUG # delta(t)=delta0+killing*treat(t) # ------------------------------------------------------------------------------------------- # ----------------------------------------DELAYS--------------------------------------------- par tS=30, tM=3, tP0=2, theta2=20 # TIME-DEPENDENT DELAY tP(t)=tP0*f2(t-theta2) # time derivative of the delay tPp(t)=tP0*f2p(t-theta2) tfct(t)=(1-tPp(t)) # TOTAL DELAY tau(t)=tS+tP(t-tM)+tM # ------------------------------------------------------------------------------------------- # ----------------------------------PROLIFERATION RATE BETA---------------------------------------- par beta0=0.04, theta=5.75, kb=0.2,k0beta=1,hbeta=3 beta(t)=beta0*f(t-theta) # --------------------------------CELL CYCLE EQUATIONS--------------------------------------- dN/dt=-(delta(t)+beta(t))*N+2*tfct(t-tM)*sigma(t)*beta(t-tau(t))*delay(N,tau(t)) dS/dt=-gS(t)*S-sS*beta(t-tS)*delay(N,tS)+beta(t)*N dP/dt=-gP(t)*P-tfct(t)*sP(t)*delay(sS,tP(t))*beta(t-tS-tP(t))*delay(N,tS+tP(t))\ +sS*beta(t-tS)*delay(N,tS) dM/dt=-gM(t)*M-tfct(t-tM)*sigma(t)*beta(t-tau(t))*delay(N,tau(t))\ +tfct(t)*sP(t)*delay(sS,tP(t))*beta(t-tS-tP(t))*delay(N,tS+tP(t)) # ------------------------------------------------------------------------------------------- # -------------------------------SURVIVING FRACTION SIGMA------------------------------------ sS(t)=exp(-int{heav(-(t-tS-t'))*gS(t')}) sP(t)=exp(-tP(t)*gP(t)) sM(t)=exp(-tM*gM(t)) sigma(t)=delay(sS,tM+tP(t-tM))*sP(t-tM)*sM(t) # ------------------------------------------------------------------------------------------- # ----------------------------------AUXILIARY VARIABLES-------------------------------------- # TOT: total cell number, LI: labeling index S phase fraction, G1I: G1 phase fraction, # MI: M phase fraction, G2I: G2 phase fraction, G2MI: G2 and M phases fraction, # SF: survival fraction sigma(t), TG2: G2 phase duration, TR: treatment function, # CLOCK: circadian clock input to the cell cycle, BT: proliferation rate beta(t) total=N+S+P+M aux TOT=total aux LI=S/total aux G1I=N/total aux MI=M/total aux G2I=P/total aux G2MI=(P+M)/total aux SF=sigma(t) aux TG2=tP(t) aux TR=killing*treat(t) aux CLOCK=clockout aux BT=beta(t) # CLOCK OUTPUT FUNCTION clockout=f(t) # ------------------------------------------------------------------------------------------- # ----------------------------------INITIAL CONDITIONS--------------------------------------- init N=1,S=0,P=0,M=0,sS=1 # ------------------------------------------------------------------------------------------- # ==================================CIRCADIAN CLOCK========================================== # ------------------------------OUPUT FROM CIRCADIAN CLOCK----------------------------------- par alpha=0.5, alpha2=0.2,phi2=14,sensty=2, Tclock=24 f(t)=1+alpha*(cos(2*pi*t/Tclock)+alpha2*cos(4*pi*(t-phi2)/Tclock)) # sensty is the clock sensitivity of tau_P relative to beta f2(t)=1+sensty*alpha*(cos(2*pi*t/Tclock)+alpha2*cos(4*pi*(t-phi2)/Tclock)) # derivative of f2 (to use with tPp(t)) f2p(t)=-sensty*alpha*pi/Tclock*(2*sin(2*pi*t/Tclock)+alpha2*4*sin(4*pi*(t-phi2)/Tclock)) #fbeta=lgpcnp # ------------------------------------------------------------------------------------------- # =================================GENERAL FUNCTIONS========================================= # HILL-FUNCTION hill(v0,k0,h,X)=v0*k0^h/(k0^h+X^h) # MICHAELIS-MENTEN-FUNCTION mm(v0,k0,h,X)=v0*X^h/(k0^h+X^h) # Gaussian function gauss(x,mu,sig)=exp(-(x-mu)^2/sig^2) # ------------------------------------------------------------------------------------------- # ============================XPPAUT PARAMETERS AND OPTIONS================================== @ delay=150 @ total=240,dt=0.05,maxstor=120000 @ xlo=96,xhi=240,ylo=0, yhi=1, bound=10000 @ yplot=LI, method=volterra @ but=go:ig @ nplot=2, yp2=TR # @ nplot=3,yp2=CLOCK,yp3=TR #@ njmp=40 # AUTO parameters #@ epss=1e-7,epsu=1e-7,epsl=1e-7,parmax=15,dsmax=5,dsmin=1e-4,ntst=100 d