################################################################################# # SAVE THE FILE WITH THE EXTENSION .ODE PRIOR TO RUNNING IT IN XPP # BELOW IS THE ODE FILE ACCOMPANYING THE MANUSCRIPT "POTENTIAL ROLE OF BISTABLE HISTIDINE # KINASE IN ASYMMETRIC DIVISION CYCLE OF CAULOBACTER CRESCENTUS" # THE PARAMETERS ARE FOR SIMULATING THE ** MUTANT F778L ** # AUTHORS: KARTIK SUBRAMANIAN # MARK PAUL # JOHN TYSON # DATE: APRIL 2013 ################################################################################## ###### DIVJ,DIVK and PLEC PARAMETERS ########### param divj_tot=0.5, plec_tot=1 param ksyn_dk=0.015, kdeg_dk=0.005, kdeg_dkp=0.005 param kj_jk=1, kjk_j=0.1, ke_jkin=0.5 param kpc_ph1=5, kph1_pc=5 param kph1_p11=5, kp11_ph1=2.5 param kp11_pk0=0, kpk0_p11=0 param kpk0_pk1=0.16, kpk1_pk0=5 param kpk1_pk2=5, kpk2_pk1=0.0016 param kpk1_pk1h=5, kpk1h_pk1=5 param kpk1_pk2p=0.16, kpk2p_pk1=5 param kpk2_pt2=5, kpt2_pk2=0.15 param kpt2_pk1h=0.16, kpk1h_pt2=5 param kpk2p_pc=5, kpk1p_pc=5 param kpk2_pk3=0.16, kpk3_pk2=5 param kpk3_pt3=5, kpt3_pk3=0.15 param kpt3_pk1p=0.16, kpk1p_pt3=5 param kpk1p_1h=5, k1h_pk1p=0.16 param kpk3_pk2p=0.0016, kpk2p_pk3=5 param kpk3_pk4=5, kpk4_pk3=0.0016 param kpk4_pt4=5, kpt4_pk4=0.15 param kp11_pt4=0.0755, kpt4_p11=5 param kpc_ph2=0.05, kph2_pc=5 param kph2_p22=0.0165, kp22_ph2=1.6e-08 param kp22_pk4=0, kpk4_p22=0 param kpt4_pk3h=0.16, kpk3h_pt4=5 param kpk3_pk3h=5, kpk3h_pk3=5 param kpk1p_p3h=5, kp3h_pk1p=0.0016 param kph1_p12=1.6e-02, kp12_ph1=1.6e-04 param kp12_pk2=0, kpk2_p12=0 param kph2_p12=1.6, kp12_ph2=1.6e-04 param kh1_h2=1.6e-02, kh2_h1=1.6 ######## PLED parameters ##################################### param ksyn_pld=0.01, kdeg_pld=0.005, kdeg_pldp=0.005 param kpk1_pk5=10, kpk5_pk1=0.31 param kpk5_pt5=10, kpt5_pk5=0.31 param kpt5_pk1h=10, kpk1h_pt5=0.31 param kpk3_pk6=10, kpk6_pk3=0.31 param kpk6_pt6=10, kpt6_pk6=0.31 param kpt6_pk3h=10, kpk3h_pt6=0.31 param phos_tot=0.1, kphos_ph3=1, kph3_phos=0.1, ke_ph3=0.2 ############ DivL and CckA params ######################## param divl_tot=1, kbdl_dldk=1, kudl_dldk=0.1 param ksyndl=0.005, kdegdl=0.005 ####### DivL influencing CckA ##### param kcp_ck=1, kck_cp=0.1, Km_dl=0.75, ccka_tot=1 ### Ctra synthesis param ksyn_ctr=0.05, kdeg_ctr=0.02, kdeg_ctrp=0.02 ## Cpdr synthesis param ksyn_cpd=0.05, kdeg_cpd=0.02, kdeg_cpdp=0.02 ## CckA acting on CtrA param kck_ck1=1, kck1_ck=0.1, kck1_ct1=1, kct1_ck1=0.1 param kct1_ck1h=1, kck1h_ct1=0.1 param kbcp_cps=1, kucp_cps=0.1, ke_cps=1 ## CckA acting on CpdrP param kck_ck2=1, kck2_ck=0.1, kck2_ct2=1, kct2_ck2=0.1 param kct2_ck2h=1, kck2h_ct2=0.1 param kbcp_cps2=1, kucp_cps2=0.1, ke_cps2=1 param kpld_pld2=0, kpld2_pld=0.1, kdeg_pld2=0.04 param kph1_ph2=10, kph2_ph1=5e-03 ################# EQUATIONS ################ dDIVKP/dt = -kdeg_dkp*DIVKP -kpc_ph1*PLEC*DIVKP + kph1_pc*PLECH1 + kpk0_pk1*PK0 - kpk1_pk0*PK1*DIVKP + kpk1_pk2p*PK1 - kpk2p_pk1*PK2P*DIVKP + kpt2_pk1h*PT2 - kpk1h_pt2*PK1H*DIVKP + ke_jkin*JK + kpk2_pk3*PK2 - kpk3_pk2*PK3*DIVKP + kpt3_pk1p*PT3 - kpk1p_pt3*PK1P*DIVKP - kpk1p_1h*PK1p*DIVKP + k1h_pk1p*PK1H - kph2_p12*PLECH2*DIVKP + kp12_ph2*P12 + kpt4_pk3h*PT4 - kpk3h_pt4*PK3H*DIVKP + kh1_h2*PLECH1*DIVK - kh2_h1*PLECH2*DIVKP - kph1_p11*PLECH1*DIVKP + kp11_ph1*P11 - kbdl_dldk*divl*divkp + kudl_dldk*dldk dDIVK/dt = ksyn_dk - kdeg_dk*DIVK - kpk1_pk2*PK1*DIVK + kpk2_pk1*PK2 -kj_jk*DIVJ*DIVK + kjk_j*JK + kpk3_pk2p*PK3 - kpk2p_pk3*PK2P*DIVK - kpk3_pk4*PK3*DIVK + kpk4_pk3*PK4 - kpc_ph2*PLEC*DIVK + kph2_pc*PLECH2 - kpk1p_p3h*PK1P*DIVK + kp3h_pk1p*PK3H - kph1_p12*PLECH1*DIVK + kp12_ph1*P12 + kh2_h1*PLECH2*DIVKP - kh1_h2*PLECH1*DIVK - kph2_p22*PLECH2*DIVK + kp22_ph2*P22 dDIVJ/dt = -kj_jk*DIVJ*DIVK + kjk_j*JK + ke_jkin*JK #djk/dt = kj_jk*DIVJ*DIVK - kjk_j*JK - ke_jkin*JK #dPleC/dt = - kpc_ph1*PLEC*DIVKP + kph1_pc*PLECH1 + ke_phos*PLECH1 + kph2p_pc*PH2P + kh1p_pc*PH1P - kpc_ph2*PLEC*DIVK + kph2_pc*PLECH2 dPLECH1/dt = kpc_ph1*PLEC*DIVKP - kph1_pc*PLECH1 -kph1_p11*PLECH1*DIVKP + kp11_ph1*P11 - kph1_p12*PLECH1*DIVK + kp12_ph1*P12 + kh2_h1*PLECH2*DIVKP - kh1_h2*PLECH1*DIVK - kph1_ph2*PLECH1 + kph2_ph1*PLECH2 dP11/dt = kph1_p11*PLECH1*DIVKP- kp11_ph1*P11 + kpt4_p11*pt4 - kp11_pt4*p11 - kp11_pk0*P11 + kpk0_p11*pk0 dPK0/dt = kp11_pk0*P11 - kpk0_p11*pk0 - kpk0_pk1*PK0 + kpk1_pk0*PK1*DIVKP dPK1/dt = kpk0_pk1*PK0 - kpk1_pk0*PK1*DIVKP - kpk1_pk2*PK1*DIVK + kpk2_pk1*PK2 - kpk1_pk2p*PK1 + kpk2p_pk1*PK2P*DIVKP - kpk1_pk1h*PK1 + kpk1h_pk1*PK1H - kpk1_pk5*PK1*PLED + kpk5_pk1*PK5 dP12/dt = kph1_p12*PLECH1*DIVK- kp12_ph1*P12 + kph2_p12*PLECH2*DIVKP- kp12_ph2*P12 - kp12_pk2*P12 + kpk2_p12*pk2 dPK2/dt = kpk1_pk2*PK1*DIVK - kpk2_pk1*PK2 + kp12_pk2*P12 - kpk2_p12*pk2 -kpk2_pt2*PK2 + kpt2_pk2*PT2 - kpk2_pk3*PK2 + kpk3_pk2*PK3*DIVKP dPT2/dt = kpk2_pt2*PK2 - kpt2_pk2*PT2 -kpt2_pk1h*PT2 + kpk1h_pt2*PK1H*DIVKP dPK1H/dt = kpt2_pk1h*PT2 - kpk1h_pt2*PK1H*DIVKP + kpk1_pk1h*PK1 - kpk1h_pk1*PK1H + kpk1p_1h*PK1p*DIVKP - k1h_pk1p*PK1H + kpt5_pk1h*PT5 - kpk1h_pt5*PK1H*PLEDP dPK2P/dt = kpk1_pk2p*PK1 - kpk2p_pk1*PK2P*DIVKP - kpk2p_pc*PK2P + kpk3_pk2p*PK3 - kpk2p_pk3*PK2P*DIVK #dPH2P/dt = kpk2p_h2p*PK2P - kh2p_pk2p*PH2P - kph2p_pc*PH2P ######################################################## dPK3/dt = kpk2_pk3*PK2 - kpk3_pk2*PK3*DIVKP - kpk3_pt3*PK3 + kpt3_pk3*PT3 - kpk3_pk2p*PK3 + kpk2p_pk3*PK2P*DIVK - kpk3_pk4*PK3*DIVK + kpk4_pk3*PK4 - kpk3_pk3h*PK3 + kpk3h_pk3*PK3H - kpk3_pk6*PK3*PLED + kpk6_pk3*PK6 dPT3/dt = kpk3_pt3*PK3 - kpt3_pk3*PT3 + kpk1p_pt3*PK1P*DIVKP - kpt3_pk1p*PT3 dPK1P/dt = kpt3_pk1p*PT3 - kpk1p_pt3*PK1P*DIVKP -kpk1p_1h*PK1P*DIVKP + k1h_pk1p*PK1H - kpk1p_pc*PK1P - kpk1p_p3h*PK1P*DIVK +kp3h_pk1p*PK3H #dPH1P/dt = kpk1p_h1p*PK1P - kh1p_pk1p*PH1P - kh1p_pc*PH1P ######################################################## dP22/dt = kph2_p22*PLECH2*DIVK - kp22_ph2*P22 - kp22_pk4*P22 + kpk4_p22*PK4 dPK4/dt = kpk3_pk4*PK3*DIVK - kpk4_pk3*PK4 - kpk4_pt4*PK4 + kpt4_pk4*PT4 + kp22_pk4*P22 - kpk4_p22*PK4 dPT4/dt = kpk4_pt4*PK4 - kpt4_pk4*PT4 - kpt4_p11*pt4 + kp11_pt4*P11- kpt4_pk3h*PT4 + kpk3h_pt4*PK3H*DIVKP ################################################################# dPLECH2/dt = kpc_ph2*PLEC*DIVK - kph2_pc*PLECH2 - kph2_p22*PLECH2*DIVK + kp22_ph2*P22- kph2_p12*PLECH2*DIVKP + kp12_ph1*P12 + kh1_h2*PLECH1*DIVK - kh2_h1*PLECH2*DIVKP + kph1_ph2*PLECH1 - kph2_ph1*PLECH2 dPK3H/dt = kpt4_pk3h*PT4 - kpk3h_pt4*PK3H*DIVKP + kpk3_pk3h*PK3 - kpk3h_pk3*PK3H + kpk1p_p3h*PK1P*DIVK - kp3h_pk1p*PK3H + kpt6_pk3h*PT6- kpk3h_pt6*PK3H*PLEDP ################################################ dPLED/dt = ksyn_pld - kdeg_pld*PLED - kpk1_pk5*PK1*PLED + kpk5_pk1*PK5 - kpk3_pk6*PK3*PLED + kpk6_pk3*PK6 + ke_ph3*PH3 dPLEDP/dt = - kdeg_pldp*PLEDP + kpt5_pk1h*PT5 - kpk1h_pt5*PK1H*PLEDP + kpt6_pk3h*PT6 -kpk3h_pt6*PK3H*PLEDP - kphos_ph3*PHOS*PLEDP + kph3_phos*PH3 #- kpld_pld2*PLEDP*PLEDP + kpld2_pld*Pled2 + kdeg_pld2*pled2 dPK5/dt = kpk1_pk5*PK1*PLED - kpk5_pk1*PK5 - kpk5_pt5*PK5 + kpt5_pk5*PT5 dPK6/dt = kpk3_pk6*PK3*PLED - kpk6_pk3*PK6 - kpk6_pt6*PK6 + kpt6_pk6*PT6 dPT5/dt = kpk5_pt5*PK5 - kpt5_pk5*PT5 - kpt5_pk1h*PT5 + kpk1h_pt5*PK1H*PLEDP dPT6/dt = kpk6_pt6*PK6 - kpt6_pk6*PT6 - kpt6_pk3h*PT6 + kpk3h_pt6*PK3H*PLEDP dPHOS/dt = - kphos_ph3*PHOS*PLEDP + kph3_phos*PH3 + ke_ph3*PH3 # dPH3/dt = kphos_ph3*PHOS*PLEDP - kph3_phos*PH3 - ke_ph3*PH3 dPled2/dt = kpld_pld2*PLEDP*PLEDP - kpld2_pld*Pled2 - kdeg_pld2*pled2 ####### DivL CckA equations ###### dDIVL/dt = ksyndl - kdegdl*DIVL- kbdl_dldk*DIVL*DIVKP + kudl_dldk*DLDK ddldk/dt = kbdl_dldk*divl*divkp - kudl_dldk*dldk - kdegdl*Dldk dCTRA/dt = ksyn_ctr - kdeg_ctr*CTRA - kck_ck1*CCKAKIN*CTRA + kck1_ck*CK1 + ke_cps*CPS dCTRAP/dt = -kdeg_ctrp*CTRAP - kbcp_cps*CCKAPHOS*CTRAP + kucp_cps*CPS + kct1_ck1h*CT1 - kck1h_ct1*CCKAKIN*CTRAP dCCKAPHOS/dt = - kbcp_cps*CCKAPHOS*CTRAP + kucp_cps*CPS + ke_cps*CPS -kcp_ck*CCKAPHOS*(DIVL^2/(DIVL^2+km_dl^2)) + kck_cp*CCKAKIN - kbcp_cps2*CCKAPHOS*CPDRP + kucp_cps2*CPS2 + ke_cps2*CPS2 dCCKAKIN/dt = kcp_ck*CCKAPHOS*(DIVL^2/(DIVL^2+km_dl^2)) - kck_cp*CCKAKIN - kck_ck1*CCKAKIN*CTRA + kck1_ck*CK1 + kct1_ck1h*CT1 - kck1h_ct1*CCKAKIN*CTRAP - kck_ck2*CCKAKIN*CPDR + kck2_ck*CK2 + kct2_ck2h*CT2 - kck2h_ct2*CCKAKIN*CPDRP dCK1/dt= kck_ck1*CCKAKIN*CTRA - kck1_ck*CK1 - kck1_ct1*CK1 + kct1_ck1*CT1 dCT1/dt = kck1_ct1*CK1 - kct1_ck1*CT1 - kct1_ck1h*CT1 + kck1h_ct1*CCKAKIN*CTRAP #dcps/dt = kbcp_cps*cckaphos*ctrap - kucp_cps*cps - ke_cps*cps dCPDR/dt = ksyn_cpd - kdeg_cpd*CPDR - kck_ck2*CCKAKIN*CPDR + kck2_ck*CK2 + ke_cps*CPS2 dCPDRP/dt = -kdeg_cpdp*CPDRP - kbcp_cps2*CCKAPHOS*CPDRP + kucp_cps2*CPS2 + kct2_ck2h*CT2 - kck2h_ct2*CCKAKIN*CPDRP dCK2/dt= kck_ck2*CCKAKIN*CPDR - kck2_ck*CK2 - kck2_ct2*CK2 + kct2_ck2*CT2 dCT2/dt = kck2_ct2*CK2 - kct2_ck2*CT2 - kct2_ck2h*CT2 + kck2h_ct2*CCKAKIN*CPDRP dCPS2/dt = kbcp_cps2*CCKAPHOS*CPDRP - kucp_cps2*CPS2 - ke_cps2*CPS2 ############# totals ############################################### # pleckint = total kinase dPLECKINT/dt=pleckinase-PLECKINT # plecdivk = divk bound plec dplecdk/dt = plecdivk-plecdk # cckakint = total ckkakinase dcckakint/dt = cckakinase-cckakint # divkint = divk_p fraction ddivkint/dt = divkpf-divkint #### conservation rule ###### PLEC = -((PLECH1 +PK1+PK2+PK0+PK1H + PT2 +PK2P + pk3+ pt3 + pk1p +pk4 +pt4+plech2+pk3h+pk5+pt5+pk6+pt6+p11+p12+p22) - plec_tot) aux PLEC=PLEC jk = -(divj-divj_tot) aux jk = jk pleckinase=(PK0 +PK1+PK2+PK1H + PT2 +PK2P + pk3+ pt3 + pk1p +pk4 +pt4+pk3h+pk5+pt5+pk6+pt6+0.5*p11+p12+p22) aux pleckinase=pleckinase ph3 = -(phos-phos_tot) aux ph3=ph3 Cps = -((Cckakin+ck1+ct1+cckaphos+ck2+ct2+cps2)-ccka_tot) aux cps=cps Cckakinase= (Cckakin+ck1+ct1+ck2+ct2) aux cckakinase=cckakinase #dldk = -(divl-divl_tot) #aux dldk = dldk plecdivk= (PLECH1+ P11 +PK1+PK2+PK0+PK1H+pk3+pk4+pt4+plech2+p22+p12+pt2+pt3+pk3h+pk5+pt5+pk6+pt6) aux plecdivk=plecdivk ############################################################################## divk_p = divkp+plech1+2*p11+2*pk0+pk1+pk2+p12+2*pt2+pk1h+pt3+pt4 aux divk_p=divk_p divk_up = divk+plech2+2*p22+p12+2*pk4+pk2+pk3+pk3h aux divk_up=divk_up divkpf=divk_p/(divk_p+divk_up) aux divkpf=divkpf ############################## INITIAL CONDITIONS ################# init DIVK=3 init DIVJ=1 init DIVL=1 ###################### NUMERICS #################################### @ total=200 # AUTO Settings @ NTST=150, NMAX=2000, NPR=50, DS=-1e-5 @ PARMIN=0, PARMAX=1 @ AUTOXMIN=0, AUTOXMAX=1, AUTOYMIN=0, AUTOYMAX=2 done