function dy=mcode(t, y, v,w) %%------------------------------------------------------------------------- %This ode file was modified from matlab file provided by Goldbeter et.al. and describes %the model for mammalian circadian incorporating periodic transcriptional inhibition effects. %All parameters except v are from original model of Leloup and Goldbeter[1]. The v parameter %in this file representing periodic transcriptional inhibition pulse. %To study the effect of noise on the entrainment of circadian clock by %transcriptional inhibition, a noise term was added to the third %differential equation, which governs the fluctuation of Bmal1 mRNA %concentration. % The original model of Leloup and Goldbeter is described in the following reference: % 1. Leloup JC, Goldbeter A. Toward a detailed computational model for the % mammalian circadian clock.(2003) Proc Natl Acad Sci U S A.100(12):7051-6. %%------------------------------------------------------------------------- dy=zeros(16,1); %[M_P, M_C, M_B, P_C, C_C, P_CP, C_CP, PC_C, PC_N, PC_CP, PC_NP, B_C, B_CP, B_N, B_NP, I_N]=y; M_P=y(1); %Transcription of the Per genes into the corresponding mRNAs M_C=y(2); %Transcription of the Cry genes into the corresponding mRNAs M_B=y(3); %Transcription of the Bmal1 genes into the corresponding mRNAs P_C=y(4); %Translation of these mRNAs into the cytosolic, unphosphorylated proteins PER C_C=y(5); %Translation of these mRNAs into the cytosolic, unphosphorylated proteins CRY P_CP=y(6); %concentrations of the phosphorylated PER C_CP=y(7); %concentrations of the phosphorylated CRY PC_C=y(8); %In the cytosol, formation of the unphosphorylated PER每CRY complex PC_N=y(9); %concentrations of the nuclear forms of the unphosphorylated complexes PC_CP=y(10);%the concentration of the phosphorylated form of PER-CRY complex PC_NP=y(11);%concentrations of the nuclear forms of the phosphorylated complexes B_C=y(12); %Translation of these mRNAs into the cytosolic, unphosphorylated proteins BMAL1 B_CP=y(13); %concentrations of the phosphorylated forms of BMAL1 B_N=y(14); %concentrations of the nuclear forms of unphosphorylated BMAL1 B_NP=y(15); %concentrations of the nuclear forms of phosphorylated BMAL1 I_N=y(16); %(the concentration of the inactive complex between CLOCK每BMAL1 and PER每CRY %params k1 = 0.4 ; %Rate constant for entry of the PER每CRY complex into the nucleus k2 = 0.2 ; %Rate constant for exit of the PER每CRY complex from the nucleus k3 = 0.4 ; %Rate constant for the formation of the PER每CRY complex k4 = 0.2 ; %Rate constant for dissociation of the PER每CRY complex k5 = 0.4 ; %Rate constant for entry of the BMAL1 protein into the nucleus k6 = 0.2 ; %Rate constant for exit of the BMAL1 protein from the nucleus k7 = 0.5 ; %Rate constant for the formation of the inactive PER每CRY每CLOCK每BMAL1 complex k8 = 0.1 ; %Rate constant for the dissociation of the PER每CRY每CLOCK每BMAL1 complex kap = 0.7 ; %Activation constant for enhancement of Per expression by nuclear BMAL1 kac = 0.6 ; %Activation constant for enhancement of Cry expression by nuclear BMAL1 kib = 2.2 ; %Inhibition constant for repression of Bmal1 expression by nuclear BMAL1 kdmb = 0.01 ; %Nonspecific degradation rate constant for Bmal1 mRNA kdmc = 0.01 ; %Nonspecific degradation rate constant for Cry mRNA kdmp = 0.01 ; %Nonspecific degradation rate constant for Per mRNA kdnc = 0.12 ; %Nonspecific degradation rate constant for cytosolic non-phosphorylated CRY kdn = 0.01 ; %Nonspecific degradation rate constant for other protein species kd = 0.3 ; %Michaelis constant for protein degradation kdp = 0.1 ; %Michaelis constant for protein dephosphorylation kp = 0.1 ; %Michaelis constant for protein phosphorylation kmb = 0.4 ; %Michaelis constant for degradation of Bmal1 mRNA kmc = 0.4 ; %Michaelis constant for degradation of Cry mRNA kmp = 0.31 ; %Michaelis constant for degradation of Per mRNA kstot = 1 ; %Rate constant for protein synthesis ksb = 0.12*kstot ; %Rate constant for synthesis of BMAL1 ksc = 1.6*kstot ; %Rate constant for synthesis of CRY ksp = 0.6*kstot ; %Rate constant for synthesis of PER n = 4 ; %Degree of cooperativity of activation of Per and Cry expression by BMAL1 m = 2 ; %Degree of cooperativity of repression of Bmal1 expression by BMAL1 vphos = 0.4 ; %Phosphorylation rate v1b = 0.5 ; %Maximum rate of cytosolic BMAL1 phosphorylation v1c = 0.6 ; %Maximum rate of cytosolic CRY phosphorylation v1p = vphos ; %Maximum rate of cytosolic PER phosphorylation v1pc = vphos ; %Maximum rate of phosphorylation of cytosolic PER-CRY complex v2b = 0.1 ; %Maximum rate of cytosolic BMAL1 dephosphorylation v2c = 0.1 ; %Maximum rate of cytosolic CRY dephosphorylation v2p = 0.3 ; %Maximum rate of cytosolic PER dephosphorylation v2pc = 0.1 ; %Maximum rate of cytosolic PER每CRY complex dephosphorylation v3b = 0.5 ; %Maximum rate of nuclear BMAL1 phosphorylation v3pc = vphos ; %Maximum rate of phosphorylation of nuclear PER每CRY complex vphos v4b = 0.2 ; %Maximum rate of nuclear BMAL1 dephosphorylation v4pc = 0.1 ; %Maximum rate of dephosphorylation of nuclear PER每CRY complex vdbc = 0.5 ; %Maximum rate of degradation of cytosolic phosphorylated BMAL1 vdbn = 0.6 ; %Maximum rate of degradation of nuclear phosphorylated BMAL1 vdcc = 0.7 ; %Maximum rate of degradation of cytosolic phosphorylated CRY vdin = 0.8 ; %Maximum rate of degradation of nuclear PER每CRY每CLOCK每BMAL1 complex vdpc = 0.7 ; %Maximum rate of degradation of cytosolic phosphorylated PER vdpcc = 0.7 ; %Maximum rate of degradation of cytosolic phosphorylated PER每CRY complex vdpcn = 0.7 ; %Maximum rate of degradation of nuclear phosphorylated PER-CRY complex vmb = 0.8 ; %Maximum rate of Bmal1 mRNA degradation vmc = 1 ; %Maximum rate of Cry mRNA degradation vmp = 1.1 ; %Maximum rate of Per mRNA degradation vstot = 1 ; %Maximum transcription rate vsb = vstot ; %Maximum rate of Bmal1 mRNA synthesis vsc = 1.1*vstot ; %Maximum rate of Cry mRNA synthesis vsp = 1.5*vstot ; %Maximum rate of Per mRNA synthesis % parameter v in the following three equations represents periodic % transcriptional inhibition with v =(1-square(2*pi/period*t,0.5/24*100))/2 % where "period" denotes the period of the transcriptional inhibition cycle % parameter w in the follwoing first equation represents light cycle % with w= square ( 2 * pi / 24 * t, 50 ) * 0.1 + 1.1; vsp=v*vsp*w; vsc=v*vsc; vsb=v*vsb; dM_P=vsp*B_N^n/(kap^n+B_N^n)-vmp*M_P/(kmp+M_P)-kdmp*M_P; dM_C=vsc*B_N^n/(kac^n+B_N^n)-vmc*M_C/(kmc+M_C)-kdmc*M_C; dM_B=vsb*kib^m/(kib^m+B_N^m)-vmb*M_B/(kmb+M_B)-kdmb*M_B;%+ 0.2* randn; %noise was added to this equation when studying the effect of noise dP_C=ksp*M_P-v1p*P_C/(kp+P_C)+v2p*P_CP/(kdp+P_CP)+k4*PC_C-k3*P_C*C_C-kdn*P_C; dC_C=ksc*M_C-v1c*C_C/(kp+C_C)+v2c*C_CP/(kdp+C_CP)+k4*PC_C-k3*P_C*C_C-kdnc*C_C; dP_CP=v1p*P_C/(kp+P_C)-v2p*P_CP/(kdp+P_CP)-vdpc*P_CP/(kd+P_CP)-kdn*P_CP; dC_CP=v1c*C_C/(kp+C_C)-v2c*C_CP/(kdp+C_CP)-vdcc*C_CP/(kd+C_CP)-kdn*C_CP; dPC_C=-v1pc*PC_C/(kp+PC_C)+v2pc*PC_CP/(kdp+PC_CP)-k4*PC_C+k3*P_C*C_C+k2*PC_N-k1*PC_C-kdn*PC_C; dPC_N=-v3pc*PC_N/(kp+PC_N)+v4pc*PC_NP/(kdp+PC_NP)-k2*PC_N+k1*PC_C-k7*B_N*PC_N+k8*I_N-kdn*PC_N; dPC_CP=v1pc*PC_C/(kp+PC_C)-v2pc*PC_CP/(kdp+PC_CP)-vdpcc*PC_CP/(kd+PC_CP)-kdn*PC_CP; dPC_NP=v3pc*PC_N/(kp+PC_N)-v4pc*PC_NP/(kdp+PC_NP)-vdpcn*PC_NP/(kd+PC_NP)-kdn*PC_NP; dB_C=ksb*M_B-v1b*B_C/(kp+B_C)+v2b*B_CP/(kdp+B_CP)-k5*B_C+k6*B_N-kdn*B_C; dB_CP=v1b*B_C/(kp+B_C)-v2b*B_CP/(kdp+B_CP)-vdbc*B_CP/(kd+B_CP)-kdn*B_CP; dB_N=-v3b*B_N/(kp+B_N)+v4b*B_NP/(kdp+B_NP)+k5*B_C-k6*B_N-k7*B_N*PC_N+k8*I_N-kdn*B_N; dB_NP=v3b*B_N/(kp+B_N)-v4b*B_NP/(kdp+B_NP)-vdbn*B_NP/(kd+B_NP)-kdn*B_NP; dI_N=-k8*I_N+k7*B_N*PC_N-vdin*I_N/(kd+I_N)-kdn*I_N; %dy=[]; dy(1)=dM_P; dy(2)=dM_C; dy(3)=dM_B; dy(4)=dP_C; dy(5)=dC_C; dy(6)=dP_CP; dy(7)=dC_CP; dy(8)=dPC_C; dy(9)=dPC_N; dy(10)=dPC_CP; dy(11)=dPC_NP; dy(12)=dB_C; dy(13)=dB_CP; dy(14)=dB_N; dy(15)=dB_NP; dy(16)=dI_N;