%biopepa.independent.replications: 1
%biopepa.show.all.replications: false
%biopepa.simulation.stoptime: 1
%stochkit.opt.progress.interval: 100


%CIRCADIAN CLOCK MODEL Akman et al. 2008
%version with auxiliary species to avoid the use of integrals
%Notation is the one used in the Bio-PEPA Workbench
%all enzymes and inhibtors are represented as generic modifiers

%******************************************************
%definition of kinetic laws
%******************************************************

%Transcription of MF, with inhibition by PF and activation by PWL
transcription_MF_1 = [(a1*PWL^n)/((1+(PF/b1)^g)*(PWL^n + b2^n))];

%Transcription of MF, with inhibition by PF and activation by PW
transcription_MF_2 = [(a2*PW^m)/((1+(PF/b3)^h)*(PW^m + b4^m))];

%degradation of MF
degradation_MF =[d1*(MF/(MF + b5))];

%Translation of E1F from MF (instead of translation of PF from MF)
translation_E1F =[a3*MF];

%Transformation of E1F into E2F/creation of E2F: E1F -> E2F
%In the SBML of another paper is different (see other model)
transformation_E1F_E2F =[f1*E1F];

%degradation E1F(not sure)
degradation_E1F =[gamma1*E1F];

%degradation of E2F
degradation_E2F =[gamma1*E2F];

%Transformation/Creation of PF from E2F
transformation_E2F_PF =[f1*E2F];

%degradation of PF
degradation_PF =[d2*(PF/(PF + b6))];

%transcription of MW
transcription_MW_1 =[a4];

%transcription of MW activated by PWL
transcription_MW_2 =[(a5*PWL^k)/(PWL^k + b7^k)];

%degradation of MW
degradation_MW  =[d3*(MW/(MW + b8))];

%Translation of E1W from MW
translation_E1W =[a6*MW];

%Translation of E1W Modified enhanced by PF
translation_E1W_2=[a7*PF*MW];

%Transformation of E1W into E2W
transformation_E1W_E2W=[f2*E1W];

%degradation E1W
degradation_E1W= [gamma2*E1W];

%degradation of E2W
degradation_E2W=[gamma2*E2W];

%Creation of PF/transformation of E2W into PF
transformation_E2W_PW=[f2*E2W];

%transformation from PW to PWL after light influence
transformation=[amp*theta( ((time - period*floor(time/period)) - tdawn)*(tdusk - (time - period*floor(time/period))) )*r1*PW];

%transformation inverse
transformation_inverse=[r2*PWL];

%degradation of PW 
degradation_PW = [d4*(PW/(PW + b9))];

%degradation of PWL
degradation_PWL=[d5*(PWL/(PWL + b10))];


%***************************************************
%Definition of species
%***************************************************

%frq mRNA
MF = transcription_MF_1>> +
     transcription_MF_2>> +
     degradation_MF<< +
     (translation_E1F,1)(.) ;

%FRQ protein
PF = (transcription_MF_1,1)(.) +
     (transcription_MF_2,1)(.) +
     transformation_E2F_PF>> +
     degradation_PF<< +
     (translation_E1W_2,1)(.) ;

%Auxiliary species E1F

E1F = translation_E1F>> +
      transformation_E1F_E2F<< +
      degradation_E1F<< ;

%Auxiliary species E2F

E2F = transformation_E2F_PF<< +
      transformation_E1F_E2F>> +
      degradation_E2F<< ;

% wc-1 mRNA
MW = transcription_MW_1>> +
     transcription_MW_2>> +
     degradation_MW<< +
     (translation_E1W,1)(.) +
     (translation_E1W_2,1)(.) ;

%WC-1 protein
PW = (transcription_MF_2,1)(.) +
     transformation_E2W_PW>> +
     transformation<< +
     transformation_inverse>> +
     degradation_PW<< ;

%Auxiliary species E1W

E1W = translation_E1W>> +
      translation_E1W_2>> +
      transformation_E1W_E2W<< +
      degradation_E1W<< ;

%Auxiliary species E2W

E2W = transformation_E2W_PW<< +
      transformation_E1W_E2W>> +
      degradation_E2W<< ;

%WC-1 protein enhanced by light
PWL = (transcription_MF_1,1)(.) +
      (transcription_MW_2,1)(.) +
      transformation>> +
      transformation_inverse<< +
      degradation_PWL<< ;

res = (degradation_MF,1)(.) +
      (degradation_PF,1)(.) +
      (degradation_E1F,1)(.) +
      (degradation_E2F,1)(.) +
      (degradation_MW,1)(.) +
      (degradation_PW,1)(.) +
      (degradation_PWL,1)(.) +
      (degradation_E1W,1)(.) +
      (degradation_E2W,1)(.) +
      (transcription_MW_1,1)(.) ;

%****************************************
%System equation
%****************************************

MF <> E1F <> E2F <> PF<> MW <> PW <> PWL <> E1W <> E2W

%LD: 6-12-6

%EVENTS = [
%(event_dusk, t= 6, theta = thetaamp, 0);
%(event_dawn, t= 18, theta = 0, 0);
%(event_dusk2, t= 30, theta = thetaamp, 0);
%(event_dawn2, t= 42, theta = 0, 0);
%(event_dusk3, t= 54, theta = thetaamp, 0);
%(event_dawn3, t= 66, theta = 0, 0);
%(event_dusk4, t= 78, theta = thetaamp, 0);
%(event_dawn4, t= 80, theta = 0, 0);
%(event_dusk5, t= 92, theta = thetaamp, 0);
%(event_dawn5, t= 104, theta = 0, 0)
% ]