%Code for semi-stochastic model simulation for 5 ng/mL and 50 ng/mL of death
%ligand (DL) with the clustering and disrupted clustering option. The code
%compiled as the supplimentary material to the manuscript:
%Heterogeneous responses to low level death receptor activation are explained by random molecular assembly of the Caspase-8 activation platform.
%Anna Matveeva, Michael Fichtner, Katherine McAllister, Christopher McCann, Marc Sturrock, Daniel B. Longley, Jochen H.M. Prehn.


BaseNameMV='MVfb';
BaseNameMVfollow='MVfollowfb';
BaseNameTF='TFfb';

% DL dose
DLdose=5;  %5 ng/mL of DL;  
%DLdose=50;  %50 ng/mL of DL

% Scenario
clustering=1; %if DR clustering scenario
%clustering=0; %if DR disrupted clustering scenario  

for kkk=1:1 % calculate trajectory for 1 cell
    FileNameMV=[BaseNameMV,num2str(kkk)];
    FileNameMVfollow=[BaseNameMVfollow,num2str(kkk)];
    FileNameTF=[BaseNameTF,num2str(kkk)];
    %------------------------------------------------------------------------------------------------------------------------------------------
    tic;
    if DLdose==5
        d=155+0; %DR5+DR4 functional origins in Hela treated with 50 ng/ml DL
    end
    if DLdose==50
        d=289+34; %DR5+DR4 functional origins in Hela treated with 50 ng/ml DL
    end
    
    sf=100000000; %time looping
    tmax=600; %max time in minutes for simulation
    tstep=1; %step to record in output
    
    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%% Initial ODE param %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    proCas8=54801;
    proCas3=187888;
    proCas6=1204;
    XIAP=98641;
    
    keffc8c3=3.33391E-05;
    keffc3c6=7.66416E-06;
    keffc6c8=2.56749E-08;
    keffc3c3=1.53283E-06;
    
    kdon=4.97404E-09;
    kdoff=0.0257;
    
    kxiapon=9.96341E-05;
    kxiapoff=0.144;
    kcat=1.75;
    
    y=[0,0,0,0,0,0];
    y(end,1)=0; %Dimer of active Caspase 8 (Casp8*)
    y(end,2)=0; %Monomer of active Caspase 3 (Casp3*)
    y(end,3)=0; %Monomer of active Caspase 6 (Casp6*)
    y(end,4)=0; %Monomer of active Caspase 8 (Cs8*)
    y(end,5)=0; %Monomeric active Caspase 3 in the complex with XIAP (Casp3*:XIAP)
    y(end,6)=0; %Ubiquitinated monomeric Caspase 3 (Casp3*ub)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    aon=2.22261E-07; aoff=0.0609; % DED to DED
    bon=2.22261E-07; boff=0.0609; % DED to DED1
    con=2.22261E-07; coff=0.0609; % DED2 to DED1
    don=9.19660E-07; doff=0.4651; % DD to DD
    eon=1.14962E-04; eoff=0.6000; % RHIM-RHIM

    % G{j,1} is a matrix (M,V) size of (ix2) describing the composition of j-th filament
    %%% - M is the molecular type: (1) FADD
    %%%                            (2) Casp8
    %%%                            (3) RIP1
    %%%                            (4) RIP3
    %%%                            (5) CAI (DED1-DED2)
    %%% - V is type of domain via M associated with j-th filament: (1) DD
    %%%                                                            (2) DED
    %%%                                                            (3) DED1
    %%%                                                            (4) RHIM
    %%%                                                            (5) DED2
    %%%                                                            (0) not bound yet
    
    MV=cell(d,1);                %to follow a current state of a filament
    MVfollow=cell(d,tmax/tstep); %to record filament conformation each time step
    TF=cell(14,1);                %to follow remaining free or modified components
    
    for j=1:d
        MV{j,1}=[3 0]; % initially each origin is represented as one molecule of RIP1
    end

    % CF is a matrix (P,A) of size (jx2) that is describing the domains at the end of j-th filament
    CF=zeros(d,2);
    for j=1:d
        CF(j,1)=1;
        CF(j,2)=4;
    end
    P=CF(:,1);
    A=CF(:,2);
    
    % Mfree is a vector of size (1x7) that is describing the amount of free species in the single cell:
    Fc=proCas8; %amount of free proCasp8
    Ff=236574; %amount of free FADD
    Fr1=1942026;  %amount of free RIP1
    Fr3=100; %amount of free RIP3
    Fcifree=0; %amount of free inactivated Casp8 so only DED1-DED2
    Fcibound=0; %...
    Casact=0; %amount of active caspase8 dimer
    Mfree=[Ff,Fc,Fr1,Fr3,Fcifree,Fcibound,Casact];

    % GG array for reaction propensities of j-th filament (total=d):
    % Association rates:
    %%% (kup,kua,krp,kra,knp,kna,kep,kea,krpi,krai)
    % Dissociation rates:
    %%% (kdp,kda,klp,kla,ksp,ksa,kwp,kwa,klpi,klai)

    GG=zeros(d,20);
    %Association
    kup=GG(:,1);
    kua=GG(:,2);
    krp=GG(:,3);
    kra=GG(:,4);
    knp=GG(:,5);
    kna=GG(:,6);
    kep=GG(:,7);
    kea=GG(:,8);
    krpi=GG(:,9);
    krai=GG(:,10);
    
    %Dissociation
    kdp=GG(:,11);
    kda=GG(:,12);
    klp=GG(:,13);
    kla=GG(:,14);
    ksp=GG(:,15);
    ksa=GG(:,16);
    kwp=GG(:,17);
    kwa=GG(:,18);
    klpi=GG(:,19);
    klai=GG(:,20);
    
    ta=0;
    
    % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
    % % % % % % % % % % % % % % TIME LOOP ..... % % % % % % % % % % % % % %
    
    tn=0;
    for v=1:sf

        %   old time
        tiold=tn;
        if tiold<=tmax
            
            
            %++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
            %++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
            % CASPASE ACTIVATION EVENT if DIMER IS BOUND EITHER at P or A tail
            for j=1:d
                if MV{j}(1,1) == 2 && MV{j}(2,1) == 2
                    MV{j}(1,1)=5; MV{j}(2,1)=5; Fcibound=Fcibound+2; Casact=Casact+1;
                end
                if MV{j}(end,1) == 2 && MV{j}(end-1,1) == 2
                    MV{j}(end,1)=5; MV{j}(end-1,1)=5; Fcibound=Fcibound+2; Casact=Casact+1;
                end
            end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% CLUSTERING OPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  START  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%            
if clustering==1           
           
            
            if DLdose==5
                % CASPASE ACTIVATION EVENT if two ProCasp8 molecules are BOUND within one cluster EITHER at P or A tail
                Funvn =[1,2,3,4,5,6,7];
                %TRAIL DR5 and DR4 stimulation with 5 ng/ml of DL
                FUNclust=[16,14,6,6,6,3,3]; 
            end
            
            if DLdose==50
                % CASPASE ACTIVATION EVENT if two ProCasp8 molecules are BOUND within one cluster EITHER at P or A tail
                Funvn =[1,2,3,4,5,6,7,1,2,3,4,5,6,7];
                %TRAIL DR5 and DR4 stimulation with 50 ng/ml of DL
                FUNclust=[30,26,11,12,11,6,5,3,3,1,1,1,1,1];
            end
            
            l=Funvn.*FUNclust;
            ll=cumsum(l);
            
            for cnl=2:7
                for li=1:FUNclust(cnl)
                    jind=[];
                    a=0;
                    jind2=[];
                    a2=0;
                    
                    for j=(ll(cnl-1)+1)+cnl*(li-1):(ll(cnl-1))+cnl*li
                        
                        
                        ind1=find(MV{j}(1,1) == 2);
                        if ind1==1
                            jind=[jind;j]; a=a+1;
                        end
                        ind2=find(MV{j}(end,1) == 2);
                        if ind2==1
                            jind2=[jind2;j]; a2=a2+1;
                        end
                    end
                    
                    if a==2
                        MV{jind(1)}(1,1)=5; MV{jind(2)}(1,1)=5; Fcibound=Fcibound+2; Casact=Casact+1;
                    end
                    if a2==2
                        MV{jind2(1)}(end,1)=5; MV{jind2(2)}(end,1)=5; Fcibound=Fcibound+2; Casact=Casact+1;
                    end
                end
                
            end
            
            if DLdose==50
                for cnl=9:14
                    for li=1:FUNclust(cnl)
                        jind=[];
                        a=0;
                        jind2=[];
                        a2=0;
                        
                        for j=(ll(cnl-1)+1)+(cnl-7)*(li-1):(ll(cnl-1))+(cnl-7)*li
                            
                            
                            ind1=find(MV{j}(1,1) == 2);
                            if ind1==1
                                jind=[jind;j]; a=a+1;
                            end
                            ind2=find(MV{j}(end,1) == 2);
                            if ind2==1
                                jind2=[jind2;j]; a2=a2+1;
                            end
                        end
                        
                        if a==2
                            MV{jind(1)}(1,1)=5; MV{jind(2)}(1,1)=5; Fcibound=Fcibound+2; Casact=Casact+1;
                        end
                        if a2==2
                            MV{jind2(1)}(end,1)=5; MV{jind2(2)}(end,1)=5; Fcibound=Fcibound+2; Casact=Casact+1;
                        end
                    end
                    
                end
            end
   
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  END  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% CLUSTERING OPTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            
            %ASSIGNING RATES FOR CURRENT SYSTEM CONFORMATION
            for j=1:d
                
                %ASSOCIATION
                
                if P(j)==1 %Prepend tail association with filament via DD
                    kup(j)=don*Ff; krp(j)=0; knp(j)=don*Fr1; kep(j)=0; krpi(j)=0; end
                if A(j)==1 %Append tail association with filament via DD
                    kua(j)=don*Ff; kra(j)=0; kna(j)=don*Fr1; kea(j)=0; krai(j)=0; end
                
                if P(j)==2 % ... with filament via DED
                    kup(j)=aon*Ff; krp(j)=bon*Fc; knp(j)=0; kep(j)=0; krpi(j)=bon*Fcifree; end
                if A(j)==2
                    kua(j)=aon*Ff; kra(j)=bon*Fc; kna(j)=0; kea(j)=0; krai(j)=bon*Fcifree; end
                
                if P(j)==3 % ... with filament via DED1 would not work for initial setup with RIP1 origin release
                    kup(j)=bon*Ff; krp(j)=con*Fc; knp(j)=0; kep(j)=0; krpi(j)=con*Fcifree; end
                if A(j)==3 % would not work for initial setup with RIP1 origin release
                    kua(j)=bon*Ff; kra(j)=con*Fc; kna(j)=0; kea(j)=0; krai(j)=con*Fcifree; end
                
                if P(j)==4 % ... with filament via RHIM
                    kup(j)=0; krp(j)=0; knp(j)=eon*Fr1; kep(j)=eon*Fr3; krpi(j)=0; end
                if A(j)==4
                    kua(j)=0; kra(j)=0; kna(j)=eon*Fr1; kea(j)=eon*Fr3; krai(j)=0; end
                
                if P(j)==5 % ... with filament via DED2
                    kup(j)=0; krp(j)=con*Fc; knp(j)=0; kep(j)=0; krpi(j)=con*Fcifree; end
                if A(j)==5
                    kua(j)=0; kra(j)=con*Fc; kna(j)=0; kea(j)=0; krai(j)=con*Fcifree; end
                
                %DISSOCIATION
                
                %%% PREPEND TAIL
                if MV{j}(1,1)==1 % Prepend tail First M(j) -FADD
                    if MV{j}(1,2)==1 % Prepend tail First V(j) -via DD
                        kdp(j)=doff; klp(j)=0; ksp(j)=0; kwp(j)=0; klpi(j)=0;
                    elseif MV{j}(1,2)==2 % Prepend tail First V(j) -via DED
                        kdp(j)=aoff; klp(j)=0; ksp(j)=0; kwp(j)=0; klpi(j)=0;
                    end
                end
                
                if MV{j}(1,1)==2 % Prepend tail First M(j) -Casp8
                    if MV{j}(1,2)==3 % Prepend tail First V(j) -via DED1
                        kdp(j)=0; klp(j)=boff; ksp(j)=0; kwp(j)=0; klpi(j)=0;
                    elseif MV{j}(1,2)==5 % Prepend tail First V(j) -via DED2
                        kdp(j)=0; klp(j)=coff; ksp(j)=0; kwp(j)=0; klpi(j)=0;
                    end
                end
                
                if MV{j}(1,1)==3 % Prepend tail First M(j) -RIP1
                    if MV{j}(1,2)==1 % Prepend tail First V(j) -via DD
                        kdp(j)=0; klp(j)=0; ksp(j)=doff; kwp(j)=0; klpi(j)=0;
                    elseif MV{j}(1,2)==4 % Prepend tail First V(j) -via RHIM
                        kdp(j)=0; klp(j)=0; ksp(j)=eoff; kwp(j)=0; klpi(j)=0;
                    end
                end
                
                if MV{j}(1,1)==4 % Prepend tail First M(j) -RIP3
                    if MV{j}(1,2)==4 % Prepend tail First V(j) -via RHIM
                        kdp(j)=0; klp(j)=0; ksp(j)=0; kwp(j)=eoff; klpi(j)=0;
                    end
                end
                
                if MV{j}(1,1)==5 % Prepend tail First M(j) -CAI (DED1-DED2)
                    if MV{j}(1,2)==3 % Prepend tail First V(j) -via DED1
                        kdp(j)=0; klp(j)=0; ksp(j)=0; kwp(j)=0; klpi(j)=boff;
                    elseif MV{j}(1,2)==5 % Prepend tail First V(j) -via DED2
                        kdp(j)=0; klp(j)=0; ksp(j)=0; kwp(j)=0; klpi(j)=coff;
                    end
                end

                %%% APPEND TAIL
                
                if MV{j}(end,1)==1 % Append tail First M(j) -FADD
                    if MV{j}(end,2)==1 % Append tail First V(j) -via DD
                        kda(j)=doff; kla(j)=0; ksa(j)=0; kwa(j)=0; klai(j)=0;
                    elseif MV{j}(end,2)==2 % Append tail First V(j) -via DED
                        kda(j)=aoff; kla(j)=0; ksa(j)=0; kwa(j)=0; klai(j)=0;
                    end
                end
                
                if MV{j}(end,1)==2 % Append tail First M(j) -Casp8
                    if MV{j}(end,2)==3 % Append tail First V(j) -via DED1
                        kda(j)=0; kla(j)=boff; ksa(j)=0; kwa(j)=0; klai(j)=0;
                    elseif MV{j}(end,2)==5 % Append tail First V(j) -via DED2
                        kda(j)=0; kla(j)=coff; ksa(j)=0; kwa(j)=0; klai(j)=0;
                    end
                end
                
                if MV{j}(end,1)==3 % Append tail First M(j) -RIP1
                    if MV{j}(end,2)==1 % Append tail First V(j) -via DD
                        kda(j)=0; kla(j)=0; ksa(j)=doff; kwa(j)=0; klai(j)=0;
                    elseif MV{j}(end,2)==4 % Append tail First V(j) -via RHIM
                        kda(j)=0; kla(j)=0; ksa(j)=eoff; kwa(j)=0; klai(j)=0;
                    end
                end
                
                if MV{j}(end,1)==4 % Append tail First M(j) -RIP3
                    if MV{j}(end,2)==4 % Append tail First V(j) -via RHIM
                        kda(j)=0; kla(j)=0; ksa(j)=0; kwa(j)=eoff; klai(j)=0;
                    end
                end
                
                if MV{j}(end,1)==5 % Append tail First M(j) -CAI (DED1-DED2)
                    if MV{j}(end,2)==3 % Append tail First V(j) -via DED1
                        kda(j)=0; kla(j)=0; ksa(j)=0; kwa(j)=0; klai(j)=boff;
                    elseif MV{j}(end,2)==5 % Append tail First V(j) -via DED2
                        kda(j)=0; kla(j)=0; ksa(j)=0; kwa(j)=0; klai(j)=coff;
                    end
                end
                
            end
            
            %UPDATE RATES MATRIX GG
            %Association
            GG(:,1)=kup;
            GG(:,2)=kua;
            GG(:,3)=krp;
            GG(:,4)=kra;
            GG(:,5)=knp;
            GG(:,6)=kna;
            GG(:,7)=kep;
            GG(:,8)=kea;
            GG(:,9)=krpi;
            GG(:,10)=krai;
            
            %Dissociation
            GG(:,11)=kdp;
            GG(:,12)=kda;
            GG(:,13)=klp;
            GG(:,14)=kla;
            GG(:,15)=ksp;
            GG(:,16)=ksa;
            GG(:,17)=kwp;
            GG(:,18)=kwa;
            GG(:,19)=klpi;
            GG(:,20)=klai;
            
            %Monte Carlo Algorithm
            poss=cat(1,kup,kua,krp,kra,knp,kna,kep,kea,krpi,krai,kdp,kda,klp,kla,ksp,ksa,kwp,kwa,klpi,klai);
            po=cumsum(poss/sum(poss));
            r1=rand;
            dt=-log(r1)/sum(poss);
            r2=rand;
            
            %UPDATE SYSTEM ACCORDING TO RANDOMLY CHOSEN REACTION:
            % % FADD binding
            %kup
            if r2 >= 0 && r2 < po(1)
                if P(1)==1
                    MV{1}=[[1 1];MV{1}]; P(1)=2;
                    Ff=Ff-1;
                elseif P(1)==2
                    MV{1}=[[1 2];MV{1}]; P(1)=1;
                    Ff=Ff-1;
                    
                end
            end
            for i=1:(d-1)
                if r2 >= po(i) && r2 < po(i+1)
                    if P(i+1)==1
                        MV{i+1}=[[1 1];MV{i+1}]; P(i+1)=2;
                        Ff=Ff-1;
                    elseif P(i+1)==2
                        MV{i+1}=[[1 2];MV{i+1}]; P(i+1)=1;
                        Ff=Ff-1;
                        
                    end
                end
                
            end
            
            for i=1:d
                
                %kua
                if r2 >= po(i-1+d*1) && r2 < po(i+d*1)
                    if A(i)==1
                        MV{i}=[MV{i};[1 1]]; A(i)=2;
                        Ff=Ff-1;
                    elseif A(i)==2
                        MV{i}=[MV{i};[1 2]]; A(i)=1;
                        Ff=Ff-1;
                        
                    end
                end
                
                
                % % Casp8 binding
                %krp
                if r2 >= po(i-1+d*2) && r2 < po(i+d*2)
                    if     P(i)==2
                        MV{i}=[[2 3];MV{i}]; P(i)=5;
                        Fc=Fc-1;
                    elseif P(i)==5
                        MV{i}=[[2 3];MV{i}]; P(i)=5;
                        Fc=Fc-1;
                        
                    end
                end
                %kra
                if r2 >= po(i-1+d*3) && r2 < po(i+d*3)
                    if     A(i)==2
                        MV{i}=[MV{i};[2 3]]; A(i)=5;
                        Fc=Fc-1;
                    elseif A(i)==5
                        MV{i}=[MV{i};[2 3]]; A(i)=5;
                        Fc=Fc-1;
                        
                    end
                end
                
                
                % % RIP1 binding
                %knp
                if r2 >= po(i-1+d*4) && r2 < po(i+d*4)
                    if     P(i)==1
                        MV{i}=[[3 1];MV{i}]; P(i)=4;
                        Fr1=Fr1-1;
                    elseif P(i)==4
                        MV{i}=[[3 4];MV{i}]; P(i)=1;
                        Fr1=Fr1-1;
                    end
                end
                %kna
                if r2 >= po(i-1+d*5) && r2 < po(i+d*5)
                    if     A(i)==1
                        MV{i}=[MV{i};[3 1]]; A(i)=4;
                        Fr1=Fr1-1;
                    elseif A(i)==4
                        MV{i}=[MV{i};[3 4]]; A(i)=1;
                        Fr1=Fr1-1;
                    end
                end
                
                
                % % RIP3 binding
                %kep
                if r2 >= po(i-1+d*6) && r2 < po(i+d*6)
                    if     P(i)==4
                        MV{i}=[[4 4];MV{i}]; P(i)=4;
                        Fr3=Fr3-1;
                    end
                end
                %kea
                if r2 >= po(i-1+d*7) && r2 < po(i+d*7)
                    if     A(i)==4
                        MV{i}=[MV{i};[4 4]]; A(i)=4;
                        Fr3=Fr3-1;
                    end
                end
                
                % % CAI binding (DED1-DED2)
                %krpi
                if r2 >= po(i-1+d*8) && r2 < po(i+d*8)
                    if     P(i)==2
                        MV{i}=[[5 3];MV{i}]; P(i)=5;
                        Fcifree=Fcifree-1; Fcibound=Fcibound+1;
                    elseif P(i)==5
                        MV{i}=[[5 3];MV{i}]; P(i)=5;
                        Fcifree=Fcifree-1; Fcibound=Fcibound+1;
                        
                    end
                end
                %krai
                if r2 >= po(i-1+d*9) && r2 < po(i+d*9)
                    if     A(i)==2
                        MV{i}=[MV{i};[5 3]]; A(i)=5;
                        Fcifree=Fcifree-1; Fcibound=Fcibound+1;
                    elseif A(i)==5
                        MV{i}=[MV{i};[5 3]]; A(i)=5;
                        Fcifree=Fcifree-1; Fcibound=Fcibound+1;
                        
                    end
                end
                
                % % FADD dissociation
                %kdp
                if r2 >= po(i-1+d*10) && r2 < po(i+d*10)
                    if MV{i}(1,1)==1
                        if      MV{i}(1,2)==1
                            MV{i}(1,:)=[]; P(i)=1;
                            Ff=Ff+1;
                        elseif  MV{i}(1,2)==2
                            MV{i}(1,:)=[]; P(i)=2;
                            Ff=Ff+1;
                        end
                    end
                end
                %kda
                if r2 >= po(i-1+d*11) && r2 < po(i+d*11)
                    if MV{i}(end,1)==1
                        if      MV{i}(end,2)==1
                            MV{i}(end,:)=[]; A(i)=1;
                            Ff=Ff+1;
                        elseif  MV{i}(end,2)==2
                            MV{i}(end,:)=[]; A(i)=2;
                            Ff=Ff+1;
                        end
                    end
                end
                
                
                % % Casp8 dissociation
                %klp
                if r2 >= po(i-1+d*12) && r2 < po(i+d*12)
                    if MV{i}(1,1)==2
                        if      MV{i}(1,2)==3
                            MV{i}(1,:)=[]; P(i)=5;
                            Fc=Fc+1;
                            
                        end
                    end
                end
                %kla
                if r2 >= po(i-1+d*13) && r2 < po(i+d*13)
                    if MV{i}(end,1)==2
                        if      MV{i}(end,2)==3
                            MV{i}(end,:)=[]; A(i)=5;
                            Fc=Fc+1;
                            
                        end
                    end
                end
                
                
                % % RIP1 dissociation
                %ksp
                if r2 >= po(i-1+d*14) && r2 < po(i+d*14)
                    if MV{i}(1,1)==3
                        if      MV{i}(1,2)==1
                            MV{i}(1,:)=[]; P(i)=1;
                            Fr1=Fr1+1;
                        elseif  MV{i}(1,2)==4
                            MV{i}(1,:)=[]; P(i)=4;
                            Fr1=Fr1+1;
                        end
                    end
                end
                %ksa
                if r2 >= po(i-1+d*15) && r2 < po(i+d*15)
                    if MV{i}(end,1)==3
                        if      MV{i}(end,2)==1
                            MV{i}(end,:)=[]; A(i)=1;
                            Fr1=Fr1+1;
                        elseif  MV{i}(end,2)==4
                            MV{i}(end,:)=[]; A(i)=4;
                            Fr1=Fr1+1;
                        end
                    end
                end
                
                
                % % RIP3 dissociation
                %kwp
                if r2 >= po(i-1+d*16) && r2 < po(i+d*16)
                    if MV{i}(1,1)==4
                        if      MV{i}(1,2)==4
                            MV{i}(1,:)=[]; P(i)=4;
                            Fr3=Fr3+1;
                        end
                    end
                end
                %kwa
                if r2 >= po(i-1+d*17) && r2 < po(i+d*17)
                    if MV{i}(end,1)==4
                        if      MV{i}(end,2)==4
                            MV{i}(end,:)=[]; A(i)=4;
                            Fr3=Fr3+1;
                        end
                    end
                end
                
                % % CAI dissociation (DED1-DED2)
                %klpi
                if r2 >= po(i-1+d*18) && r2 < po(i+d*18)
                    if MV{i}(1,1)==5
                        if      MV{i}(1,2)==3
                            MV{i}(1,:)=[]; P(i)=5;
                            Fcifree=Fcifree+1; Fcibound=Fcibound-1;
                            
                        end
                    end
                end
                %klai
                if r2 >= po(i-1+d*19) && r2 < po(i+d*19)
                    if MV{i}(end,1)==5
                        if      MV{i}(end,2)==3
                            MV{i}(end,:)=[]; A(i)=5;
                            Fcifree=Fcifree+1; Fcibound=Fcibound-1;
                            
                        end
                    end
                end
            end
            
            tn = ta + dt;
            
            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ODE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            y(end,1)=Casact; %amount of active caspase8 dimer
            proCas8bound=proCas8-Fc-Fcibound-Fcifree;
            
            tspan = [ta ta+dt];
            y0 = [y(end,1) y(end,2) y(end,3) y(end,4) y(end,5) y(end,6)];
            [t,y] = ode15s(@(t,y) odefcn2(t,y,proCas8,proCas8bound,proCas3,proCas6,XIAP,keffc8c3,keffc3c6,keffc6c8,keffc3c3,kdon,kdoff,kxiapon,kxiapoff,kcat), tspan, y0);
            
            Casact=y(end,1); %amount of active caspase8 dimer update
            Fcifree=2*y(end,1)+y(end,4)-Fcibound; %amount of free inactivated Casp8 (CAI) update
            Fc=proCas8-proCas8bound-Fcifree-Fcibound; %amount of free proCasp8 update
            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            
            ta=tn;
            ti=tn;

            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% OUTPUT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            for wi=0:tmax/tstep
                
                if tiold<=wi*tstep && ti>=wi*tstep
                    
                    
                    % RIP1 and RIP3 together in filament, total number over all filaments
                    R1R3=0;
                    for j=1:d
                        k=find(MV{j}(:,1)==4);
                        kz=size(k,1);
                        for kk=1:size(k,1)
                            if k(kk)~=size(MV{j},1) && MV{j}(k(kk)+1,1)==3
                                R1R3=R1R3+1;
                            end
                            if k(kk)~=1 && MV{j}(k(kk)-1,1)==3
                                R1R3=R1R3+1;
                            end
                        end
                    end
  
                    TF{1}=[TF{1},Ff];
                    TF{2}=[TF{2},Fc];
                    TF{3}=[TF{3},Fr1];
                    TF{4}=[TF{4},Fr3];
                    TF{5}=[TF{5},Casact];% Casp8* dimer
                    TF{6}=[TF{6},Fcifree];
                    TF{7}=[TF{7},Fcibound];
                    TF{8}=[TF{8},R1R3]; % RIP1 and RIP3 together in filament, total number over all filaments
                    TF{9}=[TF{9},y(end,2)];% Casp3* monomer
                    TF{10}=[TF{10},y(end,3)];% Casp6* monomer
                    TF{11}=[TF{11},y(end,4)];% Cs8 monomer
                    TF{12}=[TF{12},y(end,5)];% [Casp3*:XIAP]
                    TF{13}=[TF{13},y(end,6)];% Casp3*ub
                    TF{14}=[TF{14},wi]; %time
   
                    for j=1:d
                        MVfollow{j,wi+1}=MV{j};
                    end
                    
                end
                
            end
            %%%%%%%%%%%%%%%%%%%%%%%%%%%% OUTPUT.....END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            
        end
    end
    
    % % % % % % % % % % % % % TIME LOOP.....END % % % % % % % % % % % % % % %
    % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

    save(FileNameMV,'MV')
    save(FileNameMVfollow,'MVfollow')
    save(FileNameTF,'TF')
    
end


%%%PLOT%%%
% % % % % % % % % % % % % % % % % % % % %
set(0,'defaultFigureColor',[1 1 1])
set(0, 'DefaultFigureRenderer', 'painters');
% % % % % % % % % % % % % % % % % % % % %

keff=1.03466E-04;
QQ = 2.61E-03*1; %threshold rate of FRET probe cleavage


f1 = figure('Units','inches','Position',[0 0 4 4],'PaperPositionMode','auto');
for kkk=1 % show cell number ...
    load(['TFfb',num2str(kkk),'.mat']);
    semilogy(TF{14},TF{5},TF{14},TF{9},TF{14},TF{10},TF{14},TF{11},TF{14},TF{12},TF{14},TF{13})
    legend('Casp8* dimer','Casp3* monomer','Casp6* monomer','Cs8 cleaved monomer','Casp3*:XIAP','Casp3*ub')
    xlabel('Time, min')
    ylabel ('Molecules per cell, #')
    set(gca,'XLim',[0 tmax],'YLim',[0.01 1000000],'Units','normalized','FontUnits','points','FontWeight','normal','FontSize',12);
    hold on
end
hold off

f2 = figure('Units','inches','Position',[0 0 4 4],'PaperPositionMode','auto');
for kkk=1 % show cells numbers [1,2,3]
    load(['TFfb',num2str(kkk),'.mat']);
    y7=1-exp(-keff.*cumsum(TF{5}));
    lin=keff*TF{5}.*(1-y7);
    linb = find(lin > QQ);
    sz=size(linb);
    if sz(end)==0
        lin=lin;
        axesTF=TF{14};
    else
        lin=lin(1:(linb(1)));
        axesTF=TF{14}(1:(linb(1)));
    end
    plot(axesTF,lin,'-')
    set(gca,'XLim',[0 tmax],'YLim',[0 0.005],'Units','normalized','FontUnits','points','FontWeight','normal','FontSize',12);
    xlabel('Time, min')
    ylabel ('Rate of FRET probe cleavage, a.u.')
    axis square
    hold on
end
hold off

function dydt = odefcn2(t,y,proCas8,proCas8bound,proCas3,proCas6,XIAP,keffc8c3,keffc3c6,keffc6c8,keffc3c3,kdon,kdoff,kxiapon,kxiapoff,kcat)
dydt = zeros(6,1);
dydt(1) = kdon*(y(4))^2 - kdoff*y(1);
dydt(2) = (keffc8c3*y(1) + keffc3c3*(y(2)^2))*(proCas3-y(2)-y(5)-y(6))-kxiapon*y(2)*(XIAP-y(5))+kxiapoff*y(5);
dydt(3) = keffc3c6*(y(2)^2)*(proCas6-y(3));
dydt(4) = keffc6c8*(y(3)^2)*(proCas8-2*y(1)-y(4)-proCas8bound) + 2*kdoff*y(1) - 2*kdon*(y(4))^2;
dydt(5) = kxiapon*y(2)*(XIAP-y(5))-y(5)*(kxiapoff+kcat);
dydt(6) = kcat*y(5);
end