% RainbowTroutModel.m is a program that solves the system of ODEs that
% model the HPOL axis in rainbow trout.  This program can be executed with
% either Octave or MATLAB.  The output of this program is a vector of
% time points (in hours) with a corresponding solution matrix where each
% column represents a different protein in the HPOL axis. The input is the 
% number of successive reproductive cycles you want to predict.  The GnRH 
% function provided (GnRH.xlsx) will run up to three consecutive cycles 
% beginning from the first reproductive cycle.  
 
% Both Octave and MATLAB require the files GnRH.xlsx and
% Parameters.xlsx to run; both of which are included as supplementary
% files.  Further explanation of those files and how to customize the model
% for a specific data set can be found in Appendix S5.
 
% Running the code in MATLAB requires the Statistics Toolbox and the Curve
% Fitting Toolbox. Running the code in Octave requires the following 
% packages: io, odepkg, splines, and statistics.  When running the code in 
% Octave uncomment the line of code which loads the packages needed.
  


function [Time, Solution]=RainbowTroutModel(cycles)
    
   % Packages needed for Octave. Uncomment the following line when using
   % Octave.
   % pkg load io; pkg load odepkg; pkg load splines; pkg load statistics;
   
   % Gets the parameters
   p=getParameters();
   
   % Creates the function for GnRH
   GnRHData=xlsread('GnRH.xlsx'); GnRH=pchip(GnRHData(:,1),GnRHData(:,2)); 
   save GnRHInput.mat GnRH
   
   % End time for one reproductive cycle (approximately 3 weeks after
   % ovulation)
   endTime = 361; % Days

    for i=1:cycles
        if i==1
            % Initial conditions for the initial spawning cycle
            mFSH_0 = 36;
            mLH_0 = 0.01;
            FSHP_0 = 4.2;
            LHPit_0 = 0;
            LHP_0 = 0;
            E2_0 = 0.5;
            DHP_0 = 0;
            OAvg_0 = 0.42;
            mR_0 = 0;			
            R_0 = 0;				
            ER_0 = 0;
            mVTG_0 = 0;
            VTGL_0 = 0;
            VTGP_0 = 0;
            VTGN_0 = 0;
            DHPGreater_0 = 0; 
            FOMGreater_0 = 0; 

            % Note: Transit compartment initial conditions are equal to the
            % hormone being delayed.
            ICs = [mFSH_0 mLH_0 FSHP_0 LHPit_0 LHP_0 E2_0 DHP_0 OAvg_0 ...
                mR_0 R_0 ER_0 mVTG_0 VTGL_0 VTGP_0 VTGN_0 FSHP_0 FSHP_0 ...
                FSHP_0 FSHP_0 FSHP_0 FSHP_0 FSHP_0 E2_0 E2_0 E2_0 LHP_0...
                DHPGreater_0 FOMGreater_0];

        else
            % Sets the initial protein levels of the new cycle to the
            % protein levels at the end of the previous cycle and resets 
            % the average oocyte growth for a new batch of oocytes and 
            % resets the conditions required for ovulation.
            ICs = Y(length(Y),:);
            ICs(8)=OAvg_0;
            ICs(27)=DHPGreater_0;
            ICs(27)=FOMGreater_0;
        end

    % Solves the Differential Equations (time is measured in hours)
       BegT=(i-1)*endTime*24; EndT=i*endTime*24;
       [T,Y] = ode23s(@(t,y) getDifferentialEquations (t, y, p),...
           [BegT EndT],ICs);
        
        if i==1
            Time=T;
            Solution=Y;
        else
            Time=[Time;T];
            Solution=[Solution;Y];
        end
    end
end

%% System of Differential Equations
function differentialEquations = getDifferentialEquations(t,y,p)
    % Variable names and corresponding position in the solutions matrix
    mFSH       = y(1); %FSH beta subunit mRNA (Pituitary)
    mLH        = y(2); %LH beta subunit mRNA (Pituitary)
    FSHP       = y(3); %Follicle Stimulating Hormone (Plasma)
    LHPit      = y(4); %Luteinizing Hormone (Pituitary)
    LHP        = y(5); %Luteinizing Hormone (Plasma)
    E2         = y(6); %Estradiol-17beta (Plasma)
    DHP        = y(7); %17alpha,20beta-hihydroxy-4-pregnen-3-one (Plasma)
    OAvg       = y(8); %Average oocyte follicle diameter
    mR         = y(9); %Estrogen receptor mRNA (Liver)
    R          = y(10); %Estrogen receptor (Liver)
    ER         = y(11); %Estrogen receptor complex (Liver)
    mVTG       = y(12); %Vitellogenin mRNA (Liver)
    VTGL       = y(13); %Vitellogenin protein (Liver)
    VTGP       = y(14); %Vitellogenin protein (Plasma)
    VTGN       = y(15); %Vitellogenin protein (Other)
    TCFSHP1    = y(16); %Transit compartment FSH to E2 (1)
    TCFSHP2    = y(17); %Transit compartment FSH to E2 (2)
    TCFSHP3    = y(18); %Transit compartment FSH to E2 (3)
    TCFSHP4    = y(19); %Transit compartment FSH to E2 (4)
    TCFSHP5    = y(20); %Transit compartment FSH to E2 (5)
    TCFSHP6    = y(21); %Transit compartment FSH to E2 (6)
    TCFSHP7    = y(22); %Transit compartment FSH to E2 (7)
    TCE21      = y(23); %Transit compartment E2 to mLH (1)
    TCE22      = y(24); %Transit compartment E2 to mLH (2)
    TCE23      = y(25); %Transit compartment E2 to mLH (3)
    TCLHP      = y(26); %Transit compartment LH to DHP (1)
    DHPGreater = y(27); %Total time DHP has been higher than DHP_final
    FOMGreater = y(28); %Total time FOM has been higher than FOM_final
    
    % Input value for GnRH - estimated from the experimental data
    GnRH = getGnRHInput(t);

    % Conditions for Ovulation.  When DHP is greater than DHP_final,
    % DHPbigger will be positive and when FOM is greater than FOM_final
    % then FOMbigger will be positive.  When both DHPGreater and FOMGreater
    % are positive Ovulation will equal 1, otherwise it is 0.  The
    % approximation of the Heaviside is used to satisfy uniqueness and
    % existence of solutions.
    Ovulation=Hsidecont(DHPGreater*FOMGreater);
    
    % Oocyte growth stages
    [k,l]=WeibullParameters(OAvg,p,Ovulation);
    S1=wblcdf(p.s1,k,l);
    S2=wblcdf(p.s2,k,l)-wblcdf(p.s1,k,l);
    S3=wblcdf(p.s3,k,l)-wblcdf(p.s2,k,l);
    S4=wblcdf(p.s4,k,l)-wblcdf(p.s3,k,l);
    S5=wblcdf(p.s5,k,l)-wblcdf(p.s4,k,l);
    S6=(wblcdf(p.s6,k,l)-wblcdf(p.s5,k,l))*(1-Ovulation);
    SFOM=(1-wblcdf(p.s6,k,l))*(1-Ovulation);

    
    % The sytem of ODEs
    differentialEquations = [...
         p.ks_mFSH*(1+p.alpha_mFSH_GnRH*GnRH)-p.kd_mFSH*mFSH %1: mFSH
        p.ks_mLH*(1+p.alpha_mLH_GnRH*GnRH+p.alpha_mLH_E2*TCE23)-...
             p.kd_mLH*mLH %2: mLH
        (1/p.V_FSH)*(p.w_Pit*p.ks_FSH*mFSH-p.Cl_FSH*FSHP) %3: FSH_P
        p.ks_LH*mLH-p.kd_LH*LHPit-p.kr_LH*(LHPit-p.N_E2*E2-p.N_DHP*DHP)*...
             Hside(LHPit-p.N_E2*E2-p.N_DHP*DHP)*...
             (E2^p.n_E2/(E2^p.n_E2+p.T_E2_LH^p.n_E2)) %4: LH_Pit
        (1/p.V_LH)*(p.w_Pit*p.kr_LH*(LHPit-p.N_E2*E2-p.N_DHP*DHP)*...
             Hside(LHPit-p.N_E2*E2-p.N_DHP*DHP)*(E2^p.n_E2/(E2^p.n_E2+...
             p.T_E2_LH^p.n_E2))-p.Cl_LH*LHP) %5: LH_P
        (1/p.V_E2*(p.n_oocyte*(p.k_E2+TCFSHP7*(p.Cl_E2_S2*S2+...
             p.Cl_E2_S3*S3+p.Cl_E2_S4*S4+p.Cl_E2_S5*S5+p.Cl_E2_S6*S6))-...
             p.Cl_E2*E2)) %6: E2
        (1/p.V_DHP)*(p.n_oocyte*(TCLHP*(p.Cl_DHP_S2*S2+p.Cl_DHP_S3*S3+...
            p.Cl_DHP_S4*S4+p.Cl_DHP_S5*S5+p.Cl_DHP_S6*S6+...
            p.Cl_DHP_SFOM*(SFOM)))-p.Cl_DHP*DHP) %7: DHP
        (p.k_NV_OAvg*(S1+S2+SFOM)+p.k_V_OAvg*p.Cl_VTG_Seq*(1+FSHP/(FSHP+...
             p.T_Seq_FSH))*(S3+S4+S5+S6)*VTGP) %8: O_Avg
        p.ks_mR*(1+ER*p.alpha_mR_ER)-p.kd_mR*mR %9: mR 
        p.ks_R*mR-p.kd_R*R-p.kon_ER*E2*R+p.koff_ER*ER %10: R
        p.kon_ER*E2*R-(p.koff_ER+p.kd_ER)*ER %11: ER
        p.ks_mVTG*(1+p.alpha_mVTG_ER*ER)-p.kd_mVTG*mVTG %12: mVTG 
        p.ks_VTG*(mVTG/p.N_mVTG)^(p.gamma)-p.kr_VTG*VTGL %13: VTG_L
        (p.kr_VTG*VTGL*p.w_L+p.Cl_VTG_Trans*VTGN-(p.Cl_VTG_Trans+...
             p.Cl_VTG_Seq*((1+FSHP/(FSHP+p.T_Seq_FSH))*(S3+S4+S5+S6))+...
             p.Cl_VTG)*VTGP )/p.V_VTG_P	%14: VTG_P
        (p.Cl_VTG_Trans*VTGP-p.Cl_VTG_Trans*VTGN)/p.V_VTG_N %15: VTG_N
        (7/p.D_FSH_E2)*(FSHP-TCFSHP1) %16: TCFSHP1
        (7/p.D_FSH_E2)*(TCFSHP1-TCFSHP2) %17: TCFSHP2
        (7/p.D_FSH_E2)*(TCFSHP2-TCFSHP3) %18: TCFSHP3
        (7/p.D_FSH_E2)*(TCFSHP3-TCFSHP4) %19: TCFSHP4
        (7/p.D_FSH_E2)*(TCFSHP4-TCFSHP5) %10: TCFSHP5
        (7/p.D_FSH_E2)*(TCFSHP5-TCFSHP6) %21: TCFSHP6
        (7/p.D_FSH_E2)*(TCFSHP6-TCFSHP7) %22: TCFSHP7
        (3/p.D_E2_mLH)*(E2-TCE21) %23: TCE21
        (3/p.D_E2_mLH)*(TCE21-TCE22) %24: TCE22
        (3/p.D_E2_mLH)*(TCE22-TCE23) %25: TCE23
        (1/p.D_LH_DHP)*(LHP-TCLHP) %26: TCLHP
        Hsidecont(DHP-p.DHP_final) %27: DHPbigger
        Hsidecont(SFOM-p.FOM_final) % 28: FOMbigger
    ];
    % Eliminates the small imaginary part sometimes caclulated as a result 
    % of approximating the solution for the system of odes.
    differentialEquations=real(differentialEquations);

end

%% Heaviside function
function Hside = Hside(t)
  if t>0
      Hside = 1;
  else
      Hside = 0;
  end
end

%% Continuous approximation of the Heaviside function
% Uses the Logistic function and is adjusted to have an ouput of 0 when
% evaluated at t=0.
function Hsidecont = Hsidecont(t)
    Hsidecont = 1/(1+exp(-100000000*(t-10^(-3))));
end

%% Parameters for the Weibull Distribution
% Uses Nelder-Mead simplex method optimization to solve for the Weibull
% distribution parameters.  The mean is defined by O_Avg and the variance 
% is defined by the stages.
function [k l]=WeibullParameters(mean,p,Ovulation)
    options = optimset('MaxFunEvals',5000);
    pars = fminsearch(@(a) WeibullParameterConditions([a(1),a(2)],mean,...
        p,Ovulation),[mean,1],options);
    k=pars(1); l=pars(2);
end

function obj = WeibullParameterConditions(abvector,mean,p,Ovulation)
    k = abvector(1); l = abvector(2); 
    [m v]=wblstat(k,l);

    if Ovulation<1
        S1=wblcdf(p.s1,k,l);
        S2=wblcdf(p.s2,k,l)-wblcdf(p.s1,k,l);
        S3=wblcdf(p.s3,k,l)-wblcdf(p.s2,k,l);
        S4=wblcdf(p.s4,k,l)-wblcdf(p.s3,k,l);
        S5=wblcdf(p.s5,k,l)-wblcdf(p.s4,k,l);
        S6=wblcdf(p.s6,k,l)-wblcdf(p.s5,k,l);
        SFOM=1-wblcdf(p.s6,k,l);
    else
        S1=0; S2=0; S3=0; S4=0; S5=0; S6=0; SFOM=0;
    end

    % Oocyte Variance
    var=(p.alpha_OVar_S1*S1+p.alpha_OVar_S2*S2+p.alpha_OVar_S3*S3+...
        p.alpha_OVar_S4*S4+p.alpha_OVar_S5*S5+p.alpha_OVar_S6*S6)+...
        p.alpha_OVar_SFOM*SFOM+p.alpha_OVar_S1*Ovulation;

    obj= norm([mean var]-[m v]); 
end

%% Parameters for the model
function p = getParameters()
	p = struct;
    [ParameterValues,ParameterNames]=xlsread('Parameters.xlsx');
    for i=1:length(ParameterNames)
        p.(ParameterNames{i}) = ParameterValues(i);
    end
end

%% Calls the GnRH function
function GnRH = getGnRHInput(t)
    load GnRHInput.mat; GnRH=fnval(t,GnRH);
    GnRH=(GnRH+abs(GnRH))/2;
end