TysonNovak2001OdeSystem.cpp

/*

Copyright (C) University of Oxford, 2005-2010

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/
#include "TysonNovak2001OdeSystem.hpp"
#include "OdeSystemInformation.hpp"
#include "UblasCustomFunctions.hpp"

TysonNovak2001OdeSystem::TysonNovak2001OdeSystem()
        : AbstractOdeSystemWithAnalyticJacobian(6)
{
    mpSystemInfo = OdeSystemInformation<TysonNovak2001OdeSystem>::Instance();
    
    Init();
}

TysonNovak2001OdeSystem::~TysonNovak2001OdeSystem()
{
    // Do nothing
}

void TysonNovak2001OdeSystem::Init()
{
    // Initialise model parameter values
    mK1 = 0.04;
    mK2d = 0.04;
    mK2dd = 1.0;
    mK2ddd = 1.0;
    mCycB_threshold = 0.1;
    mK3d = 1.0;
    mK3dd = 10.0;
    mK4d = 2.0;
    mK4 = 35;
    mJ3 = 0.04;
    mJ4 = 0.04;
    mK5d = 0.005;
    mK5dd = 0.2;
    mK6 = 0.1;
    mJ5 = 0.3;
    mN = 4u;
    mK7 = 1.0;
    mK8 = 0.5;
    mJ7 = 1e-3;
    mJ8 = 1e-3;
    mMad = 1.0;
    mK9 = 0.1;
    mK10 = 0.02;
    mK11 = 1.0;
    mK12d = 0.2;
    mK12dd = 50.0;
    mK12ddd = 100.0;
    mKeq = 1e3;
    mK13 = 1.0;
    mK14 = 1.0;
    mK15d = 1.5;
    mK15dd = 0.05;
    mK16d = 1.0;
    mK16dd = 3.0;
    mJ15 = 0.01;
    mJ16 = 0.01;
    mMu = 0.01;
    mMstar = 10.0;
}

void TysonNovak2001OdeSystem::EvaluateYDerivatives(double time, const std::vector<double>& rY, std::vector<double>& rDY)
{
    double x1 = rY[0];
    double x2 = rY[1];
    double x3 = rY[2];
    double x4 = rY[3];
    double x5 = rY[4];
    double x6 = rY[5];
    
    double dx1 = 0.0;
    double dx2 = 0.0;
    double dx3 = 0.0;
    double dx4 = 0.0;
    double dx5 = 0.0;
    double dx6 = 0.0;

    double temp1 = 0.0;
    double temp2 = 0.0;
    double temp3 = 0.0;
    
    dx1 = mK1-(mK2d+mK2dd*x2)*x1;
    
    // The commented line below models the start transition, no cycling, without Cdc20A
//    temp1 = ((mK3d)*(1.0-x2))/(mJ3+1.0-x2);
    
    temp1 = ((mK3d+mK3dd*x4)*(1.0-x2))/(mJ3+1.0-x2);
    temp2 = (mK4*x6*x1*x2)/(mJ4+x2);
    dx2 = temp1-temp2;
    
    temp1 = mK5dd*(SmallPow(x1*x6/mJ5,mN)/(1+SmallPow(x1*x6/mJ5,mN)));
    temp2 = mK6*x3;
    dx3 = mK5d + temp1 - temp2;
    
    temp1 = (mK7*x5*(x3-x4))/(mJ7+x3-x4);
    temp2 = (mK8*mMad*x4)/(mJ8+x4);
    temp3 = mK6*x4;
    dx4 = temp1 - temp2 - temp3;
    
    dx5 = mK9*x6*x1*(1.0-x5) - mK10*x5;
    
    dx6 = mMu*x6*(1.0-x6/mMstar);
    
    // Multiply by 60 beacuase the Tyson and Noval 2001 paper has time in minutes, not hours
    rDY[0] = dx1*60.0;
    rDY[1] = dx2*60.0;
    rDY[2] = dx3*60.0;
    rDY[3] = dx4*60.0;
    rDY[4] = dx5*60.0;
    rDY[5] = dx6*60.0;
}

void TysonNovak2001OdeSystem::AnalyticJacobian(const std::vector<double>& rSolutionGuess, double** jacobian, double time, double timeStep)
{
    timeStep *= 60.0; // to scale Jacobian so in hours not minutes
    double x1 = rSolutionGuess[0];
    double x2 = rSolutionGuess[1];
    double x3 = rSolutionGuess[2];
    double x4 = rSolutionGuess[3];
    double x5 = rSolutionGuess[4];
    double x6 = rSolutionGuess[5];
    
    // f1
    double df1_dx1 = -mK2d - mK2dd*x2;
    double df1_dx2 = -mK2dd*x1;
    
    jacobian[0][0] =  1-timeStep*df1_dx1;
    jacobian[0][1] = -timeStep*df1_dx2;
    
    // f2
    double df2_dx1 = -mK4*x6*x2/(mJ4+x2);
    double df2_dx2 = -mJ3*(mK3d + mK3dd*x4)/(SmallPow((mJ3 + 1 - x2),2))
                     -mJ4*mK4*x6*x1/(SmallPow((mJ4+x2),2));
    double df2_dx4 =  mK3dd*(1-x2)/(mJ3+1-x2);
    double df2_dx6 = -mK4*x1*x2/(mJ4+x2);
    
    jacobian[1][0] = -timeStep*df2_dx1;
    jacobian[1][1] =  1-timeStep*df2_dx2;
    jacobian[1][3] = -timeStep*df2_dx4;
    jacobian[1][5] = -timeStep*df2_dx6;
    
    //f3
    double z = x1*x6/mJ5;
    double df3_dx1 = (mK5dd*x6/mJ5)*mN*SmallPow(z,mN-1)/(SmallPow((1-SmallPow(z,mN)),2));
    double df3_dx3 = -mK6;
    double df3_dx6 = (mK5dd*x1/mJ5)*mN*SmallPow(z,mN-1)/(SmallPow((1-SmallPow(z,mN)),2));
    
    jacobian[2][0] = -timeStep*df3_dx1;
    jacobian[2][2] = 1-timeStep*df3_dx3;
    jacobian[2][5] = -timeStep*df3_dx6;
    
    // f4
    double df4_dx3 =  mJ7*mK7*x5/(SmallPow(mJ7+x3-x4,2));
    double df4_dx4 = -mJ7*mK7*x5/(SmallPow(mJ7+x3-x4,2)) - mK6 - mJ8*mK8*mMad/(SmallPow(mJ8+x4,2));
    double df4_dx5 =  mK7*(x3-x4)/(mJ7+x3-x4);
    
    jacobian[3][2] = -timeStep*df4_dx3;
    jacobian[3][3] = 1-timeStep*df4_dx4;
    jacobian[3][4] = -timeStep*df4_dx5;
    
    // f5
    double df5_dx1 =  mK9*x6*(1-x5);
    double df5_dx5 = -mK10 - mK9*x6*x1;
    double df5_dx6 =  mK9*x1*(1-x5);
    
    jacobian[4][0] = -timeStep*df5_dx1;
    jacobian[4][4] = 1-timeStep*df5_dx5;
    jacobian[4][5] = -timeStep*df5_dx6;
    
    // f6
    double df6_dx6 = mMu - 2*mMu*x6/mMstar;
    
    jacobian[5][5] = 1-timeStep*df6_dx6;
}

bool TysonNovak2001OdeSystem::CalculateStoppingEvent(double time, const std::vector<double>& rY)
{
    std::vector<double> dy(rY.size());
    EvaluateYDerivatives(time, rY, dy);
    
    // Only call this a stopping condition if the mass of the cell is over 0.6
    // (normally cycles from 0.5-1.0 ish!)
    return ( (rY[5] > 0.6 )&& (rY[0] < mCycB_threshold) && dy[0] < 0.0 );
}

double TysonNovak2001OdeSystem::CalculateRootFunction(double time, const std::vector<double>& rY)
{
    std::vector<double> dy(rY.size());
    EvaluateYDerivatives(time, rY, dy);

    // Only call this a stopping condition if the mass of the cell is over 0.6
    // (normally cycles from 0.5-1.0 ish!)
    if (rY[5]<0.6)
    {
        return 1.0;
    }

    if (dy[0] >= 0.0)
    {
        return 1.0;
    }
    return rY[0]-mCycB_threshold;
}

template<>
void OdeSystemInformation<TysonNovak2001OdeSystem>::Initialise()
{
    /*
     * Initialise state variables.
     *
     * These initial conditions are the approximate steady state
     * solution values while the commented out conditions are taken
     * from the Tyson and Novak 2001 paper.
     */
    this->mVariableNames.push_back("CycB");
    this->mVariableUnits.push_back("nM");
//    this->mInitialConditions.push_back(0.1);
    this->mInitialConditions.push_back(0.099999999999977);

    this->mVariableNames.push_back("Cdh1");
    this->mVariableUnits.push_back("nM");
//    this->mInitialConditions.push_back(9.8770e-01);
    this->mInitialConditions.push_back(0.989026454281841);

    this->mVariableNames.push_back("Cdc20T");
    this->mVariableUnits.push_back("nM");
//    this->mInitialConditions.push_back(1.5011e+00);
    this->mInitialConditions.push_back(1.547942029285891);

    this->mVariableNames.push_back("Cdc20A");
    this->mVariableUnits.push_back("nM");
//    this->mInitialConditions.push_back(1.2924e+00);
    this->mInitialConditions.push_back(1.421110920135839);

    this->mVariableNames.push_back("IEP");
    this->mVariableUnits.push_back("nM");
//    this->mInitialConditions.push_back(6.5405e-01);
    this->mInitialConditions.push_back(0.672838844290094);

    this->mVariableNames.push_back("mass");
    this->mVariableUnits.push_back("");
//    this->mInitialConditions.push_back(4.7039e-01);
    this->mInitialConditions.push_back(0.970831277863956 / 2);

    this->mInitialised = true;
}