Creating And Using A New Cell Cycle Model

This tutorial is automatically generated from TestCreatingAndUsingANewCellCycleModelTutorial.hpp at revision 614d6f177ea6. Note that the code is given in full at the bottom of the page.

An example showing how to create a new cell-cycle model and use it in a cell-based simulation

Introduction

In the previous cell-based Chaste tutorials, we used existing cell-cycle models to define how cells proliferate. In this tutorial, we show how to create a new cell-cycle model class, and how this can be used in a cell-based simulation.

Including header files

We begin by including the necessary header files.

#include <cxxtest/TestSuite.h>
#include "CheckpointArchiveTypes.hpp"
#include "AbstractCellBasedTestSuite.hpp"

The next header includes the Boost shared_ptr smart pointer, and defines some useful macros to save typing when using it.

#include "SmartPointers.hpp"

The next header includes the NEVER_REACHED macro, used in one of the methods below.

#include "Exception.hpp"

The next header defines a base class for simple generation-based cell-cycle models. A cell-cycle model is defined as simple if the duration of each phase of the cell cycle is determined when the cell-cycle model is created, rather than evaluated on the fly (e.g. by solving a system of ordinary differential equations for the concentrations of key cell cycle proteins), and may depend on the cell type. A simple cell-cycle model is defined as generation-based if it keeps track of the generation of the corresponding cell, and sets the cell type according to this. Our new cell-cycle model will inherit from this abstract class.

#include "AbstractSimpleGenerationalCellCycleModel.hpp"

The remaining header files define classes that will be used in the cell-based simulation test. We have encountered each of these header files in previous cell-based Chaste tutorials, except for CheckReadyToDivideAndPhaseIsUpdated(), which defines a helper class for testing a cell-cycle model.

#include "CheckReadyToDivideAndPhaseIsUpdated.hpp"
#include "HoneycombMeshGenerator.hpp"
#include "WildTypeCellMutationState.hpp"
#include "GeneralisedLinearSpringForce.hpp"
#include "OffLatticeSimulation.hpp"
#include "StemCellProliferativeType.hpp"
#include "TransitCellProliferativeType.hpp"
#include "DifferentiatedCellProliferativeType.hpp"
//This test is always run sequentially (never in parallel)
#include "FakePetscSetup.hpp"

Defining the cell-cycle model class

As an example, let us consider a cell-cycle model in which the durations of S, G2 and M phases are fixed, but the duration of G1 phase is an exponential random variable with rate parameter λ. This rate parameter is a constant, dependent on cell type, whose value is chosen such that the mean of the distribution, 1/λ, equals the mean G1 duration as defined in the AbstractCellCycleModel class. We will also assume that cells divide a certain number of generations before becoming differentiated. To implement this model we define a new cell-cycle model, MyCellCycleModel, which inherits from AbstractSimpleGenerationalCellCycleModel and overrides the SetG1Duration() method.

Note that usually this code would be separated out into a separate declaration in a .hpp file and definition in a .cpp file.

class MyCellCycleModel : public AbstractSimpleGenerationalCellCycleModel
{
private:

We only need to include the next block of code if we wish to be able to archive (save or load) the cell-cycle model object in a cell-based simulation. The code consists of a serialize method, in which we first archive the cell cycle model using the serialization code defined in the base class AbstractSimpleGenerationalCellCycleModel. We then archive an instance of the RandomNumberGenerator singleton class, which is used in the SetG1Duration() method. Note that serialization of singleton objects must be done with care. Before the object is serialized via a pointer, it must be serialized directly, or an assertion will trip when a second instance of the class is created on de-serialization.

    friend class boost::serialization::access;
    template<class Archive>
    void serialize(Archive & archive, const unsigned int version)
    {
        archive & boost::serialization::base_object<AbstractSimpleGenerationalCellCycleModel>(*this);
        RandomNumberGenerator* p_gen = RandomNumberGenerator::Instance();
        archive & *p_gen;
        archive & p_gen;
    }

We override the SetG1Duration() method as follows.

    void SetG1Duration()
    {

As we will access the cell type of the cell associated with this cell cycle model, we should assert that this cell exists.

        assert(mpCell != NULL);

We now set the G1 duration based on cell type. For stem and transit cells, we use the RandomNumberGenerator singleton class to generate a random number U drawn from U[0,1], and transform this into a random number T drawn from Exp(λ) using the transformation T = -log(U)/λ. For differentiated cells, which do not progress through the cell cycle, we set the G1 duration to DBL_MAX.

        double uniform_random_number = RandomNumberGenerator::Instance()->ranf();

        if (mpCell->GetCellProliferativeType()->IsType<StemCellProliferativeType>())
        {
            mG1Duration = -log(uniform_random_number)*GetStemCellG1Duration();
        }
        else if (mpCell->GetCellProliferativeType()->IsType<TransitCellProliferativeType>())
        {
            mG1Duration = -log(uniform_random_number)*GetTransitCellG1Duration();
        }
        else if (mpCell->GetCellProliferativeType()->IsType<DifferentiatedCellProliferativeType>())
        {
            mG1Duration = DBL_MAX;
        }
        else
        {
            NEVER_REACHED;
        }
    }

The first public method is a default constructor, which just calls the base constructor.

public:

    MyCellCycleModel()
    {}

The second public method overrides CreateCellCycleModel(). This is a builder method to create new copies of the cell-cycle model. We first create a new cell-cycle model, then set each member variable of the new cell-cycle model that inherits its value from the parent.

There are a number of things to mention regarding the CreateCellCycleModel() method: these are quite technical, but are worth stating here for the sake of completeness. If we look at which member variables MyCellCycleModel inherits from its base class, we will find that some of these member variables are not set here. This is for two main reasons. First, some of the new cell-cycle model’s member variables (namely mBirthTime, mCurrentCellCyclePhase, mReadyToDivide) will already have been correctly initialized in the new cell-cycle model’s constructor. Second, the member variable mDimension remains unset, since this cell-cycle model does not need to know the spatial dimension, so if we were to call SetDimension() on the new cell-cycle model an exception would be triggered; hence we do not set this member variable. It is also worth noting that in a simulation, one or more of the new cell-cycle model’s member variables may be set/overwritten as soon as InitialiseDaughterCell() is called on the new cell-cycle model; this occurs when the associated cell has called its Divide() method.

    AbstractCellCycleModel* CreateCellCycleModel()
    {
        MyCellCycleModel* p_model = new MyCellCycleModel();

        p_model->SetBirthTime(mBirthTime);
        p_model->SetMinimumGapDuration(mMinimumGapDuration);
        p_model->SetStemCellG1Duration(mStemCellG1Duration);
        p_model->SetTransitCellG1Duration(mTransitCellG1Duration);
        p_model->SetSDuration(mSDuration);
        p_model->SetG2Duration(mG2Duration);
        p_model->SetMDuration(mMDuration);
        p_model->SetGeneration(mGeneration);
        p_model->SetMaxTransitGenerations(mMaxTransitGenerations);

        return p_model;
    }
};

We need to include the next block of code if you want to be able to archive (save or load) the cell-cycle model object in a cell-based simulation. It is also required for writing out the parameters file describing the settings for a simulation - it provides the unique identifier for our new cell-cycle model. Thus every cell-cycle model class must provide this, or you’ll get errors when running simulations.

#include "SerializationExportWrapper.hpp"
CHASTE_CLASS_EXPORT(MyCellCycleModel)

Since we’re defining the new cell-cycle model within the test file, we need to include the following stanza as well, to make the code work with newer versions of the Boost libraries. Normally the above export declaration would occur in the cell-cycle model’s .hpp file, and the following lines would appear in the .cpp file. See Boost Serialization Guide for more information.

#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(MyCellCycleModel)

This completes the code for MyCellCycleModel. Note that usually this code would be separated out into a separate declaration in a .hpp file and definition in a .cpp file.

The Tests

We now define the test class, which inherits from AbstractCellBasedTestSuite.

class TestCreatingAndUsingANewCellCycleModelTutorial : public AbstractCellBasedTestSuite
{
public:

Testing the cell-cycle model

We begin by testing that our new cell-cycle model is implemented correctly.

    void TestMyCellCycleModel()
    {

Test that we can construct a MyCellCycleModel object:

        TS_ASSERT_THROWS_NOTHING(MyCellCycleModel cell_model3);

Now we construct and initialise a large number of MyCellCycleModels and associated cells:

        unsigned num_cells = (unsigned) 1e5;
        std::vector<CellPtr> cells;
        MAKE_PTR(WildTypeCellMutationState, p_state);
        MAKE_PTR(StemCellProliferativeType, p_stem_type);
        MAKE_PTR(TransitCellProliferativeType, p_transit_type);
        for (unsigned i=0; i<num_cells; i++)
        {
            MyCellCycleModel* p_cell_cycle_model = new MyCellCycleModel;
            CellPtr p_cell(new Cell(p_state, p_cell_cycle_model));
            p_cell->SetCellProliferativeType(p_stem_type);
            p_cell->InitialiseCellCycleModel();
            cells.push_back(p_cell);
        }

To check the CCM has been set up correctly we get a pointer to the one stored on the first cell. We use a static_cast so we can access all the member variables in the concrete class MyCellCycleModel.

Find the mean G1 duration and test that it is within some tolerance of the expected value:

        double expected_mean_g1_duration = static_cast<MyCellCycleModel*>(cells[0]->GetCellCycleModel())->GetStemCellG1Duration();
        double sample_mean_g1_duration = 0.0;

        for (unsigned i=0; i<num_cells; i++)
        {
            sample_mean_g1_duration += static_cast<MyCellCycleModel*>(cells[i]->GetCellCycleModel())->GetG1Duration()/ (double) num_cells;
        }

        TS_ASSERT_DELTA(sample_mean_g1_duration, expected_mean_g1_duration, 0.1);

Now construct another MyCellCycleModel and associated cell. To check it works for transit cells.

        MyCellCycleModel* p_my_model = new MyCellCycleModel;
        CellPtr p_my_cell(new Cell(p_state, p_my_model));
        p_my_cell->SetCellProliferativeType(p_transit_type);
        p_my_cell->InitialiseCellCycleModel();

Use the helper method CheckReadyToDivideAndPhaseIsUpdated() to test that this cell progresses correctly through the cell cycle.

        unsigned num_steps = 100;
        double mean_cell_cycle_time = p_my_model->GetTransitCellG1Duration()
                                        + p_my_model->GetSG2MDuration();

        SimulationTime::Instance()->SetEndTimeAndNumberOfTimeSteps(mean_cell_cycle_time, num_steps);

        for (unsigned i=0; i<num_steps; i++)
        {
            SimulationTime::Instance()->IncrementTimeOneStep();

The numbers for the G1 duration below is taken from the first random number generated:

            CheckReadyToDivideAndPhaseIsUpdated(p_my_model, 2.35762);
        }

Lastly, we briefly test that archiving of MyCellCycleModel has been implemented correctly. Create an OutputFileHandler and use this to define a filename for the archive.

        OutputFileHandler handler("archive", false);
        std::string archive_filename = handler.GetOutputDirectoryFullPath() + "my_cell_cycle_model.arch";

Create an output archive.

Destroy the current instance of SimulationTime and create another instance. Set the start time, end time and number of time steps.

            SimulationTime::Destroy();
            SimulationTime::Instance()->SetStartTime(0.0);
            SimulationTime* p_simulation_time = SimulationTime::Instance();
            p_simulation_time->SetEndTimeAndNumberOfTimeSteps(3.0, 4);

Create a cell with associated cell-cycle model.

            MyCellCycleModel* p_model = new MyCellCycleModel;
            CellPtr p_cell(new Cell(p_state, p_model));
            p_cell->SetCellProliferativeType(p_transit_type);
            p_cell->InitialiseCellCycleModel();

Move forward two time steps.

            p_simulation_time->IncrementTimeOneStep();
            p_simulation_time->IncrementTimeOneStep();

Set the birth time of the cell and update the cell cycle phase.

            p_model->SetBirthTime(-1.0);
            p_model->ReadyToDivide();

            TS_ASSERT_EQUALS(p_model->GetCurrentCellCyclePhase(), S_PHASE);

Now archive the cell-cycle model through its cell.

            CellPtr const p_const_cell = p_cell;

            std::ofstream ofs(archive_filename.c_str());
            boost::archive::text_oarchive output_arch(ofs);
            output_arch << p_const_cell;
        }

Now create an input archive. Begin by again destroying the current instance of SimulationTime and creating another instance. Set the start time, end time and number of time steps.

        {
            SimulationTime::Destroy();
            SimulationTime* p_simulation_time = SimulationTime::Instance();
            p_simulation_time->SetStartTime(0.0);
            p_simulation_time->SetEndTimeAndNumberOfTimeSteps(1.0, 1);

Create a pointer to a cell.

            CellPtr p_cell;

Create an input archive and restore the cell from the archive.

            std::ifstream ifs(archive_filename.c_str(), std::ios::binary);
            boost::archive::text_iarchive input_arch(ifs);

            input_arch >> p_cell;

Test that the private data has been restored correctly. Note we cast it to the correct type so we can acess all the member variables

            MyCellCycleModel* p_model = static_cast<MyCellCycleModel*>(p_cell->GetCellCycleModel());

            TS_ASSERT_DELTA(p_model->GetBirthTime(), -1.0, 1e-12);
            TS_ASSERT_DELTA(p_model->GetAge(), 2.5, 1e-12);
            TS_ASSERT_EQUALS(p_model->GetCurrentCellCyclePhase(), S_PHASE);
        }
    }

Using the cell-cycle model in a cell-based simulation

We conclude with a brief test demonstrating how MyCellCycleModel can be used in a cell-based simulation.

    void TestOffLatticeSimulationWithMyCellCycleModel()
    {

We use the honeycomb mesh generator to create a honeycomb mesh covering a circular domain of given radius.

        HoneycombMeshGenerator generator(10, 10, 0);

Get the mesh using the GetCircularMesh() method.

        boost::shared_ptr<MutableMesh<2,2> > p_mesh = generator.GetCircularMesh(5);

Next, we create some cells. First, define the cells vector.

        std::vector<CellPtr> cells;

We must create a shared_ptr to a CellMutationState with which to bestow the cells. We make use of the macro MAKE_PTR to do this: the first argument is the class and the second argument is the name of the shared_ptr.

        MAKE_PTR(WildTypeCellMutationState, p_state);
        MAKE_PTR(StemCellProliferativeType, p_stem_type);

Then we loop over the nodes.

        for (unsigned i=0; i<p_mesh->GetNumNodes(); i++)
        {

For each node we create a cell with our cell-cycle model.

            MyCellCycleModel* p_model = new MyCellCycleModel();
            CellPtr p_cell(new Cell(p_state, p_model));
            p_cell->SetCellProliferativeType(p_stem_type);

Now, we define a random birth time, chosen from [-T,0], where T = t,,1,, + t,,2,,, where t,,1,, is a parameter representing the G,,1,, duration of a stem cell, and t,,2,, is the basic S+G,,2,,+M phases duration.

            double birth_time = - RandomNumberGenerator::Instance()->ranf() * (p_model->GetStemCellG1Duration() + p_model->GetSG2MDuration());

We then set the birth time and push the cell back into the vector of cells.

            p_cell->SetBirthTime(birth_time);
            cells.push_back(p_cell);
        }

Now that we have defined the mesh and cells, we can define the cell population. The constructor takes in the mesh and the cells vector.

        MeshBasedCellPopulation<2> cell_population(*p_mesh, cells);

We then pass in the cell population into an OffLatticeSimulation, and set the output directory and end time.

        OffLatticeSimulation<2> simulator(cell_population);
        simulator.SetOutputDirectory("TestOffLatticeSimulationWithMyCellCycleModel");
        simulator.SetEndTime(10.0);

We create a force law and pass it to the OffLatticeSimulation.

        MAKE_PTR(GeneralisedLinearSpringForce<2>, p_linear_force);
        p_linear_force->SetCutOffLength(3);
        simulator.AddForce(p_linear_force);

To run the simulation, we call Solve().

        simulator.Solve();
    }
};

Full code

#include <cxxtest/TestSuite.h>
#include "CheckpointArchiveTypes.hpp"
#include "AbstractCellBasedTestSuite.hpp"

#include "SmartPointers.hpp"
#include "Exception.hpp"

#include "AbstractSimpleGenerationalCellCycleModel.hpp"

#include "CheckReadyToDivideAndPhaseIsUpdated.hpp"
#include "HoneycombMeshGenerator.hpp"
#include "WildTypeCellMutationState.hpp"
#include "GeneralisedLinearSpringForce.hpp"
#include "OffLatticeSimulation.hpp"
#include "StemCellProliferativeType.hpp"
#include "TransitCellProliferativeType.hpp"
#include "DifferentiatedCellProliferativeType.hpp"
//This test is always run sequentially (never in parallel)
#include "FakePetscSetup.hpp"

class MyCellCycleModel : public AbstractSimpleGenerationalCellCycleModel
{
private:

    friend class boost::serialization::access;
    template<class Archive>
    void serialize(Archive & archive, const unsigned int version)
    {
        archive & boost::serialization::base_object<AbstractSimpleGenerationalCellCycleModel>(*this);
        RandomNumberGenerator* p_gen = RandomNumberGenerator::Instance();
        archive & *p_gen;
        archive & p_gen;
    }

    void SetG1Duration()
    {
        assert(mpCell != NULL);

        double uniform_random_number = RandomNumberGenerator::Instance()->ranf();

        if (mpCell->GetCellProliferativeType()->IsType<StemCellProliferativeType>())
        {
            mG1Duration = -log(uniform_random_number)*GetStemCellG1Duration();
        }
        else if (mpCell->GetCellProliferativeType()->IsType<TransitCellProliferativeType>())
        {
            mG1Duration = -log(uniform_random_number)*GetTransitCellG1Duration();
        }
        else if (mpCell->GetCellProliferativeType()->IsType<DifferentiatedCellProliferativeType>())
        {
            mG1Duration = DBL_MAX;
        }
        else
        {
            NEVER_REACHED;
        }
    }

public:

    MyCellCycleModel()
    {}

    AbstractCellCycleModel* CreateCellCycleModel()
    {
        MyCellCycleModel* p_model = new MyCellCycleModel();

        p_model->SetBirthTime(mBirthTime);
        p_model->SetMinimumGapDuration(mMinimumGapDuration);
        p_model->SetStemCellG1Duration(mStemCellG1Duration);
        p_model->SetTransitCellG1Duration(mTransitCellG1Duration);
        p_model->SetSDuration(mSDuration);
        p_model->SetG2Duration(mG2Duration);
        p_model->SetMDuration(mMDuration);
        p_model->SetGeneration(mGeneration);
        p_model->SetMaxTransitGenerations(mMaxTransitGenerations);

        return p_model;
    }
};

#include "SerializationExportWrapper.hpp"
CHASTE_CLASS_EXPORT(MyCellCycleModel)

#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(MyCellCycleModel)

class TestCreatingAndUsingANewCellCycleModelTutorial : public AbstractCellBasedTestSuite
{
public:

    void TestMyCellCycleModel()
    {
        TS_ASSERT_THROWS_NOTHING(MyCellCycleModel cell_model3);

        unsigned num_cells = (unsigned) 1e5;
        std::vector<CellPtr> cells;
        MAKE_PTR(WildTypeCellMutationState, p_state);
        MAKE_PTR(StemCellProliferativeType, p_stem_type);
        MAKE_PTR(TransitCellProliferativeType, p_transit_type);
        for (unsigned i=0; i<num_cells; i++)
        {
            MyCellCycleModel* p_cell_cycle_model = new MyCellCycleModel;
            CellPtr p_cell(new Cell(p_state, p_cell_cycle_model));
            p_cell->SetCellProliferativeType(p_stem_type);
            p_cell->InitialiseCellCycleModel();
            cells.push_back(p_cell);
        }

        double expected_mean_g1_duration = static_cast<MyCellCycleModel*>(cells[0]->GetCellCycleModel())->GetStemCellG1Duration();
        double sample_mean_g1_duration = 0.0;

        for (unsigned i=0; i<num_cells; i++)
        {
            sample_mean_g1_duration += static_cast<MyCellCycleModel*>(cells[i]->GetCellCycleModel())->GetG1Duration()/ (double) num_cells;
        }

        TS_ASSERT_DELTA(sample_mean_g1_duration, expected_mean_g1_duration, 0.1);

        MyCellCycleModel* p_my_model = new MyCellCycleModel;
        CellPtr p_my_cell(new Cell(p_state, p_my_model));
        p_my_cell->SetCellProliferativeType(p_transit_type);
        p_my_cell->InitialiseCellCycleModel();

        unsigned num_steps = 100;
        double mean_cell_cycle_time = p_my_model->GetTransitCellG1Duration()
                                        + p_my_model->GetSG2MDuration();

        SimulationTime::Instance()->SetEndTimeAndNumberOfTimeSteps(mean_cell_cycle_time, num_steps);

        for (unsigned i=0; i<num_steps; i++)
        {
            SimulationTime::Instance()->IncrementTimeOneStep();

            CheckReadyToDivideAndPhaseIsUpdated(p_my_model, 2.35762);
        }

        OutputFileHandler handler("archive", false);
        std::string archive_filename = handler.GetOutputDirectoryFullPath() + "my_cell_cycle_model.arch";

        {
            SimulationTime::Destroy();
            SimulationTime::Instance()->SetStartTime(0.0);
            SimulationTime* p_simulation_time = SimulationTime::Instance();
            p_simulation_time->SetEndTimeAndNumberOfTimeSteps(3.0, 4);

            MyCellCycleModel* p_model = new MyCellCycleModel;
            CellPtr p_cell(new Cell(p_state, p_model));
            p_cell->SetCellProliferativeType(p_transit_type);
            p_cell->InitialiseCellCycleModel();

            p_simulation_time->IncrementTimeOneStep();
            p_simulation_time->IncrementTimeOneStep();

            p_model->SetBirthTime(-1.0);
            p_model->ReadyToDivide();

            TS_ASSERT_EQUALS(p_model->GetCurrentCellCyclePhase(), S_PHASE);

            CellPtr const p_const_cell = p_cell;

            std::ofstream ofs(archive_filename.c_str());
            boost::archive::text_oarchive output_arch(ofs);
            output_arch << p_const_cell;
        }

        {
            SimulationTime::Destroy();
            SimulationTime* p_simulation_time = SimulationTime::Instance();
            p_simulation_time->SetStartTime(0.0);
            p_simulation_time->SetEndTimeAndNumberOfTimeSteps(1.0, 1);

            CellPtr p_cell;

            std::ifstream ifs(archive_filename.c_str(), std::ios::binary);
            boost::archive::text_iarchive input_arch(ifs);

            input_arch >> p_cell;

            MyCellCycleModel* p_model = static_cast<MyCellCycleModel*>(p_cell->GetCellCycleModel());

            TS_ASSERT_DELTA(p_model->GetBirthTime(), -1.0, 1e-12);
            TS_ASSERT_DELTA(p_model->GetAge(), 2.5, 1e-12);
            TS_ASSERT_EQUALS(p_model->GetCurrentCellCyclePhase(), S_PHASE);
        }
    }

    void TestOffLatticeSimulationWithMyCellCycleModel()
    {
        HoneycombMeshGenerator generator(10, 10, 0);
        boost::shared_ptr<MutableMesh<2,2> > p_mesh = generator.GetCircularMesh(5);

        std::vector<CellPtr> cells;
        MAKE_PTR(WildTypeCellMutationState, p_state);
        MAKE_PTR(StemCellProliferativeType, p_stem_type);
        for (unsigned i=0; i<p_mesh->GetNumNodes(); i++)
        {
            MyCellCycleModel* p_model = new MyCellCycleModel();
            CellPtr p_cell(new Cell(p_state, p_model));
            p_cell->SetCellProliferativeType(p_stem_type);

            double birth_time = - RandomNumberGenerator::Instance()->ranf() * (p_model->GetStemCellG1Duration() + p_model->GetSG2MDuration());
            p_cell->SetBirthTime(birth_time);
            cells.push_back(p_cell);
        }

        MeshBasedCellPopulation<2> cell_population(*p_mesh, cells);

        OffLatticeSimulation<2> simulator(cell_population);
        simulator.SetOutputDirectory("TestOffLatticeSimulationWithMyCellCycleModel");
        simulator.SetEndTime(10.0);

        MAKE_PTR(GeneralisedLinearSpringForce<2>, p_linear_force);
        p_linear_force->SetCutOffLength(3);
        simulator.AddForce(p_linear_force);

        simulator.Solve();
    }
};

Creating And Using A New Cell Based Simulation Modifier

Creating And Using A New Cell Killer

Creating And Using A New Cell Cycle Model

An example showing how to create a new cell-cycle model and use it in a cell-based simulation#

Introduction#

Including header files#

Defining the cell-cycle model class#

The Tests#

Testing the cell-cycle model#

Using the cell-cycle model in a cell-based simulation#

Full code#