Tutorial on two romatic hearts

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We illustrate the practical advantage of having submodels within a project and an important consequence of understanding biological growth within the GPT-framework.

The aim is to grow a disc into a romantic heart

Interaction function in detail (A newly created, empty, interaction function is shown here.)

Uniform polariser (no polariser gradient). Creating a shape using a specified pattern of isotropic growth.	Pattern of isotropic specified growth (no polariser)	Pattern of isotropic specified growth after growing to 3 times the original area.
Uniform specified growth. Creating a shape using a specified pattern of diffusable polariser.	Pattern of specified polariser levels (green-cyan). Polariser can diffuse and the gradient is arrowed. Uniform specified growth (red).	Patterns and shape after growing to 3 times the original area.

Section 1
function m = gpt_twowayheart_20110531( m )
%m = gpt_twowayheart_20110531( m )
%   Morphogen interaction function.
%   Written at 2011-05-31 19:51:32.
%   GFtbox revision 3548, 2011-05-31 14:37:10.747930.

% The user may edit any part of this function between delimiters
% of the form "USER CODE..." and "END OF USER CODE...".  The
% delimiters themselves must not be moved, edited, deleted, or added.

    if isempty(m), return; end

    fprintf( 1, '%s found in %s\n', mfilename(), which(mfilename()) );

    try
        m = local_setproperties( m );
    catch
    end

    realtime = m.globalDynamicProps.currenttime;

Section 2
%%% USER CODE: INITIALISATION

% In this section you may modify the mesh in any way whatsoever.
    if (Steps(m)==0) && m.globalDynamicProps.doinit % First iteration
        % Set up names for variant models.  Useful for running multiple models on a cluster.
        m.userdata.ranges.modelname.range = { 'PolariserBased', 'DifferentialGrowthBased' };  % CLUSTER
         m.userdata.ranges.modelname.index = 1;                       % CLUSTER
    end
    modelname = m.userdata.ranges.modelname.range{m.userdata.ranges.modelname.index};  % CLUSTER
    disp(sprintf('\nRunning %s model %s\n',mfilename, modelname));
    	
    % Set priorities for simultaneous plotting of multiple morphogens, if desired.
    m = leaf_mgen_plotpriority( m, {'ID_PLUSORG', 'ID_MINUSORG'}, [1,2], [0.4,0.4] );

    % Set colour of polariser gradient arrows.
    m = leaf_plotoptions(m,'highgradcolor',[0,0,0],'lowgradcolor',[1,0,0]);
    m = leaf_plotoptions(m,'decorscale',1.5);

    % setup a multiplot of the following morphogens
    m = leaf_plotoptions( m, 'morphogen', {'V_KAREAL','ID_PLUSORG','ID_MINUSORG'});
%%% END OF USER CODE: INITIALISATION

Section 3
%%% SECTION 1: ACCESSING MORPHOGENS AND TIME.
%%% AUTOMATICALLY GENERATED CODE: DO NOT EDIT.

    if isempty(m), return; end

    setGlobals();
    global gNEW_KA_PAR gNEW_KA_PER gNEW_KB_PAR gNEW_KB_PER
    global gNEW_K_NOR gNEW_POLARISER gNEW_STRAINRET gNEW_ARREST
    dt = m.globalProps.timestep;
    polariser_i = gNEW_POLARISER;
    P = m.morphogens(:,polariser_i);
    [kapar_i,kapar_p,kapar_a,kapar_l] = getMgenLevels( m, 'KAPAR' );
    [kaper_i,kaper_p,kaper_a,kaper_l] = getMgenLevels( m, 'KAPER' );
    [kbpar_i,kbpar_p,kbpar_a,kbpar_l] = getMgenLevels( m, 'KBPAR' );
    [kbper_i,kbper_p,kbper_a,kbper_l] = getMgenLevels( m, 'KBPER' );
    [knor_i,knor_p,knor_a,knor_l] = getMgenLevels( m, 'KNOR' );
    [strainret_i,strainret_p,strainret_a,strainret_l] = getMgenLevels( m, 'STRAINRET' );
    [arrest_i,arrest_p,arrest_a,arrest_l] = getMgenLevels( m, 'ARREST' );
    [id_plusorg_i,id_plusorg_p,id_plusorg_a,id_plusorg_l] = getMgenLevels( m, 'ID_PLUSORG' );
    [id_minusorg_i,id_minusorg_p,id_minusorg_a,id_minusorg_l] = getMgenLevels( m, 'ID_MINUSORG' );
    [v_kareal_i,v_kareal_p,v_kareal_a,v_kareal_l] = getMgenLevels( m, 'V_KAREAL' );
    [id_tip_i,id_tip_p,id_tip_a,id_tip_l] = getMgenLevels( m, 'ID_TIP' );
    [id_top_i,id_top_p,id_top_a,id_top_l] = getMgenLevels( m, 'ID_TOP' );
    [s_growth_i,s_growth_p,s_growth_a,s_growth_l] = getMgenLevels( m, 'S_GROWTH' );
    [id_mid_i,id_mid_p,id_mid_a,id_mid_l] = getMgenLevels( m, 'ID_MID' );

% Mesh type: circle
%          centre: 0
%       circumpts: 24
%       coneangle: 0
%         dealign: 0
%          height: 0
%        innerpts: 0
%      randomness: 0.1
%           rings: 4
%         version: 1
%          xwidth: 2
%          ywidth: 2

%            Morphogen   Diffusion   Decay   Dilution   Mutant
%            -------------------------------------------------
%                KAPAR        ----    ----       ----     ----
%                KAPER        ----    ----       ----     ----
%                KBPAR        ----    ----       ----     ----
%                KBPER        ----    ----       ----     ----
%                 KNOR        ----    ----       ----     ----
%            POLARISER         0.1    ----       ----     ----
%            STRAINRET        ----    ----       ----     ----
%               ARREST        ----    ----       ----     ----
%           ID_PLUSORG        ----    ----       ----     ----
%          ID_MINUSORG        ----    ----       ----     ----
%             V_KAREAL        ----    ----       ----     ----
%               ID_TIP        ----    ----       ----     ----
%               ID_TOP        ----    ----       ----     ----
%             S_GROWTH        0.01    ----       ----     ----
%               ID_MID        ----    ----       ----     ----


%%% USER CODE: MORPHOGEN INTERACTIONS

% In this section you may modify the mesh in any way that does not
Section 4
% alter the set of nodes.

% Use the same pattern for both submodels
     RangeTip=(m.nodes(:,1)<-0.8)&...
         (abs(m.nodes(:,2))<0.2);
     RangeMid=(m.nodes(:,1)<=0.5)&...
         (m.nodes(:,1)>-0.5)&...
         (abs(m.nodes(:,2))<0.3);
     RangeTops=(m.nodes(:,1)<=max(m.nodes(:,1))&...
         (m.nodes(:,1)>0.5)&...
         (abs(m.nodes(:,2))>0.3));
    if (Steps(m)==0) && m.globalDynamicProps.doinit  % Initialisation code.
        switch modelname
             case 'PolariserBased'  % 
                % One way to set up a morphogen gradient is by ...
                % Setting up a gradient by clamping the ends (execute only once)
                P(RangeTip)=0;
                P(RangeMid)=0.5;
                P(RangeTops)=1;
                id_plusorg_p=P;
                id_minusorg_p(RangeTip)=1;
                m.morphogenclamp( RangeTops|RangeTip|RangeMid, polariser_i ) = 1;
                m = leaf_mgen_conductivity( m, 'POLARISER', 0.1 );  %specifies the diffusion rate of polariser
                m = leaf_mgen_absorption( m, 'POLARISER', 0.0 );     % specifies degradation rate of polariser
             case 'DifferentialGrowthBased'  % 
                P(:)=0;
                % One way to set up a morphogen gradient is by ...
                % Setting up a gradient by clamping the ends (execute only once)
                s_growth_p(RangeTip)=1;
                s_growth_p(RangeMid)=0.05;
                s_growth_p(RangeTops)=0.8;
                m.morphogenclamp( RangeTops|RangeTip|RangeMid, s_growth_i ) = 1;
                m = leaf_mgen_conductivity( m, 's_growth', 0.001 );  %specifies the diffusion rate of polariser
                m = leaf_mgen_absorption( m, 's_growth', 0.0 );     % specifies degradation rate of polariser
        end
    end
    BasicGrowth=0.01;
    switch modelname
        case 'PolariserBased'  %
            % Every equation to be formatted should end with an at-at Eqn N comment.
            kapar_p(:) = BasicGrowth;  % when isotropic this will be 0.005
            kaper_p(:) = 0.0;   % when isotropic this will be 0.005
            kbpar_p(:) = BasicGrowth;  % when isotropic this will be 0.005
            kbper_p(:) = 0.0;   % when isotropic this will be 0.005
            knor_p(:)  = 0;  % thickness
         case 'DifferentialGrowthBased'  %  
            % Every equation to be formatted should end with an at-at Eqn N comment.
            kapar_p(:) = BasicGrowth*s_growth_p; %0.01;  % when isotropic this will be 0.005
            kaper_p(:) = BasicGrowth*s_growth_p; %0.0;   % when isotropic this will be 0.005
            kbpar_p(:) = BasicGrowth*s_growth_p; %0.01;  % when isotropic this will be 0.005
            kbper_p(:) = BasicGrowth*s_growth_p; %0.0;   % when isotropic this will be 0.005
            knor_p(:)  = 0;  % thickness
    end
    v_kareal_p=kapar_p+kaper_p; % total specified areal growth
Section 5
%%% END OF USER CODE: MORPHOGEN INTERACTIONS

%%% SECTION 3: INSTALLING MODIFIED VALUES BACK INTO MESH STRUCTURE
%%% AUTOMATICALLY GENERATED CODE: DO NOT EDIT.
    m.morphogens(:,polariser_i) = P;
    m.morphogens(:,kapar_i) = kapar_p;
    m.morphogens(:,kaper_i) = kaper_p;
    m.morphogens(:,kbpar_i) = kbpar_p;
    m.morphogens(:,kbper_i) = kbper_p;
    m.morphogens(:,knor_i) = knor_p;
    m.morphogens(:,strainret_i) = strainret_p;
    m.morphogens(:,arrest_i) = arrest_p;
    m.morphogens(:,id_plusorg_i) = id_plusorg_p;
    m.morphogens(:,id_minusorg_i) = id_minusorg_p;
    m.morphogens(:,v_kareal_i) = v_kareal_p;
    m.morphogens(:,id_tip_i) = id_tip_p;
    m.morphogens(:,id_top_i) = id_top_p;
    m.morphogens(:,s_growth_i) = s_growth_p;
    m.morphogens(:,id_mid_i) = id_mid_p;

%%% USER CODE: FINALISATION

%%% END OF USER CODE: FINALISATION

end


%%% USER CODE: SUBFUNCTIONS

Section 6
function m = local_setproperties( m )
end