Tutorial on the basic interaction function

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Creating an interaction function

The goal is to re-create the model used to illustrate why we use matlab. We will create two new variables A and B - in the interaction function they are labelled id_a_p and id_b_p (why? see below). The x,y,z coordinates of mesh nodes (vertices) are stored in the Mesh data structure in a field called nodes. Thus the x coordinate of node 1 is stored in m.nodes(1,1), the y coordinate in m.nodes(1,2) and z coordinate in m.nodes(1,3). The patterns of morphogens A and B are set up by

       id_a_p(m.nodes(:,1)<-0.03)=1; 
       id_b_p(m.nodes(:,2)<-0.01)=1; 

where id_a_p is the A morphogen. m.node(:,1) refers to the x coordinates of all nodes (vertices) in the mesh
The expression (m.nodes(:,1)<-0.03) means find all vertices with x coordinates that are less than -0.03.

Similarly, (m.nodes(:,2)<-0.01) means find all vertices with y coordinates that are less than -0.01.

The model is articulated in the following code.

   if (Steps(m)==0) && m.globalDynamicProps.doinit  % Initialisation code.
       id_a_p(m.nodes(:,1)<-0.03)=1; % setup region for A where identity factor A is represented by id_a_p
       id_b_p(m.nodes(:,2)<-0.01)=1; % setup region for B
   else
       % @@KRN Growth Regulatory Network
       kapar_p(:) = id_a_l .* inh(1,id_b_l); % growth rate
       kaper_p(:) = kapar_p; % isotropic growth
       kbpar_p(:) = kapar_p; % same on both sides of the sheet
       kbper_p(:) = kapar_p; % same
       knor_p(:)  = 0;       % thickness not growing
   end

Creating the interaction function from the GUI

The GFtbox user interface. Start a new project, with a disc shaped mesh and add two new morphogens id_a and id_b (Panel: Morphogens: New). Save As Now create and edit the interaction function by clicking on (Panel: Interaction function: Edit) (bottom left) There is lots of 'green stuff' - lines that are comments. Just for the moment we will more than ignore them - delete them. Look at the listing below to get an idea of what to delete. Now in Section 4 add the code shown above - it is shown in the listing below. A free-text file with the same name as the interaction function is also created automatically on pressing Panel:Interaction function: notes. This makes it easier to keep notes on what you are doing. Note: you can see the internal data structure by clicking Menu: Wizard: Export mesh and follow the instructions shown at the command line. Another way to see Mesh m is to set a break point in the interaction function and running (e.g. Panel: Run: Step, or Panel: Interaction function: Call, etc.) Note: a history of commands that have been run recently can be displayed (can be used to help write custom modelling programs that exploit the GFtbox library)

Variables and utility functions

Variables that need to be seen in the GUI (morphogens, growth factors, signals, etc.) are always set up (declared) from the GUI using Morphogen Panel. We have evolved a naming convention

prefixes	id_ identity factor s_ signalling factor v_ visual monitor f_ finite element monitor
suffixes	_p, _l, _a, _i

Full details of types of morphogens and factors

Pre-defined variables	dt computational step size realtime virtual time of the model
Pre-defined functions	Steps(m) current step number in Mesh m pro(k,id) promote by k in regions designated by factor, id (pro(k,x)=1+kx) inh(k,id) inhibit by k in regions designated by factor, id (inh(k,x)=1/(1+kx)) local_setproperties( m ) initialise Mesh properties leaf_*( m, *) A large library of functions for manipulating the Mesh data structure, m. Many are listed in the GUI help system, Menu:Help

The interaction function in more detail

A large number of comments have been deleted to allow us to focus on the essential components. (What are these deleted comments? They provide hints and clues on how to program a model - many people use the system and we found the easiest way for people to remember how to program models is to provide comments in the appropriate place - which can be deleted when not needed. Ok so you want see an uncensored version, here is a full freshly minted interaction function. It is discussed in more detail here.)

This part is generated automatically from the GUI

The name matches the project name (the project name is forced into lowercase), GFtbox revision number refers to 
our source code control, lines starting with % are comments
    function m = gpt_why_matlab_2011_05_05( m )
    %m = gpt_why_matlab_2011_05_05( m )
    %   Morphogen interaction function.
    %   Written at 2011-05-28 08:08:11.
    %   GFtbox revision 3544, 2011-05-25 13:37:23.907904.

    % 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;
    %%% USER CODE: INITIALISATION
Section 2 This part could contain user code
but in this case there is nothing we need to do before the system extracts information from the Mesh data structure

    %%% END OF USER CODE: INITIALISATION

Section 3 This part is generated automatically from the GUI
Variables are extracted from Mesh and the mesh itself is summarised in a set of comments
    %%% 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_a_i,id_a_p,id_a_a,id_a_l] = getMgenLevels( m, 'ID_A' );
        [id_b_i,id_b_p,id_b_a,id_b_l] = getMgenLevels( m, 'ID_B' );
    % Mesh type: circle
    %          centre: 0
    %       circumpts: 48
    %       coneangle: 0
    %         dealign: 0
    %          height: 0
    %        innerpts: 0
    %      randomness: 0.1
    %           rings: 6
    %         version: 1
    %          xwidth: 0.2
    %          ywidth: 0.2

    %            Morphogen   Diffusion   Decay   Dilution   Mutant
    %            -------------------------------------------------
    %                KAPAR        ----    ----       ----     ----
    %                KAPER        ----    ----       ----     ----
    %                KBPAR        ----    ----       ----     ----
    %                KBPER        ----    ----       ----     ----
    %                 KNOR        ----    ----       ----     ----
    %            POLARISER        ----    ----       ----     ----
    %            STRAINRET        ----    ----       ----     ----
    %               ARREST        ----    ----       ----     ----
    %                 ID_A        ----    ----       ----     ----
    %                 ID_B        ----    ----       ----     ----

Section 4 This part contains user code that articulates the model
    %%% USER CODE: MORPHOGEN INTERACTIONS
        if (Steps(m)==0) && m.globalDynamicProps.doinit  % Initialisation code.
            id_a_p(m.nodes(:,1)<-0.03)=1; % setup region for A
            id_b_p(m.nodes(:,2)<-0.01)=1; % setup region for B
        else
            % @@KRN Growth Regulatory Network
            kapar_p(:) = id_a_l .* inh(1,id_b_l); % growth rate
            kaper_p(:) = kapar_p; % isotropic growth
            kbpar_p(:) = kapar_p; % same on both sides of the sheet
            kbper_p(:) = kapar_p; % same
            knor_p(:)  = 0;       % thickness not growing
        end
Section 5 This part is generated automatically from the GUI
Variables are put back into the data structure (Mesh).
Note: only variables with the _p suffix (promotors) are stored (levels _l can be computed on the fly and activities _a are  
generally set in the GUI - they can only be changed in the interaction function by altering the data structure itself.
    %%% END OF USER CODE: MORPHOGEN INTERACTIONS
    %%% SECTION 6: 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_a_i) = id_a_p;
        m.morphogens(:,id_b_i) = id_b_p;
    %%% USER CODE: FINALISATION

    %%% END OF USER CODE: FINALISATION

    end

    %%% USER CODE: SUBFUNCTIONS

Section 5
    function m = local_setproperties( m )
    end