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


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
       % @@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

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)

GFtbox interface

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

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