The MAPK Signaling Cascade

Up until now, many of the tutorials have used simple geometry and reaction pathways. The goal of this tutorial is to give you a better idea of what is possible with MCell by creating a more complicated and realistic model. Based on the work of Huang (1996), we will create an MCell model of the MAPK signalling cascade. Modifications were made in adapting the ODE model for both practical and illustrative purposes.

Creating the Mesh

If you would rather skip the mesh creation portion of this tutorial, you can download the blend file and advance to the Annotating the Model section. Otherwise you should watch the video or follow along with the instructions immediately after the video.

After starting up Blender, we need to enable an addon that we'll use later.

Click File>User Preferences, select Addons near the top middle, and then click 3D View under the list of Categories. Select 3D View: Copy Attributes Menu. This will allow us to copy properties (like Modifiers) from one object to another. Optional: Hit Save As Default if you would like to use this Addon every time Blender is started.

Hit a twice so that everything (Cube, Camera, Lamp) in the Scene is selected. Hit x and click Delete to delete these objects.

Creating the Cell

Next add a sphere by hitting Shift-a and selecting Mesh>Icosphere. Change Subdivisions to 5 and Size to 5.0. This will be the cell membrane.

Select the Modifiers button in the Properties window. Select Displace from the Add Modifier drop-down menu. Hit the New button by the Texture drop-down menu. Change Strength to 10. This will add some procedural randomness to our model, so it is not perfectly round.

Next, select Smooth from the Add Modifier drop-down menu. Change Factor to 1 and Repeat to 10. This will smooth out the rough edges that we introduced with the Displace modifier.

We should give our mesh a name. Hit the Object button and change IcoSphere to Cell.

Hit z to switch to a wireframe view of our model so that we can see inside of it.

Creating the Nucleus

We will now add the Nucleus which will be very similar to our Cell but smaller. Hit Shift-a and select Mesh>Icosphere. Change Subdivisions to 3 and Size to 2.0.

We want to add in the randomness like we did before, but let's save ourselves some steps by using the Copy Attributes addon that we enabled earlier. Select the inner sphere first by left clicking on it. Then while holding Shift, select the outer sphere. Hit Ctrl-c and select Copy Modifiers.

Once again, let's rename our mesh. Right click on the nucleus, so only it is selected. Hit the Object button and change IcoSphere to Nucleus.

Creating the Mitochondria

Now, we are going to create some mitochondria. But, first, we have to create a template version which we will then duplicate many times using the Array Modifier.

Hit Shift-a and select Mesh>UV Sphere. Change Segments to 12, Rings to 12, and Size to 0.5. Hit Tab to change into Edit Mode and a to deselect everything. Hit o to change into Proportional Editing mode.

Hold Shift-Alt and right click on the ring around the middle of the circle to select the entire ring. This is what is called a Edge/Vertex Loop Select. Next hit s to scale and Shift-z to constrain the scaling to xy-plane. Roll the mouse wheel down until the Proportional size is listed as 1.46. Type 0.4 and hit Enter. Hit Tab to switch back into Object Mode.

Hit n to open up the Properties panel display. Under the Transform section, change X, Y, and Z to -5.0.

Adding Modifiers

Now we are going to begin duplicating the mitochondria. Hit the Modifier button. Select Array from the drop-down menu. Change Count to 5. Deselect Relative Offset and select Constant Offset. Change X to 2.5. Add two more Array modifiers with similar settings, except one has Y set to 2.5 and the other has Z set to 2.5. You should now have a cuboidal array of mitochondria extending through the cell.

We want to add the same variability to the meshes that we did for the cell and the nucleus. With the mitochondria selected, hold Shift and right click on the cell. Hit Ctrl-c and pick Copy Select Modifiers. Select Displace and Smooth and hit OK. Right click on the mitochondria so only they are selected. Change the Strength of Displace to 0.5. Change the Factor of Smooth to 0.5.

Like we did before, let's name our mesh. Hit the Object button and change Sphere to Mitochondrion.

Move the mitochondria to the second layer by hitting m and 2. Then hit 2 again to switch to layer 2.

Now, we want to add some randomness to their positions and rotations. First, apply all of the modifiers by hitting the Apply underneath each modifier's name. Hit Tab to change into Edit Mode.

Hit p and select By loose parts to separate each discontinuous section of the mesh into a unique object. Hit Tab to change into Object Mode. Select all of them by hitting a twice.

Under Object Tools, hit the Origin button and select Origin to Geometry.

Randomizing Mitochondria Placement

In the Screen layout drop-down menu, which should currently say Default, select Scripting. This should change the types and positioning of the Editors. On the left, is a Text Editor. Hit the New button and paste the following text into the editor:

import bpy, math, random
from mathutils import Euler, Vector

def main(context):
    for ob in context.scene.objects:
        if ob.select == True:
            x_loc = ob.location[0]+random.uniform(-1,1)
            y_loc = ob.location[1]+random.uniform(-1,1)
            z_loc = ob.location[2]+random.uniform(-1,1)
            x_rot = random.uniform(0,2)*math.pi
            y_rot = random.uniform(0,2)*math.pi
            z_rot = random.uniform(0,2)*math.pi
            ob.location = Vector((x_loc,y_loc,z_loc))
            ob.rotation_euler = Euler((x_rot,y_rot,z_rot))

class SimpleOperator(bpy.types.Operator):
    '''Tooltip'''
    bl_idname = "object.simple_operator"
    bl_label = "Simple Object Operator"

    @classmethod
    def poll(cls, context):
        return context.active_object != None

    def execute(self, context):
        main(context)
        return {'FINISHED'}

def register():
    bpy.utils.register_class(SimpleOperator)

def unregister():
    bpy.utils.unregister_class(SimpleOperator)

if __name__ == "__main__":
    register()

    # test call
    bpy.ops.object.simple_operator()

Note: This is merely the Operator Simple Template with several new lines added, which have been highlighted for emphasis.

Hit the Run Script button and all the mitochondrion should be randomly rotated and shifted around. You should now switch back to the Default screen layout. Next, we want to remove any mitochondria that might be outside of the Cell or inside of the Nucleus. Hold Shift and hit 1 so that layer 1 and 2 are both showing. You may want to hit z to turn off wireframe mode.

Remove Extra Mitochondria

We cannot give exact instructions for this next section, because the positioning of your mitochondria will be different. Nevertheless, it shouldn't be too hard to remove the extras. Hit c to do bring up a circle select. Left click and drag around the mitochondria that are outside of the cell being careful not to select the cell itself. You can adjust the size of the circle selector by rolling the mouse wheel up or down. Some that are very close or overlapping with the cell may need to be removed using the normal method of selecting right click. Once you have a group of them selected, hit x and click Delete. Don't forget to check all sides of the cell by holding down the middle mouse button and dragging around.

Next you will want to delete any mitochondria that might be inside the nucleus. The best way to do this is by selecting and hiding everything outside of it first. Select the Cell and hit h to hide it. Then begin circle selecting every mitochondria outside of the nucleus and hit h again. Once you have done that, you can hide the nucleus itself and delete (hit x) anything inside of it.

The numbering of the mitochondria's names will almost certainly have breaks in it. If you'd like to fix this, change to layer two. Select all the mitochodria and hit Ctrl-j to join them all together. Hit the Object button and change them name from Mitochondrion.0## to Mitochondrion. Hit Tab to change into Edit Mode. Hit p and select By loose parts. Select all of them by hitting a twice. Under Object Tools, hit the Origin button and select Origin to Geometry. Now the numbering of the names should be fixed.

We need to make one final set of changes to our Cell and Nucleus. Apply the Displace and Smooth modifiers like you did for the mitochondria.

Setting CellBlender Parameters and Exporting

Select both layers again.

In the 3D View Editor, hit a twice to select everything. Hit the Scene button. Expand the Model Objects panel. Hit the + button. The list should fill with all the objects names. Expand Model Initialization. Change Simulation Iterations to 30000.

Under Reaction Output Settings, enable Include Reaction Output. Next, enable Include Viz Output under Visualization Output Settings.

Let's export what we have right now and fill in the missing pieces with a text editor and the command line. Although we could certainly annotate this fully in CellBlender, it might be quicker to hand edit the files. Expand CellBlender Project Settings and hit Set CellBlender Project Directory. Navigate to /home/user/mcell_tutorial/mapk (where user is your user name) and hit Set Project Directory. Next hit Export CellBlender Project and Export MCell MDL.

Annotating the Model

Molecules

Open mapk.molecules.mdl and put the following into:

DEFINE_MOLECULES
{
    e1 {DIFFUSION_CONSTANT_3D = 6e-6}
    e2 {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkkk {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkkkp {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkk {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkkp {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkkpp {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkkpase {DIFFUSION_CONSTANT_3D = 6e-6}
    mapk {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkp {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkpp {DIFFUSION_CONSTANT_3D = 6e-6}
    mapkpase {DIFFUSION_CONSTANT_3D = 6e-6}

    e1_mapkkk {DIFFUSION_CONSTANT_3D = 6E-6}
    e2_mapkkkp {DIFFUSION_CONSTANT_3D = 6E-6}

    mapkkkp_mapkk {DIFFUSION_CONSTANT_3D = 6E-6}

    mapkkkp_mapkkp {DIFFUSION_CONSTANT_3D = 6E-6}

    mapkkpase_mapkkp {DIFFUSION_CONSTANT_3D = 6E-6}
    mapkkpase_mapkkpp {DIFFUSION_CONSTANT_3D = 6E-6}
    mapkkpp_mapk {DIFFUSION_CONSTANT_3D = 6E-6}
    mapkpase_mapkp {DIFFUSION_CONSTANT_3D = 6E-6}
    mapkkpp_mapkp {DIFFUSION_CONSTANT_3D = 6E-6}
    mapkpase_mapkpp {DIFFUSION_CONSTANT_3D = 6E-6}
}

Reactions

Save and quit. Next open mapk.reactions.mdl and put the following into it:

k1 = 1e8
k2 = 10
k3 = 1e3

DEFINE_REACTIONS
{
    e1 + mapkkk -> e1_mapkkk [k1]
    e1_mapkkk -> e1 + mapkkk [k2]
    e1_mapkkk -> e1 + mapkkkp [k3]

    e2 + mapkkkp -> e2_mapkkkp [k1]
    e2_mapkkkp -> e2 + mapkkkp [k2]
    e2_mapkkkp -> e2 + mapkkk [k3]

    mapkkkp + mapkk -> mapkkkp_mapkk [k1]
    mapkkkp_mapkk -> mapkkkp + mapkk [k2]
    mapkkkp_mapkk -> mapkkkp + mapkkp [k3]

    mapkkpase + mapkkp -> mapkkpase_mapkkp [k1]
    mapkkpase_mapkkp -> mapkkpase + mapkkp [k2]
    mapkkpase_mapkkp -> mapkkpase + mapkk [k3]

    mapkkkp + mapkkp -> mapkkkp_mapkkp [k1]
    mapkkkp_mapkkp -> mapkkkp + mapkkp [k2]
    mapkkkp_mapkkp -> mapkkkp + mapkkpp [k3]

    mapkkpase + mapkkpp -> mapkkpase_mapkkpp [k1]
    mapkkpase_mapkkpp -> mapkkpase + mapkkpp [k2]
    mapkkpase_mapkkpp -> mapkkpase + mapkkp [k3]

    mapkkpp + mapk -> mapkkpp_mapk [k1]
    mapkkpp_mapk -> mapkkpp + mapk [k2]
    mapkkpp_mapk -> mapkkpp + mapkp [k3]

    mapkpase + mapkp -> mapkpase_mapkp [k1]
    mapkpase_mapkp -> mapkpase + mapkp [k2]
    mapkpase_mapkp -> mapkpase + mapk [k3]

    mapkkpp + mapkp -> mapkkpp_mapkp [k1]
    mapkkpp_mapkp -> mapkkpp + mapkp [k2]
    mapkkpp_mapkp -> mapkkpp + mapkpp [k3]

    mapkpase + mapkpp -> mapkpase_mapkpp [k1]
    mapkpase_mapkpp -> mapkpase + mapkpp [k2]
    mapkpase_mapkpp -> mapkpase + mapkp [k3]
}

Surface Regions

Next we need to add in the surface regions for the meshes. Run the following command:

sed -n '1h;1!H;${;g;s/  \}\n\}/  \}\n  DEFINE_SURFACE_REGIONS\n  \{\n    all\{ELEMENT_LIST = [ALL_ELEMENTS]\}\n  \}\n\}/g;p;}' mapk.geometry.mdl > test.mdl

If you are unfamiliar with sed, this command might look strange and intimidating to you. However, we are merely searching for every instance of this:

  }
}

And replacing it with this:

  }
  DEFINE_SURFACE_REGIONS
  {
    all{ELEMENT_LIST = [ALL_ELEMENTS]}
  }
}

This command will create a surface region called all for every object with every element assigned to it.

Partitions and Release Sites

Next, open mapk.main.mdl and add the following text to the beginning:

e1_conc = 1e-5
e2_conc = 1e-5
mapkkk_conc = 1e-5
mapkk_conc = 1e-5
mapk_conc = 1e-5
mapkkpase_conc = 1e-8
mapkpase_conc = 1e-8

half_length = 1.1
partition_step = 0.1
PARTITION_X = [[-half_length TO half_length STEP partition_step]]
PARTITION_Y = [[-half_length TO half_length STEP partition_step]]
PARTITION_Z = [[-half_length TO half_length STEP partition_step]]

In the INSTANTIATE section after the last object, add the following:

e1_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]-Scene.Mitochondrion.022[all]-Scene.Mitochondrion.023[all]
    MOLECULE = e1
    CONCENTRATION = e1_conc
}

e2_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]-Scene.Mitochondrion.022[all]-Scene.Mitochondrion.023[all]
    MOLECULE = e2
    CONCENTRATION = e2_conc
}

mapkkk_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]
    MOLECULE = mapkkk
    CONCENTRATION = mapkkk_conc
}

mapkk_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]
    MOLECULE = mapkk
    CONCENTRATION = mapkk_conc
}

mapk_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]
    MOLECULE = mapk
    CONCENTRATION = mapk_conc
}

mapkkpase_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]
    MOLECULE = mapkkpase
    CONCENTRATION = mapkkpase_conc
}

mapkpase_release RELEASE_SITE {
    SHAPE = Scene.Cell[all]-Scene.Nucleus[all]-Scene.Mitochondrion[all]-Scene.Mitochondrion.001[all]-Scene.Mitochondrion.002[all]-Scene.Mitochondrion.003[all]-Scene.Mitochondrion.004[all]-Scene.Mitochondrion.005[all]-Scene.Mitochondrion.006[all]-Scene.Mitochondrion.007[all]-Scene.Mitochondrion.008[all]-Scene.Mitochondrion.009[all]-Scene.Mitochondrion.010[all]-Scene.Mitochondrion.011[all]-Scene.Mitochondrion.012[all]-Scene.Mitochondrion.013[all]-Scene.Mitochondrion.014[all]-Scene.Mitochondrion.015[all]-Scene.Mitochondrion.016[all]-Scene.Mitochondrion.017[all]-Scene.Mitochondrion.018[all]-Scene.Mitochondrion.019[all]-Scene.Mitochondrion.020[all]-Scene.Mitochondrion.021[all]
    MOLECULE = mapkpase
    CONCENTRATION = mapkpase_conc
}

Note: Your amount of mitochondria will almost certainly differ, and you will need to change your SHAPE accordingly.

Visualization and Reaction Data

Next open mapk.viz_output.mdl" and add the following:

VIZ_OUTPUT
{
    MODE = CELLBLENDER
    FILENAME = "mapk"

    MOLECULES
    {
        NAME_LIST {ALL_MOLECULES}
        ITERATION_NUMBERS {ALL_DATA @ [[0 TO iterations STEP iterations/100]]}
    }

}

Finally, open mapk.rxn_output.mdl" and add this text:

conv = 6.022141e23*1e-15

REACTION_DATA_OUTPUT
{
    OUTPUT_BUFFER_SIZE = 1000
    STEP = dt * 1

    {COUNT[e1,WORLD]} => "reaction_data/e1.dat"
    {COUNT[e2,WORLD]} => "reaction_data/e2.dat"
    {COUNT[mapkkk,WORLD]} => "reaction_data/mapkkk.dat"
    {COUNT[mapkkkp,WORLD]} => "reaction_data/mapkkkp.dat"
    {COUNT[mapkk,WORLD]} => "reaction_data/mapkk.dat"
    {COUNT[mapkkp,WORLD]} => "reaction_data/mapkkp.dat"
    {COUNT[mapkkpp,WORLD]} => "reaction_data/mapkkpp.dat"
    {COUNT[mapk,WORLD]} => "reaction_data/mapk.dat"
    {COUNT[mapkp,WORLD]} => "reaction_data/mapkp.dat"
    {COUNT[mapkpp,WORLD]} => "reaction_data/mapkpp.dat"
    {COUNT[mapkkpase,WORLD]} => "reaction_data/mapkkpase.dat"
    {COUNT[mapkpase,WORLD]} => "reaction_data/mapkpase.dat"

    {COUNT[e1,WORLD] / conv} => "reaction_data/e1_conc.dat"
    {COUNT[e2,WORLD] / conv} => "reaction_data/e2_conc.dat"
    {COUNT[mapkkk,WORLD] / conv} => "reaction_data/mapkkk_conc.dat"
    {COUNT[mapkkkp,WORLD] / conv} => "reaction_data/mapkkkp_conc.dat"
    {COUNT[mapkk,WORLD] / conv} => "reaction_data/mapkk_conc.dat"
    {COUNT[mapkkp,WORLD] / conv} => "reaction_data/mapkkp_conc.dat"
    {COUNT[mapkkpp,WORLD] / conv} => "reaction_data/mapkkpp_conc.dat"
    {COUNT[mapk,WORLD] / conv} => "reaction_data/mapk_conc.dat"
    {COUNT[mapkp,WORLD] / conv} => "reaction_data/mapkp_conc.dat"
    {COUNT[mapkpp,WORLD] / conv} => "reaction_data/mapkpp_conc.dat"
    {COUNT[mapkkpase,WORLD] / conv} => "reaction_data/mapkkpase_conc.dat"
    {COUNT[mapkpase,WORLD] / conv} => "reaction_data/mapkpase_conc.dat"

}

Now you can run your mdl by typing mcell mapk.main.mdl at the command line.