Creating the Yeast Cell Morphology with Shmoo

1) Start the Simmune CellDesigner.
2) Set the dimensions of the compartment to Width=45, Height and Length=25. 
3) Click "New Cell" and "Center Cells".
4) Deselect "Show Ruler". Increase the size of the Cell to 1189 cubic microns (at a grid constant of 1 micron).
Note: Cells in the CellDesigner are composed of "Protrusions". A cell contains at least one, the fundamental protrusion determining the spatial origin of the cell. This protrusion can only be modified in size. Modifying its position means moving the cell. Additional protrusions can be moved relative to the fundamental protrusion to permit creating (almost) any (simply-connected) cell shape. The protrusion should have a size of 12.
5) Click "New Protrusion".
Note that the new protrusion is hidden in the fundamental protrusion. Move its x Position to make it visible. When it leaves the fundamental protrusion the cell size increases. Note that you can regulate size and positions of protrusions independently for each protrusion.
6) Move the second protrusion to an x-position of 5 (it will then be hidden again in the larger first protrusion). Increase its size to 7.
Note that you can see the contrinution of a protrusion within a cell by moving the mouse over its controls. 
7) Create a third protrusion at position x=10 and size 6.
8) Create a fourth protrusion at position x=14 and size 5.
9) Create a fifth protrusion at position x=19 and size 5.
10) In order to reproduce exactly the cell shape that was used in the manuscript we now use a protrusion with negative size. Such protrusions are subtracted from the cell geometry. Create a protrusion at x=22. This protrusion (if it has size 2) is hidden in the last protrusion we created (at x=19).
11) Now set the size of the protrusion at x=22 to -3. This will remove the end of the tip, thereby adjusting the cell shape to what was used in the yeast MAPK simulations. 'Negative' protrusions in general can be used to remove unwanted regions from cell shapes. You can also use them to create indentations in cell surfaces. Note that the simulations would work just as well with the tip protrusion as it was before adding the negative protrusion. 
12) Now, we will create a nucleus. Set "Nucleus" as "Edit Mode". 
13) The cell surface now is transparent so we will be able to see the nucleus.
14) Click "New Source".
15) Resize the source of the nucleus to size 5.5 and move it to x=6. Note that you can use the mouse wheel to zoom into the display.
16) Add a second and a third source. Position them at x=9 and x=3 and resize them to 1.5. (Note: even though the display shows a source as a one-cube element for sizes 0.5, 1, 1.5 the internal representation has a higher resolution. If you change the size of one of the two smaller sources to 1 you will see a difference.)
17) Now, we create the Regions for populating the biochemistry of the cell differently in the Shmoo tip and the residual cell body. Set "Regions" as "Edit Mode". 
18) Then click "New Region". Resize and move the Region until it just covers the cell except for a small region at the tip.
19) Click "New Region" and resize and move the new Region until it covers the tip. Note that the two regions repell each other.
20) Call the first Region "Body", the second region "Shmoo".
21) Go back to the "Geometry" "Edit Mode". Select "Show Ruler" and draw a line (click, draw, click) to position the ruler anywhere.
22) Move the ruler until its ends coincide with the tip ...
23) and the end (along the x-axis) of the cell.
24) Enter "7.5" in the text field next to the "Rescale Ruler length to" button. Then click the button.
Note how the Grid Constant and the Volume of the cell has changed. The cell is now 7.5 microns long.
25) Click "Save" and then enter a name for the geometry file (e.g. "Yeast.geo"). Click "Save" in the dialog. Close the CellDesigner.


A short Guided Tour of the Yeast MAPK Signaling Model

Note: Here, we provide a guided tour of the yeast pheromone signaling model. To learn how to create such a model, please take a look at the "G protein Signaling" tutorial.

Practical Note: The windows of the Simmune Modeler contain modules that can be resized to give more space to those aspects of the interface most important for a specific task.

1) Start the Simmune Modeler.
2) Click "Model" -> "Open" and select the model file YeastMAPK.dbf. Click "Open".
3) The Modeler will open the Model Summary page.
4) You can expand the 'Molecule' entry in the treeview to see a listing of the molecules in the model.
5) ...or you can expand the 'Complex Species' entry to see a listing of all complex species and, in subtrees, the complexes that have been defined based on those species.
6) You can some display options of the modeler with the help of the tools->preferences menu.
7) For instance, you can change the icon size of the icons representing molecules and complex species / complexes.
8) Click "Molecule" on the second menu bar to switch to the Molecule page.
9) Double-click the molecule icon/name Gbg in the molecule list to view its properties. The page displays the properties of the Gbg G-protein subunit in the model. The annotation gives some information about the roel that this molecule plays for the model and explains, for instance, why the diffusion coefficient of this molecule is set to a very small value.
10) Clicking on the molecule icon or on 'molecule component1' in the 'molecule composition' window section will switch to a display of the properties of the (only) component of this molecule. For example, the location of this membrane bound molecule is specified as 'Inside-membrane'. This setting will instruct the simulator application to insert this molecule into the inner leaflet of the membrane of a simulated cell. 
11) Double-click the molecule icon/name Ste5 in the molecule list. Ste5 in the model has four binding sites with binding partners as indicated by the (optional) names of the binding sites: Gbg, Ste11, Ste7, Fus3. In contrast to Gbg it is cytosolic, freely diffusing.
12) Double-click the molecule icon/name Ste11 in the molecule list. Ste11, in addition to its binding sites, has four state tags that influence its interactions with other molecules/complexes. These states are associated with the (only) component of the molecule. 
13) Select "Molecule component 1" from the "Molecule Composition" tree view. It is the only component of the molecule Ste11. The component should be highlighted in the molecule graph. 
14) Clicking on "Add/Modify/Remove" next to the "States" field displaying the state tag names for the component opens a small window showing the states "phosphorylated", "bnd1", "bnd2", "Ste5_bnd". These states are used in the model to represent the phosphorylation state, and keep track of the binding state of the molecule for the purpose of using it to modulate molecular interaction possibilities.
Note1: The simulator internally keeps track of the binding state of molecules within complexes independent of these state tags. For example, when a molecule within a complex is bound to another molecule through some binding site then this binding site will not be used by the simulator to establish another binding interaction: every binding site is assumed to be able to bind only to one other site. 
Note2: All molecules in this model have only one component. Please have a look at the Simmune Tutorial "G protein Signaling" for a model including a multi-component transmembrane receptor.
15) Click on "Complex" on the second menu bar to switch to the Complex page.
16) Double-click Species:Ste11. The page displays information about the Complex Species Ste11, including about participation of Ste11 in reactions (Transformations (none), Associations (3), Dissociations (7).
The list below "Complex" shows the various state combinations, formed by different combinations of component tags, that play a role in the model. 
Note: Simmune distinguishes between "Complex Species" and "Complexes". The Complex Species outlines the molecular structure and the possible states of the Complexes belonging to the Species. In other words: A member of a Complex Species with a particular set of states (among which there can be "don't care" entries) is a Complex.
17) Double-click the "pSte11_free" entry in the Complex list. In this Complex (called "pSte11_free"), the phosphorylated state is set to "Active", indicating that this complex represents a phosphorylated version of Ste11 (Note: the model uses simple - as opposed to dual - phosphorylation of the components of the Mating Pheromone triggered MAPK cascade.). All binding related states are "Inactive"  
18) Double-click the "MP2C_Ste11 assoc" entry in the "Relations"->"Associations" list of the Complex. The Complex Association page shows the two interacting, single-molecular complexes "Complex 1" MP2C and "Complex 2" pSte11_free. By requiring that all binding tags are "Inactive" we assume (and define in the model) that the phosphatase MP2C can only bind to its target, phosphorylated Ste11 when Ste11 is not bound to any other molecule, for instance the scaffold Ste5. Note that the definition of the association involves a switch of the "bnd2" tag of Ste11 from "Inactive" to "Active". Using the tags to keep track of bound binding sites allows us to query the model efficiently for all versions of Ste11 that are, for instance, not bound at all, or only bound at site 2 etc. without having to enumerate the various complexes that contain Ste11 in the requested binding state. We will return to this aspect below. The properties of the association furthermore include specifications of the location of the binding partners relative to a membrane ("No Orientation", "trans-binding", "cis-binding"). Both binding partners are cytosolic here (which also means that the association rate has 3D units l/(mol*s)), so that the interaction has "No Orientation" selected. (Please take a look at the E-cadherin model accompanying the manuscript "Computational modeling of cellular signaling processes embedded into their dynamic spatial contexts" for situations that involve orientation issues.) Return to the Complex page for Ste11 by hitting the back button (blue arrow in the second menu bar) twice.
19) Scroll down in the "Complexes" list and select the Species MP2C_Ste11, the result of the association we just took a look at. Double-click the Species.
20) On the complex page for MP2C_Ste11 double-click the Transformation "Ste11 dephosphorylation". The Transformation page shows that the complex consisting of the phosphatase MP2C and phosphorylated Ste11 is transformed into a complex containing non-phosphorylated Ste11. This dephosphorylation is encoded in the state switch of the 'phosphorylated' tag of Ste11. Note that the rules specifying the transformation contain "Don't care" entries for all state tags in the result complex, except for the 'phosphorylated' tag which is set to 'Inactive'. The algorithms generating the reaction networks based on the rules specified with the modeler will leave states that are set to "Don't care" in the result complex(es) of any reaction unchanged relative to the start complex(es). Note that we could have defined the start complex with the state tag 'bnd2' set to "Don't care" since this tag is only used to keep track of the binding state of site 2 of Ste11 in other reaction definitions that do not show all binding partners of Ste11 but require a specific binding state. 
21) For example, in our model, Ste11 can bind to Ste20 only when Ste11 is already bound to Ste5. In the definition of the association between Ste11 and Ste20, however, Ste5 does not explicitely appear as part of a complex involving Ste11 and Ste5 but only implicitely in the tags 'bnd2' and 'Ste5_bnd' which both have to be active in order to permit the association between Ste11 and Ste20. To see this page of the modeler select either complex species Ste11 or complex species Ste20 and then double click the association with name "Ste20_Ste11_unphos assoc".
22) Return to the complex page and double-click the Species Ste7_Fus3. The complex page shows the complex species consisting of the MAPKK Ste7 (yellow) bound to the MAPK Fus3 (red). This complex species is the source of phosphorylated Fus3 in the model. Double-click the transformation "Fus3 phosphorylation at scaffold". 
23) The transformation shows how the encoded binding state of the complexes can be used to specify reaction properties. Ste7, in order to be able to phosphorylate Fus3 according to the scheme shown here, has to be phosphorylated, it is bound to Fus3 through its binding site 1 ("bnd1" is therefore Active) and it is bound via site 2 (active "bnd2" tag) with the tag "Ste5_bnd" specifying that the binding partner for that site is Ste5, the scaffold molecule bundling the components of the pheromone response of yeast. For Fus3, on the other hand, the interaction with Ste7 uses the binding site that would allow Fus3 to interact with Ste5 ("bnd2" is Active but "Ste5_bnd" is not). This activation scheme for Fus3 was used, instead of the more classical view that both Ste7 and Fus3 should be directly Ste5-bound, based on the report by Good, M. et al "The Ste5 Scaffold Directs Mating Signaling by Catalytically Unlocking the Fus3 MAP Kinase for Activation" (Cell, 2009 Mar 20;136(6):1085-97) and based on the constraints given by the measurements of Fus3 phosphorylation and complexation with Ste5 given in Maeder C.I. et al "Spatial regulation of Fus3 MAP kinase activity through a reaction-diffusion mechanism in yeast pheromone signalling" (Nat Cell Biol. 2007 Nov;9(11):1319-26). See the Text "Discussion of experimentally provided constraints for computational modeling of the yeast pheromone response" accompanying the manuscript "Computational modeling of cellular signaling processes embedded into their dynamic spatial contexts".
Finally, we will take a look at some of those complexes that will be used to explore the behavior of the model when it is simulated with the simulator. 
The complex 'scaffold_bnd_pSte7_Fus3_unphos' that is the start complex in the transformation "Fus3 phosphorylation at scaffold" is one of them. As discussed above, the state tags specifying the state of Ste7 in this complex require that Ste7 be active (phosphorylated) and bound to Ste5. The state of Ste5 itself, however is not specified. This means that this two-molecule complex pattern will match any complex containing phosphorylated Ste7, unphosphorylated Fus3 bound to Ste7 and Ste5. As will be shown below, this applies to 28 different complexes for which we can query the total (summed) concentration in the different regions of the simulated cell simply by querying the concentration of this pattern.
24) Return to the complex page and double-click the Species Ste5_Ste7. This complex species consists of Ste7 bound to the scaffold Ste5. Its only complex Ste5_Ste7_all will match any complex containing Ste7 bound to Ste5. Similar patterns are defined for Ste11 bound to Ste5 (Ste5_Ste11_all) and Fus3 bound to Ste5 (Ste5_Fus3_all). 

Exploring the Behavior of the Signaling Model in the Polarized Yeast Cell

1) Start the Simmune Simulator. Select the Simulation Description File "YeastMAPK.sdc" and click "Open".
2) The window for editing the initial biochemistry shows which complexes will be used to populate the regions specified for the yeast geometry. It also shows the membrane pores permitting selective nuclear in- and export (see Simmune simulator documentation on for details on the implementation of nuclear (and other) membrane pores) Note that Gbetagamma ("Gbg") and Spa2p are positioned at the membrane of the "Shmoo" region. The very high concentration of Gbetagamma is used to recruit the experimentally reported concentrations of Ste5 to the Shmoo membrane. Since we are mainly interested in the behavior of the system after successful polarization of Gbg and other adaptors recruiting the components of the MAPK cascade,  we simplify the recruitment process which, in reality, in addition to Gbg depends on several other Shmoo-membrane-localized binding partners for Ste5, among them, for example, the phospholipid PIP2. The maximum complex size of 8 defined as one simulation parameter means that complexes are build containing up to 8 molecules. For the signaling model simulated here, this complex size represents the saturation size given by the specified binding possibilities: allowing for larger complexes does not increase the number of possible complexes (229 in total for this model). With decreasing max. complex size the reaction network becomes smaller with increasingly different biochemical behavior. The network with max. complex size 4 (with 97 different complexes) behaves significantly differently. This is due to the importance of complexes containing Gbg, Ste20, Ste11, Ste5 and complexes containing Gbg bound to Ste5, Ste11, Ste7, Fus3 
Comparing the initial cytoplasmic concentrations of Ste5, Ste11, Ste7 and Fus3 with the concentration values determined in the study by Maeder et al. you will notice that the concentrations used here are consistently higher. This discrepancy is due to the fact that many molecules of the MAPK cascade are recruited to the membrane in the shmoo and do thus not contribute to the concentrations that can be measured in the cyoplasm using FCS after the cells have reached a dynamic equilibrium of their biochemistry (with constant amounts of membrane-bound and cytosolic components). In addition to the initial concentrations, the simulation description used here contains specifications of membrane pores allowing molecular exchange between the cytoplasm and the nucleus. Maeder et al. had measured a three-fold higher concentration of Fus3 in the nucleus than in the cytoplasm. We therefore assume a three-fold higher concentration of nuclear membrane pores importing Fus3 than of pores exporting it. We assume that the same import/export ratio holds for phosphorylated Fus3, pFus3. For Msg5, the phosphatase dephosphorylating pFus3, the measurements had found a 1.5 fold higher concentration in the cytoplasm than in the nucleus. This is, again, reflected in the ratio of importing and exporting membranes pores for this single-molecular complex. Dig, the molecule representing the nuclear binding partners Dig1 and Dig2 of pFus3 is created in the nucleus with a concentration adjusted to reproduce the experimentally reported (Maeder et al.) concentration profile of pFus3 across the cell. Without the interaction with a relatively high concentration of Dig, nuclear pFus3 would be exposed to Msg5 without any of those competing binding partners that can be found in the cytoplasm and at the cytoplasmic membrane. (Ste5 and Ste7 were found to be present in the nucleus in very low concentrations (61-fold lower than Fus3). For the simulations, we chose to exclude them from the nucleus.)
After you have inspected the initial concentrations click OK. Unless you changed the simulation description you don't have to save it again and can click "Cancel" to proceed to the main simulation interface.
3) The simulation interface consists of several components that permit exploring various aspects of the simulation such as the overall behavior of the cells in the system (main "Simulation Window"), the concentration profiles in 2D cut planes through the entire simulated system or selected cells (using the "Slice Selection Window" in combination with the "Slice View Window") and the time course of concentrations (or molecular amounts) for the complexes in the simulated cells. 
4) Clicking and moving the mouse in the 3D display area of the simulator main window allows you to change the aspect of the view.
5) To start the simulation first specify a Time Step. Note: This time step will determine the frequency of updates of the user interface and of exported data, such as automated screenshots. It has no influence on the internal time-stepping procedure used by the algorithms of the simulator to solve the reaction-diffusion equations and perform morphological updates. Click on the "Time Step" button, then enter 10. Click OK.
6) Click on "Simulate for X Seconds" and enter 400.0. Click OK to start the simulation. 
7) The simulator will block the interface as long as a simulation runs but you can interrupt at any point. Note that depending on the complexity of the model the simulator may need some time to finish the simulation step it is currently working on.
8) After the simulation has reached 400 seconds shift-click on the cell (it will change its color to indicate that it has been selected for inspection).
9) Go to the 'Time Trace Window' and select "Now Showing: Patterns", then select pFus3_all from the list. 
10) As the Time Trace Window shows, the production of phosphorylated Fus3 (pFus3_all) has approached a steady level. 
11) Deselect the checkbox 'Display in Mol/ltr' to view the total number of complexes containing pFus3. Move the mouse within the graph to obtain precise concentrations/amounts at the mouse position. The number of roughly 7549 complexes can be compared to the total amount of Fus3 molecules in the system by selecting 'Now Showing: Molecules' and then selecting Fus3. (Since we initialized the simulation with a concentration(!) of Fus3 instead of a number of molecules we would have to multiply this initial concentration by the volume of the cell to get this number - but querying the simulation directly is easier.)
12) We find a number of 17574.3 Fus3 molecules per cell. The cell has thus phosphorylated a fraction of 7549/17574 = 0.43 (or 43%) of its Fus3 contents. 
13) Since we compared the number of complexes containing pFus3 (matched by the pattern pFus3_all) with the total number of Fus3 molecules we have to make sure that we don't have a significant amount of complexes containing more than one pFus3. Selecting "Now Showing: Complexes with Molecule" and then Fus3 we find the total number of complexes containing Fus3 to be around 17373, meaning that only a very small fraction of Fus3 is contained in complexes containing more than one Fus3 molecule. Note: Alternatively, we could have selected the pattern Fus3_all (not pFus3_all!) to inspect the total number of complexes containing Fus3. 
14) In the main Simulation Window select Slice Views -> view slice of a cell. 
15) The Slice Selection Window now shows the cell with a small fraction of its surface singled out. 
16) Click in the 3D display area, press the 'x' key on your keyboard to zoom out ('z' will zoom in again) and move the mouse to see the whole picture: A slice plane cuts through the cell, selecting a region of the cell for a 2D view. 
17) Moving the 'Translation' slider will move the plane and change the region selected for 2D view. Position the plane such that it cuts through the center axis of the cell.
18) Select 'Volume Concentration' (as opposed to 'Surface Concentration') and Patterns (as opposed to Complexes).
19) Select the pattern pFus3_all and click 'Update Display'. Then click 'View Slice'.
20) The Slice View Window will show a 2D concentration profile of the selected pattern (pFus3_all). 
21) To inspect the intracellular gradient of pFus3 in a more quantitative way, click 'Volume Elements intersected by line' then draw a line starting
at the tip of the cell through to its end. After releasing the mouse, a control window will allow you to select the sampling line width and whether a simple averaging of the volume elements contained in the sampling width should be performed or a sampling that weighs off-center contributions with a gaussian. If 'Gaussian' is chosen, and the line width is either 3 or 5, then the concentrations are weighted using a Gaussian distribution. The
function is formed such that the full width at half maximum is equal to the line width.
22) Select 'Gaussian' and Line width:5. Note: In the Cell Designer we built a representation of the yeast cell that has a grid constant of 277 nm. Using a sampling line width of 5 volume elements and a Gaussian sampling function we are thus using a sampling procedure that is close to the way a high-resolution confocal microscope would be able to resolve - in z-direction (along the stacking axis) - a line concentration profile drawn in the xy-plane. 
23) The line profile shows a high concentration of pFus3 at the tip of the shmoo of the cell. Much of this pFus3 accumulation is membrane bound, as can be seen by the rapid decay away from the tip that contains a high relative contribution of the membrane. This rapid initial decay happend on a length scale (277 nm) that exceeds even the lateral resolution of usual, non-super-high-resolution, techniques. To render the profile more similar to an experimentally acquired profile one would have to export the profile (File->Write plot to file) and use a gaussian convolution along the profile axis. This is explained in the supplement accompanying the manuscript "Computational modeling of cellular signaling processes embedded into their dynamic spatial contexts" 
Then click "Slice Views"->"View a slice of a cell" in the main "Simulation Window".
24) Now we will explore specific intracellular complex concentrations region averages and compare them with experimentally reported numbers. Go back to the Slice Selection Window, select the pattern Fus3_all, then click 'Update Display' and 'View Slice'.
25) Click with the mouse somewhere within the cell but outside of the nucleus. The concentration of Fus3 is 577 nano moles. Maeder et al. had measured 571 nano moles in the cytoplasm of pheromone stimulated cells.
26) To measure the concentration at the cell tip go the window menu and click 'Regions of Interest' -> 'Set New Area Region'.
27) Confirm your intend to set a new region.
28) Draw a line around the first two layers of the tip. (The full 3D region corresponding to this selection will incorporate about 2% of the cell's volume -- equalling the tip volume as estimated by Maeder et al.) The Region info reports an average concentration of the selected complex pattern (Fus3_all) of 1.4 micro moles.
29) Go back to the Slice Selection Window, select the pattern Ste5, then click 'Update Display' and 'View Slice'. Adjust the color threshold until the exclusion of Ste5 from the nucleus can be seen clearly. Click with the mouse somewhere within the cell but outside of the nucleus. The concentration of Ste5 is 30.6 nano moles. Maeder et al. had reported 29 nano moles.
30) To measure the concentration at the cell tip go the window menu and click 'Regions of Interest' -> 'Set New Area Region'. Confirm your intend to set a new region. Draw a line around the first two layers of the tip.The Region info reports an average concentration of Ste5 of 850 nano moles.
This means a ratio of 1400/850 = 1.65 of Fus3 to Ste5. Experimentally reported: 1.7.
31) Go back to the Slice Selection Window, select the pattern Ste7_all, then click 'Update Display' and 'View Slice'. Adjust the color threshold until the exclusion of Ste7 from the nucleus can be seen clearly. Click with the mouse somewhere within the cell but outside of the nucleus. The concentration of Ste7 is 61 nano moles. Maeder et al. had reported 63 nano moles.
32) To measure the concentration at the cell tip go the window menu and click 'Regions of Interest' -> 'Set New Area Region'. Confirm your intend to set a new region. Draw a line around the first two layers of the tip.The Region info reports an average concentration of Ste7 of 842 nano moles.
This means that the tip concentration of Ste7 is very close to that of Ste5, in accord with the experimental findings.
33) Now, select Ste11_all as pattern for the slice view. The cytoplasmic concentration is 28 nano moles, as experimentally reported.
34) At the tip, we find 157 nano moles. This means a ratio of 157/850 = 0.18 of Ste11 to Ste5 (experimentally reported: 0.15).
35) Now, select Ste5_Ste7_all as pattern for the slice view. This pattern samples over all complexes containing Ste7 bound to Ste5. 
36) The cytoplasmic concentration is 11 nano moles. This means that a fraction of 11/30.6 = 0.36 of Ste5 is bound to Ste7 (experimentally reported: 0.27 +- 0.3).
37) Select the pattern Ste5_Ste11_all. The cytoplasmic concentration is 8.54 nano moles. This means that a fraction of 8.54/30.6 = 0.28 of Ste5 is bound to Ste11 (experimentally reported: 0.33 +- 0.3).
38) Select the pattern 'Scaffold_bound_Ste7_Fus3_all'. This pattern samples over all complexes containing Ste7 bound to Ste5 and Fus3. Its cytoplasmic concentration is 7.1 nano moles. Thus, a fraction of 7.1/30.6 = 0.23 of Ste5 is in complex with Fus3 through Ste7. 
39) Shift-click with the mouse in the cytoplasm. A window will appear to report details of the local biochemistry. It will a list of concentration-ranked (from low to high) complexes matching the selected complex pattern. Scroll down until you see the largest contributions to the pattern.  The complex {Ste5<>/_:_:_/_:_:_/1:0:1/_:_:_ | Ste7<phosphorylated=on;bnd1=on;bnd2=on;Ste5_bnd=on>/1:0:2/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=off>/_:_:_/0:0:1} contributes 67%. This complex consists of Ste5 that through its 3rd binding site (index 2, since the counting starts at 0) is bound to the Ste7 ( 1:0:1 means: site 1, component 0, molecule index 1; and Ste7 has index 1 within the complex). Ste7 (at its first binding site) is bound to Fus3 (site 1, component 0, molecule index 2). The next highest two contributors also contain Fus3.
40) The fourth highest contributor (5%) contains phosphorylated Fus3 (Fus3<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=off>). 
Since the total fraction of Ste5 bound to Fus3 was reported to be 0.19 (+- 0.01) one might want to find a model parameter 
set that reduces the amount of Ste5-Ste7-Fus3 complexes, especially since the high contribution of this pattern forced us to set 
the affinity of Fus3 binding directly (not via Ste7) to Ste5 to a very low value. However, these complexes are the source of 
phosphorylated Fus3 (see main manuscript, Supplementary Text 5). We had specified the affinity of the Ste5-Ste7 bond (Kd = 76 nano moles) 
according to the findings of Good et al. (Cell 136, 1085–1097, 2009). Reducing the amount of Fus3 bound to Ste7 in this complex would 
require decreasing the affinity of Fus3 for Ste7, that, in our model is much higher than reported by Good et al. 
(Kd = 2.5 nano moles, compared to 80 nano moles) or increasing the catalytic rate of Fus3 phosphorylation. 
The catalytic rate used in the model is, however, already more than three orders of magnitude higher (7.5 per sec. compared to 0.0043 per sec.) 
than the in-vitro value reported by Good et al. Strongly increasing the Kd of the Ste7:Fus3 bond and/or decreasing the Kcat for 
Fus3 phosphorylation would dramatically reduce the production of phosphorylated Fus3 below the reported 40% (of all Fus3 molecules in the cell) 
unless we would assume that the phosphatase Msg5, that dephosphorylates Fus3, has a very low activity - which in turn would destroy the 
intracellular gradient of phosphorylated Fus3. 





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Simulator:
11) Deselect the checkbox 'Display in Mol/ltr' to view the total number of complexes containing pFus3. Move the mouse within the graph to obtain precise concentrations/amounts at the mouse position. The number of roughly 6896 complexes can be compared to the total amount of Fus3 molecules in the system by selecting 'Now Showing: Molecules' and then selecting Fus3. (Since we initialized the simulation with a concentration(!) of Fus3 instead of a number of molecules we would have to multiply this initial concentration by the volume of the cell to get this number - but querying the simulation directly is easier.)
12) We find a number of 17360.3 Fus3 molecules per cell. The cell has thus phosphorylated a fraction of 6896/17360 = 0.397 (or about 40%) of its Fus3 contents.
13) Since we compared the number of complexes containing pFus3 (matched by the pattern pFus3_all) with the total number of Fus3 molecules we have to make sure that we don't have a significant amount of complexes containing more than one pFus3. Selecting "Now Showing: Complexes with Molecule" and then Fus3 we find the total number of complexes containing Fus3 to be around 17352, meaning that only a very small fraction of Fus3 is contained in complexes containing more than one Fus3 molecule. Note 1: Alternatively, we could have selected the pattern Fus3_all (not pFus3_all!) to inspect the total number of complexes containing Fus3. Note 2: The small fluctuations you can see in the time course are due to tolerances in the simulator engine. They can be eliminated (or, more precisely: made smaller) by reducing the tolerance of the integrator. For details, see the simulator documentation.

25. Click with the mouse somewhere within the cell but outside of the nucleus. The concentration of Fus3 is 570 nano moles. Maeder et al. had measured 571 nano moles in the cytoplasm of pheromone stimulated cells.

28. Draw a line around the first two layers of the tip. (The full 3D region corresponding to this selection will incorporate about 2% of the cell's Fus3 -- as estimated by Maeder et al.) The Region info reports an average concentration of the selected complex pattern (Fus3_all) of 1.385 micro moles.
29. Go back to the Slice Selection Window, select the pattern Ste5, then click 'Update Display' and 'View Slice'. Adjust the color threshold until the exclusion of Ste5 from the nucleus can be seen clearly. Click with the mouse somewhere within the cell but outside of the nucleus. The concentration of Ste5 is 30.6 nano moles. Maeder et al. had reported 29 nano moles.
30. To measure the concentration at the cell tip go the window menu and click 'Regions of Interest' -> 'Set New Area Region'. Confirm your intend to set a new region. Draw a line around the first two layers of the tip.The Region info reports an average concentration of Ste5 of 852 nano moles.
This means a ratio of 1385/852 = 1.63 of Fus3 to Ste5. Experimentally reported: 1.7.
31. Go back to the Slice Selection Window, select the pattern Ste7_all, then click 'Update Display' and 'View Slice'. Adjust the color threshold until the exclusion of Ste7 from the nucleus can be seen clearly. Click with the mouse somewhere within the cell but outside of the nucleus. The concentration of Ste7 is 60 nano moles. Maeder et al. had reported a concentration of about 63 nano moles.
32. To measure the concentration at the cell tip go the window menu and click 'Regions of Interest' -> 'Set New Area Region'. Confirm your intend to set a new region. Draw a line around the first two layers of the tip. The Region info reports an average concentration of Ste7 of 872 nano moles.
This means that the tip concentration of Ste7 is very close to that of Ste5, in accord with the experimental findings.
34. At the tip, we find 155 nano moles. This means a ratio of 155/852 = 0.18 of Ste11 to Ste5 (experimentally reported: 0.15).

36. The cytoplasmic concentration is 11 nano moles. This means that a fraction of 9.3/30.6 = 0.3 of Ste5 is bound to Ste7 (experimentally reported: 0.27 +- 0.03).
37. Select the pattern Ste5_Ste11_all. The cytoplasmic concentration is 8.45 nano moles. This means that a fraction of 8.45/30.6 = 0.28 of Ste5 is bound to Ste11 (experimentally reported: 0.33 +- 0.03). Note that there is a slight gradient of this complex pattern across the cell. It stems from the fact that we had to reduce the affinity of phosphorylated Ste11 for Ste5 to satisfy the constraint that the tip contains a smaller fraction of Ste11-bound Ste5 than the main cell body (see index (34), above).
38a. Select the pattern 'Scaffold_bound_Ste7_Fus3_all'. This pattern samples over all complexes containing Ste7 bound to Ste5 and Fus3.
38. Its cytoplasmic concentration is 3.2 nano moles. Thus, a fraction of 3.2/30.6 = 0.1 of Ste5 is in complex with Fus3 through Ste7. The total fraction of Ste5 in complexes containing Fus3 was reported to be 0.19 (+- 0.01). This leaves a fraction of 0.09
(or about 2.8 nano moles) of complexes in which Fus3 is directly bound to Ste5.
39. We adjusted the affinity of Fus3 for Ste5 accordingly (select the pattern 'Ste5_Fus3_all' to see the concentration) which resulted in a Kd of the direct binding between Fus3 and Ste5 of 37 micro moles. This is in accordance with the measurements of Good et al. (Cell 136, 10851097, 2009) who had determined the Kd to be greater than 10 micro moles, but is significantly lower than the Kd of around 1 micro mole that generally was assumed for this interaction.
40) Shift-click with the mouse in the cytoplasm. A window will appear to report details of the local biochemistry. It will a list of concentration-ranked (from low to high) complexes matching the selected complex pattern. Scroll down until you see the largest contributions to the pattern. {Ste5<>/_:_:_/_:_:_/_:_:_/1:0:1 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0} contributes 50.1577 %. This complex consists of Ste5 that through its 4th binding site (index 3 -- counting starts at 0) is bound to Fus3 ( 1:0:1 means: site 1, component 0, molecule index 1; and Fus3 has index 1 within the complex). The binding code at the second binding site of Fus3 show the inverse information -- 3:0:0 means: bound to site 3 of component 0 of molecule 0 in the complex.
41) To illustrate the advantage provided by the usage of patterns, we listed the complexes that contain Ste5, pSte7 and Fus3 and analyze their composition manually: Those in blue contain Fus3 directly bound to Ste5, as indicated by the binding codes. 
In the red complexes Fus3 is not bound to Ste5 but only to Ste7.
 
BLUE:
{Ste5<>/_:_:_/_:_:_/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=on;bnd2=on;Ste5_bnd=on>/1:0:3/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Fus3<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=off>/_:_:_/0:0:1  concentration: 1.45788e-11 mol per liter.}(0.515583 %)

BLUE:
{Ste5<>/_:_:_/1:0:3/1:0:1/1:0:2 | Ste7<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Ste11<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/1:0:0  concentration: 1.48186e-11 mol per liter.}(0.524062 %)

BLUE:
{Ste5<>/_:_:_/1:0:4/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=on;bnd2=on;Ste5_bnd=on>/1:0:3/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=off>/_:_:_/0:0:1 | Ste11<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/1:0:0  concentration: 2.18676e-11 mol per liter.}(0.773351 %)

BLUE:
{Ste5<>/_:_:_/1:0:3/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Ste11<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/1:0:0  concentration: 4.0276e-11 mol per liter.}(1.42437 %)

BLUE:
{Ste5<>/_:_:_/_:_:_/1:0:1/1:0:2 | Ste7<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0  concentration: 4.15978e-11 mol per liter.}(1.47112 %)

BLUE:
{Ste5<>/_:_:_/1:0:4/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=on;bnd2=on;Ste5_bnd=on>/1:0:3/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=off>/_:_:_/0:0:1 | Ste11<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/1:0:0  concentration: 5.29944e-11 mol per liter.}(1.87416 %)

RED:
{Ste5<>/_:_:_/1:0:3/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Ste11<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/1:0:0  concentration: 9.73037e-11 mol per liter.}(3.44117 %)

BLUE:
{Ste5<>/_:_:_/1:0:2/_:_:_/1:0:1 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Ste11<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/1:0:0  concentration: 1.49618e-10 mol per liter.}(5.29126 %)

BLUE:
{Ste5<>/_:_:_/_:_:_/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=on;bnd2=on;Ste5_bnd=on>/1:0:3/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=off>/_:_:_/0:0:1  concentration: 1.94573e-10 mol per liter.}(6.88114 %)

RED:
{Ste5<>/_:_:_/_:_:_/1:0:1/1:0:2 | Ste7<phosphorylated=on;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=on>/_:_:_/3:0:0  concentration: 3.57152e-10 mol per liter.}(12.6308 %)

About 19% of the total concentration of the complexes that match this pattern (Fus3 bound directly to Ste5) is represented by a complex that contains phosphorylated Ste7 an could thus potentially contribute to phosphorylation of directly scaffold-bound Fus3. Thus maximally 0.53 nano moles could become such a source of pFus3 -- compared to 3.2 nano moles found for the pattern 'Scaffold_bound_Ste7_Fus3_all'.

The complex {Ste5<>/_:_:_/_:_:_/1:0:1/_:_:_ | Ste7<phosphorylated=on;bnd1=on;bnd2=on;Ste5_bnd=on>/1:0:2/2:0:0 | Fus3<phosphorylated=off;bnd1=off;bnd2=on;Ste5_bnd=off>/_:_:_/0:0:1} contributes 67%. This complex consists of Ste5 that through its 3rd binding site (index 2, since the counting starts at 0) is bound to the Ste7 ( 1:0:1 means: site 1, component 0, molecule index 1; and Ste7 has index 1 within the complex). Ste7 (at its first binding site) is bound to Fus3 (site 1, component 0, molecule index 2). The next highest two contributors also contain Fus3.

We had specified the affinity of the Ste5-Ste7 bond (Kd = 76 nano moles) according to the findings of Good et al. (Cell 136, 10851097, 2009). Reducing the amount of Fus3 bound to Ste7 in this complex (to allow for more Fus3 bound directly to Ste5) would require decreasing the affinity of Fus3 for Ste7 or increasing the catalytic rate of Fus3 phosphorylation. The Km in our model was chosen according to the findings reported by Good et al. (Km = 80 nano moles) but we had to use a much higher catalytic rate (7.5 per sec. compared to 0.0043 per sec.). Strongly increasing the Kd of the Ste7:Fus3 bond and/or decreasing the Kcat for Fus3 phosphorylation would dramatically reduce the production of phosphorylated Fus3 below the reported 40% (of all Fus3 molecules in the cell) unless we would assume that the phosphatase Msg5, that dephosphorylates Fus3, has a very low activity. This, in turn, would not only destroy the phosphatase-induced intracellular gradient of phosphorylated Fus3 but would also mean that the cells would not be able to reach their max. level of Fus3 phosphorylation within an hour, in contrast to what hd been reported by Maeder et al. Using a Kd of 2 micro moles for the interaction of Msg5 with Fus3 (Remnyi et al. Mol Cell. 2005;20(6):951-62) and a Kcat of 0.06 per sec. (as measured for a phosphatase similar to Msg5 acting on a MAPK in Zhao & Zhang, J Biol Chem. 2001 Aug 24;276(34):32382-91) leads to a system that not only fails to reach an equilibrium within an hour but also accomplishes a phosphorylation of only about 20% of the cellular Fus3 pool. The model "YeastMAPK_slow.sdc" provided with the reference model simulation description ("YeastMAPK.sdc") incorporates these alternative parameters. Additional quantitative experimental studies will be useful to provide more insights into the roles that Msg5 activity and recruitment of Fus3 to the tip play for the intracellular gradient of Fus3 activity. 






