Start the Simmune Simulator. Select the Simulation Description File "YeastMAPK.sdc" and click "Open".

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.

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.

Clicking and moving the mouse in the 3D display area of the simulator main window allows you to change the aspect of the view. Right/left cursors on your keyboard allow you shift the aspect (move the cell to the right and left).

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.

Click on "Simulate for X Seconds" and enter 400.0. Click OK to start the simulation. Depending on the power of the computer used completing the 400 seconds simulation time may take between a couple of minutes to more than an hour.

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.

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).

Go to the 'Time Trace Window' and select "Now Showing: Patterns", then select pFus3_all from the list.

As the Time Trace Window shows, the production of phosphorylated Fus3 (pFus3_all) has approached a steady level. The 'coordinates' shown (142.683, 2.29253e-07) indicate the position the mouse pointer was at when the screenshot was made.

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.)

We find a number of 17360 Fus3 molecules per cell. The cell has thus phosphorylated a fraction of 6896/17360 = 0.397 (or about 40%) of its Fus3 contents. Note: 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.

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 after some equilibration, 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.

In the main Simulation Window select Slice Views -> view slice of a cell.

The Slice Selection Window now shows the cell with a small fraction of its surface singled out.

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.

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.

Select 'Volume Concentration' (as opposed to 'Surface Concentration') and Patterns (as opposed to Complexes).

Select the pattern pFus3_all and click 'Update Display'. Then click 'View Slice'.

The Slice View Window will show a 2D concentration profile of the selected pattern (pFus3_all). You can adjust the color threshold to optimize the contrast of the color coding.

To inspect the intracellular gradient of pFus3 in a more quantitative way, click 'Draw new straight line profile' 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.

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.

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".

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'.

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.

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 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.

Go back to the Slice Selection Window, select the pattern Ste5_all, 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.

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.

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.

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.

Now, select Ste11_all as pattern for the slice view. The cytoplasmic concentration is 28 nano moles, as experimentally reported.

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).

Now, select Ste5_Ste7_all as pattern for the slice view. This pattern samples over all complexes containing Ste7 bound to Ste5.

The cytoplasmic concentration is 9.3 nano moles when measured at the shoo-distal cytoplasmic region. This means that a fraction of 9.3/30.6 = 0.3 of Ste5 is bound to Ste7 (experimentally reported: 0.27 +- 0.03).

Select the pattern Ste5_Ste11_all. The cytoplasmic concentration is 8.45 nano moles when measured at the shmoo-distal cytoplasmic region. 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).

Select the pattern 'scaffold_bound_Ste7_Fus3_unphos'. This pattern samples over all complexes containing Ste7 bound to Ste5 and unphosphorylated Fus3.

Its cytoplasmic concentration is 3.0 nano moles. Thus, a fraction of 3.0/30.6 = 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.

We adjusted the affinity of Fus3 for Ste5 accordingly 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, 1085–1097, 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.

Select the pattern 'Ste5_Fus3_all'. Shift-click with the mouse in the cytoplasm. A window will appear to report details of the local biochemistry. It will display 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 50.15 %. 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. Note that depending on the precision used for the simulation there may be very small negative concentrations being listed. These are due to the tolerance of the numerical algorithms and in most cases (such as here) have no significant influence on the result of the simulation. The documentation for the simulator describes how to increase the precision of the numerical algorithms in cases where you suspect very high precision may be important.

To illustrate the advantage provided by the usage of patterns, we list the complexes with the highest concentrations and analyze their composition manually as opposed to using a predefined pattern: Those in blue contain phosphorylated Ste7 in addition to Ste5 and Fus3. Those in red contain either no Ste7 or unphosphorylated Ste7.

{Ste7<phosphorylated=on>/1:0:2/2:0:1 | Ste5<>/_:_:_/_:_:_/1:0:0/1:0:3 | Fus3<phosphorylated=on>/_:_:_/0:0:0 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 1.45879e-11 mol per liter.}(0.515562 %)

{Ste7<phosphorylated=off>/_:_:_/2:0:1 | Ste5<>/_:_:_/1:0:2/1:0:0/1:0:3 | Ste11<phosphorylated=off>/_:_:_/1:0:1 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 1.48395e-11 mol per liter.}(0.524456 %)

{Ste7<phosphorylated=on>/1:0:3/2:0:1 | Ste5<>/_:_:_/1:0:2/1:0:0/1:0:4 | Ste11<phosphorylated=on>/_:_:_/1:0:1 | Fus3<phosphorylated=off>/_:_:_/0:0:0 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 2.18569e-11 mol per liter.}(0.772461 %)

{Ste7<phosphorylated=on>/_:_:_/2:0:1 | Ste5<>/_:_:_/1:0:2/1:0:0/1:0:3 | Ste11<phosphorylated=on>/_:_:_/1:0:1 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 4.0196e-11 mol per liter.}(1.4206 %)

{Ste7<phosphorylated=off>/_:_:_/2:0:1 | Ste5<>/_:_:_/_:_:_/1:0:0/1:0:2 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 4.15618e-11 mol per liter.}(1.46887 %)

{Ste7<phosphorylated=on>/1:0:3/2:0:1 | Ste5<>/_:_:_/1:0:2/1:0:0/1:0:4 | Ste11<phosphorylated=off>/_:_:_/1:0:1 | Fus3<phosphorylated=off>/_:_:_/0:0:0 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 5.31783e-11 mol per liter.}(1.87942 %)

{Ste7<phosphorylated=on>/_:_:_/2:0:1 | Ste5<>/_:_:_/1:0:2/1:0:0/1:0:3 | Ste11<phosphorylated=off>/_:_:_/1:0:1 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 9.74988e-11 mol per liter.}(3.44579 %)

{Ste5<>/_:_:_/1:0:1/_:_:_/1:0:2 | Ste11<phosphorylated=on>/_:_:_/1:0:0 | Fus3<phosphorylated=off>/_:_:_/3:0:0 concentration: 1.49581e-10 mol per liter.}(5.28645 %)

{Ste7<phosphorylated=on>/1:0:2/2:0:1 | Ste5<>/_:_:_/_:_:_/1:0:0/1:0:3 | Fus3<phosphorylated=off>/_:_:_/0:0:0 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 1.94694e-10 mol per liter.}(6.88085 %)

{Ste7<phosphorylated=on>/_:_:_/2:0:1 | Ste5<>/_:_:_/_:_:_/1:0:0/1:0:2 | Fus3<phosphorylated=off>/_:_:_/3:0:1 concentration: 3.56843e-10 mol per liter.}(12.6115 %)

{Ste5<>/_:_:_/1:0:1/_:_:_/1:0:2 | Ste11<phosphorylated=off>/_:_:_/1:0:0 | Fus3<phosphorylated=off>/_:_:_/3:0:0 concentration: 4.1937e-10 mol per liter.}(14.8213 %)

{Ste5<>/_:_:_/_:_:_/_:_:_/1:0:1 | Fus3<phosphorylated=off>/_:_:_/3:0:0 concentration: 1.41903e-09 mol per liter.}(50.151 %)

About 28% of the total concentration of the complexes that match this pattern (Fus3 bound directly to Ste5) come from complexes that contain phosphorylated Ste7 an could thus potentially contribute to phosphorylation of directly scaffold-bound Fus3 according to the classical scaffold scheme. Thus at most 0.77 nano moles could contribute as a source of pFus3 -- compared to 3.2 nano moles found for the pattern 'Scaffold_bound_Ste7_Fus3_all'.

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 (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 had been reported by Maeder et al. Using a Kd of 2 micro moles for the interaction of Msg5 with Fus3 (Remýnyi 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 by 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 and allows you to experiment with this alternative parameter set. 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.