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## WHAT IS IT?

In this model, a cascade of biochemical reactions that are part of the MAPK pathway inside the cell are simulated.

The MAPK pathway is a signal transduction network that mammals, plants and yeast use for intracellular signalling. This network is a small portion of the EGF pathway. After signalling molecules have linked up to receptors in the cellular membrane, the biochemical reactions of the MAPK pathway take place inside the cell. Mitogen-activated protein kinases (MAPKs) are involved in this pathway by mediating the signal transductions.

## HOW IT WORKS

The environment is divided into three compartments:

* Extracellular space (light blue)
* Membrane (green circles)
* Cytoplasmic solution (white)

There are eight types of molecular species:

* Ras (yellow circles)
* Raf (red circles)
* MEK (orange circles)
* ERK (turquoise circles)
* GTP (violet triangles)
* P1 (blue arrows)
* P2 (dark green arrows)
* P3 (light green arrows)

All the molecules that participate in the reactions are in the cell. For the pathway simulation, we considered eleven reactions:

1. GTP binds to Ras molecule to activate it, forming the Ras-GTP complex, which is represented in the model by adding a "*" on the Ras molecule. When this reaction occurs, GTP molecule disappears.
> _[Ras] + [GTP] <-> [Ras-GTP*]_
2. Ras-GTP complex can activate a Raf molecule by making contact, which is represented by adding a * on the Raf molecule. When this occurs, Ras-GTP complex loses its reactivity, which is represented by removing the "*" of the molecule.
> _[Raf] + [Ras-GTP*] <-> [Raf*] + [Ras-GTP]_

3. The Raf activated phosphorylates the MEK protein, which is represented by adding a "P" on the MEK molecule.
> _[MEK] + [Raf*] <-> [MEK-P] + [Raf*]_

4. Raf molecule can phosphorylate MEK at two locations, giving rise to single and double phosphorylated MEK species. This second phosphorylation is represented by adding another "P" to MEK.
> _[MEK-P] + [Raf*] <-> [MEK-PP] + [Raf*]_

5. MEK phosphorylates ERK molecule. This reaction is represented by adding a "P" on the ERK molecule.
> _[ERK] + [MEK-PP] <-> [ERK-P] + [MEK-PP]_

6. ERK can be single and double phosphorylated as well, which is represented by adding another "P" on the ERK molecule.
> _[ERK-P] + [MEK-PP] <-> [ERK-PP] + [MEK-PP]_

7. Raf can be deactivated by P1, which is represented by removing the "*".
> _[Raf*] + [P1] <-> [Raf] + [P1]_

8. P2 dephosphorylates MEK protein, which is represented by removing a "P" of the MEK molecule.
> _[MEK-PP] + [P2] <-> [MEK-P] + [P2]_

9. MEK can be single and double dephosphorylated by P2, which is represented by removing another "P" of the MEK molecule.
> _[MEK-P] + [P2] <-> [MEK] + [P2]_

10. P3 can dephosphorylates ERK protein, which is represented by removing a "P" of the ERK molecule.
> _[ERK-PP] + [P3] <-> [ERK-P] + [P3]_

11. ERK can be single and double dephosphorylated by P3, which is represented by removing one "P" of the ERK molecule.
> _[ERK-P] + [P3] <-> [ERK] + [P3]_

The simulation stops when the concentration of non and singly phosphorylated ERK molecules is zero.

## HOW TO USE IT

First put the switch `Doc` on if you want a document with the record of the reactions ocurring over time. Then click the `SETUP` button to set up the environment and molecules and type the _name_ for the **reaction record file** (if the switch is on) to be written and save it. After the simulation has ended, click the `file-close` button to close the file. This file contains the information of the occurrence of every reaction, you can open it with a text editor.

You can adjust the initial concentration of each molecular species using the sliders. There is a slider for every molecular species that we mentioned before. According to Schoeberl et al. (2002), an idealized cell has a volume of 1 x 10^-12 L, we used this volume for the concentration calculations.

The Mutated-Ras switch changes the activity of Ras-GTP complex. When the switch is on, Ras-GTP complex is mutated and it doesn't lose its activity after reacting with a Raf molecule. When the switch is off, Ras-GTP complex can only react once with Ras, after one reaction loses its ability to react with another Ras molecule.

The `GO` button starts the simulation.

There are nine graphs that shows the concentration levels of the different molecular species, the graphics are listed below.

* **MAPK cascade:** Shows the levels of the activated Ras and Raf, and the double phosphorylated ERK and MEK.

* **ERK phosphorylation:** Shows the levels of the three forms of the ERK molecules, not phosphorylated, single phosphorylated and double phosphorylated.

* **MEK phosphorylation:** Shows the levels of the three forms of the MEK molecules, not phosphorylated, single phosphorylated and double phosphorylated.

* **GTP:** Shows the concentration levels of the GTP.

* **Ras:** Shows the concentration levels of the active and inactive Ras.

* **Raf:** Shows the concentration levels of the active and inactive Raf.

* **No phosphorylated molecules:** Shows the concentration levels of no phosphorylated ERK and MEK molecules.

* **Single phosphorylated molecules:** Shows the concentration levels of single phosphorylated ERK and MEK molecules.

* **Double phosphorylated molecules:** Shows the concentration levels of double phosphorylated ERK and MEK molecules.

For every molecular species there is a monitor showing the number of molecules existing in that moment.

## EXTENDING THE MODEL

The MAPK cascade is activated by growth factors. You can extend this model by adding these growth factors so when they get to the membrane from the extracellular space and link up with receptors, the biochemical reactions of the MAPK cascade will occur in consequence inside the cell.

Also, ERK-PP molecule can phosphorylate and regulate many proteins that induce cellular responses, including nuclear transcription factors going into the nucleus to induce transcription of certain genes that participate in cell growth, mitosis, survival or differentiation. You can add a fourth compartment to simulate the nucleus and add a new breed of agents representing the transcription factors going inside of the nucleus after being phosphorylated by ERK-PP.

After Ras-GTP molecule dissociates from Raf and if the switch of Mutated-Ras is off, Ras-GTP loses its reactivity and can only react again with another Raf if a GTP molecule activates Ras again. According to Schoeberl et al., this happens slightly different in the cell: after the reaction, Ras-GTP is recycled to Ras-GDP by activated GTPase-activating protein (GAP), and can be phosphorylated again to recover its activity. This introduces the new breed of agents GAP and the phosphorylation reaction of the Ras-GDP.

Finally, we did not take into account a theoretical concept involved in the interactions between molecules. This concept is related to the reaction time: reactions within a pathway can proceed at different velocities, even in the presence of equivalent initial concentrations. After a new product is formed, something called "sleep" time can be introduced to temporarily stall the product to mimic the relative time it would take for that product's reaction to have occured. You can add this delay time to the products recently formed to simulate the sleep time.

## CREDITS AND REFERENCES

- Khan, S., et al., 2003. A Multi-Agent System for the Quantitative Simulation of Biological Networks. AAMAS '03, 385-392.

- Schoeberl, B., et al., 2002. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nature Biotechnology 20, 370-375.

This model was created at Autonomous University of Baja California on 2015.

Authors:
- Alberto Abaroa Villanueva
- Rubén Alfonso Castañeda Martínez
- Carlos Alberto Castro Estrada

Tutors:
- Dora Luz Flores Gutiérrez, Ph.D.
- Claudia M. Gómez Gutiérrez, Ph.D.
- Edgar Manzanarez Ozuna, M.D.