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Multiagent System based modeling

Spatial simulation of a bacteria

We have also developed a spatial simulation of the basic bi-stable by considering the interaction between the different components in the interior of a bacterium using NetLogo. This way we provide a friendly program that allows the researcher to study the influence of several parameters in the global behavior of the system. Moreover, it is possible to analyze parameters not considered in the simulation based on differential equations like the spatial (volumetric) concentrations of the.

About NETLOGO

NetLogo is a programmable modeling environment for simulating natural and social phenomena. It was authored by Uri Wilensky in 1999 and has been in continuous development ever since at the Center for Connected Learning and Computer-Based Modeling.

NetLogo is particularly well suited for modeling complex systems developing over time. Modelers can give instructions to hundreds or thousands of "agents" all operating independently. This makes it possible to explore the connection between the micro-level behavior of individuals and the macro-level patterns that emerge from the interaction of many individuals.

NetLogo web

Simulating the bistable

The program can be launched in two different ways. You can open the file biestable-simulation.nlogo (that you can download here) or you just can click here to run an online simulation. ¡¡ADD LINKS!!

If you want to do it in the first way, you also have to download the NetLogo environment from his web page

How does it worK

In this view (me queda añadir las imagenes que tengo en la carpeta y alguna más) we have represented a layer of the cytoplasm of an E.Coli specimen, with a thickness of 5 nm. The actual dimensions of an E.coli have been obtained from the CyberCell Database añadir enlace), a fantastic information source. We have considered the next measures to model the bacterium.

To use these dimensions in the “NetLogo’s patch world” (where the world is made of a grid of stationary agents called patches) we have taken as reference the size of a standard protein (5 nm) ) and adjusted the sizes in order to get that every patch has the same size of a protein with this features. This way, the whole world is made of a grid of 400 x 160. As we have taken a layer with a thickness of only 5nm, we have scaled the typical ammount of several molecules (like ribosomes or RNAps) accordingly (we do that by dividing the numbers by 120, corresponding with the number of patches that theorically would measure the high of an E.Coli).

Once we click setup, we can see several molecules. To initiate a simulation just click on go.

What can we see?

On the left we can see several genes (one couple of genes by default), represented by lines.

The longer genes are LacI genes (Repressor 1), while the shorter ones represent c1ts genes (Repressor2). From now on we will use the terms LacI/Repressor1 and c1ts/Repressor2 indistinctly

Both genes are to scale. In the real bacteria they both would appear in the same plasmid and completely twisted. They both have a promoter at the beginning and a terminator at the end.

After this, we have RNAP (green circles) which can move freely around the cytoplasm until they find a promoter. Once they do it, they have a given chance of starting to transcribe. When they transcribe, they generate a RNAm molecule. When they finish transcription, this RNA molecule will move till stop in a randomly place in the cytoplasm. Each RNAm molecule remains a given time in the cell before it “dies” and disappears; this time is given by a normal distribution with mean of 5 minutes and a standard deviation of 1 minute (by default, but you can change this value to experiment with it).

The big yellow circles represent ribosomes, which move freely around the cytoplasm until they find the Shine-Dalgarno of a RNA. At that moment they start the translation. When they finish, they generate a repressor protein. The size of the ribosomes is also to scale, measuring 20 nm of diameter.

Repressors1, in red in the plots, represent LacI, which become inactive if they are attached to IPTG. If the user adds IPTG to the cell he will able to inactivate lots of them. The monitors allow you to see online how many repressors are inactive.

Repressors2, in blue, represent c1ts repressors, which become unstable and “die” when the temperature is increased. If the user establishes the temperature at 42 degrees, repressors2 will start to disappear. The temperature effect tells us how many times faster the repressors2 disappear if the temperature is 42.

Repressors1 can attach to kind-2 promoters and repress them, blocking their transcription, and vice-versa. The number of repressor molecules that a promoter can admit can be chosen by the user (0 means no limit)

The amounts of all molecules (except RNA polymerases and ribosomes to simplify the simulation) decrease sharply to the half once the bacterium passes through a cell cycle. All free molecules move following the rules of the Brownian movement.

How to use it

To initiate the program with the selected variables you just have to click on the setup button. If you want to adjust all variables to the values by default just click on reset.

To initiate the simulation click on the go button. (aquí me falta añadir junto al texto las imágenes de los botones a los que me refiero con sus correspondientes pies)

The user can modify many variables and see which are the effects of modifying these variables in the simulation:

• He can change the number of starting molecules or select the number of repressors that can admit every promoter.
• The user can also control the life-span of RNA and repressors. The life-span of these molecules is distributed according to a normal distribution.
• He can regulate the strength of the interaction with several molecules. The repressor strength is inversely proportional to the given number, because it gives the chances per second that an attached repressor to the DNA falls from it. Since the strength of the promoters gives the chances (in percentage) that a given RNAP which detects a promoter starts transcription.
• The parameter called time-constant gives us the number of steps (or ticks) of simulation that the program performs by each second of evolution of the system and has a value of one hundred per default. The movement of the proteins in the cytoplasm and the speed of the RNAPs and ribosomes when they are “reading” has an optimal value if this number is 1000, but it also makes the program run slower. Taking as reference a medium-size protein (40 kDA) which moves with a speed of 5 nm per ms, the program only runs this thousand steps if the constant-time values 1000. If the number decrease, the simulation loss realism but it will run much faster, which could be interesting if we are interested in obtain just a more qualitative comprehension of the system.
• The slider cell-cycle-length gives us the length of a cell cycle, by default 30 minutes.
• The button divide-cells? allows us to eliminate half of the repressors and RNAs in a randomly way every cell-cycle.

Under the title of Actions, the user can interact with the simulation in real time. This way, the user can toggle the bistable switch between the two possible states. For convenience, we have taken as “On” the state in which the protein LacI has a high concentration in the cell. To turn off the bistable we have to release a high concentration of IPTG and be patient. We have to give enough time to the simulation, because the RNA must be transcribed to produce after this the protein c1ts and the RNA, and free LacI proteins must disappear.

To turn on the bistable, we only have to increase the temperature. The temperature-effect gives us how many times faster grows old the protein c1ts. We can see that it is rather easier to turn the bistable on than to turn it off.

The show-view button allows us to turn-off the simulation window, although the plots and the monitor will carry on actualizing. To turn-off the view enables the simulation to run much faster, so it is strongly recommended.

The program also allows to export data to a .csv file with the name Simulation data, and it is saved in the root folder where is saved the simulation. It is recommended that if you want to use the simulation to produce data the program must be open from the .nlogo file.

The simulation represents the concentration of RNAs and repressors in the plot. Moreover, we can see in the monitors the amount of molecules of every kind, how many repressors can be found repressing, how many repressors with kind 1 are bound to IPTG and the temperature.

The color legend is in the next table:

By default, the LacI promoter is 10 times stronger than the c1ts promoter and for this reason, if the user do not provide any input, LacI ends winning as the dominant repressor and blocks the transcription of c1ts.

Extending the model

This model could become more complicated adding more and more details of the real biological system, but it would increase the complexity of it and so the ability of making simulations in a reasonable time. Some of the improvements that could be implemented without making the program much more complex is the strength of the SD or adding a cycle life to the ribosomes and the RNA polymerases. A more interesting improvement and still plausible could be representing the growth of the bacterium while the time goes by and the sharply decrease of the size to the half after the binary fission.