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Multiagent System based modeling

Spatial simulation of a bacteria

We have also developed a '''spatial simulation''' of the basic flip-flop by considering the interaction between the different components in the interior of a bacterium using '''NetLogo'''. This kind of model allows to analyze some parameters not considered in the simulations based on the differential equations governing the concentrations of diverse elements, like the spatial (volumetric) variation of these concentrations. Moreover, we wanted to provide a friendly program that allows the researcher to study the influence of several parameters in the global behavior of the system.

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.

Simulating the bistable

To run the simulation you have to download the NetLogo environment from his web page and open after the file biestable-simulation.nlogo (download here)

How does it work

In the General View of the program we represent 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, 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 of the world so that every patch has the same size of a protein. 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 in a E. Coli (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 multiagent system simulation

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.