Biology Reference
In-Depth Information
Fig. 7. A tiny Petri net model for a bacteria cell performing quorum sensing (AI, autoinducer)*.
is determined by the number of bacteria but can be balanced by an adjusting parameterization of the
transitions. Figure 9 represents a more detailed view on the communication system within a colony. All
relevant Petri net structures and processes are included and simulated.
In vivo
single bacteria in a population do not always show the same behavior at the same face of the
development. If the space is a constraint of interest the cells can be arranged in a grid. In nature, the
bacteria are seemingly not well-arranged but appear scattered in space. However, in the model they can
be arranged in hexagonal, square or other grid forms. In the following examples a square grid is shown.
The grid can even have a third dimension (
z
-dimension), to model and simulate space in nature.
A three-dimensional grid is the intuitive approach to model a bacteria population and it makes the
cell-to-cell communication more realistic. Diffusion can be modeled with simple transitions without
respect to the place of transitions, because diffusion mechanism takes place everywhere in the same
manner. A disadvantage is that the model cannot be displayed clearly on two-dimensional screens and
the simulation needs much more computing power.
An advantage of a one-dimensional Petri net concatenation like that in Fig. 10 is that the net is small
and easy to simulate. It is more complicated to simulate the diffusion if behavior in three-dimensional
space is simulated because a bacterial population is denser at the center.
A two-dimensional model is able to capitalize on the advantages of a one-dimensional and the three-
dimensional model. It can be displayed on a two-dimensional screen and utilizes acceptable computa-
tional power. A part of such Petri net is shown in Fig. 11. Figure 12 demonstrates an overview of a
complete quorum sensing system consisting of 4 cells.
An important factor of quorum sensing is the size of a population. To switch from a concentration
below the threshold to a concentration above the threshold, the population has to grow. The growth
of a bacteria population can be modeled by adding 'mass' and 'alive' places as indicated in Fig. 13.
The possible bacteria positions are created by the Petri subnets for the cells. A bacterium only exists
*A colored version of the figure/chart is available at
In Silico Biol.
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http://www.bioinfo.de/isb/2010/10/0003/
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February 2010.
