Colored Petri Net Model and 3D Visualization Tool of the Mycobacterial Infection Process and Innate Immune Response
This pages is in support of:
Coupling Petri Net Models of the Mycobacterial Infection Process and Innate Immune Response.
Rafael V. Carvalho, Jeroen van de Heuvel, Jetty Kleijn, Fons J. Verbeek,
Computational Studies of Immune System Function, Submitted (2015)
We have modelled the role of the innate immune system in the early stages of a mycobacterial infection and dissemination using Colored Petri Net (CPN) as a model formalism. We structured the model in 4 interconnected levels that reproduce the dynamics of the steps that are involved in the infection process as well as the signaling that activates/inhibits the pathways related to the macrophage response to the bacteria. The environment of the model represents innate immune response based on the Mycobacterium marinum infection process on the zebrafish embryo. The levels works as compartment connecting the submodels in a hierarchical structure. The information is always triggered at the top level but the information flows in both directions. Each submodel represent the biological interactions as described in section 3 of the paper,i.e.:
- Level 1
- Represents the large scale of the hierarchical strucuture. it models the phases of the infection process: bacteria detection, phagocytosis, phagolysosome failure, bacterial proliferation, migration of infected macrophage to tissue, death of macrophage, recruitment of new macrophages, granuloma formation, intracellular spread and granuloma dissemination
- Level 2
- Represents the intercellular interaction between macrophage and bacteria once it is phagocytosed. It models the events that triggers the macrophage to eliminate the bacteria and the response of the pathogen to keep alive and proliferate inside the host immune cell
- Level 3
- Represents the intercellular interaction between macrophage and bacteria. It models important pathways related to the phagoseme and apoptosis from the macrophage, and how the bacteria interact to proliferate
- Level 4
- Represents the molecular interactions that influence the infection process. It models production and inhibition/degradation of important proteins from the phagosome maturation pathway and apoptosis pathway that are related to the elimination of the pathogen and how the bacteria exploit to survive
We have used the Snoopy software to implement and animate our net with two different operating systems (OS): Windows 7 (HP Intel core i7, 4 Gb RAM) and Mac OS 10.6 (MacBook Pro Intel core i7, 4 Gb RAM). The colored Petri net model runs with the same accuracy on both OS-versions. This illustrates the platform independence of the Snoopy software framework. We have performed the same experiments for the 3D visualization tool obtaining similar results.
The animation mode in Snoopy allows you to observe the token-flow that represents the behaviour of the model. It is possible to animate the token-flow manually by clicking on the transitions or using the animation steering panel, where you can play/pause the animation, step-wise forward and backward or sequentially as long as one transition can be enabled. You can also change further animation properties under options, like refreshment, duration and stepping where you can control the behave of the animation. By saving the end state result of the animation mode it becomes possible to substract the state space from the Petri net file which is used as input for the 3D visualization tool.
The following 2 videos illustrate the animation sequences in Snoopy from the hierarchical model in which you can verify the dynamic behaviour of the system. We start the simulation by defining the amount of bacteria and their initial position at the place Infection adding the initial marks: E{1'(1,mm)++1'(2,mm)++1'(3,mm)}. The animation stops when there is no transition enable to occur, this final results will provide the quantity of granuloma formed during this process as well as their respective positions, accumulated at the place MatureGranuloma. The 3rd video illustrate the simulation of the model in the 3D visualization tool by reading the Snoopy file.
Video 1: Top level of the hierarchical Petri net model that represents the phases of the infection process
This video shows the work flow of the net governed by the firing rules. The animation starts by the firing of the transition Phagocytosis and reach its end state at the place MatureGranuloma. This model interacts with the submodels at Level 2 by the transition PhagolysosomeFail firing a token dot to the coarse place IntracellularInteraction which "send" another token dot to the transition MigrationDeepTissue.
Video 2: Intercellular, intracellular and molecular submodels
This video shows the interaction at the submodels that represent the macrophage-bacteria interaction. Positioned on the center, we have the submodel that represents the intercelluar scale (IntracellularInteraction). The place PhagolysosomeFail interacts with the lower levels (3 and 4) through the coarse transitions Apoptosis_Pathaway and Phagosome_Maturation_Pathaway triggering those pathways. It also interact with the top level once the infected macrophage necrosis, when a token reach the place Necrotic_Macrophage signalling to the macrophage to migrate to the tissue.
Video 3
This video shows the animation of the Petri net model simulated previously in the 3D visualization tool. The 3D mesh object represents the zebrafish embryo with its 12 regions (represented by a red boxes). The bacteria are represented by red sphere and initially positioned according to the information from the Petri net file. The non-infected macrophages are represented by blue spheres and are in constant movement, to represent their presence at the blood circulation. A small windows provide information read from the Petri net file i.e. the constants that regulate the infection process i.e. the number of infected macrophage that forms one granuloma (MaxAggregation) and the amount of infected macrophage will leave agranuloma to disseminate the infection (MaxDissemination). It is possible to visualize which region the granuloma will be positioned and also the information about the initial state (number of bacterias and where they are initially positioned).
Contact Rafael V. Carvalho or Fons Verbeek for information.