Davide Chiarugi , Diana Hermith , Moreno Falaschi, Carlos Olarte and Catuscia Palamidessi
The molecular mechanisms of cell communication with the environment involve many concurrent processes governing dynamically the cell function. This concurrent behavior makes traditional methods, such as differential equations, unsatisfactory as a modeling strategy since they do not scale well when a more detailed view of the system is required.
We specify a biological system by means of a set of stoichiometric-like equations resembling the essential features of molecular interactions. We represent these equations by a timed concurrent constraint (tcc) language. Due to the constraint nature of tcc, we can effectively deal with partial information and thus, with the fact that several features of the biological system may be undetermined. Furthermore, we can represent the time for a reaction to occur.
BioWayS is a Mozart Oz implementation of the frameworks proposed in  and . BioWayS takes as input a set of stoichiometric equations modeling a biological systems and outputs the concentration of each component along the time.
We describe here the model of interaction of G-protein-coupled receptors with their respective G-proteins that activates signaling pathways inside the cell.
- BioWays - System Requirements - Downloads - Input and Output File Formats - The interaction of G protein-coupled receptors (GPCRs) with heterotrimeric G-proteins - General Description - Simulation of the system: encoding, signaling modes with stoichiometric and kinetic parameters - References
Assume a simple system comprised of four components
X4. This components react according to the following reactions:
3time units to produce
X3and the second equation takes
2time units to produce
X4. Furthermore, assume that the first (resp. second) reaction occurs with a probability of
These system is represented with the following input file:
time-units=10 indicates the time window of the simulation. The components of the system are declared in the section
variables. In our example, we are stating that the initial concentration of
X2 is 100, while it is 50 for
Equations are labeled (
eq2) and then, the time needed for the right hand components to be produced (
eq1) and the rate (probability) for the reaction to occur (
eq1 ) are indicated.
The components with a negative number (
eq1) are the left hand side elements to be consumed yielding to the positive ones (
eq1) representing the right hand side of the equation.
The system is simulated by using the Oz script
exec.oz. In this file, the input and the output files are specified:
The cell membrane, the surface that acts as the boundary, contains many receptors that are responsible for concurrently interacting with diverse signals molecules and sensing external information over time. Each receptor recognizes specific molecules that may bind to it. Binding activates signaling pathways that regulate molecular mechanisms and the flow of information in the cell. There is a special class of receptors, which constitutes a common target of pharmaceutical drugs, the G-protein-coupled receptors (GPCRs). These receptors interact with their respective G proteins to induce an intracellular signaling. The most simple picture of the system is the cell-surface receptor, the ligand, the G-proteins components, and other supporting molecules interacting in three environmental domains (Figure 1). The extracellular domain (ED) is the model of the signaling of G Protein. The transmembrane domain (TD) is the model of signaling of the GPCRs including G Protein activation and receptor desensitization. The intracellular domain (ID) is the model for the cycle of the heterotrimeric G Protein.
Fig 1. The interaction of GPCRs with heterotrimeric G-proteins.
Fig 2. Simulation results for the trimeric G-protein Cycle, only the variables of interest are shown.
Fig 3. Simulation results for the trimeric G-protein Cycle, only the variables of interest are shown in a shortest time range.
Fig 4. Simulation results for the reaction scheme of G-protein signaling, only the variables of interest are shown.
Fig 5. Simulation results for GPCR signaling including G-protein activation and receptor desensitization, only the variables of interest are shown.
Fig 6. Simulation results for GPCR signaling including G-protein activation and receptor desensitization, only the variables of interest are shown in a shortest time-concentration range.
Fig 7. Simulation results for GPCR signaling including ligand-receptor desensitization_LRds and activation_LR*.
Fig 8. Simulation results for GPCR signaling including ligand-receptor desensitization_LRds and activation_LR* in a shortest time range.
Fig 9. Simulation results for GPCR signaling including receptor desensitization_Rds and activation_R*.
Fig 10. Simulation results for GPCR signaling including receptor desensitization_Rds and activation_R* in a shortest time range.
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