BioWayS: A CCP-based tool for simulating biological systems

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 [1] and [2]. 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

BioWays

System Requirements

BioWays requires the Mozart Programming System version 1.4 available here.

Downloads

- Binary Files bioways.zip.

Input and Output File Formats

Biological systems are represented in BioWays by means of a set of stoichiometric-like equations resembling the essential features of molecular interactions.

Assume a simple system comprised of four components X1,X2,X3 and X4. This components react according to the following reactions:

X1 + 2(X2) ===> X3
3(X3) + 4(X1) ===> 2(X4)
Assume also that we know that the first equation takes 3 time units to produce X3 and the second equation takes 2 time units to produce X4. Furthermore, assume that the first (resp. second) reaction occurs with a probability of 0.4 (resp. 0.6).

These system is represented with the following input file:

time-units=10

variables

X1 = 100:100

X2 = 100:100

X3 = 50:50

X4 = 50:50

equations

eq1:3:40 = X1:~1 X2:~2 X3:1;

eq2:2:60 = X3:~3 X1:4 X4:2;

The parameter 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 X1 and X2 is 100, while it is 50 for X3 and X4.

Equations are labeled (eq1,eq2) and then, the time needed for the right hand components to be produced (3 in eq1) and the rate (probability) for the reaction to occur (40 in eq1 ) are indicated.

The components with a negative number (~1 and ~2 in eq1) are the left hand side elements to be consumed yielding to the positive ones (1 in 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:

INPUTFILE = "data1.txt"
OUTPUTFILE = "out.txt"
The output file for the previously described system is the following:

The interaction of G protein-coupled receptors (GPCRs) with heterotrimeric G-proteins

General Description

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.

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Fig 1. The interaction of GPCRs with heterotrimeric G-proteins.

Simulation of the system: encoding, signaling modes with stoichiometric and kinetic parameters


Focus on the Intracellular Domain: Models the trimeric G Protein Cycle [3]

Input and Output File Formats here

some_text some_text some_text some_text

Fig 2. Simulation results for the trimeric G-protein Cycle, only the variables of interest are shown. some_text

Fig 3. Simulation results for the trimeric G-protein Cycle, only the variables of interest are shown in a shortest time range.


Focus on the Extracellular Domain: Models the reaction scheme of G Protein signaling [4]

Input and Output File Formats here

some_text some_text some_text

Fig 4. Simulation results for the reaction scheme of G-protein signaling, only the variables of interest are shown.


Focus on the Transmembrane Domain: Models the G Protein coupled receptor (GPCR) signaling including G-Protein activation and receptor desensitization [5]

Input and Output File Formats here

some_text some_text some_text some_text some_text some_text

Fig 5. Simulation results for GPCR signaling including G-protein activation and receptor desensitization, only the variables of interest are shown. some_text

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. some_text

Fig 7. Simulation results for GPCR signaling including ligand-receptor desensitization_LRds and activation_LR*. some_text

Fig 8. Simulation results for GPCR signaling including ligand-receptor desensitization_LRds and activation_LR* in a shortest time range. some_text

Fig 9. Simulation results for GPCR signaling including receptor desensitization_Rds and activation_R*. some_text

Fig 10. Simulation results for GPCR signaling including receptor desensitization_Rds and activation_R* in a shortest time range.


References

[1] D. Chiarugi, M. Falaschi, C. Olarte and C. Palamidessi. Compositional modelling of signalling pathways in timed concurrent constraint programming. In Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology, BCB'10. ACM Press, 2010.
[2] Diana Hermith, Carlos Olarte, Camilo Rueda and Frank D. Valencia. Modeling Cellular Signaling Systems: An Abstraction-Refinement Approach. Submitted to PAAMS'11.
[3] Vladimir L. Katanaev and Matey Chornomorets. Kinetic diversity in G-protein-coupled receptor signalling. Biochem J., 401(2):485-495, 2006.
[4] David Csercsika, Katalin M. Hangosa, and Gyrgy M. Nagy. A simple reaction kinetic model of rapid (g protein dependent) and slow (betha-arrestin dependent) transmission. Journal of Theoretical Biology , 255(1):119–128, 2008.
[5] Todd A. Riccobene, Geneva M. Omann, and Jennifer J. Linderman. Modeling activation and desensitization of g-protein coupled receptors provides insight into ligand efficacy. Journal of Theoretical Biology , 200(2):207–222, 1999.